Full text of "Outlines of the evolution of weights and measures and the metric system"

See other formats

OUTLINES  OF  THE EVOLUTION  OF  WEIGHTS  AND  MEASUEES AND   THE  METRIC  SYSTEM OUTLINES  OF THE  EVOLUTION  OF WEIGHTS  AND  MEASURES AND THE    METRIC    SYSTEM BY WILLIAM  HALLOCK  Ph.D. PROFESSOR   OF   PHYSIOS   IN   COLUMBIA   UNIVERSITY   IN  THE   CITY   OF   NEW   YORK AND HERBERT   T.  WADE EDITOR    FOR   PHYSICS    AND    APPLIED   SCIENCE,    '  THK   NEW    INTERNATIONAL    ENCYCLOPAEDIA THE    MACMILLAN    COMPANY LONDON  :  MACMILLAN  AND  CO.  LTD. 1906 ac 2b SEP  8 ;\ <i OFT 9239G3 GLASGOW  I    PRINTED   AT  THE   UNIVERSITY BY  ROBERT  MACLEHOSE  AND  CO.    LTD. PREFACE. In  the  following  pages  it  has  been  the  aim  of  the  authors  to present  in  simple  and  non-technical  language,  so  far  as  possible,  a comprehensive  view  of  the  evolution  of  the  science  of  metrology as  it  is  now  understood.  Inasmuch  as  the  introduction  of  the Metric  System  into  the  United  States  and  Great  Britain  is  a topic  of  more  or  less  general  interest  at  the  present  time,  it  has seemed  that  a  work  designed  both  for  the  student  of  science  and for  the  general  reader,  in  which  this  system  is  discussed  in  its relation  to  other  systems  of  weights  and  measures  past  and present,  would  fill  a  certain  need.  While  there  are  many  works on  metrology  that  treat  at  considerable  length  the  historic  and scientific  sides  of  the  subject,  as  well  as  the  economic  and archaeological  questions  involved,  and  a  large  number  of  books and  pamphlets  dealing  with  the  teaching  of  the  Metric  System, besides  those  supplying  tables  and  formulas  for  converting  from one  system  to  the  other,  yet  there  is  apparently  a  distinct  lack  of works,  which  in  small  compass  discuss  the  subject  comprehensively from  its  many  points  of  view.  Indeed,  the  student  of  metrology is  apt  to  be  embarrassed  by  an  extensive  literature  rather  than by  any  deficiency  in  the  amount  of  collected  material,  though much  of  the  latter,  to  be  sure,  is  included  in  various  Eeports  and Proceedings  of  learned  societies  and  official  documents  rather  than in  single  works.  A  large  amount  of  this  literature  devoted  to metrology  represents  a  minute  specialization  and  critical  analysis often  discussing  either  a  certain  epoch,  or  a  single  system  or group  of  weights  and  measures,  where  the  treatment  is  from  the standpoint  of  either  archaeology,  economics,  or  physical  or  mathe- matical science,  and  but  rarely  combining  the  three  points  of vi  PREFACE view.  In  addition,  much  of  this  literature  is  of  an  argumentative nature,  and  debate  and  discussion  rather  than  definite  conclusions compelling  universal  acceptance  seem  to  be  characteristic  of metrological  writing. It  has  been  the  intention  of  the  authors  to  consider  briefly  and systematically  the  general  history  of  weights  and  measures,  the scientific  methods  by  which  units  and  standards  have  been determined,  the  concrete  standards  by  which  the  units  are represented,  and  the  present  aspect  of  modern  systems  of  weights '  and  measures,  together  with  the  difficulties  and  advantages involved  in  any  proposed  changes.  Experience  derived  while giving  instruction  in  physics  to  students  in  applied  science  has suggested  the  general  plan  of  treatment,  and  it  has  seemed desirable  to  present  from  an  American  standpoint  the  most essential  facts  in  as  logical  relation  as  is  possible  in  a  science that  is  often  marked  by  conditions  quite  illogical.  From  the copious  notes  and  bibliographical  references,  which  it  is  hoped  will be  appreciated  by  advanced  students  and  those  specially  interested in  the  subject,  it  will  be  seen  that  at  the  outset  any  claims  to striking  originality  must  be  dismissed,  and  the  obligations  of  the authors  to  the  various  authorities  mentioned  in  the  notes  are ungrudgingly  acknowledged. The  authors  hope  that  their  work  will  serve  two  useful  ends : first,  as  an  introduction  to  metrological  science  designed  especially for  the  student  entering  on  the  study  of  physics  to  whom  a knowledge  of  units  and  standards  is  most  necessary ;  and  second, as  preparatory  to  an  intelligent  understanding  of  the  discussions involved  in  the  proposed  adoption  of  the  Metric  System  by English-speaking  peoples,  especially  by  those  to  whom  Metric and  Anti-Metric  arguments  are  being  addressed  with  such frequency  and  persistence.  It  has  been  the  intention  of  the authors  to  avoid  as  far  as  possible  all  controversy  for  several reasons ;  the  first  and  most  important  of  which  is  that  this  side of  the  question  has  been  and  is  being  abundantly  covered elsewhere,  so  that  it  has  seemed  preferable  in  this  work  to include  a  mere  statement  of  facts  rather  than  to  repeat  or  even add  to  the  arguments.  Such  has  been  their  intention,  but  they are  also  compelled  to  admit  that  they  are  supporters  of  the Metric    propaganda,    and    they    must    ask    indulgence    for    any PREFACE  vii departures  from  the  plan  determined  on.  However  that  may be,  they  have  endeavored  to  give  a  fair  and  concise  history  of the  Metric  System  so  that  its  logical  development  and  character- istics will  be  apparent,  and  this,  together  with  the  experience  of European  nations  as  briefly  described,  will  supply  sufficient  data on  which  may  be  formed  an  intelligent  opinion  as  to  the desirability  of  adopting  in  America  and  Great  Britain  at  an early  date  the  International  System  of  weights  and  measures. In  view  of  the  fact  that  such  a  work  has  involved  the  use  of  a vast  number  of  authorities,  it  is  manifestly  impossible  to  specify in  detail  other  than  in  the  notes  the  great  indebtedness  on  the part  of  the  authors  to  the  labors  of  many  famous  metrologists. Naturally  they  have  consulted  freely  the  classic  work  of  Mechain and  Delambre,  Base  du  sysUme  Mttrique ;  General  Morin's Notice  historique  sur  le  systtme  Mdtrique ;  Bigourdan's  Le  syst&me MStrique ;  Guillaume's  La  Convention  du  Metre ;  and  his  excellent little  treatise  on  UniUs  et  Etalons,  as  well  as  Benoit's  Eeport  on Standards  of  Length  to  the  International  Physical  Congress  of 1903.  In  addition  they  have  used  the  various  publications  of  the International  Bureau  of  Weights  and  Measures.  For  ancient weights  and  measures  many  sources  have  been  consulted,  while for  English  standards  and  metrology  the  works  of  Chisholm  and Chaney  have  been  found  most  helpful,  but  they  have  been supplemented  by  various  papers  of  Parliamentary  commissions and  the  Proceedings  of  scientific  societies.  In  the  United  States the  Keports  and  other  papers  of  the  Coast  and  Geodetic  Survey, the  recently  established  National  Bureau  of  Standards,  and  the Committees  on  Coinage,  Weights  and  Measures,  of  the  House  of Eepresentatives  have  formed  a  nucleus  that  has  been  supple- mented by  extensive  reference  to  other  scientific  literature. In  conclusion  the  authors  would  gratefully  acknowledge  their obligations  to  M.  Ch.  Ed.  Guillaume,  Assistant  Director  of  the International  Bureau  of  Weights  and  Measures,  and  Professor S.  W.  Stratton,  Director  of  the  U.S.  Bureau  of  Standards,  who most  kindly  consented  to  look  over  the  proofs  and  have rendered  assistance  in  many  substantial  ways. CONTENTS. CHAPTER  I. PAGE Beginnings  and  Development  of  the  Science  of  Metrology,      1 Underlying  Principles  of  Metrology.  Development  of  the  Science among  Primitive  Peoples.  Metrology  of  the  Babylonians.  Hebrew Metrology.  Weights  and  Measures  among  the  Egyptians.  Greek Weights  and  Measures.  The  Roman  System  and  its  Spread. Mediaeval  Conditions.  Development  of  Anglo-Saxon  Metrology. Early  French  Weights  and  Measures.  European  Conditions Generally. CHAPTER   II. Origin  and  Development  of  the  Metric  System,       -        -      41 Reasons  for  the  Change  and  Preliminary  Efforts.  Scientific  and Other  Steps  in  its  Development.  The  Derivation  of  the  Meter and  Kilogram.  Adoption  of  the  System.  Method  of  bringing about  the  Change.  Systeme  Usuelle.  Spread  of  the  Metric System  and  Compulsory  Legislation  of  1837.  The  Metric  Treaty and  the  Formation  of  the  International  Bureau  of  Weights  and Measures.     Work  and  Organization  of  the  Bureau. CHAPTER   III. Extension  of  the  Metric  System  throughout  Europe  and elsewhere,         -  80 Confusion  Existing  and  Reasons  for  the  Change.  Dates  and Methods  of  Making  the  Change — Germany.  Austria.  Hungary. Belgium.  Egypt.  Greece.  Italy.  Japan.  Netherlands.  Portugal. Russia.  Spain.  Sweden  and  Norway.  Switzerland.  Turkey. Great  Britain.  Mexico.  South  and  Central  America.  Table showing  Dates  when  Metric  System  was  adopted. PAGE x  CONTENTS CHAPTER   IV. Weights  and  Measures  in  the  United  States,  -  109 Connection  of  Weights  and  Measures  with  Systems  of  Currency. Development  of  the  Decimal  Principle.  Early  National  Legisla- tion. Various  Plans  Proposed.  John  Quincy  Adams'  Report  on Weights  and  Measures.  The  Development  of  a  National  System and  Progress  towards  Uniformity.  Early  Standards  and  Definitions. Spread  of  the  Metric  System.     Summary  of  Metric  Legislation. CHAPTER  V. The  Metric  System  of  To-Day — Its  Essential  Character- istics and  Fundamental  Principles,       -        -        -        -    135 General  Characteristics.      Linear  Measures.      Superficial  Measures. Cubical  Measures.     Measures  of  Capacity.     Measures  of  Mass. CHAPTER   VI. The  Metric  System  for  Commerce,      -        -        -        -        -    150 The  Advantages  of  a  Universal  System.  The  Metric  System  for International  Trade.  Its  Applicability  to  the  Ordinary  Transaction of  Commerce.  The  Advantages  of  a  Homogeneous  and  Decimal System. CHAPTER   VII. The  Metric  System  in  Manufacturing  and  Engineering,     172 Simplicity  of  Metric  System.  Ease  with  which  Change  could  be made.  Question  of  Gauges.  Linear  Measurements  in  Mechanical Engineering.  The  Question  of  Screw  Threads.  Introducing  the Metric  System  into  a  Machine  Shop. CHAPTER   VIII. The  Metric  System  in  Medicine  and  Pharmacy,       -        -    191 General  Nature  of  its  Use  and  its  Advantages.  Adoption  by U.S.  Army  and  Navy  Medical  Departments. CONTENTS  xi CHAPTER   IX. PAGE International  Electrical  Units,  -        -  -    199 The  Absolute  System.  Derivation  of  Electrical  Units  from  the Metric  System.  The  C.G.S.  System  of  the  British  Association. Definitions  of  Electrical  Units  at  Chicago,  1893.  Specifications for  the  Practical  Application  of  these  Definitions.  New  Magnetic Units.     Shortcomings  of  Present  Units. CHAPTER   X. Standards  and  Comparison,  -        -        -        -  -        -    218 Nature  and  History  of  Standards.  Methods  of  Comparison. Present  Day  Standards.  Definition  of  the  Meter  in  terms  of  the Wave  Length  of  Light. APPENDIX. Tables  of  Equivalents  and  Useful  Constants,  -        -    267 U.S.  Legal  Equivalents.  British  Legal  Equivalents.  Table  for Conversion  of  Units  of  Length.  Table  for  Conversion  of  Units of  Mass.  Equivalents,  Millimeters  and  Fractions  of  an  Inch. Comparison  of  Prices  :  Length — Inches  and  Centimeters,  Feet  and Meters,  Yards  and  Meters,  Miles  and  Kilometers.  Areas — Acres and  Hectares.  Capacity — Liquid  Quarts  and  Liters,  Gallons  and Liters.  Mass — Avoirdupois  Pounds  to  Kilograms,  Comparison  of Tons  and  Pounds.  Capacity — Various  Equivalents.  Mass — Various Equivalents.  Apothecaries'  Weight — Table  of  Equivalents.  Den- sity, Melting  Point  and  Boiling  Point  Tables.  Thermometer  Scales — Table  of  Equivalents.     Miscellaneous  Constants  and  Equivalents. Index,      -  -    295 CHAPTEE  I. ORIGIN  AND  DEVELOPMENT  OF  THE   SCIENCE  OF METROLOGY. Few  questions  concern  the  human  race  more  directly  and universally  than  the  subject  of  weights  and  measures.  In  fact, so  intimate  is  this  connection  that  the  common  weights  and measures  of  a  people  bear  much  the  same  relation  to  it  as  does the  language  of  ordinary  speech,  being  assumed  and  applied  in their  daily  occupations  without  active  thought,  and  resisting changes  and  reforms,  even  when  brought  about  by  the  most strenuous  efforts  and  with  convincing  proof  of  their  desirability or  necessity.  For  the  origin  of  weights  and  measures  it  is necessary  to  go  back  to  the  earliest  days  of  the  human  race  and deal  with  the  elementary  mental  processes  of  primitive  man.  The idea  of  measuring  must  have  been  closely  akin  to  that  of number,  which,  of  course,  implied  the  perception  that  certain objects  could  be  grouped  together  either  actually  or  at  least ideally.  The  next  step  would  be  the  comparison  of  the  various objects  of  such  a  group,  and  this  would  involve  a  simple  ratio in  terms  of  one  of  the  members  of  the  group.  When  the comparison  was  extended  to  other  groups,  there  was  need  of  a standard,  and,  when  various  classes  of  objects  were  compared, a  standard  had  to  be  selected  which  would  answer  in  common. Such  standards  would  readily  suggest  themselves.  If  it  took  a certain  number  of  days  and  nights  to  make  a  journey,  the  distance travelled  in  one  day,  that  is  from  one  sunrise  or  sunset  to the  next,  would  straightway  be  considered  as  a  natural  measure of  journeys  of  considerable  duration,  while,  for  shorter  distances, A 2         EVOLUTION   OF  WEIGHTS   AND   MEASURES the  pace  as  a  regularly  recurring  interval  would  be  adopted for  measuring  the  total  distance,  and  the  single  pace  would be  taken  as  a  unit. For  measuring  still  smaller  distances  the  primitive  man  would take,  say  the  length  of  his  foot  or  the  breadth  of  his  hand,  as  it would  be  most  convenient  for  him  to  employ  as  units  in  his measurements  the  objects  usually  at  hand,  and  it  was  but natural  that  the  dimensions  of  the  body  would  furnish  such units.  Thus  for  linear  measures  there  would  be  employed  the breadth  of  the  first  joint  of  the  forefinger,  the  breadth  of  the hand,  the  span  of  the  extended  fingers  of  one  hand,  the  length  of the  foot,  the  length  of  the  forearm,  the  step  or  single  pace,  the double  pace,  and  the  distance  between  the  tips  of  the  fingers when  the  arms  were  outstretched.  All  of  these  distances  figured in  the  early  systems  of  linear  measures  of  the  ancients,  and,  in fact,  great  diversity  of  measures  was  a  characteristic  of  early civilization,  due  to  the  fact  that  originally  only  the  convenience of  the  individual  had  to  be  consulted.  With  the  growth  of society  the  tendency  was  toward  uniformity,  and  this  tendency, with  but  occasional  retrogressions,  has  been  maintained.  When several  persons  were  concerned  in  the  comparison  of  the  size  of an  object  or  some  other  kind  of  measurement,  it  was  necessary to  consult  the  convenience  of  the  group  rather  than  that  of  the individual,  while  with  the  development  of  trade  there  was also  added  the  idea  of  equity. Along  with  the  general  tendency  of  progress  from  diversity to  uniformity  of  measures  in  the  evolution  of  society,  must  also be  considered  the  securing  of  uniformity  of  single  measures. Thus,  if  a  pace  or  length  of  a  forearm  was  a  convenient  unit  for a  number  of  individuals,  it  would  soon  become  necessary  to specify  the  class  of  individuals,  or,  better  still,  the  single  indi- vidual whose  pace  or  forearm  was  to  be  the  standard;  was  it  to be  that  of  a  man  six  feet  in  height  or  one  considerably  shorter  ? Such  a  discussion  could  not  but  lead  to  the  actual  measuring of  the  pace  or  forearm  which  would  by  common  consent  serve  as the  measure,  and  then  by  laying  off  the  distance  on  some  surface a  standard  or  concrete  reproduction  of  the  unit  would  be  con- structed which  would  answer  for  the  family  or  small  group* Just    as    it  was    necessary    for    the    family    to    come    to    some THE   SCIENCE   OF   METROLOGY  3 understanding  as  to  what  measures  would  be  standard  for  their household,  so  it  was  soon  realized  that  the  interests  of  all would  best  be  subserved  if  a  single  system  should  be  employed throughout  the  tribe,  either  by  a  gradual  adoption  of  a  common mean,  or  by  having  some  standard  imposed  by  authority  emana- ting from  the  ruler  or  headmen  of  the  tribe.  This  latter  practice was  the  more  prevalent,  and,  remarkable  to  say,  has  persisted to  modern  times.  So  late  as  the  time  of  Henry  I.  the  length  of the  English  yard,  according  to  tradition,  was  fixed  by  the  length of  the  sovereign's  arm,  while  even  in  the  United  States  in  nearly all  cases  the  national  standards  of  weights  and  measures  have been  determined  by  executive  order  rather  than  by  legislative action. While  the  foregoing  observations  would  also  hold  true  in  the case  of  weights,  yet  in  connection  with  the  latter  there  are certain  additional  matters  to  be  considered.  When  the  primitive man  had  advanced  in  civilization  to  a  point  where  he  looked beyond  his  immediate  needs,  he  would  doubtless  own  a  certain number  of  slaves  and  domestic  cattle,  and  his  life  being  spent  in an  habitation  or  home  more  or  less  permanent,  it  would  be natural  for  him  to  accumulate  stores  of  grain  and  other substances  both  for  his  future  wants  and  to  barter  for  other commodities.  Now,  it  seems  that  the  earliest  unit  of  wealth and  basis  of  exchange  was  the  ox  or  cow,  and  this  soon  found an  equivalent  in  a  certain  amount  of  gold,  a  substance  which, on  account  of  its  practically  universal  distribution  and  its uniform  scarcity,  could  readily  be  given  a  fixed  value  in  terms of  cows  or  oxen.1  This  would  involve  some  rude  form  of measurement,  such  as  a  goose-quill  for  the  measurement  of  gold dust  by  capacity,  or  a  linear  measurement  if  the  gold  was  in  the form  of  wire  or  strips,  and  eventually  the  use  of  a  primitive balance  with  the  natural  seeds  of  plants  for  weights.  These seeds  indisputably  were  the  first  weights,  as  can  be  proved  by studying  the  habits  of  primitive  peoples  past  and  present,  where such  use  of  seeds  has  been  and  is  practically  universal,  and  this custom,  furthermore,  has  survived  in  the  grains  of  the  Anglo- Saxon  weights  and  the  carat  (from  the  Arab  carob  or  bean)  of the  dealers   in   precious  stones.     But   this   early   weighing   was 1Ridgeway,  Origin  of  Metallic  Money  and  Weights  (Cambridge,  Eng.,  1892). 4        EVOLUTION   OF   WEIGHTS   AND   MEASURES confined  to  gold  for  purposes  of  trade,  and  to  other  metals,  such as  silver  and  copper,  when  they  were  subsequently  used  for a  similar  purpose;  and  this  is  amply  demonstrated  by  early Egyptian  records  where  mention  is  made  of  weighing  only  gold, silver,  and  copper,  and  lapis  lazuli,  until  the  time  of  the  seven- teenth dynasty.  As  it  was  not  until  the  seventh  century  B.C. that  coined  money  was  used,  this  weighing  of  metals  was universal,  and  the  use  of  the  balance  was  required  in  practically all  transactions,  as  when  "  Abraham  weighed  to  Ephron  the silver  which  he  had  named  in  the  audience  of  the  sons  of Heth,  four  hundred  shekels  of  silver,  current  money  with  the merchant  "  (Gen.  xxiii.  16). It  followed  naturally  from  such  universal  weighing  that certain  units  should  be  formed,  made  up  of  a  certain  number  of seeds  and  reproduced  by  stone  or  metal  standards.  Though  we may  agree  with  Eidgeway  that  the  ,  earliest  weighings  were empirical,  and  were  carried  on  by  seeds  and  natural  standards "  before  ever  the  sages  of  Thebes  or  Chaldaea  had  dreamed  of applying  to  metrology  the  results  of  their  first  gropings  in Geometry  or  Astronomy,"  1  yet  we  must  admit  that  some  sort  of a  mathematical  system  of  units  of  weight  was  bound  to  come where  weighing  was  so  widespread.  Then  with  the  development of  civilization,  especially  as  regards  science  and  commerce,  it  was but  natural  that  these  weights  should  be  defined  either  by  royal decree  or  by  common  consent,  and  be  based  upon  a  standard which,  according  to  some  metrologists,  was  scientifically  deter- mined, or  in  the  opinion  of  others  was  merely  an  arbitrary weight  or  weights.  At  all  events  it  must  be  borne  in  mind  in considering  questions  of  metrology  from  the  earliest  times  down to  within  the  last  two  centuries  that  accuracy  in  weights  and measures  was  neither  demanded  nor  possible,  and  that  attempts of  archaeologists  accurately  to  weigh  the  weights  or  measure  the linear  scales  from  old  ruins,  and  to  use  small  differences  in forming  their  theories,  are  in  most  cases  quite  unwarranted. There  is,  however,  indisputably  a  certain  amount  of  corre- spondence among  the  weights  and  measures  of  antiquity  due  to commercial  intercourse  which  took  place  both  by  sea  and  by caravan,  and  which  was  much  greater  than  we  would  be  apt  to 1  Ridgeway,  p.  232. THE   SCIENCE   OF   METROLOGY  5 suspect,  and  this  should  of  course  receive  due  weight  in  all discussions  of  the  metrology  of  the  ancients. For  the  measure  of  capacity  it— is— tfuito  obvious  tha-t  the earliest  units  were  natural  objects  such  as  eggs  or  gourds,  and  that  a basket  or  jar  would  be  constructed  by  a  certain  tribe  which  would be  of  a  convenient  capacity  for  the  purposes  for  which  it  was used,  such  as  carrying  grain  or  water.  Such  natural  or  arbitrary units  would  straightway  find  application  and  would  doubtless  fill all  needs,  as  capacity  measurements  would  be  of  the  simplest nature  possible.  In—kcct,  with  certain  primitive -  peoples,  as  is now  the  case  among  some  Asiatic  tribes,  units  of  measure  of capacity  were  quite  unknown,  and  it  is  the  general  tendency  for units  of  capacity  to  come  after  units  of  weight.  If  we  are  to follow  the  theories  of  some  metrologists  we  must  assume  that  the ancients  derived  their  units  of  capacity  from  a  cube  one  of  whose sides  was  the  linear  unit,  and  that  the  unit  of  weight  was  this, or  a  proportionate  cube,  which  was  filled  with  pure  water.  In fact,  such  a  process  would  give  a  unit  of  area  by  taking  a  square whose  side  was  a  linear  unit,  and  a  cubical  measure  formed  by  a unit  cube  whose  edge  was  a  linear  unitj  Whether  or  not  the ancients  followed  such  a  process  of  reasoning  it  is  impossible  to say,  but  on  both  sides  of  the  question  there  are  many  arguments which  will  briefly  be  referred  to  a  few  pages  further  on. While  the  development  of  weights  and  measures  is  a  gradual evolution,  yet  it  is  a  complex  matter  to  which  so  many  influences have  contributed  that  it  is  difficult  to  trace  any  clear  course  or logical  development.  Ethnic  conditions,  the  whims  and  caprices of  rulers,  imposition  and  fraud,  conquest,  and  methods  and  habits of  thought  and  life,  all  in  turn  have  had  their  effect.  Never- theless the  growth  of  scientific  knowledge  and  its  application,  the influence  of  the  market-place,  as  well  as  that  of  a  broader commerce  and  laws  and  customs,  in  every  nation  have  tended  to bring  together  into  something  more  or  less  resembling  a  system all  matters  connected  with  weighing  and  measuring  built  up  on such  units  as  the  tribe  or  nation  had  selected  for  their  inter- change of  commodities  and  ideas. For  the  units  or  bases  of  such  systems  it  is  possible  to  select two  different  classes  of  quantities,  arbitrary  and  natural,  and  to use   them   in  their   development.     By  an    arbitrary  quantity  is 6         EVOLUTION   OF   WEIGHTS   AND   MEASURES meant  one  that  is  selected  without  reference  to  its  occurrence  in any  natural  object  or  condition,  but  merely  a  certain  distance, mass,  etc.,  which  will  furnish  a  convenient  basis  both  in  its original  state  and  by  its  multiples  and  submultiples,  for  the measurements  to  which  it  will  be  applied.  In  actual  practice the  result  has  been,  in  spite  of  many  attempts  to  construct systems  based  on  natural  units,  that  the  fundamental  units  are arbitrary,  and  where  interrelated  are  based  upon  actual  standards of  length  rather  than  distances  found  in  nature.  As  examples  of natural  units  might  be  cited  the  measures  derived  from  the human  body  already  mentioned,  which  readily  connect  themselves one  with  another  by  certain  relations.      Thus : The  Digit,     -----  equals  1   part Palm  or  handbreadth, „      4      , Span,     ----- „    12      , Foot,      - n      16        , Cubit, „    24      , Step  or  single  pace,  -          -          - „    40      , Double  pace,   -          -          -          - „    80      , Fathom,  or  distance  between  ex- tended arms,    -          -           - n     96        , This  ratio  we  find  observed  in  early  systems  of  measurement,  and it  must  be  borne  in  mind  in  considering  them. As  typical  of  early  natural  measures  as  found  in  the  Orient, the  following  passage  from  the  writings  of  Hiuen  Tsiang  (Yuan Chwang),  603-668  A.D.,  a  Chinese  traveller  and  author,  of  Ho-ran, written  in  a.d.  629  in  regard  to  the  measures  of  India,  may  be cited : 1 "  In  point  of  measurements,  there  is  first  of  all  the  yojana (yu-shen-na) ;  this  from  the  time  of  the  holy  kings  of  old  has been  regarded  as  a  day's  march  for  an  army.  The  old  accounts say  it  is  equal  to  40  li ;  according  to  the  common  reckoning  in India  it  is  30  li,  but  in  the  sacred  book  (of  Buddha)  the  yojana is  only  16  li.  In  the  subdivision  of  distances  a  yojana  is  equal to  eight  kros'as  (keu-lu-she) :  a  kros'a  is  divided  into  500  bows (dhanus) :  a  bow  is  divided  into  four  cubits  (hastas) :  a  cubit  is divided  into  24  fingers  (angulis):  a  finger  is  divided  into  7  barley- 1Beal,  Buddhist  Records  of  the  Western  World  (London,  1884),  vol.  i.  p.  70. THE   SCIENCE   OF   METROLOGY  7 corns  (yavas) :  and  so  on  to  a  louse  (yuka),  a  nit  (liksha),  a  dust grain,  a  cow's  hair,  a  sheep's  hair,  a  hare's  down,  a  copper  water,1 and  so  on  for  seven  divisions,  till  we  come  to  a  small  grain  of dust :  this  is  divided  sevenfold  till  we  come  to  an  excessively small  grain  of  dust  (ami) :  this  cannot  be  divided  further  without arriving  at  nothingness,  and  so  it  is  called  the  infinitely  small (paramanu)." Leaving  out  of  consideration  the  source  or  antiquity  of  these particular  measures,  they  may  be  considered  as  exemplifying  the use  of  natural  circumstances  or  objects  as  units  and  their  connec- tion into  a  system.  However,  as  is  mentioned  in  the  case  of  the yojana,  and  the  same  may  be  found  in  numerous  other  instances in  early  measures  not  only  in  the  Orient  but  throughout  the civilized  world,  the  ancient  systems  may  have  contained  units varying  in  value  and  in  their  relation  to  other  units.  It  may  be said  in  passing  that  it  is  fair  to  assume  that  these  particular measures  were  much  older  than  would  at  first  glance  appear  from the  date  of  the  work  quoted,  as  India  and  the  adjoining  countries boasted  a  civilization  that  was  nothing  if  not  conservative,  and traced  its  traditions  to  a  remote  past. Another  example  of  a  natural  unit,  according  to  some  of  the older  authorities  on  metrology,  including  Paucton,2  though  the theory  is  now  regarded  as  entirely  erroneous,  was  the  base  of  the Great  Pyramid,  which  was  constructed  equal  to  the  five  hundredth part  of  a  "  degree,"  and  was  divided  into  600  Ptolemaic  feet  or 400  Ptolemaic  cubits.  Likewise  in  the  determination  of  the  meter an  attempt  was  made  to  measure  the  ten-millionth  part  of  a quadrant  of  a  great  circle  of  the  earth,  but  it  was  subsequently found  that  the  meter  thus  obtained  did  not  represent  this  fraction with  sufficient  accuracy,  and  it  was  concluded  to  retain  such  a  meter as  an  arbitrary  standard  and  as  the  basis  of  the  metric  system rather  than  attempt  to  secure  a  new  natural  unit  which  might require  subsequent  changing  with  future  scientific  developments. Even  after  the  metric  system  had  been  developed,  Sir  John Herschel,  the   British  astronomer,   proposed   as   a   standard  the 1  Possibly  the  size  of  the  small  hole  in  the  tamri  or  copper  cup  for  the  admis- sion of  water. 2  Paucton,  M&rologie,  ou  Traits  des  Mesures,  Poids  et  Monnoies  (Paris,  1780), chap.  i.  p.  109  et  seq. 8         EVOLUTION   OF   WEIGHTS   AND   MEASURES length  of  the  polar  axis  of  the  earth,  as  ,nnAnftnn  Part  °f this  quantity  would  give  the  present  British  inch  very  closely.1 Another  class  of  natural  units  that  were  employed  as  the  basis of  systems  of  weights  and  measures  consisted  of  the  dimensions  or weight  of  grains  of  barley  or  corn,  a  number  of  such  grains  being placed  in  a  row  to  form  such  a  unit  as  the  English  inch,  or  col- lected to  a  certain  number  to  form  by  their  weight  an  English pound. Whether  the  units  be  natural  or  arbitrary  there  must  be  some that  are  fundamental,  and  on  them  can  be  based  and  developed others  as  civilization,  commerce,  and  science  need  additional  units to  express  the  magnitudes  with  which  they  are  forced  to  deal. For  example,  in  the  eighteenth  century  it  was  not  possible  to make  any  measurements  of  electricity,  nor  indeed  were  such demanded,  yet  one  hundred  years  later  a  complete  system  of electrical  measurements  was  developed  based  on  measures  and units  previously  used.2 For  fundamental  units  it  is  possible  and  most  convenient  to start  with  the  unit  of  length  and  develop  from  it  units  of  weight and  capacity  by  taking  a  volume  equal  to  that  of  a  cube,  each side  of  which  is  equal  to  the  selected  unit  of  length,  and  then filling  it  with  water,  as  was  done  with  the  modern  metric  system, and  is  a  feature  claimed  for  the  weights  and  measures  of  the ancient  Babylonians.  Similarly,  units  of  area  could  be  developed by  taking  a  square  whose  side  is  the  linear  unit,  and  with  the addition  of  a  unit  of  time,  units  of  velocity,  acceleration,  etc., could  readily  be  derived.  By  the  time  that  these  and  other required  units  were  obtained,  they  naturally  would  become  asso- ciated into  a  system  of  more  or  less  logical  relation  and  arrange- ment. In  such  a  system  there  necessarily  would  be  a  number  of different  units  for  different  classes  of  quantities,  and  these  would be  multiples  and  sub-multiples  of  each  other.  Such  arrangements and  systems  would  reflect  the  methods  of  thought  of  the  people by  whom  they  were  developed.  Accordingly  in  ancient  Egypt and  also  in  China  we  find  a  decimal  system  employed  as  in  their system  of  numerical  notation,  while  among  the  Babylonians, Chaldaeans,  Assyrians,  and  the  Egyptians  of  certain  later  dynasties 1See  chapter  vi.,  p.  164. 2  See  chapter  ix. — Electrical  Units. THE   SCIENCE   OF   METROLOGY  9- the  basis  of  division  was  sexagesimal,  as  is  retained  in  our  modern notation  of  time.  The  Eomans  used  the  duodecimal  system, where  the  foot,  sextarius  (measure  of  capacity),  libra  (pound),  etc.,. were  divided  into  twelve  equal  parts.  With  the  Hindus  there was  the  binary  subdivision  which  was  also  followed  by  the  Ger- manic and  Teutonic  peoples,  and  also  by  the  Arabs,  despite  their decimal  system  of  notation.  These  examples  show  how  national or  racial  conditions  affect  the  development  of  a  system  of  weights and  measures,  and  of  course  as  the  political,  commercial,  or  intel- lectual influence  of  a  nation  extended  it  was  but  natural  that with  it  would  go  its  weights  and  measures,  which,  if  not  sup- planting those  of  other  countries,  at  least  in  many  cases  would have  a  corrupting  and  disintegrating  influence. In  any  attempt  at  a  brief  historical  survey  of  the  origin  and history  of  weights  and  measures  there  are  many  matters  to  be  taken into  consideration  which  prevent  a  complete  and  comprehensive sketch  of  the  subject.  For  over  two  centuries  there  has  been  much attention  devoted  to  ancient  metrology,  and  many  and  contra- dictory theories  have  been  advanced.  They  are  for  the  most part  founded  on  data  or  hypotheses  by  no  means  satisfactory ; though  in  nearly  all  instances  plausible  cases  which  often  show the  greatest  study  and  ingenuity  have  been  made  out  by  workers whose  sincerity  and  industry  cannot  be  questioned.  In  certain of  these  systems  and  theories  the  ancients  are  credited  with  a knowledge  of  mathematics,  both  theoretical  and  applied,  which some  scholars  do  not  think  at  all  warranted,  while  other  systems have  been  built  up  on  limited  data,  often  text  allusions  in  ancient literature  and  inscriptions,  which  though  harmonious  to  a  greater or  less  extent  do  not  absolutely  convince  one  that  the  harmony  is not  quite  as  much  the  result  of  chance  as  of  design. Assuming  that  the  parts  of  the  body  were  employed  by  many ancient  races  as  the  basis  of  measures  of  length,  it  is  desirable  to ascertain  how  these  were  united  into  a  system  and  how  such  a system  spread.  It  is  usual  to  credit  the  origin  of  systems  of weights  and  measures  to  Babylon  or  Egypt,  the  systems  of  both countries  showing  a  common  source,  and  there  being  various remains,  literary  and  archaeological,  on  which  have  been  based explanations  of  the  origin  of  all  ancient  measures.  Thus  the great  pyramid  of  Ghizeh,  dating  from  about  4000  B.C.,  by  some  has 10       EVOLUTION   OF   WEIGHTS   AND   MEASURES been  thought  to  have  an  important  bearing  on  metrology,  and  has figured  in  many  discussions  and  theories,  since  by  its  dimensions and  inscriptions  it  supplies  data  which  are  susceptible  of  various interpretations.  Thus  Paucton  and  Jomard,1  two  distinguished metrologists  of  the  eighteenth  century,  assumed  that  the  side  of  the pyramid  represented  a  fraction  of  a  degree  of  the  earth  just  as the  French  scientists  based  the  meter  on  a  fraction  of  the  earth's quadrant ;  while  later  Prof.  Piazzi  Smyth2  and  Lieut.  C.  A.  L. Totten3  derived  the  Anglo-Saxon  weights  and  measures  directly from  its  dimensions.  These  theories,  as  well  as  the  idea  that  the great  pyramids  played  an  important  part  in  ancient  astronomy, have  been  amply  controverted,  and  according  to  the  opinion  of Lieut.-Gen.  Sir  Chas.  Warren4  in  the  light  of  the  most  recent investigations,  "  The  Pyramid  is  simply  a  record  of  the  measures, linear,  capacity,  and  weight,  which  were  in  use  in  former  days." There  is  nothing  astronomical  about  it  except  its  orientation  and the  direction  of  its  great  gallery  to  a  point  in  the  northern  sky. There  were,  however,  other  great  structures  in  Egypt  and Babylonia  in  which  stone  and  brick5  of  regular  dimensions  were used,  and  even  in  the  earliest  times  of  which  we  have  record  it seems  conclusive  that  there  must  have  existed  fairly  complete systems  of  weights  and  measures. According  to  the  Jewish  tradition  given  in  Josephus,  we  are informed  in  the  quaint  language  of  Dr.  Arbuthnot,  "  that  Cain was  the  first  monied  man,  that  he  taught  his  band  luxury  and rapine,  and  broke  the  public  tranquillity  by  introducing  the  use  of weights  and  measures."6     What  happened  in  the  land  of  Nod, 1  Paucton,  Metrologie,  ou  Traits  des  Mesures,  Poids  et  Monnoies  (Paris,  1780); ■Jomard,  Memoire  sur  le  Systeme  Me'trique  des  Anciens  Egyptiens  (Paris,  1817). 2C.  Piazzi  Smyth,  Life  and  Work  at  the  great  Pyramid  (Edinburgh,  1867) ;  Our Inheritance  in  the  great  Pyramid  (London,  1864).  These  works  and  Professor Smyth's  theories  are  discussed  by  Dr.  F.  A.  P.  Barnard  in  Proceedings  Am. Metrological  Society  (New  York),  vol.  iv.,  1884,  pp.  197-219. 3 Charles  A.  L.  Totten,  An  Important  Question  in  Metrology  (New  York,  1884). 4 Warren,  "The  Ancient  Standards  of  Measure  in  the  East,"  p.  222,  Palestine Exploration  Fund  Quarterly,  1899. 5  In  Babylonia  square  bricks  were  used  which  measure  13  inches  on  each  edge, •or  \  of  the  double  cubit  as  given  by  the  Gudea  Scale  (see  p.  14). 6  Arbuthnot,  p.  1,  Tables  of  Ancient  Coins  (London,  1754). THE   SCIENCE   OF   METROLOGY  11 whither  Cain  had  wandered  with  his  band  and  where  he  founded his  city  (Genesis  iv.  16  and  17),  soon  must  have  become  universal, for  we  find  the  dimensions  of  the  ark  as  Noah  was  told  to  construct it  given  in  cubits  (Genesis  vi.  15). Apart  from  such  traditions  and  scriptural  legends  we  know from  brick  tablets  and  other  remains  that  weights  and  measures in  some  form  or  other  flourished  in  Babylonia  and  Egypt,  and that  the  systems  of  the  two  countries  doubtless  had  a  common origin.  Although  it  cannot  be  definitely  proved  it  is  likely  that this  origin  was  Babylonian,  and  much  that  has  been  written  on ancient  metrology  is  based  on  this  view.  Hommel,  in  speaking  of the  Babylonian  metrology,1  states  that  from  it  "  admittedly  all the  ancient  metrological  systems  (that  of  ancient  Egypt  included) were  derived."  This  is  also  the  opinion  of  Dr.  Brandis.2  Assum- ing such  to  be  the  case,  we  are  brought  at  once  face  to  face  with a  great  diversity  of  opinion  on  the  point  as  to  whether  a  well- developed  and  scientific  system  of  weights  and  measures  existed in  Babylonia,  from  which  were  derived  the  weights  and  measures of  the  adjoining  nations,  and  which,  through  trade  and  commerce, spread  over  the  then  civilized  earth,  or  whether  various  systems of  weights  and  measures  came  into  existence  separately  in different  countries  and  gradually,  with  the  development  of  civi- lization and  under  similar  conditions,  spread  abroad  and  became more  or  less  assimilated.  The  first  is  the  point  of  view  of Boeckh 3  and  the  members  of  a  distinguished  school  of  Conti- nental archaeologists  and  metrologists,  and  from  available monumental  and  literary  remains  with  endless  patience  and ingenuity  they  have  evolved  theories  so  scientifically  constructed that  they  excite  admiration  if  they  do  not  convince.  On  the other  hand  there  are  a  number  of  students  of  archaeology  who dispute  the  scientific  basis  on  which  such  systems  are  constructed, and  deny  that  requisite  knowledge  and  mental  ability  for  such scientific  reasoning  and  construction  was  possessed  by  these  early ^ee  article  "Babylonia,"  Hastings'  Dictionary  of  the  Bible  (New  York,  1903), vol.  i.  p.  218. 2  See  J.  Brandis,  Das  Mum-  Maass-  und  Gewichlswesen  in  Vorderasien  bis  auf Alexander  den  Grossen  (Berlin,  1866). 3  Boeckh,  Metrologische  Untersuchungen  iiber  Gewichte,  Miinzfmse  und  Masse  des Alterthums  (Berlin,  1838). 12       EVOLUTION   OF  WEIGHTS   AND   MEASURES peoples.  They  claim  that  weights  and  measures  from  some early  body  measures  and  natural  standards  developed  according to  the  needs  of  the  people  and  depended  on  widely  understood ratios  and  rules  of  exchange  rather  than  on  any  scientific basis. In  considering  the  first  point  of  view  it  is  necessary  to  assume that  considerable  mathematical  and  astronomical  knowledge  was possessed  by  the  ancient  Babylonians  and  was  used  by  them  in standardizing  their  weights  and  measures.  In  other  words,  from ancient  and  arbitrary  measures,  doubtless  of  the  body,  they developed  such  a  system  as  was  early  required  by  the  demands of  their  scientific  work  in  astronomy  and  their  active  building operations.  As  measuring  is  essential  to  all  scientific  work,  it  is not  to  be  doubted  that  its  importance  was  thus  early  recognized, and  in  conjunction  with  their  system  of  numerical  notation  a permanent  system  was  arranged.  This  was  also  brought  into direct  relation  with  their  astronomical'  work,  which  was  by  no means  inconsiderable  for  these  early  times.  In  the  course  of their  observations  it  was  ascertained  that  at  the  equinox  the apparent  diameter  of  the  sun  on  the  horizon  was  ^-J-^  of  the  half circle.  Furthermore,  by  using  a  water  clock,  where  water  was allowed  to  flow  through  a  small  orifice  from  one  jar  into  another,  it was  found  that  the  amount  received  in  the  twelve  hours  between sunrise  and  sunset  was  360  times  as  much  as  when  the  sun  was traversing  a  distance  equal  to  its  own  diameter  or  two  minutes  of time.1  This  afforded  an  accurate  method  of  measuring  time,  and formed  the  foundation  of  the  sexagesimal  system  which  was  the underlying  principle  of  all  Babylonian  metrology  and  harmonized perfectly  with  their  system  of  numeration.  This  idea  naturally involved  the  division  of  the  circle  into  360  degrees,  or  rather  720 parts,  which  has  continued  to  the  present  day,  and  the  important geometrical  fact  that  the  radius  is  equal  the  chord  of  one-sixth the  circumference  was  also  well  known  at  this  time.2 1L.  Ideler,  "  Ueber  die  Sternkunde  der  Chaldaeer,"  Abhandl.  der  k.  A  had. Wissenschaft  in  Berlin,  1814-1815,  p.  214.  Referring  to  Cleomedes  Cyclom. (On  the  Circular  Theory  of  the  Heavenly  Bodies),  1.  11.  p.  75  ed.  Balfor ; Proclus  Hypotyp.  p.  41  (ed.  Basil.  1540-4) ;  Pappus,  especially  in  his  Com- mentary on  the  Fifth  Book  of  the  Almagest  of  Ptolemy. 2Hommel,  article  "Babylonia,"  Hastings'  Dictionary  of  the  Bible  (New  York, 1903),  vol.  i.  p.  219. THE   SCIENCE   OF   METROLOGY  13 By  some  authorities  it  was  believed  that  the  water  jar  referred to  above  was  also  used  as  a  measure  of  capacity,  and  that  it  was divided  on  a  duodecimal  basis  corresponding  to  the  hour  division. It  was  then  assumed  that  from  a  cube  equal  to  such  a  volume the  unit  of  length  was  derived  by  taking  the  length  of  one  of  its edges,  which  was  the  Babylonian  foot,  and  bore  a  natural  relation to  the  cubit.  This  unit  of  volume  when  filled  with  water  gave the  Babylonian  talent,  from  which  other  units  of  the  same  name were  derived.  This  theory,  however,  which  was  supported  for many  years,  has  been  abandoned,  and  it  is  believed  that  the  unit of  weight  was  derived  from  the  unit  of  length,  just  as  is  done  in the  modern  metric  system. The  relation  of  numbers  and  linear  distances  in  Babylonian measures  is  best  derived  from  a  study  of  the  Senkereh  Tablet, which  dates  back  to  about  2500  B.C.,  and  was  discovered  in  1850 in  a  small  Arab  village  on  the  site  of  the  ancient  city  of  Larsam or  Larsa.  It  is  now  in  the  British  Museum,  and  affords  con- siderable information  as  to  the  Babylonian  measures  and  the methods  of  computation.  It  is  a  clay  tablet,  on  one  side  of which  are  the  fractions  and  multiples  of  the  ell  or  cubit,  and  on the  other  are  the  squares  and  cubes  of  the  cubit  from  1  to  40.1 This  tablet  has  received  the  attention  of  a  number  of  scholars, including  the  late  Professor  Eawlinson,  and  the  sexagesimal character  of  the  measures  has  been  clearly  demonstrated.  In connection  with  the  scale  of  Gudea,  to  be  described  a  few  lines below,  it  has  been  examined  by  the  Rev.  W.  Shaw-Caldecott,  who concludes  that  "  The  breadth  of  the  hand-palm  conventionalized was  the  fundamental  of  all  length  measures,"  and  "  That  there were  three  ell  (cubit)  lengths  in  simultaneous  use,  each  probably in  a  different  kind  of  trade  like  our  own  Troy  and  avoirdupois weights."  2 1Hommel,  article  "  Babylonia,"  Hastings'  Dictionary  of  the  Bible  (New  York, 1903),  vol.  i.  p.  218. 2 Shaw-Caldecott,  "Linear  Measures  of  Babylonia  about  2500,"  p.  263,  Journal Royal  Asiatic  Society,  1903,  London.  In  this  article  the  characters  on  the tablet  are  reproduced.  See  also  R.  Lepsius,  "  Der  Baby lonisch- Assy rischen Langenmasse  nach  der  Tafel  von  Senkereh,"  in  the  Abhandlungen  der Kbniglichen  Akadernie  der  Wissenschaften  %u  Berlin,  1877.  With  this  article is  printed  a  photographic  reproduction  of  the  tablet,  together  with  a  recon- struction. 14       EVOLUTION   OF   WEIGHTS   AND   MEASURES Accordingly  from  the  tablet  Mr.  Shaw-Caldecott  derives  the following  units  and  proportions  : Line        -  -  =  y^  of  a  palm. Sossus      -  -  -      =-gL Twentieth  of  a  palm  -      =  -^  „ Twelfth  of  a  palm  -      =  t?  » Third  of  a  palm,  or  digit  =  ^  „ Palm. Small  ell  (cubit)  -      =3  palms. Medium  ell  (cubit)  -      =  4  palms. Large  ell  (cubit)  -      =5  palms. Small  reed         -  =  4  small  ells  (cubits). Medium  reed    -  =  6  medium  ells  (cubits). Large  reed         -  =  6  large  ells  (cubits). While  the  Senkereh  Tablet  establishes  the  ratios  between  the various  units  yet  it  does  not  afford  any'  information  as  to  their absolute  value,  and  for  this  recourse  is  had  to  a  tablet  forming part  of  a  statue  discovered  in  1881  at  Telloh  in  southern Babylonia,  not  far  from  Senkereh,  by  M.  E.  de  Sarzec,  and now  in  the  Louvre.1  It  dates  from  about  the  same  period  as the  Senkereh  Tablet,  and  represents  King  Gudea  in  a  position of  prayer,  and  holding  on  his  knees  a  slab  of  stone  on  which is  engraved  the  ground  plan  of  a  palace,  a  graving  tool,  and  a double  line,  the  latter  being  cut  near  the  outer  edge  and  being crossed  by  a  number  of  indentations  or  cuts.  This  unmistakably is  a  scale,  and,  furthermore,  it  is  the  oldest  scale  that  has  been discovered  up  to  the  present  time.  By  assuming  that  it  is the  same  size  as  the  scale  of  linear  measures  then  in  use,  and by  applying  the  proportions  obtained  from  the  Senkereh  Tablet, it  is  possible  to  obtain  the  lengths  of  the  various  units  in  terms of  modern  equivalents,  preserving  the  decimal  and  duodecimal division  characteristic  of  the  Babylonian  arithmetical  system. Thus  we  have  the  handbreadth  or  palm  equal  to  99-99*6  mm. (3*9-4,l   inches),  and  the    cubit    composed  of    five  handbreadths 1 E.  de  Sarzec,  De'couvertes  en  Chaldee,  1884-1889,  PI.  15.  See  also  Shaw- Caldecott,  loc.  cit.  See  also  Toy,  "  The  Book  of  the  Prophet  Ezekiel "  (Part  12, Sacred  Books  of  the  Old  Testament,  "Polychrome  Bible")  (New  York,  1889),. Notes,  pp.  179-180  for  illustrations  and  description. THE   SCIENCE   OF   METROLOGY  15 equal  to  495  mm.  (19*483  inches),  and  also  in  early  and  wide- spread use  a  double  cubit  twice  this  length  or  990  mm.  (38*976 inches).  This  latter  unit  is  of  interest  on  account  of  its  close approximation  to  the  modern  meter  of  1000  mm.,  and  also  on account  of  the  fact,  first  discovered  by  Lehmann,  that  it  is  almost exactly  the  length  of  the  second's  pendulum  for  the  latitude  of Babylon  (31  degrees  north,  at  which  point  the  theoretical  length of  a  second's  pendulum  would  be  992*35  mm.).  Consequently he  argues  that  the  theory  of  the  pendulum  must  have  been known  to  the  early  Babylonians,  who  doubtless  derived  it  from the  plumb-line,  which  must  have  been  employed  in  their building  operations.1  This  fact,  however,  cannot  be  regarded as  more  than  a  mere  coincidence,  and  while  it  is  most interesting  it  is  not  considered  possible  that  such  an  important physical  principle  should  have  been  known  at  so  early  a  day and  then  allowed  to  lapse  from  human  knowledge  until  the time  of  Galileo. Multiplying  the  great  cubit  by  6  the  "  reed "  was  obtained, and  by  taking  12  great  cubits  the  gar.  To  form  the  ush  or stadion  60  gar  were  required,  and  30  ush  made  a  parasang  or kasbu,  which  was  equivalent  to  about  21  kilometers.  These longer  linear  measures  are  again  connected  with  the  measure of  time,  as  360  great  cubits  represented  the  distance  an  average walker  could  accomplish  in  four  minutes,  while  the  great  kasbu of  21,600  cubits  was  the  distance  traversed  during  a  night  watch of  four  hours  or  J  of  a  day,  and  the  small  kasbu  would  be  one half  of  this  distance. Measures  of  area  constructed  by  squaring  the  linear  measures are  also  claimed  for  the  Babylonians,  and  here  again  the  sexa- gesimal ratio  was  preserved ;  thus  180  she  made  a  gin,  which  was possibly  equal  to  a  square  cubit.  A  "  garden  "  (sar)  was  com- posed of  60  gin,  and  1800  gardens  formed  a  "field"  (gan).  But the  Babylonians,  in  common  with  other  Asiatic  nations,  also employed  for  measuring   land   the   amount  of   seed  required  to 1  Lehmann,  p.  89,  "  Ueber  das  babylonische  metrische  System  und  dessen Verbreitung, "  Verh.  der  Physikalischen  Gesellschaft  zu  Berlin  (Berlin,  1890),  vol. viii.  pp.  81-101  ;  also  in  abstract,  pp.  167-168,  vol.  lxi.,  Nature  (London,  1889). In  this  connection  a  paper  by  the  same  author,  "  Alt-babylonisches  Maass  und Gewicht  und  deren  Wanderung,"  Zeitschriflfur  Ethnologie  (Berlin,  1889),  pp.  245- 328,  may  also  be  consulted  with  profit. 16       EVOLUTION   OF   WEIGHTS   AND   MEASURES sow  a  field,  and  statements  based  on  this  idea  are  found  in  many old  Assyrian  documents.1 The  Babylonian  capacity  measures  started  with  a  cube  whose edge  was  a  handbreadth  in  length  (99-99*6  mm.),  and  which when  filled  with  water  gave  the  unit  of  weight,  the  great  mina, which,  occupying  as  it  does  almost  the  volume  of  a  cubic  deci- meter, would  correspond  quite  closely  with  the  modern  kilogram. Such  a  capacity  measure  was  known  as  the  ka,  and  was  nearly the  equivalent  of  the  modern  liter.  As  multiples  of  the  ka there  was  the  gur,  which  was  composed  of  either  360  or  300 of  the  smaller  units,  there  being  not  only  two  such  gurs  but a  third  divided  into  180  parts  and  based  on  a  double  ka,  from which  the  Hebrews  probably  obtained  their  kor,  which  they divided  into  180  kab.  Likewise  in  the  subdivision  of  the Babylonian  measures  there  was  the  gin  or  ^  of  a  ka,  which in  the  Hebrew  system  was  paralleled  by  the  hin. The  relation  between  the  capacity  and' weight  we  have  already seen  in  the  case  of  the  great  mina,  which  weighing,  as  it  did, between  982*4  and  985*8  grams  giy^s  a  noticeably  close  approxi- mation to  the  modern  kilogram.  \This  great  or  heavy  mina  was composed  of  60  shekels,  each  of  3(T0  she  or  grains  of  corn,  thus combining  in  a  system  of  weights  two  classes  of  natural  units. The  greater  weight  was  the  talent  composed  of  60  minas.  \  Such a  system  would  have  been  simplicity  itself,  were  it  notmr  the fact  that  several  systems  of  weights,  just  as  of  linear  measures, are  found  employed  at  the  same  time.  There  was  a  light  mina which  weighed  one  half  of  the  heavy  mina,  and  in  fact whole  light  and  heavy  systems  standing  to  each  other  in  the ratio  of  1 : 2  are  believed  to  have  existed,  of  which  representative weights  have  been  found.  Furthermore,  as  gold  and  silver, whose  values  were  in  the  ratio  of  40 : 3,  were  used  as  currency, other  systems  designed  to  accommodate  both  weight  and  value arose,  and  there  was  a  mina  of  gold  which  was  composed  of 50  units,  each  a  shekel  or  g1^  of  the  weight  mina.  Then  there was  a  silver  mina  which  weighed  about  ^  more  than  the  Baby- lonian mina  of  weight,  while  there  was  a  Phoenician  mina  which was  also  divided  into  50  units,  which  made  the  whole  equal  to J$$  of  the  original  weight  mina. *C.  H.  W.  Johns,  Assyrian  Deeds  and  Documents  (London,  1902),  vol.  ii. pp.  219-220. THE   SCIENCE   OF   METROLOGY  17 The  subject  of  Babylonian  units  of  weight  is  one  of  consider- able complexity  on  account  of  the  fact  that  weight  and  currency had  so  intimate  a  relation  and  that  gold  and  silver  were  both standards.  Furthermore,  there  was  doubtless  legislation  stan- dardizing certain  other  weights  so  that  discrepancies  would  be found  on  that  score. Having  considered  such  a  carefully  erected  structure  we  must now  discuss  briefly  the  position  of  those  that  would  demolish utterly  any  such  scientific  arrangement  and  basis  for  ancient weights  and  measures,  and  more  particularly  any  connection between  the  two.  We  are  called  upon  to  proceed  further  along the  lines  indicated  in  the  beginning  of  this  chapter,  and  to observe  that  the  use  of  weights  and  measures  accompanied  the gradual  development  of  civilization,  and  that  exactness  in  either the  determination  of  units  of  measure  or  in  the  preservation  of standards  was  no  more  characteristic  of  the  twentieth  or  thirtieth century  B.C.  than  it  was  of  the  second  or  third.  Although  the  early Babylonians  may  have  known  how  to  divide  time  on  a  sexa- gesimal basis  and  to  observe  eclipses,  yet  so  simple  a  mathematical process  as  obtaining  area  by  multiplying  length  and  breadth together  seems  to  have  been  unknown  according  to  a  study  of their  literary  remains,  since  for  the  measurements  of  land  areas the  unit  was  not  a  square,  but  a  strip  of  uniform  width.1 Furthermore,  the  extensive  use  of  the  amount  of  seed  required superficial  measures.  The  most  strenuous  objection  has  been made  to  any  systematic  relation  and  connection  between  weights and  measures,  and  this  feeling  on  the  part  of  continental  scholars is  considered  due  to  their  intimate  knowledge  and  use  of  the metric  system,  which  acquired  by  them  so  readily  would  doubtless suggest  the  possibility  of  the  employment  of  its  fundamental features  by  the  ancients.  Why  several  thousand  years  should intervene  before  the  mind  of  man  would  return  to  such  devices, it  is  difficult  if  not  impossible  to  explain,  and  like  many  other phenomena  considered  now  so  simple,  it  is  most  natural  to assume  that  it  was  known  to  the  ancients,  yet  at  the  same  time it  is  impossible  to  prove  it.  Thus  any  such  relations  must  be entirely  hypothetical,  and  the  only  arguments  to  be  advanced  in 1 C.   H.  W.   Johns,  Assyrian  Deeds  and  Documents  (London,    1902),   vol.   ii. pp.  219-220. B 18       EVOLUTION   OF   WEIGHTS   AND   MEASURES their  support  must  be  founded  on  circumstances  which  are  pro- bably mere  coincidences,  and  doubtless  most  delusive.  Professor Flinders  Petrie,  in  speaking  of  this  subject,  says : 1  "  All  that can  be  said  therefore  to  the  many  theories  connecting  weights and  measures  is  that  they  are  possible,  but  our  knowledge  at present  does  not  admit  of  proving  or  disproving  their  exactitude.'* Though  this  was  written  some  years  ago,  nevertheless  it  is  fair to  say  that  there  has  been  no  discovery  or  research  that  would warrant  any  different  expression  from  one  holding  Mr.  Flinders Petrie's  views.  According  to  another  leading  authority,  the Kev.  C.  H.  W.  Johns,  who  has  carefully  examined  many  literary remains  of  the  old  Babylonians,  there  is  not  afforded  by  these documents  any  ground  for  believing  in  any  connection  between Babylonian  measures  of  length  and  weight,  while  to  him Lehmann's  idea  of  the  double  cubit  derived  from  the  second's pendulum  seems  quite  ridiculous.  According  to  Bidgeway,2 considering  the  Hindus  as  an  ancient  people  of  culture,  with whose  literature  we  have  some  acquaintance,  we  find  that "  though  they  were  clever  mathematicians,  yet  they  fixed  their standards  of  weights  by  natural  seeds  in  the  good  old  primi- tive fashion,  and  did  not  make  the  slightest  attempt  to  find a  mathematical  basis  for  their  metrological  work." In  short,  from  this  point  of  view  the  situation  for  the Babylonians,  and  indeed  for  any  other  nation  whose  claim for  a  similar  priority  should  be  advanced,  may  be  summarized as  follows :  The  Babylonians  in  common  with  other  nations from  body  measures  and  seeds  of  grain  or  other  plants  developed such  systems  of  measurements  as  sufficed  for  their  wants;  their standards  were  arbitrary  and  changing,  but  since  they  were the  leading  people  of  this  part  of  the  world  as  regards  culture, their  measures  were  impressed  on  their  neighbors,  and  especially on  the  Phoenicians,  by  whom  as  the  chief  traders  of  this  period of  antiquity  they  were  spread  abroad.  There  is  no  reason  to believe  that  the  weights  were  preserved  in  any  kind  of  purity, nor  is  there  any  reason  to  see  why  this  should  have  occurred, and   when   we  consider   the   variation   in   weights   and  measures aW.  M.    Flinders  Petrie,  article    "Weights   and    Measures,"   Encyclopaedia firitannica,  9th  ed.  vol.  xxiv.  p.  482. 2Ridgeway,  Origin  of  Metallic  Coinage  and  Weights,  Cambridge,  1892,  p.  178. THE   SCIENCE    OF   METROLOGY  19 during  more  recent  centuries  with  their  scientific  men  and methods,  their  mints  and  their  standards,  not  to  mention government  regulation,  as  exampled,  say,  in  Great  Britain,  it is  not  natural  to  believe  that  those  ancient  units  could  have been  fixed  to  any  basis  with  scientific  exactness.  Such  mere coincidences  as  that  a  cubic  foot  of  water  weighs  1000  ounces, and  that  a  British  imperial  gallon  of  water  at  temperature  of maximum  density  weighs  ten  pounds,  if  put  back  into  the  past would  form  a  far  better  basis  upon  which  to  form  decimal and  other  systems  than  many  of  the  facts  that  have  been employed  by  scientific  metrologists.1 As  an  argument  of  this  kind  depends  largely  upon  quoting authorities,  and  dealing  in  detail  with  apparent  and  actual inconsistencies,  it  is  manifestly  impossible  to  do  justice  to  it  in these  few  paragraphs ;  but  reference  to  Johns  and  Eidgeway in  the  volumes  quoted  will  amply  repay  the  student  interested in  this  phase  of  archaeology  and  metrology,  as  by  both  authors the^i-ase  is  stated  most  ably  and  critically. {  The  Jews,  unlike  their  neighbors  in  Babylonia  and  Assyria, \iere  not  a  people  of  scientific  tastes,  and  their  weights  and measures  were  derived  largely  from  the  nations  whose  territory they  adjoined,  consequently  it  is  not  natural  to  expect  much uniformity  of  weights  and  measures  among  them.  Indeed,  there are  indications  that  there  were  at  a  single  time  among  the Israelites  as  many  as  three  different  and  distinct  units  of  weight, Babylonian,  Syrian,  and  Phoenician,  and  in  each  case  there  was both  a  heavy  and  a  light  system  standing  towards  each  other  as two  to  one.  Undeniably  there  were  Egyptian  influences  on  the Hebrew  weights  and  measures,  but  far  more  is  due  to  Babylon, as  the  civilization  of  that  country  was  predominant  in  Canaan up  to  the  fifteenth  century  B.C.  according  to  records  in  the Tel-el-Amarna  correspondence,  and  this  predominance  carried with  it  undoubtedly  the  Babylonian  weights  and  measures.  By the  eighth  century  B.C.,  however,  the  Israelites  had  a  legal  system of  weights  and  measures,  put  long  before  this  they  were accustomed  to  their  use,  "as  when  Abraham  bought  the  field  of Ephron   he  "weighed   to   Ephron    the   silver"  (Gen.   xxiii.   16). 1  Flinders  Petrie,  article  "Weights  and  Measures,"  Encyclopaedia  Britannica, 9th  ed.  vol.  xxiv.  p.  482. 20       EVOLUTION   OF   WEIGHTS   AND   MEASURES In  fact,  the  Israelites  became  so  accustomed  to  the  use  of  the balance  and  of  measures  that  they  began  to  employ  false  weights and  wrong  measures,  with  the  result  that  not  once  but  many times1  their  prophets  and  teachers  are  forced  to  emphasize  honest dealing  in  matters  of  measurements  and  the  weighings  of  daily life.  The  chief  unit  of  length  of  the  Hebrews  was  the  cubit,  ^ and  with  it  were  employed  the  usual  body  measures,  such  as finger  breadths  or  digits,  palms,  spans,  and  fathoms  and  reeds. For  these  measures  we  have  practically  no  data  for  determining their  equivalents,  and  Professor  A.  E.  S.  Kennedy  expresses  the opinion  "  that  reliable  data  for  the  exact  evaluation  of  the Hebrew  cubit  do  not  exist."2  In  fact,  values  from  16  to  25*2 inches  have  been  proposed  for  this  unit,  and  by  many  it  is believed  that  there  were  two  cubits,  one  the  "  cubit  of  man " of  six  handbreadths,  and  also  "  a  cubit  and  an  handbreadth  "  or seven  handbreadths,  which  was  used  in  the  construction  of  the temple  (Ezekiel  xl.  5).  This  would  correspond  to  similar  cubits of  the  Egyptians,  and  there  is  reason  for  believing  that  the weights  and  measures  of  the  two  nations  were  intimately  con- nected, if  not  quite  similar  at  the  time  of  the  Exodus,  but  like many  other  points  in  metrology  it  is  not  possible  to  bring forward  absolute  proof.  For  the  measurement  of  area  the Hebrews  employed  generally  the  amount  of  seed  required  to sow  the  land,  or  the  amount  of  ground  that  could  be  ploughed by  a  yoke  of  oxen,  the  latter  unit  being  the  zemed,  which  in  the Old  Testament  is  translated  by  acre.3  This  is  thought  to  be  an area  equivalent  to  the  Egyptian  aroura,  which  was  a  square  100 cubits  on  each  side. The  capacity  measures  of  the  Hebrews  for  both  wet  and  dry commodities  were  arranged  upon  a  systematic  basis  which  has  in not  a  few  cases  been  obscured  by  imperfect  translation  in  the ,  English  Bible.TThe  relation  of  the  different  measures  is  expressly stated  in  Ezekiel  (xlv.  11  et  seq.),  where  we  learn  that  the  ephah and  bath  were  one  and  the  same  unit,  the  former  being  used  for 1  Leviticus  xix.  35  et  seq.     Deuteronomy  xx v.  13-16.     Ezekiel  xlv.  9-14.     Amos viii.  5.     Hosea  xii.  7.     Micah  vi.  10.     Proverbs  xi.  1,  xvi.  11,  xx.  10. 2  Kennedy,  article  "Weights  and  Measures,"  Hastings'  Dictionary  of  the  Bible (New  York,  1903),  vol.  v.  p.  907. 3  1  Samuel  xiv.  14  and  Isaiah  v.  10. vy THE   SCIENCE   OF   METROLOGY  21 dry  measure  and  the  latter  for  liquids.  This  unit  was  one-tenth of  the  homer,  a  dry  measure,  and  its  liquid  equivalent  was  the kor.  One-third  of  the  ephah  gave  the  seah,  which  was  divided  in half  and  formed  a  dry  measure  equivalent  to  the  liquid  hin. One-tenth  of  the  ephah  gave  a  dry  measure  known  as  the  oner, while  the  next  smaller  unit,  used  for  both  dry  and  liquid measure,  was  the  kab,  which  was  T-|^  of  the  homer  or  kor.  *  The fourth  of  the  kdb  gave  the  log,  the  smallest  liquid  measure.  I  By taking  the  ephah-bath  as  equal  to  36*92  liters,  or  65  (British) imperial  pints,  a  value  derived  from  a  study  of  Greek  and Hebrew  literature,  the  modern  equivalents  can  be  approximated, though  this  equivalent  is  variously  stated  from  3 6 '3 7  liters  to 40*5  liters. In  considering  the  Hebrew  units  of  weight  we  must  bear  in mind  what  has  been  stated  about  the  Babylonian  units  and  their fundamental  proportions,  where  the  talent  was  equal  to  60  minas, each  composed  of  60  shekels,  or  in  the  case  of  the  gold  mina  of 50  shekels.  There  was  the  heavy  and  the  light  systems,  stand- ing in  the  ratio  of  2:1,  and,  as  we  have  said  above,  systems based  on  Babylonian,  Syrian,  and  Phoenician  standards.  Here of  course  it  must  be  remembered  that  the  units  of  weight  were also  units  of  currency,  and  to  this  fact  is  dudn  no  small  degree much  of  the  variation  in  the  standards.  The  shekel  was  for  the Hebrews  the  principal  unit,  and  in  the  three  different  systems mentioned  from  literary  evidence  and  actual  weights  the  follow- ing values  have  been  assigned : Babylonian  unit,  -  -  -      252  grains. Syrian  unit,        -  -  -  -320,, Phoenician  unit,  -  -  224      „ The  Hebrews'  weights  without  doubt  were  not  preserved  in anything  like  purity,  and  besides  showing  the  effect  of  their Babylonian  origin,  in  later  times  there  are  evidences  of  Persian, Greek,  and  Boman  influences,  so  that  our  only  means  of  iden- tifying them  consists  largely  in  the  connections  established  by the  later  Hebrew  and  the  Greek  and  Latin  authors.  The weights  of  the  Bible  have  received  considerable  study,  and  the only  warrant  for  dismissing  the  subject  here  so  summarily  is that   each   separate    phase   demands   detailed    treatment   and    a i 22       EVOLUTION   OF   WEIGHTS   AND   MEASURES critical  examination  of  authorities.  Furthermore,  the  absence of  positive  conclusions  which  can  be  stated  definitely  relieves us  of  the  necessity  for  fuller  discussion  in  this  brief  historical skatch-1 In  the  study  of  Egyptian  measures  there  is  considerable  data  * for  the  metrologist,  which  is  in  the  form  of  literary  remains,  such as  papyri,  monuments  of  one  form  or  other  from  the  Great  Pyra- mid of  Ghizeh  to  wall  carvings,  and  actual  wooden  and  stone scales.  In  the  main  there  is  little  variation  from  the  measures of  Babylonia  and  many  points  of  similarity  both  in  the  weights and  measures  and  in  the  etymology  of  the  words  expressing  them are  seen,  which  indicate  a  common  origin  for  the  weights  and measures  of  both  nations,  and  aid  in  substantiating  any  theory based  on  the  assumption  that  there  was  a  definite  parent  systeml There  is  a  correspondence  between  the  royal  or  building  ciiDit  of seven  palms  and  28  digits  which  has  been  constructed  from  the measurements  of  temples  and  other .  buildings  in  Egypt  and the  so-called  sacred  or  building  cubit  of  the  Babylonians.  Actual representatives  of  the  former  have  been  found  in  the  nilometer cubit  of  Elephantis,  and  the  wooden  scale  of  Amenoemopht  from the  necropolis  at  Memphis,  and  other  scales  both  wooden  and stone.2  A  mean  value  obtained  from  actual  scales  and  measure- ment gives  for  the  modern  equivalent  of  the  cubit  525  mm. or   20-63  inches. With  this  royal  cubit  was  also  used  a  natural  or  common (short)  cubit  which  was  of  the  length  of  six  palms,  and  cor- responded to  the  Greek  cubit.  The  Egyptians  employed  the various  subdivisions  on  the  basis  of  the  body  measures,  but  they do  not  seem  to  have  used  either  the  foot  or  the  fathom.  All  of these  can  be  found  expressed  in  their  hieroglyphics,  and  are  found in  many  of  the  ancient  papyri.      For  long  measure  there  was  the 1  For  further  information  and  detailed  references  the  following  authorities  may be  consulted :  Kennedy,  article  "  Weights  and  Measures,"  in  Hastings'  Dic- tionary of  the  Bible  (New  York,  1902),  vol.  v.  p.  901  et  seq.  ;  G.  F.  Hill,  article "  Weights  and  Measures,"  in  Encyclopaedia  Biblica  (New  York,  1903),  vol.  iv. p.  5292  et  seq.  These  and  allied  articles  contain  full  and  detailed  bibliography. See  also  C.  R.  Conder,  "Hebrew  Weights  and  Measures,"  Palestine  Exploration Fund  Quarterly  Statement,  1902. 2  For  description  and  illustrations,  see  Lepsius,  Ueber  die  alt-aegyptische  Elle und  ihre  EintheUung  (Berlin,  1865). THE   SCIENCE   OF   METROLOGY  23 khet,  which  was  equal  to  100  cubits,  and  was  represented  by  a hieroglyphic  of  a  coil  of  cord,  as  undoubtedly  a  line  and  reel  were used  for  such  measurements,  just  as  Ezekiel  (xl.  3)  speaks  of  a "" flaxen  line"  and  "measuring  rod"  being  used  in  measuring  the  new temple,  and  Jeremiah  (xxxi.  32)  mentions  the  use  of  the  "  measur- ing line"  in  surveying  land.  For  very  long  distances  the  Egyptians had  a  measure,  the  ater,  equal  to  from  30  to  60  or  more  stades and  known  to  the  Greeks  as  a  schoenus,  but  it  is  expressly  stated by  Strabo  that  it  varied  in  different  parts  of  the  country.  It  is. of  some  importance,  however,  as  it  figures  in  geographical  descrip- tions of  Egypt,  and  has  been  actually  found  marked  on  the Memphis-Faium  road.1  The  Egyptians  had  a  series  of  square measures  with  a  chief  unit  in  the  set  equal  to  the  Greek  aroura and  comprising  a  square,  a  khet,  or  100  royal  cubits  on  each  side, the  latter  unit  forming  the  basis  of  land  measurement.  For capacity  the  principal  measure  was  the  hekt,  which  was  equal  to -g1^-  of  the  cubit  cubed,  while  for  corn  there  was  employed  the khar  ("sack")  of  20  hekt  until  superseded  by  the  sack  of  16  hekt or  the  Greek  medimnus,  at  or  before  the  XVIII.  dynasty.  After  U the  Macedonian  conquest  the  latter  measure  was  halved  to  form the  artdba,  doubtless  to  conform  with  a  measure  introduced  from Persia.  Then  there  was  the  henu  or  ^  of  the  hekt,  used  both for  solids  and  liquids,  as  well  as  numerous  other  measures. According  to  Griffiths,  whom  we  have  followed  in  this  description of  Egyptian  weights  and  measures,2  the  Egyptian  measures  were not  derived  from  a  cubit  or  fraction  of  a  cubit  cubed,  but  it  is probable  that  the  cubic  idea  was  introduced  a  considerable  time after  the  measures  had  been  quite  definitely  fixed  by  custom. In  striking  contrast  to  the  many  allusions  to  measures  that  are found  in  the  early  papyri  there  is  a  lack  of  information  as  regards weights.  That  weights  existed  and  were  used  is  known  from  a large  number  of  weights  that  have  been  discovered,  and  from  the blinders  Petrie  in  Encyclopaedia  Britannica,  9th  ed.  vol.  xxiv.,  article "Weights  and  Measures,"  p.  483.  Also  id.,  Season  in  Egypt,  pi.  xxvi.  (London, 1888). 2F.  L.  Griffiths,  "Notes  on  Egyptian  Weights  and  Measures,"  Proceedings Society  of  Biblical  Archaeology  (London),  vol.  xiv.  p.  403  et  seq.,  1892.  In  this paper  will  be  found  the  various  hieroglyphics  and  a  full  explanation  of  their  use. See  also  a  continuation  of  this  paper  by  the  same  author  in  same  Proceedings, vol.  xv.  p.  301,  1893. 24       EVOLUTION   OF   WEIGHTS   AND   MEASURES fact  that  balances  are  shown  in  the  decorations  of  the  tombs  of the  V.,  XI.,  XII.,  and  XVIII.  dynasties.  In  fact,  the  earliest known  weight  is  inscribed  with  the  cartouche  of  Chufu  (IV. dynasty),  the  builder  of  the  Great  Pyramid  at  Ghizeh,  whose date  was  approximately  4000  B.C. The  use  of  the  balance  in  the  earliest  times  was  probably  con- fined to  exchange  of  gold  and  silver,  and  it  doubtless  was invented  for  this  purpose.  But  one  reference  is  found  to  weights before  the  XVII.  dynasty,  and  only  gold,  silver,  copper,  and  lapis lazuli  were  weighed  even  at  that  time,  as  no  mention  of  weight  is made  in  the  so-called  medical  papyri,  where  it  would  be  natural to  find  such  an  allusion  were  weights  in  current  use.  Their application  increased  slowly,  and  by  the  time  of  the  Ptolemies, incense,  honey,  and  drugs,  as  well  as  metals  and  precious  stones, were  weighed.  About  the  time  of  the  XVII.  dynasty  the deben  or  uten,  a  weight  of  1400-1500  grains,  and  its  tenth  part, the  kiti  (also  called  Jcat)  are  found  to,  be  the  only  recognized units  of  weight  in  the  various  documents,  but  there  have  been found  a  wide  variety  of  actual  weights,  which  it  is  quite  impos- sible to  identify  either  with  any  system  or  among  themselves, and  which  serve  to  embarrass  the  investigator.1 Later  the  units  of  weight  in  widespread  use  were  the  talent, the  mina,  and  the  shekel,  as  in  other  ancient  nations,  but  con- siderable diversity  is  shown,  though  in  general  plan  much  the same  division  was  followed  as  for  the  weights  of  the  Babylonians and  Hebrews  already  described.  By  some  authorities  the  basis of  the  Egyptian  unit  of  weight  is  considered  to  be  a  cubic volume  (the  cubic  foot  or  cubit)  of  water,  but  at  all  events  there were  also  various  foreign  influences,  such  as  Greek  and  Asiatic units  of  weight,  which  produced  a  certain  amount  of  confusion, and  prevented  any  universal  and  single  system.  Under  Ptolemy Lagos  (d.  283  B.C.),  however,  certain  reforms  of  weights  and measures  were  effected  that  resulted  in  perpetuating  the  old Egyptian  system,  and  the  talent  weights  thus  defined  were known  subsequently  as  the    Alexandrian   talents.     These    were 1  Flinders  Petrie,  article  "Weights  and  Measures,"  Encyclopaedia  Britannica, 9th  ed.  vol.  xxiv.  p.  486.  Griffiths,  loc.  cit.  p.  435,  and  vol.  xv.  p.  307.  A.  E. Weigall,  "Some  Egyptian  Weights  in  Professor  Petrie's  Collection,"  Proceedings Society  Biblical  Archaeology  (London),  vol.  xxiii.  p.  378,  1901. THE   SCIENCE   OF   METROLOGY  25 of  two  classes,  each  of  which  were  divided  into  60  minas  of 50  shekels  or  100  didrachms  each,  but  the  greater  Alexandrian talent  of  copper  or  brass  weighed  just  twice  as  much  as  the smaller  or  lesser  Alexandrian  talent  of  silver.  The  former  was divided  into  125  pounds  by  the  Eomans  when  they  occupied Egypt,  while  the  mina  derived  from  the  lesser  talent  was divided  into  12  ounces  (unciae),  and  weighing  as  it  did  5460' grains,  it  became  the  predecessor  of  the  series  of  European pounds  of  which  the  Troy  pound  is  a  type.  From  one  of  these ounces,  if  we  may  believe  a  Syrian  authority,  Anania  de Schiraz,  who  wrote  in  the  sixth  century,  by  taking  the  T\± part  the  carats  or  diamond  weight  was  originally  formed.1 In  Greece  the  fundamental  unit  of  length  was  the  foot,  and while  we  find  the  cubit,  yet  it  is  the  foot  that  plays  the  principal part.  The  same  unit,  namely,  the  Olympian  foot,  was  found throughout  Greece,  though,  of  course,  there  was  necessarily considerable  divergence  from  any  one  value  at  different  times and  different  places.  A  clue  to  the  actual  length,  however,  is found  in  the  ruins  of  the  Parthenon,  where  the  main  hall  of the  Temple  of  Athena  is  called,  according  to  Plutarch,2  Heka- tompedos  (one  hundred  feet),  and  measurements  show  that  it was  100  Attic  feet  in  breadth  by  225  in  length,  these  numbers being  derived  from  the  ratio  of  the  breadth  to  the  length,  and giving  an  Attic  foot  equal  to  '30828  meter  or  12 '1375  inches. One  hundred  times  the  foot  gave  the  plethron,  which  was squared  and  used  as  a  measure  of  area.  The  Greek  cubit,  or 1-J-  times  the  foot,  closely  resembles  the  natural  cubit  rather than  the  sacred  or  building  cubit  of  the  Babylonians  and  Egyp- tians, and  four  of  them  made  the  orguia  or  fathom,  that  is  the distance  between  the  tips  of  the  fingers  when  the  arms  were extended.  This  multiplied  by  100  gave  the  stadion,  originally the  distance  that  a  strong  man  could  run  without  stopping  for breath,  and  then  fixed  as  the  length  of  the  Olympian  stadion  or athletic  track,  which  was  600  feet  in  length.3     This  stadion  was 1 H.  W.  Chisholm,  The  Art  of  Weighing  and  Measuring  (London,  1877),  p.  42. 2  Plutarch,  Pericles,  13. 3Hultsch,  Griechische  und  Rbmische  Metrologie,  2nd  ed.  (Berlin,  1882),  p.  33. This  will  be  found  a  standard  authority  in  classical  measures,  and  will  give text  references  to  all  authorities.  On  it  are  based  most  of  the  statements  in the  pages  devoted  to  Greek  and  Roman  metrology. 26       EVOLUTION   OF   WEIGHTS   AND   MEASURES about  one  eighth  of  the  Koman  mile,  and  this  ratio,  as  well  as  8-^, is  used  by  Strabo  and  Polybius. It  was  most  natural  that  the  measures  of  Greece  should  pass  to Home,  and  we  find  between  the  two  a  close  connection.  The principle  of  subdivision  was  duodecimal,  and  we  find  the  Greek foot  introduced  as  a  unit  of  length.  It,  as  well  as  the  as,  or  unit of  weight,  was  divided  into  twelve  unciae,  whence  our  English words  inch  and  ounce.  Among  the  other  measures  of  length employed  by  the  Eomans  was  the  palmipes,  or  foot  and  hand- breadth  ;  and  the  cubitus  (cubit),  or,  as  it  was  also  known,  the ulna,  from  which  is  derived  the  French  word  aulne  and  the English  ell.  The  passus  or  unit  of  itinerary  measure  was equivalent  to  5  Eoman  feet,  and  when  multiplied  by  1000  gave the  millia  passuum,  from  which  was  derived  the  mile  as  subse- quently used  in  Britain  and  elsewhere.  The  passus  was  a  double step  or  gradus,  and  was  the  distance  covered  from  the  time  when one  foot  was  taken  from  the  ground  until  it  was  placed  down again.  For  architects  and  surveyors  there  was  a  unit  ten  feet  in length  known  as  a  pertica  or  decempeda,  and  the  square  of  this distance  gave  the  unit  of  area  employed  in  surveying,  twelve times  which  gave  the  actus  or  distance  that  a  plow  would encompass  in  a  single  course,  while  the  actus  multiplied  by  two would  give  the  jugerum  or  Eoman  acre  (*6229  English  acre). Perhaps  the  foot  is  the  most  important  of  the  Eoman  measures, as  it  not  only  extended  throughout  Europe  as  a  fundamental unit,  but  in  some  form  it  has  survived  almost  everywhere  until supplanted  by  the  meter.  True,  there  were  marked  variations, and  the  standards  employed  were  most  arbitrary,  but  the  supre- macy of  the  foot  as  the  unit  of  length  was  maintained  in  Europe until  the  nineteenth  century.  The  connection  of  the  Eoman foot  to  that  of  Greece  has  already  been  shown,  but  attention should  be  called  to  the  fact  that  it  gradually  become  shorter, and  in  the  time  of  Pliny  it  bore  the  relation  to  the  Greek  foot of  25 :  24.  There  was  also  a  foot  of  Drusus  which  was  used outside  of  Italy  for  measuring  land,  and  became  permanent  in the  countries  along  the  Ehine  and  Lower  Germany.  This  foot contained  13-|-  Eoman  inches  or  13*1058  English  inches,  332*6  mm., and  doubtless  came  to  Europe  in  some  way  from  Asia  Minor. It    is    worthy    of    note    that,    besides    persisting   in    the   Ehine THE   SCIENCE   OF   METROLOGY  27 countries,  it  was  adopted  by  the  Belgic  tribes,  and  by  them introduced  into  Britain,  where  it  endured,  as  will  subsequently be  shown,  until  the  fifteenth  century.1 Greece  originally  had  as  its  standard  of  weight  the  heavier Babylonian  talent,  or,  speaking  more  exactly,  this  was  in  use in  Aegina,  and  thence  extended  into  the  Spartan  States  and  to Corinth,  whose  inhabitants  being  actively  engaged  in  commerce did  much  to  spread  its  use.  This  talent  was  considered  equal to  the  weight  of  a  cube  of  water  whose  edge  was  an  Olympic cubit,  or  1^-  times  a  Greek  or  Olympic  foot.  By  diminishing the  Babylonian  talent  one-sixth,  was  obtained  the  Euboic  talent which  nourished  in  Greece  and  especially  in  Athens  before  the time  of  Solon.  This  latter  ruler  in  order  to  release  the  people from  the  usurers  established  by  decree  (c.  592  B.C.)  a  smaller talent  which  amounted  to  §  of  the  Babylonian  talent,  and weights  were  derived  from  it  which  alone  were  lawful  in  Athens. The  close  connection  between  money  and  weight  then  existing must  be  appreciated,  and  we  find  in  ancient  writings  that  the material  of  the  talent  when  used  as  currency  is  mentioned,  as  a talent  of  silver  (the  standard)  or  a  talent  of  gold.  The  Athenian talent  was  divided  into  60  minas,  each  composed  of  100  drachmas containing  each  6  obols  or  48  ehalkus.  There  was  a  half  mina and  a  double  drachma  or  didrachm,  and  also  a  gramma  equal to  one  third  of  a  drachma  or  2  obols,  one  third  of  which  was  a lupine  whose  half  in  turn  was  a  siliqua.  The  unit  of  liquid measure  in  the  Athenian  system  was  the  metretes  (3 9 '39  liters), which  was  subdivided  into  12  chus  or  amphora,  and  so  on  on  a duodecimal  basis.  The  metretes  was  -^  of  a  Babylonian  cubic foot.  J  The  Attic  unit  of  dry  measure  was  the  medimnos,  which corresponded  to  1  -J-  metretes  or  in  modern  equivalents  to  52*53  -j liters.  It  was  divided  into  six  hekteus  or  modius,  each  of  which  v' was  composed  of  two  hemiekton  or  eight  choinix.  The  choinix was  made  up  of  two  xestes,  and  two  kotule  formed  a  xestes. The  Roman  unit  of  weight  was  the  libra,  or  pound  which corresponded  in  money  to  the  as,  and  was  divided  on  the duodecimal  basis  characteristic  of  the  Romans.  Thus  the  pound (327*45  grams)  was  composed  of  12  unciae,  each  of  4  sicilii,  each ■of  2   drachmas,  each  of  33wri_pula,  each  of  2  obola,  and  each  of JSee  p.  31. r~ 28       EVOLUTION   OF   WEIGHTS   AND   MEASURES 3  siliquae,  these  names  surviving  in  modern  apothecaries' measure.  Its  connection  by  water  with  the  amphora  and  thus with  the  Greek  measures  will  be  given  below,  and  may  be further  explained  by  stating  that  while  the  Attic  talent  of Solon  was  divided  into  60  minas,  the  same  weight  of  water contained  in  the  amphora  was  divided  into  80  pounds,  thus- making  3  Attic  minas  equal  to  4  Eoman  pounds.  Originally the  Eoman  pound  was  established  on  the  basis  of  the  Aeginetan weight,  and  was  equal  to  T^  of  the  Aeginetan  half  mina, this  basis  being  used  in  the  Eoman  coinage. As  a  measure  of  liquid  capacity  the  Eomans  had  the  amphora, which  was  equal  to  a  cubic  footfand  contained  80  librae  (pounds) of  water.  This  was  divided  into  8  congii,  each  composed  of 6  sextarii  with  further  subdivisions.  For  dry  measure  one  third of  the  amphora  or  modius  served  as  the  unit,  and  was  made  up of  16  sextarii.  These  measures  harmonized  with  those  of  Greece, inasmuch  as  the  amphora  was  two  thirds  of  the  JUtic  metre tes, and  the  modius  was  one  sixth  of  the  medimnos.|  In  passing, mention  might  be  made  of  the  fact  that  a  foot  derived  theo- retically from  the  amphora  would  not  give  a  cube  equal  to the  amphora,  but  differing  by  as  much  as  a  twentieth  part and  in  some  cases  by  as  much  as  one  twelfth,  depending,  of course,  upon  the  cubical  contents  of  surviving  examples,  of  which there  are  several.1 The  Eoman  weights,  measures,  and  coinage,  by  virtue  of  the conquests  and  influence  of  the  empire,  found  their  way  all  over Western  Asia  and  Europe ;  and  with  the  decline  of  the  imperial power  formed  the  foundation  for  local  systems,  but  with  the  lack of  interest  in  science  which  soon  began  to  characterize  the  age and  the  general  decline  of  culture,  weights  and  measures  were  no longer  maintained  in  conformity  with  any  system  or  with  any due  regard  to  primary  standards.  Consequently  there  was  a distinct  corruption  of  measures,  and  until  the  revival  of  experi- mental science  in  the  middleages  but  little  attention  was- paid  to  the  subject.  Indeed, /all  standards  and  systems  were practically  neglected,  and  by  the  sixteenth  century  there  was virtually  a  return  to  the  body  measures  throughout  Europe. 1  Flinders  Petrie,  article  ' '  Weights  and  Measures,"  Encyclopaedia  Britannica, 9th  ed.  vol.  xxiv.  p.  486. THE   SCIENCE   OF   METROLOGY  29 __^-  Breyious  to  the  beginnings  of  European  scientific  investiga- tion^there  was,  however,  important  work  done  by  the  Arabs,  and as  measurement  is  an  essential  of  all  experimental  science,  it  was natural  that  they  should  have  devoted  much  attention  to  the subject,  and  included  the  discussion  of  measures  in  their  writings. It  is  quite  certain  that  the  measures  of  the  Arabs  owe  their origin  to  the  old  Babylonian  measures,  especially  as  their philosophers  were  careful  students  of  antiquity ;  but  it  is  evident that  while  the  measures  were  maintained  they  lost  sight  of  the underlying  principles,  and  when  it  became  necessary  to  define them  or  refer  them  to  standards,  entirely  new  methods  were employed.  In  these  an  attempt  was  made  to  secure  a  natural basis,  and  such  fundamental  units  as  a  degree  of  the  earth,  hairs of  horses  or  mules,  and  grains  of  barley  were  used.  Then,  too, the  contact  between  the  Arabs  and  the  Egyptians  had  its  effect, and  old  and  new  measures  were  blended  so  that  the  absolute value  of  the  weights  and  measures  is  quite  impossible  to determine,  though  by  references  to  ancient  authorities  relative values  can  be  obtained  in  many  cases.2  It  was  from  the  Arabs that  the  Yusdruman  pound  of  Charlemagne,  for  so  many  years the  standard  of  France,  was  obtained,  and  the  idea  of  using barleycorns  for  the  measure  of  length,  as  was  done  subsequently in  England  by  statute. In  this  connection  mention  might  be  made  of  a  unit  of  length, namely,  the  "  black  cubit,"  which  figured  in  an  important measurement  of  a  degree  of  the  earth's  surface  executed  in  830 A.D.  by  the  astronomers  of  the  Caliph  Al-Mamun  (713-833). This  measurement,  made  on  the  plains  of  Mesopotamia,  is generally  spoken  of  in  connection  with  similar  measurements made  by  Eratosthenes  (c.  276 — c.  196  B.C.),  the  Alexandrian,  as they  were  the  forerunners  of  later  geodetic  work,  on  which  in part  the  modern  metric  system  was  founded,  it  being  of  course unnecessary  to  say  that  this  and  other  ancient  astronomers believed  in  the  spheroidal  form  of  the  earth.     The  "  black  cubit," 1  About  the  earliest  systematic  works  in  Metrology  in  England  are  A  Discourse on  the  Roman  Foot  and  Denarius  and  Origin  and  Antiquity  of  our  English  Weights and  Measures  (London,  1745),  by  John  Greaves  (1602-1652),  and  De  Mensuris et  Ponderibus  Antiquis  (Oxford,  1699),  by  Edward  Bernard  (1636-1696[7J). 2  See  Boeckh,  Metrologische  Untersuchungen  (Berlin,  1838),  pp.  246  et  seq. 30       EVOLUTION   OF   WEIGHTS   AND   MEASURES however  scientific  the  use  to  which  it  was  put,  was  not  due  to any  particular  metrological  study,  but,  according  to  tradition,  was the  length  of  the  arm  of  a  favorite  black  slave  of  the  Caliph,  and has  been  said  by  Jomard  to  have  been  equal  to  519*16  mm.1 The  source  from  which  the  Anglo-Saxons  derived  their  weights and  measures  is  not  particularly  certain,  yet  they  early  en- deavoured to  secure  uniformity  by  enacting  good  laws,2  and  in this  they  were  so  successful  that  they  were  enabled  to  maintain these  weights  and  measures  in  their  integrity  despite  the  Norman conquest.3  In  fact,  they  were  specially  recognized  and  preserved by  a  decree  of  William  the  Conqueror,  which  stated  that  "  the measures  and  weights  shall  be  true  and  stamped  in  all  parts  of the  country,  as  had  before  been  ordained  by  law."  The  stan- dards of  the  Saxon  kings  which  had  been  preserved  at  Winchester were,  however,  removed  to  London,  where  they  were  deposited  in the  crypt  chapel  of  Edward  the  Confessor  in  Westminster  Abbey, which  later  became  known  as  the  Pyx  Chapel,  as  here  were  also preserved  the  standard  trial  plates  for  gold  and  silver  coin  used at  the  trials  of  the  pyx,  or  formal  official  assay  of  the  coin  of  the realm.4  With  Winchester  are  associated  the  earliest  Anglo- Saxon  weights  and  measures,  and  their  authority  as  standards is  said  to  date  back  to  King  Edgar  (reigned  958-975),  who  decreed that  "  the  measures  of  Winchester  shall  be  the  standard."  The unit  of  length  was  the  yard  or  gird,  which  was  identical  with  the 1  See  Boeckh,  Metrologische  Untersuchungen  (Berlin,  1838),  pp.  246,  250-3. 2  Greaves,  Origin  and  Antiquity  of  our  English  Weights  and  Measures  (London, 1745),  p.  68. 3 Bishop  Fleetwood's  Chronicon  Preciosum  (London,  1745),  p.  27:  "It  was  a good  law  of  King  Edgar  that  there  should  be  the  same  money,  the  same  weight, and  the  same  measures,  throughout  the  kingdom,  but  it  was  never  well  observed. What  can  be  more  vexatious  and  unprofitable  both  to  men  of  reading  and  practice, than  to  find  that  when  they  go  out  of  one  country  into  another,  they  must  learn a  new  language  or  cannot  buy  or  sell  anything.  An  acre  is  not  an  acre  ;  nor  a bushel  a  bushel  if  you  but  travel  ten  miles.  A  pound  is  not  a  pound  if  you  go from  a  goldsmith  to  a  grocer,  nor  a  gallon  a  gallon  if  you  go  from  the  alehouse  to the  tavern.  What  purpose  does  this  variety  serve,  or  what  necessity  is  there, which  the  difference  of  price  would  not  better  answer  and  supply  ?  " 4  See  H.  J.  Chaney,  Our  Weights  and  Measures  (London,  1897),  pp.  120-121. An  interesting  account  of  the  Pyx  Chamber  together  with  a  description  of  the Jewel  Tower,  now  the  Office  of  the  Standards,  will  be  found  in  "The  Story  of  a Tower,"  The  Art  Journal  (London,  1900),  pp.  200-203  and  244-247. THE   SCIENCE   OF   METROLOGY  31 ell,  and  as  late  as  the  reign  of  Eichard  II.  (1377-1399)  the  words virga  or  verge  (yard)  and  ulna  or  aulne  (ell)  are  found  in  the  laws and  official  documents  in  Latin  or  Norman  French,  as  the  case may  be,  to  denote  the  same  unit  of  length.  In  addition  to  the purely  Saxon  measures  there  were  those  which  had  been  brought by  the  Eoman,  and  which,  though  incommensurable  with  Saxon measures,  had  survived  and  become  assimilated  with  the  older measures.  Among  these  were  the  mile,  corresponding  to  the Eoman  millia  passuum,  the  inch  and  the  foot,  which  soon  became recognized  as  purely  English  measures  and  to  have  their  own fixed  values.  Then,  in  addition,  when  the  Belgic  tribes  migrated to  Britain,  they  brought  the  Belgic  foot  of  the  Tungri,  which was  -J-  longer  than  the  Eoman  foot,  and  was  used  until  the fifteenth  century.1  The  average  length  of  this  foot  was  13 '22 inches,  and  a  yard  formed  by  three  such  feet  would  be  39*66 inches,  which  would  correspond  most  closely  with  the  meter  of to-day,  which  is  equivalent  to  3 9 '3 7  inches.  Such  a  yard  existed and  was  known  as  the  yard  and  the  full  hand,  and  eventually was  suppressed  by  law  in  1439.  This  was  extremely  unfortunate, as  had  this  yard  been  retained  it  would  have  ensured  a  corre- spondence with  the  French  metric  system  without  the  slightest difficulty.  Furthermore,  we  are  informed  that  the  old  English system  was  largely  decimal,  and  had  these  features  been  pre- served a  vast  improvement  would  have  been  worked  in  the wretched  system,  or  lack  of  system,  with  which  the  English- speaking  people  have  been  afflicted  for  centuries. In  the  Domesday  Book  (1086)  we  find  the  Saxon  yard  used  a& a  unit  of  measure,  and  land  thus  measured  is  referred  to  as  terra virgata,  and  shortly  afterwards,  from  the  reign  of  Henry  I. (reigned  1100-1135),  the  tradition  is  current  that  the  legal  yard was  established  from  the  length  of  that  monarch's  arm.  \  In  the reign  of  Eichard  I.  (reigned  1189-1199)  there  were  laws  '  enacted providing  for  standards  of  length  constructed  of  iron  and  for measures  of  capacity  whose  brims  should  be  of  this  material  also, suitable  standard  measures  to  be  kept  by  sheriffs  and  magistrates.2 1  Flinders  Petrie,  article  "Weights  and  Measures,"  Encyclopaedia  Briianuica, 9th  ed.  vol.  xxiv.  p.  484. 2  See  Kelly,  Metrology  (London,  1816),  p.  336.     A  brief  and  interesting  account of  early  history  of  British  Weights  and  Measures,  with  summary  of  legislation. V v 32       EVOLUTION   OF  WEIGHTS   AND   MEASURES CThe  most  important  early  English  legislation  was  contained  in Magna  Charta  (1215),  and  laid  stress  on  the  principle  of  uni- formity by  providing  that  there  should  be  throughout  the  realm, one  measure  of  wine,  one  of  ale,  and  one  of  corn,  viz.,  the  quarter ■of  London :  and  that  it  should  be  of  weights  as  of  measures] This  declaration  of  uniformity  was  considered  so  fundamental  that it  was  subsequently  repeated  in  numerous  statutes  in  essentially its  original  form,  and  we  find  many  acts  passed  as  occasion demanded  to  carry  out  its  manifest  intention.  This  naturally involved  the  definition  of  the  standards  and  measures,  and  from time  to  time  statutes  are  found  which  supply  us  with  more  or less  complete  information  about  the  measures  of  the  period. Thus,  while  we  know  that  the  unit  of  monetary  weight  was  a  pound used  from  the  times  of  the  Saxon  kings,  yet  we  do  not  find  it •defined  until  the  time  of  Henry  III.  (51  Henry  III.,  stat.  I.  1266), when!  the  relation  of  the  various  weights  and  measures  are  given by  the  following  law,  forming  a  part  of  the  well  known  statute  of the  Assize  of  Bread  and  Ale,  where  it' is  stated,  "that  by  the ■consent  of  the  whole  realm  of  England,  the  measure  of  our  Lord the  king  was  made,  viz.,  an  English  penny  called  a  sterling,  round and  without  any  clipping,  shall  weigh  thirty-two  wheatcorns  in the  midst  of  the  ear ; l  and  twenty  pence  do  make  an  ounce,  and twelve  ounces  a  pound:  and  eight  pounds  do  make  a  gallon  of wine,  and  eight  gallons  of  wine  do  make  a  bushel,  which  is  tnV eighth  part  of  a  quarter."  Thus  we  have  defined  the  ancient Tower  Pound,  which,  having  the  same  weight  as  the  old  German medicinal  or  apothecaries  pound,  is  believed  to  have  been  derived from  the  mina  of  Ptolemy  or  one-sixtieth  part  of  the  Lesser Alexandrian  Talent  of  silver,  as  it  was  but  63  grains  lighter  than that  weight.  This  was  the  earliest  form  of  the  British  sterling pound,  and  the  division  into  20  shillings  of  12  pence  each  was the  same  as  is  now  practised,  and  in  fact  was  the  same  as  the •division  of  the  livre  esterlin  of  Charlemagne,  which  was  slightly heavier  (5666  Troy  grains  as  compared  with  5400,  see  p.  38). In  addition,  the  English  monetary  weights  were  connected  with those  of  Germany,  based  on  the  Cologne  mark,  by  a  mint  weight 1,4  This  pennyweight  was  equal  to  22^  Troy  grains,  which  is  found  to  be  the average  weight  of  existing  coined  silver  pennies  of  the  Saxon  Norman  Kings  " (Chisholm,  Weighing  and  Measuring,  London,  1877). THE   SCIENCE   OF   METROLOGY  33 substantially  equivalent  to  the  latter  and  equal  to  two-thirds  of the  Tower  pound.  This  was  known  as  a  mark,  and  was  used  for denoting  both  the  weight  and  value  of  silver  under  the  Norman kings.1  While  the  Tower  pound  was  defined  in  terms  of  grains of  wheat,  nevertheless  it  did  not  originally  depend  upon  them, and  their  inclusion  in  the  English  system  of  weights  was  doubt- less due  to  French  influences  subsequent  to  the  Norman  Conquest, as  the  French  had  doubtless  derived  this  idea  from  Oriental sources.  With  the  Tower  pound  used  for  mint  purposes,  and  for the  derivation  of  measures  of  capacity,  as  well  as  for  precious metals  in  general  and  drugs,  there  must  be  considered  the  com- mercial pound  {libra  mercatoria),  which  is  of  almost  as  great antiquity  and  of  far  more  general  use.  It  also  is  defined  in  a statute  of  Henry  III.  (54  Henry  III.)  and  was  the  weight  of  25 shillings,  or  in  other  words  equivalent  to  15  ounces  of  the  Tower pound.  Commercial  pounds  were  used  also  on  the  continent of  Europe  along  with  the  Troy  pound,  and  it  is  to  one  of these,  namely  the  French  commercial  pound  of  16  ounces,  that we  have  to  look  for  the  source  of  the  English  avoirdupois pound  which  soon  supplanted  the  commercial  pound  in  that country. The  early  English  Tower  and  commercial  pounds  were  forced to  give  way  before  the  French  weights,  the  Troy  pound  and  the avoirdupois  pound,  whose  use  the  more  intimate  contact  following the  English  victories  in  France  at  Poitiers  and  on  other  fields  had doubtless  spread  through  the  English  realm.  As  to  the  source  of the  Troy  pound  there  is  a  difference  of  authorities,  but  it  is  usual to  credit  it  to  the  city  of  Troyes  in  France,  and  in  support  of  this view  it  is  stated  that  associated  with  this  city,  a  town  of  some commercial  importance,  were  a  livre  cle  Troyes  and  a  marc  cle  Troyes, whose  weights  were  comparable  with  the  modern  Troy  pound. Going  back  still  further,  it  is  possible  to  derive  the  Troy  pound from  the  Roman  weight  of  57592  grains,  which  was  the  3-^5  of the  large  Alexandrian  talent.  This  weight,  after  the  fashion  of the  Romans,  was  divided  into  12  ounces,  and  the  original  unit and  its  division  may  possibly  have  survived.  At  all  events  the Troy  pound  slowly  made  its  way  in  England,  and  from  as  early as  the  first  year  of  the  reign  of  Henry  IV.,  when  it  was  employed 1H.  W.  Chisholm,  The  Art  of  Weighing  and  Measuring  (London,  1877),  p.  55. C 34       EVOLUTION   OF   WEIGHTS   AND   MEASURES in  an  inventory  of  the  Royal  plate,  it  was  increasingly  used.  In 1495,  in  defining  the  bushel  and  the  gallon,  Henry  VII.  made  use of  the  Troy  pound,  and  in  1527  the  Tower  pound  was  formally abolished  as  the  legal  standard  at  the  Mint  by  an  Ordinance (18  Henry  VIII.)  enacting  that  "  the  Pounde  Towre  shall  be  no more  used  and  occupied,  but  al  maner  of  golde  and  sylver  shall be  wayed  by  the  Pounde  Troye,  which  maketh  xii  oz.  Troye, which  excedith  the  Pounde  Towre  in  weight  iii  quarters  of  the oz."  Likewise,  as  we  have  indicated,  the  avoirdupois  pound  was adopted  as  a  commercial  pound,  and  formed  of  16  avoirdupois ounces,  and  composed  of  7000  Troy  grains,  it  is  mentioned  in a  statute  (Tractatus  Ponderibus  et  Mensuris)  of  Edward  I. (31  Edward  I.  1303).  From  these  origins  the  English  Troy  and avoirdupois  pound  have  descended  in  substantial  integrity  to  the present  time,  and  such  changes  as  have  been  made  have  been  due to  the  restoration  of  standards,  and  have  been  of  a  minute  and unavoidable  character. Many  standards  of  weight  were  constructed  based  on  these fundamental  definitions,  and  a  number  of  them  are  still  in  exist- ence, having  been  used  on  numerous  occasions  for  deriving  other standards.  In  fact,  one  bell-shaped  avoirdupois  pound  of  the Exchequer  of  the  reign  of  Queen  Elizabeth  was  continuously  used for  this  purpose  from  1588  to  1825.  This  weight,  which  at  the time  of  its  construction  in  1588  was  supposed  to  be  equal  to  7002 Troy  grains,  was  found  in  1873  to  weigh  6999  grains  of  the imperial  standard  pound.1 In  1758  a  standard  Troy  pound  was  constructed  and  standard- ized by  Harris  under  authorization  of  an  Act  of  Parliament,  but it  was  not  legalized  until  1824  (5  Geo.  IV.  c.  74).  It  was  then specified  (§  5)  that  in  the  event  of  the  loss  or  destruction  of  this standard,  that  it  should  be  reconstructed  by  considering  that  a cubic  inch  of  distilled  water  at  62  degrees  Fahrenheit,  weighed  in air  with  brass  weights,  and  at  30  inches  pressure  of  the  mercurial barometer,  should  weigh  252*458  grains,  of  which  the  Troy  pound contained  57 60.2       This  standard  was    destroyed    together  with 1 H.  W.  Chisholm,  The  Art  of  Weighing  and  Measuring  (London,  1877),  pp.  62 and  63. 2  This  definition  bound  the  unit  of  weight  to  the  unit  of  length,  which  was  then considered  fixed  by  its  reference  to  the  second's  pendulum. THE   SCIENCE   OF   METROLOGY  35 the  standard  yard  by  the  fire  of  October  16,  1834,  when  the Houses  of  Parliament  were  burnt.  To  construct  new  standards  a Standards  Commission  was  appointed  in  1843,  and  for  the  unit  of weight  the  avoirdupois  pound  was  taken  as  the  basis.  The  new standard  was  defined  in  terms  of  the  lost  Troy  pound  as  given  by various  existing  standards,  and  was  duly  legalized  in  1855  (18  and 19  Vict.  c.  72).  This  standard  pound  will  be  more  specifically described  when  we  come  to  discuss  the  subject  of  Standards  in  a subsequent  chapter.1 From  the  definition  of  the  measures  of  capacity,  given  in  the Statute  of  the  Assize  of  Bread  and  Ale  referred  to  above,  the gallon  and  the  bushel  were  obtained  from  the  pound,  using  wine as  the  measuring  medium.  This  class  of  measures  was  one  that greatly  concerned  the  government  on  account  of  the  collection  of the  excise  duties,  and  there  are  numerous  statutes  defining  or regulating  in  one  way  or  another  the  capacity  and  use  of  these measures.  On  the  basis  of  the  early  legal  definition,  however, Henry  VII.  caused  to  be  constructed  a  standard  corn  gallon  and a  standard  corn  bushel,  the  former  having  __a  capacity  of  27  4  -\ cubic  inches  and  the  latter  2 150  J  cubic  inches.  1  These-  standards date  from  1495,  and  are  now  in  actual  existence.  The  Win- chester corn  gallon,  as  the  measure  is  known,  was  employed until  it  was  supplanted  in  1824  by  the  imperial  gallon,  while  its companion,  the  Winchester  bushel,  which  was  similarly  outlawed in  1824  in  favour  of  the  imperial^  bushel  in  Great  Britain,  has survived  in  the  United  States.  |  In  1601  we  find  the  British  ale gallon  with  a  capacity  of  282  cubic  inches  duly  recognized  by Queen  Elizabeth/Jand  there  is  extant  an  Exchequer  standard quart  which  bears  this  date  and  the  royal  initials  and  crown. In  the  reign  of  Queen  Anne  the  standard  wine  gallon  was defined  by  statute  (5  Ann.  cap.  27,  17)  as  "  any  cylinder  7  inches in  diameter,  and  6  inches  deep,  or  any  vessel  containing  231 cubical  inches  and  no  more  shall  be  a  lawful  wine  gallon." Such  a  standard  of  the  Exchequer  dated  1707  is  still  extant.  On the  reorganization  of  the  weights  and  measures  in  1824  the  wine gallon  was  abolished,  but  it  was  never  supplanted  in  the  United 1  Chas.  Ed.  Guillaume,  Unite's  et  Etalons  (Paris,  1893),  p.  96.  H.  W .  Chisholm, The  Art  of  Weighing  and  Measuring  (London,  1877),  pp.  69-81.  W.  H.  Miller, Philosophical  Transactions  (London,  1856),  part  iii. 36       EVOLUTION   OF   WEIGHTS   AND   MEASURES States,  and  remains  as  the  legal  gallon.  The  British  imperial gallon,  legalized  in  1824  (5  Geo.  IV.  c.  74)  to  the  exclusion  of  the three  former  gallon  measures,  and  which  forms  the  basis  of  the present  British  measures  of  capacity,  instead  of  being  based  on  a given  number  of  cubic  inches,  was  taken  as  the  volume  of  ten pounds  of  pure  distilled  water  at  62  degrees  Fahrenheit.  This corresponds  to  277*274  cubic  inches.  [JWith  the  gallon  as  the unit  of  capacity  for  liquid  measures,  it  was  determined  to  derive the  imperial  standard  bushel  or  unit  of  capacity  by  taking  a volume  equal  to  eight  imperial  gallons,  or  a  volume  corresponding to  2218*192  cubic  inches.  ) Unlike  the  measures  of  weight  and  capacity,  there  have  been few  changes  in  those  of  length  from  the  times  of  the  Saxons,  and the  earliest  surviving  standards  of  length,  those  of  Henry  VII. (about  1490),  and  Elizabeth  (about  1588),  vary  scarcely  more than  a  hundredth  of  an  inch  from  the  present  imperial  yard.1 With  the  second  of  these  standards  there  is  also  an  ell  rod  of 45  inches,  and  a  bar  with  a  bed  or  matrix  for  both  the  yard  and the  ell  rods,  but  such  an  ell,  which  doubtless  corresponded  to  the French  measure  of  cloth,  does  not  appear  in  any  statute  or  in the  records  of  the  standards  of  this  time.  In  fact,  we  find  the Anglo-Saxon  measures  of  length  perpetuated  on  the  same  basis as  is  given  in  the  statute  of  Edward  II.  (17  Edward  II.  1324), where  there  is  a  restatement  in  statutory  form  of  what  has  since become  the  well-known  rule  that  three  barley-corns,  round  and dry,  make  an  inch,  twelve  inches  a  foot,  three  feet  a  yard  (ulna), five  and  a  half  yards  a  perch,  and  forty  perches  in  length  and four  in  breadth  an  acre.2 Consequently  the  general  discussion  that  has  been  devoted  to 1  See  chapter  x.  on  Standards,  pp.  243-244. 2  See  H.  W.  Chisholm,  Seventh  Annual  Report  of  the  Warden  of  the  Standards, 1872-3  (London),  pp.  25  and  34,  English  Parliamentary  Papers,  Reports  from Commissioners,  1873,  vol.  xxxviii.  Id.,  Weighing  and  Measuring  (London, 1877),  pp.  51-53.  George  Graham,  "  Description  of  Standards  and  Use  of  Beam Compasses,"  Philosophical  Transactions  (London,  1742-3),  vol.  xlii.  pp.  541-556. Francis  Baily,  Memoirs  Royal  Astronomical  Society  (London),  vol.  ix.  1836, pp.  35-184.  William  Harkness,  "The  Progress  of  Science  as  Exemplified  in  the Art  of  Weighing  and  Measuring,"  vol.  x.  Bulletin  Philosophical  Society  of Washington,  D.C.,  published  as  vol.  xxx.  Smithsonian  Miscellaneous  Collec- tions. The  latter  contains  a  good  resume  of  British  weights  and  measures  as well  as  a  useful  bibliography. THE   SCIENCE   OF   METROLOGY  37 the  British  measures  of  length  has  been  mainly  towards  securing standards  of  greater  accuracy,  or  with  the  object  of  obtaining either  a  decimal  division  or  the  adoption  of  the  metric  system. With  the  exception  of  the  act  of  1824,  which  defined  the  yard  in terms  of  the  second's  pendulum,  and  provided  in  case  of  its  loss or  destruction  that  it  should  be  replaced  on  that  basis,  little has  been  done  in  the  way  of  legislative  enactment  save  to recognize  and  establish  legally  new  standards  of  length.  The determination  and  construction  of  such  standards,  however,  has been  of  extreme  importance,  and  has  involved  most  careful  and accurate  scientific  work,  so  that  for  this  reason  the  various  British standards  and  their  development  can  best  be  treated  in  that portion  of  the  present  volume  devoted  to  this  subject.1 While  there  have  been  for  well  over  a  century  many  and earnest  advocates  of  a  decimal  division  of  British  weights and  currency,  yet  the  net  results  of  their  labors  and  agitation have  been  practically  nothing  other  than  to  strengthen  the cause  of  the  metric  partisans.  In  fact,  decimalization  never has  progressed  to  the  same  point  as  in  the  United  States,  and it  is  probable  that  the  old  weights,  measures,  and  methods will  remain  until  supplanted  by  the  metric  system.2 Although  the  preservation  of  the  French  standards  of  measure in  the  royal  palace  is  recorded  from  the  time  of  Dagobert  (650),3 yet  it  is  usual  to  trace  back  such  measures  as  might  properly be  considered  as  forming  the  national  system  to  the  time  of Charlemagne  (768-814),  since  during  his  reign  there  was  a uniformity  of  weights  and  measures,  and  reproductions  of  the royal  standards  were  widely  distributed  over  the  realm.4  The unit  of  length  in  this  system  was  the  pied  de  Roi,  or  royal foot,    representing,    according    to    tradition,    the    length    of    the foot    of     the     monarch,    and    which,  following    the    duodecimal • xSee  chapter  x. — Standards  and  Comparison. 2  For  progress  of  Metric  System  in  Great  Britain,  see  chapter  iii.  pp.  98  et  seq. It  is  of  course  impossible  in  the  present  space  to  describe  the  various  measures of  Scotland,  Ireland,  and  other  local  systems.  These  will  be  found  quite  fully described  in  Kelly,  Metrology  (London,  1816),  and  also  in  Chaney,  Our  Weights and  Measures  (London,  1897),  the  latter  containing  also  a  description  of  the various  standards. 3  Paucton,  Metrologie  ou  TraiU  des  Mesures,  Poids  et  Monnoies  (Paris,  1780),  p.  8. 4  Ibid.  p.  13. 38       EVOLUTION   OF   WEIGHTS   AND   MEASURES division  derived  from  the  Komans,  was  divided  into  12  inches (police)  of  12  lines,  which  in  turn  were  composed  of  12  points. The  French  foot  was  longer  than  the  English  foot,  being  equal to  12*79  inches  of  the  latter,  and  considerably  longer  than  the ancient  Eoman  foot,  which  was  11*65  English  inches  in  length. In  the  French  system  there  was  also  the  toise  or  fathom  of  six feet,  and  the  earliest  record  of  a  standard  of  length  dates  back  to the  Toise  du  Grand  Chatelet,  constructed  in  1668,  and  based  (though five  lignes  shorter)  on  the  ancient  toise  de  magons  of  Paris,  which was  doubtless  as  old  as  the  times  of  Charlemagne.1  It  is  said by  La  Condamine2  to  represent  one  half  the  distance  (12  feet) between  the  walls  of  the  inner  gate  of  the  Louvre.  Subsequently, copies  of  this  were  made,  and  the  toise  was  used  as  the  basis  for standards  of  linear  measures,  such  as  the  Toise  de  Perou?  There was  also  the  aune  or  ell,  which,  originally  a  double  cubit,  became adopted  as  a  unit  of  linear  measure  for  cloth,  and  survived  until displaced  by  the  meter.  A  standard  Aune  des  Marchands, Merciers  et  Grossiers,  1554,  divided  into  halves,  quarters,  thirds, sixths,  etc.,  was  preserved  by  that  guild,  and  was  the  basis  of this  unit.  The  aune  of  Paris  corresponded  to  46^  Eng.  inches, but  it  was  never  adopted  in  the  latter  country  to  any  considerable extent  or  authorized  by  law,  though  a  cloth  aune  or  ell  of  45  in. is  found  marked  on  the  standard  yard  of  Queen  Elizabeth.4 For  the  origin  of  standards  of  weight  in  France  we  have  to  go back  to  the  Arabs,  as  the  basis  of  the  ancient  French  system  is  re- puted to  be  an  Arab  yusdruma,  which  was  sent  by  Caliph  Al  Mamun (786-833)  to  Charlemagne.  This  yusdruma,  or  later  Arab  pound, was  the  monetary  pound  or  livre  esterlin  of  Charlemagne,  and amounted  to  5666  J  grains,  or  367*128  grams.5  It  was  divided  into 12  ounces,  or  20  sols,  of  12  deniers,  of  2  oboles  of  12  grains,  or 5760  grains  in  the  aggregate,  each  grain  weighing  *063738  grams. 1  La  Hire,  Mem.  de  VAcad.  Roy.  des  Sciences,  1714,  pp.  394-400  (Paris,  1717). 2 La  Condamine,    Memoires   de  VAcad.    Roy.    des   Sciences,    1772,   2nd    part, pp.  482-501  (Paris,  1776). 3  See  chapter  x.  on  Standards. 4  See  chapter  on  Standards,  p.  243.     Also  ante,  p.  31. 5 The  name  "esterlin"  was  employed  at  one  time  in  the  French  language  to signify  "true,"  being  equivalent  to  the  modern  Fr.  word  "veritable."  It  has, however,  disappeared  from  use,  but  has  been  retained  in  English,  with  the  same signification,  in  the  form  of  "sterling,"  as,  for  example,  "pounds  sterling." THE   SCIENCE   OF   METROLOGY  39 The  livre  esterlin  of  Charlemagne  was  one  and  a  half  times  the weight  of  the  marc  of  the  monetary  system  which  was  established between  1076  and  1093  by  Philip  L,  who  used  8  of  the  12  ounces of  the  former  system  for  this  purpose.  This  marc  was  doubled, and  made  to  consist  of  16  ounces,  by  King  John  the  Good,  in 1350,  and  it  was  adjusted  according  to  the  weights  of  Charlemagne. The  weights  of  King  John  were  known  as  the  "  pile  de  Charle- magne," and  were  the  French  standards  of  weight  until  the adoption  of  the  Metric  System  in  1789.1  In  this  system  the livre  poid  de  marc,  or  pound,  consisted  of  two  marcs  or  half- pounds,  4  quarterons,  8  half -quarterons,  16  ounces,  32  half-ounces, 128  gros  (drachme)  or  grams,  384  scruples,  or  deniers,  9216  grains. There  were  also  in  France  four  other  marcs  duly  and  legally recognized,  viz.,  that  of  Kochelle,  which  was  called  English,  equal to  13  sols,  4  deniers,  in  terms  of  the  livre  esterlin;  that  of Limoges,  equivalent  to  13  sols,  3  oboles ;  that  of  Tours,  equal  to 12  sols,  11  deniers,  1  obole ;  and  that  of  Troyes  and  Paris,  equi- valent to  14  sols,  2  deniers.2 We  have  referred  specifically  to  early  measures  only  in  Great Britain  and  France,  as  throughout  the  rest  of  Europe  there  was such  great  diversity  until  well  into  the  nineteenth  century  that little  would  be  gained  for  our  purpose  by  considering  the  dozens of  kingdoms,  principalities,  free  cities,  etc.,  each  with  their separate  systems.  Local  conditions  and  traditions  everywhere governed,  and  riolTonly  in  different  countries  in  the  same  region would  there  be  different  values  for  the  same  weights  and measures,  but  also  in  different  towns  of  the  same  state.3  While the  names  feet,  pounds,  etc.,  were  quite  universally  employed,  yet they  designated  different  quantities,  and  save  for  arbitrary standards,  possibly  in  many  cases  not  even  duly  legalized,  there was  no  attempt  at  securing  uniformity.     A  foot  might  be  divided 1  Guillaume,  p.  94,  Les  Unites  et  Etalons  (Paris, 2  Quoted  by  Guillaume,  p.  95,  Les  Unite's  et  Etalons,  from  Chronique  de  1329 ■environ. 3  "At  the  close  of  the  last  (eighteenth)  century,  in  different  parts  of  the world,  the  word  pound  was  applied  to  391  different  units  of  weight  and  the word  foot  to  282  different  units  of  length."  T.  C.  Mendenhall,  Measurements  of Precision.  Such  a  list  with  British  and  metric  equivalents  may  be  found  in Barnard,  The  Metric  System  (Boston,  1879),  pp.  348-360.  The  kilogram  has .superseded  over  370  of  the  different  pounds. 40       EVOLUTION   OF   WEIGHTS   AND   MEASURES duodecimally,  as  was  done  by  the  Eomans,  or,  on  the  other  hand, it  might  be  divided  into  nine,  ten,  eleven,  or  thirteen  inches. Then  again  the  actual  distance  represented  by  a  foot  varied from  9  to  18  inches,  and  equivalents  are  now  known  for  many different  European  feet. As  to  the  sources  of  these  measures,  we  have  to  look  to  the Eomans  and  to  the  East,  as  the  former  nation  in  its  conquests overran  a  great  part  of  Europe, .  and  implanted  its  weights  and measures  with  more  or  less  permanence,  while  the  effects  of  trade with  the  Orient  and  the  intellectual  influence  of  the  Arabs doubtless  served  to  introduce  new  measures  or  to  corrupt  old ones.  Several  mark  weights  soon  became  known  as  standards for  coinage  and  precious  metals,  notably  that  at  Cologne,  while  the Ehine  foot  enjoyed  a  pre-eminence  in  the  neighboring  countries.1 As  practically  no  scientific  work  of  a  quantitative  character  was done  for  many  centuries,  the  influence  of  science  in  systematizing and  demanding  exact  standards  of  measure  was  not  felt,  so  that only  the  needs  of  trade,  often  of  a  most  restricted  character, which  could  be  satisfied  by  crude  and  imperfect  systems,  had to  be  provided  for.  The  lineage  of  many  of  the  old  European weights  and  measures  has  been  traced  more  or  less  satisfactorily back  to  ancient  times,  but  the  subject  presents  little  scientific attraction,  save  to  the  historian  or  archaeologist  and  the  student of  metrology.2  Lack  of  system  prevailed,  and  apparently  was quite  satisfactory,  but  gradually  the  minds  of  scientists  and statesmen  became  aroused  to  the  importance  of  the  subject  and the  need  of  fundamental  changes,  and  a  rational  systematization was  urged,  which  found  its  first  substantial  fruit  in  the  develop- ment in  France  of  the  metric  system. 1  This  Rhine  foot  defined  in  Prussia  by  law  in  1816  was  standardized  by  Bessel in  1835-1838,  and  survived  in  that  kingdom  until  the  adoption  of  the  metric system.    It  is  still  (1906)  the  standard  of  length  in  Denmark. 2  An  interesting  summary  of  ancient  and  modern  measures,  which,  however, must  be  modified  in  many  aspects,  and  considered  in  the  light  of  modern researches  and  theories,  is  contained  with  a  wealth  of  bibliographical  material in  Karsten,  Allgemeine  Encyklopddie  der  Physik,  vol  i.  "  Maass  und  Messen  " (Leipsic,  1869). CHAPTER  II. ORIGIN  AND  DEVELOPMENT  OF  THE  METRIC   SYSTEM.1 While  the  inconveniences  and  difficulties  attending  arbitrary systems  of  weights  and  measures  were  appreciated,  nevertheless philosopher  and  peasant  alike  submitted,  and  it  took  many  years for  a  feeling  in  favour  of  a  rational  and  fixed  system  to  develop. Such  a  system  at  its  best,  as  we  have  seen,  would  involve  an invariable  unit  derived  from  nature  itself,  which  not  only  could be  reproduced  readily,  but  was  capable  of  being  measured  with  a 1In  this  chapter  detailed  references  have  been  given  to  authorities  for particular  statements  for  the  benefit  of  those  who  desire  to  pursue  the  subject further.  The  history  of  the  Metric  System  has  been  well  summed  up  in  a treatise  by  M.  Bigourdan  (Le  Systdme  Me'trique,  Paris,  1901),  in  which  will  be found  usually  the  text  of  all  French  legislation  and  the  salient  features  of discussion  by  lawmakers  and  scientists,  as  well  as  a  complete  bibliography. There  is  also  an  excellent  historical  sketch,  "Notice  historique  sur  le  Systeme Metrique,  sur  ses  developpements  et  sur  sa  propagation,"  contained  in  the Annales  du  Conservatoire  (Imperial)  des  Arts  et  Metiers,  by  General  A.  Morin (Paris,  1870),  vol.  ix.  pp.  573-640.  This  is  a  brief  but  excellent  description  of the  origin  and  development  of  the  system  by  a  member  of  the  Committee  of Verification,  director  of  the  Conservatoire  des  Arts  et  Metiers,  and  a  member of  the  first  International  Commission.  "A  Historical  Sketch  of  the  Foundation of  the  Metric  System,"  by  General  Bassot,  was  published  in  the  Annuaire  pour Van  1901,  of  the  Bureau  of  Longitude,  Paris  (translated  into  English  by  Miss F.  E.  Harpham  of  the  Astronomical  Department  of  Columbia  University,  and published  in  the  School  of  Mines  Quarterly,  vol.  xxiii.  No.  1,  November,  1901. First  and  foremost,  however,  is  the  classical  work  of  Mechain  and  Delambre, Base  da  SystSme  Me'trique,  3  vols.  (Paris,  1806-1810),  which  is  the  primary source  of  information  for  the  early  work  in  establishing  the  Metric  System.  It is,  of  course,  unnecessary  to  say  that  in  the  following  pages  these  works  have been  most  freely  used,  and  can  be  recommended  for  those  desiring  additional information  on  the  subject. 42       EVOLUTION   OF   WEIGHTS   AND   MEASURES high  degree  of  precision.  Obviously  such  standards  as  barley- corns and  human  feet  did  not  possess  the  slightest  claim  to invariability,  and  as  soon  as  the  subject  began  to  be  considered seriously  and  earnestly  by  scientific  men,  the  choice  for  the fundamental  unit  of  linear  distance  became  narrowed  to  two classes  of  lengths,  and  around  them  most  of  the  subsequent discussion  centred.  One  was  the  length  of  a  fraction  of  a  great  * circle  of  the  earth,  while  the  other  was  the  length  or  a  fraction of  the  length  of  a  pendulum,  vibrating  in  intervals  of  one  second or  some  other  chosen  unit  of  time.  For  the  first,  proceeding  on the  assumption  that  the  earth  was  a  spheroid  (or  very  nearly  so), it  was  possible  to  measure  the  arc  of  a  great  circle  even  in  the seventeenth  century  without  any  great  difficulty.  Such  a  measure- ment involved  the  determination  with  considerable  accuracy  of  the geographical  position,  or  in  other  words  the  latitude  and  longi- tude, of  two  points,  and  then  a  geodetic  'or  trigonometrical  ' survey  which  took  into  consideration  the  curvature  of  the  earth's surface,  measuring  the  actual  distance  between  them  in  terms  of a  unit  of  length  selected  for  that  purpose  and  represented  by  a standard  which  was  employed  in  the  measurement  of  a  base- line. The  distance,  as  found  by  the  triangulation,  could  then  be compared  with  the  difference  in  latitude  between  the  two  points, and  thus  the  actual  distance  in  degrees  could  be  obtained  in terms  of  the  selected  linear  standard.  The  other  invariable standard  of  length  was  that  of  a  pendulum,  which  in  a  given place  executed  its  vibrations  always  in  the  same  time.  By  the  / law  of  the  pendulum,  the  time  of  vibration  is  inversely  pro- portional to  the  square  root  of  the  acceleration  due  to  gravity,  and directly  as  the  square  root  of  the  length.  Consequently,  being able  to  measure  time,  and,  assuming  that  the  acceleration  of gravity  at  a  given  point  is  constant,  it  is  possible  to  determine  or reproduce  accurately  a  given  length  by  this  instrumentality. After  considering  the  invariability  of  the  original  standard,  the next  important  matter  to  bear  in  mind  is  the  symmetry  and convenience  in  actual  use  of  any  system  of  measures  which  is based  thereon.  In  the  light  of  the  development  of  the  science  of arithmetic  and  of  the  popular  methods  of  reckoning,  it  can  be safely  said  that  the  decimal  system  for  money,  weights,  and measures,  must  stand  as  the  most  simple  and  useful.     Therefore DEVELOPMENT   OF  THE   METRIC   SYSTEM        43 in  considering  the  genesis  of  the  modern  metric  system,  as  a universal  system  founded  on  an  invariable  standard  and  sym- metrically and  conveniently  developed,  it  is  necessary  to  go  back to  Gabriel  Mouton,  Vicar  of  St.  Paul's  Church,  Lyons,  who  first proposed  in  1670  a  comprehensive  decimal  system  having  as  a  basis the  length  of  an  arc  of  one  minute  of  a  great  circle  of  the  earth. One  minute  of  arc  would  give  the  length  of  a  milliare  or  mille, which  would  be  subdivided  decimally  into  cenhtria,  decuria,  virga, virgula,  decima,  centesima,  millesimal  The  virga  and  virgida  would be  the  chief  units  of  the  system  corresponding  to  the  toise  and  the foot  then  in  use.  This  geometric  foot  {virgula  geometrica)  was further  defined  by  Mouton  as  corresponding  to  the  length  of  a pendulum  making  3,959*2  vibrations  in  a  half  hour  at  Lyons.2 This  proposition  contained  essentially  the  germ  of  the  modern metric  system  and  Mouton's  suggestion  of  the  pendulum  was  soon repeated  by  Picard  (1671),  and  by  Huygens3  (1673).  The  former said4  "  The  length  of  a  pendulum  beating  seconds  of  mean  time would  be  called  the  astronomical  radius  (Rayon  Astronomique),  of which  the  one-third  would  be  the  universal  foot :  the  double  of the  astronomical  radius  would  be  the  universal  toise,  which  would be  at  Paris  as  881  to  864 If  we  should  find  by  experience that  the  pendulums  were  of  different  lengths  in  different  places, the  supposition  we  had  made  touching  a  universal  measure depending  on  the  pendulum  would  not  stand,  but  it  would  not alter  the  fact  that  in  each  place  the  measure  would  be  perpetual and  invariable." aSee  Bassot,  "Historical  Sketch  of  the  Foundation  of  the  Metric  System," Annuaire  pour  Van  1901,  publie  par  le  Bureau  des  Longitudes,  Paris.  Translated in  School  of  Mines  Quarterly  (New  York),  vol.  iii.  No.  1,  Nov.,  1901. 2  Mouton,  Observationes  diametrorum  Soils  et  Lunae .  . .  Huic  adjecta  est  brevis dissertatio  de.  .  .  nova  mensurarum  geometricarum  idea  (Lyons,  1670),  p.  427.  In reference  to  Mouton's  work  an  interesting  paper  by  Professor  J.  H.  Gore,  "The Decimal  System  of  Measures  of  the  Seventeenth  Century,"  in  the  American  Journal of  Science  (Third  Series,  vol.  xli.  Jan.,  1891,  p.  22),  should  be  consulted. Professor  Gore  quotes  from  Mouton's  writings  and  describes  his  researches  in  order to  show  that  the  essential  features  of  the  Metric  System  were  first  announced  by him.  Furthermore  he  does  not  consider  that  due  credit  was  given  by  the  French scientists  who  founded  the  system  and  made  use  of  Mouton's  ideas. 3  Horologium  Oscillatorium,  4  prop.  25  (Paris,  1673). 4  Mesure  de  la  Terre,  reprinted  in  Anciens  Me'moires,  vol.  vii.  p.  133. ,.\ 44       EVOLUTION   OF   WEIGHTS   AND   MEASURES Similar  in  character  to  the  plan  of  Mouton,  but  considerably  later (1720),  was  a  proposition  made  by  Cassini,  in  his  celebrated  work, Be  la  grandeur  et  de  la  figure  de  la  Terre  (pp.  158,  159),  recom- mending the  adoption  of  a  unit  known  as  the  pied  geomttrique. This  was  equal  to  ^FOTF  Par^  °^  a  mmute  of  arc  of  a  great  circle, and  6  pieds  formed  a  toise.  J  This  foot  had  a  length  almost  half that  given  by  the  x  q  o  o^)  o  o  o  Par^  °^  tne  ra(lius  of  the  earth. Subsequently  another  plan  involving  the  length  of  the  second's pendulum  as  a  unit,  was  brought  forward  and  developed  by  Du  Fay, and  this,  after  his  death,  was  elaborated  and  continued  by  La Condamine  (1747),1  who  provided  against  the  variation  in  length at  various  latitudes  by  taking  as  his  unit  the  length  of  the second's  pendulum  at  the  equator  (36  inches  7'15  lignes  of  the  toise of  Peru),  which  he  together  with  Godin  and  Bouguer  had  quite accurately  determined  at  Quito,  while  engaged  in  measuring  an arc  of  meridian  at  the  equator  in  1735-1737.  La  Condamine  also appreciated  the  advantages  of  the  decimal  division  of  measures  of length,  and  saw  the  necessity  for  reforms  in  the  measures  of  area, capacity,  weight,  etc.,  so  that  all  might  be  brought  into  harmony with  the  linear  measures,  and  thus  be  equally  stable  and  invariable. He  was  farsighted  enough  to  suggest,  what  has  since  been  such  a valuable  feature  of  the  metric  system,  namely  the  advantages  of international  joint  effort  in  making  the  desired  changes,  and advocated  consulting  with  the  academies  of  foreign  countries  in this  matter. Worthy  of  record  also  is  the  proposition  made  by  M.  Prieur Du  Vernois,2  who  urged  as  the  unit  of  length,  that  of  the  second's pendulum,  in  preference  to  that  of  a  fraction  of  an  arc  of  meridian, on  the  ground  that  the  former  could  be  reproduced  more  readily. He  advocated  taking  the  length  of  the  pendulum  at  a  single  point, suggesting  the  Eoyal  Observatory  at  Paris,  and  then  making  a standard  of  platinum,  correct  at  a  certain  temperature  such  as  10°, which  would  be  deposited  in  the  Hotel  de  Ville.  One-third  of  the length  of  this  standard  would  be  the  French  or  natural  foot, which  would  be  divided  into  10  inches,  each  inch  in  turn  being 1  Me"moires  de  VAcademie  des  Sciences,  p.  489,  1747. 2  See  Prieur  (Du  Vernois),  Me'moire  sur  la  ne'cessite'  et  les  moyens  de  rendre uniformes  dans  le  royaume  toutes  les  mesures  d'entendue  et  de  pesanteur,  etc.  (Paris, 1790),  pp.  9-11. DEVELOPMENT   OF   THE   METRIC   SYSTEM       45 s/ divided  into  10  lignes.     Multiplying  the  foot  by  ten  would  give the  national  perch,  while  an  area  ten  perches  square  would  .be  the national  arpent.     Units  of  volume  would  be  measured  by  cubes  of lignes,  inches,  and  feet,  and  the  unit  of  mass  would  be  a  national pound  corresponding  to  the  mass  of  a  cube  of  distilled  water  at some  determined  temperature,  ten  inches  square  on  each  edge. Prieur  also  advocated  a  decimal  system  of  money,  in  which  the lime  (franc)  was  divided  into  tenth  and  hundredth  parts  known as  decimes  and  centimes. During  the  eighteenth  century  such  schemes  as  have  just  been described  were  proposed  by  scientists  for  the  improvement  of  the weights  and  measures,  and  although  they  were  brought  to  the attention  of  the  French  Government  they  did  not  meet  with such  approval  as  to  secure  their  adoption.  Indeed  there  was  no lack  of  plans  proposed  by  the  scientific  men,  and  the  government realized  the  necessity  for  uniformity  throughout  the  realm,  but the  various  schemes  were  discussed  and  discarded  without  any definitive  action,  and,  just  as  in  later  times,  the  difficulties attending  the  introduction  of  a  new  system  were  anticipated and  feared.  In  fact  Necker,  in  a  report  made  to  Louis  XVI. in  1778,  speaks  of  the  proposed  reform  of  weights  and  measures with  considerable  diffidence.  He  writes,  "  I  have  occupied myself  in  examining  the  means  which  might  be  employed  to render  the  weights  and  measures  uniform  throughout  the  king- dom, but  I  doubt  yet  whether  the  unity  which  would  result would  be  proportionate  to  the  difficulties  of  all  kinds  which  this operation  would  entail  on  account  of  the  changing  of  values which  would  necessarily  be  made  in  a  multitude  of  contracts,  of yearly  payments,  of  feudal  rights  and  other  acts  of  all  kinds.  I have  not  yet  renounced  the  project,  and  I  have  seen  with satisfaction  that  the  Assembly  of  Haute-Guyenne  have  taken  it into  consideration.  It  is  in  effect  a  kind  of  amelioration  which can  be  undertaken  partially,  and  the  example  of  a  happy  success in  one  province  would  essentially  influence  opinion."1 With  the  changes  wrought  by  the  Kevolution  it  was  possible to  gain  at  the  hands  of  the  public  consideration  for  radical  ideas in  science  as  well  as  in  government  and  religion.     The  .schemes 1  Necker,  Compte  rendu  au   Roi  de  1778,  Bigourdan,  Le   Syst&me  Me'trique, <Paris,  1901),  p.  11. 46       EVOLUTION   OF  WEIGHTS   AND   MEASURES and  discussions  already  mentioned  paved  the  way  for  the  favour- able reception  of  a  plan  for  reform  when  it  was  urged  in  the National  Assembly  by  a  bold  and  able  leader.  Such  was Talleyrand,  then  Bishop  of  Autun,  who  brought  the  matter  to the  attention  of  the  National  Assembly  in  April,  1790.  He  not only  appreciated  the  necessity  for  a  uniform  system  of  weights and  measures  for  France,  but  also  the  desirability  of  a  system that  would  be  truly  international  rather  than  merely  the  weights and  measures  of  Paris.  He  proposed  as  a  fundamental  unit  the length  of  a  pendulum  beating  seconds  at  45°  latitude,  and  as  a unit  of  weight  that  of  a  cube  of  water  whose  height  should  be one  twelfth  the  length  of  the  pendulum.  New  and  most  careful measurements  were  to  be  undertaken  to  determine  the  length  of the  pendulum,  and  for  this  purpose  a  joint  commission  of  the Paris  Academy  of  Sciences  and  the  Eoyal  Society  of  London  was to  be  established.  Talleyrand's  proposal,  after  being  considered by  the  Committee  on  Agriculture  and  Commerce  and  discussed in  a  report  by  the  Marquis  de  Bonnay,  was  brought  before  the National  Assembly,  where,  in  the  course  of  the  general  discussion upon  it,  the  advantages  of  a  decimal  division  were  urged.  The report  was  accepted  and  a  decree  was  rendered  on  May  8,  1790, which  was  sanctioned  by  Louis  XVI.  on  August  22  of  the  same year.  Inasmuch  as  this  decree  describes  with  some  detail  the existing  condition  and  the  method  of  making  the  change,  it  is given  below  in  full.      It  runs : "  The  National  Assembly,  desiring  that  all  France  shall  forever enjoy  all  the  advantages  which  will  result  from  uniformity  in weights  and  measures,  and  wishing  that  the  relation  of  the  old measures  to  the  new  should  be  clearly  determined  and  easily understood,  decreed  that  His  Majesty  shall  be  asked  to  give orders  to  the  administrators  of  the  different  departments  of  the kingdom,  to  the  end  that  they  procure  and  cause  to  be  remitted to  each  of  the  municipalities  comprised  in  each  department  and that  they  send  to  Paris  to  be  remitted  to  the  Secretary  of  the Academy  of  Sciences  a  perfectly  exact  model  of  the  different weights  and  elementary  measures  which  are  in  usage. "  It  is  decreed  further  that  the  King  shall  also  beg  His Majesty  of  Britain  to  request  the  English  Parliament  to  concur with  the  National  Assembly  in  the  determination  of  a  natural DEVELOPMENT   OF   THE   METRIC   SYSTEM        47 unit  of  measures  and  weights ;  and  in  consequence,  under  the auspices  of  the  two  nations,  the  Commissioners  of  the  Academy of  Sciences  of  Paris  shall  unite  with  an  equal  number  of  members chosen  by  the  Eoyal  Society  of  London,  in  a  place  which  shall be  respectively  decided  as  most  convenient,  to  determine  at  the latitude  of  45°,  or  any  other  latitude  which  may  be  preferred, the  length  of  the  pendulum,  and  to  deduce  an  invariable  standard for  all  the  measures  and  all  the  weights ;  and  that  after  this operation  is  made  with  all  the  necessary  solemnity,  His  Majesty will  be  asked  to  charge  the  Academy  of  Sciences  to  fix  with precision  for  each  royal  municipality  the  relation  of  the  old weights  and  measures  to  the  new  standard,  and  to  compose afterward  for  the  use  of  the  municipalities  the  usual  books  and elementary  treatises  which  will  indicate  with  clearness  all  these propositions. "  It  is  decreed  further  that  these  elementary  books  shall  be sent  at  the  same  time  to  all  the  municipalities  to  be  distributed : at  the  same  time  there  shall  be  sent  to  each  of  the  municipalities a  certain  number  of  new  weights  and  measures  which  they  shall distribute  gratuitously  to  those  who  would  be  caused  great expense  by  this  change ;  and  finally,  six  months  only  after  the distribution,  the  old  measures  shall  be  abolished  and  replaced by  the  new. "  The  National  Assembly  decrees  that  the  Academy,  after  con- sultation with  the  officers  of  the  Mint,  shall  offer  their  opinion as  to  the  suitability  of  fixing  invariably  the  inscription  of  the coined  metal  to  the  end  that  the  kinds  shall  never  be  altered except  in  their  weight,  and  whether  it  would  not  be  useful  that the  difference  tolerated  in  the  coins  under  the  name  of  remedy be  always  beyond  requirement,  that  is  to  say  one  piece  may exceed  the  weight  prescribed  by  law  but  must  never  be inferior. "Finally,  the  Academy  shall  indicate  the  scale  of  division which  it  believes  most  convenient  for  all  weights,  measures and  coins." Under  the  terms  of  this  decree  the  Academy  took  up  its  work in  earnest,  and  on  October  27,  1790,  its  committee  consisting  of Borda,  Lagrange,  Laplace,  Tillet,  and  Condorcet,  made  a  report  in which   they  urged  the  adoption  of  the  decimal  division  of  the 48       EVOLUTION   OF   WEIGHTS   AND  MEASURES moneys,  weights,  and  measures.  This  report  dealt  with  the comparative  merits  of  the  decimal  and  duodecimal  system  of calculation,  and  discussed  many  of  the  questions  bearing  on  this subject  which  have  been  argued  at  such  length  before  and  since. Next  in  importance  after  settling  on  the  principle  of  decimal division  was  the  selection  of  a  unit  of  length,  and  a  committee consisting  of  Borda,  Lagrange,  Laplace,  Monge,  and  Condorcet, presented  a  report  to  the  Academy  on  March  19,  1791,  in  which they  stated  that,  in  their  opinion,  the  units  suitable  for  adoption as  the  basis  of  a  uniform  and  rational  system  of  weights  and measures  were  three  in  number,  as  follows :  the  length  of  a second's  pendulum,  the  quadrant  of  a  great  circle  of  the  equator, and  the  quadrant  of  a  great  circle  of  meridian.  Considering  the relative  advantages  and  drawbacks  of  each  of  these  with  great care  and  deliberation,  the  committee  concluded  that  while  the length  of  the  second's  pendulum  was  easily  determined  and susceptible  of  verification,  it  was  dependent  on  the  acceleration  ' due  to  gravity,  and  that  it  was  necessary  to  have  the  position specified  exactly.  The  most  desirable  point  would  be  at  45° latitude,  a  mean  distance  between  the  equator  and  the  pole.  At the  latter  points,  owing  to  flattening  of  the  earth  at  the  poles, pendulums  vibrating  with  the  same  period  would  have  unequal lengths,  that  at  the  equator  being  shorter  as  the  force  of  gravity there  owing  to  the  greater  radius  of  the  earth  is  less  intense. But  with  the  pendulum  a  new  and  unlike  element,  namely  the second,  is  introduced,  and  this  depends  upon  the  arbitrary division  of  the  day.  The  preference  of  the  committee  was  for  a terrestrial  arc,  inasmuch  as  it  bore  a  nearer  relation  to  the ordinary  method  of  measuring  distances,  and  their  choice  was  in favor  of  an  arc  of  a  meridian  rather  than  one  of  the  equator. This  decision  was  due  to  the  fact  that  such  an  arc  could  be measured  with  greater  facility,  and  also  in  several  countries, while  in  addition  no  more  assurance  of  the  regularity  of  the equator  than  that  of  a  meridian  could  be  given. After  an  arc  had  been  measured  the  length  of  a  quadrant could  then  be  computed,  and  one  ten-millionth  of  its  length  could be  taken  as  the  base  or  fundamental  unit  of  length.  In  other words  the  quadrant  was  to  be  measured  in  a  single  unit  of  length on  a  decimal  basis,  instead  of  in  the  former  degrees,  minutes,  and DEVELOPMENT   OF  THE   METRIC   SYSTEM        49 seconds.  The  plan  proposed  by  the  committee  was  to  measure an  arc  of  meridian  between  Dunkirk,  on  the  northern  coast  of France,  and  Barcelona  on  the  Mediterranean  Sea,  largely  because these  two  places  were  each  situated  at  the  sea-level  in  the  same medidian,  because  they  afforded  a  suitable  intervening  distance  of about  9°  30',  the  greatest  in  Europe  available  for  a  meridian measurement,  because  the  country  so  traversed  had  in  part  been surveyed  trigonometrically  previously  by  Lacaille  and  Cassini  in 1739-1740,  and  furthermore  because  such  an  arc  extended  on both  sides  of  latitude  45°.  The  committee  outlined  six  distinct operations  essential  for  the  work.     They  were  as  follows : 1.  The  determination  of  the  difference  in  latitude  between Dunkirk  and  Barcelona. 2.  The  measurement  of  the  old  bases. 3.  The  verification  and  measurement  of  the  series  of  triangles used  in  a  previous  survey,  and  extending  the  same  to  Barcelona. 4.  The  observation  of  the  pendulum  at  45°  latitude. 5.  Verification  of  the  weight  in  vacuum  of  a  given  volume  of distilled  water  at  the  temperature  of  melting  ice. 6.  Comparison  of  the  old  and  new  measures,  and  the  con- struction of  scales  and  tables  of  equalization. The  National  Academy  straightway  adopted  the  recommenda- tions of  the  committee,  adopting  the  length  of  one  fourth  of  a terrestrial  meridian  as  the  basis  for  the  measures  of  length,  and providing  for  the  measurement  of  the  arc  from  Dunkirk  to Barcelona,  and  the  appointment  of  supervisory  committees  by  the Academy  of  Sciences.  This  latter  body  then  addressed  itself  to the  consideration  of  a  suitable  nomenclature,  and  fixed  the  length of  the  new  unit  provisionally  at  36  inches  11*44  lignes,  and assigning  the  name  Metre  to  the  one  ten-millionth  part  of  the quadrant  of  the  earth's  meridian.1  The  relations  between  the measures  of  length  and  capacity,  capacity  and  weight,  and  weight and  money  were  also  considered.  The  provisional  meter  was derived  from  a  calculation  of  the  observations  made  by  Lacaille when  measuring  a  meridian  in  France  in  1740.  By  this  the value  of  one  degree  was  given  as  57,027  toises,  which  multiplied by  90  would  give  the  length  of  the  quadrant  or  distance  from pole  to  equator,  as   5,132,430  toises.      Taking  the   ten-millionth 1  Report  of  May  29,  1793. D 50       EVOLUTION   OF    WEIGHTS   AND   MEASURES 73 2 45 o -<u 1— 1 4D ■ s ^H © 8 d p 0) < 8 §    §    § § 5 O     p1 © © G> 42 1 g 1 1 1 > o ©   ©   © — 1—1 1 g  8  2 ** 0) E o 4J s CD Q ri ■ • ■ .  ■ • . . ■ ■ 13 n ' 1 ' ■ ' * ? t>  ^  ^ 1 1          1 i y -a  S o 1 1     1     . • 1 . . o . 1 of §| Ph     S a Ph -t-T o Q '3 E H 2 1 n a 8 m 'o ^3 © d © s > ri ■ • '        ' • • • • • • ta c3     . a>  in ^S 51~ 4flK 11 p  J? be*" 00 O 1 0) 1    1  M S >> i 43 •© s 5 3 E 3 s C Q S m *-      • •© S    © K     ft P  s •r E +-> -1; a 5 «© Q of i 1 a 3 E I E & O 3 aT E 'o 4a o CD B in O P aT E 3 a Q a ^ • • • • ■ • ■ ' • CO 0) s I-M 9 *© '  "3 | ■ ' ■ ■ ' ■ ■ ' 1 3  ft "8 s 9 1      '3   1 «  E 1  Sd © E I of E 4J 1 •a P E +-> a d O <iT E g 1 •a 3 © i 'o >© Q aT a .2 CP O ^7 1 1 JTj •      •      • ' • ■     ■ • • • • • ' ■      i      i , , , , , , , , N  q,  g gi;S SI* | | | •<  i3  a> O   W'3 «§g to 1  1 1 *<l>      <x>      o Q    P    Ph 1 -a 1 QQ 1  t IS © | ft Eg) 'o P E H 3 9 a G 0 H © 4a t B 5 "o C2 © 4a q «5 ■ • „ • • • 3 a <u S o to 1 1      1      1 © E 1 1  f 43 | 'o n 43 -CU a "-t-3 E -(-3 s 1 'B g '3 •© P 1 '4a d O © 45 d 1 1 •3 ^ / o J •SHXONai •sawa^iOA DEVELOPMENT   OF   THE   METRIC   SYSTEM       51 1   1   1   1   1   1   1   1   1   1 10.000  metres  carres. 1.000 100 10 6      , ■S  i o 0) fa ;9 1      1      1 Millier,   - Quintal,  -         -         - Livre,      -         - Once, Gros, Denier,    - Grain, ID fa             -o> ..->  S  i.l 8         B «           "a           <o ll| 3      £      % CC     GO Franc, Sol,          - Denier,    -         - Myriagramme, Kilogramme,  - Hectogramme, Decagramme,  - Gramme, Decigramme,  - Centigramme, Milligramme,  - Hectare, Are, Centiare, of fa -<u ~    +=» i  i QQ    P Franc,     - Decime,  - Centime, Bar  or  Millier, Decibar,  - Centibar, Grave,     - Decigrave,       -         - Centigrave, Gravet,    - Decigravet,     - Centigravet,    - Milligravet,    - Are, Deciare,  - Centiare, 1        1 Franc  d'argent, I      1 §  .9  J  g  S  £  «g  -a 1      1      1      1      1 1        i i*  I •+3                   | ND       , * a o      ~    <u 3  1  -1 3  3  i £>  Q  o f  Millier, Grave,  - Deci-grave,   - Centi-grave,  - Milli-grave,  - 1      1      1      1      1 1        1 •aoo^w -ni3 1     1     1 'SAHNOJ^ •SXHDI3A\ •saoYJHns 3 1 3 I ! 52       EVOLUTION   OF   WEIGHTS   AND   MEASURES part  of  this  value,  and  reducing  it  to  the  feet  and  lignes  into which  the  toise  was  divided,  the  length  of  3  feet  11*44  lignes was  obtained.  To  show  how  little  this  provisional  meter  varied from  the  meter  finally  determined  by  the  commission  in  1799,  it may  be  stated  that  the  latter  length  in  the  same  units  is  3  feet 11*296  lignes,  or  a  difference  of  about  *33  millimeters,  an  amount considered  quite  insignificant  in  every-day  dealings.  A  standard of  the  provisional  meter  in  brass  was  duly  constructed  by  Lenoir in  Paris,  and  is  preserved  in  the  Conservatoire  des  Arts  et Metiers  at  Paris.1 The  committee  was  unable  to  decide  definitely  on  a  system  of nomenclature,  and  accordingly  proposed  two  schemes :  one,  as they  termed  it,  methodical,  in  which  Latin  prefixes  were  used  for the  various  units ;  the  other  simple  monosyllabic  names  which they  believed  would  be  more  readily  adopted  by  the  general population.  The  Convention,  which  in  the  meanwhile  had replaced  the  National  Assembly,  adopted  the  recommendations of  the  committee,  but  preferred  to  use  the  methodical  nomen- clature. This  decree  was  dated  August  1,  1793,  and  called  atten- tion to  the  importance  of  the  steps  being  taken  to  secure uniformity  of  weights  and  measures  in  France,  and  outlined the  methods  of  practically  establishing  the  new  system  through- out the  country.  The  suppression  of  the  Academy  of  Sciences occurred  a  few  days  (August  8,  1793)  after  passing  this  decree, and  this  event,  together  with  various  legislative  enactments  from time  to  time,  had  the  effect  of  causing  changes  in  the  personnel of  the  scientific  staff  entrusted  with  the  development  of  the system  and  some  differences  in  the  method  of  procedure.  The place  of  the  Academy  was  taken  by  a  newly  constituted  National Institute  of  Sciences  and  Arts,  which  continued  the  scientific oversight,  and  in  general  the  undertaking  was  pushed  forward  as rapidly  as  is  possible  with  work  of  such  character. As  showing  the  extent  to  which  the  desire  for  changes  and reforms  was  being  manifested  in  France  at  this  time,  it  may  not be  inappropriate  to  refer  at  this  point  to  the  innovations  intro- duced in  the  calendar  whereby  the  decimal  system  was  here applied  also.     By  a  decree  of  November  24,  1793,  time  was  to  be ^igourdan,  Le  Systeme  Mttrique  (Paris,  1901),  chap.  ix.  pp.  90-93.     Mechain and  Delambre,  Base  du  Systeme  MUrique  (Paris,  1806-1810),  vol.  iii.  pp.  673-690. DEVELOPMENT   OF  THE   METRIC   SYSTEM        53 reckoned  from  the  establishment  of  the  French  Eepublic,  Sep- tember 22,  1792,  the  day  of  the  autumnal  equinox.  The  year  as formerly  was  to  be  divided  into  twelve  months,  but  each  of  these was  to  be  divided  into  three  weeks,  or  decads,  of  ten  days  each. Each  day  was  to  be  divided  into  ten  hours,  and  each  hour  into one  hundred  minutes  of  one  hundred  seconds  each.  A  picturesque feature  was  the  grouping  of  the  months  according  to  the  seasons with  a  different  termination  for  the  names  of  each  season.  Thus, beginning  with  the  autumn  equinox,  Vende'miaire  was  the  month of  vintage,  and  was  followed  by  Brumaire,  the  month  of  fogs,  and Frimaire,  the  month  of  incipient  cold.  At  the  winter  solstice came  Mvose,  the  month  of  snow,  and  then  Pluviose,  the  month  of rain,  and  Ventose,  the  month  of  wind.  The  spring  months  were, Germinal,  the  month  of  buds ;  Floreal,  the  month  of  blossoms ; and  Prairial,  the  month  of  flowering  fields.  In  the  summer  came Messidor,  the  month  of  harvests ;  Thermidor,  the  month  of  heat ; and  Fructidor,  the  month  of  fruits. This  changed  calendar  was  used  until  1806,  when  the  Gregorian calendar  was  resumed,  but  the  division  of  the  day  into  100,000 parts  was  abandoned  in  1795.  The  lack  of  success  of  this  method of  dividing  time  can  readily  be  explained,  and  by  reasons  which have  but  little  bearing  on  the  science  of  metrology.  The  doing away  with  the  Christian  Sabbath,  the  addition  of  a  festival  season, the  changing  of  well-established  modes  of  life  by  legislative  enact- ment could  hardly  but  be  expected  to  fail  of  adoption.  Further- more, the  Gregorian  calendar  was  at  this  time  practically  universal, and  furnished  no  inconvenience  either  to  scientific  men  or  to  the general  public.  It  was  a  case  of  change  merely  for  the  sake  of innovation,  and  as  such  was  destined  to  fail. The  time  being  ripe  for  further  and  more  definite  legislation on  the  subject  of  the  new  scheme  of  weights  and  measures,  after Prieur  (de  la  Cote  d'Or)  had  made  a  full  and  comprehensive report  describing  the  status  of  the  work  of  establishment  and recommending  a  new  system  of  nomenclature,  the  Convention enacted  the  Law  of  18  Germinal  an  III.  (April  7,  1795),  which defined  precisely  the  different  units,  provided  for  standards,  and the  proper  distribution  of  secondary  standards,  and  the  exact determination  of  the  units  of  length  and  mass  according  to  the original  plan.     Article  5  of  this  decree  is  worth  quoting  in  full,. 54       EVOLUTION   OF   WEIGHTS   AND   MEASURES as  it  gives  precise  definitions  of  the  elementary  units  of  the metric  system.      It  reads  : "  Art.  5. — The  new  measures  will  be  distinguished  by  the  name of  measures  of  the  Eepublic :  their  nomenclature  is  definitely adopted  as  follows : "  Meter,  the  measure  of  length  equal  to  the  ten-millionth  part of  a  terrestrial  meridian  contained  between  the  north  pole  and the  equator. "  Are,  the  measure  of  area  for  land  equal  to  a  square  ten meters  on  each  side. "  Stere,  the  measure  designed  especially  for  fire- wood,  and  which shall  be  equal  to  a  meter  cube. "Liter,  the  measure  of  capacity  both  for  liquids  and  dry materials,  whose  extent  will  be  that  of  a  cube  of  one-tenth  of  a meter. "  Gramme,  the  absolute  weight  of  a  volume  of  pure  water  equal to  a  cube  of  one-hundredth  part  of  a  meter,  and  at  the  tempera- ture of  melting  ice. "  Finally  the  unit  of  coinage  shall  take  the  name  of  franc  to replace  the  livre  used  until  to-day." Greek  prefixes  were  provided  to  denote  the  multiples  of  the various  units  and  the  Latin  prefixes  for  the  subdivisions,  while  in the  measures  of  weight  and  capacity,  provision  was  made  in  addi- tion for  double  and  half  measures. Under  the  provision  of  this  law,  the  scientific  work  was  taken up  with  vigor,  and  the  Government  appointed  a  commission  of twelve  to  complete  the  original  determinations  of  length  and mass.  This  body  included  Berthollet,  Borda,  Brisson,  Coulomb, Delambre,  Haiiy,  Lagrange,  Laplace,  Mechain,  Monge,  Prony,  and Vandermonde,  all  of  whom  had  been  interested  actively  in  the work  previously  accomplished.  This  commission  was  then  sub- divided, Delambre  and  Mechain  taking  charge  of  the  astronomical and  geodetic  work,  Borda,  Haiiy,  and  Prony  of  the  determination of  the  units  of  weight,  Borda  and  Brisson  of  the  construction  and verification  of  the  provisional  meter,  and  Berthollet,  Monge  and Vandermonde  of  the  construction  of  the  definite  meter.  The length  of  a  second's  pendulum  had  already  been  determined  by Cassini  and  Borda  at  Paris,  and  was  found  to  be  equal  to  3  feet 8*5593  lignes  of  the  toise  of  Peru. DEVELOPMENT   OF   THE   METRIC   SYSTEM        55 The  measurement  of  the  arc  of  meridian  was  the  most  impor- tant of  the  duties  of  the  commission,  and  involved  a  vast  amount of  labor,  both  in  observations  in  the  field  and  in  the  reduction and  calculation  of  these  observations.  The  work  was  originally commenced  in  1792  by  M^chain  and  Delambre,  and  was  carried on  by  them  through  various  vicissitudes  caused  by  changes  in political  conditions,  with  their  consequent  effect  on  the  general and  scientific  plans  for  the  various  operations. Before  describing  their  work,  however,  it  may  be  of  advantage  to outline  the  underlying  principles  of  a  geodetic  or  trigonometrical survey  such  as  is  necessary  to  determine  the  length  of  an  arc on  the  surface  of  the  earth.  Such  a  survey  naturally  involves the  measurement  of  considerable  distances,  taking  into  considera- tion the  curvature  of  the  earth's  surface,  and  requires  a  system or  network  of  triangles  connected  one  with  another  by  means  of common  sides.  The  vertices  are  stations  usually  situated  on some  high  altitude,  or  at  any  event  so  selected  that  each  is visible  with  a  telescope  from  several  others.  Always  at  one  end, and  often  at  or  near  both  ends,  there  is  what  is  known  as  a  base- line, a  horizontal  distance  on  level  ground  actually  measured with  a  linear  standard  to  as  high  a  degree  of  precision  as  is possible.  This  involves  measuring  a  distance  of  from  one  to  ten kilometers  by  means  of  rods,  bars,  or  steel  tapes,  whose  lengths have  been  determined  with  great  accuracy  at  a  standard  tempera- ture, to  which  by  correction  the  actual  measurements  may  be reduced.  Care  must  be  taken  to  place  the  standards  perfectly horizontal  and  end  to  end  when  they  are  being  moved  over  the measured  distance,  or  to  make  suitable  corrections,  and  to observe  the  temperature.  In  this  way  the  base  line,  or  one  side of  the  triangle,  marked  in  the  accompanying  diagram  by  a heavy  line,  is  accurately  determined,  and  it  is  advantageous in  an  extended  survey  to  have  the  base  lines  at  or  near  sea-level. After  the  base  line  is  determined,  then  the  triangulation  may be  reduced  and  the  distance  calculated  between  the  remote  ends of  the  arc.  If  reference  is  made  to  plate  vii.  vol.  i.  of  the work 1  of  Delambre  and  Mechain  here  reproduced,  it  will  be possible  to  illustrate  the  general  method.  The  base  shown between  Salces  and  Vernet  is  near  Perpignan,  in  the  south  of 1  Le  Base  du  Systeme  Metrique,  vol.  i. 56      EVOLUTION   OF   WEIGHTS   AND   MEASURES France,  and  at  the  end  of  the  old  arc  previously  measured.  This distance  is  actually  measured  with  the  base  line  apparatus. Then  by  means  of  a  divided  circle,  capable  of  measuring  angles in  both  a  horizontal  and  vertical  plane,  and  transit  or  theodolite placed  at  the  "  terme  boreal  "  (north  end  of  the  base  line),  the angle  between  the  direction  to  Mt.  d'Espira  and  to  Mt.  Forceral is  measured,  and  then  at  the  "  terme  austral "  the  corresponding similar  angles  are  measured.  Thereupon  the  instrument  is  taken to  Mt.  d'Espira  and  the  angles  around  that  point  determined. This  is  the  beginning  of  a  long  series  of  angle  determinations  at all  the  points  of  observation,  as  Mt.  de  Tauch,  Pic  de  Bugarach, Mt.  Alaric,  Carcassonne,  etc.  All  of  the  measurements  are  con- tinually checked  by  the  fact  that  the  sum  of  all  the  angles around  a  single  point,  as  Mt.  Alaric,  must  equal  360°,  and  that the  sum  of  the  three  angles  in  any  triangle  must  equal  180°.  In any  triangle,  if  one  side  and  two  angles,  or  two  sides  and  one angle,  are  known,  then  it  is  a  simple1  matter  to  calculate  the other  parts. In  this  way  it  is  not  only  possible  to  calculate  the  length  of the  sides  of  all  the  numerous  triangles  formed  between  Barcelona and  Dunkirk,  but  also  the  projection  of  each  upon  the  true  north and  south  meridian.  For  example,  as  soon  as  the  linear  distance from  Mt.  Alaric  to  St.  Pons  is  known,  and  the  angle  which  the direction  makes  with  the  true  meridian,  then  it  is  simple  to calculate  how  far  one  is  north  of  the  other,  or  in  other  words, the  section  of  the  meridian  corresponding  to  the  distance  of  St. Pons  due  north  of  Mt.  Alaric.  Thus  ultimately  the  distance  of Dunkirk  due  north  of  Barcelona  is  calculated.  The  numerous triangles  give  continual  checks  upon  the  work,  as  do  also  other base  lines  distributed  along  the  line  of  triangulation. The  foregoing  gives  the  merest  outline  of  the  work  of  triangu- lation, as  there  are  numerous  refinements  and  modifications involved  in  both  observation  and  computation,  which  make  the calculation  one  of  no  small  magnitude.  This,  however,  is  but half  of  the  work.  There  must  be  found,  with  an  equal  degree  of precision,  the  geographical  position,  or,  more  particularly,  the latitude,  of  the  two  extremities  of  the  meridian  by  astronomical methods.  In  kind  this  is  similar  to  the  finding  of  the  position of  a  vessel  at  sea,  but  more  refined  methods  of  observation  are :veO? e*° u* Rodez Carcassonne de ^ fc^ St.  Pons M*  de  Tauch ir« .Salces terme  borda» 7^*  '- -jf Yem  e  I" M  Forceral  ferme  austral 58      EVOLUTION   OF   WEIGHTS   AND   MEASURES necessary,  and,  at  the  present  day,  the  nse  of  the  zenith  telescope is  considered  the  most  accurate  of  the  several  methods  of  deter- mining the  latitude  of  a  place. At  the  time  of  the  measurement  of  the  Dunkirk-Barcelona  arc, however,  the  astronomers  used  the  method  of  upper  and  lower transits  of  certain  stars  near  the  north  pole  of  the  heavens. Keferring    to    the   accompanying   figure,    NDBES    represents    a DEVELOPMENT   OF   THE    METRIC   SYSTEM        59 meridian  of  longitude  through  the  place,  D,  the  latitude  of  which is  sought.  That  is,  the  plane  of  the  paper  is  a  plane  through  the axis  of  the  earth  NS  and  the  place  D.  Evidently  then  the  angle DCE  is  the  latitude  of  the  place  D,  and  the  angle  DCN  is  called the  colatitude.  If  the  line  DM  indicates  the  direction  in  which &  star  appears,  as  seen  from  D  at  the  instant  when  it  passes  the meridian,  then  the  angle  ZDM  may  be  observed,  and  is  called  the zenith  distance  of  the  star.  The  lines  DP,  DP'  and  SCN  are parallel,  and  indicate  the  direction  to  the  celestial  pole,  that  is, to  the  point  where  the  axis  NS  pierces  the  heavens,  then  the angle  ZDP  is  equal  to  DON  the  colatitude  of  the  place.  The angle  MDP  is  the  polar  distance  of  the  star. A  series  of  determinations  of  the  zenith  distance  of  Polaris,  the "north  star,"  made  on  Jan.  17th,  1796,  at  Dunkirk,  for  the  upper transit,  gave  37°  11'  44"*36.  Adding  to  this  the  pole  distance  of Polaris,  lc  46'  39"*60,  gives  the  colatitude  38°  57'  44"*36,  and  the latitude,  or  90°  minus  the  latitude,  51°  2'  15"*64.  In  the  case  of a  lower  transit,  where  the  star  crosses  the  meridian  below  the pole,  the  pole  distance  would  be  subtracted  from  the  zenith distance.  That  is  to  say,  Z'D'P'  =  Z'DM'  -  M'DP'.  A  similar determination  at  Barcelona,  made  on  Dec.  17th,  1793,  gave  as the  latitude  of  that  place,  41°  22'  47"*83.  This  would  give  as the  difference  of  latitude  between  Dunkirk  and  Barcelona, 9°  39'  27"*81. A  final  determination  of  the  difference  of  latitude  between Dunkirk  and  Montjouy  (Barcelona)  9°*67380,  and  the  distance, measured  in  toises,  was  found  to  be  551  584*72.  If  the  refine- ments of  the  polar  flattening  of  the  earth,  etc.,  are  neglected  for the  moment,  then  551  58472  divided  by  9*67380  would  give 57  018*7  as  the  number  of  toises  in  one  degree  of  latitude.  This number,  57018*7,  multiplied  by  90,  gives  5  131  680.  One  ten- millionth  part  of  this,  or  0*5131680  of  a  toise,  would  then  be  the ideal  meter.  Naturally,  in  the  actual  calculation,  all  the  cor- rections and  refinements  were  applied. It  must  be  remembered  that  in  making  these  measurements much  depends  upon  the  accuracy  of  graduation  of  the  circles,  and that  many  measurements  must  be  made  and  an  average  taken  so as  to  obtain  in  each  instance  a  mean  value.  The  errors  can  be •distributed  by  the  two  considerations  referred  to  above,  that  the 60       EVOLUTION   OF   WEIGHTS   AND   MEASURES sum  of  all  the  angles  around  a  point  must  be  360  degrees,  and that  the  sum  of  the  three  interior  angles  of  any  triangle  must equal  180  degrees.  Furthermore,  when  the  observations  are reduced,  allowance  must  be  made  for  the  difference  in  elevation  of the  stations  and  for  the  curvature  of  the  earth,  which,  amounting to  as  much  as  7  inches  for  each  mile,  becomes  an  important quantity  in  an  extended  survey.  Triangulations  analogous  to those  here  indicated,  carried  out  over  the  whole  surface  of  a country,  are  the  basis  of  all  accurate  map  making,  and,  in.  the United  States,  an  arc  of  longitude  has  been  measured  which extends  across  the  continent. The  task  of  measuring  the  French  meridian  was  divided  by Delambre  and  Mechain,  the  former  being  assigned  the  northern portion  between  Dunkirk  and  Eodez,  a  distance  of  380,000  toises, while  to  Mechain  was  given  from  Eodez  to  Barcelona,  a  distance of  170,000  toises.  The  reason  for  this  unequal  division  was  that the  northern  part  of  the  meridian  was  situated  in  a  much  more accessible  country,  while  Mechain's  portion  was  in  the  moun- tainous region  of  Spain.  In  addition,  the  northern  part  had been  measured  twice  previously,  and  the  stations  had  been selected  and  recorded.  On  June  10,  1792,  the  King  issued  a proclamation,  in  which  Delambre  and  Mechain  were  commended to  the  good  offices  of  government  officials  and  citizens  generally, and  various  rights  and  privileges  were  secured  to  them.  Both scientists  straightway  proceeded  to  their  duties,  but,  owing  to  the turbulent  conditions  in  the  country,  due  to  the  Eevolution,  they encountered  from  the  beginning  constant  embarrassment  and difficulties.  In  addition  to  being  arrested  and  deprived  of ordinary  facilities  to  carry  on  their  work,  they  met  with  little sympathy  and  co-operation  on  the  part  of  officials  and  people,  and experienced  great  difficulty  in  erecting  and  maintaining  their signals,  which  were  oftentimes  believed  to  have  been  built  for purposes  of  military  communication. Mechain  in  Spain  had  a  certain  amount  of  assistance  from  the government  of  that  country,  but  here,  as  in  southern  France,  he was  harassed  and  interfered  with  by  political  troubles.  In  fact, these  two  resolute  engineers  experienced  almost  incredible difficulties,  being  arrested  by  the  various  governing  bodies  that were  at  that  time  successively  administering  the  affairs  of  France, DEVELOPMENT   OF  THE    METRIC   SYSTEM        61 deprived  of  liberty  and  freedom,  prevented  from  working  by accident  and  disease,  and,  in  short,  accomplishing  most  creditable results  under  remarkably  adverse  circumstances. Finally,  in  November,  1798,  Mechain  and  Delambre,  having completed  their  work,  arrived  at  Paris  with  a  record  of  their observations,  and  an  international  commission  invited  by  the Directory  proceeded  to  examine  and  approve  the  geodetic  and other  scientific  work  accomplished  in  laying  the  foundation  for the  metric  system.  This  commission  consisted  of  delegates  from the  Batavian  Eepublic,  the  Cis-Alpine  Eepublic,  Denmark,  Spain, Switzerland,  the  Ligurian  Eepublic,  Sardinia  (later  from  the  pro- visional government  of  Piedmont),  the  Eoman  Eepublic,  and  the Tuscan  Eepublic,  in  addition  to  a  French  Committee  composed  of the  physicists  and  mathematicians  who  had  been  chiefly  concerned with  the  development  of  the  system.  The  commission  divided itself  into  three  sections,  each  of  which  carried  on  a  most thorough  examination  of  the  work  already  done,  and  made further  calculations  and  verifications  to  establish  its  accuracy  and reliability.1 The  first  section  made  a  comparison  of  the  bar  used  in  measur- ing the  length  of  the  two  bases  at  Melun  and  Perpignan,  and found  that  it  corresponded  exactly  with  the  toise  of  Peru. Examining  the  toise  of  Mairan,  constructed  from  the  length  of the  pendulum  beating  seconds  at  Paris,  it  was  found  to  be  "03413 line  shorter  than  the  toise  of  Peru.  The  second  section  studied the  measurement  of  the  arc  of  meridian  and  the  actual  length  of the  meter,  measuring  the  bases,  examining  the  angles  of  each triangle,  and  finally  computing  separately  their  dimensions,  em- ploying different  tables  of  logarithms.  The  report  which  was prepared  by  Van  Swinden,  the  delegate  of  the  Batavian  Eepublic, one  of  the  committee  to  whom  was  assigned  the  actual  calcula- tion, shows  how  carefully  the  work  had  been  done,  for,  employing the  base  at  Melun  as  a  starting  point  in  computing  the  triangles, it  was  found  that  the  difference  between  the  computed  and measured  lengths  of  the  base  at  Perpignan  was  '160  toise  (12'28 inches  =  31 '19  cm.).  When  it  is  remembered  that  the  length  of the  Perpignan  base  was  6006'25  toises,  and  that  of  Melun  6075*9 1  For  a  full  account  of  this  work  reference  should  be  made  to  Mechain  and Delambre,  Base  du  Systeme  Metrique  (Paris,  1806-1810),  vol.  iii. 62       EVOLUTION   OF  WEIGHTS   AND   MEASURES toises,  and  that  they  were  550,000  toises  apart,  the  accuracy  of the  measurement  may  be  appreciated. The  flattening  of  the  earth  was  also  computed,  employing  the present  measurements  in  connection  with  those  made  in  Peru, and  it  was  found  to  be  3-J-4.1  The  most  important  result  was the  calculation  of  the  length  of  the  quadrant  of  the  earth's meridian,  5,130,740  toises,  which  straightway  gave  3  feet  11*296  *' lignes  as  the  true  length  of  the  meter  instead  of  3  feet  11*442. lignes,  the  length  of  the  provisional  meter  provided  by  the  law  of August  1,  1793. The  third  section,  for  which  Tralles,  the  Swiss  scientist,  pre- pared the  report,  considered  the  determination  of  the  unit  of weight  and  the  construction  of  the  standard  kilogram  which  had been  prepared  by  Lefevre-Gineau,  according  to  plans  made  by Lavoisier  and  Hauy,  who  performed  the  first  experiments  for this  determination.2  The  preparation  of  this  standard  required much  elaborate  experimental  work,  and  it  was  finally  ascertained that  the  weight  of  a  cubic  decimeter  of  distilled  water  at  its temperature  of  maximum  density  and  weighed  in  vacuo,  was *  18,827*15  grains,  the  mean  of  the  sum  of  the  weights  of  Charle- magne, which  had  been  employed  as  the  French  standard  for over  500  years.  While  it  is  not  possible  here  actually  to  describe this  determination  of  the  unit  of  weight,  nevertheless  it  is  inter- esting to  record  that  Lefevre-Gineau  and  his  assistant  Fabbroni *  discovered  that  the  maximum  density  of  water  was  reached  at 4°  Centigrade. From  the  sectional  reports  just  mentioned,  a  general  report was  compiled  by  Van  Swinden  and  presented  to  the  Institute.3 The  actual  meter  standards  were  then  constructed  by  Lenoir  and carefully  compared  with  the  toise  standards.  A  platinum  meter was  adopted  as  the  true  meter,  and  was  deposited  in  the  Archives of  State,  whence  it  was  subsequently  known  as  the  Meter  of  the Archives.     Two  other  platinum  standards4  were  constructed  at  the 1The  accepted  value  to-day  is  x — ,  Clarke's  Spheroid,  1866. r  J       294-9784  r 2  See  Dumas,  Lavoisier's  Works,  vol.  v. 3  See  Mechain  and  Delambre,  Base  du  Systeme  Metrique,  vol.  iii.  p.  592. 4  See  C.  Wolf,  "Recherches  historiques  sur  les  etalons  de  poids  et  mesures  de l'Observatoire,"  Ann.  de  V Observatoire,  Mem.  xvii.  p.  52,  1883 ;  also  Ann.  de Chim.  et  Phys.,  5  s.  vol.  xxv.  p.  5,  1882. DEVELOPMENT   OF  THE   METRIC   SYSTEM        6a same  time,  and  are  now  known  as  the  Meters  of  the  Conservatory and  Observatory  respectively.  Iron  standards  were  constructed also,  and  were  distributed  among  the  delegates.  There  was  also constructed  at  the  same  time  a  platinum  kilogram,  and  these standards  (kilogram  and  meter)  were  formally  presented  by  a delegation  of  the  Institute  to  the  Corps  Legislatif  on  June  22, 1799,  and  after  being  duly  received  were  deposited  in  the Archives  of  the  Eepublic.  On  December  10  of  the  same  year by  statute  the  provisional  meter  was  abolished,  and  the  new meter  and  kilogram  definitely  fixed  and  defined,  and  the  stan- dards presented  by  the  Institute  to  the  Eepublic  were  adopted  as the  definite  standards  of  weight  and  length. This  act  was  known  as  the  law  of  the  19  Frimaire,  year  VIIL, and  is  as  follows.1  "  Article  first. — The  provisional  determination of  the  length  of  the  meter  at  3  pieds,  11  '44  lignes,  ordained  by the  laws  of  Aug.  1st,  1793,  and  the  18th  Germinal,  year  III. (April  7,  1795),  stands  revoked  and  void.  The  said  length,  form- ing the  ten-millionth  part  of  the  arc  of  the  terrestrial  meridian, comprised  between  the  North  Pole  and  the  Equator,  is  definitely fixed,  in  its  relation  with  the  old  measures,  at  3  pieds,  11*296 lignes. "Article  second. — The  meter  and  the  kilogram  in  platinum, transmitted  the  four  Messidor  last,  to  the  Corps  Legislatif,  by the  National  Institute  of  Sciences  and  Arts,  are  the  definite standards  of  the  measures  of  length  and  of  weight  throughout  the Eepublic.  Some  exact  copies  of  the  same  will  be  put  in  the hands  of  the  Consular  Commission,  in  order  to  serve  as  models for  the  construction  of  new  measures  and  new  weights.2 "  Article  third. — The  other  dispositions  of  the  law  of  the  18 Germinal,  year  III.,  concerning  all  that  is  relative  to  the  Metric System,  as  well  as  to  the  nomenclature  and  the  construction  of the  new  weights  and  the  new  measures,  will  continue  to  be observed." Provision  was  made  (Article  IV.)  for  a  commemorative  medal, which,  however,  was  never  made  officially,  and  not  actually  until ^igourdan,  Le  Systeme  Metrique,  (Paris,  1901),  pp.  176-177. 2  This  article  was  repealed  in  the  law  of  July  11,  1903,  by  which  the  inter- national meter  and  kilogram  were  officially  recognized,  and  the  French  copies (meter  8  and  kilogram  35)  were  made  the  national  standards. 64       EVOLUTION   OF   WEIGHTS   AND   MEASURES 1837,  when  the  ideas  of  the  Institute  in  regard  to  such  a  medal were  carried  out  by  MM.  Gonon  and  Penin. With  the  scientific  determination  of  the  units  and  the  con- struction of  the  standards  accomplished,  there  remained  but  to effect  the  general  adoption  of  the  new  weights  and  measures. Several  conditions  tended  to  delay  this,  and  at  times  there  was even  pronounced  opposition.  Chief,  perhaps,  was  the  change  in political  conditions  occurring  in  France,  and  it  was  but  natural to  expect  on  the  part  of  an  imperial  government  little  interest  in reforms  effected  during  the  republican  regime.  Furthermore, there  was  criticism  of  the  system  on  account  of  the  lack  of uniformity  and  organization,  as  shown  by  contradictory  legislation, and  also  on  account  of  its  nomenclature,  much  opposition  being manifested  to  the  use  of  Greek  prefixes.  The  chief  difficulty, however,  was  the  lack  of  secondary  standards,  which  were  to have  been  constructed  and  distributed  at  the  expense  of  the  State. Accordingly,  it  was  necessary  to  repeal  such  legislation,  as  the expense  involved  was  much  greater  than  the  government  could afford.  Moreover,  the  temporary  office  or  agency  of  weights  and measures  had  been  abolished  too  early  to  give  the  much-needed assistance  in  accustoming  the  people  to  the  use  of  the  new system.  There  was  also  embarrassment,  due  to  the  fact  that, previous  to  March  15,  1790,  there  had  been  public  scales  where the  people  could  weigh  their  merchandise.  These  institutions, which  had  been  done  away  with  by  law,  it  became  necessary  to re-establish,  and  this  was  done  for  cities  of  over  5000  inhabitants by  the  Act  of  27  Brumaire,  year  VII.  (November  17,  1798),  and subsequently  for  such  other  cities  as  was  necessary. In  the  meantime,  there  were  not  only  officials  for  weighing and  measuring,  but  also  private  individuals  who  carried  on  a similar  business,  and  were  ready  to  employ  the  old  as  well  as  the new  and  legal  measures.  As  a  result,  serious  abuses  and  frauds prevailed,  and  the  general  appreciation  of  the  merits  of  the  new system  was  decidedly  lukewarm.  Nevertheless,  it  made  progress, and  was  early  adopted  for  all  scientific  works  and  papers published  by  the  Institute  to  the  exclusion  of  all  other  systems. The  growth,  however,  was  not  as  much  among  the  citizens  at large  as  among  the  government  officials  and  scientific  men.  The reasons  given   were    chiefly  that   both    names   and  values   were DEVELOPMENT   OF  THE  METRIC   SYSTEM        65 changed,  that  foreign  names  and  words  were  employed,  that  the names  were  too  long,  and  that  the  old  weights  and  measures  were persistently  used  in  bills  and  accounts.  To  answer  these objections,  but  with  the  result  of  complicating  matters  further,  a decree  was  issued  13  Brumaire,  year  IX.  (November  4,  1800), which  stated  that  the  decimal  system  of  weights  and  measures would  definitely  be  put  into  execution  for  the  entire  republic beginning  1  Vend£miaire,  year  X.,  and,  in  order  to  facilitate  its use,  the  names  given  to  weights  and  measures  in  public  documents, .as  in  customary  usage,  should  be  explained  by  French  names  as given  in  a  list,  which  to  a  certain  extent  corresponded  to  the  simple nomenclature  tentatively  submitted  by  the  committee  of  the Academy  of  Sciences  in  1793.  There  was  to  be  no  synonym  for the  meter,  and  every  measure  to  which  a  public  denomination was  assigned  must  be  a  decimal  multiple  or  subdivision  of  that unit.  For  the  measurement  of  cloth  the  meter,  with  its  tenth and  hundredth  divisions,  was  to  be  employed,  while  the  term Mere  was  to  be  used  still  as  a  measure  of  firewood  and  as  a solid  measure,  a  tenth  part  of  this  measure  being  adopted  for carpentry  and  known  as  a  solive.  The  decree  also  provided  that the  new  names  should  be  inscribed  on  the  weights  already constructed,  and  that  either  one  system  or  the  other  must  be employed. While  this  action  tended  to  weaken  the  integrity  of  the  metric system,  yet  it  preserved  its  fundamental  feature  of  decimal division,  but  it  was  followed  by  a  decree  of  Napoleon  of  February 12,  1812,  which  had  a  most  serious  effect  on  the  work  already accomplished,  and  threatened  its  very  existence.  Despite  the objections  of  Laplace  and  other  scientists,  a  system  of  measures termed  "  usuelle  "  was  established  in  which  the  metric  system  was •employed  as  the  basis,  but  which  made  use  of  such  multiples  and fractions  as  would  bring  about  measures  that  would  harmonize with  those  long  established  by  the  usage  of  commerce  and  of  the people  generally.  The  space  of  ten  years  was  fixed  for  a  period during  which  actual  experience  might  occasion  further  needs  of further  changes  in  weights  and  measures.  The  legal  or  metric system  was  to  be  taught  in  all  the  schools,  including  the  primary schools,  and  was  to  be  employed  in  all  official  transactions, markets,  etc.     To    carry  out    the   provisious  of   this   decree  an E 66       EVOLUTION   OF   WEIGHTS   AND   MEASURES elaborate  series  of  rules  were  published  by  Montalivet,  Minister of  the  Interior,  March  28,  1812. The  " usuelle"  measures  were  all  denned  in  terms  of  the metric  system,  and  there  were  included  a  large  number  corre- sponding to  those  in  daily  use.  Thus  the  toise  was  the  length  of two  meters,  and  was  divided  into  six  feet,  each  of  which  was denned  as  one-third  of  a  meter.  The  foot,  in  turn,  was  divided into  12  inches,  and  each  inch  into  12  lignes.  For  the  measure- ment of  cloth  and  fabrics  there  was  an  aune,  equal  to  12  deci- meters, divided  into  halves,  quarters,  and  sixteenths,  and  also into  thirds,  sixths,  and  twelfths.  These  divisions  for  toise  and aune  were  to  be  marked  along  one  face  of  the  scale  or  measure, while  the  other  must  have  the  regular  metric  divisions  on the  decimal  basis.  Various  weights  and  measures  for  retail business  were  provided  and  denned,  in  which  the  subdivision  was by  halves  or  some  other  non- decimal  factor  not  always  the  same* Thus,  for  the  measure  of  capacity,  such  as  grain,  there  was  the boisseau,  defined  as  ^  of  a  hectoliter,  with  a  double,  half,  and quarter  boisseau.  The  liter  also  was  divided  into  halves,  quarters,, and  eighths,  and  the  shape  and  material  of  measures  for  various liquids  was  specified.  The  lime  or  pound  was  defined  as  equal to  500  grams  or  a  half  kilogram,  and  was  divided  into  16  ounces of  8  gros  each.  Provision  was  made  for  the  verification  and sealing  of  weights  and  measures  by  a  government  bureau,  and also  for  the  construction  and  distribution  of  secondary  standards to  the  various  departments. The  use  of  measures  other  than  the  legal  ones  and  those specified  in  the  decree  was  forbidden  as  contrary  to  law.  The legal  system  was  still  to  be  employed  in  all  government  works, officially  and  in  commerce,  and  it  was  explained  that  the  decree was  designed  only  to  affect  retail  business  and  the  small  trading of  daily  life.  All  formal  notices  must  be  expressed  in  legal measures  rather  than  in  those  tolerated,  and  the  legal  system was  to  be  taught  in  the  public  schools,  including  the  primary schools,  in  its  completeness.  This  law  was  in  force  until 1837,  and  its  results  were  most  unsatisfactory,  since  it  simply added  to  the  confusion  by  increasing  the  number  of  weights, and  measures.  As,  in  any  event,  it  was  necessary  to  wait until  the  people  at  large  gradually  abandoned  the  old  measures, DEVELOPMENT   OF  THE   METRIC   SYSTEM        67 it  served  no  useful  purpose  in  the  transition  period  to  add new  measures  that  essentially  were  neither  new  nor  old. The  prejudice  of  the  people  was  slowly  overcome,  however, and  the  instruction  given  in  the  schools  gradually  had  its effect.  From  government  use  and  general  commerce  the  use of  the  legal  system  extended  slowly  among  retail  dealers  and small  consumers. After  an  experience  of  a  quarter  of  a  century  with  the usuelle  measures,  it  was  thought  that  the  time  had  arrived  to  use the  metric  system  exclusively,  and  an  attempt  to  that  end  was made  in  a  bill  presented  in  the  House  of  Deputies,  February  28, 1837.  The  matter  was  vigorously  discussed  in  the  chamber,  and was  considered  by  several  committees,  by  whom  a  plan  for suitable  legislation  was  proposed.  Attention  was  called  to  the survival  of  the  old  measures  and  their  general  use,  and  to  the fact  that  the  mesures  usuelles,  while  they  had  contributed  much to  increasing  the  use  of  the  metric  system,  nevertheless,  being founded  on  the  measures  of  Paris,  were  not  particularly  useful where  these  measures  had  not  been  previously  employed,  as was  the  case  in  certain  parts  of  the  realm.  A  general discussion  of  nomenclature,  systems  of  division,  etc.,  took  place, but  the  advocates  of  the  metric  system  were  most  earnest  in resisting  any  modifications,  and  it  was  argued  that  the  yield- ing to  prejudice  manifested  in  the  legislation  of  1812  had been  a  serious  mistake.  It  was  also  urged  that  people  forced to  employ  the  new  system,  in  order  to  sell  their  goods,  would soon  learn,  and  that  no  new  measures  should  be  constructed whose  contents  were  not  in  exact  accord  with  the  metric  system. Accordingly,  after  considerable  discussion,  the  following  Act  was passed  by  the  Chamber  of  Peers  and  the  Chamber  of  Deputies, and  was  promulgated  July  4,  1837. Article  I. — The  decree  of  February  12,  1812,  concerning  weights and  measures,  is  hereby  repealed. Article  II. — The  use  of  instruments  for  weighing  and  mea- suring, constructed  in  accordance  with  Articles  II.  and  III. of  said  decree,  shall  be  permitted  until  January  1,  1840. Article  III. — After  January  1,  1840,  all  weights  and  measures, other  than  the  weights  and  measures  established  by  the  laws  of 18  Germinal,  year  III.,  and  19  Frimaire,  year  VIII.,  constituting 68       EVOLUTION   OF   WEIGHTS   AND   MEASURES the  decimal  metric  system,  shall  be  forbidden,  under  the  penalties provided  by  article  470  of  the  Penal  Code. Article  IV. — Those  possessing  weights  and  measures,  other than  the  weights  and  measures  above  recognized,  in  their  ware- houses, shops,  workshops,  places  of  business,  or  in  their  markets, fairs,  or  emporiums,  shall  be  punished  in  the  same  manner  as those  who  use  them,  according  to  article  479  of  the  Penal  Code. Article  V. — Beginning  at  this  same  date  all  denominations of  weights  and  measures  other  than  those  given  in  the  table annexed  to  the  present  law,  and  established  by  the  law  of  the 18  Germinal,  year  III.,  are  forbidden  in  public  acts,  documents, and  announcements.  They  are  likewise  forbidden  in  acts  under private  seal,  commercial  accounts,  and  other  private  legal  docu- ments. Public  officers  violating  this  law  are  subject  to  a  fine of  20  francs,  which  shall  be  collected  compulsorily  as  in  a  matter of  registration.  The  fine  shall  be  10  francs  for  other  violators, and  shall  be  imposed  for  every  single  act  or  writing  under private  signature,  but  in  commercial  accounts  there  shall  be  only one  fine  for  every  case  in  which  the  prohibited  terms  are  used. Article  VI. — Judges  and  arbitrators  are  forbidden  to  render any  judgment  or  decision  in  favor  of  any  particular  items  in the  accounts  or  writings  in  which  the  denominations  forbidden by  the  preceding  article  shall  have  been  inserted  until  the  fines provided  by  the  preceding  article  shall  have  been  paid. Article  VII. — The  inspectors  of  weights  and  measures  shall discover  violations  provided  for  by  the  laws  and  rules  concerning the  metric  system  of  weights  and  measures.  They  may  proceed to  seize  weights  and  instruments  whose  use  has  been  prohibited by  the  said  laws  and  rules.  Their  testimony  in  a  court  of justice  shall  be  considered  as  direct  proof.  The  inspectors  will take  oath  before  the  tribunal  of  the  arrondissement. Article  VIII. — A  royal  ordinance  shall  regulate  the  manner in  which  the  inspection  of  weights  and  measures  shall  be accomplished. As  the  metric  system  gradually  became  firmly  established in  France,  the  French  Government,  through  diplomatic  channels, called  attention  of  the  various  nations  to  its  many  advantages, and,  at  the  same  time,  distributed  a  number  of  copies  of  the Meter  of  the   Archives,  which  had  been  prepared  at  the  Con- DEVELOPMENT   OF   THE   METRIC   SYSTEM        69 servatoire  des  Arts  et  Metiers,  where  now  the  work  of  preparing standards  and  of  carrying  on  other  operations  in  connection  with the  weights  and  measures  took  place.  For  this  bureau,  a  new comparator,  capable  of  exact  measurement  and  facilitating  the operation  of  comparison,  had  been  constructed  by  Gambey,  and  it enabled  a  large  number  of  accurate  standards  to  be  prepared  for commercial  and  industrial  use,  though  in  most  cases  no  remark- able degree  of  precision  was  obtained.  Important  work,  however, was  done  in  the  study  of  platinum  standards  of  the  meter  for  the Prussian  Government,  preparatory  to  the  general  adoption  by that  country,  of  the  metric  system.  This  work  was  carried on  by  Eegnault,  Le  Verrier,  Morin,  and  Brix.1 With  the  growing  use  of  the  metric  system  for  scientific  work, not  only  in  France,  but  throughout  Europe,  the  importance  of the  accuracy  of  its  fundamental  units  became  a  matter  of interest  to  mathematicians  and  geodesists  in  several  countries. Increased  activity  in  geodesy  had  brought  about  a  number  of measurements  of  arcs  of  meridian,  and  with  the  resulting  data it  became  possible  to  compute  anew  the  shape  of  the  earth and  the  length  of  the  quadrant.  Any  change  in  this  last  quantity, of  course,  affected  the  length  of  the  meter  as  the  fundamental unit  of  length,  and  called  it  into  question  as  an  absolute  and natural  standard.  That  such  was  the  case  was  early  demon- strated by  Bessel,2  while  General  T.  F.  De  Schubert  of  the Eussian  Army,  Colonel  George  Everest  of  the  British  Army,  and Captain  A.  E.  Clarke  of  the  British  Ordnance  Survey,  made geodetic  measurements  and  studies,  which  enabled  them  more accurately  to  determine  the  shape  of  the  earth.  As  a  result  of this  work,  it  was  found  impossible  to  depend  upon  the  accuracy of  the  determination  of  the  measurement  of  the  quadrant  of  a great  circle,  as  it  would  vary  in  different  places,  and  required a  most  exact  knowledge  of  the  shape  of  the  earth. These  questions,  it  must  be  remembered,  were  purely  scientific, and  did  not  influence  the  practical  development  of  the  system ^enolt,  "De  la  Precision  dans  la  Determination  des  Longueurs  en Metrologie,"  Rapports  Congr&s  International  de  Physique,  Tome  1,  1900,  p.  45. 2"Ueber  einen  Fehler  in  der  Berechnung  der  Franzosischen  Gradmessuug  und seinen  Einfluss  auf  die  Bestimmung  der  Figur  der  Erde."  Schum.  Ast. Nachrichten,  1844,  vol.  xix.  No.  438,  pp.  98-1160. 70      EVOLUTION   OF   WEIGHTS   AND   MEASURES either  in  France  or  abroad,  but  they  provoked  much  discussion among  scientific  men.  With  the  series  of  world's  expositions, which  began  with  that  at  London  in  1851,  an  opportunity  was given  to  the  people  at  large  to  examine  and  appreciate  the benefits  of  an  international  system  of  measures,  while  statistical and  scientific  congresses  saw  the  advantages  resulting  from  the use  of  uniform  weights  and  measures.  Important  among  these was  a  convention  formed  largely  of  the  official  delegates  to  the Paris  Exposition  of  1867,  which  adopted  a  series  of  resolutions  in which  the  superiority  of  the  metric  system  of  weights  and measures  was  conceded,  the  benefits  of  uniformity  stated,  and  its adoption  by  the  civilized  world  urged.  Furthermore,  the  con- vention deemed  it  advisable  to  advocate  the  study  of  the  metric system  in  the  public  schools,  and  to  recommend  its  use  for scientific  publications,  public  statistics,  postal  service,  in  customs, and  in  all  works  carried  on  by  the  governments. In  the  same  year  the  International  Geodetic  Association,  com- posed of  delegates  from  the  leading  countries  of  Europe,  met  at Berlin,  and  was  engaged  in  the  discussion  of  topics  of  great concern  to  all  interested  in  scientific  measurement.  Inasmuch  as many  of  the  standards  of  length  used  for  base  measurements  were all  end  standards,1  which  doubtless  had  become  worn,  or  possibly were  inexact,  these  geodesists  considered  it  of  the  utmost  import- ance that  there  should  be  new  and  common  standards  as  abso- lutely correct  as  then  existing  conditions  of  metrological  science could  make  them.  This  having  been  done  all  base  measurements could  be  referred  to  the  same  linear  standard,  thus  insuring  that all  European  geodetic  work  could  be  comparable,  and  could  be reduced  so  that  a  degree  of  a  great  circle  of  the  earth  could be  determined  with  accuracy  from  a  number  of  different  measure- ments. This  convention  decided  that  the  interests  of  science  in general,  and  of  geodesy  in  particular,  demanded  a  uniform  decimal system  of  weights  and  measures  throughout  Europe,  and  recom- mended the  adoption  of  the  metric  system  without  essential change,  and   especially  without   the  metric   foot.2     In   order  to 1  There  were  by  this  time  a  few  geodetic  line  standards,  among  others  those  of Spain,  Egypt,  and  probably  that  of  Clarke. 2Berieht  iiber  die  Verhandlungen  der  von  30  September  bis  7  Octobre,  1867,  zu Berlin  abgehaltenen  allgemeinen  Conferenz  der  Europaischen  Gradmessung,  Berlin, 1868,  p.  126. DEVELOPMENT   OF  THE   METRIC   SYSTEM        71 secure  such  a  uniformity  of  measures  the  convention  decided  in favor  of  the  construction  of  a  new  European  prototype  meter differing  in  length  as  little  as  possible  from  the  Meter  of  the Archives  at  Paris,  and  compared  with  it  to  the  highest  degree  of accuracy  possible.  In  its  construction  there  would  be  observed all  refinements  secured  by  the  advance  of  metrological  science, and  especially  there  would  be  considered  its  availability  for comparisons  with  secondary  standards  of  length.  The  con- struction of  the  new  standard  was  to  be  undertaken  by  an international  commission  appointed  by  the  respective  governments, and  the  desirability  of  establishing  an  international  bureau  of weights  and  measures  was  expressed.  Thus  the  metric  system came  to  be  recognized  as  something  of  international  concern,  and its  preservation  and  improvement  a  matter  that  concerned  the world  at  large  as  well  as  France. The  action  of  the  Association  G-eod6sique  was  echoed  by  the St.  Petersburg  Academy  of  Sciences,  and  this  body  expressed  the interest  of  the  scientific  world  at  large  in  a  proper  standard  of mass,  as  well  as  a  new  standard  of  length,  in  a  communication  to the  Paris  Academy  of  Sciences  in  1869,  in  which  they  suggested taking  common  steps  towards  the  establishment  of  an  inter- national metric  system.  This  proposition  was  not  enthusiastically received  in  France,  where  many  of  the  scientific  men  thought that  the  meter  and  the  kilogram  were  the  work  of  French savants,  and  looked  upon  them  as  something  that  should  not  be tampered  with,  especially  by  alien  scientists ;  but  those  more especially  interested  in  metrology  perceived  that  the  application of  recent  advances  in  the  theory  and  practice  of  the  science  of weighing  and  measuring  was  desirable,  and  that  new  standards •could  be  constructed  with  profit,  provided  that  the  original standards  should  remain  as  the  underlying  basis  of  the  system. Accordingly,  on  the  representation  of  the  Paris  Academy  of Sciences,  the  French  Government  took  up  the  matter,  and  after an  examination  of  the  question  in  its  different  aspects  by  a •committee  consisting  of  representatives  from  the  Academy  of Sciences  and  the  Bureau  of  Longitude,  a  report  was  made  in favor  of  the  proposed  plan,  and  the  Minister  of  Agriculture  and Commerce  (Alfred  Leroux)  brought  the  matter  to  the  attention of   the   Emperor,  Napoleon  III.,   in   a   long  and  comprehensive 72       EVOLUTION   OF   WEIGHTS   AND   MEASURES statement,  dated   September  1,  1869,  favoring  the  calling  of  an international  conference.1 This  report  was  approved  by  the  Emperor,  and  the  French Government  communicated  through  diplomatic  channels  with  the various  nations,  inviting  them  to  send  delegates  to  a  conference to  be  held  at  Paris  to  discuss  the  construction  of  a  new  prototype meter  as  well  as  a  number  of  identical  standards  for  the  various participating  nations.  This  action  was  especially  important  as emphasizing  the  international  character  of  the  system  by  allowing the  participation  of  a  number  of  nations  in  the  construction  of  a standard  that  would  serve  for  all,  France  included.  It  was  also an  admission  on  the  part  of  the  French  Government  that  a  new (line)  standard  (mMre  a  trait)  was  necessary,  and  that  every means  should  be  taken  to  conserve  the  metric  system  by  putting its  standards  on  a  permanent  basis. The  invitation  was  accepted  by  the  nations  to  which  it  was extended,  and  in  August,  1870,  delegates  from  twenty -four  States met  at  Paris.  In  the  meantime,  in  order  to  make  suitable preparations,  and  to  lighten  the  work  of  the  International  Com* mission  as  much  as  possible,  the  French  members  had  assembled, and  since  September  1st,  1869,  had  been  actively  engaged  in studying  the  subject,  especially  on  its  scientific  side,  and  preparing a  working  basis  for  the  conference.2  Owing  to  the  breaking  out of  the  war  between  Germany  and  France  this  session  was  of short  duration,  but  it  was  decided  that  instead  of  a  single  new standard  a  number  of  identical  standards  should  be  constructed for  the  nations  participating  in  the  convention,  and  that  one  of the  number  should  be  chosen  as  the  international  standard,  and should  be  deposited  in  some  convenient  place  accessible  to  all  the participating  countries,  and  under  their  common  care. Summoned  anew  by  the  French  Government,  the  International Commission  met  under  more  peaceful  auspices  at  Paris,  on  Sep- tember 24,  1872,  thirty  States  being  represented  by  fifty-one delegates,  among  whom  were  included  many  distinguished scientists,  and,  as  was  natural,  the  foremost  metrologists  of  the world.  By  reason  of  the  previous  session,  and  the  activity  of the  French  committee  in  the  interval  that  had  elapsed,  the work    of    the    Commission   was  very  clearly   mapped    out,   and 1  Bigourdan,  Le  Systeme  Mitrique  (Paris,  1901),  pp.  265-272.  *  Ibid.  p.  273. DEVELOPMENT   OF  THE   METRIC   SYSTEM        73 little  time  was  spent  in  mere  preliminary  discussion.  The  first- and  most  important  announcement  was  the  report  of  the  French Committee,  that  after  a  careful  examination  had  heen  made  of the  standards  of  the  Archives,  the  Meter  was  found  in  a. very  satisfactory  state  of  preservation,  and  in  such  condition as  to  inspire  all  confidence  in  any  operations  for  which  it  might serve  as  a  base.  Likewise,  the  Kilogram  of  the  Archives  also- was  found  to  be  perfectly  preserved.  Comparisons  which  were effected  between  the  prototype  meter  and  its  contemporaries  of the  Conservatory  and  the  Observatory  demonstrated  that  the- Meter  of  the  Archives  had  not  appreciably  altered  in  length.1 The  Commission  was  divided  into  eleven  committees  composed of  delegates  specially  qualified  for  the  separate  branches  of  the- work,  and  the  subjects  assigned  to  each  committee  were  as  follows: Study  of  the  ends  of  the  meter  of  the  Archives,  material  for  the- new  meter,  its  form  and  method  of  support,  thermometry  and expansion,  normal  temperature  of  the  meter  and  kilogram,  weights- in  vacuum  or  in  air,  comparator,  creation  of  an  international  bureau of  weights  and  measures,  weight  of  a  cubic  decimeter  of  waterr material  and  form  of  the  standard  kilogram,  balances  and methods  of  weighing,  and  preservation  of  the  standards  and providing  for  their  invariability. Addressing  themselves  to  the  consideration  of  these  topics,  the commission  speedily  reached  satisfactory  conclusions,  and  specific- resolutions  were  adopted  outlining  the  plans  to  be  followed  and the  direct  decisions  which  the  Commission  had  arrived  at.2 These  resolutions  were  in  substance  as  follows  :  The  Mttre  des- Archives  was  to  be  the  point  of  departure,  and  was  to  be  repro- duced by  a  mMre  a  traits  (line  standard),  it  having  been  found that  the  ends  of  the  platinum  bar  of  the  historic  meter  were sufficiently  well  preserved  to  warrant  employing  it  as  an  original standard.  This  last  matter,  however,  would  be  finally  determined when  the  actual  work  of  comparison  had  commenced.  The- identical  copies  of  the  standard  meter  to  be  furnished  to  each  of 1  Bigourdan,  Le  Systtme  Metrique,  p.  274. 2  For  complete  text  of  resolutions  and  discussion,  see  Bigourdan,  Le  SysQme Mdtrique,  pages  299-313.  A  translation  of  the  same  will  be  found  pages  52-55, "Report  of  the  Committee  on  Coinage,  Weights  and  Measures,"  of  the  House  of Representatives,  46th  Congress,  first  Session,  Report  14,  1879. 74       EVOLUTION   OF   WEIGHTS   AND   MEASURES the  countries  were  to  be  metres  a  traits,  but  at  the  same  time  a number  of  end  standards  {mhtres  a  bouts)  whose  equations  would also  be  determined,  would  be  constructed  for  such  countries  as specially  desired  them.  The  new  standards  were  to  represent the  length  of  a  meter  at  0  degree  centigrade,  and  the  material was  to  be  an  alloy  of  platinum  90  per  cent,  and  iridium  10  per cent.,  with  a  tolerance  of  2  per  cent,  either  in  excess  or  defici- •ency.  The  measuring  bars  were  to  be  constructed  from  a  single ingot  produced  at  one  casting  and  carefully  annealed.  Their length  in  the  case  of  the  metres  a  traits  was  to  be  102  centi- meters, and  their  cross  section  was  carefully  designed  according to  specification  by  Tresca.1  Detailed  instructions  were  also .adopted  for  the  determining  of  the  expansion,  the  marking,  and the  calculation  of  the  equations  of  the  different  standards.  The .action  of  the  Commission  in  reference  to  the  kilogram  was  as follows  (Section  xxii.) :  "  Considering  that  the  simple  relation which  was  established  by  the  originators  of  the  metric  system .between  the  unit  of  weight  and  the  unit  of  volume  is  represented by  the  actual  kilogram  in  a  manner  sufficiently  exact  for  the •ordinary  uses  of  industry  and  of  commerce,  and  even  for  most of  the  ordinary  requirements  of  science  ;  considering  also  that  the exact  sciences  have  not  the  same  need  of  a  simple  numerical relation,  but  only  of  a  determination  of  such  relation  as  perfect  as possible ;  and  considering  the  difficulties  that  would  arise  from  a ^change  in  the  actual  unit  of  the  metric  system,  it  is  decided  that the  international  kilogram  shall  be  derived  from  the  kilogramme <des  Archives  in  its  actual  state."  The  international  kilogram  was to  be  determined  with  reference  to  its  weight  in  a  vacuum,  and the  material  of  the  standards  was  to  be  the  same  alloy  of platinum-indium  as  was  employed  for  the  standard  meters.  In form  the  international  kilograms  were  to  resemble  the  Kilo- gram of  the  Archives,  being  cylindrical,  with  height  equal  to the  diameter,  and  with  the  edges  slightly  rounded.  It  was  also decided  that  the  determination  of  the  weight  of  a  cubic  decimeter of  water  should  be  made  by  the  Commission,  and  that  a  new balance  of  extreme  precision  should  be  constructed  and  employed. The  method  of  weighing  and  determining  the  volume  of  the kilograms  was  outlined,  but  it  was  decided  that,  as  also  in  the 1See  chapter  x.,  p.  254. DEVELOPMENT   OF   THE   METRIC   SYSTEM        75 case  of  the  mUre  des  Archives,  the  kilogramme  des  Archives  should not  be  placed  in  a  liquid  until  the  end  of  the  operations. The  plan  for  actually  carrying  out  the  work  of  the  Commis- sion involved  the  construction  of  as  many  identical  standard meters  and  kilograms  as  were  needed  by  the  countries  interested, all  of  which  should  be  made  and  compared  by  the  Commission, and  required  that  a  standard  meter  and  a  standard  kilogram should  be  selected  as  international  prototype  standards  in  terms of  which  the  equations  of  all  the  others  should  be  expressed. The  actual  construction  of  these  new  standards,  the  tracing  of the  denning  lines,  and  the  comparison  with  the  standards  of  the Archives,  were  entrusted  to  the  French  section  of  the  Commission, which  was  to  perform  the  work  with  the  concurrence  and  under the  general  direction  of  a  permanent  committee  of  twelve  mem- bers duly  appointed  to  have  general  supervision  of  the  work. The  Commission  also  advocated  the  founding  of  an  inter- national bureau  of  weights  and  measures,  to  be  located  at  Paris, which  would  be  both  international  and  neutral,  and  supported  by the  common  contributions  from  the  nations  party  to  a  treaty creating  such  an  establishment.  It  was  proposed  that  it  should be  under  the  supervision  of  the  permanent  committee  of  the International  Metric  Commission,  and  should  be  used  for  the comparison  and  verification  of  the  new  metric  standards,  for the  custody  and  preservation  of  the  new  prototype  standards,  and for  such  other  appropriate  comparisons  of  weights  and  measures as  might  come  before  it  in  proper  course.  In  accordance  with the  suggestions  of  the  Commission,  the  French  Government  again communicated  diplomatically  with  the  various  governments  rela- tive to  the  establishment  of  such  a  bureau,  and  the  reports  of the  various  delegates  having  in  the  meantime  been  made,  and  the project  in  all  its  details  thoroughly  understood,  on  May  20,  1875, a  treaty  was  concluded  at  Paris,  in  which  the  recommendations of  the  Commission  were  put  into  effect.1  This  treaty  was  duly signed  by  accredited  representatives  of  the  following  countries : United    States,     Germany,    Austria-Hungary,    Belgium,    Brazil,2 ^ee  Bigourdan,  Le  Systeme  M&rique,  pp.  328-337.  U.S.  House  Representa- tives, Committee  on  Coinage,  Weights  and  Measures,  46th  Congress,  1st  Session, Heport  No.  14,  pp.  43-50. 2  Brazil  did  not  ratify  the  treaty. 76       EVOLUTION   OF   WEIGHTS   AND   MEASURES Argentine  Confederation,  Denmark,  Spain,  France,  Italy,  Perur Portugal,  Kussia,  Sweden  and  Norway,  Switzerland,  Turkey,  and Venezuela.  Of  the  countries  present  at  the  conferences,  Great Britain  and  Holland  declined  to  participate  in  the  treaty  or  to contribute  to  the  expense  of  an  international  establishment  for the  metric  system.  The  British  Government,  in  explanation  of this  action,  stated  that  they  could  not  recommend  to  Parliament any  expenditure  in  connection  with  the  metric  system,  inasmuch as  it  was  not  legalized  in  that  country,  nor  could  it  support  a permanent  institution  established  in  a  foreign  country  for  its encouragement.  A  change  of  feeling,  however,  took  place  in England,  and  in  September,  1884,  Great  Britain  joined  the Convention.  With  the  treaty  were  signed  at  the  same  time  a series  of  regulations  for  the  newly  created  bureau,  and  a  set of  temporary  or  transient  provisions  referring  to  the  work  already in  hand  which  had  been  undertaken  by  the  French  section  under the  direction  of  the  conference  of  1872. * The  treaty  provided  for  the  establishment  and  maintenance, at  the  joint  charge  of  the  contracting  parties,  of  a  scientific and  permanent  international  bureau  of  weights  and  measures,  to be  located  at  or  near  Paris,  in  a  territory  to  be  kept  strictly neutral.  The  bureau  was  to  be  installed  in  a  special  building, supplied  with  the  necessary  instruments  and  apparatus,  and  was to  be  conducted  by  an  international  committee,  composed  of fourteen  delegates,  each  from  a  different  country,  with  a  personal scientific  staff  of  a  director  with  assistants  and  workmen.  The first  duty  of  the  bureau  would  be  the  verification  of  the  new international  metric  standards  then  in  progress  of  construction, but,  in  addition,  it  would  have  such  permanent  functions  as  the custody  of  the  new  international  metric  prototypes,  all  future official  comparison  with  those  of  the  national  standards,  com- parisons with  the  metric  standards  of  other  units,  the  stan- dardizing of  geodetic  instruments  and  other  standards  and  scales of  precision,  and,  in  short,  to  undertake  such  scientific  work connected  with  metrology  as  would  be  possible  with  its  equip- ment, and  which  would  supply  the  greatest  benefits  to  the supporting  nations.  The  expense  of  the  new  establishment  was to  be  met  by  contributions  from  the  various  signatories  to  the convention,  on  the  basis  of  their  respective  population,  multiplied DEVELOPMENT   OF  THE   METRIC   SYSTEM        77 by  the  factor  3  for  countries  where  the  metric  system  was obligatory,  by  2  where  it  was  legalized  but  not  obligatory,  and  by 1  where  it  was  not  yet  legalized.1 The  treaty  was  ratified  by  the  various  contracting  governments, and  the  international  committee  from  the  conference  of  1872  was continued  under  the  presidency  of  General  Ibanez  of  Spain,  and authorized  to  begin  the  preliminary  operations.  The  first question  was  to  find  a  suitable  location  for  the  laboratories  of the  bureau,  and  this  was  solved  by  the  offer  of  the  French Government  to  turn  over,  without  charge,  the  Pavilion  de  Breteuil, including  a  tract  of  land  about  two  and  a  half  hectars  in  extent, situated  on  the  bank  of  the  Seine  near  Sevres,  at  the  entrance of  the  Park  of  St.  Cloud.2  This  building,  which  is  on  a  hill, dates  back  to  the  time  of  Louis  XV.,  and  was  used  by  kings and  emperors  as  a  palace  and  place  of  resort,  especially  by Napoleon  I.,  who,  it  is  said,  was  at  times  wont  to  study  here. The  pavilion  itself  was  in  bad  repair,  having  been  damaged  in  the siege  of  Paris,  but  the  walls  were  in  good  condition,  and  it  was decided  to  put  the  building  in  order  to  be  used  for  the  offices  of the  bureau  and  the  residence  of  the  staff,  and  to  construct  a  new and  special  building  for  the  actual  scientific  work  and  for  the safe  keeping  of  the  international  prototypes.  The  latter  obser- vatoire  or  laboratory,  a  one-story  building,  was  completed  and the  apparatus  installed  from  1878,  and  has  been  in  constant  use ever  since.  Its  equipment  has  for  the  most  part  been  specially provided,  and  includes,  without  doubt,  the  most  complete  and accurate  instruments  of  precision  in  existence.  Each  of  these merits  a  complete  description,  which  is  of  course  not  possible in  these  pages,  but  some  of  the  essentials  of  the  more  im- portant instruments  will  be  found  described  in  the  chapter  on Standards.3 The  construction  of  the  new  standards  involved  greater difficulties  than  had  been  anticipated.  The  French  section had  melted  an  ingot  of  the  platinum-iridium  alloy  specified  by the  conference  of  1872,  but  it  was  found  to  contain  impurities 1  It  has  recently  (1906)  been  proposed  by  the  Committee  to  drop  the  coefficients. 8  For  description  see  Bigourdan,  Le  Systeme  Me'trique  (Paris,  1901),  pp.  353-362. Ouillaume,  La  Convention  du  Metre  (Paris,  1902),  pp.  21-25. 3  See  chapter  x. 78       EVOLUTION   OF   WEIGHTS   AND   MEASURES in  the  form  of  slight  admixtures  of  rhodium,  ruthenium,  and iron.  This,  accordingly,  provoked  a  controversy,  which,  however, was  settled  by  obtaining  eventually  material  which  satisfied all  the  requirements. From  time  to  time,  as  occasion  demanded,1  the  International Committee  held  various  meetings  connected  with  the  maintenance and  operation  of  the  Bureau  International,  and  in  1887  a resolution  was  passed  denning  the  unit  of  mass  as  follows : "  The  mass  of  the  international  kilogram  is  taken  as  unity  for the  international  use  of  weights  and  measures."2 This  definition  enabled  a  more  perfect  statement  of  the  funda- mental basis  of  the  metric  system  to  be  made,  and  produced  an increased  exactness  which  was  most  desirable.  In  1889  a  second International  Conference  was  assembled,  which  passed  on  the work  of  the  International  Committee,  and  approved  the  standards which  were  submitted  for  their  examination,  together  with  a record  of  all  experiments  and  investigations  that  had  been  made in  their  preparation.  The  conference  definitely  adopted  the international  prototypes  of  the  meter  and  of  the  kilogram  as  the standards  of  length  and  mass  respectively,  and  the  centigrade scale  of  the  hydrogen  thermometer  was  adopted  for  their definition  and  determination.  The  national  prototype  standards were  also  approved,  and  were  distributed  by  lot  to  the  various countries  contributing  to  the  Bureau,  and,  finally,  a  committee was  appointed  to  deposit  the  international  standards, — meter and  kilogram, — in  the  safe  of  the  vault  of  the  Observatory at  Breteuil  designed  for  their  reception,  and  this  was  accom- plished with  the  observance  of  all  due  formality, — the  various keys  of  the  apartment  being  distributed  to  different  officers,5 whose  joint  presence  was  necessary  for  any  examination  of  the standards. Mention  might  properly  be  made  of  the  elaborate  scientific researches  carried  on  at  the  Bureau,  and  the  valuable  memoirs4 1  Formerly  every  year  ;  now  every  two  years. 2  Proces-verbaux  du    Comite"  International    des   Poids  et   Mesures  pour   1887, p.  88. ,  3The  president  of  the  International  Committee,  the  director  of  the  French Archives,  and  the  director  of  the  Bureau. 4  See    Travaux  et   Me" moires  du  Bureau  International  des   Poids   et   Mesures (Paris,  1881—). DEVELOPMENT   OF  THE   METRIC   SYSTEM        79- published  at  frequent  intervals  in  which  these  are  described. With  the  determination  of  the  prototype  standards  for  the  meter and  the  kilogram  accomplished,  many  other  problems  in  metrology, such  as  the  study  of  temperature  measurements,  the  determina- tion of  the  meter  in  terms  of  the  wave-length  of  light,  the construction  of  standards  for  electrical  measurements,  the  study of  alloys  for  standards,  especially  those  used  in  geodesy,  etc.,, have  received  attention  from  the  scientific  staff,  and  the  work accomplished  has  been  of  marked  and  permanent  value. CHAPTER    III. DEVELOPMENT  OF  THE   METRIC  SYSTEM  IN  EUROPE. While  an  international  system  of  weights  and  measures  was ■contemplated  by  the  French  scientists,  yet  in  the  formulation  of the  metric  system  comparatively  little  general  interest  was manifested  by  other  nations,  and  comparatively  little  aid  was given  by  their  scientific  men.  We  have  seen  how  an  international •commission  of  scientists  examined  and  approved  the  determination of  the  meter  and  kilogram,  and  the  important  parts  played  by Van  Swinden  and  Tralles  in  this  work  of  verification.1  These foreign  delegates  appreciated  the  advantages  of  the  new  system, as  did  other  men  of  science,  but  the  times  were  unpropitious  for innovations  which  would  unsettle  and  change  the  ordinary  habits .and  customs  of  the  people.  Inasmuch  as  France  was  at  war with  the  greater  part  of  Europe  during  the  opening  years  of  the nineteenth  century,  the  mere  mention  of  the  source  of  reforms  in weights  and  measures  was  in  many  instances  an  argument  against their  adoption.  Furthermore,  the  actual  governments  themselves were  changing  constantly  in  many  parts  of  Europe,  and  the struggle  for  territory  and  national  existence  was  of  more  im- mediate importance  than  such  minor  matters  as  those  concerning commerce  and  the  domestic  life  of  the  people.  Indeed,  had  the change  been  attempted  generally  at  this  time  it  would  hardly have  met  with  success ;  for,  as  we  have  seen  in  the  case  of  France, not  only  was  compulsory  legislation  eventually  necessary,  but  an 1  The  names  of  nine  foreign  scientists  were  attached  to  the  documents  accom- panying the  standard  meter  and  kilogram  when  given  to  the  French  Government for  deposit  in  the  Archives. THE   METRIC   SYSTEM   IN   EUROPE  81 able  and  active  administration  working  on  some  wise  and  per- manent plan  was  required  to  put  it  into  effect.  Consequently, before  any  general  consideration  of  adopting  the  new  system could  take  place,  it  was  necessary  that  there  should  be  perman- ence and  stability  in  the  various  governments. As  the  fixing  of  weights  and  measures  is  manifestly  an attribute  of  government,  so  any  successful  reforms  must  depend upon  the  character  and  strength  of  a  particular  government,  and in  order  to  influence  neighboring  countries  the  territory  affected should  be  comparatively  large  and  the  number  of  its  inhabitants considerable.  Consequently  the  adoption  of  the  metric  system, in  a  half-hearted  way,  by  a  petty  kingdom  here  and  a  principality there,  likely  at  any  time  either  to  be  absorbed  by  its  neighbors,  or to  conquer  and  to  rule  them,  would  and  did  have  little  influence on  the  general  ultimate  use  of  the  new  weights  and  measures. This,  however,  must  not  be  understood  as  implying  that  at  the beginning  of  the  nineteenth  century  there  was  no  need  for reforms  either  in  Europe  at  large  or  in  particular  states. Mediaeval  conditions  survived,  and  the  same  evils  that  prevailed in  France  were  experienced  throughout  Europe.  The  same  name was  applied  to  measures  whose  values  varied  considerably  not only  in  different  states  but  even  in  different  cities  of  the  same state.  Lack  of  uniformity,  both  in  units  and  standards,  was universal,  with  the  natural  result  of  hindering  commerce  and  of generally  cheating  the  less  intelligent  party  to  any  transaction. True,  French  conquest  had  carried  with  it  the  metric  system,  but it  was  used  merely  under  compulsion,  and  so  soon  as  there  was  a change  in  political  conditions  the  old  measures  were  resumed. Aside  from  the  scientific  propaganda,  due  to  the  undisputed pre-eminence  of  French  workers  in  exact  and  applied  science, comparatively  little  could  be  done  towards  forcing  the  issue,  and the  adoption  of  the  metric  system  waited  largely  on  political circumstances  which  affected  the  life  and  commerce  of  the  people at  large,  and  which  were  duly  appreciated  by  statesmen.  These conditions  were  brought  about  by  the  decline  of  war,  and  the resulting  opportunity  for  the  people  to  turn  to  the  pursuits  of farming,  commerce,  and  manufacturing.  If  a  number  of  states  or cities  were  brought  into  closer  political  relations,  forming  a  larger state    or    possibly  a    confederation,    their    commercial    relations F 82       EVOLUTION   OF  WEIGHTS   AND   MEASURES naturally  developed,  and  in  order  to  increase  the  wealth  and resources  of  the  state,  both  material  and  military,  it  was  essential that  the  government  should  take  such  measures  as  would  best stimulate  commerce  and  manufactures.  Accordingly,  it  was  early recognized  that  uniformity  of  weights  and  measures  within  the boundaries  of  a  state  not  only  contributed  but  was  essential  to the  welfare  of  its  inhabitants,  while,  furthermore,  its  foreign commerce  was  increased  by  having  the  same  weights  and measures  as  its  neighbors.  When  we  join  to  these  considerations the  fact  that  the  separate  systems  in  nearly  all  cases  were illogical,  inconvenient,  and  lacking  in  uniformity  and  facility  of use,  we  have  the  explanation  of  the  eventual  spread  of  the  metric system  in  Europe. On  the  return  of  Tralles  from  Paris  he  endeavored  to  introduce into  Switzerland  the  metric  weights  and  measures,  and  on  March 4th,  1801,  a  law  was  passed  adopting  these  measures  ;  but,  against his  advice,  special  names  were  given^  to  the  various  measures. Likewise,  Van  Swinden,  after  his  return  to  Holland  from  Paris, attempted  to  bring  about  the  adoption  of  the  metric  weights  and measures  in  his  own  country,  and  in  1802  the  Corps  Legislatif decided  in  part  on  the  new  system.  Yet  so  many  features  were lacking  from  their  plan,  that  the  completeness  and  general availability  characteristic  of  the  system  were  much  impaired,  to the  great  regret  of  the  scientist.  No  record  has  been  found  to .indicate  whether  the  law  was  repealed  or  never  came  into  effect, but  with  the  invasion  of  Holland  by  Napoleon,  a  decree  of January  11,  1811,  referred  the  weights  and  measures  of  that country  to  those  of  the  metric  system.1 In  Milan,  in  1803,  the  meter  and  the  kilogram  were  adopted  as the  basis  of  a  series  of  measures  arranged  on  a  decimal  scale,  but new  and  local  names  were  given  to  them.  Thus  the  braccio,  as the  unit  of  length,  was  equivalent  to  the  meter,  while  the  kilogram was  known  as  a  libbra  metrica,  or  metric  pound.  In  Baden,  in 1810,  a^jfund,  equal  to  one-half  of  the  kilogram,  was  adopted  as  the unit  of  weight,  and  was  decimally  subdivided.  The  unit  of  linear measure  was  the  ruthe,  which  was  equivalent  to  three  meters, 1Bigourdan,  Le  Systeme  M&rique,  p.  241.  On  August  21,  1816,  a  law  was. enacted  establishing  the  metric  system,  and  later  additional  Acts  were  passed which  will  be  alluded  to  in  the  course  of  a  few  pages. THE   METRIC   SYSTEM   IN   EUROPE  83 while  the  dry  and  liquid  measures  of  capacity  were  also  defined in  terms  of  the  French  metric  measures.  However,  subsequent legislation  was  required,  and  by  an  order  dated  August  21,  1828,  the new  measures  were  made  compulsory  with  the  year  1831.  Some- what similar  steps  were  taken  also  in  Hesse-Darmstadt  in  1821, the  pfund  and  the  shoppen  being  made  equal  to  one-half  a  kilogram and  one-half  a  liter  respectively,  while  the  fuss,  or  linear  unit,  was one-fourth  of  the  meter,  and  the  elle  four-fifths.  In  Switzerland, in  1828,  it  was  proposed  to  adopt  a  common  system  of  weights  and measures  for  the  various  cantons,  and  in  1835  twelve  of  these divisions  entered  into  an  agreement  known  as  the  "  Maass concordats,"  to  which  reference  will  be  made  later.  This  plan consisted  essentially  of  the  usual  measures  defined  in  terms  of  the metric  units. The  French  Government,  as  we  have  seen,  having  experienced difficulty  in  securing  the  exclusive  use  of  the  metric  system  by  its own  people  did  not  take  active  measures  towards  extending  its  use abroad  until  after  the  passage  of  the  law  of  1837,  which  rendered the  system  universal  and  compulsory  throughout  France.  In  1841 the  Minister  of  Agriculture  and  Commerce,  Cunin-Gridaine,  con- sidered that  much  good  would  be  accomplished  by  the  exchange of  standards  of  weights  and  measures  between  France  and  the important  commercial  countries  of  the  world.  He  was  supported by  the  Minister  of  Foreign  Affairs,  Guizot,  who  arranged  for  such an  exchange  through  the  diplomatic  channels  of  the  various governments.1  Accordingly  these  standards  were  duly  sent,  and in  1853  the  United  States  received  a  complete  series  of  French standards,  which  included  a  steel  meter  that  had  been  compared with  the  platinum  standard  at  the  Conservatoire  des  Arts  et Metiers,  and  likewise  a  gilt  kilogram  whose  constants  had  been determined  in  terms  of  the  kilogram  of  the  Archives. The  beginning  of  a  general  feeling  in  favor  of  the  universal adoption  of  a  single  system  of  weights  and  measures,  and  the opinion  that  for  this  purpose  the  metric  system  was  the  most suitable,  may  be  considered  to  date  from  the  London  Exposition of  1851,  to  which  reference  has  already  been  made.  Despite the  fact  that  metric  weights  and  measures  had  been  used,  and their  adoption  advocated  by  scientific  workers,  it  cannot  be  said 1  Bigourdan,  Le  Systeme  M6trique,  p.  245. 84       EVOLUTION   OF   WEIGHTS   AND   MEASURES that  before  this  time  the  importance  of  the  subject  was  recognized generally,  and  that  economists  and  statesmen  had  thoroughly realized  the  benefits  that  would  ensue  from  a  single  and universal  system  of  weights  and  measures,  as  well  as  a  common and  universal  basis  for  coinage,  in  which  there  should  be  a single,  and  preferably  decimal,  principle  of  division.  But  from such  a  beginning  the  agitation  spread,  and  nearly  every  nation soon  had  a  group  of  earnest  advocates  of  the  metric  system, which  included  not  only  such  scientific  men  as  chemists, physicists,  astronomers,  and  engineers,  not  to  mention  economists and  statisticians,  but  also  merchants  and  manufacturers.  This was  due  to  the  bringing  together  from  many  quarters  of  the globe  of  a  large  number  of  representative  merchants,  producers, and  manufacturers,  with  their  various  wares  and  products,  and also  scientific  men  and  others  who  were  called  to  pass  upon  the comparative  merits  of  the  various  articles  on  exhibition.  At the  conclusion  of  the  London  Exposition,  the  Society  of  Arts, in  a  communication  addressed  to  the  Lords  of  the  Treasury,  asked if  it  were  not  possible  that  some  arrangement  could  be  made whereby  a  universal  decimal  system  of  moneys,  weights,  and measures  could  be  adopted  in  common  for  all  the  nations  of  the world.  This  was  possibly  the  first  expression  in  England,  outside of  scientific  circles,  of  the  general  advantages  of  universal  weights and  measures,  and  particularly  those  that  would  accrue  to  com- merce by  the  adoption  of  a  uniform  decimal  system.  In  1855 an  international  statistical  congress  was  held  at  Paris,  and  on the  motion  of  James  Yates,  a  member  of  the  Eoyal  Society of  London,  it  was  decided  to  form  an  International  Association, to  advance  the  adoption  of  a  decimal  system  of  weights  and measures  and  moneys.  This  association  made  an  examination  of the  different  systems  employed  throughout  the  earth,  and  decided that  the  metric  system,  on  account  of  its  scientific  character  and general  availability  for  international  trade,  was  to  be  preferred, and  accordingly  made  a  recommendation  in  its  favor.  The sentiment  was  further  echoed  by  members  of  the  International Jury  of  the  Paris  Exposition  of  1855,  who  formally  adopted resolutions  in  favor  of  the  metric  system,  recommending  it  to the  attention  of  their  respective  governments,  and  urging  its adoption  on  the  ground  that  it  would  not  only  promote  commerce, THE   METRIC   SYSTEM   IN   EUROPE  85 but  also  peace  and  unity  of  feeling  throughout  the  world,  praising especially  its  decimal  basis.1 A  Committee  of  Weights  and  Measures  and  of  Moneys,  com- posed of  delegates  of  various  countries  to  the  Paris  Exposition of  1867,  was  formed  at  the  initiative  of  these  delegates,  and  took action  in  favor  of  the  decimal  system,  and  urged  the  adoption of  uniform  weights  and  measures  throughout  the  world.  While this  committee  enjoyed  no  official  standing,  yet  it  adopted  reso- lutions recommending  the  study  of  the  metric  system  in  all  the schools,  and  its  recognition  in  all  public  meetings.  Furthermore, its  exclusive  use  in  scientific  and  statistical  publications,  for postal  purposes,  in  the  customs,  as  well  as  in  public  works, and  in  all  other  branches  of  government  administration  was recommended.2 In  the  meanwhile,  the  inconvenience  and  confusion  caused  by different  weights  and  measures  throughout  Central  Europe  had reached  a  point  where  positive  action  was  necessary.  Under more  peaceful  conditions,  commerce  and  industry  were  beginning to  flourish,  and  the  lack  of  uniformity  in  weights  and  measures was  proving  a  serious  hindrance  to  trade.  In  a  comparatively small  territory  there  was  a  considerable  number  of  different states  with  different  systems  of  weights  and  measures,  as  well  as with  different  tariff  and  customs  regulations,  which  seriously interfered  with  the  easy  transaction  of  international  business. The  multiplicity  of  these  measures  involved  the  employment  of an  inordinately  large  number  of  clerks  and  computers  in  custom houses  and  counting  rooms  to  change  from  one  system  to  another weights,  measures,  and  moneys,  as  specified  in  invoices,  and  other documents.  It  was  doubtless  also  realized  that  to  carry  on commerce  there  must  be  an  easy  standard  of  comparison  between the  goods  of  the  home  country  and  those  of  other  foreign  coun- tries. The  money  alone  was  recognized  as  a  sufficient  cause  of trouble,  and  extensive  reforms,  such  as  the  decreeing  of  uniform (Metric)  weights  for  metallic  currency  by  the  Vienna  Coin Treaty  of  January  24,  1857,  and  a  similar  action  by  the  so-called Latin  Union  of  1865,  improved  materially  conditions  in  this respect,  and  it  may  be  remarked  that  in  both  instances  the currency  was  put  on  a  decimal  basis. 1  Bigourdan,  Le  Systeme  Mttrique,  p.  248.  2  Ibid.  p.  248. 86       EVOLUTION   OF   WEIGHTS   AND   MEASURES With  the  weights  and  measures,  however,  the  first  steps  to- ward uniformity  were  taken  when  the  metric  system  was  adopted for  customs  purposes,  some  time  before  its  legal  adoption  for general  use  in  the  separate  states.  Thus  the  German  Zollverein (Customs  Unions)1  adopted  for  use  in  the  customs  a  standard metric  pound  {zollpfund)  which  was  one-half  of  a  kilogram,  and with  it  a  centner  of  50  kilograms.  These  units  of  weight  came into  effect  January  1,  1854,  and  the  pfund,  which  was  divided into  30  loth,  was  adopted  by  the  German- Austrian  Zollverein,  for postal  purposes,  on  the  same  date.  In  1856  the  use  of  the  metric pound  and  centner  was  further  extended,  and  in  1857  a  coin pound  or  munzpfund  (500  grams)  was  employed  for  coinage purposes.  The  railways  also  followed  the  example  set  by  the customs,  and  throughout  the  countries  constituting  the  Zoll- verein all  freight  was  weighed  by  the  metric  pound.  Thus  it will  be  seen  that  the  entering  wedge  of  the  metric  system  in Europe  outside  of  France  was  in  the  adoption  of  uniform  weights for  international  trade,  which  led  to  a  general  knowledge  of  its merits  and  appreciation  of  the  advantages  of  uniformity. The  natural  and  immediate  result  was  the  adoption  of  the "  zollpfund  "  as  the  unit  of  weight  in  a  number  of  states,  and  with this  came  a  general  understanding  of  the  inconvenience  attending the  use  of  different  standards  for  measures  of  length,  capacity, etc.  In  consequence,  a  commission  of  scientific  men  was appointed  from  the  federated  German  states  to  examine  the question  thoroughly,  and  formulate  a  national  system  of  weights and  measures.  They  reported  in  1861  that  the  metric  system already  possessed  the  advantages  sought  after,  and  that  greater benefits  would  ensue  from  its  adoption  as  a  whole  than  by devising  a  new  system  or  by  endeavoring  to  harmonize  existing standards. The  method  of  the  change  in  Germany  is  well  worth  careful study  from  the  student  of  metrology  and  of  public  affairs,  inas- much as   here  were  represented   most    of    the  problems   which 1  The  Zollverein,  or  union  of  German  states  to  secure  among  themselves  freedom of  trade  and  uniformity  of  duties  on  foreign  imports,  was  proposed  by  Prussia  in 1818.  The  North  and  South  German  Unions,  formed  for  this  purpose,  were united  in  1829  by  a  treaty  which  became  effective  in  1834,  and  in  1854  a  strong union  of  nearly  all  the  German  states  was  brought  about. THE   METRIC   SYSTEM   IN   EUROPE  87 would  be  encountered  were  the  same  change  to  be  made  in  the near  future  either  in  the  United  States  or  in  Great  Britain.  In fact,  the  conditions  may  be  said  to  be  practically  the  same,  for although  standards  and  processes  based  on  Anglo-Saxon  measures have  since  developed  to  such  an  extent  that  a  change  would  be  a serious  matter,  yet,  at  the  same  time,  the  use  and  knowledge  of the  metric  system  have  also  increased,  so  that  on  this  score  the change  would  be  far  less  difficult  now  than  it  was  for  Germany in  1870.  Furthermore,  reforms  in  arbitrary  gauges  and  methods of  measurement  are  now  required  in  various  lines  of  industry  and manufacturing,  which  make  the  present  an  especially  appropriate •time  for  a  general  change  in  measures.  Consequently,  by  study- ing methods  and  conditions  in  Germany  at  the  time  of  this change,  it  is  fair  to  say  that  an  accurate  knowledge  of  the  general features  of  any  present  problems  of  this  description  will  be  gained, and  it  is  also  safe  to  say  that  the  final  advantageous  outcome would  be  reproduced  in  either  the  United  States  or  Great  Britain, though  the  time  necessary  to  accomplish  such  a  consummation  may reasonably  be  a  subject  for  difference  of  opinion  and  argument. The  first  legislative  step  in  the  introduction  of  the  metric system  into  Germany  was  the  adoption  of  resolutions  to  that effect  by  the  Federal  Council  and  the  Parliament  of  the  North German  Confederation,  which  were  published  under  the  date  of August  17,  1868.1  These  resolutions  provided  that  the  metric system  should  be  adopted  in  place  of  the  weights  and  measures previously  in  use,  and  that  the  system  should  be  optional  on January  1,  1870,  and  obligatory  on  January  1,  1872.  No  change in  the  nature  or  execution  of  this  plan  occurred  when  in  April, 1871,  the  confederation  was  superseded  by  the  empire.  There was  duly  established  the  "  Normal- Aichungs-Kommission,"  which was  charged  with  the  work  of  furnishing  detailed  directions  and specifications  as  to  the  material,  shape,  and  other  characteristics of  the  weights  and  measures,  and  also  with  supplying  the *'  marking  "  office  and  its  various  local  branches  with  such  imple- ments as  would  enable  it  to  mark  and  stamp  all  weights  and measures  which  should  be  presented  to  it.     It  was  also  ordered 1  W.  Foerster  (former  Chief  of  the  German  Bureau  of  Weights  and  Measures, and  President  of  the  International  Committee  of  Weights  and  Measures),  pp.  12, 13,  House  of  Representatives,  Paport  No.  2885,  54th  Congress,  2nd  Session,  1897. 88       EVOLUTION   OF    WEIGHTS   AND   MEASURES that  the  confederated  governments  publish  the  calculations  giving the  figures  for  the  legal  equivalents  of  the  new  weights  and measures  as  compared  with  the  old.1  The  Commission  had  charge of  the  introduction  of  the  new  system  throughout  the  confedera- tion, supervising  all  measures  to  facilitate  its  speedy  acceptance, and  with  definitely  carrying  it  into  effect.  The  various  states  of the  confederation  appointed  officials  for  the  actual  marking  and stamping  of  the  measures  and  weights,  and  prescribed  regulations for  the  administration  of  such  bureaus.  In  the  ten  months previous  to  the  date  assigned  for  the  beginning  of  the  optional use  of  the  metric  weights  and  measures,  the  Commission  provided all  the  marking  offices  with  standards  for  the  verification  of  such weights  and  measures  as  should  be  presented  to  them  for  legaliza- tion, and  immediately  after  these  needs  had  been  met  the manufacturers  were  provided  with  proper  standards,  so  that  they could  at  once  commence  the  manufacture  of  weights  and  measures for  general  sale  and  use.  Such  weights  and  measures,  adequate in  number  and  of  high  accuracy,  were  soon  forthcoming,  and  by the  end  of  the  first  half  of  the  year  1870  a  large  part  of  the people  of  Germany  became  well  acquainted  with  the  new measures,  their  decimal  division  appealing  particularly  to  the industrial  and  technical  workers. In  1870  occurred  the  war  with  France,  and,  while  it  prejudiced many  of  the  people  against  the  new  weights  and  measures,  never- theless it  more  closely  united  Germany  and  thus  offset  any difficulties  on  this  score.  In  short,  on  the  arrival  of  the specified  date,  January  1,  1872,  when  the  use  of  the  old  weights and  measures  must  cease  and  the  metric  system  be  the  only legal  system,  not  only  were  the  new  weights  and  measures supplied  to  all  places  throughout  Germany  where  merchandise was  sold,  but  the  various  tradesmen  and  others  concerned  had actually  learned  the  use  of  meter  sticks,  liter  measures,  and  the series  of  gram  weights.  This  record  is  somewhat  remarkable,, as  in  Germany  there  was  not  one  system  of  weights  and measures,  but,  as  has  been  shown,  a  large  number  of  different systems  which  the  new  measures  had  to  supplant.  Germany, however,  enjoyed  one  great  advantage  in  the  adoption  of  the metric  system  in  the  extensive  use  in  a  number  of  the 1  Same  Report,  pp.  7,  8. THE   METRIC   SYSTEM   IN   EUROPE  89- states  of  the  "  zollpfund "  or  customs  pound,  above  mentioned, which  we  have  seen  was  the  weight  of  500  grams  or  a  half kilogram.  Weights  of  this  denomination  were  actually  in existence  in  considerable  numbers  and  were  widely  employed, but  the  subdivisions  were  not  usually  on  a  decimal  or  metric basis,  and  only  in  one  state,  Hanover,  was  there  a  division  into 1000  half  grams.  Two  of  these  pfund  weights  immediately furnished  a  legal  kilogram,  and,  while  their  use  interfered somewhat  with  the  development  of  the  decimal  principle,  never- theless it  served  to  accustom  the  people  at  large  to  the  new mode  of  reckoning.  The  liter  measures  were  accepted  even more  readily  than  those  of  mass.  The  relation  between  the unit  or  liter  and  the  measure  of  length  and  the  weight  of  water served  to  commend  the  new  system  readily  to  those  dealing- with  fluids,  while  a  number  of  simple  tables  were  prepared officially  to  explain  the  simplicity  of  the  system. In  contrast  to  the  ease  with  which  the  liter  and  the  gram series  were  adopted,  mention  must  be  made  of  the  change in  the  measures  of  length.  The  principal  measures  of  length were  the  ell  and  the  foot,  which,  though  varying  greatly  among the  various  German  states  from  a  metrological  standpoint,  were approximately  the  same,  or  sufficiently  so  at  least,  to  conveys to  the  ordinary  person  a  certain  rough  idea  of  extension  which for  many  purposes  sufficed.  Furthermore,  the  foot  and  ell differed  so  much  from  the  meter  and  its  subdivisions  that  the purchasing  public  could  not  transfer  readily  the  price  of  cloth  or other  material  when  conceived  or  expressed  in  these  units  to  the meter,  and  thus  obtain  even  an  approximate  idea  of  value.  It was  also  argued  that  the  meter  was  not  as  convenient  to  think in  as  the  foot  for  architects  and  mechanics,  by  some  of  whom opposition  to  the  new  measures  was  manifested ;  but  this  feeling soon  died  away,  and  the  new  measures  were  soon  universally employed  in  all  works  and  calculations. That  the  metric  system  has  contributed  materially  towards  the- upbuilding  of  German  commerce  and  industry  is  universally conceded,  but,  of  course,  since  its  adoption  so  many  causes  have acted  to  this  end,  that  it  is  not  possible  to  state  precisely  just what  part  the  international  measures  have  played.  Suffice  it  to say,  that  in  manufacturing,  especially  of  articles  where  precision r 90       EVOLUTION   OF   WEIGHTS   AND   MEASURES of  measurement,  and  interchangeability  of  parts  are  essential, the  Germans  have  vastly  improved  and  increased  their  output, which  must  in  a  certain  degree  be  due  to  this  cause.  Inasmuch as  the  metric  system  was  employed  extensively  in  scientific work  previous  to  its  general  adoption,  the  increased  activity  of German  investigators  in  fields  where  measuring  is  essential  is not  necessarily  a  result,  but  the  readiness  with  which  industrial workers  have  availed  themselves  of  the  scientists'  labors  has doubtless  been  facilitated  by  the  fact  that  their  processes  and results  were  expressed  in  a  language  that  readily  could  be understood.1 Austria,  where  there  was  much  the  same  variation  of  feet, pounds,  etc.,  as  in  Germany,  followed  that  country's  example, and  on  July  23,  1871,  the  Parliament  passed  a  law  providing for  the  permissive  use  of  the  metric  system  after  January  1, 1873,  and  its  compulsory  use  after  January  1,  1876.  At the  same  time  it  published  official  tables  of  equivalents between  the  old  and  new  measures,  and  established  a  standard meter,  which  was  an  end  standard  of  glass,  and  a  standard kilogram  of  rock  crystal,  these  being  legally  supplanted  in 1893  by  the  copies  of  the  international  standard  meter  and kilogram  received  from  the  International  Bureau.  The  old measures,  especially  those  known  as  the  "  Lower  Austrian System,"  were  quite  unlike  those  of  the  metric  system,  and  at first  it  would  appear  that  there  would  have  been  great  difficulty in  bringing  about  a  change ;  but  for  a  while  a  binary  system of  division  was  tolerated,  and  certain  weights  and  measures approximate  in  value  to  the  older  ones  temporarily  were employed.  In  the  meantime  newspapers  and  schools  were zealously  educating  the  people  to  the  new  order,  while  the government  prepared  an  adequate  number  of  approved  weights and  measures,  as  well  as  supervised  the  construction  of  others according  to  standard  regulations.  The  four  years  appointed for  the  transitional  period  proved  ample,  and  there  was  no expressed  or  obstinate  resistance  on  the  part  of  the  people. In  fact,  it  was  the  general  opinion  that  any  lack  of  completeness 1See  Promemoria  of  German  Imperial  "  Normal- Aichungs  Kommission  "  in House  of  Representatives,  Report  No.  2885,  54th  Congress,  2nd  Session,  1897, pp.  7-9. THE   METRIC   SYSTEM   IN   EUROPE  91 in  the  adoption  of  the  system  was  due  rather  to  laxity  on  the part  of  the  municipal  authorities  than  to  any  pronounced  feeling of  the  public  at  large.1 In  Hungary,  by  the  law  of  1874,  Article  VIII.,  the  metric system  was  established  to  be  in  force  from  January  1,  1876,  but its  use  was  sanctioned  six  months  earlier,  and  finally,  in  1901,  the international  standards  were  duly  established  by  law.  The method  of  making  the  change  was  in  the  main  the  same  as  in Austria,  and  the  new  weights  and  measures  were  quickly naturalized  and  adopted  by  the  people  generally,  though  in isolated  districts  the  old  usage  was  maintained  for  many  years. Outside  of  France,  Belgium  is  one  of  the  earliest  countries  to use  the  metric  system,  as  it  was  established  there  by  the  law  of August  21,  1816,  at  a  time  when  that  country  was  united  with Holland.2  The  names  of  the  old  units  were  applied  to  the metric  values,  but  instruction  in  the  metric  system  was  given  in the  schools,  so  that,  after  the  system  had  been  rendered  com- pulsory from  1820,  by  1836  it  was  possible  to  withdraw  the Belgian    names,   and    in   1855   the  exclusive  use  of   the  French 1See  pp.  9,  10,  House  of  Representatives,  Report  No.  2885,  54th  Congress, 2nd  Session,  1897.  In  addition  to  this  report,  which  contains  information furnished  by  European  governments  to  ambassadors  and  ministers  of  the  United States  on  the  subject  of  the  adoption  of  the  metric  weights  and  measures  by the  different  countries,  a  summary  of  foreign  legislation  on  the  Metric  System prepared  by  J.  K.  Upton,  chief  clerk  of  the  Treasury  Department,  and  later Assistant  Secretary  of  Treasury,  contained  in  Report  No.  14,  House  of  Repre- sentatives, Committee  on  Coinage,  Weights  and  Measures,  46th  Congress,  1st Session,  1879,  has  been  drawn  upon  for  dates  and  details  given  in  the  following pages  concerning  the  adoption  of  the  metric  system  by  the  nations  of  Europe. Somewhat  more  recent  are  the  summaries  contained  in  Guillaume,  La  Convention du  Metre  (Paris,  1902),  Annexe  iv.  pp.  218-226;  "Resume  de  quelques  Legis- lations relatives  aux  Poids  et  Mesures,"  Annexe  aux  Proces-verbaux  des  Stances du  Comite'  international  des  Poids  et  Mesures,  Session  de  1901,  2e  Serie,  Tome  1 (Paris,  1901) ;  Reports  from  Her  Majesty's  Representatives  in  Europe  on  the  Metric System,  part  i.,  July,  1900,  English  Parliamentary  Accounts  and  Papers,  1900, vol.  xc.  ;  Reports  from  Her  Majesty's  Representatives  Abroad,  part  ii.,  February, 1901,  English  Parliamentary  Accounts  and  Papers,  1901,  vol.  lxxx.  The  latter are  particularly  full,  and  give  an  interesting  account  of  the  transition  period,  as well  as  the  extracts  from  the  laws  in  many  instances.  There  is  also  available  the Beizieme  Rapport  aux  gouvernements  signatoires  de  la  Convention  du  Metre  and  the Comptes  rendus  de  la  deuxieme  Conference  generate  des  Poids  et  Mesures,  1895. 2  See  ante,  p.  82. 92       EVOLUTION   OF   WEIGHTS   AND   MEASURES names  and  measures  was  established  by  law.  The  Belgian standards  of  mass  and  length  were  copied  from  those  in  France, being  legalized  in  1848,  but  they  were  damaged  in  the  fire  of 1883  at  the  Palais  du  Nation,  so  that  the  international  prototypes which  were  received  in  1894,  and  duly  legalized,  were  most acceptable. The  use  of  the  metric  system  in  Egypt  is  of  interest,  inasmuch as  that  country  is  so  largely  under  British  influences,  both commercial  and  political.  The  metric  system  was  established  on a  permissive  basis  in  1873,  by  a  decree  of  Khedive  Ismail,  which, however,  was  not  enforced,  so  that  in  1886  a  commission  was appointed  to  consider  the  adoption  of  the  metric  system,  and reported  in  its  favor.  By  1892  its  use  had  extended,  so  that  it was  possible  for  the  government  to  adopt  it  for  use  in  all  trans- actions between  it  and  private  parties,  except  for  measurement  of land  and  the  tonnage  of  ships.  It  has  been  employed  in  the public  works  department,  where  large  engineering  projects  have been  supervised  and  executed  by  British  engineers,  who  have recognized  its  many  advantages,  and  also  in  the  customs,  post office,  and  railways.  While  the  old  native  measures  still  remain in  daily  use,  yet  the  metric  system  is  being  taught  in  the government  schools,  and  as  rapidly  as  is  possible  for  an  oriental people,  with  their  traditions  and  conservatism,  it  is  growing  into increased  use. Greece  is  an  example  of  a  country  where  the  Government though  having  adopted  the  metric  system  is  unable  to  secure its  use  by  the  masses  of  the  people.  The  metric  system  was established  by  a  royal  decree  of  September  28,  1836,  with  Greek names  for  the  different  weights  and  measures;  but  its  use  is  largely confined  to  the  Government  in  its  various  transactions  involving measures  of  distance  and  area,  the  Government  in  common  with the  general  public  employing  the  oke  —  T282  kilograms  as  a  unit of  weight,  and  a  measure  of  the  same  name  =  1*33  liters  as  a, unit  of  capacity.  This  is  undoubtedly  due  to  the  fact  that  the amount  of  international  commerce  in  Greece  is  comparatively limited,  and  that  the  people  at  large  have  but  little  interest in  general  commerce  as  such,  while  the  Government  is  indisposed to  press  reforms  of  this  character. The  conquest  of  Lombardy  and  Venetia  by  Napoleon  in  1803- THE   METRIC   SYSTEM   IN   EUROPE  93 was  the  means  of  inaugurating  the  metric  system  in  Italy,  but its  general  use  did  not  follow  except  in  governmental  transactions, and  the  bulk  of  the  people  resisted  this  effort  on  the  part  of foreign  conquerors.  In  some  of  the  various  kingdoms  and  princi- palities it  was  found  convenient  to  adopt  the  metric  weights  and measures,1  but  it  required  the  establishment  of  the  Kingdom  of Italy  in  1861  to  ensure  complete  uniformity  and  the  thorough adoption  of  the  system.  Here,  again,  we  see  that  one  of  the consequences,  or  possibly  a  necessary  attribute,  of  the  establish- ment of  a  nation  from  a  number  of  separate  states  is  that  there should  be  a  single  and  uniform  system  of  weights  and  measures. Accordingly,  by  the  law  of  July  28,  1861,  the  metric  system  was rendered  obligatory  throughout  the  kingdom  after  January  1,  1863, and  this  was  reinforced  by  a  law  passed  in  June  23,  1874;  and on  August  23,  1890,  the  international  standards  were  established by  a  royal  decree. The  Japanese  have  for  some  time  used  metric  weights  in  their coinage,  and  in  1891  a  law  was  passed  in  which  the  ancient measures  were  reorganized  and  based  on  those  of  the  metric system,  which  was  also  duly  recognized.  The  various  national units,  which  are  divided  either  decimally2  or  sexagesimally,  are defined  in  terms  of  the  metric  units,  so  that  little  difficulty would  be  experienced  in  passing  from  one  to  the  other,  and, in  fact,  tape  measures  are  frequently  graduated  on  both  sides  with the  two  scales,  while  on  a  map  both  scales  are  usually  given. We  have  seen  above  3  how  the  metric  system  was  introduced into  Holland  when  it  formed  one  country  with  Belgium  in 1816,  and  it  gradually  enjoyed  wider  use  until  in  1869  the ^French  names  were  adopted  to  designate  the  different  units, while  permitting  the  older  and  national  names  to  be  used  for ten  years  longer.  The  royal  standards  of  the  Netherlands  were constructed  by  a  commission  of  Dutch  scientists,  and  while  they 1  Metric  System  was  made  compulsory  in  Piedmont  in  1845  ;  introduced  into Modena  in  1849,  with  eight  years  for  its  gradual  adoption  ;  adopted  in  part of  Papal  States  in  1859 ;  in  1861  adopted  in  Sardinia ;  in  1863  adopted  in Neapolitan  provinces,  in  1869  in  Venice,  and  in  1870  in  Rome. 2 Japanese  measures  below  a  shaku=  -99421  feet  =  ^  meter  are  decimally divided,  rendering  their  comparison  with  metric  measures  in  the  case  of drawings  or  diagrams  very  easy. 3  See  ante,  pp.  82  and  91. 94      EVOLUTION   OF   WEIGHTS   AND   MEASURES resemble  those  of  the  International  Commission,  were  derived directly  from  the  standards  of  the  Archives.  The  Dutch standard  meter  is  2#7  microns  longer  than  the  international standard. When  a  decree  was  issued  in  Portugal  in  1852  providing  for the  introduction  of  the  metric  system,  it  was  provided  that  it should  be  in  full  legal  operation  within  a  space  of  ten  years.  It was  planned  that  the  introduction  should  be  by  successive  stages, beginning  with  the  Government,  and  various  schemes  and  tables of  legal  equivalents  were  to  be  prepared  and  distributed.  It  was not  possible  to  bring  about  the  change  during  the  specified  time, so  that  subsequent  statutes  were  necessary,  and  it  was  not  until 1872  that  the  metric  system  was  officially  in  universal  use.  The introduction  of  the  new  weights  and  measures  was  attended  with no  difficulty,  save  the  lack  of  intelligence  of  the  people  of  the lower  and  agricultural  classes,  and  among  them  the  force  of custom  and  tradition  has  proved  so  strong  that  old  weights  and measures  still  remain,  though  they  cannot  be  used  in  any  receipt or  legal  document.  The  metric  system  is,  however,  greatly appreciated  by  the  commercial  interests,  and  is  slowly  but  surely making  progress  among  the  people  at  large.  In  fact,  it  will  be seen  that  among  intelligent  people  such  a  change  occasions comparatively  small  inconvenience  and  is  quickly  effected ;  but where  there  is  a  low  general  standard  of  education,  as  in  Portugal, the  people  are  conservative  and  unwilling  to  accept  innovations, as  they  are  unable  to  appreciate  their  utility. Russia,  no  less  than  other  countries,  early  felt  the  necessity  for reforms  in  its  systems  of  weights  and  measures,  and  in  1833  the original  Russian  units  were  denned  in  terms  of  English  feet, — the  legal  unit  being  the  sagdne,  which  was  equal  to  seven  English feet.  The  standard  for  this  unit  was  constructed  with  great exactness,  and  was  compared  with  the  English  yard,  and  from  it the  various  other  measures  were  derived.  Nevertheless  it  was found  necessary  to  replace  the  sagdne  by  the  archinne,  which  is i  sagdne  or  '71112  meter.  The  metric  system  is  now  permissive under  the  terms  of  the  law  of  June  4-16,  1899,  which  became effective  January  1,  1900 ;  yet  it  is  noteworthy  that  its  inter- national character  is  recognized  by  denning  the  national  stan- dards, the  livre  and  the  archinne,  in  terms  of  the  international THE   METRIC   SYSTEM   IN   EUROPE  95 prototypes.1  The  metric  units  are  largely  employed  in  Russia,  as elsewhere,  for  scientific  work,  and  there  is  said  to  be  a  strong feeling  towards  the  complete  adoption  of  the  system,  which  for  a number  of  years  has  been  used  by  the  pharmacists  of  the  empire, and  since  1896  by  the  medical  departments  of  the  Russian  army and  navy.  The  metric  system  is  also  used  in  the  customs  ser- vice, with  indications  of  further  extensions.  In  Finland,  where  a higher  standard  of  education  prevails,  the  metric  system  has  been employed  with  considerable  success  since  1892,  and  no  difficulty attending  its  introduction  was  experienced. Notwithstanding  the  fact  that  a  large  part  of  the  preparatory work  in  determining  the  length  of  the  earth's  quadrant  had  been done  in  Spain,  that  country  did  not  adopt  the  metric  system  until 1849,  though  previously  it  had  been  under  discussion,  and  so  early as  1807  a  number  of  metric  scales  had  been  constructed  at  Madrid. The  law  of  1849,  which  provided  that  the  system  should  go  into force  in  1853,  and  actually  became  operative  throughout  the  entire kingdom  in  1855,  defined  the  meter  in  terms  of  the  dimensions  of the  earth,  and  the  other  units  as  deduced  from  the  meter.  These definitions  remained  in  force  until  1892,  when  the  receipt  of  the copies  of  the  international  prototype  meter  and  kilogram,  prepared by  the  Bureau  International,  necessitated  the  restatement  of  the law  in  which  these  standards  and  their  relation  to  the  inter- national prototypes  of  the  Bureau  were  duly  recognized. In  Sweden  a  royal  decree  was  issued  November  22,  1878,  by which  the  use  of  the  metric  system  was  made  optional  from  the following  January  1 ,  and  after  ten  years  was  to  be  made  compulsory. The  usual  official  tables  and  information  in  various  and  convenient forms  were  distributed  during  this  transition  period,  but  it  was  not until  the  end  of  the  appointed  time  that  the  metric  system  came to  be  used  generally.  After  that  its  employment  became  prac- tically universal  and  no  difficulties  or  opposition  were  experienced. In  Norway  the  metric  system  was  employed  in  the  postal service,  by  the  Act  of  May  3,  1871,  and  in  the  same  year  the  gram was  adopted  as  the  unit  of  weight  by  the  medical  profession  of that  kingdom.  In  1879,  on  July  1,  the  use  of  the  metric  system for  all  private  business  became  optional,  but  from  this  date  it  was 1  See  Proces-verbavx  dn  Comity  international  des  Poids  et  Mesures,  Session  1897, p.  155. 96       EVOLUTION   OF   WEIGHTS   AND   MEASURES to  be  used  exclusively  by  the  Government  in  all  its  transactions, such  as  the  collection  of  customs  duties,  public  accounts,  taxes, etc.  Then  on  July  1,  1882,  the  use  of  the  metric  system  was made  obligatory  in  all  transactions,  both  public  and  private,  and no  other  weight,  measure,  or  coinage  other  than  metric  was permitted.  It  is  interesting  to  note  that  during  the  three  years of  the  transitional  period  the  government  altered  certain  of  the older  weights  and  measures,  making  them  conform  to  the metric  system.  Thus  all  weights  of  one  pound  and  over  during the  first  two  years  were  regulated  and  made  over  free  of  cost,  so that  the  old  Norwegian  "  skaal-pund  "  and  the  old  "  bismer-pund  " used  with  the  steelyards  were  slightly  increased  so  as  to  weigh half-kilograms.  Likewise  the  old  "  korn-tonde,"  or  corn  measure, was  adjusted  to  hold  140  liters,  and  a  half  measure  to  hold  70 liters.  In  the  third  year  of  the  change  period,  however,  a  fee  was required  for  these  alterations,  and  after  the  compulsory  use  of  the new  weights  and  measures  they  were  absolutely  prohibited. In  the  case  of  Norway  we  have  an  approximate  statement1  of the  cost  of  the  introduction  of  the  metric  system  as  given  in  a statement  of  the  value  of  instruments  sold  in  the  years  1877-84 by  the  Weights  and  Measures  Office,  but  this  does  not  of  course include  the  private  sale  of  metric  weights  and  measures.  In  this €onnection  it  must  be  borne  in  mind  that  the  population  of Norway  at  this  time  was  somewhat  less  than  2,000,000.2  The statement  is  as  follows : Public  expenses — Purchase  of  standards,  weights  and  measures and  apparatus      -----      £2,844 Plans  and  drawings-  -  -  -  -  217 Models 306 Controlling  apparatus  for  town  and  country police         - 1,650 Adaptation  of  old  instruments  to  the  metric equivalents  -  -  -  -  3,111 £8,128 1  Reports  from  Her  Majesty's  Representatives  in  Europe  on  the  Metric  System, part  i.,  July,  1900,  pp.  63,  64 ;  E.P.P.,  1900,  vol.  xc. 2  Dec.  31,  1882,  1,913,000. THE   METRIC   SYSTEM   IN  EUROPE  97 Private  expenses- Adaptation  of  old  instruments  to  the  metric equivalents  -  £2,044 Purchase  of  new  metric  instruments     -  -      35,761 Total  cost  of  introduction    £45,933 In  Switzerland  there  was  even  more  than  the  usual  diversity  of weights  and  measures  in  the  different  cantons,  but  after  1822  in some  of  these  divisions  a  system  based  on  the  metric  measures  and having  a  foot  of  30  centimeters  and  a  pound  of  500  grams  was established.  By  an  agreement  known  as  the  "  Maass  concordats," dated  August  17,  1835,  twelve  cantons  united  in  establishing  this system,  and  by  subsequent  additions  to  the  convention  and  by legislation  it  became  operative  throughout  the  nation,  being  by  an Act  of  Dec.  24,  1851,  the  national  and  compulsory  system  through- out the  confederation  after  December  31,  1856.  In  this  system the  legal  unit  of  length  was  the  pied  or  foot,  equal  to  30  centi- meters, divided  decimally,  and  having  such  multiples  as  the  brache, 2  feet ;  the  mine,  4  feet ;  the  toise,  6  feet ;  the  perche,  10  feet ; and  the  lieue,  16,000  feet.  The  livre  or  pound  equal  to  500  grams could  be  divided  either  on  a  binary  or  a  decimal  system,  while for  dry  capacity  the  unit  established  was  the  quarteron,  equal to  15  liters,  and  for  liquid  capacity  the  pot,  equal  to  one  and a  half  liters.  On  July  3,  1875,  the  Federal  Chamber  passed  a law  providing  that  the  complete  metric  system  should  be  used after  January  1,  1877,  and  that  the  standards  then  in  course of  preparation  by  the  International  Commission  should  be  the legal  and  national  standards.  These  international  prototype standards  were  received  in  1889,  and  were  duly  substituted  for the  older  standards. In  Turkey,  metrological,  like  other  reforms,  have  not achieved  the  success  deserved,  largely  on  account  of  the  char- acter of  the  people  and  the  Government.  In  1886  a  law  was passed  providing  for  the  establishment  of  the  metric  weights  and measures  in  Constantinople,  and  making  their  use  compulsory after  five  years,  and  in  1891  ancient  measures  were  confiscated and  destroyed  ;  but  it  has  been  recognized  as  practically  impossible to  enforce  the  system,  and  old  and  new  units  and  standards  have nourished  side    by  side.      In  fact,  experience   demonstrates   the G 98       EVOLUTIOxN   OF   WEIGHTS   AND   MEASURES strength  of  the  proposition  that  weights  and  measures  and  their preservation  intact  and  uniform  are  correlatives  of  government, and  where  the  latter  is  weak  or  deficient  in  character,  a  satis- factory condition  of  these  necessary  adjuncts  to  commerce  cannot be  maintained.  Nevertheless,  in  1900,  it  was  reported1  that  all scales  imported  into  the  Ottoman  Empire  must  be  marked  in  the metric  system,  and  all  weights  and  measures  marked  according  to the  old  systems  were  liable  to  confiscation. In  England  the  need  of  an  international  and  decimal  system  of weights  and  measures  was  realized  as  early2  as  1783  by  James Watt,  who  had  considerable  difficulty  in  reducing  the  weights and  measures  used  by  Lavoisier  and  Laplace  in  some  experiment to  the  English  weights  and  measures  used  by  Kirwan  in  some similar  work.  Writing  to  the  latter  under  date  of  November  14, 1783,  he  said : 3  "It  is  therefore  a  very  desirable  thing  to  have these  difficulties  removed,  and  to  get  all  philosophers  to  use pounds  divided  in  the  same  manner,  and  I  flatter  myself  that may  be  accomplished,  if  you,  Dr.  Priestley,  and  a  few  of  the French  experimenters  will  agree  to  it ;  for  the  utility  is  so evident  that  every  thinking  person  must  immediately  be  con- vinced of  it.     My  proposal  is  briefly  this : Let  the  philosophical  pound  consist  of  10  ounces  or  10,000  grains. „  „  ounce        „        „   10  drachms  or  1000        „ „  „  drachm     „        „   100  grains. Let  all  elastic  fluids  be  measured  by  the  ounce  measure  of  water, by  which  the  valuation  of  different  cubic  inches  will  be  avoided, and  the  common  decimal  tables  of  specific  gravities  will  im- mediately give  the  weights  of  these  elastic  fluids."  Farther  on in  the  letter  he  says,  "  I  have  some  hopes  that  the  foot  may  be fixed  by  the  pendulum,  and  a  measure  of  water,  and  a  pound derived  from  that ;  but  in  the  interim  let  us  at  least  assume  a proper  division  which  from  the  nature  of  it  must  be  intelligible, as  long  as  decimal  arithmetic  is  used." 1  Board  of  Trade  Journal  (London,  Feb.  22,  1900),  vol.  xxviii.  p.  449. 2  In  1620  Edmund  Gunter  had  proposed  a  decimal  measure  for  land  with  a surveyor's  chains  of  100  links. 3  A.  Siemens,  Journal  Institution  of  Elect.  Engineers  of  Great  Britain,  vol.  xxxiL pp.  278-9. THE   METRIC   SYSTEM   IN   EUROPE  99 A  few  days  later  (Nov.  23,  1783),  Watt  wrote  to  M.  de  Luc calling  attention  to  the  difficulties  of  comparing  the  work  of investigators  in  different  countries  on  account  of  the  diversity  in weights,  and  also  on  account  of  "  the  absurd  subdivisons  used  by all  Europe,"  even  if  the  weights  were  the  same.  He  describes the  plan  outlined  above,  and  suggests  dividing  the  Paris  pound into  1000  parts.  M.  de  Luc  was  asked  to  communicate  with Laplace  on  this  subject,  and  three  years  later  when  Watt  visited Paris  he  met  Lavoisier,  Laplace,  Monge,  and  Berthollet,  whom  we have  seen  were  deeply  interested  in  the  reform  of  weights  and measures.  It  is  fair  to  assume  that  the  subject  was  discussed  by Watt  among  them,  and  that  they  listened  to  the  suggestions  and ideas  of  the  English  engineer,  and  this  view  is  strengthened  by the  provision  inserted  in  the  bill  for  the  reform  of  the  French weights  and  measures  that  the  French  Academy  and  the  Royal Society  appoint  a  joint  committee  to  discuss  universal  weights and  measures.1 England,  however,  declined  to  co-operate  with  the  International Commission  which  examined  the  work  of  the  French  scientists  on which  the  metric  system  was  based,  and  this  attitude,  as  well  as a  subsequent  antipathy  to  the  French  system,  was  doubtles  due to  the  national  feeling  towards  France.  Mention,  however, should  be  made  of  the  fact  that  in  1789  Sir  John  Riggs  Miller called  the  attention  of  Parliament  to  reforms  in  weights  and measures,  moving  for  the  appointment  of  a  committee  "  to investigate  and  report  on  the  best  means  for  adopting  an uniformity  of  weights  and  measures."  He,  too,  had  in  mind  the length  of  the  second's  pendulum  as  a  basis  of  linear  measure,  and his  plan  was  supported  by  the  Rev.  George  Skene  Keith,  who further  urged  that  any  new  system  should  be  a  decimal  one. The  desirability  of  a  decimal  system  that  should  include  not  only weights  and  measures,  but  also  coinage,  began  to  be  felt,  and  in 1814  Sir  John  Wrottesley  brought  such  a  scheme  to  the  notice  of Parliament.  The  result  of  the  agitation  was  that  in  1819  a commission  which  included  Dr.  Thomas  Young,  William  H. Wollaston,  and  Captain  Henry  Kater  reported  adverse  to  the adoption   of   the   decimal  scale,  but  the  cause  continued  to  be 1See  M'Leod,  "Notes  on  the  History  of  the  Metrical  Measures  and  Weights," Nature  (London,  1904),  No.  1792,  vol.  lx.  pp.  425-427. 100     EVOLUTION   OF   WEIGHTS   AND   MEASURES argued,  and  at  every  discussion  of  changes  in  weights  and measures,  the  metric  system  had  its  advocates  in  increasing numbers. In  1816  a  resolution  was  passed  in  Parliament  providing  for  a comparison  of  the  imperial  standard  yard  with  the  Trench standard  meter,  this  duty  being  assigned  to  the  Eoyal  Society. That  body  received  from  Paris  two  platinum  meters  which  had been  compared  by  Arago  with  the  French  standard.  One  was  an end  standard  which  was  exactly  equal  to  the  meter  at  the temperature  of  melting  ice,  while  the  other  was  a  line  standard which  at  the  same  temperature  was  short  by  "01759  mm.  These meters  were  carefully  compared  by  Captain  Kater  with  the Shuckburgh  scale,  and  when  referred  to  the  Parliamentary standard  the  true  length  of  the  meter  was  determined  at  39*37079 British  inches,  a  value  which  was  legalized  by  Parliament  in  its Act  of  1864  which  permitted  the  use  of  the  weights  and  measures of  the  metric  system. Meantime  the  scientists  and  others  had  called  for  reforms  in the  British  system  which  would  involve  more  than  merely  the construction  of  new  standards.  In  considering  this  subject,  and especially  in  its  bearing  on  the  adoption  of  a  decimal  system,  a committee  of  the  House  of  Commons,  reporting  in  1862,  stated that  "  it  would  involve  almost  as  much  difficulty  to  create  a special  decimal  system  of  our  own,  as  simply  to  adopt  the  metric decimal  system  in  common  with  other  nations.  And,  if  we  did so  create  a  national  system  we  would,  in  all  likelihood,  have  to change  it  again  in  a  few  years,  as  the  commerce  and  intercourse between  nations  increased,  into  an  international  one."  The scientific  men,  and  those  who  had  been  careful  observers  at international  expositions  and  conventions,  were  now  making  their influence  felt,  and  in  1864  was  passed  the  Act  mentioned  above, which  allowed  the  use  of  the  metric  system  of  weights  and measures.  Not  satisfied  with  this  step,  the  metric  advocates  in 1868  proposed  a  bill  making  the  system  compulsory,  but  after  a second  reading  it  was  dropped.  In  the  meanwhile  the  Standards Commission,  of  which  Sir  G.  B.  Airy,  the  astronomer-royal,  was chairman,  carefully  studied  the  subject  of  weights  and  measures for  the  kingdom,  and  their  second  report,  dated  April  3,  1869,  is devoted  to  the  metric  system THE   METRIC   SYSTEM   IN   EUROPE  101 The  status  of  the  metric  system  was  defined  in  1878  by  the Weights  and  Measures  Act,  under  the  terms  of  which  (clause  32) the  Board  of  Trade  was  authorized  "  to  verify  metric  weights  and measures  which  are  intended  to  be  used  for  the  purposes  of science  or  of  manufacture  or  for  any  lawful  purpose,  not  being for  the  purpose  of  trade  within  the  meaning  of  this  Act." The  legislation  of  August  8,  1878,  still  left  much  to  be  desired, and  in  1895,  in  response  to  demands  for  further  action,  a  com- mittee was  appointed  from  the  House  of  Commons  to  investigate the  matter  anew.  This  committee  heard  numerous  witnesses  and carefully  considered  their  testimony,  giving  ample  opportunity  for both  sides  of  the  question  to  be  discussed.  In  their  report  they recommended : "  {a)  That  the  metric  system  of  weights  and  measures  be  at once  legalized  for  all  purposes. "  (b)  That  after  a  lapse  of  two  years  the  metric  system  be rendered  compulsory  by  Act  of  Parliament. "  (c)  That  the  metric  system  of  weights  and  measures  be taught  in  all  public  elementary  schools  as  a  necessary  and integral  part  of  arithmetic,  and  that  decimals  be  introduced  at  an earlier  period  of  the  school  curriculum  than  is  the  case  at present." Parliament  acted  on  that  portion  of  the  report  providing  for the  legalization  of  the  metric  weights  and  measures  for  all purposes,  passing  a  bill  to  that  end  May  27,  1897,  but  hesitated when  it  came  to  making  the  system  compulsory.  On  the following  year  in  an  Order  in  Council  dated  May  19,  1898,  after an  investigation  by  a  committee  of  the  Royal  Society,  the  various units  were  defined  and  their  legal  equivalents  in  the  customary weights  and  measures  given.  These  differ  by  minute  amounts from  those  of  the  United  States. In  1903  it  seemed  to  the  members  of  the  Decimal  Association, an  influential  organization  which  had  been  formed  to  further  the adoption  of  the  metric  system  and  of  a  decimal  system  of  coinage, that  popular  feeling  in  favor  of  radical  reforms  in  the  system  of weights  and  measures  was  increasing,  and  that  it  was  an  oppor- tune time  to  make  another  attempt.  Accordingly  Lord  Belhaven and  S  ten  ton  introduced  such  a  bill,  which  was  supported  on  its introduction    by    Lord    Kelvin     and    later    by    Lords   Rosebery, 102     EVOLUTION   OF   WEIGHTS   AND   MEASURES Spencer,  and  Tweedmouth,  and  after  a  third  reading  was  passed and  sent  to  the  House  of  Commons,  where,  however,  it  was  never brought  up  for  passage. This  bill  was  endorsed  by  a  large  number  of  town,  city,  and county  councils,  and  by  over  fifty  chambers  of  commerce,  includ- ing some  of  the  most  important  in  the  kingdom.  Furthermore, in  addition  to  petitions  from  forty-two  trades  unions,  representing some  300,000  members,  received  while  the  bill  was  in  the  House of  Lords,  there  was  a  resolution  unanimously  passed  by  the Congress  of  Trades  Unions  meeting  at  Leeds  in  September,  1904, and  representing  some  5,000,000  workmen,  in  which  it  was resolved  to  petition  the  House  of  Commons  in  favor  of  the  bill. There  were  also  petitions  from  sixty  Teachers'  Associations, Inspectors  of  Weights  and  Measures  in  eighty  districts,  and thirty  Ketail  Trades'  Associations,  besides  numerous  Chambers of  Agriculture  and  Farmers'  Associations.  Thus  it  will  be  seen that  the  bill  was  supported  by  eminently  practical  people  as well  as  scientists  and  theorists,  and  it  is  interesting  to  state  that in  Great  Britain  retail  tradesmen  and  workmen  have  been  alive to  the  many  merits  of  the  metric  system. The  bill  of  1904  provided  for  the  establishment  of  the  standard kilogram  and  meter  from  the  first  day  of  April,  1909,  as  the imperial  standards  of  weight  and  of  measure,  though  for  sufficient cause  this  date  could  be  postponed  by  an  Order  in  Council.  It also  provided  for  Parliamentary  copies  of  the  substituted  imperial standards,  and  that  future  deeds,  contracts,  etc.,  must  be  in  terms of  the  metric  system.  The  bill  also  made  due  provision  for various  adaptations  made  necessary  by  the  change,  and  prescribed the  general  method  in  which  it  should  be  carried  out. In  Australia  an  active  demand  was  made  for  the  introduction of  the  metric  system,  and  in  1905  it  was  proposed  to  introduce into  the  Federation  Parliament  a  bill  with  this  object.  In  the same  year  the  neighboring  colony  of  New  Zealand  adopted  the metric  system  as  its  legal  system  of  weights  and  measures. Great  Britain,  however,  played  an  important  part  in  the  de- velopment of  scientific  measures,  namely,  in  working  out  the C.G.S.,  or  Centimeter-Gram-Second  system,  as  was  done  by  the British  Association  for  the  Advancement  of  Science.  This  system was  based,  as  the  name  implies,  on  the  metric  units  of  length THE   METRIC   SYSTEM   IN   EUROPE  103 and  mass,  and  has  been  of  the  greatest  benefit  to  science,  being universally  adopted  by  physicists  and  engineers,  and  will  be found  discussed  more  at  length  farther  on  in  this  volume.1 In  Mexico  the  Metric  System  came  into  effect  on  the  first of  January,  1862,  in  accordance  with  the  terms  of  a  law  of March  15,  1857,  and  a  second  law  of  March  15,  1861,  which provided  for  the  exclusive  use  of  the  Metric  Weights  and Measures  for  all  purposes.  While  the  new  system  was  adopted by  the  Government,  yet  private  individuals  did  not  take  it up,  and  there  was  needed  an  imperial  decree,  issued  in  Nov- ember, 1865,  which  declared  the  Metric  System  alone  valid throughout  the  country.  For  a  number  of  years  the  old  and new  measures  were  used  side  by  side,  and  also,  with  the introduction  of  railways  and  of  machinery  for  mining  and  other purposes  from  the  United  States,  the  English  foot  and  pound; but  gradually  the  Metric  measures  asserted  their  supremacy,  and now  they  are  almost  exclusively  used.  Mexico  became  a  party to  the  International  Convention  of  Weights  and  Measures  in 1890,  and  in  1896  it  formally  adopted  the  international  standards for  the  meter  and  kilogram. Throughout  South  and  Central  America  the  Metric  System is  largely  employed,  and  in  nearly  all  cases  it  is  the  legal system  of  the  different  countries.  There  has  been,  however, great  difficulty  in  maintaining  this  system  as  the  only  one, since  in  numerous  instances  the  people  have  preferred  to  use the  older  units  derived  from  Spanish  and  other  sources,  while exporters  doing  business  with  Great  Britain  and  the  United States  have  made  use  of  the  Anglo-Saxon  units.  This,  of course,  is  due  in  great  part  to  the  lack  of  stability  of  the South  American  governments,  but  conditions  in  this  respect are  improving,  and  the  use  of  the  metric  weights  and  measures is  now  practically  universal  throughout  South  America.  It was  on  this  account  that  representatives  of  these  countries assembled  at  the  International  American  Conference  at  Washing- ton in  1890  advocated  the  adoption  by  the  United  States  of the  Metric  Weights  and  Measures.  Beyond  the  dates  of adoption,  as  given  by  the  accompanying  table,  there  is  but little  to  say  as  regards  the  individual  countries 1  See  Chapter  ix.  p.  205, 104     EVOLUTION   OF   WEIGHTS   AND   MEASURES While  in  the  foregoing  paragraphs  an  attempt  has  been made  to  summarize  briefly  when  and  how  the  metric  system was  adopted  by  the  more  important  nations  of  the  world,  it  is possible  to  obtain  this  information  for  the  remaining  countries of  the  world  by  reference  to  the  accompanying  tables,  which indicate  the  time  at  which  metric  measures  were  first  adopted, when  made  compulsory,  and,  so  far  as  can  be  ascertained  and briefly  stated,  the  extent  to  which  they  have  replaced  other and  older  measures.  These  tables  speak  for  themselves,  and illustrate  most  forcibly  the  spread  of  the  system.  They  are based  on  a  somewhat  similar  table  published  as  an  Appendix, p.  67,  of  a  Eeport  from  the  Select  Committee  on  the  Weights and  Measures  (Metric  System)  Bill  [H.L.],  May  5,  1904,  to  be found  among  the  Parliamentary  Papers  of  that  year,  on  the Reports  of  British  Consular  officials  abroad,  to  which  reference has  already  been  made  (see  footnote,  p.  91),  and  other  official sources  of  information. o M P .-5  <x> e 0)^3         eS    S e la Kg <X>    3 S£ O    cS £^H Is O .3    03 O    5 xt2  ^ it a     2-H s  I  e 3  s  £ ■£wb§ a  2^ ce    -£> tn     3     03 O    o>    3 «*H   ^     O ^  >»3 2  02 .G  (1) G  *>  3 o   M 5 rt  cS  H ^,f»  CO ^5 •3*  & a  a)  « •i-H       (1)      S-l O    o^ o  a n-        o 5  ?^ S3    <V    a •sfl h O a  * Oh CO   o £^  2 Sh     >     <L>    W b  «  »r*  a <x>  ce  -a  >»  3 5^ O    d 0 ,3  02  ~  ~*   ^ 0) •ft.  5    S3    S3    <D    O -  ■  M  ^o  «3  "  5  - =0     O     j.     73     Mh 3       S  -^  d ts      rd  3 a>  a)  _2  bo  § E-S  8  ^  g 1-8  ?*p §  a  *•  >  S.SPS  ^^'s  o  5 o bD       ,-P    QD  v >  a — 1  M o    o -  fee     , 0-^0    o O IS •43  o Is T3    d    S3 a. 0,0 O    £    03 •go^> ^  ??  a ai .2  &b  8 lie ?a^^ ^    03  . 02    Jh    d    O aa o a  73  -ij |^« 43     • o  ,•  ** =»  o ^  ^  2 o»  -a bo>^ .a  a  s> o  p-" a  a>  03 g  »  a >d^ 3     03  " .2'"^ *!* -a  3 [3d CO od  for  Com- >ry  Adoption. )  Nominal. 1  Actual. OQ     03 03 a 0 a CO 3|  years 39  years 3  years 1  year 47  years 3£  years i 1      1 1 1  §  AS ^^, .<— V,-— ^X~N <^x~^/— N nS^ 2 e-o  e sS^W a v_--v»»^'s_<' +=>   1 a  *° <D  ^ Jh  00 £  0 n  diflfe from  1 816 S^ ,_, CD CD         00 co      00 CD 00 ««  3 t^ t« .-H             CO a      to CO 00 '      11 00 00 00          00 t-         00 00 00 1—1 1—1 ^H             |-H r— (           1— 1 1—1 'o-pO " •gas bo a 3 W fT .sf-2  ' a 1 1 t-  si  <o d 0 'So ^3  3 a Si 0 8 ^» 0 3    <u   S <u E 4§ I-H w WQF^ 0 O a X 3 +3       © U£ at ©  a -S  9 -L3      O •J Hi 2S ^-d d  8 o ©^ D*2 II 5.2 ^  ce -    Oh +3     O -5  £  9  ° ci    p    ~ -sua ! 'S  2  a;  5  5 5  ©  ^ ClS'd I'S  -s ©3 S    .2      §< 2  o O)         ^2  .P    oj 8  p£-d£ ^.2<~  2-2 sITflii «  s  s  ^  S w  ft £~  1 1  cq  ce D-^GO   © 55  .5  9 *s  Cg E  s J  p£ 2  is  9  ©  5 .Malt .id    _  Q0-T3    E 3     rH     >     © 9 So p    .  • ce    co  © -3  5  §8 ^  © ce    %A BS  3 B    ,  bo * J ST? as  «*     o Mi  y •5  s  8     * "*"   rt  »         © fctO 2  *  S  1  S «_2  1  -•« ©_  ©  Ss2 oo    R    *■'  oo    © >v2     ©     >>_H •I  i  ij! <u_,  -»j    a •a  co Pr* a  *    o Nl g  J    ^ "■■■Ifl p—  9  2 •a       oo  h — .     CO     ft <  p  -d nifested Her  tow perience perience ommerc lower  c n  the  t ce  ma in  sma lty  ex lty  ex the  c a  the ulty  i 9  _-  0 3   t     o   w •P    2jc OKwa3 CD  cil  ^ great  di comed hardsh] great  d issive  r still o  great o           o Ph      ft fc         Jzj a;       g I s a  . o  s °^ M '"S  ce p a L*  O  B *  °  ^ 9   ©   co 00 © 5 I3jl. fe^S-S 2  E 9  c3 o  a CO oo   co    ^  co oo   5h    J-    a3  E E  ce  ce  <v  ce ce  a>  a>  >^  © 9-s ^3 si .22 Oi 10 CD as x>> 00 00 00 00 p ce ce B a) ,P P .2 •5 © 02 © o Ph p 3 02 p 1 ce b u ce © -s P L N -t-5 * O E w XA w < o « H O a < o >»d n a  -a o3    o3 .°,    d73 d  <4-«  02 >*73 bfi-io Co ■s    a a OS beg a  *  * 3        .d d  f. si-s ga.S -i  73  '© S  3-° s-    o3 .3  73 1  3 *T3       •  02 O     02  02 tt     C  0> ^.2  8 _03  02 Q5  73  - -    02      . £    O    s *  02  ^ "g     CO     OJ C4-.    2    * O  32 73 d © Sh qa    o3 §   M _o~   *:: 73   r^ H  S  3 2  9  a a    d  0) go  * 5g     00  S •FH    o>  d 'II jl>  £  E& i— i    <±> 73   o373 8'§'s *  3  o £  2  « o  2£ «  «  fe "-^ o  ;d  33 ~        9 O  02 3     «     g 03     02     *     d 8  §~§ 73  3    .'53 C  .2    O)     H »S    >*02 o  Id    02  CG 73 o  Jv  o *-  73    <*> n  «  a S  S3  « 'ill* ^2  7^    03    e3 4->  a.  8  d _  a)  73 'is fcr 'a  2  9 •h  d  o  ii SS    «    2    03 .2  "8°  J* ri    ^     d d    d  OS    02 d   02  00   bo ■p  J)H-P 0)     O go 1 ,6 *h73  d 02  02  '2 >  +3  -d o  «d  « ^1 02  ^ ^  >  02 02    o3    £ ■"0"    02    O) o   m U     02 02   (3 a^ a-g >»  o3 o  d o  d 02  d s :^d 9 ■ 13 X £ 02 S>  d  a 03  03  5 d  +3  *3 1-1  —  02 C    S  73 d    ~  p c    02    © d  o73 ^  d  g O    to    S o3 02 O E  t o3  o3 02  02 ^^ O  CN e-o 03 O) O I  I "2 SI ©  o c  3 o  d- '■§  a d-  O vSvS CO  t^ CD  GO CO  CO CO CO CD ^ 0 lO 0 Oi CO CO CO CO ^v  o 73  J2 d^ c  Ph '£  a cd  a CO   CO I         I o3 d • d o3 ^^ 02 > •rs ta OS O B < m PQ 4   I i§   6 w a d bo I Ph 21 d  d  5 a>  a  ;£ O  'S o  d  «§ 111 ioj %  fe  £ III .2     5 *<P^ 1  EH d-5.3 g    03     05 «  «  a> ■TM a  i4 Sip* d.s a  3 if  *& ^H^ ^Q ^03.2 "S  s  I w  ai  d -  s  5- 03 g  a>  <u O  <u  & o3   P   § bC  o>  § 2  a  »- p^2 o  M  o lbs srp 2  E o  ^5 P   4; 03     P S    ■ •rt  o -d  2 5"   P d$   o3 M     L     K     j]   -P 5  •  1 J  S  ^ I     i     I p ^-v ^-v  0 o3 •a  J P 3  s O O     Oh*^ -M (opti (com 185 a 0 CD cn  ^ CD CD  CT> CO  CO rH  r-H 03 % of 3 k»        'o C/J 3            £ E5       n 73 S3          S3 !h           0) p p   >•   D H3 0) 9 •si -w '.£ •£  * 0 03 ? 03 O     03 P 9 B -1-3 p 5'S s ^^ pO «3 £  d <U O O    o3 i s 8 a 1  ^ 2 0 ^a -u °T3 > •ta ■a-a '3 cr1 a o3    02 J8  0* <D f su It °3 0 i •a  a o3  <^3 ^ <D g^2 a  j2 3 03 +3 S 0>  ^^ 0 t— i H3 03 a 03 ■ E P I 40 .13 P *'"* a O a ■1 5 a m 3*  i ~o3 CD 0 a &&  u ft 0 Q 1 o3 1  p  i M r^  53    P s 03 sg 1      1    1      1 VI M 03 U >*» O o3 *    * 53 co ^  'S  CO  <M         O P  Cd  t-  Oi         C7i Ph  M  co  co      co 1— ( 1" C75  CM CO  Oi CO  CO —' 1— 1 a 03 a^ 1                  1 >>      p 55J0              P ►^ m W         H CHAPTEK    IV. WEIGHTS  AND   MEASUKES   IN  THE   UNITED   STATES. )  In  the  early  days  of  the  American  colonies  the  weights  and |  measures,  like  the  coinage,  were  based  almost  entirely  on  those of  the  mother  country,  and  where  statutes  were  enacted  pro- viding for  standards,  these  were  derived  from  the  standards of  the  Exchequer  of  England.  Inasmuch  as  that  country  was the  chief  source  of  supply  as  well  as  a  market  for  merchandise, and  the  commercial  dealings  were  very  largely  with  its inhabitants,  such  a  condition  was  most  natural,  and  inasmuch as  trade  was  not  particularly  extensive,  such  a  system  of weights  and  measures  amply  sufficed.1  During  the  Eevolution, however,  it  was  realized  that  all  possible  means  should  be  taken to  secure  uniformity  in  commercial  practices,  and  the  need  of a  single  national  system  of  money  and  weights  and  measures was  early  appreciated.  In  the  Articles  of  Confederation  adopted by  the  Continental  Congress,  November,  15,  1777,  it  was  pro- vided in  section  4,  article  ix.,  that  "  The  United  States  in Congress  assembled  shall  also  have  the  sole  and  exclusive right  and  power  of  regulating  the  alloy  and  value  of  coin struck  by  their  own  authority,  or  by  that  of  the  respective states ;  fixing  the  standard  of  weights  and  measures  throughout the  United  States ;  .  .  ."  By  the  Federal  Constitution,  Congress is  explicitly  given  the  power  to  fix  the  standard  of  weights and  measures,  the  fifth  paragraph  of  section  8  of  article  i. stating  that  the  Congress  shall  have  the  power  "  to  coin  money, 1  See  John  Quincy  Adams,  "  Report  on  Weights  and  Measures"  (Washington, 1821),  for  summary  of  colonial,  state,  and  territorial  legislation,  pp.  94-117. 110     EVOLUTION   OF   WEIGHTS   AND   MEASURES regulate  the  value  thereof  and  of  foreign  coins,  and  fix  the standards  of  weights  and  measures."  It  is  somewhat  curious that  the  fixing  of  the  standards  of  weights  and  measures  is almost  the  only  power  expressly  and  specifically  conferred  on Congress  which  that  body  has  refrained  from  exercising  down to  the  present  time,  notwithstanding  its  constant  and  most active  interest  in  the  coinage  of  money,  as  evinced  by  a  vast amount  of  discussion  and  legislation. In  the  days  before  and  during  the  Eevolution  the  coinage  of various  nations  as  well  as  from  different  state  mints  passed  in circulation,  causing  an  inexpressible  confusion  of  values  and  rates of  exchange,  and  it  was  but  natural  that  uniformity  and  sim- plicity should  be  desired.  That  this  could  best  be  attained  by  a decimal  system  was  appreciated  as  early  as  1782,  when  Eobert Morris,  the  Superintendent  of  Finance,  an  office  corresponding  to that  of  the  present  Secretary  of  the  Treasury,  wrote  to  the President  of  Congress  "  that  it  was  desirable  that  money  should be  increased  in  the  decimal  Eatio,  because  by  that  means  all calculations  of  Interest,  exchange,  insurance,  and  the  like  are rendered  much  more  simple  and  accurate,  and,  of  course,  more within  the  power  of  the  great  mass  of  people.  Whenever  such things  require  much  labour,  time,  and  reflection,  the  greater number  who  do  not  know,  are  made  the  dupes  of  the  lesser number  who  do." x  In  accordance  with  the  suggestions  made,  an elaborate  report  on  the  question  of  a  system  of  currency  for  the United  States  was  prepared  by  Thomas  Jefferson,  and  on  July  6, 1785,  a  decimal  system  of  coinage  was  adopted.2  In  the  following year,  August  8,  the  complete  system  was  duly  determined,  and the  amounts,  nomenclature,  and  value  of  the  various  coins  fixed.a The  success  of  the  new  currency  was  soon  assured,  and  it  received favorable  commendation  both  at  home  and  abroad. The  reasons  influencing  its  adoption  would  seem  to  have demanded  a  similar  system  of  weights  and  measures,  and  it  is perfectly  evident  that  clear  thinkers  like  Morris  and  Jefferson 1  Watson,  History  of  American   Coinage   (New  York,  1899),  p.   10,    quoting from  Wharton's  Diplomatic  Correspondence,  vol.  v.  pp.  103-110. 2  See  Watson,  p.  16 ;  also  MS.  Reports  of  Committee  on  Finance  of  the  Continental Congress,  No.  26,  pp.  537-560. 3  Journal  of  Congress,  vol.  xxxviii.  No.  1. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     111 were  alive  to  its  advantages;  but  even  at  these  early  times,  as well  as  subsequently,  there  was  considerable  disinclination  on the  part  of  Congress  to  take  any  measure  looking  toward  the establishment  or  reform  of  these  important  adjuncts  to  commerce. In  fact,  while  there  have  been  numerous  suggestions  on  the subject  of  weights  and  measures  from  Presidents  in  their  messages, there  has  been  comparatively  little  legislation,  and  more  has  been accomplished  in  the  way  of  establishing  and  changing  standards oy  Executive  order  than  by  direct  legislation. President  Washington,  however,  early  realized  the  importance of  the  matter,  and  in  his  first  speech  or  message  to  Congress,, delivered  January,  8,  1790,  he  said,  "  Uniformity  in  the  currency, weights,  and  measures  of  the  United  States  is  a  subject  of  great importance,  and  will,  I  am  persuaded,  be  duly  attended  to." Accordingly,  the  House  of  Eepresentatives  referred  the  matter  to the  consideration  of  the  Secretary  of  State,  Thomas  Jefferson,  and requested  him  to  prepare  a  report  dealing  with  the  subject.  Mr. Jefferson  had  been  in  Paris  as  Minister  of  the  United  States,  and doubtless  was  well  acquainted  with  the  measures  to  reform  the weights  and  measures  of  that  country  which  had  been  and  were then  under  discussion.  For  this  reason,  as  well  as  on  account  of his  connection  with  the  establishment  of  the  national  currency  on a  decimal  basis,  his  selection  was  most  fortunate,  and  within  a few  months  (July  4,  1790)  a  report  was  submitted  containing  two complete  and  distinct  plans.1  He  suggested  as  the  standard  of linear  measure  a  uniform  cylindrical  rod  of  iron  of  such  length that  in  45  degrees  latitude  at  sea  level  and  constant  temperature it  should  perform  its  vibrations  in  small  and  equal  arcs  in  one second  of  mean  time.  Such  a  rod  would  have  a  length  of  58*72368 inches,  corresponding  to  a  length  of  a  seconds'  pendulum  of 39*14912  inches.  In  one  of  the  plans  proposed  he  adapted  the existing  system  to  this  standard,  thus  securing  uniformity  and stability,  while  in  the  other,  which  he  considered  available  for future  use,  he  proposed  a  new  and  strictly  decimal  system  which was  remarkably  complete  and  comprehensive.  Mr.  Jefferson  was convinced  of  the  utility  of  the  decimal  system,  and  in  his  proposed scheme  of  weights  and  measures  for  the  American  people  he  aimed 1See  The  Works  of  Thomas  Jefferson  (edited  by  H.  A.  Washington,  New  York, 1884),  vol.  vii.  pp.  472-495. 112     EVOLUTION   OF   WEIGHTS   AND   MEASURES to  reduce  "  every  branch  to  the  same  decimal  ratio  already  estab- lished in  their  coins,  and  thus  bringing  the  calculation  of  the principal  affairs  of  life  within  the  arithmetic  of  every  man  who can  multiply  and  divide  plain  numbers."  The  success  which  has attended  the  decimal  currency  of  the  United  States  shows  that •Jefferson  was  wise  in  his  plan  for  a  similar  division  for  weights and  measures,  and  had  his  proposals  been  adopted  much  confusion and  inconvenience  would  have  been  spared  the  people  of  the United  States.  Furthermore,  but  little  difficulty  would  have attended  its  adoption,  as  the  fundamental  unit,  the  foot,  differed but  slightly  from  the  foot  then  in  use.  This  foot  was  derived  by Jefferson  by  taking  one-fifth  of  the  length  of  the  rod  forming  the second's  pendulum  and  then  employing  multiples  and  sub-multiples in  building  up  a  series  of  measures  of  length.  A  table  of  these units  would  read  as  follows  : 1 10  points  make  1  line. 10  lines  make  1  inch; 10  inches  make  1  foot. 10  feet  make  1  clecad. 10  decads  make  1  rood. 10  roods  make  1  furlong. 10  furlongs  make  1  mile. Naturally  the  squares  and  the  cubes  of  these  units  formed  the units  for  area  and  volume,  while  for  capacity  the  cubic  foot  was selected  forming  the  bushel,  which  was  then  divided  and  multi- plied decimally  to  give  other  measures.  Likewise  the  cubic  foot of  water,  which  weighed  100  pounds  of  10  ounces  each,  gave  the basis  of  the  measures  of  weight,  and  these  also  were  arranged decimally.  Hardly  too  much  in  praise  of  this  system  of  Jeffer- son's can  be  said,  and  its  adoption  by  Congress  would  have exerted  a  wonderful  effect  on  metrology,  not  only  in  the  United States  but  also  in  the  world  at  large.  It  will  be  remembered that  at  this  very  time  France  was  constructing  its  metric  system, while  England,  appreciating  the  confusion  attending  its  complex and  unwieldy  system  of  measures,  was  in  good  temper  for  a change.  Jefferson's  system,  although  designed  to  have  certain points  of  contact  with  the  then  existing  system  so  as  to  make 1  The  Works  of  Thomas  Jefferson  (New  York,  1884),  vol.  vii.  p.  488. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     113 it  easy  of  adoption,  nevertheless  was  perfectly  uniform  and symmetrical,  and  while  possibly  less  scientific  and  precise  than the  French  system,  yet  it  possessed  all  the  characteristic  features of  convenience,  symmetry,  and  completeness.  Congress  received this  able  report,  but  did  not  adopt  either  of  Jefferson's  suggestions, doubtless  on  account  of  the  similar  agitation  for  changes  in weights  and  measures  then  taking  place  in  France  and  England, and  its  desire  to  await  their  outcome. The  pressing  need  of  some  action  for  this  country,  neverthe- less, was  realized  by  the  executive  branch  of  the  Government, and  again  in  his  annual  message  to  Congress  on  October  25,  1791, President  Washington  reverted  to  the  subject,  stating  that  "A uniformity  in  the  weights  and  measures  of  the  country  is  among the  important  measures  submitted  to  you  by  the  Constitution  ; and,  if  it  can  be  derived  from  a  standard  at  once  invariable  and universal,  must  be  no  less  honorable  to  the  public  councils  than conducive  to  the  public  convenience." A  committee  of  the  Senate  appointed  November  1,  1791,  then took  the  matter  under  advisement,  and  on  April  5,  1792,  presented a  report1  favoring  the  adoption  of  Jefferson's  decimal  plan,  and containing  directions  for  the  scientific  construction  of  a  standard of  length  which  would  be  divided  into  five  equal  parts,  each  of which  would  correspond  to  a  foot.  The  report  also  contained information  relative  to  the  measures  for  the  survey  of  land,  units of  weights,  etc.  Several  reports  were  submitted  by  this  committee, and  it  was  finally  decided  (1793)  "  that  the  Standards  should  be the  mean  of  those  found  in  the  country."  No  legislative  action was  taken  by  the  Senate,  and  for  several  years  there  is  apparently no  record  of  any  great  interest  manifested  in  the  subject  by Congress.  In  the  meantime  France  had  adopted  the  Metric System  with  a  hope  that  it  would  become  universal,  and  on January  8,  1795,  the  President  transmitted  to  Congress  a  com- munication2 from  the  Minister  of  the  French  Eepublic,  describing in  detail  the  new  system  of  weights  and  measures,  the  standards of  length  and  weight,  and  the  method  of  dividing  the  standards into  decimal  parts.  A  committee  from  the  House  of  Eepresenta- tives  proceeded  to  study  this  plan,  together  with  that  of  Jefferson, 1  Journal  of  the  Senate,  Second  Congress,  First  Session,  pp.  173,  174. 2  Executive  Docs. ,  Third  Congress,  Second  Session. H 114     EVOLUTION   OF   WEIGHTS   AND   MEASURES and  reported  in  the  following  year ;  but  their  recommendations were  of  a  general  character,  and  involved  experimental  work  by scientists,  which  was  never  authorized  by  Congress.  It  may  be said  in  passing,  Jefferson  did  not  advocate  the  adoption  of  the French  system,  as  he  did  not  approve  of  the  use  of  a  fundamental unit  derived  from  an  arc  of  meridian  in  preference  to  the  length of  a  seconds'  pendulum.1  As  to  his  own  plans,  he  was  not  a zealous  advocate  of  either  of  the  propositions  he  had  advanced, and  was  willing  to  leave  the  entire  matter  to  Congress. The  difficulties  with  France,  the  war  with  Great  Britain,  and the  consideration  of  various  matters,  political  and  otherwise,  left little  time  for  Congress  to  act  on  matters  of  weights  and  measures, and  accordingly  there  was  no  legislative  action  for  a  number  of years.  In  the  meantime  the  Coast  and  Geodetic  Survey  requiring some  standard  of  length,  imported  from  England,  in  1814,  an 82-inch  brass  bar  scale  made  by  Troughton  of  London.  Thirty- six  inches  taken  on  this  scale,  between, divisions  27  and  63,  were adopted  as  the  standard  yard  for  the  United  States  by  the Treasury,  and  this  distance  was  used  by  other  departments.2  The meter,  however,  was  selected  at  the  outset  for  actual  surveying operations  by  the  Coast  and  Geodetic  Survey,  and  for  this  purpose has  since  been  continuously  employed  in  its  various  triangulations. The  metric  standards  were  a  brass  meter  bar  constructed  in  Paris by  Lenoir  in  1813  for  Mr.  Hassler,  and  one  of  the  original secondary  iron-bar  standards  constructed  by  the  same  maker  for the  French  Metric  Committee  in  1799,  and  presented  to  Mr. Hassler  by  Tralles.3  This  latter  standard  was  employed  by  the Coast  Survey  until  the  receipt  of  the  international  standards  in 1890,  and  is  now   to   be   seen  in   the  vault  of   the   Bureau  of 1  This  is  shown  plainly  in  several  of  Jefferson's  letters  contained  in  the  Works of  Thomas  Jefferson  (New  York,  1884),  particularly  those  to  William  Short (vol.  iii.  p.  276),  Dr.  Robert  Patterson  (vol.  vi.  p.  11),  and  John  Quincy  Adams (vol.  vii.  p.  87). 2  See  F.  R.  Hassler,  Report  on  Weights  and  Measures,  Document  299,  22nd Congress,  1st  Session,  1832,  p.  40.  Also  U.S.  Coast  and  Geodetic  Survey  Report, 1877  ;  Appendix  12. 3  See  Hassler,  loc.  cit.,  p.  75,  for  translation  of  Tralles'  description  of  these standards.  Also  Transactions  of  American  Philosophical  Soc.  (Phila.,  1825),  vol. ii.  p.  252 ;  and  Special  Publication  No.  4,  U.  S.  Coast  and  Geodetic  Survey,  p.  31 (Washington,  1900). WEIGHTS  AND  MEASURES  IN  UNITED  STATES     115 Standards   at   Washington.      It   is   of    rectangular   cross   section 9  mm.  x  29  mm.,  and  is,  of  course,  an  end  standard. Eeforms  in  weights  and  measures  were  not  proceeding  any  more satisfactorily  abroad  than  in  the  United  States.  Great  Britain had  been  unable  "  to  reduce  into  any  simple  order  the  chaos  of their  weights  and  measures,"1  as  Jefferson  wrote  to  Secretary  of State  Adams  in  1817,  while  in  France  the  Metric  System  was  not securing  the  ready  adoption  that  was  desired.  The  countries conquered  by  Napoleon  and  compelled  to  adopt  it,  returned  to their  old  ways  once  compulsion  was  removed;  and  even  in  France, as  we  have  seen,  there  was  considerable  doubt  as  to  the  practical and  ultimate  success  of  the  new  system,  while  the  decimal  division of  time  and  the  decimal  measurement  of  the  circle  had  proved distinct  failures.  Therefore,  it  is  not  hard  to  explain  the  hesita- tion in  the  United  States  about  adopting  the  French  system. That  some  measures  were  needed  we  learn  from  the  message  of President  Madison  to  Congress  in  1816,  when  he  said: "  Congress  will  call  to  mind  that  no  adequate  provision  has yet  been  made  for  the  uniformity  of  weights  and  measures  con- templated by  the  Constitution.  The  great  utility  of  a  standard fixed  in  its  nature,  and  founded  on  the  easy  rule  of  decimal  pro- portions, is  sufficiently  obvious.  It  led  the  Government  at  an early  stage  to  preparatory  steps  for  introducing  it,  and  a  com- pletion of  the  work  will  be  a  just  title  to  the  public  gratitude." Congress  referred  the  matter  to  the  Secretary  of  State,  John Quincy  Adams,  and  that  official  undertook  a  thorough  analysis and  study  of  the  whole  subject.  To  him  Jefferson  wrote  in  the letter  already  quoted  : 2  "  I  sincerely  wish  you  may  be  able  to  rally us  to  either  standard,  and  to  give  us  an  unit,  the  aliquot  part of  something  invariable  which  may  be  applied  simply  and  con- veniently to  our  measures,  weights,  and  coins,  and  most  especially that  the  decimal  divisions  may  pervade  the  whole."  Adams realized  that  the  matter  was  one  of  extreme  importance  that could  not  be  settled  offhand,  and  on  his  own  account  examined the  question  in  all  its  many  aspects,  his  conclusions  being  given in  a  report3  submitted  on  February  22,  1821,  that  has  since  been 1  Works  of  Thomas  Jefferson,  vol.  vii.  p.  89. 2  Ibid. 3  J.  Q.  Adams,  Report  upon  Weights  and  Measures,  Washington,  1821. 116     EVOLUTION   OF   WEIGHTS   AND   MEASURES considered  almost  a  classic  in  American  metrology.  While  the Secretary  of  State  was  so  engaged,  a  committee  from  the  House of  Kepresentatives  also  considered  the  question  of  weights  and measures,  and,  January  25,  1819,  submitted  a  report  virtually advising  the  adoption  of  the  first  plan  proposed  by  Jefferson,  and recommending  that  models  of  the  yard,  bushel,  and  pound,  con- forming to  those  in  most  common  use,  be  made  under  the direction  of  a  commission  to  be  selected  by  the  President,  and which,  if  satisfactory  to  Congress,  should  be  declared  the  standard weights  and  measures  of  the  United  States.  Again,  Congress failed  to  take  action  on  this  recommendation,  and  when,  two  years later,  Secretary  Adams  submitted  his  report,  in  which  he  recom- mended that  no  present  change  in  the  weights  and  measures  of the  country  be  attempted,  but  that  the  standards  should  remain as  they  were,  that  body  had  no  disposition  to  oppose  his  sug- gestions, and  nothing  was  accomplished. The  report,  however,  is  worth  more  *  than  passing  notice,  for although  Adams  did  not  believe  that  the  introduction  of  the Metric  System  into  the  United  States  at  that  time  was  prac- ticable, nevertheless  he  was  as  alive  to  its  symmetry,  complete- ness, and  general  desirability,  as  he  was  to  the  many  advantages attending  the  introduction  of  a  universal  system  of  weights  and measures  throughout  the  great  countries  of  the  world.  While  it is,  of  course,  impossible  to  do  justice  to  the  completeness  and philosophic  treatment  of  the  subject  in  this  report  by  any summary  or  brief  extracts,  nevertheless  a  few  passages  will  show how  keen  was  Mr.  Adams'  understanding  of  the  matter,  and  how well  he  appreciated  the  advantages  of  the  French  system.  He said : !  "  This  system  approaches  to  the  ideal  perfection  of uniformity  applied  to  weights  and  measures,  and  whether  destined to  succeed  or  doomed  to  fail,  will  shed  unfading  glory  upon  the age  in  which  it  was  conceived,  and  upon  the  nation  by  which  its execution  was  attempted,  and  has  in  part  been  achieved.  In  the progress  of  its  establishment  there  it  has  often  been  brought  in conflict  with  the  laws  of  physical  and  of  moral  nature,  with  the impenetrability  of  matter,  and  with  the  habits,  passions,  pre- judices, and  necessities  of  man.  It  has  undergone  various important  modifications.      It  must  undoubtedly  submit  to  others 1  J.  Q.  Adams,  Report,  p.  48. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     117 before  it  can  look  for  universal  adoption.  But,  if  man  upon earth  be  an  improvable  being ;  if  that  universal  peace,  which  was the  object  of  a  Savior's  mission,  which  is  the  desire  of  the philosopher,  the  longing  of  the  philanthropist,  the  trembling  hope of  the  Christian,  is  a  blessing  to  which  the  futurity  of  mortal man  has  a  claim  of  more  than  mortal  promise ;  if  the  spirit  of evil  is,  before  the  final  consummation  of  things,  to  be  cast  down from  his  dominion  over  men,  and  bound  in  the  chains  of  a thousand  years,  the  foretaste  here  of  man's  eternal  felicity,  then this  system  of  common  instruments,  to  accomplish  all  the  changes of  social  and  friendly  commerce,  will  furnish  the  links  of sympathy  between  the  inhabitants  of  the  most  distant  regions ; the  meter  will  surround  the  globe  in  use  as  well  as  multiplied extention,  and  one  language  of  weights  and  measures  will  be spoken  from  the  equator  to  the  poles." As  regards  the  metric  or,  as  he  terms  it,  the  French  system  in the  abstract  or  as  an  ideal  system,  no  one  could  be  more enthusiastic  than  Mr.  Adams.  He  says  : 1  "  The  single  standard, proportional  to  the  circumference  of  the  earth ;  the  singleness of  the  units  for  all  the  various  modes  of  mensuration ;  the universal  application  to  them  of  decimal  arithmetic  ;  the  un- broken chain  of  connection  between  all  weights,  measures, moneys,  and  coins;  and  the  precise,  significant,  short,  and complete  vocabulary  of  their  denominations :  altogether  forming a  system  adapted  equally  to  the  use  of  all  mankind ;  afford  such a  combination  of  the  principle  of  uniformity  for  all  the  most important  operations  of  the  intercourse  of  human  society ;  the establishment  of  such  a  system  so  obviously  tends  to  that  great result,  the  improvement  of  the  physical,  moral,  and  intellectual condition  of  man  upon  earth ;  that  there  can  be  neither  doubt nor  hesitancy  in  the  opinion  that  the  ultimate  adoption  and universal,  though  modified,  application  of  that  system  is  a  con- summation devoutly  to  be  wished." The  strongest  praise  for  the  French  system  is  for  the  time that  it  will  save,  and  here  Mr.  Adams  states,2  "  Considered merely  as  a  labor-saving  machine,  it  is  a  new  power  offered to  man  incomparably  greater  than  that  which  he  has  acquired by  the  new  agency  which   he   has   given   to  steam.      It   is   in 1  J.  Q.  Adams,  Report,  p.  90.  2Ibid.,  p.  91. 118     EVOLUTION   OF  WEIGHTS   AND   MEASURES design    the   greatest  invention   of    human    ingenuity   since   that of  printing." Mr.  Adams,  while  he  realized  the  desirability  of  universal measures,  believed  that  they  could  only  come  "  by  consent  and not  by  force,"  and  mindful  of  the  difficulties  attending  the  intro- duction of  the  metric  system  in  France,  and  of  certain  of  its features  being  susceptible  of  further  improvement,  thought  it  to be  the  best  policy  for  the  United  States  first  to  confer  with foreign  nations  as  regards  the  future  and  ultimate  establishment of  universal  and  permanent  uniformity,  and,  meanwhile,  to secure  for  the  weights  and  measures  in  use  throughout  the United  States  a  more  perfect  uniformity  by  suitable  legislation especially  avoiding  for  the  time  being  any  innovations.  The conclusion  of  the  report  is  no  less  interesting  than  its  other sections :  It  states,1  "  France  first  surveyed  the  subject  of  weights and  measures  in  all  its  extent  and  all  its  compass.  France  first beheld  it  as  involving  the  interests,  the  comforts,  and  the  morals of  all  nations  and  of  all  after  ages.  In  forming  her  system  she acted  as  the  representative  of  the  whole  human  race,  present  and to  come.  She  has  established  it  by  law  within  her  own  terri- tories, and  she  has  offered  it  as  a  benefaction  to  the  acceptance  of all  other  nations.  That  it  is  worthy  of  their  acceptance  is believed  to  be  beyond  question.  But  opinion  is  the  queen  of  the world,  and  the  final  prevalence  of  this  system  beyond  the boundaries  of  France's  power  must  await  the  time  when the  example  of  its  benefits,  long  and  practically  enjoyed,  shall acquire  that  ascendancy  over  the  opinions  of  other  nations which  gives  motion  to  the  springs  and  direction  to  the  wheels of  power." It  is  doubtful  if  a  stronger  statement  of  the  abstract  merits  of the  metric  system  could  be  made  than  is  contained  in  this  report. Mr.  Adams,  however,  was  in  error  in  believing  that  concerted action  was  necessary  to  secure  the  adoption  of  a  universal  system, as  it  has  come  about  gradually,  and  has  been  adopted  by  the various  nations  of  the  world  at  such  times  as  seemed  to  them suitable  and  convenient.  Again,  experience  has  shown  the  error of  Mr.  Adams'  view  on  the  decimal  division  of  the  United  States coinage.       He    says    (page    81),  "The    convenience    of    decimal lJ.  Q.  Adams,  Report,  p.  135. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     119 arithmetic  is  in  its  nature  merely  a  convenience  of  calculation ; it  belongs  essentially  to  the  keeping  of  accounts ;  but  it  is  merely an  incident  to  the  transactions  of  trade.  It  is  applied,  therefore, with  unquestionable  advantage  to  moneys  of  account,  as  we  have done :  yet  even  in  our  application  of  it  to  the  coins,  we  have  not only  found  it  inadequate,  but  in  some  respects  inconvenient." This  famous  report  has  been  quoted  most  extensively  by writers  on  American  metrology,  and  passages  are  cited  with  great enthusiasm  by  both  metric  and  anti-metric  advocates  in  support of  their  respective  positions.  While  conceding  its  great  breadth and  philosophical  character,  yet  at  the  present  time  it  is  worth considering  whether  too  much  stress  has  not  been  laid  on  this celebrated  document.  Although  President  Adams  was  a  zealous student,  errors  of  statement  are  to  be  noted,  while  at  the  same time  advances  in  the  science  of  metrology  have  made  it  necessary to  look  at  certain  matters  in  a  new  light. There  was  at  least  one  department  of  the  U.S.  Government — namely,  the  Mint — where  any  uncertainty  of  weight  could  not  for obvious  reasons  be  tolerated.  Accordingly,  Minister  Gallatin was  instructed  to  procure  from  England  a  copy  of  the  imperial standard  Troy  pound  which  had  been  adopted  in  1825.  This  he did,  and  the  standard,  after  having  been  most  carefully  compared by  Captain  Kater,  was  transmitted  to  the  United  States,  and  by Act  of  Congress  of  May  19,  1828,1  was  duly  established  as  the coinage  standard  of  the  United  States,  the  Act  being  remarkable in  that  it  is  the  only  legislative  Act  legalizing  any  of  the •customary  measures,  and  establishing  a  standard  for  such  purpose. The  Act  provides,  that  "  For  the  purpose  of  securing  a  due  con- formity in  weight  of  the  coins  of  the  United  States  to  the provisions  of  this  title,  the  brass  troy -pound  weight  procured  by the  minister  of  the  United  States  at  London,  in  the  year  eighteen hundred  and  twenty-seven,  for  the  use  of  the  Mint,  and  now  in the  custody  of  the  Mint  at  Philadelphia,  shall  be  the  Standard troy  pound  of  the  Mint  of  the  United  States,  conformably  to which  the  coinage  thereof  shall  be  regulated." 2 1C.  131,  Sec.  50,  17  statutes  432.     Revised  statutes  3548. 2  A  description  of  this  standard,  together  with  the  various  certificates  of individuals  concerned  with  its  construction,  testing,  receipt,  etc.,  including Oaptain  Henry  Kater,  Minister  Gallatin,  and  President  John  Quincy  Adams, 120     EVOLUTION   OF   WEIGHTS   AND   MEASURES On  May  29,  1830,  the  Senate  passed  a  resolution  ordering  the comparison  of  the  standards  of  weights  and  measures  used  by  the different  custom-houses,  and  when  these  measures  or  copies  were called  in  to  the  Treasury  Department  for  examination,  it  was found  that  there  was  the  greatest  lack  of  uniformity  throughout the  various  customs  districts.  In  many  cases  the  various  state or  local  sealers  of  weights  and  measures  were  appealed  to  not only  for  purposes  of  comparison,  but  even  for  the  correction  of the  standards.1 The  resulting  diversity  of  weights  and  measures  naturally  was not  without  its  effect  on  the  revenues  of  the  Government,  in addition  to  violating  that  section  of  the  Constitution  which  pro- vides that  taxes  shall  be  uniform  throughout  the  United  States. The  national  standards  upon  which  the  measurements  made  in the  custom-houses  were  based  are  thus  described  in  the  following extract  from  the  report  of  S.  D.  Ingham,  Secretary  of  the Treasury,  March  3,  1831  : "  Among  the  instruments  which  had  been  procured,  some  years ago,  under  the  direction  of  the  President,  for  the  survey  of  the coast,  was  a  standard  measure  of  length,  exactly  corresponding with  the  British  Parliamentary  standard,  as  established  in  1758, with  which  that  of  1760  is  identical,  as  tested  by  Sir  George Shuckburgh  in  1798,  and  by  Captain  Kater  in  1821,  on  the occasion  of  the  last  determination  of  the  weights  and  measures  in England,  when  it  was  adopted  as  the  legal  unit.  This  standard measure  has,  by  means  which  will  be  explained  in  a  future report,  been  compared  with  the  pendulum  vibrating  seconds  in London,  and  also  with  the  French  meter,  which  is  based  upon measurements  of  arcs  of  a  meridian  of  the  earth.  With  such, evidence  of  its  character,  and  such  an  opportunity  of  correcting any  alteration  by  reason  of  decay,  it  was  without  hesitation, adopted  as  the  unit  for  the  comparison  of  measures  of  length. "  The  troy  pound  used  in  the  Mint  is  known  to  be  identical with  the  latest  established  standard  troy  pound  of  Great  Britain, as  regulated   by  the  British  laws,  and    standarded   by  Captain will  be  found  contained  in  an  interesting  history  of  the  weights  and  measures  of the  United  States,  by  0.  H.  Tittman,  in  the  United  States  Coast  and  Geodetic Survey  Report  for  1890,  Appendix  18,  pp.  736-8. 1Hassler,  p.  6  (House  of  Reps.  Doc.,  No.  299,  22nd  Congress,  1st  Session). WEIGHTS  AND  MEASURES  IN  UNITED  STATES     121 Kater  in  1824,  having  been  constructed  by  him  at  the  special request  of  Mr.  Gallatin,  upon  the  same  principles  and  in  the same  manner  that  he  had  employed  in  the  construction  of  the British  standard."  1 Preparations  were  duly  made  to  construct  from  these  standards the  standards  for  the  custom-houses,  and  on  June  14, 1836,  a  joint resolution  was  adopted  by  both  Houses  of  Congress  providing that  there  should  be  constructed  in  the  office  of  the  Coast Survey  for  every  state  and  territory,  complete  sets  of  standards equal  to  those  made  for  the  custom-houses,  "  to  the  end  that a  uniform  standard  of  weights  and  measures  may  be  established throughout  the  United  States,"  and  in  July,  1838,  it  was  ordered that  balances  for  the  accurate  comparison  of  weights  should  be similarly  constructed  and  distributed  to  the  states  and  territories. The  standard  weights  were  given  to  the  custom-houses  in  1836, and  in  the  following  years  the  standard  yards,  which  were  based on  the  Troughton  scale,  and  liquid  measures  were  distributed. By  1856  the  various  states  of  the  Union  were  supplied  with sets  of  standards,  and  shortly  after  their  receipt  the  individual states  enacted  statutes  establishing  them  as  the  standards  of weights  and  measures.2  This  work  was  important,  as  being the  first  practical  and  systematic  attempt  to  secure  general uniformity  of  weights  and  measures  throughout  the  country,, and  as  an  early  example  of  refined  constructive  scientific  work being  carried  on  by  the  national  government  for  the  benefit of  the  people  at  large  in  their  commercial  relations. It  should  be  said  in  passing  that  the  early  work  of  estab- lishing the  standards  of  weights  and  measures  for  the  United States  was  done  by  Professor  F.  E.  Hassler,  the  superintendent of  the  Coast  Survey,  from  its  inception  to  his  death,  and  during these  years  many  interesting  reports  dealing  with  the  scientific and  other   features   of   the  work  were  prepared    by  him.3     To Extract  from  the  report  of  S.  D.  Ingham,  Secretary  of  State,  March  3,  1831 1 House  of  Representatives,  Doc.  No.  299,  July  2,  1832,  22nd  Congress,  1st Session. 2  See  Laws  Concerning  the  Weights  and  Measures  of  the  United  States,  an  official compilation  of  the  United  States  Bureau  of  Standards  of  legislation  on  this- subject  (Washington,  1904). 3  See  partial  bibliography  in  House  of  Representatives,  Report  No.  3005,  56th Congress,  2nd  Session. 122     EVOLUTION   OF   WEIGHTS   AND   MEASURES Professor  Hassler  was  due  the  derivation  of  the  standard  avoir- dupois pound  from  the  standard  Troy  pound,  and  so  accurately was  the  work  accomplished  that  when  the  British  Government sent  over  in  1856  a  copy  of  the  standard  avoirdupois  pound,  there was  found  a  difference  of  '001  of  a  grain  between  British  and American  standards.  He  also  connected  the  units  of  capacity with  those  of  weight,  by  using  in  his  experiments,  which  were begun  in  1830,  distilled  water  at  its  temperature  of  maximum density,  and  thus  was  able  to  determine  and  construct  accurate standards. On  the  death  of  Mr.  Hassler  in  1843,  Professor  A.  D.  Bache became  the  head  of  the  Coast  Survey,  and  manifested  consider- able interest  in  the  work  of  the  Office  of  Weights  and  Measures, supervising  the  completion  and  distribution  of  the  state  standards begun  by  Mr.  Hassler,  and  in  his  reports  making  recommenda- tions looking  towards  the  improvement  of  the  United  States system  of  weights  and  measures,  and  also  the  establishment  of a  universal  system. With  the  distribution  of  the  standard  weights  and  measures, there  resulted  the  natural  inquiries  as  to  their  origin  and  value, and  the  legal  enactments  upon  which  they  were  founded.  Pro- fessor Bache  in  his  report  for  18481  summarizes  the  essential facts  relating  to  them.  The  actual  standard  of  length  is  the 8 2 -inch  Troughton  scale  (which  has  been  already  described) ; "  the  units  of  capacity  measure  are  the  gallon  for  liquid  and  the bushel  for  dry  measure.  The  gallon  is  a  vessel  containing 58,372*2  grains  (8*3389  pounds  avoirdupois)  of  the  standard  pound of  distilled  water,  at  the  temperature  of  maximum  density  of water,  the  vessel  being  weighed  in  air  in  which  the  barometer is  30  inches  at  62°  Fahrenheit.  The  bushel  is  a  measure containing  543,391 '89  standard  grains  (77'6274  pounds  avoir- dupois) of  distilled  water  at  the  temperature  of  maximum density  of  water,  and  barometer  30  inches  at  62°  Fahrenheit." The  gallon  is  thus  the  wine  gallon  of  231  cubic  inches  nearly, and  the  bushel  the  Winchester  bushel  nearly.  The  temperature of  maximum  density  of  water  was  determined  by  Mr.  Hassler to  be  39'85°  Fahrenheit.  The  standard  of  weight  is  the  Troy pound  copied  by  Captain  Kater  in  1827  from  the  imperial  Troy ^Oth  Congress,  1st  Session,  Senate  Executive  Doc.  73  (1848),  p.  8. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     123 pound  for  the  United  States  Mint,  and  preserved  in  that establishment.  The  avoirdupois  pound  is  derived  from  this : its  weight  being  greater  than  that  of  the  Troy  pound,  in  the proportion  of  7000  to  5760 ;  that  is,  the  avoirdupois  pound  is equivalent  in  weight  to  7000  grains  Troy.  The  multiples,  as  well as  subdivisions  of  the  pound,  are  based  upon  this  standard,  the weight  of  which  was  determined  by  the  best  means  attainable  at that  time,  in  grain  weights,  by  Troughton,  at  the  Mint,  and  at the  Office  of  Weights  and  Measures,  in  presence  of  Mr.  Hassler, and  of  the  Director  of  the  Mint,  Dr.  Moore.  From  these determinations  resulted  the  pound  weights  of  the  Office  of Weights  and  Measures,  which  are  therefore  copies  of  the  Troy pound  of  the  United  States  Mint  or  derived  from  it.  The pound  is  a  standard  at  30  inches  of  the  barometer  and  62° Fahrenheit  thermometer.  The  Troy  pound  of  the  Mint  was found,  in  the  comparisons  of  Captain  Kater,  to  be  heavier  than the  imperial  Troy  pound  by  only  '0012  of  a  grain. "  The  measures  of  length  and  capacity,  and  the  weights  just referred  to,  have  been  adopted  by  the  Treasury  Department  as standards  for  the  measures  and  weights  of  the  custom  houses  of the  United  States,  and  reported  as  such  to  Congress  in  1832.  .  ." That  the  system  was  then  unsatisfactory  in  many  respects  we have  abundant  testimony.  The  simplification  of  the  existing weights  and  measures,  and  the  issuing  of  correct  standards  had been  provided  for  as  Adams  had  suggested,  but  nothing  had  been done  to  improve  the  system  or  towards  co-operating  with  foreign nations  in  establishing  a  universal  system,  as  Adams  had  also suggested.  On  the  conditions  as  they  then  existed  Professor Bache's  observations  are  of  interest.  In  a  report  made  in  1848 he  says : x "  No  one  who  has  discussed  the  subject  of  weights  and measures  in  our  country  has  considered  the  present  arrangement as  an  enduring  one.  It  has  grown  up  with  the  growth  of European  society,  and  is  deficient  in  simplicity  and  in  system. The  labor  which  is  expended  in  mastering  the  complex  denomi- nations of  weights  and  measures  is  labor  lost.  Every  purpose for  which  weights  and  measures  are  employed  can  be  answered by  a  simple  and  connected  arrangement." 1  Executive  Document  84,  Thirteenth  Congress,  1st  Session,  July  30,  1848. 124     EVOLUTION   OF   WEIGHTS   AND   MEASURES Professor  Bache  believed  that  inasmuch  as  it  was  the  prac- tically universal  opinion  of  all  who  had  studied  and  written  on American  weights  and  measures  that  the  system  then  in  use must  be  considered  temporary,  and  eventually  be  replaced  by  a more  convenient  and  systematic  arrangement,  and  wrote  in reference  to  Adams'  plan  for  an  international  conference  on  the subject  as  follows :  "  The  present  time  seems  especially  to  invite an  effort  of  this  kind.  In  England  the  subject  of  weights  and measures  is  under  consideration  by  a  commission ;  and  on  the Continent  the  new  relations  of  states  hitherto  separated  appears to  be  favorable  to  this  object.  Such  changes  can  be  readily effected  by  suitable  means  in  one  generation,  by  introducing  the new  measures  through  the  elementary  schools."  In  a  subsequent report  Professor  Bache  asks,  "  Has  not  the  time  arrived,  in  the general  progress  of  commercial  and  international  intercourse,  and the  rapid  advance  of  our  own  country  in  science,  wealth,  and power,  when  her  voice  should  be  heard  in  an  important  matter like  this  ?  Should  not  Congress  make  the  proposition  to  all nations,  to  meet,  by  their  representatives,  and  consult  for  the purpose  of  establishing  uniformity  of  weights  and  measures  ? Such  action  could  not  fail  to  meet  with  a  response  due  to  the greatness  of  the  subject,  and  if  the  great  object  be  attained,  to lead  to  results  productive  of  vast  and  lasting  benefit  to  the human   race." While  it  is  quite  natural  that  opinions  in  favor  of  the  adoption of  the  metric  system  should  be  given  by  officials  of  the  bureau  of weights  and  measures,  and  by  Secretaries  of  the  Treasury,  it  is possible  to  recognize  the  beginning  of  a  distinct  general  feeling and  movement  in  favor  of  reforms  in  American  weights  and measures.  This  may  be  traced  largely  to  the  increasing  numbers of  scientific  and  professional  men  who  were  sent  to  Europe  for education,  and,  who  having  used  the  metric  system  in  the  schools and  laboratories  of  France  and  Germany,  became  enthusiastic advocates  of  the  system,  with  the  result  that  on  their  return to  the  United  States  they  adopted  it  for  their  own  scientific work,  and  taught  it  to  their  students.  In  chemistry  especially its  pre-eminence  was  early  recognized,  and  American  chemists soon  fell  in  with  the  universal  system  which  by  this  time was    employed    in    all    the     European    journals     and    standard WEIGHTS  AND  MEASURES  IN  UNITED  STATES     125 works.1  American  diplomats  and  representatives  to  various  inter- national conferences  also  became  convinced  of  the  desirability  of a  uniform  system  of  weights  and  measures,  and  their  influence was  also  exerted  in  stimulating  a  feeling  in  favor  of  reforms. In  February,  1854,  the  American  Geographical  and  Statistical Society,  of  which  George  Bancroft,  the  historian  and  Minister  to Spain,  was  then  president,  presented  a  memorial  to  Congress  in which  the  appointment  of  a  joint  scientific  commission  to  consider a  uniform  system  of  weights  and  measures  based  on  a  decimal system  was  urged.  This  was  one  of  the  earliest  of  a  number  of similar  resolutions  which  have  since  been  addressed  to  Congress. Of  more  importance,  however,  as  coming  from  the  people  at  large rather  than  from  scientific  bodies,  were  the  resolutions  adopted by  the  legislatures  of  various  States.  The  legislature  of  New Hampshire,  by  joint  resolution  approved  on  June  28,  1859,  re- quested their  senators  and  representatives  to  urge  upon  Congress the  adoption  of  a  decimal  system,  while  the  legislature  of  Maine, March  20,  1860,  by  joint  resolution,  expressed  in  still  more decided  language,  their  desire  for  a  uniform  international  system of  weights,  measures,  and  coins.  This  action  was  soon  followed by  a  similar  resolution  by  the  legislature  of  the  State  of  Con- necticut, which  in  June,  1864,  took  an  important  step  in  recom- mending to  the  proper  school  officers,  that  they  should  provide for  the  teaching  of  the  metric  system  in  all  the  schools  of  the State.  From  this  time  interest  in  the  metric  system  in  con- nection with  the  study  of  the  arithmetic  in  the  schools  increased, so  that  the  pupils  within  a  few  years  became  aware  of  the existence  of  the  system,  although  often  in  the  method  of  pre- sentation of  the  subject  in  text-books,  and  by  teachers  there  was little  to  commend  it  to  the  young  mind.  The  problems  were usually  those  involving  conversion  from  the  common  system  to the  metric,  and  as  such,  were  not  likely  to  inspire  any  great degree  of  appreciation  for  the  latter. The  Civil  War  so  occupied  the  legislative  and  executive departments  of  the  Government  that  there  was  little  opportunity 1  The  use  of  the  metric  measures  in  American  College  text-books,  in  physics  and chemistry,  dates  from  1868-1870.  In  similar  works  for  high  schools  the  new system  was  used  from  1878.  R.  P.  Williams  before  Am.  Chem.  Soc,  June, 1900. 126     EVOLUTION   OF   WEIGHTS   AND   MEASURES for  any  marked  progress  on  the  part  of  Congress  or  the  officials. The  condition  of  affairs  is  stated  by  Salmon  P.  Chase,  Secretary of  the  Treasury,  in  his  annual  report  December  9,  1861,  where  he writes :  "  The  Secretary  desires  to  avail  himself  of  this  oppor- tunity to  invite  the  attention  of  Congress  to  the  importance  of  a uniform  system  and  a  uniform  nomenclature  of  weights  and measures,  and  coins  to  the  commerce  of  the  world  in  which  the United  States  already  so  largely  shares.  The  wisest  of  our statesmen  have  regarded  the  attainment  of  this  end  so  desirable in  itself  as  by  no  means  impossible.  The  combination  of  the decimal  system  with  appropriate  denominations  in  a  scheme  of weights,  measures,  and  coins  for  the  international  uses  of  com- merce, leaving,  if  need  be,  the  separate  systems  of  nations untouched,  is  certainly  not  beyond  the  reach  of  the  daring  genius and  patient  endeavor  which  gave  the  steam  engine  and  the telegraph  to  the  service  of  mankind.  The  Secretary  respect- fully suggests  the  expediency  of  a  small  appropriation  to  be used  in  promoting  interchange  of  opinions  between  intelligent persons  of  our  own  and  foreign  countries  on  this  subject." In  1863  the  United  States  was  represented  abroad  at  two important  international  congresses,  both  of  which  took  action  on the  matter  of  weights  and  measures  which  commended  itself  to the  American  delegates.  At  the  International  Statistical  Con- gress held  at  Berlin,  a  committee  appointed  at  the  Paris  meeting three  years  previously,  to  consider  the  question  of  uniform international  weights,  presented  a  report  in  which  the  subject was  carefully  considered  and  as  a  result  of  which  the  Congress resolved  that  the  same  measures  for  international  commerce  was of  the  highest  importance,  and  that  the  metric  system  was  the most  convenient  of  all  that  could  be  recommended  for  inter- national measures.1  At  a  previous  session  this  body  had recommended  that  the  countries  which  employed  weights  and measures  other  than  the  metric  should  give  in  adjoining  columns the  metric  equivalents  of  all  statistics. The  other  international  congress  referred  to  was  a  postal congress  held  at  Paris  in  May,  1863,  and  which  resulted  in important    measures    towards     securing     uniformity    of    weights 1  Samuel  B.  Ruggles,  Report  on  International  Statistical  Congress  at  Berlin  in, respect  to  Uniform  Weights,  Measures,  and  Coins  (Albany,  1864),  pp.  43,  44. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     127 throughout  the  world.  It  was  here  recommended,  that,  "  Sec.  7. The  rates  upon  international  correspondence  shall  be  established according  to  the  same  scale  of  weight  in  all  countries,"  that "  Sec.  8.  The  metrical  system,  being  that  which  best  satisfies  the demands  of  the  postal  service,  should  be  adopted  for  international postal  relations,  to  the  exclusion  of  every  other  system  " ;  and that  "  Sec.  9.  The  single  rate  upon  international  letters  shall  be applied  to  each  standard  weight  of  15  grams  or  fractional  part  of it."  This  proposition  proved  satisfactory  to  the  various  nations and  accordingly  was  incorporated  in  the  International  Postal Convention. In  1866,  when  the  resolutions  authorizing  the  use  of  the metric  system  of  weights  and  measures  was  passed  by  the Congress  of  the  United  States,  which  is  referred  to  at  more length  below,  an  Act  was  also  passed  enabling  the  Post  Office Department  to  use  the  metric  weights  and  measures  for  foreign and  other  purposes,  and  the  law  was  re-enacted  in  1872  and now  reads  {Revised  Statutes  of  the  United  States,  Sec.  3880), "  The  Postmaster-General  shall  furnish  the  post-offices  ex- changing mails  with  foreign  countries,  and  to  such  other offices  as  he  may  deem  expedient,  postal  balances  denoted  in grams  of  the  metric  system,  fifteen  grams  of  which  shall  be the  equivalent  for  postal  purposes  of  one  half  ounce  avoirdupois, and  so  on  in  progression."  The  interchange  of  mail  by  all the  civilized  countries  of  the  world  represents  the  most  extensive use  of  a  uniform  system  of  weights  and  measures  in  the  world and  has  been  carried  on  for  many  years  without  the  slightest confusion  or  embarrassment.  All  mail  matter  transported  be- tween the  United  States  and  the  fifty  or  more  nations, signatories  of  the  International  Postal  Convention,  including the  United  States  and  Great  Britain  even,  is  weighed  and  paid for  entirely  by  metric  weight. The  serious  consideration  of  the  metric  system  in  the  United States  by  the  people  at  large  may  be  said  to  date  from  1866 when  Congress  passed  a  Bill  which  was  approved  by  the President  authorizing  the  use  of  the  metric  system  of  weights and  measures.  In  this  action  Congress  had  the  advice  of the  National  Academy  of  Science,  which  had  appointed  in 1863,  at  the  request  of  the  Secretary  of  the  Treasury,  a  special 128     EVOLUTION   OF   WEIGHTS   AND   MEASURES committee  to  consider  the  matter.  In  its  report,  which  was adopted  by  the  Academy,  occurs  the  following  passage,  which seems  to  sum  up  the  situation :  "  The  committee  are  in  favor of  adopting,  ultimately,  a  decimal  system :  and  in  their  opinion, the  metrical  system  of  weights  and  measures,  though  not without  defects,  is,  all  things  considered,  the  best  in  use. The  committee  therefore  suggest  that  the  Academy  recommend to  Congress  to  authorize  and  encourage  by  law  the  introduction and  use  of  the  metrical  system  of  weights  and  measures,  and that,  with  a  view  to  familiarize  the  people  with  the  system, the  Academy  recommend  that  provision  be  made  by  law  for the  immediate  manufacture  and  distribution  to  the  custom- houses and  States,  of  metrical  standards  of  weights  and measures :  to  introduce  the  system  into  the  post-offices  by making  a  single  letter  weigh  15  grammes  instead  of  14^^, or  half  an  ounce :  and  to  cause  the  new  cent  and  two  cent pieces  to  be  so  coined  that  they  shall  weigh  respectively 5  and  10  grammes,  and  that  their  diameters  shall  be  made to  bear  a  determinate  and  simple  ratio  to  the  metrical  unit of  length."1  Accordingly,  by  the  law  of  May  16,  1866,  the weight  of  the  5  cent  copper  nickel  piece  was  fixed  at  5  grams. This  idea  was  extended  to  the  silver  coinage,  and  by  the  law of  Feb.  12,  1873  {Revised  Statutes  of  the  United  States,  Sec. 3513),  it  was  provided  that  "The  weight  of  the  half  dollar shall  be  twelve  grams  and  one-half  of  a  gram;  the  quarter dollar  and  the  dime  shall  be,  respectively,  one-half  and  one- fifth  of  the  weight  of  said  half  dollar."  The  Act  passed by  Congress  (Revised  Statutes  of  the  United  States,  Sec.  3569) on  July  28,  1866,  making  the  metric  system  permissive,  pro- vided that  "it  shall  be  lawful  throughout  the  United  States of  America  to  employ  the  weights  and  measures  of  the  metric system,  and  no  contract  or  dealing,  or  pleading  in  any  court, shall  be  deemed  invalid  or  liable  to  objection  because  the weights  and  measures  expressed  or  referred  to  therein  are weights  or  measures  of  the  metric  system."  The  Act  further provided  a  series  of  legal  tables  of  equivalents,  and  upon  them are  based  in  the  United  States  all  conversions  from  one  system 1  House  of  Representatives,   Report   of  the   Committee  on    Coinage,    Weights, and  Measures,  46th  Congress,  1st  Session,   Report  No.   14,  p.  23,  part  i. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     129 to  the  other,  as,  for  example,  those  contained  in  the  tables  in the  Appendix  of  this  book.  To  further  the  use  of  the  metric system  Congress  passed  an  Act,  approved  July  27,  1866, authorizing  and  directing  the  Secretary  of  the  Treasury  to furnish  to  each  State  one  set  of  the  standard  weights  and measures  of  the  metric  system.  With  this  start  the  metric system  has  grown  in  the  United  States,  and  various  measures looking  towards  its  final  adoption  have  been  urged  in  Congress and  among  the  people  generally. The  delegates  to  the  Paris  Exposition  of  1867  were  par- ticularly enthusiastic  in  this  respect,  and  among  them  Professor F.  A.  P.  Barnard,  President  of  Columbia  College,  who,  with .a  number  of  other  advocates  of  reforms  in  weights  and  measures, formed  December  30,  1873,  the  American  Metrological  Society, and  was  its  president  until  his  death  in  1889.1  This  society, while  interested  in  such  kindred  subjects  as  the  adoption of  standard  time  and  international  currency,  carried  on  an active  propaganda  in  behalf  of  the  metric  system,  while  the Metric  Bureau  which  was  organized  July,  1876,  with  head- quarters in  Boston,  supplied  material  both  in  the  way  of literature  and  actual  weights  and  measures,  charts,  tables, etc.,  that  was  of  the  greatest  assistance  to  the  general  public, especially  teachers,  who  were  now  called  upon  in  many  States to  explain  and  teach  the  principles  of  the  system. Sufficient  interest  was  manifested  in  the  subject  for  the  United States  Government  to  accept  the  invitation  of  the  Government of  France  to  send  delegates  to  Paris  to  form  an  international commission  to  construct  new  metric  standards.  America  was accordingly  represented  by  Professor  Joseph  Henry  and  J.  E. Hilgard,  the  latter  being  an  active  member  of  various  important committees  concerned  with  the  construction  of  the  standards. When  this  commission,  after  reassembling  in  1872,  decided  that an  International  Bureau  of  Weights  and  Measures  should  be established  in  Paris,  the  plan  had  the  approval  of  the  delegates of  this  country  and  of  the  American  scientific  world  generally, the  National  Academy  of  Sciences  formally  favoring  the  scheme and  recommending  to  the  Government  the  signing  of  such a    treaty.       The    work    of    the    Commission    has    already    been aSee  Proceedings,  American  Metrological  Society,  1873-1888  (New  York). I 130     EVOLUTION   OF   WEIGHTS   AND   MEASURES discussed,1  and  in  this  connection  it  is  necessary  merely  to  record the  fact  that  when  the  American  Minister  to  France,  Mr.  E.  B. Washburne,  signed  the  convention,  together  with  delegates  from sixteen  other  nations,  agreeing  to  establish  and  support  the International  Bureau  of  Weights  and  Measures,  the  United States  became  committed  to  the  principle  of  international  weights and  measures,  and  privileged  to  participate  in  the  benefits  accru- ing from  a  common  system  and  common  standards. In  1889,  after  accurate  and  careful  construction  and  adjustment and  comparison,  the  international  prototype  standards  of  the standard  meter  and  kilogram  were  completed  by  the  bureau,  and were  distributed  to  the  various  countries  supporting  the  Com- mission. In  a  distribution  by  lot,  the  United  States  received meters  Nos.  21  and  27,  and  kilograms  Nos.  4  and  20.  The  seals of  meter  No.  27  and  kilogram  No.  20  were  broken  by  President Benjamin  Harrison  on  January  2,  1890,  and  they  were  straight- way deposited  in  a  fireproof  room  at  the  Office  of  Weights  and Measures  in  the  Coast  Survey  Building.2  These  standards  were immediately  adopted  as  the  national  prototype  meter  and  kilo- gram, and  the  primary  standards  for  the  United  States,  and  were employed  as  fundamental  standards  for  deriving  customary units,  the  yard  and  the  pound,  as  well  as  for  constructing  and standardizing  secondary  metric  standards.  To  obviate  any possible  misunderstanding,  however,  a  formal  order,  approved  by the  Secretary  of  the  Treasury,  was  issued  on  April  5,  1893, recognizing  "  the  International  Prototype  Meter  and  Kilogram as  fundamental  standards,  and  the  customary  units,  the  yard  and the  pound,  will  be  derived  therefrom  in  accordance  with  the  Act of  July  28,  1866."  3 Here,  again,  we  find  a  matter  of  fundamental  importance settled  by  Executive  order,  and  the  United  States  firmly  com- mitted to  the  metric  system  as  the  basis  of  all  measures  in  use, 1  See  pp.  72-77.  For  text  of  treaty,  diplomatic  correspondence,  reports,  etc  , see  chapters  ii.  and  iv.,  Report  No.  14,  46th  Congress,  1st  Session,  House  of  Repre- sentatives, Committee  on  Coinage,   Weights,  and  Measures  (Washington,  1879). 2  For  technical  description  of  the  standards,  certificates,  reports,  etc.,  consult Report  U.S.  Coast  and  Geodetic  Survey,  1890,  Appendix  18,  pp.  746-758. 3 Bulletin  No.  26,  U.S.  Coast  and  Geodetic  Survey,  "Fundamental  Standards of  Length  and  Mass."  Republished  as  Appendix  No.  6,  1893,  U.S.  Coast  and Geodetic  Survey  Report. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     131 no  matter  what  their  source.  So  far  as  fundamental  standards go,  the  only  ones  used  by  the  United  States  are  metric  and international,  and  to  them  must  be  referred  all  measures,  whatever their  nature.  These  standards  are  known  in  their  relation  to the  standards  of  the  International  Bureau  at  Sevres,  and  to those  of  the  various  foreign  countries,  so  that  in  case  of  their destruction  they  could  readily  be  reproduced,  thus  guaranteeing the  permanency  of  weights  and  measures  founded  upon  them. In  fact,  meter  No.  27  was  transported  to  Paris  in  1904  for comparison  with  the  standards  of  the  International  Bureau, and  after  several  series  of  careful  observations  its  value  was redetermined  in  terms  of  the  international  standard  prototype. It  was  found  that  No.  27  at  0°  centigrade  was  too  short  by 2  microns,  a  discrepancy  greater  by  '55  microns  than  that obtained  in  1888,  when  it  was  tested  with  the  other  national prototypes.  This  change,  however,  was  so  minute  that  the U.S.  Bureau  of  Standards  decided  to  employ  the  old  value in  all  of  its  determinations  until  an  opportunity  had  been given  to  compare  standard  No.  27  directly  with  the  international prototype  meter  and  with  other  national  prototypes.  Inasmuch as  the  relation  of  No.  27  to  No.  21  is  accurately  known,  as also  are  the  values  of  various  secondary  standards  in  terms of  both  national  standards,  it  will  be  seen  that  the  Bureau of  Standards  is  now  in  a  position  to  guarantee  the  accuracy and  permanency  of  the  measures  of  the  United  States.1 That  progress  was  being  made  in  the  use  of  the  metric  system is  shown  by  the  fact  that  when  Congress,  on  March  3,  1893, passed  an  Act2  establishing  a  standard  scale  for  the  measurement of  sheet  and  plate  iron  and  steel,  it  was  expressed  in  terms  of both  the  customary  and  metric  measures.  Of  perhaps  greater importance  was  the  Act  approved  July  12,  1894  {Revised Statutes  of  the  United  States,  Supplement,  vol.  ii.  chap.  131, 1894),  which  denned  and  established  the  units  of  electrical measure.     These  were  the  international  electrical  units  based  on 1See  L.  A.  Fischer,  "  Recornparison  of  the  United  States  Prototype  Meter," Bulletin  of  the  Bureau  of  Standards  (Washington),  pp.  5-19,  No.  1,  vol.  i. 1904.  The  discrepancy  mentioned  has  since  been  accounted  for  through  a small  error  in  the  coefficient  of  expansion  of  No.  27,  which  was  compared  at different  temperatures  in  1888  and  1904. 2Bevised  Statutes,  3570,  c.  231,  Sec.  1,  27  Statute,  746. 132     EVOLUTION   OF  WEIGHTS   AND   MEASURES the  metric  system  which  were  in  use  by  electrical  engineers throughout  the  world,  having  been  definitely  settled  at  a  congress held  at  Chicago  in  1893.1 In  1901  the  National  Bureau  of  Standards  was  established  by Act  of  Congress  to  take  over  the  duties  of  the  old  Office  of Weights  and  Measures  of  the  Coast  and  Geodetic  Survey,  and to  have  somewhat  broader  functions,  especially  in  carrying  on standardization  and  other  scientific  work  of  general  public advantage.  To  this  bureau  was  assigned  the  custody  of  the national  standards  and  the  construction  and  comparison  of secondary  and  other  standards  of  weights  and  measures  of  all kinds.  In  the  event  of  the  adoption  of  the  metric  system,  it would  fall  to  this  bureau  to  oversee  the  construction  and  certify to  the  correctness  of  the  many  new  standards  that  would  be required  in  science,  commerce,  and  the  arts.  This  it  is  well equipped  to  do,  and  has  large  laboratories  with  every  facility  for such  work. When  new  territories  were  added  to  the  United  States  as  a result  of  the  Spanish  war  in  1898,  it  was  found  that  the  metric system  of  weights  and  measures  was  employed  in  both  Porto Eico  and  the  Philippine  Islands,  and  the  status  of  the  system  in these  possessions  was  duly  confirmed.  In  the  proclamation  of the  Military  Governor  of  Porto  Rico,  March  18,  1899,  it  was stated,  "  1.  The  use  of  the  metrical  system  of  weights  and measures  and  its  nomenclature  are  obligatory.  2.  Its  use  is enforced  in  all  transactions,  sales,  contracts,  ...  3.  Wholesale and  retail  mercantile  establishments  shall  sell  their  goods  to the  public  conformably  to  the  metric  system."  The  Political Code  of  Porto  Rico  (1902),  sections  230-246,  definitely  fixes  the metric  systems  and  gives  the  legal  definitions.  The  Philippine Tariff  Act  (No.  230,  September  17,  1901,  sec.  9)  contained  a  pro- vision that  "  The  metrical  system  of  weights  and  measures  as authorized  by  sections  3569  and  3570  of  the  Revised  Statutes  of the  United  States,  and  at  present  in  use  in  the  Philippine Islands,  shall  be  continued."  In  the  Government  Bill  of  1902  it was  provided  that  "  Sections  (of  the  former2  Act)  are  hereby amended  by  reducing  all  measurements  therein,  whether  of  dis- tance, area,  or  value,  to  the  metric  system." 1  See  p.  208,  chap.  ix.  2  Philippine  Government  Act  of  1902. WEIGHTS  AND  MEASURES  IN  UNITED  STATES     133 Since  the  first  permissive  legislation  in  1866  there  have  been various  Bills  introduced  into  Congress  to  establish  the  metric system,  and  each  successive  one  has  come  before  Congress  with stronger  support,  and  likewise  with  stronger  opposition  on  the part  of  those  opposed  to  any  change.  The  matter  of  weights  and measures  has  been  investigated  most  carefully  by  various  House Committees  on  Coinage,  Weights,  and  Measures,  and  their  reports are  replete  with  information  on  the  subject  treated  from  different standpoints.  In  1896  two  interesting  reports1  were  prepared after  the  committee  had  made  a  careful  consideration  of  the subject  extending  over  two  sessions,  and  a  Bill  to  establish  the metric  system  was  unanimously  recommended  for  adoption, but,  however,  did  not  pass  a  third  reading.  Again  in  1901  a somewhat  similar  Bill  was  reported  from  the  Committee,  accom- panied by  a  brief  report 2  in  which  its  passage  was  recommended, but  unfortunately  this  Bill  was  received  too  late  to  be  considered by  the  Congress  then  in  session.  Once  more,  in  1902  and  1903, the  subject  was  discussed  in  committee  and  numerous  hearings were  held,  the  record  of  which  was  embodied  in  an  interesting report3  in  which  the  establishing  of  the  metric  weights  and measures  as  the  legal  standards  of  the  United  States  was recommended. The  general  tendency  of  all  these  Bills  was  the  same.  It  was proposed  that  within  a  few  months  after  their  passage,  usually at  the  commencement  of  the  next  calendar  year,  that  the  national Government  in  all  its  business  relations,  as  well  as  in  all  its constructive  work,  should  adopt  the  metric  weights  and  measures exclusively,  while  for  the  public  at  large  two  or  three  years should  elapse,  after  which  they  would  become  the  legal  system of  the  country.  It  was  not  proposed  to  resort  to  compulsory measures,  but  to  so  establish  the  new  system  that  it  would gradually  extend  into  universal  use.  In  the  Littauer  Bill  intro- duced in  1905  it  was  provided  only  that  the  metric  system should  be  employed  by  the  Government  in  all  its  transactions and  activities. ^H.R.   Report  No.    795,   and    H.R.    Report  No.    2885,   February    10,    1897, 54th  Congress. 2  H.R.  Report  No.  3005,  56th  Congress,  2nd  Session,  March  1,  1901. ZH.R.  Report  No.  1701,  57th  Congress,  1st  Session,  April  21, 1902. 134     EVOLUTION   OF   WEIGHTS   AND   MEASURES Secretaries  of  State  and  Treasury,  irrespective  of  political party,  as  well  as  other  executive  officers  of  the  Government,  have urged  the  adoption  of  the  international  system,  and  diplomats and  consuls  have  repeatedly  called  attention  to  the  benefits  to commerce  that  would  ensue.  Scientific  men  and  educators  have unanimously  urged  the  desirability  of  the  change,  as  have  many engaged  in  foreign  commerce.  Against  any  innovation  at  the present  time  are  many  manufacturers  and  mechanical  engineers, many  of  whom  have  secured  in  their  work  a  considerable  accu- racy of  construction,  especially  as  regards  patterns  based  on  the English  measures,  which  they  assert  could  only  be  abandoned  at an  expense  entirely  incommensurate  with  any  possible  benefit.1 At  Congressional  hearings,  in  the  scientific  press,  and  at  meetings and  conventions,  the  question  has  been  thoroughly  debated  by those  interested,  and  the  material  for  information  is  most  ample. It  is  now,  however,  a  matter  for  the  American  nation  at  large, and  when  the  people  are  thoroughly  convinced  of  the  great benefits  that  will  ensue,  there  will  be  no  outcry  against  temporary inconvenience.  The  adoption  of  the  metric  system  is  surely  in the  line  of  progress,  and  when  once  it  is  realized,  the  United States,  with  its  superior  school  system  and  general  high  order  of intelligence  possessed  by  its  people,  especially  its  workers,  can make  the  change  with  a  minimum  of  embarrassment  and  can avail  themselves  of  its  benefits  more  quickly  than  has  been  done in  the  past  by  European  nations. 1  This  point  of  view  will  be  found  strongly  represented  in  Halsey  and  Dale, The  Metric  Fallacy,  New  York,  1903,  one  of  the  ablest  of  the  anti-metric  books, and  one  that  attracted  considerable  attention  at  the  time  of  its  publication  on account  of  the  bitterness  of  its  attacks  on  the  metric  system  and  its  advocates. It  furnished  material  for  many  reviews  and  discussions  in  the  technical  press, both  favorable  and  hostile.  Of  the  latter  possibly  the  most  interesting  and  able were  those  in  the  Electrical  World  and  Engineer  (New  York),  vol.  xliv.  No.  19, pp.  784-794,  Nov.  5,  1904,  and  in  The  Physical  Review  (Ithaca),  1904. A  somewhat  more  scholarly,  though  less  argumentative  paper  from  a similar  point  of  view,  by  George  W.  Colles,  entitled  "  The  Metric  versus  the Duodecimal  System,"  will  be  found  in  the  Transactions  of  the  American  Society  of Mechanical  Engineers,  vol.  xviii.  pp.  492-611,  1896-1897.  See  also  a  paper  by J.  H.  Linnard,  "The  Metric  System  in  Shipbuilding,"  Transactions  of  the  Society of  Naval  Architects  and  Marine  Engineers  (New  York,  1903),  vol.  ii.  pp.  168-188. CHAPTEE  V. THE  METRIC  SYSTEM  OF  TO-DAY—ITS   ESSENTIAL  CHAR- ACTERISTICS AND  FUNDAMENTAL  PRINCIPLES. The  metric  system  to-day  represents  a  complete,  uniform,  and simple  international  system  of  weights  and  measures,  and  as  such may  be  considered  briefly  in  its  entirety,  and  with  a  view  of  the relation  of  the  various  units  to  one  another.  In  the  beginning it  must  be  understood  that  any  particular  metric  unit  as  such does  not  possess  any  intrinsic  superiority  over  other  units,  but by  reason  of  being  united  into  a  system  which  is  strictly  symme- trical and  systematized  on  one  base  ratio  throughout,  and  with that  base  ratio  10,  metric  units  have  many  and  preponderating advantages  over  those  of  other  systems.  Nevertheless,  bearing  in mind  the  two  conditions  mentioned,  which  are  fundamental,  there is  nothing  to  prevent  other  systems  being  constructed  with  other units  which  would  no  doubt  be  equally  satisfactory.  But  in  reply it  may  be  said,  Why  should  this  be  done,  when  a  system  exists, used  not  only  by  men  of  science  generally  but  by  a  large  part  of the  civilized  world,  the  abandonment  of  which  would  surely  accom- plish no  particular  purpose.  "  For,"  says  Professor  R.  H.  Smith,1 "  no  other  can  possibly  be  better  in  practical  essentials  except  in substituting  for  ten  the  base  twelve  or  thirty  for  measures  and written  numeration  alike,  and  this  latter  is  humanly  impossible." For  ordinary  purposes  of  simple  measurement,  units  are grouped  into  five  different  classes,  those  pertaining  to  measures  of 1  Professor  R.  H.  Smith  in  Journal  oj  Institution  of  Electrical  Engineers,  quoted by  A.  Siemens  in  Proceedings,  Royal  Statistical  Society  (London),  p.  693,  vol.  lxvi. 1903. \ 136     EVOLUTION   OF   WEIGHTS   AND   MEASURES length,  surface,  volume,  capacity,  and  weight,  or,  as  regards  the last,  speaking  more  exactly  and  scientifically,  mass.  These  all depend  upon  the  meter  as  the  fundamental  unit,  and  as  a  primary and  essential  condition  of  the  system,  all  must  bear  a  strictly decimal  relation  to  each  other.  Inasmuch  as  in  the  metric system  all  are  referred  to  one  primary  standard,  the  Meter,  there must  be  necessarily  absolute  uniformity,  and  as  means  have  been taken  to  preserve  this  standard  from  any  deterioration  due  to- time  or  other  causes,  there  is  every  guarantee  of  the  stability  of the  system  and  of  its  standards.  Furthermore,  what  was  once- deemed  desirable  but  found  to  be  impossible  of  realization,, namely,  the  definition  of  a  standard  by  some  object  or  circum- stance in  nature,  has  been  accomplished,  and  to-day  we  have  the meter  precisely  defined  in  terms  of  the  wave-length  of  cadmium light  by  a  method  which  is  described  elsewhere.1  Thus  in  the event  of  the  loss  or  the  destruction  of  the  International  Prototype Meter  or  of  the  copies  thereof,  it  would  be  possible  to  reproduce the  exact  length  by  experiments  that  to  the  practised  physicist involve  no  serious  difficulty. With  the  fundamental  unit,  the  International  Prototype  Meter, defined  as  the  distance  between  two  fine  lines  on  a  particular platinum-iridium  bar,  at  the  temperature  of  melting  ice,  and reproduced  by  national  standards  accurately  copied  therefrom  and duly  recognized  by  the  laws  of  the  countries  owning  them,  by simply  multiplying  by  ten  successively  or  by  a  similar  simple process  of  decimal  subdivision,  is  built  up  a  system  of  measures of  length  which  have  been  demonstrated  as  sufficient  for  the needs  of  science,  commerce,  and  industry.  Each  unit  is either  ten,  one  hundred,  one  thousand,  ten  thousand,  or  a  million times  as  great  as  the  fundamental  unit  of  length,  the  meter,  or  a similar  fraction  or  sub-fraction.  This  relation  for  many  purposes it  is  convenient  to  express  by  means  of  the  number  10  and  the appropriate  exponent  or  index,  and  then  speak  of  a  certain number  of  meters  multiplied  by  10,  102,  103,  104,  106,  or  for  the sub-multiples  10"1,  10 ~2,  10" 3,  etc.  Consequently,  in  a  number expressing  a  length  in  a  metric  unit,  it  is  possible  to  change  the unit  merely  by  moving  the  decimal  point  or  adding  a  requisite number  of  zeros  to  correspond  with  the  necessary  decimal  multi- 1  See  chapter  x.  pp.  261-266. THE   METRIC   SYSTEM   OF  TO-DAY  137 plication  or  division.  Thus,  as  will  be  seen  from  the  following table,  1  kilometer  may  be  written  as  1000  meters  simply  by  adding three  zeros  to  the  1,  while  1  decimeter  may  be  expressed  in terms  of  the  meter  simply  by  moving  the  decimal  point  one place  to  the  left.  Taking  fundamental  units  other  than  those  of length,  which,  however,  are  derived  from  the  meter,  a  similar method  of  decimal  multiplication  and  subdivision  enables  us  to derive  complete  sets  of  units  for  surface,  volume,  capacity,  and mass  measurements.  For  the  first  two  we  use  the  square  meter and  the  cubic  meter  as  the  fundamental  units,  and  for  capacity the  liter,  and  for  mass  the  gram. For  the  multiples  of  its  principal  units    the   metric  system employs  prefixes  derived  from  the  G-reek  as  follows : Deca  meaning  10  times  derived  from  Greek  Seica.  =  10 Hecto       „        100  „  „  €kclt6v=  100 Kilo         „        1000         „  „  x^a  =  1000 Myria       „        10000       „  „  fwpia  =  10000 Similarly,  prefixes  derived  from  the  Latin  are  employed  for  the- submultiples  of  the  various  units.     These  are  as  follows : Deci  meaning    ^     derived  from  Latin  decern  =  10 Centi       „         y^  „  „         centum  =  100 Milli       „        TJ}^U         „  „  mille=1000 These  seven  prefixes  always  used  in  the  same  relation  supply  the means  of  obtaining  units  of  a  size  convenient  for  the  work  in hand,  and  alway  instantly  available  for  conversion  into  units  of another  denomination.  To  facilitate  remembering  the  fact  that the  Greek  prefixes  indicate  multiples,  and  the  Latin  the  sub- multiples,  one  has  merely  to  think  of  the  word  "  Gild,"  and understand  that  it  stands  for  the  initials  of  the  motto,  "  Greek increases,  Latin  decreases."  With  the  three  primary  units,  in- volving the  three  names  meter,  liter,  aud  gram,  and  the  two more  arbitrary  units  are  and  stere,  together  with  the  seven prefixes  given  above,  it  is  possible  to  construct  all  the  metric units  in  ordinary  use,  inasmuch  as  their  relation  to  each  other- is  perfectly  uniform  and  simple. 138     EVOLUTION   OF   WEIGHTS   AND   MEASURES Metric   Measures  of  Length. Unit. Abbrevia- tion. Where  Employed. Value  in  Terms of  Meter. Power of  10. Megameter,  - Astronomy 1,000,000m. lO^m. Myriameter, Mm. Geography 10,000m. 104m. Kilometer,   - Km. Distance 1,000m. 103m. Hectometer, Hm. Artillery 100m. 102m. Decameter,  - Dm. Surveying 10m. 10m. Meter, m. lm. Decimeter,   - dm. [Commerce •lm. lO^m. Centimeter,  - cm. -j  Industry •01m. 10"2m. Millimeter,  - mm. 1  Science •001m. 10"3m. Micron  = /*,  - (Metrology •000,001m. 10~6m. Millimicron, ■I  Spectroscopy [Microscopy •000,000,001m. 10-9m. While  the  foregoing  represent  the  various  units  of  length  in the  metric  system,  and  indicate  the  principal  departments  of knowledge  in  which  they  are  used,  it  does  not  follow  that  all  of them  are  used,  or  that  a  given  length  is  expressed  in  terms of  more  than  one.  For  example,  a  distance  is  not  expressed  as 34  kilometers,  9  hectometers,  3  decameters,  and  4  meters,  but as  34*934  kilometers,  and  all  measures  of  length,  where  it  is desirable  to  use  kilometers,  are  expressed  in  that  unit  and  a decimal  fraction.  Thus,  for  each  class  of  measurements,  as  a general  rule,  there  is  used  but  one  of  the  above  units,  as  will  be discussed  below,  and  any  measurement  is  expressed  in  whole numbers  and  decimal  fractions.  Each  of  the  above  units  is  well suited  for  a  number  of  varieties  of  measurements,  and  a  few  of these  may  be  conveniently  outlined.  The  megameter,  which  has not  received  legal  sanction,  is  but  rarely  encountered,  and  then  only in  astronomical  work  where  distances  of  considerable  magnitude are  discussed.  As  it  appears  only  in  calculations  it  does  not possess  much  general  interest,  and  the  same  holds  true  for  the myriameter  formerly  used  in  geographical  work.  The  kilometer, on  the  contrary,  as  a  unit  of  distance  such  as  would  be  used  in the  measurement  of  the  length  of  a  railway  or  road,  is  of  vast THE   METRIC   SYSTEM   OF  TO-DAY  139 importance,  and  is  universally  employed  both  scientifically,  as  by engineers,  and  also  in  non-technical  matters.  It  is  a  unit  whose use  presents  very  little  difficulty  to  those  accustomed  to  Anglo- Saxon  measures,  in  that  it  corresponds  so  closely  to  six-tenths  of a  mile  that  such  an  approximation  suffices  for  most  purposes  and is  readily  made. The  hectometer  does  not  find  extensive  practical  application, and  is  encountered  chiefly  in  the  calculations  of  artillerists ;  but even  here  it  is  preferable  to  use  meters,  and  velocities,  etc.,  are now  usually  calculated  in  the  latter  units.  The  decameter  is used  in  surveying  where  it  forms  a  base  for  the  measure  of  land, since  the  decameter  squared  gives  the  are,  which  is  the  principal unit  of  land  measure.  The  classes  of  measurement  for  which  the meter  is  available  are  numerous  and  apparent.  For  the  measure of  cloth  and  similar  fabrics  it  is  eminently  suitable,  and  as  the yard  is  approximately  '9  of  the  meter  there  is  no  very  violent break  in  passing  from  one  to  the  other,  as  would  be  done  by the  purchaser  of  cloth  for  a  dress.  The  meter  would  be  used  by the  stone  mason  in  the  measurements  of  a  length  of  wall,  or  by  a carpenter  or  architect  in  his  specifications  and  plans  for  structural work,  and  is  in  every  way  as  suitable  a  unit  as  the  yard,  aside from  the  inherent  merits  of  its  connection  with  the  metric system.  In  the  decimeter  there  is  a  unit  intermediate  between the  meter  and  the  centimeter,  and  on  that  account  not  as  much used  as  either.  Furthermore,  the  decimeter  does  not  correspond to  any  unit  that  has  been  in  recent  use  by  non-metric  countries, and  in  the  Anglo-Saxon  system  its  nearest  equivalent  is  the  hand of  four  inches,  long  obsolete,  except  in  measuring  the  height  of horses.  The  decimeter  is  too  short  to  fill  the  place  of  the  foot and  too  long  to  supplant  such  a  unit  as  the  inch.  Nevertheless, it  is  at  the  disposal  of  those  who  desire  such  a  unit,  and  as three  decimeters  will  approximate  a  foot,  it  may  find  increased application,  but  its  use  has  never  been  great  in  the  countries employing  the  metric  system.  The  centimeter,  on  the  other  hand, is  a  most  useful  and  convenient  unit,  and  is  susceptible  of  wide application.  For  the  carpenter  or  cabinetmaker  in  giving  the dimensions  of  a  door  or  window,  the  size  of  a  plank,  that  is,  its breadth  and  thickness,  or  the  dimensions  of  any  ordinary  objects, such  as  tables,  chairs,  etc.,  the  centimeter  fills  every  requirement, 140    EVOLUTION   OF  WEIGHTS   AND   MEASURES and  in  scientific  work  it  is  customary  to  express  dimensions  of apparatus  and  all  ordinary  measurements  in  its  terms.  For many  years  in  the  United  States  library  catalogue  cards  and other  furnishings,  such  as  pamphlet  cases,  have  been  standardized and  sold  according  to  metric  measure,  and  the  centimeter  has been  the  unit  adopted.  It  takes  the  place  of  the  inch,  and  while it  requires  a  larger  number  to  express  a  given  distance,  yet  it  is likely  to  lead  to  greater  exactness  where  it  is  not  desirable  to employ  fractions.  The  millimeter  is  the  unit  of  science  and exact  mechanical  work.  It  affords  an  integral  unit  for  minute measures,  speaking  comparatively,  and  its  decimal  subdivision  is peculiarly  suitable  for  this  class  of  work.  In  ordinary  life  its chief  application  is  to  the  measurement  of  thickness,  such  as metals,  paper,  glass,  etc.,  and  particularly  in  the  measurement of  diameters  of  wire,  tubing,  and  other  materials  which  enter into  mechanical  construction.  Thus,  measurements  in  millimeters are  designed  to  take  the  place  of  arbitrary  gauges  where  the problem  of  original  standards,  which  in  turn  are  based  on standards  of  length,  works  against  general  uniformity  and  con- venience. For  the  measurement  of  screw-threads  the  millimeter is  also  employed,  and  in  France,  Germany,  and  Switzerland millimeter  sizes  for  screws  and  thickness  and  diameters  have been  found  to  be  far  more  convenient  than  arbitrary  gauges. While  the  millimeter  answers  many  purposes  of  the  scientist, yet  it  does  not  carry  him  far  enough,  and  accordingly  there  is the  micron,  which  is  one-thousandth  part  of  it.  This  affords  a convenient  unit  for  the  microscopist  and  the  spectroscopist  when they  venture  into  the  regions  beyond  the  range  of  the  human eye ;  and  to  secure  a  still  greater  refinement  we  have  the millimicron,  or  again  the  thousandth  part. With  such  units  as  the  foregoing,  the  next  point  is  how  are they  applied,  and  how  are  they  concretely  represented  by  scales or  other  devices  ?  The  longest  scale  is  that  of  the  geodesist or  engineer  employed  in  measuring  his  base  line  for  trigono- metrical surveying  of  greater  or  less  accuracy  as  the  occasion may  warrant.  The  best  modern  practice  involves  the  use  of  a steel  tape  or  wire,  or  one  made  of  an  alloy  of  steel  with  a  smaller tendency  to  expand  and  contract  with  changes  in  temperature, which  under  a  constant  tension  gives  an  exact  representation  of THE   METRIC   SYSTEM   OF  TO-DAY  141 a  distance  as  determined  with  a  standard  of  length.1  Such  tapes or  wires  are  usually  of  100,  200,  or  300  meters,  while  the  ordinary- chain  or  tape  of  the  land  surveyor  is  either  a  double  or  single decameter  on  which  are  marked  the  meters  and  such  other subdivisions  as  are  desired,  the  double  decameter  being  known  as a  metric  chain.  The  next  measure  of  length  in  point  of  size is  the  double  meter,  which  may  be  either  a  rod  or  tape.  If  a rod,  its  material  and  subdivision  are  dependent  on  the  use  for which  it  is  designed,  as  a  metal  scale  lends  itself  more  readily  to permanent  and  accurate  graduation,  and  is  less  susceptible  to change  with  time  and  temperature ;  the  latter  condition,  in  fact, may  be  accurately  and  satisfactorily  accounted  for  by  knowing the  coefficient  of  expansion  of  the  bar  and  the  temperature  at which  it  is  used.  The  tape  may  be  either  of  metal  or  linen, and  is  a  convenient  measure  for  many  purposes.  There  are  also constructed  meter  scales,  half-meter  scales,  double  and  single decimeter  scales,  the  shape  and  material  as  well  as  the  accuracy of  graduation  depending  on  the  purposes  for  which  they  are  to be  used.  When  it  comes  to  the  division  of  millimeters  it  is necessary  to  employ  a  dividing  engine,2  and  the  finest  scales  are ruled  on  glass  or  upon  a  smooth  and  even  substance,  such  as speculum  metal  platinum-iridium,  or  nickel  steel.  The  glass scales  are,  of  course,  to  be  used  with  the  microscope,  and  similar scales  can  be  constructed  photographically  by  reducing  in  a desired  proportion. 1  There  are  also  standard  bars  used  in  the  most  refined  base  measurements,  such as  that  at  Holton,  Mich.,  which  was  of  5  meters  length.  These  bars  require  the most  careful  levelling,  are  packed  in  ice  at  the  time  of  making  the  measurement, and  are  only  used  when  the  greatest  accuracy  is  desired,  as  the  refinements  of  a laboratory  are  involved  in  a  field  operation.  See  Woodward,  "The  iced  bar  and long  tape  base  apparatus  and  the  results  of  measures  made  with  them  on  the Holton  and  St.  Albans  bases,"  part  ii.  of  Appendix  No.  8  of  Report  of  United States  Coast  and  Geodetic  Survey  for  1892,  pp.  334-489.  Professor  Woodward also  discusses  "Long  Steel  Tapes"  in  a  paper  presented  to  the  International Engineering  Congress  of  1893,  and  printed  in  the  Transactions  of  the  American Society  of  Civil  Engineers,  vol.  xxx.  p.  81. 2  See  chapter  x. — Standards  and  Comparison,  p.  225. 142     EVOLUTION   OF   WEIGHTS   AND   MEASURES Number  of  Square Abbreviation. Meters. km2. 1,000,000m2. ha.  —  hm2. 10,000m2. a.  —  dm2. 100m2. ca.  or  m2. lm2. dm2. •01m2. cm2. •0001m2. mm2. •000,001m2. Measures  of  Surface. Square  kilometer, Hectar  (square  hectometer), Ar  (square  decameter),     - Centiar  or  square  meter, Square  decimeter, Square  centimeter, Square  millimeter, For  the  measurement  of  surfaces  it  is  customary  to  employ as  a  unit  a  square  or  quadrilateral  figure  bounded  by  four  equal sides  at  right  angles  to  each  other.  In  such  a  unit  the  sides  are usually  made  equal  to  the  linear  unit,  hence  in  the  metric  system a  square  of  this  nature  would  have  for  each  side  a  meter,  and would  be  known  as  a  square  meter,  forming  the  principal  unit for  the  measurement  of  surface.  The  next  greater  unit  would  be formed  by  a  square  whose  bounding  sides  were  each  equal  to  a decameter,  and  consequently  would  include  100  of  the  principal units.  If  our  units  of  length  increase  by  a  ratio  of  10,  it  is obvious  that  the  unit  of  surface  based  on  these  same  units  of length  must  increase  by  the  square  of  10  or  by  100  as  is  indicated by  the  table.  The  same  nomenclature  is  retained,  but  the  word square  is  prefixed,  and  in  the  case  of  the  units  formally  adopted for  the  measure  of  land,  the  terms  hectar  and  ar  have  been selected  to  designate  respectively  the  square  hectometer  and  the square  decameter.  In  writing  and  converting  the  measures  of area  it  is  necessary  to  multiply  or  divide  by  100  when  changing to  a  larger  or  smaller  unit,  consequently  in  the  decimal  fraction each  metric  unit  must  be  given  two  places  of  figures.  For example,  to  write  as  square  meters  984*8963  square  decimeters,  it would  be  necessary  to  move  the  point  two  places  to  the  left  and we  would  have  9*848963  square  meters,  which  also  could  be written  9  square  meters,  84  square  decimeters,  89  square  centi- meters and  63  square  millimeters,  or  even  9848963  square  milli- meters if  it  was  so  desired.  The  square  kilometer  is  employed in  topographical  work  on  a  large  scale,  or  in  cartography  in summing   up  the  area  of  a  country  or  large  region.     For  fields THE   METRIC   SYSTEM   OF  TO-DAY  143 the  hectar  is  used,  and  is  parallel  to  the  acre,  which  contains •4047  hectars.  For  land  of  smaller  dimension,  such  as  city  lots, it  is  customary  to  use  the  are.  The  measurement  of  surfaces,  as of  walls  by  the  painter  or  paperhanger,  or  of  floors  by  the  dealer in  carpets,  is  naturally  made  by  the  square  meter.  Such  measure- ments as  the  square  decimeter  and  the  square  centimeter  are useful  for  purposes  that  will  naturally  suggest  themselves,  but again  attention  may  be  called  to  the  fact  that  scientific  men prefer  to  use  the  square  centimeter  and  the  cubic  centimeter also  as  much  as  possible. Measures  of  Volume. The  volume  of  a  body,  or  the  amount  of  space  that  it  occupies, is  usually  measured  by  a  unit  known  as  a  cube,  which  is  a parallelopipedon  bounded  by  six  equal  squares.  In  the  metric system  the  principal  unit  is  the  cubic  meter,  a  cube  each  of whose  faces  is  a  square  meter,  and  consequently  whose  edges  are each  a  meter  in  length.  The  cubic  meter  is  the  largest  unit  of volume  in  the  metric  system,  though  logically  there  is  no  reason why  cubic  decameters,  hectometers,  and  kilometers  should  not  be employed  were  there  any  necessity  for  their  use,  which  there  is not.  Therefore  we  have  only  to  concern  ourselves  with  the  sub- multiples  of  the  cubic  meter.  On  the  decimal  principle  the next  smaller  unit  must  be  one  in  which  the  size  is  determined by  the  tenth  of  the  meter,  or  the  decimeter,  or  a  cube  each  of whose  edges  is  a  decimeter.  Obviously,  to  make  a  cubic  meter ten  rows  of  these  cubes,  arranged  so  that  they  are  ten  in length,  will  have  to  be  placed  ten  deep,  or  one  thousand  of  our cubic  decimeters  must  be  used.  So  that  where  the  unit  of  area required  a  ratio  of  100  to  pass  from  a  smaller  to  a  greater,  the units  of  volume  need  a  ratio  of  1000  ;  that  is,  three  figures  of integers  or  of  the  decimal  fraction  are  required  for  each  unit. Thus  a  cubic  meter  will  contain  1000  cubic  decimeters,  or 1  000  000  cubic  centimeters,  or  1  000  000  000  cubic  millimeters. We  may  read  76'854  673  2  cubic  meters  as  76  854*673  cubic centimeters,  or,  were  it  desirable,  76  854  673  cubic  millimeters. Or  we  could  read  the  above  expression  as  76  cubic  meters, 854  cubic  decimeters,  and  673  cubic  centimeters. I 144     EVOLUTION   OF   WEIGHTS   AND   MEASURES The  cubic  meter  is  employed  in  all  cases  where  any  con- siderable quantity  of  a  substance  must  be  considered.  Thus the  amount  of  material  excavated  from  a  foundation,  railway cut,  or  canal,  would  be  expressed  in  cubic  meters,  as  would  be blocks  of  marble  or  the  contents  of  a  tank  or  reservoir.  When the  cubic  meter  is  applied  to  the  measurement  of  firewood  it receives  a  new  name,  stere  (  =  35*317  cubic  feet  or  *27  cord),  and as  a  pile  of  wood  can  be  divided  or  increased  readily,  the  name of  decistere  is  given  to  the  one-tenth  part,  and  that  of  decastere  to ten  times  the  unit  quantity.  The  cubic  decimeter  is  an  inter- mediate unit  like  the  corresponding  decimeter  and  square decimeter,  but  it  possesses  importance,  inasmuch  as  it  is  the volume  of  the  liter  (very  nearly),  and  as  such  is  frequently employed  in  calculations  where  it  is  desired  to  obtain  the capacity  of  a  given  space,  as  will  be  explained  further  on  under measures  of  capacity.  The  cubic  centimeter  answers  for  many purposes,  and  is  the  usual  unit  for  scientific  work.  Thus  in pharmacy  by  the  volumetric  method  (see  page  194)  almost  all liquids  are  compounded  by  taking  the  desired  quantities  in  cubic centimeters,  while  to  determine  standard  pressure  reference  is made  to  that  of  a  column  of  75  cubic  centimeters  of  mercury  at 0°  centigrade. Measures  of  Capacity. Hectoliter,  - Decaliter,  - Liter,  - Deciliter,  - Centiliter,  - Milliliter,    -  ml.  -001  liter. The  close  connection  between  measures  of  volume  and  capacity is  obvious,  and  the  founders  of  the  metric  system  took  as  their unit  of  capacity  the  volume  of  a  cubic  decimeter.  Subsequent measures  of  the  kilogram,  and  the  mass  of  water  necessary  to amount  to  this  weight,  resulted  in  the  conclusion  that  for  strictly scientific  purposes  this  was  inaccurate,  and  consequently  the  legal definition  is  in  the  words  of  the  International  Committee,  "  The liter  is  the  volume  occupied  by  the  mass  one  kilogram  of  pure hi. 100  liters. dal. 1. dl. 10  liters. •1  liter. cl. •01  liter. THE   METRIC   SYSTEM   OF  TO-DAY  145 water  at  its  maximum  density  and  under  normal  atmospheric pressure,"  and  this  decision  was  duly  sanctioned  by  the  general conference  of  1901.  As  the  result  of  a  large  number  of  careful experiments  it  was  found  that  a  mean  value  for  the  mass  of  a cubic  decimeter  of  water  at  4  degrees  centigrade  (its  temperature of  maximum  density)  would  be  '999974  kilogram,  and  that  the error  of  assuming  the  liter  equal  to  the  cubic  decimeter  would  be only  about  one  part  in  30,000,  an  amount  only  appreciable  in  the most  refined  measurements.  The  liter  is  subdivided  on  a decimal  basis,  while  its  multiples  are  similarly  arranged,  and from  what  has  preceded  it  will  be  possible  to  understand  the various  units  merely  by  referring  to  the  table.  In  actual  practice the  liter  and  the  hectoliter  are  the  units  chiefly  employed,  as  for many  reasons  it  is  preferable  to  employ  cubic  centimeters  for smaller  measures,  while  the  decaliter,  being  an  intermediate measure,  does  not  come  into  wide  use.  The  liter  and  all  the measures  of  capacity  are  used  for  both  dry  and  liquid  substances ; but  it  is  a  tendency  of  modern  metrology  quite  independent  of the  metric  system  to  do  away  so  far  as  possible  with  dry measures  of  capacity  and  buy  and  sell  such  substances  by  weight.1 ^  The  liter,  however,  can  be  used  to  measure  all  liquids  (such  as water,  milk,  wine,  beer,  oil,  etc.),  vegetables,  grains,  seeds,  etc.,  in ordinary  retail  transactions.  When  large  quantities  of  the commodity  are  dealt  in  or  discussed,  then  it  is  customary  to  use hectoliters.  The  liter  corresponded  so  closely  to  the  ancient French  pinte  ('981  liter)  which  it  supplanted  that  its  use  did  not occasion  any  difficulty,  and  as  it  is  intermediate  in  value  between the  American  dry  (  =  1*1012  liter)  and  liquid  quarts  (  =  '94636 liter)  its  employment  would  result  in  a  simplification  of  measures, and  would  involve  no  inconvenience. The  adoption  of  metric  measures  of  capacity  in  the  United States  would  result  in  important  simplifications,  as  the  present measures  differ  from  those  of  Great  Britain,  and  possess  no intrinsic  merits  of  their  own.  In  fact,  in  the  Anti-metric Argument  of  the  Committee  of  the  American  Society  of  Mechanical Engineers  (vol.  xxiv.  New  York,  1902),  which  opposes  most bitterly  any  attempt  at  the  introduction  of  the  metric  system,  it is    stated   (p.  676),  "  That    there   is   no   reason  for   the  English 1  In  Europe  the  practice  of  selling  liquids  by  weight  is  also  increasing. K \ 146     EVOLUTION   OF  WEIGHTS   AND   MEASURES .z system  retaining  the  gallon  and  the  bushel  except  that  they  are in  such  common  use.  For  convenience  in  computation  it  would be  well  if  the  gallon  were  216  cubic  inches,  or  the  cube  of  6 inches,  and  the  bushel  1728  cubic  inches,  or  1  cubic  foot." In  constructing  the  actual  measures  of  capacity  their  range  is extended  by  binary  subdivision  and  doubling,  so  that  all  possible capacities  can  be  measured  and  substances  sold  on  a  basis  of  the simplest  mental  process,  namely,  that  of  halving.  Actual  measures in  the  form  of  wooden  vessels  for  measuring  grain  with  a  capacity of  one  hectoliter  and  less  are  constructed  with  their  internal height  and  diameter  equal,  while  for  measuring  liquors,  wines, and  alcohol,  the  French  laws  provide  that  the  internal  height should  be  twice  the  internal  diameter.  Oil  and  milk  measures are  of  tin,  and  their  internal  height  and  diameter  are  equal. Measures  of  Mass. Metric  ton, t. 10  Quintals 1000  Kilogran as  1,000,000 grains io6g. Quintal, q- 10  Myriagrams 100 100,000 n 10%. Myriagram, 10  Kilograms 10 10,000 i 10*g. Kilogram, kg. 10  Hectograms — 1,000 )i io3g. Hectogram, 10  Decagrams — 100 i io2g. Decagram, 10  Grams — 10 i lOg. Gram, g- 10  Decigrams — 1 i E- Decigram, dg. 10  Centigrams — •1 , io-ig Centigram, eg. 10  Milligrams — •01 i io-V Milligram, mg — — •001 i 10"3g. V By  mass  is  meant  the  actual  quantity  of  matter  which  a  body contains,  and  it  is  to  be  distinguished  from  weight,  which  is  the force  with  which  a  body  is  attracted  to  the  earth.  Now,  as  this force  of  attraction  depends  upon  the  mass  of  a  body,  it  follows that  the  weight  of  different  bodies  at  the  same  place  is  pro- portional to  their  respective  masses.  But  as  the  force  of attraction  or  gravity  varies  at  different  points  on  the  earth's surface,  it  is  obvious  that  bodies  of  the  same  mass  will  have different  weights  at  different  places.  Originally,  as  we  have seen,  the  gram  was  defined  by  the  decree  of  18  Germinal,  year III.,1  as  "  The  absolute  weight  of  a  volume  of  pure  water  equal  to a  cube  of  the  one-hundredth  part  of  a  meter  and  at  the  temperature 1  See  p.  54. THE   METRIC   SYSTEM   OF  TO-DAY  147 of  melting  ice,"  and  on  this  basis  the  Kilogram  of  the  Archives was  constructed.  However,  after  the  construction  of  the  Inter- national standard  kilogram  it  was  deemed  desirable  to  define formally  the  kilogram,  and  at  a  meeting  of  the  International Committee  on  October  15,  1889,  it  was  decided  that  "The  mass of  the  international  kilogram  is  taken  as  unity  for  the  inter- national system  of  weights  and  measures,"  and  this  decision  was confirmed  at  the  third  general  conference  held  at  Paris  in  1901. While  the  gram  is  the  fundamental  unit  of  mass,  yet  in  actual practice,  as  in  the  construction  of  the  standard,  it  has  been  found rather  small  for  most  weighings,  and  consequently  the  kilogram is  employed  as  a  practical  unit. There  is,  of  course,  the  same  wide  range  of  units  of  weights  as in  other  classes  of  measures,  and  on  precisely  the  same  decimal basis,  as  the  table  plainly  sets  forth.  The  same  considerations govern  their  use,  and  we  find  that  the  number  of  units  in  actual use  is  but  a  small  part  of  those  available.  Thus,  for  large weights  the  metric  ton  is  the  unit  employed,  and  is  used  in  the weighing  of  ore,  coal,  hay,  and  other  substances  dealt  in  in large  quantities.  It  is  employed  in  estimating  the  mineral  pro- duction of  the  world,  being  a  convenient  weight  to  which  the output  of  different  nations  may  best  be  reduced  for  purposes  of comparison  and  statistical  study.  It  corresponds  so  closely  with the  long  ton  of  2240  pounds  (a  metric  ton  equals  2204*62  lbs.) that  for  many  purposes  it  is  practically  equivalent.  The  quintal has  the  same  line  of  uses  as  the  hundredweight,  which  either as  112  pounds  or  100  pounds  is  still  employed  in  some  branches of  trade.  It  would  be  substantially  equivalent  to  twice  the former,  and  would  not  vary  greatly  from  the  American  barrel  of flour,  which  contains  196  pounds  net.  / The  myriagram  is  rarely,  if  ever,  used,  but  the  kilogram  is  a unit  which  is  found  universally.  Being  the  weight  of  a  cubic decimeter  of  water  it  enables  one  instantly  to  determine  the weight  of  a  body  whose  volume  and  specific  gravity  are  known,  «/ and  for  that  reason  is  very  convenient  in  calculation,  such  as  to determine  the  weight  of  cut  stone,  etc.  It  is  the  unit  most frequently  employed  in  trade  and  industry  for  the  sale  of merchandise  of  all  descriptions.  By  using  the  half  kilogram there    is   a  weight  which    approximates    the    pound,   and   being 148     EVOLUTION   OF   WEIGHTS   AND   MEASURES slightly  larger  there  is  an  element  in  favor  of  the  purchaser. Instead  of  using  hectograms  and  decagrams  it  is  found  more convenient  to  express  such  quantities  in  terms  of  fractions  of kilograms  or  as  grams,  and  such  is  the  usual  practice.  The  gram is  extensively  employed  in  science,  as  by  the  chemist,  and  by those  dealing  in  small  and  valuable  materials,  as  jewellers  and coiners.  In  multiples  of  ten  it  affords  a  convenient  substitute for  the  ounce,  30  grams  (28*3495  exactly)  corresponding  to  one ounce  avoirdupois.  Its  relation  to  the  cubic  centimeter  of  water makes  it  a  useful  unit  for  the  physicist  or  chemist,  and  unless there  is  reason  to  the  contrary  it  is  always  used  to  record  and describe  the  results  of  his  experimental  and  other  work.  As  the gram  is  so  constantly  used  for  measures  of  weight  of  this  nature by  those  having  to  do  with  masses  of  a  size  convenient  for  its use  the  adoption  of  this  part  of  the  metric  system  would  work  no hardship,  as  apothecaries'  weight,  which  it  would  supplant,  has  few defenders,  and  is  destined  to  disappear:  Decigrams,  centigrams, and  milligrams  are  used  in  the  form  of  fractions  of  the  gram, though  milligrams  are  employed  to  a  certain  extent,  especially  as the  riders  or  smallest  weights  of  a  fine  balance  enable  weighings to  be  made  in  milligrams  and  fractions  of  a  milligram. In  the  actual  weights  there  is  not  only  the  diversity  indicated by  the  table,  but  also  others  obtained  by  doubling  or  halving  the various  units  there  mentioned.  The  construction  and  design  of these  weights  as  also  their  accuracy  depends  upon  the  purpose for  which  they  are  intended,  and  vary  from  the  platinum  iridium and  rock  crystal  copies  of  the  international  standard  down  to  the cast-iron  weights  of  the  retail  dealer.  The  cast-iron  weights range  from  50  kilograms  to  50  grams  or  J  hectogram,  while  the brass  weights,  which  are  usually  cylindrical  in  shape,  with  the upper  part  fashioned  into  a  knob  for  more  convenient  handling, range  from  20  kilograms  to  1  gram.  Fractions  of  a  gram  are usually  made  of  sheet  metal,  such  as  platinum,  german  silver,  or aluminium,  as  in  this  shape  they  are  more  readily  handled  with the  forceps  employed  to  transfer  them  from  their  case  to  the pans  of  the  balance.  The  very  smallest  or  milligram  weights  are known  as  "  riders,"  and  are  twisted  loops  of  wire  which  may  be placed  at  any  desired  position  along  the  graduated  beam  of  the balance,  and  thus  enable  the  observer  to  read  to  fractions. THE   METRIC   SYSTEM   OF   TO-DAY  149 While  there  have  been  enumerated  under  each  class  of measures  a  number  of  units,  yet  it  is  necessary  to  state  again  that only  a  comparatively  small  number  are  employed.  In  this respect  the  metric  system  is  similar  to  the  United  States monetary  system,  where  there  are  mills,  dimes,  and  eagles,  as  well as  quarters  and  halves,  in  addition  to  dollars  and  cents,  but  in computation  everything  settles  down  to  a  dollars  and  cents  basis. This  is  precisely  the  case  with  the  metric  system,  and  while  the intermediate  units  appear  in  the  tables  we  have  taken  care  to explain  how  infrequently  they  are  employed.  In  fact,  it  is  a tendency  in  metrology  to  eliminate  from  use  as  many  units  as possible,  and  all  existing  measures  are  on  a  far  less  liberal  scale in  point  of  numbers  than  those  of  a  century  ago,  not  to  speak  of those  of  ancient  times  or  of  the  middle  ages.  With  the  metric system  this  elimination  can  be  done  without  any  trouble,  as  it  is the  work  of  but  a  moment  to  change  from  one  unit  to  another for  any  purpose  whatsoever. CHAPTEE  VI. THE   METRIC  SYSTEM   FOR  COMMERCE. Feom  what  has  been  said  regarding  the  development  and  present conditions  of  the  metric  system,  the  advantages  of  its  use  by all  nations  would  seem  apparent ;  nevertheless,  as  its  employ- ment is  not  as  yet  universal,  it  would  seem  desirable  here  to deal  first  with  the  benefits  to  the  commercial  world  at  large  of a  single  system  of  weights  and  measures,  and  second  with  the profit  that  would  accrue  to  an  individual  nation  from  the  adop- tion of  the  metric  system.  It  is  a  mere  truism  to  say  that anything  that  enlarges  the  circle  of  exchange  of  either  ideas  or commodities  works  for  the  welfare  of  the  world,  and  the  happiest and  most  prosperous  nations  are  those  that  have  the  advantages of  such  interchange  with  their  fellows  most  firmly  established. A  striking  example  of  this  is  seen  when  it  is  considered  that the  improvements  in  navigation  following  the  application  of  steam have  not  redounded  to  the  benefit  of  any  one  nation  to  the exclusion  of  others,  but  have  stimulated  trade  and  prosperity  in all  parts  of  the  world.  Likewise  by  means  of  the  telegraph  and submarine  cable  the  exchange  of  ideas  and  rapid  transaction  of business  between  distant  places  have  been  made  possible,  and  that again  has  brought  about  benefits  confined  to  no  single  nation. Furthermore,  international  banking  has  also  contributed  to  extend and  develop  trade,  and  here  we  find  that  through  the  pre-eminence of  Great  Britain  in  this  field  pounds  sterling  are  adopted  as  a universal  measure  of  value.  Facilities  have  been  supplied  by the  British  merchant  and  banker  which  have  resulted  in  no small  profit  to  him,  simply  because  he  has  been  able  to  occupy the  world  with  his  commercial  machinery  and  force  the  use  of  a standard  of  value  adequate  for  a  large  part  of  the  world's  trade. THE   METRIC   SYSTEM   FOR   COMMERCE        151 On  the  other  hand,  a  result  of  international  co-operation  is  the International  Postal  Union,  where  mails  from  all  countries  of the  world  are  exchanged  with  equal  and  proportionate  expense and  advantage  to  all.  Here,  as  we  have  seen,1  it  was  necessary at  the  outset  to  find  a  common  system  of  weights  and  measures to  regulate  the  payments  and  the  exchanges  of  mail,  and  it  was found  desirable  to  adopt  the  metric  system,  which  has  since  been employed  for  many  years  with  complete  success  even  among non-metric  nations.  In  general,  wherever  there  has  been  inter- national co-operation  to  secure  uniformity  in  commerce,  as  in cable  and  telegraph  conventions,  treaties  to  establish  uniform classifications  and  definitions,  etc.,  the  results  have  invariably resulted  in  promoting  general  prosperity  and  in  increasing business.  Furthermore,  an  international  language,  as  well  as an  international  currency,  would  serve  to  increase  commerce  and from  many  points  of  view  would  be  an  important  benefit. However,  international  language  and  international  currency  are outside  the  province  of  the  present  consideration,  but  inter- national weights  and  measures  must  be  discussed,  especially  as the  metric  system  is  destined  eventually  to  hold  such  a  position, even  in  a  fuller  sense  than  at  present.  The  reasons  for  this present  pre-eminence,  as  we  shall  soon  see,  are  obvious.  First, in  different  contiguous  countries,  there  was  the  realization  of  a need  of  a  single  system  of  measures  that  would  conform  to  those of  the  other  nations ;  and  second,  there  was  the  natural  desire for  the  best  and  most  useful  system.  The  result  was  that  in every  instance  where  a  change  was  made,  save  that  of  Russia2  in 1835,  the  metric  weights  and  measures  were  adopted  in  preference to  those  of  any  other  system,  and  in  no  case  have  they  been given  up,  nor  is  the  slightest  desire  for  any  change  expressed.3 For  the  benefits  of  a  single  and  international  system  of  units, we  have  only  to  refer  in  passing  to  the  electrical  units  which are  subsequently  discussed  at  some  length,4  For  the  measure- ment of  electrical  quantities  throughout  the  world  a  single  system 1  See  ante,  p.  127. 2  Russia  adopted  as  a  unit  of  length  7  English  feet,  but  neither  multiples  or submultiples  were  as  in  the  British  system.  Furthermore  the  British  pound  was not  adopted. 3  See  chapter  iii.  ante.  4  See  chapter  ix. 152     EVOLUTION   OF   WEIGHTS   AND   MEASURES of  units  is  employed,  and  this  system,  based  on  the  metric units,  was  developed  in  Great  Britain,  and  has  been  adopted  by scientists  and  engineers  universally.  When  great  industries were  established  to  apply  to  the  everyday  uses  of  mankind  the discoveries  and  inventions  of  men  of  science  in  this  field,  these same  units  were  retained,  and  were  later  sanctioned  by  inter- national agreements.  No  voice  has  ever  been  heard  to  dispute the  advantages  of  such  a  system,  and  the  result  has  been  that there  has  been  more  progress  in  electricity  through  the  inter- change of  ideas  than  in  any  other  branch  of  applied  science. When  electrical  congresses  meet  every  communication  is  in- telligible at  once  to  every  member  so  far  as  the  expression of  quantities  goes.  When  tenders  are  asked  for  electrical machinery,  materials,  or  apparatus,  the  manufacturers  of  every nation  of  the  world  are  on  the  same  footing  as  regards  under- standing the  specifications  and  utilizing  materials  for  a  desired output.  Accuracy  in  measurement  is  not  restricted  to  any single  nation  or  its  scientific  workers,  as  the  work  of  the  latter can  be  put  immediately  at  the  disposal  of  the  world,  and  the highest  precision  can  be  secured  by  joint  effort  and  co-operation. In  fact,  when  the  Physicalisch-Technische  Keichsanstalt  at  Char- lottenburg,  near  Berlin,  was  the  only  important  governmental testing  bureau  and  physical  laboratory,  it  received  apparatus  and materials  from  many  nations  outside  of  Germany  to  be  examined and  standardized  according  to  the  common  system.  To-day  elec- trical measuring  instruments  certified  to  by  the  Keichsanstalt,  the Laboratoire  Central  d'Electricite*  at  Paris,  the  National  Physical Laboratory  of  England,  or  the  U.S.  Bureau  of  Standards,  can  be used  for  electrical  measurements  anywhere  in  the  world,  as  the units  employed  depend  for  their  derivation  on  the  same  defini- tions. In  fact,  so  much  a  matter  of  course  is  the  single  system of  electrical  units  that  no  one  would  think  of  proposing  any  other, and  its  existence  is  so  taken  for  granted  that  its  advantages  are rarely  spoken  of  or  even  considered  until  the  possible  chaos  of  sub- stituting a  number  of  systems  in  its  place  is  mentioned.  Indeed, while  the  various  units  are  frequently  criticized,  no  electrician or  physicist  would  venture  to  propose  the  adoption  of  new  units locally,  despite  the  fact  that  universal  reforms  in  units  and standards  are  advocated  before  international  congresses. THE   METRIC   SYSTEM   FOR   COMMERCE        15S Looking  at  the  question  of  weights  and  measures  from  a strictly  commercial  standpoint  it  is  clear  that,  as  commerce involves  primarily  the  exchange  of  quantities  of  various  com- modities, the  use  of  a  simple  and  convenient  method  for  the rapid  calculation  of  weight,  length,  and  capacity  must  promote ease  and  security  of  commercial  intercourse.  The  metric  system being  decimal,  and  consequently  the  most  easily  grasped  and applied,  is  therefore  the  best  for  commerce,  and  when  to  this is  coupled  the  fact  that  its  use  is  all  but  universal  and  is  em- ployed in  the  major  portion  of  international  commercial  trans- actions, it  is  easy  to  see  that  a  great  saving  of  time  in  business operations  must  result  from  its  adoption.  That  this  saving  of time  and  simplicity  is  real,  and  not  the  mere  hope  or  opinions of  reformers,  can  be  demonstrated  by  reference  to  the  reports  of American  and  British  consular  and  diplomatic  officials  who  are acquainted  with  both  the  Anglo-Saxon  and  the  metric  systems. These  reports,  notable  among  which,  as  being  most  comprehen- sive and  complete,  are  those  presented  to  Parliament  in  1900' and  1901,1  to  which  reference  has  already  been  made,  speak emphatically  in  this  respect,  and  in  a  communication  from Portugal  appears  the  statement  that  "  The  large  amount  of  time saved  in  commercial  houses  by  the  simplicity  of  the  metric system,  as  well  as  by  the  uniformity  now  existing  in  place  of the  former  chaos,  is  in  itself  a  valuable  factor  in  considering the  advantages  of  the  new  system." 2 The  successful  prosecution  of  foreign  commerce  requires  a complete  understanding  between  merchants  in  different  countries as  to  each  other's  standing,  methods  of  payment,  and,  most important,  as  to  the  goods  themselves  which  form  the  subject  of the  transaction.  Aside  from  standards  of  quality,  quantities  and dimensions  must  be  considered,  and  it  is  here  that  universal measures  and  standards  are  needed.  It  is  also  of  importance  for both  buyer  and  seller  to  know  the  quantity  of  the  commodity  in existence  at  different  places,  the  quantity  produced  and  consumed in  previous  years,  and  other  statistical  information.     As  regards 1  English  Parliamentary  Accounts  and  Papers:  1900,  vol.  xc. ;  Reports  from  Her Majesty's  Representatives  in  Europe  on  the  Metric  System:  1901,  vol.  lxxx. ;. Reports  on  Metric  System,  part  ii. 2  Ibid,  part  i.  p.  54. 154     EVOLUTION   OF  WEIGHTS   AND   MEASURES the  latter,  it  will  readily  be  seen  that  the  collection  and  diffusion of  such  knowledge  would  be  facilitated  if  the  same  units  were used  in  every  country  and  port  of  the  globe,  and  trade  could  then be  carried  on  in  a  more  intelligent  manner,  and  with  the  elimina- tion of  speculative  elements,  while  tariff  laws  and  custom  regula- tions, etc.,  could  be  more  intelligently  framed  through  the  better and  more  uniform  character  of  the  statistical  information.  Such benefits  accrue  to  trade  throughout  the  world  generally,  and  are generally  recognized. But  with  no  uniform  system  of  weights  and  measures  which may  be  applied  to  the  description  of  goods,  it  is  inevitable  that there  is  a  lack  of  clear  understanding  between  buyer  and  seller, and  one  of  these  parties  is  at  a  disadvantage.  Especially  is  this true  if  there  is  a  competitor  who  is  ready  to  trade  on  a  basis  more readily  understood.  Thus,  if  a  man  is  in  doubt  as  to  certain elements  concerning  goods  which  he  desires  to  buy  or  sell,  he naturally  assumes  that  there  are  other  points  about  which  he  is equally  ignorant,  and  consequently  he  is  unwilling  to  undertake the  transaction.  True,  he  may  compute  in  his  own  system  the quantities  or  dimensions  of  the  article  or  articles,  or  may  receive these  figures  in  whole  or  in  part  from  the  other  merchant  or agent ;  but  the  basis  of  trade  is  unsatisfactory,  and  it  is  natural for  men  to  buy  or  sell  according  to  their  usual  measurements  even if  the  goods  must  be  imported  from  a  greater  distance.  This, furthermore,  is  emphasized  by  the  extensive  use  of  standards which,  at  first  designed  for  a  single  country  and  trade,  have gradually  crept  abroad  so  that  if  either  English  or  Continental goods,  such  as  pipe  or  nuts  and  bolts,  for  example,  have  secured a  foothold  in  a  certain  country,  it  is  quite  certain  that  in  all subsequent  orders  they  will  be  demanded,  and  a  newcomer  in  the field  will  have  to  conform  to  styles  and  standards  already  estab- lished. Thus  to  compel  trade  in  a  large  and  unusual  number  of sizes  is  a  most  wasteful  economic  process,  and  results  in  forcing the  manufacture  into  the  hands  of  a  comparatively  small  number of  producers,  who  can  so  control  their  business  as  to  occupy certain  fields  exclusively  rather  than  to  establish  wholesome competition  between  all  the  manufacturers  of  the  world. A  striking  example  of  the  evils  attending  lack  of  standardiza- tion in  measures,  materials,  and  machinery,  is   to  be  found  in THE   METRIC   SYSTEM   FOR   COMMERCE        155 the  mining  districts  of  South  Africa,  where  mining  and  other engineering  operations  are  carried  on  in  a  cosmopolitan  manner by  engineers  from  various  countries.  Machinery  and  supplies  are imported,  for  specific  purposes,  from  all  over  the  world,  and  con- sequently they  vary  in  dimensions,  often  in  parts  that  properly should  be  interchangeable.1  The  result  is  that  considerable  fitting is  required  in  order  to  make  the  various  parts  of  a  plant  work harmoniously.  This  of  course  involves  time  and  expense  without accompanying  benefit  to  anyone,  whereas  by  a  system  of  inter- national standards  such  waste  would  be  avoided.  Furthermore, a  proper  system  of  standardization  would  enable  the  specifications of  machinery  and  supplies  to  be  prepared  in  such  a  way  that manufacturers  and  dealers  would  know  exactly  what  was  wanted, and  make  their  bids  accordingly,  to  the  benefit  of  all  concerned. If  the  standardization  was  universal  a  simple  description  of  the desired  articles  could  be  circulated,  and  manufacturers  and  dealers all  over  the  world  could  submit  prices  and  estimates.  Thus  the whole  world  could  participate  in  the  competition,  and  not  only would  the  supplies  be  cheaper  to  the  purchaser,  but  manufacturing and  commerce  would  be  stimulated. Now,  the  first  principle  of  standardization  is  the  defining  of sizes  in  a  regular  and  systematic  manner,  and  conforming  to  a permanent  standard,  and  this  in  the  ultimate  analysis  must depend  on  a  standard  of  length  or  mass.  Consequently,  if  the dimensions  of  articles  are  referred  to  one  and  the  same  system, and  that  the  international  or  metric  system,  it  is  comparatively simple  to  reach  a  point  where  all  articles  of  a  class  are  reduced  to certain  sizes  determined  by  conference  and  mutual  consent  of  the makers  and  consumers  of  the  commodities  in  question.  There  is, in  short,  a  survival  of  the  fittest  and  most  convenient  sizes,  and machinery  and  materials,  involved  in  making  the  various  articles, are  soon  conformed  to  these  standards  of  size.2  It  will  be  seen, therefore,  that  the  standardization  which  is  a  benefit,  national  or international  in  accordance  with  its  scope,  follows  from  a  well- defined  system  of  units,  and  when  such  a  system  is  single  and 1  See  Presidential  Address  of  R.  M.  Catlin  before  Mechanical  Engineers' Association  of  the  Witwatersrand,  abstracted  in  Engineering  and  Mining  Journal <New  York),  vol.  lxxix.  1905. 2  See  p.  173,  chap.  vii. 156     EVOLUTION   OF   WEIGHTS   AND   MEASURES universal  there  is  bound  to  result  a  single  set  of  standards  in  all important  industries.  Such  a  result  is  bound  to  promote  com- merce  and  industry  by  facilitating  the  manufacture  and  exchange of  commodities,  and  the  same  benefits  would  be  experienced  by the  world  at  large  as  have  been  realized  in  the  United  States where  this  policy  has  been  followed  in  many  lines. International  weights  and  measures  soon  would  produce  truly international  standards,  both  of  size  and  of  quality,  and  the  trade of  the  world  would  be  on  a  far  more  wholesome  and  active  basis, as  there  would  not  be  material  tied  up  in  odd  sizes,  and  con- sequently  unavailable  to  other  users  except  at  increased  expense, but  there  would  be  a  common  world  stock.  As  trade  would  be stimulated  and  diversified  a  further  division  of  labor  would  take place,  and  there  would  be  greater  general  prosperity.  To  become thoroughly  convinced  of  this,  one  has  only  to  refer  to  the  reports  of American  and  British  consuls,  which  are  unanimous  and  constant in  reiterating  the  assertion  that  the  lack  of  an  international system  of  weights  and  measures  acts  most  strongly  against  the extension  of  trade  between  their  home  countries  in  those  places in  which  they  serve.  This,  of  course,  implies  a  reciprocal  loss,  as the  wider  the  distribution  of  a  nation's  commerce  the  more extensive  it  must  be,  as  also  the  more  profitable. That  there  is  need  of  an  international  system  of  weights  and measures  which  is  universal  and  invariable  is  shown  by  the  fact that  the  United  States  and  Great  Britain,  which  claim  the  same sources  for  their  various  weights  and  measures,  now  have  units that  figure  constantly  in  trade  relations  which  are  quite  unlike  in value.  For  example,  wheat  and  other  grain  from  America  is  sold by  a  bushel  which  differs  materially  from  the  British  bushel,  as does  also  the  gallon  used  in  the  measurement  of  petroleum,  while the  hundredweight  of  112  pounds  and  quarter  of  56  pounds  are rarely  used  in  America.  These  weights  were  abandoned  in Liverpool  in  1903  for  a  weight  of  50  pounds,  the  use  of  which  in trade  was  authorized  by  an  Order  in  Council  of  October  9,  1903. Since  that  time  a  standard  for  this  amount  has  been  constructed and  verified,  and  there  is  an  increasing  tendency  towards  using the  cental  of  100  lbs.  as  a  commercial  unit.  Here  are  examples of  the  inconvenience  where  two  countries  employ  measures  and weights  apparently  the  same,  but  which  must  be  adjusted  even  for THE    METRIC   SYSTEM   FOR   COMMERCE        157 transactions  between  themselves,  when  by  the  adoption  and  use  of the  metric  system  they  would  be  put  on  the  same  basis  as  regards one  another  as  they  would  enjoy  towards  the  rest  of  the  world. Foreign  commerce  presents  many  difficulties  unknown  to business  between  two  parties  in  more  or  less  proximity.  There is  the  question  of  time  and  of  freight,  both  important  items  in any  commercial  transaction,  but  especially  so  when  weeks  or months  must  elapse  before  a  delivery  can  be  effected.  Misunder- standings or  mistakes  are  most  costly  and  cannot  be  rectified promptly ;  consequently  there  should  be  the  most  complete understanding  between  the  parties  to  the  transaction.  This  must involve  an  easy  standard  or  basis  of  comparison,  for  the  present differences  in  money  and  exchange  are  troublesome  enough.  The extent  of  this  difficulty  is  best  illustrated  by  modern  methods  of doing  business  where  catalogues,  price-lists,  and  other  printed matter  are  used  so  extensively,  and  are  such  an  important  adjunct to  the  work  of  the  salesman,  who  naturally  is  unable  to  carry with  him  a  complete  line  of  samples,  even  of  agricultural  tools, not  to  mention  dynamos  and  steam  engines.  If  these  descriptions and  prices  are  understood,  and  if  the  sellers  have  a  good reputation,  much  has  been  done  towards  effecting  a  sale,  as  the prospective  buyer  can  tell  at  a  glance  whether  character,  quality, and  size  are  such  as  he  desires  and  uses,  and  especially  whether they  will  correspond  in  size  with  present  or  future  stock  or  plant. Furthermore,  in  case  of  an  immediate  demand  for  the  goods, business  can  be  transacted  satisfactorily  by  cable  or  telegraph. When,  however,  various  articles  are  presented  to  a  foreign  pur- chaser described  in  strange  units,  the  latter  is  compelled  to employ  conversion  tables,  and  even  then  fails  at  a  complete,  not to  speak  of  quick,  comprehension  of  the  goods.  With  a  single system  the  case  would  be  different,  and  no  nation  would  enjoy any  advantage  over  another  in  this  respect,  save  in  the  actual merit  of  its  goods,  and  the  increased  circulation  and  use  of  such •catalogues  would  provoke  keener  competition,  and  would  result in  a  higher  grade  of  tools  and  other  articles,  as  the  world  markets would  be  aimed  at  where  general  excellence  and  price  would carry  the  day. The  question  whether  a  country's  export  business  would  be helped  by  an  international  system  of  weights  and  measures  must 158     EVOLUTION   OF   WEIGHTS   AND   MEASURES be  considered,  no  matter  whether  that  country  is  on  a  protection basis  or  enjoys  free  trade.  In  the  latter  case  the  advantages  are obvious,  but  where  there  has  been  protection  the  result  in  many nations  is  that  the  product  is  often  greater  than  the  needs  of  the home  market,  consequently  the  manufacturer,  in  order  to  keep  up his  production  on  the  largest,  and  therefore  most  economical scale,  must  seek  to  market  his  surplus  in  a  foreign  field.  A glance  at  our  table  (page  105)  will  soon  show  that  with  the exception  of  Great  Britain  and  its  dependencies,  Eussia,  Denmark, and  China,  the  vast  majority  of  nations  are  on  the  metric  basis, and  for  reasons  we  have  already  advanced  it  is  quite  necessary that  business  with  them  should  be  done  according  to  the  inter- national measures.  That  this  is  essential  is  shown  by  the  fact that  in  the  United  States  certain  manufacturers,  and  the  number is  constantly  increasing,  not  only  describe  their  goods  in  metric measures,  but  so  construct  them,  and  stand  ready  to  increase their  business  in  this  respect.  If  the  surplus  product  is  made  so that  it  can  be  utilized  in  any  country,  it  is  of  course  obvious  that the  manufacturer  has  a  far  wider  range  of  market,  and  is  likely to  secure  better  prices. Possibly  the  best  testimony  as  to  the  advantages  to  commerce of  an  international  system  of  weights  and  measures  should  come from  countries  where  the  metric  system  has  supplanted  the  local system  or  systems,  though  the  latter  still  survive.  Such  is  the following  extract,  which  sums  up  the  conditions  in  Spain,  and which  is  typical  of  the  enlightened  opinion  in  nearly  all  metric countries :  "  The  facility  and  security  afforded  to  the  sending  of orders,  owing  to  the  amount  ordered  being  subject  to  the  same measure  in  the  different  countries,  the  conformity  in  transport, custom-house,  and  commission  tariff,  etc.,  attract,  tighten,  increase commercial  relations." 1  This  is  the  answer  of  the  Spanish Geographical  and  Statistical  Institute  attached  to  the  ministry  of Public  Instruction,  Agriculture,  Industry,  and  Public  Works,  in reply  to  a  question  as  to  how  the  adoption  of  the  metric  system had  affected  its  commerce,  and  it  is  also  the  experience  of  other countries.     The  importance  of  the  adoption  of  the  metric  system 1  Report  of  Her  Majesty's  Representatives  in  Europe  on  the  Metric  System,  pre- sented July,  1900,  part  i.  p.  61  ;  Parliamentary  Accounts  and  Papers,  1900, vol.  xc. THE   METRIC   SYSTEM   FOR   COMMERCE        15£ to  international  trade  has  been  noted  formally  by  various  com- mercial and  statistical  conferences  and  conventions,  but  of  a  more official  character  was  the  action  taken  by  the  International American  Conference  which  was  held  at  Washington  in  1890, where  the  following  resolution  was  adopted :  "  Resolved  that  the International  American  Conference  recommends  the  adoption  of the  metrical  decimal  system  to  the  nations  here  represented which  have  not  already  adopted  it."  James  G.  Blaine,  then Secretary  of  State,  whose  last  important  official  work  was  towards the  extension  of  American  commerce  through  reciprocity  treaties with  the  South  American  countries,  urged  upon  the  United  States Government  the  adoption  of  that  system  for  the  customs  service,1 and  his  recommendations  were  concurred  in  by  Secretary  of  the Treasury  Windom  (Report,  Dec.  1,  1890),  and  by  Secretary  of State  Foster,  in  his  reports  for  1891  and  1892.  Likewise,  in Great  Britain  there  was  a  conference  of  Colonial  Premiers  at London  in  1902,  and  a  resolution  was  formally  adopted  favoring the  use  of  the  metric  system  for  all  the  British  colonies.  Fol- lowing up  the  matter  the  Colonial  Office  then  communicated  with the  various  Colonial  governors,  asking  what  action  was  likely  to be  taken  with  regard  to  this  resolution.  Mauritius  and Seychelles  already  used  the  system,  but  the  following  colonies were  reported  as  favorable  to  its  adoption :  Australia,  New Zealand,2  Cape  of  Good  Hope,  Transvaal,  Orange  River  Colony, Southern  Rhodesia,  Gambia,  Northern  Nigeria,  Gibraltar,  British Guiana,  Trinidad,  Leeward  Islands  and  Windward  Islands. Sierra  Leone,  Southern  Nigeria,  Ceylon,  and  the  Falklands stipulated  that  they  were  in  favor  of  it  if  adopted  by  the  United Kingdom  or  in  the  Empire  generally.  The  Australian  states, while  favorably  disposed,  thought  that  the  matter  should  be settled  by  the  government  of  the  commonwealth,  while  Jamaica and  British  Honduras  required  the  adoption  of  the  system  by  the United  States.  Fiji  and  British  New  Guinea  would  have  to follow  Australia,  just  as  the  Straits  Settlements  and  Labuan  were dependent  on  India.  The  Bechuanaland  Protectorate  would  be compelled  to  be  in  harmony  with  the  rest  of  South  Africa. Opposition  to  the  plans  was  evinced  by  St.  Helena,  Cyprus,  Lagos, 1  Sen.  Exec.  Doc,  No.  181,  51st  Congress,  1st  Session. 2  Metric  System  adopted  by  New  Zealand  in  1905. 160     EVOLUTION   OF   WEIGHTS   AND   MEASURES Wei-hai-wei,  Barbados,  and  Bahamas,  while  the  Gold  Coast Colony  and  the  State  of  Queensland  were  ready  for  the  system, but  anticipated  inconvenience  in  its  adoption.  Natal  reported that  some  definite  general  plan  was  necessary  before  an  opinion could  be  expressed.  Of  the  remaining  colonies  definite  answers were  not  given  by  Newfoundland,  Malta,  or  Bermuda,  and  no reply  whatsoever  was  received  from  Canada,  though  it  is sufficiently  obvious  that  the  latter  country  would  be  compelled  to follow  the  example  of  the  United  States. It  will  be  seen  from  the  foregoing  that  these  colonies,  widely scattered  over  the  world,  were  for  the  most  part  alive  to  the -advantages  attending  the  adoption  of  the  metric  system,  as  by  so doing  the  great  trade  of  the  British  Empire  would  then  be  put on  the  same  terms  as  that  of  the  rest  of  the  world.  This,  of course,  leaves  out  of  consideration  the  trade  of  the  United  States ■and  its  possessions,  which,  if  brought  into  harmony  with  the above,  would  greatly  facilitate  in  the  development  and  prosecution of  commerce. An  additional  consideration  is  that  new  discoveries  of  mineral wealth  and  supplies  of  raw  materials  of  one  class  or  other  have within  comparatively  few  years  greatly  extended  the  range  of commerce,  and  many  nations  once  thought  uncivilized  and  un- productive are  becoming  great  consumers  as  well  as  producers, requiring  the  most  varied  supplies  and  machinery.  These markets  are  destined  to  prove  among  the  most  valuable  of  the world,  and  to  pre-empt  them  is  the  task  of  the  highest  wisdom. In  South  America  and  in  all  non-British  colonies  we  find  the metric  system  used,  though  with  it  are  often  various  native  or local  nondescript  units.  It  is  the  opinion  of  the  consuls  to  these places — and  they  at  least  must  be  admitted  to  be  competent judges — that  the  use  of  the  metric  system  would  greatly  increase trade  of  these  countries  with  America  and  Great  Britain. Having  pointed  out  that  the  adoption  of  a  single  system  of weights  and  measures  throughout  the  world  would  be  most advantageous,  and  would  facilitate  commerce,  therefore  benefiting each  and  every  nation  to  a  greater  or  less  extent  depending  on its  location  and  the  amount  of  its  foreign  trade,  it  is  now necessary  to  consider  just  what  advantages  a  country  not  using the  metric  system  would  secure  by  its  adoption,  and  what  dis- THE   METRIC   SYSTEM   FOR   COMMERCE        161 advantages,  if  any,  are  likely  to  be  experienced.  These  advantages must  be  practical,  especially  in  a  country  like  the  United  States, and  must  appeal  to  the  small  shopkeeper  and  farmer,  as  well  as to  the  professor  of  physics,  the  merchant,  and  the  statistician. Large,  as  the  question  seems,  it  is  possible  to  simplify  it  by eliminating  a  certain  number  of  elements.  Thus,  we  know  that workers  in  science  in  America,  Great  Britain,  and  Russia  have, for  a  long  time,  universally  employed  metric  weights  and  measures in  their  daily  work,  and  have  urged  their  adoption  for  general use,  confident  of  their  great  utility  and  superiority.  Also,  that other  scientific  men,  whose  work  is  of  a  more  practical  nature, such  as  electrical  engineers,  who  constantly  use  the  metric weights  and  measures  in  their  work,  have  also  urged  their  general adoption.  Consequently,  the  change  would  be  a  distinct  advan- tage to  workers  in  this  field,  and  there  is  no  opposition  to  the step  to  be  anticipated  from  them. At  the  other  end  of  the  scale  must  be  considered  the  average citizen  who  does  business  on  a  small  scale,  and  who,  with  his household,  uses  weights  and  measures  daily.  In  fact,  looking  at the  question  as  a  national  one,  this  seems  to  be  the  most important  aspect,  and  should  be  most  carefully  considered,  both in  the  light  of  the  experience  of  foreign  countries  and  according to  local  conditions.  Reflection,  however,  soon  establishes  the fact  that  most  of  these  transactions  take  place  where  the  actual goods  are  transferred  in  the  presence  of  the  buyer  and  seller,  and some  approximate  idea  of  the  measure  desired  is  in  the  mind  of both  of  the  parties  to  the  transaction.  Thus  a  man  buying  sugar sees  the  amount  he  is  receiving,  and  knows  the  price  paid,  so that  with  properly  sealed  weights  there  is  no  opportunity  for injustice,  as  the  man  is  free  to  buy  sugar  where  he  will,  and  at the  most  favorable  price,  the  latter  being  governed  by  the  law  of supply  and  demand  as  modified  by  trade  conditions.  When  his wife  mixes  the  sugar  to  make  cake  her  methods  of  measurement are  purely  relative,  and  neither  ounces  nor  grams  are  employed, but  approximate  measures,  such  as  tea-cups,  which  are  quite independent  of  any  laws  of  metrology.  In  fact,  the  question  has been  excellently  summed  up  by  one  of  the  most  distinguished opponents 1   of  the   introduction  of  the   metric  system  into  the 1  Dr.  Coleman  Sellers,  Cassier's  Magazine,  vol.  xvii.  p.  365,  1900. L 162     EVOLUTION   OF   WEIGHTS   AND   MEASURES United  States,  as  follows  :  "  To  the  great  bulk  of  mankind  engaged in  trade,  in  buying  and  selling,  in  bartering  and  exchanging,  it matters  little  what  system  of  weights  and  measures  they  adopt : it  matters  little  whether  they  are  obliged  to  use  a  yard-stick  or a  meter  rod,  pounds  or  kilograms,  quarts  or  liters.  The  cost  to them  is  the  cost  of  the  few  devices  needed  in  weighing  and measuring ;  the  rationale  of  the  system  may  never  enter  into their  thoughts."  Thus,  there  is  no  reason  why,  so  far  as  this class  of  people  is  concerned,  a  change  should  not  be  made  if  the new  system  supplied  is  superior  for  their  purposes.  This  the metric  system  is,  on  account  of  its  great  simplicity,  doing  away as  it  does  with  all  compound  relations  for  the  single  ratio  of  ten, connecting  weight  and  measures  by  the  weight  of  a  volume  of water  as  a  unit,  thus  eliminating  all  odd  equivalents  such  as  the fact  that  a  cubic  foot  of  water  weighs  62 \  pounds,  and  finally doing  away  with  such  anomalies  as  dry  and  liquid  measures  of capacity,  avoirdupois,  Troy,  and  apothecaries'  weight,  long  tons and  short  tons,  hundredweight  of  112  pounds,  and  other  weights and  measures  equally  arbitrary,  and  not  susceptible  of  being  put into  simple  relation  with  other  quantities. Indeed,  the  full  complexity  and  absurdity  of  the  present "  system,"  so  called,  is  hardly  realized  until  we  stop  to  consider that  in  the  United  States  copper  is  weighed  by  one  standard, silver  by  another,  medicines  by  a  third,  diamonds  and  other precious  stones  by  a  fourth,  and  platinum  and  chemicals  by  a fifth,  none  of  which  are  interchangeable  with  one  another  except by  means  of  fractions.  Nor  is  the  condition  less  striking  in  the case  of  the  measures  of  capacity.  One  unit  is  used  for  wine,  and bears  the  same  name  as  a  dissimilar  one  used  for  grain,  while gas  is  measured  by  still  a  third  unit.  In  fact,  the  condition  as regards  the  last-named  groups  of  units  is  summed  up  in  the Anti-metric  Argument  of  the  committee  of  the  American  Society of  Mechanical  Engineers,  where  it  is  stated  in  a  passage  already quoted : l  "  There  is  no  reason  for  the  English  system  retaining the  gallon  and  the  bushel,  except  that  they  are  in  such  common use."  For  convenience  of  computation  it  would  be  well  if  the gallon  were  216  cubic  inches,  or  the  cube  of  6  inches,  and  the 1  See  pp.  145,  146  ante;  Transactions  American  Society  of  Mechanical  Engineers, vol.  xxiv.  1902,  No.  972,  "  Anti-Metric  Argument,"  vii.  p.  676. THE   METRIC   SYSTEM   FOR   COMMERCE        163 bushel  1728  cubic  inches,  or  1  cubic  foot.  A  few  lines  later  in this  interesting  argument  some  comments  on  the  various  units  of weight  are  concluded  by  the  remark,  "  Both  Troy  weight  and apothecaries'  weight  might  be  abandoned."  Here,  from  a  source unfriendly  to  the  metric  system,  and  opposed  to  any  fundamental changes  in  the  weights  and  measures,  is  to  be  found  a  frank admission  that  the  measures  of  capacity  are  inconvenient,  and could  be  greatly  improved,  and  that  no  reason  other  than  use exists  for  retaining  the  Troy  and  apothecaries'  weight.  Accord- ingly, they  propose  to  reconstruct  the  measures  of  capacity  into  a new  system  which  would  occasion  all  the  inconvenience  attendant on  a  transition  from  one  system  to  another,  and  yet  would  not yield  the  advantages  of  a  decimal  basis,  and  division,  or  relation between  weights  and  measures  of  the  metric  system,  nor  would  it have  the  least  international  value. Likewise  in  England  a  society  was  formed  in  1904  under  the title  of  the  British  Weights  and  Measures  Association,  which had  as  it  object  "  the  defence,  standardizing,  and  simplifying (italics  ours)  of  British  weights  and  measures,"  and  to  oppose the  introduction  of  the  meter  as  a  British  standard.  Further- more, this  society  proposed  the  introduction  of  "simplified  and scientifically  related  weights  and  measures  based  upon  existing British  measures "  (again  italics  ours).  Now,  with  such  an admission  that  the  Anglo-Saxon  weights  and  measures  need "  simplification  "  and  to  be  "  scientifically  related,"  it  is  proposed to  proceed  on  a  new  basis,  and  construct  and  try  a  system that  has  not  been  tested  by  actual  use,  as  has  the  metric  system, and  which  in  addition  must  be  pushed  against  the  latter,  despite the  fact  that  it  will  doubtless  contain  neither  the  decimal  basis nor  the  relation  between  measures  of  length  and  weight.  In other  words,  there  would  be  experienced  all  the  inconvenience which  would  attend  a  change  to  the  metric  system,  and  at  the same  time  the  advantages  obtained  would  be  infinitely  small  in comparison  with  what  would  follow  a  decision  to  adopt  the latter  completely. Moreover,  such  a  proposition  is  by  no  means  new,  for  we have  seen  how  Sir  John  Kiggs  Miller,  at  the  end  of  the eighteenth  century,  advocated  a  decimal  division  of  the  British weights    and    measures,   while    on    October    27,    1863,    Sir  John 164     EVOLUTION   OF  WEIGHTS   AND   MEASURES Herschel,  the  eminent  scientist  and  astronomer,  in  an  address before  the  Leeds  Astronomical  Society,  advocated  the  readjust- ment of  the  British  Imperial  weights  and  measures  on  a  decimal basis  according  to  a  plan  that  at  least  appeared  scientific  and methodical.  He  proposed  to  take  as  the  standard  of  length  the earth's  polar  axis,  which  in  imperial  inches  was  computed  to be  500,482,296,  and  as  a  new,  or  as  he  termed  it,  "  geometrical  " inch,  employ  the  5~o~o~tjoo  000  Part  of  tnis>  wnicn  would  differ by  less  than  a  thousandth  from  the  customary  inch,  and  be at  the  same  time  related  to  a  natural  quantity.  The  unit of  weight  would  be  a  cubic  foot  of  water,  and  would  be approximately  equal  to  1000  ounces  avoirdupois.  Herschel  says : "  Thus  the  change,  which  would  place  our  system  of  linear measure  on  a  perfectly  faultless  basis,  would  at  the  same  time rescue  our  weights  and  measures  of  capacity  from  their  present utter  confusion,  and  secure  that  other  advantage,  second  only in  importance  to  the  former,  of  connecting  them  decimally  with that  system  on  a  regular,  intelligible,  and  easily  remembered principle ;  and  that  by  an  alteration  practically  inperceptible  in both  cases,  and  interfering  with  no  one  of  our  usages  or denominations." It  might  be  said  in  passing  that  the  length  of  the  polar radius,  as  calculated  by  Sir  John  Herschel,  was  no  more accurate  or  permanent  than  the  original  determination  of  the length  of  the  earth's  quadrant  by  the  founders  of  the  metric system,  while  similar,  though  greater,  errors  have  been  found in  his  fundamental  unit  of  weight.  It  is  now  conclusively recognized  in  metrology  that  no  terrestrial  dimensions  can  be relied  upon  to  furnish  an  accurate  standard  of  length.1  Thus we  see  that  a  simple  and  albeit  excellent  step  at  reforming British  weights  and  measure  did  not  meet  with  any  greater favor  than  the  complete  change  to  the  metric  system  advocated about  the  same  time,  and  it  is  quite  probable  that  a  like  fate would  to-day  befall  any  similar  proposition.  So  that  the question  seems  to  be  not  to  reform  weights  and  measures  by gradual  and  slight  improvements,  but,  if  any  changes  can  be made,   to  adopt   the   best    possible  system,  notwithstanding   the xSee  Mendenhall,  "The  Metric  System,"  Appleton's  Popular  Science  Monthly, October,  1896. THE   METRIC   SYSTEM   FOR   COMMERCE        165 drawback  of  temporary  inconvenience,  and  for  the  sake  of  the future  benefits  which  must  unmistakably  follow. Perhaps  the  most  important  question  in  connection  with the  adoption  of  the  metric  system  is  whether  the  change would  occasion  any  temporary  inconvenience  or  expense  to  the people  at  large.  In  the  United  States  the  great  majority  of the  people  have  been  educated  in  the  public  schools,  in  most of  which  since  1880  the  metric  system  has  been  taught  more  or less  effectively  as  an  integral  part  of  arithmetic.  Everyone is  used  to  the  decimal  system  as  employed  in  the  national currency  and  coinage,  and,  furthermore,  it  must  be  granted  that a  higher  standard  of  intelligence  and  adaptability  prevails  in the  United  States  than  in  Germany  and  other  European countries,  where  but  little  inconvenience  was  experienced  and practically  no  injury  was  done  at  the  time  of  the  change.  True, there  would  be  in  some  cases  the  cost  of  new  scales,  weights, and  measures,  but  it  must  be  remembered  that  these  are  under- going constant  deterioration,  and  in  constant  use  the  life  of scales  and  weights  is  only  about  two  years.  Therefore,  any  such expense  would  be  in  actuality  practically  negligible,  and  doubtless would  result  in  distributing  over  the  country  weights  and measures  of  increased  accuracy.  Indisputably  some  time  would be  required  for  the  complete  assimilation  of  metric  measures  and weights,  as  we  have  seen  was  the  case  in  Europe,  but  at  the  same time  the  advantages  attending  their  use  would  begin,  and  there would  be  employed  tables  of  legal  equivalents  which  would  soon educate  all  to  the  necessary  proficiency.  Then,  also,  we  would see  for  a  few  years  before  and  after  any  legislative  establishment of  the  metric  system,  all  books  for  common  use  containing formulas,  recipes,  etc.,  printed  with  all  quantities  in  both  English and  metric  measures,  so  that  the  transition  from  one  to  the  other either  ideally  or  actually  would  be  attended  with  no  inconvenience. In  addition  to  the  marked  advantages  in  the  actual  measuring and  weighing  of  everyday  life,  due  to  the  simplicity  of  the metric  system,  there  would  be  the  great  saving  of  time  in  the schools  where  the  complete  metric  system  taught  in  connection with  decimals  would  require  but  a  fraction  of  the  time  now  given to  compound  numbers.  In  fact  authorities  on  education  have estimated  that  at  least  one  year  of  the  child's  school  course  could 166     EVOLUTION   OF  WEIGHTS   AND   MEASURES be  saved  by  the  adoption  of  the  metric  system,  as  after  its employment  in  our  practical  everyday  life,  the  Anglo-Saxon measures  would  be  of  little  more  use  than  those  of  the  Greeks and  Eomans,  and  would  have  scarcely  more  interest  than  the old  measures  of  France  have  to-day. It  is  not  necessary  here  to  refer  to  the  great  saving  of  time  in making  calculations  involving  quantities  of  produce  of  various kind,  although  it  is  by  no  means  unimportant,  for  with  the  class of  citizens  we  are  now  considering,  while  bookkeeping  usually plays  but  a  secondary  part  in  their  life,  yet  it  is  employed,  and the  farmer  or  petty  shopkeeper  will  appreciate  the  saving  of time  as  much  as  the  clerk  or  accountant  whom  we  will  consider later.  For  the  mechanic  it  is  amply  demonstrated  that  a  change in  measurements  makes  but  little  difference  as  foreign  workmen educated  to  the  metric  system  are  able  to  work  in  the  Anglo- Saxon  system  without  any  difficulty  whatsoever  and  vice  versa, ample  testimony  being  forthcoming  on  both  sides  of  this  pro- position. In  short,  there  are  no  serious  drawbacks  so  far  as  the  average man  and  woman  are  concerned  why  America  and  Great  Britain should  not  adopt  the  metric  system,  and  when  it  is  recalled,  how practically  no  inconvenience  was  experienced  in  Canada  when  the change  was  made  from  shillings  and  pence  to  dollars  and  cents, or  in  the  early  days  of  the  United  States  when  its  system  of currency  was  established  on  lines  quite  new,  it  is  not  reasonable to  anticipate  any  embarrassment  or  difficulty. We  are  then  brought  face  to  face  with  the  question,  how  will the  adoption  of  a  metric  system  affect  the  internal  commerce  of  a country  using  the  term  as  referring  to  the  exchange  of  com- modities on  a  somewhat  larger  scale  than  we  have  discussed above.  While  such  commerce  depends  for  its  prosperity  on  the individual  purchaser,  yet  anything  which  facilitates  it  acts  to  the latter's  benefit  in  reduction  of  prices  and  promptness  of  delivery and  improvement  of  quality.  This  exchange  is  accomplished through  an  intricate  system  of  machinery  in  which  credits,  banks, transportation,  and  other  factors  all  enter  to  a  large  degree.  Yet, with  the  extension  of  commerce  constantly  going  on,  there  has been  no  backward  step,  and  in  its  progress  simplicity  and accuracy  in  business  transactions  have  been  the  chief  essentials THE   METRIC   SYSTEM   FOR   COMMERCE        167 which  have  been  aimed  at  and  attained.  Thus  the  use  of banking  facilities,  and  the  telegraph,  for  the  exchange  of  money have  contributed  to  save  time  and  trouble,  which  in  business  are definitely  measured  by  money,  while  typewriter,  telephone,  cal- culating machines,  and  new  methods  of  bookkeeping  have  played their  part  in  releasing  the  mind  of  the  business  man  to  new  and original  activities,  and  to  the  extension  of  his  business  along  such directions  as  his  experience  tells  him  are  most  profitable.  With such  innovations  must  be  considered  the  adoption  of  the  metric system,  as  a  step  in  advance,  since  it  will  simplify  all  calculations and  bookkeeping  by  the  elimination  of  useless  multiplications which  are  involved  in  the  use  of  the  compound  numbers  employed in  the  ordinary  weights  and  measures.  One  immediate  result would  be  the  ease  in  determining  errors  and  the  decrease  in  their number  through  less  multiplication.  Undeniably,  the  simplest mathematical  process  for  man  is  decimal  multiplication,  corre- sponding as  it  does  to  his  fundamental  notation,  and  this  simplicity has  been  established  uncontrovertibly  in  an  experience  of  over  a century  with  the  decimal  system  of  American  money,  where  there has  been  demonstrated  its  applicability  to  all  pecuniary  trans- actions, both  large  and  small,  from  the  actual  handling  of  the currency  to  the  booking  of  credits  and  the  computation  of discounts,  interest,  etc.,  not  to  mention  the  ease  with  which  such mental  calculation  as  the  determination  of  the  price  for  a  quantity from  a  price  for  an  individual  article  or  vice  versa  can  be  made. Consequently  there  has  resulted  the  widespread  use  of  per- centages and  a  decimal  division  wherever  possible.  Thus,  it  is  a matter  of  convenience  that  railway  and  other  shares  shall  be valued  on  a  percentage  basis,  and  still  more  convenient  that  the par  value  should  be  $100*00,  and  this  practice  has  largely  prevailed. For  mining  or  other  shares  where  a  smaller  par  value  is  desired, it  is  usual  to  employ  $10'00  or  $1*00,  while  bonds  are  con- veniently arranged  on  a  basis  of  $1000*00  each.  Likewise  with such  commodities  as  sugar  and  cotton,1  where  it  is  necessary to  express  intermediate  values  between  even  cents,  it  has  been found  desirable  to  give  up  common  fraction  and  use  a  decimal 1  The  Liverpool  Cotton  Association  since  October  1,  1902,  has  quoted  cotton values  in  hundredths  of  a  penny  instead  of  sixty-fourths.  A  similar  practice  is observed  in  America. 168     EVOLUTION   OF   WEIGHTS   AND   MEASURES division  to  facilitate  computation  and  bookkeeping.1  These changes  have  been  the  result  of  an  evolution  which  has  been independent  of  any  theory,  but  which  has  considered  merely  the commercial  availability  of  the  method.  For  shop  costs  a  decimal hour  is  often  employed,  and  such  clocks  are  used  in  some factories. An  instance  of  this  in  American  weights  and  measures  is found  in  the  tendency  to  eliminate  as  many  units  as  possible,  and to  use  larger  numerical  figures,  as  1000s  of  pounds  instead  of tons.  Another  example  was  the  introduction  of  the  short  ton  of 2000  pounds  to  facilitate  calculation,  and  this  unit  soon  came  to be  more  extensively  used  than  the  long  ton  of  2240  pounds inherited  from  Great  Britain.  No  difficulty  was  experienced  in making  the  transition  from  the  long  to  the  short  ton,  in  com- mercial usage,  and  there  is  no  reason  why  any  inconvenience should  attend  the  change  to  the  metric  ton.  In  fact,  in  one  of the  largest  chemical  works  in  the  United  States, — that  of  the Solvay  Process  Company, — where  the  metric  system  is  used exclusively,  it  is  customary  to  weigh  the  coal  and  other  supplies, when  received,  in  metric  units,  despite  the  fact  that  they  are bought  and  invoiced  in  ordinary  weights  and  measures.  This company  has  found  it  a  distinct  advantage  in  its  internal economy  to  make  use  of  the  metric  system,  and  employs  it  in  all calculations,  except  for  specifications  of  machinery  and  wood-work that  must  be  constructed  outside  of  their  factory  by  people  to whom  the  metric  weights  and  measures  are  practically  unknown. An  interesting  example  of  the  superiority  of  the  metric  system  for purposes  of  accounting  and  bookkeeping  may  be  cited  in  the experience  of  the  Brighton  Bailway  in  England,  which  for  a number  of  years  has  employed  the  kilogram  as  its  unit  of  weight for  all  its  European  business,  and  the  French  decimal  monetary system  for  its  accounts.2  It  is  the  opinion  of  the  officials  of  this road  that  the  keeping  of  all  accounts  would  be  simplified  by  using metric  weights  and  measures.     In  the  foreign  business  it  would 1The  Stock  Exchanges,  however,  still  use  common  fractions  and  commissions are  usually  in  eighths  and  sixteenths  of  a  per  cent. 2  See  testimony  of  Charles  A.  de  Pury,  chief  accountant  of  Brighton  Railway  in Report  by  Select  Committee  on  Weights  and  Measures  (Metric  System)  Bill [H.L.]  1904,  p.  25. THE  METRIC   SYSTEM   FOR   COMMERCE        169 have  been  possible,  of  course,  to  have  changed  the  French  weights and  currency  to  English,  but  the  auditors  of  this  corporation believed  that  the  metric  system  would  be  the  more  convenient,, and  such  it  has  proved  in  practice. The  elimination  of  the  middleman  is  one  of  the  tendencies  of modern  trade,  and  the  more  direct  relation  of  consumer  with producer  requires  that  business  should  be  done  on  the  simplest possible  basis  by  the  contracting  parties.  Now  the  middleman in  the  past  was  the  one  who  usually  made  the  transformations  of weights  and  measures,  buying  by  one  system  and  selling  by another.  Inasmuch  as  often  now  he  is  considered  superfluous, in  many  transactions  where  the  buyer  and  seller  come  together directly,  it  is  essential  that  a  single  system,  which  must  also  be the  simplest,  should  be  employed.  Thus  there  is  no  reason  why coal  should  be  sold  at  wholesale  by  the  long  ton  and  retailed  by the  short  ton  of  2000  pounds,  or  that  the  dealer  in  drugs  and chemicals  imported  by  metric  weights  should  dispose  of  them  by avoirdupois  or  apothecaries  pounds.  In  fact,  transformations  of weights  and  measures,  or  the  use  of  double  systems,  are  and always  have  been  a  fruitful  source  of  complaint  and  controversy. Indeed,  it  was  well  said  by  a  British  diplomatic  official  in speaking  of  conditions  in  Belgium,  "  The  disputes  which  were formerly  so  numerous,  and  which  rendered  long  and  complicated calculations  necessary,  have  become  few  and  far  between.  In short,  the  adoption  of  the  metric  system  has  done  much  to  ensure honesty  in  commercial  transactions."  ! With  the  decimal  system  can  be  used  such  important  labor saving  device  as  slide-rules  and  calculating  machines,  the  latter in  particular  now  being  a  feature  of  every  well  equipped  office, and  resulting  in  increased  accuracy  and  speed  of  operation.  So that  the  way  is  in  part  prepared  for  the  introduction  of  the metric  system  to  denote  units  of  quantity  on  account  of  its decimal  features,  which  would  fit  in  completely  with  modern business  computation,  and  America  could  make  the  change  with greater  facility  than  Great  Britain,  or  even  than  that  experienced by  any  foreign  country,  on  account  of  its  simple  currency  system. With  the  advent  of  the  metric  system  would  come  the  release 1  Reports  from  Her  Majesty's  Representatives  in  Europe  on  the  Metric  System> part  i.  p.  8  ;  English  Parliamentary  Accounts  and  Papers,  1900,  vol.  xc. 170     EVOLUTION   OF  WEIGHTS   AND   MEASURES from  the  various  heterogeneous  arrangements  of  tables  of  length, surface,  volume,  capacity,  and  mass  in  which  binary,  duodecimal, and  other  relations  are  maintained  and  abandoned  in  accordance with  no  consistent  theory  or  system,  constantly  requiring  refer- ence to  unwieldy  tables  and  tedious  calculation.  Not  only  is there  saving  in  the  time  required  to  learn  the  metric  system  over all  others  (and  it  is  safe  to  say  that  any  clerk  working  at  a  new task  where  quantities  or  dimensions  of  a  substance  were  involved would  have  to  brush  up  his  knowledge  of  compound  numbers and  tables,  or  proceed  with  extreme  slowness  and  caution),  but  in its  application  there  is  a  most  important  gain  of  time.  The result  is  that  more  business  can  be  transacted  with  a  smaller office  force,  and  that  the  activity  of  clerks  and  computers  can  be turned  in  other  directions. The  disadvantages  attending  the  introduction  of  the  metric system  will  be  entirely  of  a  temporary  character,  and  if  we  may take  the  experience  of  Germany  as  a  guide,  will  prove  far  less than  is  feared  by  the  timid.  The  time  lost  by  making  trans- formation from  the  old  into  the  new  weights  and  measures  will in  reality  prove  much  less  than  is  anticipated,  as  such  operations doubtless  will  be  performed  with  the  aid  of  tables,  such  as  will be  found  in  the  appendix,  which  not  only  the  government  but every  industry  doubtless  will  prepare  to  facilitate  such  work, while  for  new  calculations  employing  metric  weights  and  measures throughout  there  will  be  a  great  saving. The  difficulty  of  minds  learning  to  think  in  a  new  system  of weights  and  measures  is  not  so  easily  disposed  of,  but  we  have seen  how  convenient  and  easily  applied  are  some  of  the  approxi- mations, and  we  have  only  for  most  purposes  to  consider  a  yard equal  to  ^  of  a  meter,  two  pounds  equal  to  *9  kilogram,  a  liter  a quart,  a  long  ton  equivalent  to  a  metric  ton,  etc.  The  relation between  volume  and  capacity  should  be  appreciated  greatly  in commercial  work,  as  the  capacity  of  a  tank,  reservoir,  bin,  or  car in  appropriate  units  can  readily  be  computed  from  its  dimensions, and  then,  knowing  the  specific  gravity,  by  simple  multiplication the  weight  of  its  contents  can  be  ascertained. With  all  the  inconveniences  of  the  Anglo-Saxon  systems  of weights  and  measures  we  are  forced  to  consider  a  still  more serious  difficulty,  namely  the  growth  of  a  dual  system  due  to  the THE   METRIC   SYSTEM   FOR   COMMERCE        171 increased  use  of  the  metric  system  as  permitted  by  statute.  It cannot  be  denied  that  the  metric  system  has  made  great  progress, and  that  by  the  close  connection  of  science  with  industry  that  it is  destined  to  be  even  more  widely  employed.  Both  systems being  legal,  and  the  metric  measures  coming  into  more  wide spread  use,  there  would  result  the  perpetual  necessity  of  con- verting from  one  to  the  other  in  commercial  transactions,  and while  the  nation  was  waiting  for  the  ultimate  survival  of  the fittest  system,  or  the  birth  of  an  ideal  scheme,  incalculable inconvenience  and  damage  would  ensue,  as  has  been  shown  many times  in  the  past  where  a  nation  at  other  times  than  at  a transition  period  has  employed  a  double  standard. CHAPTEK  VII. THE  METRIC  SYSTEM  IN  MANUFACTURING  AND ENGINEERING. The  application  of  the  metric  system  to  manufacturing  and mechanical  and  other  forms  of  constructive  engineering,  where there  has  been  long  use  of  units  of  other  systems,  presents  con- fessedly the  most  serious  aspect  of  the  question  of  adopting  the international  weights  and  measures.  These  branches  of  human activity,  it  must  be  remembered,  had  their  beginnings  in  most humble  and  commonplace  sources,  such  as  the  village  smith,  the local  carpenter,  or  even  the  aboriginal  savage  with  his  primitive loom.  In  this  respect  they  differ  from  electrical  and  civil engineering,  and  applied  chemistry,  where  the  applications  of science  and  discovery  have  resulted  in  vast  industries  and important  technical  professions.  From  their  very  inception  these latter  have  been  dependent  on  the  work  of  scientific  men,  using the  term  broadly,  and  it  has  been  possible  to  use  such  units  and measurements  as  they  have  recommended.  That  these  units can  be  developed  rationally  and  systematically,  as  well  as  with extreme  simplicity  we  can  see  from  the  electrical  units  which will  be  discussed  in  a  subsequent  chapter.  But  in  mechanical engineering  and  manufacturing  simple  processes  and  methods have  gradually  been  developed  by  the  aid  of  scientific  men, and  by  applying  their  discoveries  to  every- day  work,  con- sequently the  engineers  have  been  forced  to  use  the  units and  measures  of  the  people  rather  than  to  develop  and rationalize  such  systems  as  would  best  commend  themselves  to their  judgment. THE   METRIC   SYSTEM   IN   MANUFACTURING     173 Improved  methods  of  manufacturing,  however,  have  brought about  machinery  and  processes  marked  by  simplicity  and efficiency,  and  while  the  advantages  that  will  ensue  ultimately from  the  adoption  of  international  weights  and  measures  will more  than  compensate  for  any  temporary  inconvenience,  never- theless, it  must  be  admitted  that  the  transition  will  involve  some serious  problems  and  expense.  Inasmuch  as  comparatively  few manufacturing  processes,  or  at  least  individual  plants,  remain stationary,  but  are  constantly  undergoing  improvements  either  of method  or  machinery,  the  possibility  of  adjustment  to  new conditions,  such  as  a  new  system  of  weights  and  measures,  is  not so  difficult  as  might  at  first  be  imagined.  Oftentimes  changes  of styles  or  classes  of  product  are  made  that  are  far  more  funda- mental than  any  changes  that  would  be  involved  by  new measures,  and  natural  wear  and  tear  to  machinery  require constant  renewals  and  substitutions  at  intervals,  and  in  many shops  it  is  considered  good  economy  to  strive  for  a  maximum output  at  the  expense  of  individual  machines  and  tools.  Further- more, conformation  to  standards,  so  necessary  for  successful manufacturing,  does  not  involve  the  blind  adherence  to  such standards,  however  honored  and  however  universally  observed, after  better  standards  have  been  evolved.  That  such  a  change  in units  or  standards  can  readily  be  made  we  know  from  numerous instances  in  the  past  where  various  gauges,  screw  threads,  screws, etc.,  have  been  changed  without  undue  confusion  and  expense.  A notable  instance,  inasmuch  as  the  change  was  radical  and  funda- mental, was  made  by  the  printers  of  the  United  States  in  1883, when  the  nomenclature  of  the  different  sizes  of  type  was  changed, and  a  system  of  measuring  by  points  adopted  to  take  the  place  of names  in  use  for  years.  In  fact,  the  adoption  of  various  screw threads  in  different  countries,  either  in  the  interest  of  standard- ization or  to  obtain  a  better  screw,  and  even  their  modification, has  worked  no  great  hardship,  and  such  changes  in  car  coupling and  other  devices  recommended  from  time  to  time  in  the  United States  by  the  Master  Car  Builders'  Association,  involving  as  they often  do  marked  departures  from  sizes  or  styles  in  use  by different  railroads,  seem  to  be  made  speedily  and  effectively,  and without  such  expense  as  would  occasion  objection  from  controlling officials. 174     EVOLUTION   OF   WEIGHTS   AND   MEASURES Numerous  instances  where  changes  of  systems  and  standards dealing  with  actual  concrete  things  may  be  cited  to  show  how readily  changes  in  manufacturing  and  mechanical  engineering have  been  brought  about,  proving  that  it  is  not  only  under  ideal conditions,  such  as  the  change  from  local  to  standard  time,  or in  an  improved  calendar,  that  scientific  reforms  can  be  effected. Once  the  people  concerned  are  convinced  of  the  need  of  the change  and  the  superiority  of  a  new  system,  history  shows  that the  change  can  be  made  effectively  and  expeditiously,  so  that  at present  it  remains  for  the  adherents  of  the  metric  system  to convince  the  manufacturing  public  by  demonstrating  its  superiority for  their  work,  and  to  show  how  it  may  be  adopted  with  the smallest  amount  of  inconvenience.  Possibly  this  will  best  be understood  by  considering  briefly  the  relation  of  weights  and measures  to  manufacturing  and  constructive  engineering.  If  a single  piece  of  machinery  or  a  single  fabric  is  to  be  produced, it  is  of  little  moment  what  units  of  weight  and  measures  are employed  by  the  designer,  and  what  are  used  by  the  maker, provided  that  both  can  understand  each  other,  and  provided  that time  and  expense  are  subordinate.  That  this  is  true  is  shown  by the  ease  with  which  American  and  English  workmen  can  and  do work  from  continental  designs  prepared  according  to  the  metric measures  and  vice  versa  on  special  orders.  But  when  thousands of  the  manufactured  article  are  required,  and  time  and  economy must  be  considered,  or  in  other  words,  when  the  commercial conditions  of  successful  manufacturing  have  to  be  met,  then  the influence  of  weights  and  measures  as  reflected  in  standards, processes,  and  in  numerous  more  or  less  direct  ways,  is  felt. We  may  start  with  the  raw  material,  which  may  be  in  bulk  as in  the  case  of  ore,  pig  iron,  crude  chemicals,  baled  cotton  or  wool, logs,  etc.,  to  cite  but  a  few  examples,  or  we  may  consider  as  raw material,  wire,  sheet  metal,  structural  shapes  from  the  rolling  mill, yarn,  boards,  and  other  sawed  or  milled  timber,  to  mention  some  of the  innumerable  articles  that  enter  into  manufacturing  processes. In  the  case  of  the  former  class  we  have  to  consider  the  same principles  discussed  in  the  last  chapter,  as  the  purchase  of  the materials  would  be  greatly  simplified  by  having  all  invoices  and calculations  of  prices  made  in  the  metric  system,  consequently there    would    be   a   saving   of   time   to   the   office.     The   actual THE   METRIC   SYSTEM   IN   MANUFACTURING     175 weighing  would  be  the  same  under  any  system,  though  easier with  metric  weights,  but  for  the  computations  involved  in  mixing or  otherwise  treating  raw  materials  there  would  be  a  great  saving effected  by  using  the  metric  system,  as  it  would  avoid  the employment  of  different  classes  of  units,  and  would  be  throughout on  a  strictly  decimal  basis.  However  in  this  no  particularly serious  questions  arise,  but  with  the  other  class  of  raw  materials used  in  manufacturing,  experience  has  shown  and  convenience enforces  the  demand  that  they  must  be  supplied  of  certain dimensions  which  must  be  of  sufficient  variety  to  fill  all  reason- able needs,  prepared  according  to  certain  standards,  and  packed  in certain  quantities.  The  dimensions  or  weights  are  taken,  of course,  in  conventional  units,  and  the  law  of  supply  and  demand, modified  by  co-operative  action  and  trade  customs  among  manu- facturers, consumers,  and  dealers,  has  resulted  in  the  establishment of  certain  standard  sizes  which  not  only  are  regularly  carried  in stock,  but  for  which  have  been  calculated  many  tables  dealing with  their  weight,  strength,  elasticity,  resistance,  and  other characteristics  useful  to  designer  and  maker  alike.  As  a  result the  majority  of  articles  used  in  manufacturing  and  construction are  made  only  in  standard  sizes,  for  making  which  special machinery  has  been  prepared  and  adjusted,  while  articles  of  other dimensions  must  be  specially  made  at  considerably  greater expense. This  policy  of  making  articles  in  standard  sizes  has  been productive  of  the  highest  benefit  to  the  manufacturer,  and the  specialization  that  has  been  brought  about  in  American works  and  factories  has  contributed  in  no  small  degree  to  the position  in  manufacturing  that  the  United  States  now  occupies among  the  nations  of  the  world.  This  system  of  standardiza- tion is  also  advantageous  to  the  consumer,  who  in  turn may  be  just  as  important  a  manufacturer,  only  turning  out  a more  finished  or  more  complex  article.  Let  us  see  how  the metric  system  would  apply  here.  First,  let  us  take  the  purely arbitrary  standards  which  have  no  even  dimensions.  For example,  flour  is  manufactured  and  usually  sold  196  pounds  net to  the  barrel,  yet  there  is  no  particular  reason  for  this  quantity, since  flour  sold  in  sacks  for  export,  where  it  may  be  stowed  the more  readily  in  a  vessel's  hold,  usually  is  packed  140  pounds  to 176     EVOLUTION   OF   WEIGHTS   AND   MEASURES a  sack.  Now,  if  there  was  any  reason  for  preserving  these particular  quantities  they  could  be  used  in  metric  weights  just  as readily  as  at  present,  but  appreciate  the  convenience  if  barrels  of 100  kilograms  and  sacks  of  exactly  half  that  amount  were employed.  True,  the  miller  would  have  to  adjust  his  automatic scales  for  weighing  his  flour,  but  the  product  would  be  turned  out in  even  quantities,  and  the  weight  of  carload  or  cargo  would  be  told at  a  glance  from  the  number  of  barrels  or  sacks.  Every  trans- action from  the  time  that  the  flour  left  the  mill  until  it  was  divided by  the  retail  grocer  into  10  kilogram  lots  would  be  facilitated. Then  let  us  consider  wire  and  sheet  metals  for  which  there have  been  a  number  of  gauges.  These,  for  the  most  part,  have been  and  are,  not  only  arbitrary  but  irregular  and  inconsistent,  and have  stated  the  thickness  in  decimal  fractions  of  inches,  some  of which  are  expressed  to  the  fifth  or  sixth  place.  If  these  numbers are  to  be  retained  it  is  certainly  just  as  easy  to  express  the thicknesses  in  fractions  of  a  millimeter  as^  of  an  inch,  and  in  fact this  was  officially  done  in  the  Act  of  March  3,  1893,  when  a standard  gauge  for  sheet  and  plate  iron  and  steel  was  established by  Congress  l  in  which  the  numbers  were  defined  by  equivalent values  in  inches  and  millimeters.  Consequently,  under  the existing  legal  gauge,  the  adoption  of  the  metric  system  would cause  no  difference  whatever  in  the  making  of  sheet  iron  and steel,  and  the  customer  would  find  the  same  legal  sizes  under  the metric  system  as  before.  While  no  wire  gauge  has  been  legalized, yet,  if  any  of  the  standard  gauges  is  to  be  used,  it  is  quite  as easy  to  consider  the  metric  as  the  inch  values  since  the  decimal fractions  are  no  greater.  The  gauge  system  at  best  is  bad  in  its general  aspect  as  it  always  requires  an  act  of  memory,  and  in practice  so  inexact  and  unsatisfactory  that  certain  large  consumers in  the  United  States,  notably  the  Great  Electric  Companies, have  instructed  their  draughting  rooms  and  purchasing  depart- ments to  always  specify  by  actual  dimensions  in  thousandths of  an  inch  expressed  decimally.  But  so  long  as  gauges  are generally  used,  it  is  necessary  to  consider  just  what  they signify  and  what  part  they  play  in  mechanical  operations. Formed  as  they  are  of  plates  of  sheet  steel  or  other  metal,  with holes  or  openings  with  which  to  test  the  various  samples  of 1C.  221,  Sec.  1,  27  Stat.,  746,  K.S.  3570. THE   METRIC   SYSTEM   IN   MANUFACTURING     177 materials,  they  are  in  practice  often  at  the  outset  very  inexact  in their  graduations,  and  in  any  event  they  sooner  or  later  become so  by  the  wear  of  constant  use.  As  regards  their  graduation  and division  the  various  standard  gauges  differ  widely  from  one another,  and  in  individual  cases,  as  has  been  said,  they  are  hardly ■ever  arranged  systematically  or  methodically.  This  can  readily be  appreciated  by  examining  the  tables  in  almost  any  standard engineer's  reference  or  so-called  pocket  book,  but  a  hint  can  be given  by  the  following  list,  which  shows  the  dimensions  in decimal  parts  of  an  inch  for  the  same  number  (No.  2)  of  the various  gauges  that  are  all  in  use  in  the  United  States. Dimensions  of  No.  2  gauge  according  to  different  standards : Inch. American  or  Brown  &  Sharpe,  -  '25763 Birmingham  or  Stubs'  Wire,  -  '284 Washburn  &  Moen  M'fg  Co.,  Worcester,  Mass.,  -  '2625 Imperial  Wire  Gauge,  -  -  -  -  '276 Stubs'  Steel  Wire,  " '219 U.S.  Standard  for  Plate,  ...  -  -265625 Twist  Drill  and  Steel  Wire  Gauge,  -  -  -  '221 Screw  Gauge  for  Machine  and  Wood  Screws,      -  '08416 Thus  it  will  be  seen  that  material  made  according  to  any  of  the •above  gauges  is  not  suitable  to  be  used  with  that  made  by another  gauge,  as  for  example  there  is  no  correspondence  between the  gauge  sizes  of  wire  and  th.€  twist  drill  which  would  make  the hole  in  which  the  wire  might  be  inserted,  or  the  size  of  the  wire and  the  wood  or  machine  screw  into  which  it  might  be  made. Consequently  the  present  tendency  is  to  abandon  all  arbitrary gauges  and  work  to  decimal  parts  of  an  inch  requiring  all materials  to  be  furnished  of  such  dimensions,  a  condition  which can  be  easily  determined  with  great  exactness  by  a  micrometer caliper  of  low  cost.  Now,  the  use  of  decimals  presents  no inconvenience  whatsoever  to  the  average  mechanic,  so  that  at  such a  transition  period  as  regards  standard  sizes  of  materials,  there  is every  reason  for  adopting  the  metric  system  rather  than  waiting until  further  standardization  on  an  inch  basis  shall  have  occurred. Instead  of  arbitrary  gauge  numbers  millimeters  and  decimal fractions  could  be  employed,  and  there  would  be  the  advantage  of having   a  larger    number  of  integral   numbers   and  division  by M 178     EVOLUTION   OF  WEIGHTS   AND   MEASURES tenths  and  hundredths,  amply  sufficing  for  all  ordinary  mechanical work.  The  workmen,  in  their  measurements,  would  employ  the same  form  of  micrometer,  the  reading  of  which  would  be  even more  simple,  and  much  greater  interchangeability  would  result as  soon  as  materials  were  furnished  in  a  smaller  number,  but standard  sizes. The  tendency  would  be  towards  a  more  exact  arrangement  on a  metric  basis.  Such  a  movement  would  be  gradual,  and  there would  be  few  occasions  where  any  difficulty  would  be  experienced. Metric  wire  gauges  were  introduced  in  France  in  1894,  and  have proved  satisfactory,  their  use  increasing  very  rapidly.  In  fact,  in much  work  done  with  such  materials,  as  sheet  metal  and  wire,  as well  as  with  other  material,  it  is  rarely  necessary  to  look  for  the strictest  exactness  in  conforming  to  a  certain  gauge  as  the  purpose can  be  satisfied  by  an  approximation,  and  the  customary  method of  payment  being  made  on  a  basis  of  weight  prevents  any imposition  or  injustice.  As,  however,  new  dies  or  rolls  were required,  these  would  be  carefully  adjusted  to  metric  gauge,  and the  older  sizes  would  gradually  become  obsolete,  unless  there arose  some  special  demand,  while  in  the  case  of  sheet  metal  it would  only  be  necessary  to  have  a  new  setting  of  the  rolls.  It  is impossible  to  conceive  of  any  injury  being  done  the  manufacturer, for  at  the  worst  he  has  only  to  provide  himself  with  a  few  new adjuncts  to  his  larger  tools  and  a  limited  number  of  smaller  tools,, which  are  constantly  being  replaced. Then  take  the  case  of  the  lumber  mill,  where  planks,  boards, joists,  etc.,  are  turned  out  on  an  inch  basis.  How  near  do  these dimensions  correspond  in  reality  with  the  sizes  they  are  sold  for  ? In  fact,  in  many  instances  planed  boards  of  a  certain  dimension do  not  gauge  that  dimension  at  all,  but  represent  what  remains- after  a  board  sawed  approximately  to  that  thickness  has  been planed.  The  carpenter  and  the  cabinetmaker  do  not  demand  so high  a  degree  of  precision  from  the  lumber  dealer  that  the  *4  of  a millimeter,  between  25  millimeters  and  an  inch  (25*4  mm.)  cannot be  disregarded,  and  here  again  it  is  found  that  most  standard sizes  of  lumber  can  be  readily  described  in  metric  measures- without  the  use  of  decimal  fractions,  and  no  new  machinery will  be  required  except  as  new  styles  or  sizes  are  demanded. In   actual   manufacturing,   after   the   adoption   of    the    metric THE   METRIC   SYSTEM   IN   MANUFACTURING     179 system,  the  first  step  would  be  the  provision  of  facilities  for making  various  articles,  such  as  sheet  metal,  paper,  wire,  cloth, etc.,  according  to  metric  dimensions.  This  would  be  to  meet  the requirements  of  the  government  and  other  consumers,  who desired  goods  according  to  metric  specifications.  In  other  words, the  same  process  would  be  gone  through  with  as  occurs  when  a large  new  or  special  order  is  received.  As  these  orders  would  be in  metric  sizes,  and  conformable  approximately  to  those  that experience  had  taught  were  most  serviceable  for  the  particular use  for  which  they  were  designed,  they  would  gradually  become standards,  and  would  supplant  the  older  sizes.  In  many  cases where  materials  are  sold  by  weight,  as  paper  and  wire,  the  effect of  a  change  of  dimensions  would  have  no  effect  on  the  price, while  a  minute  change  sufficient  to  adapt  the  material  to  a regular  metric  dimension  would  in  no  way  affect  its  usefulness  to the  consumer,  and  should  there  be  a  slight  increase  in  some instances  it  would  be  balanced  by  a  slight  decrease  in  others. Indeed,  in  many  instances  only  the  trimming  or  finishing  would be  involved,  and  here  it  is  probable  that  the  waste  material  would just  as  likely  be  less  than  the  amount  produced  in  making  the present  sizes  as  it  would  be  greater,  and  at  any  rate  it  could doubtless  be  worked  or  utilized  in  some  way,  the  difficulties  can hardly  be  called  serious. Linear  measures  and  standards  play  a  prominent  part  in  all mechanical  operations,  and  here  the  superiority  of  the  metric system  and  its  ready  applicability  may  be  shown.  It  has  been the  practice  to  measure  by  successively  halving  the  unit,  and  in the  case  of  the  inch  this  has  brought  us  down  to  such  fractions  as ^  and  -^g,  which  are  awkward  both  for  computation  and observation  on  a  scale.  While  it  is  quite  natural  to  halve  or quarter  a  unit,  yet  to  pursue  this  policy  of  binary  subdivision  too far  is  extremely  inconvenient.  With  the  metric  system  in  linear as  in  other  measurements  it  is  possible  to  make  use  of  any decimal  multiple  or  submultiple  of  the  meter  from  the  micron  to the  myriameter  as  the  base,  according  to  the  nature  of  the measurement  involved,  and  it  is  quite  possible  to  use  the  half  of it  simply  by  writing  "5,  or  the  quarter  by  writing  *25,  both expressions  requiring  no  more  figures  than  the  corresponding common  fractions,  and  involving  no  difficulty  in  case  it  is  desired 180     EVOLUTION   OF  WEIGHTS   AND   MEASURES to  transpose  to  a  higher  or  lower  unit.  Now,  it  has  been  found better  in  actual  experience  when  other  fractions  than  a  half  or quarter  are  desired,  to  divide  decimally,  and  where  accurate  work is  demanded  it  has  become  the  almost  universal  custom  in  the United  States  among  engineers  and  machinists  to  work  in hundredths  and  thousandths  of  inches,  the  practice  being  followed from  draughting  room  to  shop.  This  practice  involves  the  ex- pression of  all  quantities  in  terms  of  a  single  unit,  such  as  feet, inches,  or  pounds,  with  the  appropriate  decimal  fraction,  and demonstrates  the  availability  of  the  decimal  system  for  such practical  work,  as  well  as  for  mere  computation.  This  practice  is rapidly  on  the  increase,  due  largely  to  the  use  of  calipers  and gauges  thus  divided,  so  that  the  matter  of  decimal  fractions presents  no  disadvantage,  but  rather  a  convenience,  to  the workman  who  has  to  make  measurements. As  regards  the  linear  units  themselves ;  if  the  workman employs  millimeters  he  has  a  unit  which  is  a  whole  number,  and is  superior  to  ^,  as  the  latter  is  too  large,  and  represents  coarse measurement  and  work.  On  the  other  hand  ^  is  too  fine  a division  for  an  ordinary  scale,  especially  for  a  draughtsman,  and is  only  useful  on  a  steel  scale,  with  which  few  mechanics  are equipped,  consequently  the  centimeter  and  millimeter  are  quite  as convenient  as  the  inch,  while  the  foot,  which  is  rarely  used  in modern  mechanical  engineering,  is  in  no  way  missed.  Even  if  we consider  the  inch  as  the  principal  unit  we  are  forced  to  use,  either its  sixteenth  part,  or  its  tenth,  hundredth,  or  thousandth,  and  in reality  we  make  such  a  fractional  part  our  standard  unit,  and  we have  the  odd  relation  between  such  units  and  the  greater  ones, the  inch,  and  the  foot,  as  compared  with  the  simple  decimal relation  of  the  metric  linear  measures.  The  yard  and  the  meter wherever  desired  are  units  of  the  same  class,  and  what  can  be done  with  one  is  equally  possible  with  the  other,  not  to  mention, of  course,  the  advantage  of  the  decimal  relation  of  the  meter  to its  sub-multiples.  But  the  great  gain  is  that  all  calculations  are made  in  the  same  unit  as  the  original  measurement,  and  no reductions,  save  the  transfer  of  a  decimal  point,  are  ever necessary.  Contrast  this  with  the  English  system  where measurements  made  in  inches  must  be  changed  to  feet  or  yards for  use  with  tables  or  vice  versa. THE   METRIC   SYSTEM   IN   MANUFACTURING     181 But  in  most  manufacturing  there  is  comparatively  little  or  no measuring  for  the  workman  to  do,  inasmuch  as  he  is  required merely  to  make  his  work  according  to  gauges,  or  templates, or  jigs,  which  are  supplied  to  him  by  the  tool  room,  where they  have  been  carefully  worked  out  from  the  specifications of  the  draughting  room.  Holes  are  bored  and  reamed  to  a certain  gauge,  drills  are  set  so  that  several  will  come  down  on the  piece  of  work  at  places  previously  determined  by  the  jig,  and planers,  shapers,  milling  machines,  etc.,  are  all  operated  in  the same  way.  But  there  must  be  some  consideration  of  standards and  units  in  the  draughting  room  and  tool  room,  is  the  suggestion immediately  made,  and  here  possibly  would  be  one  of  the  points where  difficulty  might  be  encountered.  It  has  been  shown  in actual  experience  that  the  work  of  the  draughtsman  in  preparing plans  according  to  metric  measures  is  not  only  no  harder,  but  is facilitated  considerably  in  actual  drawing,  and  immeasurably  so if  there  are  computations  to  be  made.  Now,  in  the  construction of  gauges  and  tools  the  highest  intelligence  of  the  mechanical force  is  employed,  and  here  there  are  men  not  only  having  a knowledge  of  current  sizes  and  standards,  but  perfectly  capable  of working  in  any  kind  of  measures.  In  fact,  the  dimensions  of many  gauges  are  merely  nominal,  and  there  is  a  greater  or  less deviation  from  the  stated  dimensions,  but  which  concern  neither draughtsman  nor  workman  if  all  tools  and  gauges  are  harmonized as  they  must  be  to  these  dimensions  throughout  the  work.  This, of  course,  involves  the  use  of  micrometers  and  other  adjuncts  to fine  measuring,  and  this  class  of  work  can  be  done  with  greater facility  in  the  metric  system,  as  is  shown  by  its  adoption  by makers  of  instruments  of  precision,  opticians,  and  watchmakers universally.1  If  tools  and  gauges  in  the  factory  are  to  remain  as before  the  introduction  of  the  metric  measures,  as  they  can  be 1  The  Swiss  watchmakers  were  the  first  to  employ  a  metric  thread  for  small screws,  and  the  basis  of  the  system  was  to  start  with  a  pitch  or  distance  between threads  of  one  millimeter,  and  to  decrease  the  pitch  of  each  succeeding  size  by ten  per  cent.  In  1869  not  only  were  metric  threads  adopted  by  the  American Watch  Company  for  watches,  but  also  throughout  their  factory,  and  all  their watchmaking  machinery  has  been  constructed  on  that  basis.  In  Great  Britain  a Committee  of  the  British  Association  for  the  Advancement  of  Science  appointed to  determine  a  gauge  for  small  screws  used  in  telegraph  and  electrical  apparatus reported  in  favor  of  the  Swiss  series  of  small  screws,  and  the  same  was  adopted. 182     EVOLUTION   OF   WEIGHTS   AND   MEASURES without  the  slightest  inconvenience,  it  is  only  necessary  to designate  them  by  their  metric  values  for  purpose  of  computation, and  to  continue  employing  them  with  their  various  shop  numbers as  before.  Where  new  standards  and  gauges  are  to  be  con- structed, as  they  must  be  from  time  to  time,  then  it  would  prove desirable  to  use  the  metric  measures,  and  the  tendency  will  be  to work  toward  even  dimensions  and  universal  standards.  Such  a tendency  will  be  general,  and  if  the  manufacturer  need  tools, which  he  must  buy,  he  will  soon  find  that  the  new  ones  carefully standardized  will  be  forthcoming  in  metric  sizes,  wherever  any changes  are  made  from  existing  patterns  and  numbers.  To  such a  degree  of  exactness  is  this  work  now  carried  on  in  well- organized  American  shops,  that  the  highly  skilled  man  in  charge of  the  tools  will  find  little  trouble  in  adopting  the  metric dimensions. Making  the  supposition  now  that  a  machine  shop  or  factory  is required  to  work  to  actual  correct  dimensions  in  the  metric system,  which,  of  course,  is  not  contemplated  by  any  movement for  the  introduction  of  the  new  system,  it  does  not  mean  that  a new  equipment  of  tools  must  be  procured.  None  of  the  larger tools  would  be  changed,  as  even  in  the  case  of  the  lathes  a  single gear  wheel  connected  to  the  lead  screw  enables  metric  threads  to be  cut  on  an  ordinary  lathe  with  an  inch  lead  screw  and  vice versa,  while  the  only  important  changes  would  be  such  small tools  as  drills,  reamers,  taps,  dies,  etc.,  where  in  certain  dimensions a  new  size  might  be  demanded,  and  these,  if  not  already  made and  in  stock,  as  are  gear  cutters  for  cutting  metric  pitches  x  at the  present  time  in  the  United  States  and  England,  would  soon be  provided  by  tool  makers. In  this  connection  the  cutting  of  screws  may  be  discussed more  at  length,  as  it  is  one  of  the  principal  undertakings  in  a machine  shop,  and  involves  the  greatest  care  in  order  to  secure high  precision  and  interchangeability.  Screw  threads  originally are  made  upon  a  lathe  where  a  cutting  tool  is  given  a  lateral motion  by  means  of  a  screw  known  as  a  lead  screw  which revolves  in  a  nut  attached  to  the  tool  carriage,  and  thus  gives  a lateral  motion  to  the  tool.  The  object  on  which  the  screw  is being   cut  is  also  revolved,  and   the  proper  ratio  of  revolution 1  Bevel  gears  can  be  cut  to  metric  pitch  with  the  usual  tools. THE   METRIC   SYSTEM   IN   MANUFACTURING     183 between  the  two  is  maintained  by  suitable  gearing.  In  the United  States  and  England  lathes  are  usually  designed  to  work on  an  inch  basis,  and  consequently  the  lead  screw  is  so  divided and  the  corresponding  gears  furnished.  But,  by  the  use  of  one change  wheel  with  127  teeth1  it  is  possible  to  arrange  a  lathe  so that  with  a  lead  screw  divided  on  an  inch  basis  metric  threads may  be  cut  with  an  error  that  can  only  be  detected  by  the  most refined  methods,  if  at  all,  and  such  screws  are  entirely  suitable for  all  ordinary  use,  being  correct  to  one  part  in  6350.  By  such means  are  made  the  taps  of  hard  steel  with  which  holes  are threaded,  and  the  dies  that  are  used  for  the  more  rapid  cutting of  threads  on  a  large  scale  in  the  actual  manufacture  of  screws in  quantities. While  the  adoption  of  the  metric  system  does  not  necessarily involve  the  doing  away  with  the  present  systems  of  screw  threads in  the  United  States  and  England,  which,  however,  are  purely arbitrary,  and  could  be  measured  in  millimeters  with  equal facility,  yet  there  is  a  metric  thread  which  was  approved  at  a congress  of  engineering  societies  held  at  Zurich  in  October,  1898, and  again  at  an  international  conference  held  in  October,  1900,  at Paris,  delegates  being  present  from  all  the  important  metric nations  of  the  Continent,  including  France,  Germany,  Switzerland, and  Italy.  This  form  of  thread  was  evolved  by  the  Socidte* d'Encouragement  pour  lTndustrie  Rationale  of  France,  having  been devised  by  M.  Ed.  Sauvage,  and  used  for  a  number  of  years  on the  French  railways  previous  to  its  adoption  by  the  society. With  slight  modifications  it  was  adopted  as  an  international standard  for  shape  of  thread  and  pitch,  and  is  now  known  as  the Systeme  International,  abbreviated  to  S.I.  or  S.J.  The  shape  of this  thread  is  practically  the  same  as  that  of  the  U.S.  standard adopted  by  the  U.S.  Navy  Department  in  1868,  and  also  known as  the  Franklin  Institute  or  Sellers  Standard,  from  the  name  of its  inventor,  William  Sellers.  The  thread  of  the  bolt  or  screw consists  in  cross  section  of  an  equilateral  triangle,  giving  an  angle of  60  degrees  as  compared  with  55  degrees  in  the  Whitworth (British)  standard,  and  the  edges  and  bottom  of  the  thread  are flattened  by  an  amount  equal  to  -^  the  height.  A  modification and  improvement   over  the   Sellers  thread,  as  well  as  over  the 1  This  represents  five  times  the  ratio  of  the  inch  to  the  millimeter. 184     EVOLUTION   OF   WEIGHTS   AND   MEASURES Whitworth  thread,  consists  in  allowing  for  clearance  between  the base  of  a  nut  thread  and  the  top  of  a  bolt  thread,  though  in American  machine  shop  practice  it  has  been  usual  so  to  make Common  Sizes  of  Screw  Threads. Whitworth. S.I. (Inches.) Diam. (mm.) Diam. Diam. Thds.  per  inch. Increment. Diam. Pitch. Increment. i 20 i 6 1 2 f 16 i 8 1-25 2 i 12 1 10 1-5 2 1 11 i 12 1-75 4 J 10 i 16 2' 4 i 9 i 20 2*5 4. i 8 i 24 3* 6 i* 7 1 4 30 3'5 6 H 7 i 36 4- 6 i* 6 i 42 4*5 6 .  it 5 i 48 5 8 2 *J i 56 5-5 8 n 4 i 2 64 6 8 n 4 i 72 6-5 8 2f H 80 7' 3 H the  thread  that  there  is  such  a  clearance,  the  sides  of  the  thread and  nut  receiving  the  fit.  In  the  S.I.  thread  this  clearance  amounts to  -^  of  the  thread  in  the  form  of  a  circular  fillet  tangent  to  the thread's  side,  while  the  thread  itself  has  a  flat  top.     The  pitches THE   METRIC   SYSTEM   IN   MANUFACTURING     185 or  distances  between  the  threads  increase  regularly  by  a  half millimeter,  with  a  "25  millimeter  interval  in  some  cases,  as between  1  and  2  millimeters.  The  rate  of  increase  is  much  more regular  and  simpler  than  in  the  case  of  the  United  States standard  thread,  where  in  many  places  awkward  fractions  are introduced.  The  pitch  of  the  latter  is  finer,  thus  making  a  bolt constructed  on  the  Systeme  International  a  trifle  weaker,  but  the difference  is  not  serious,  and  no  disastrous  effects  have  been experienced  in  actual  use.  The  underlying  symmetry  and  the regularity  are,  however,  features  of  great  value,  and  the  system  at the  time  of  its  adoption  was  thought  worthy  of  widespread  use, even  to  supplant  the  Whitworth  thread,  which  despite  its  English basis  has  been  in  wide  use  for  years  even  in  metric  countries.1 In  watchmaking  the  metric  thread  is  employed  universally,  the Swiss  system  being  taken  as  the  standard ;  while  for  small machine  screws  used  in  electrical  and  other  apparatus  there  is the  B.A.  (British  Association)  standard,  which  is  also  metric The  latter  thread  was  devised  by  a  committee  of  distinguished electricians  and  experimental  physicists,  and  since  its  adoption the  regularity  and  symmetry  of  its  divisions  have  been  thoroughly appreciated. The  change  to  the  Sellers  thread  in  the  United  States  was made  without  any  paralysis  of  manufacturing  industries  or serious  injury  to  machine  work,  and  the  same  was  true  when  the railroads  adopted  a  standard  screw  thread  and  gauge  on  the recommendation  of  a  committee  of  the  Master  Car  Builders' Association,  which  reported  in  1882.  This  report2  shows  the advantages  to  be  gained  by  adopting  and  adhering  to  one  system, and  outlines  the  problem  that  was  solved  by  the  late  Professor William  A.  Eogers  and  the  Pratt  and  Whitney  Company  in preparing  suitable  standards  for  adoption  by  all  railroads.  This change  was  made  in  the  course  of  a  few  years  without  undue difficulty  or  expense,  and  since  has  been  found  amply  justified, illustrating  most  strikingly  the  advantages  of  a  common  standard in  a  single  industry. 1  Henry  Hess,  "The  S.J.  Standard  Metric  Thread  in  Continental  Europe," American  Machinist,  p.  422,  vol.  xxiii.  No.  18,  May  3,  1900. 2M.  N.  Forney,  Chairman,  Railroad  Gazette  (New  York),  July  7,  1882,  vol.  xiv. p.  407. 186     EVOLUTION   OF   WEIGHTS   AND   MEASURES The  adoption  of  the  metric  system,  however,  does  not necessarily  involve  the  changing  of  the  present  excellent  screw system  of  the  United  States,  as  it  is  perfectly  possible  to  get along  with  arbitrary  names  and  gauges  based  on  original standards,  and  well  denned  in  terms  of  metric  as  well  as  the  old measures.  Just  as  "  tenpenny "  nails  are  now  spoken  of,  so screws  could  be  denned  by  number  even  if  they  were  based  on obsolete  linear  measures  and  standards.  On  the  other  hand,  if the  tendency  should  be  towards  a  new  international  gauge  it  will come  gradually,  and  without  undue  inconvenience,  as  similar changes  have  been  made  in  the  past. In  Great  Britain,  where  possibly  the  standardizing  of  screws and  screw  threads  has  not  been  developed  so  highly  as  in  the United  States,  the  situation  has  been  most  excellently  summed  up by  Alexander  Siemens,  the  well-known  electrical  engineer  and manufacturer.  In  his  Presidential  Address  l  before  the  (British) Institution  of  Electrical  Engineers,  delivered  November  10,  1904, he  said : "  As  a  last  resort  the  expense  of  changing  the  screw  threads is  urged  against  the  change  to  the  Metric  System,  and  the Continental  practice  of  calling  their  system  '  Whitworth  thread ' is  considered  an  incontrovertible  proof  that  the  metrical  screw thread  is  impracticable.  If  all  taps  and  dies  and  leading  screws had  to  be  exchanged  at  once,  it  would  certainly  be  a  costly  affair, but  such  a  measure  is  not  likely  to  be  adopted,  as  no  advantage could  result  from  it.  For  the  real  difficulty  with  screw  threads is  that  giving  dimensions  on  paper  is  not  sufficient  to  ensure  that the  screws,  manufactured  according  to  such  instructions  in •different  works,  are  really  interchangeable.  This  subject  has been  investigated  by  a  committee  from  the  War  Office,  and  their conclusions  throw  a  very  interesting  light  on  the  controversy. In  their  opinion  it  is  only  possible  to  obtain  interchangeable ■screws,  if  the  leading  screws  by  which  they  are  made  have  all been  cut  on  the  same  screw-cutting  lathe,  or  are  at  least  cut  on benches  which  are  fitted  with  a  leading  screw  manufactured  on the  same  original  bench.  If  another  link  is  interposed,  differences in  the  screws  turned  out  become  perceptible.  As  a  consequence of  the  finding  of  the  committee  a  screw-cutting  lathe  has  been  set 1  Electrician  (London),  Nov.  11,  1904,  p.  149. THE   METRIC   SYSTEM   IN   MANUFACTURING     187 up  at  the  National  Physical  Laboratory,  where  leading  screws for  screw-cutting  lathes  are  to  be  manufactured.1  The  same experience  has  been  had  in  other  countries,  where  nominally *  Whitworth's  threads '  are  used.  It  is  not  possible  to  make screws  interchangeable  by  prescribing  their  dimensions,  the  only way  is  to  obtain  taps  and  dies  or  leading  spindles  cut  by  the same  tools.  If  it  is  a  case  of  extreme  accuracy,  there  is  no difficulty  in  cutting  English  thread  by  means  of  a  metric  lathe,  or vice  versa." To  appreciate  just  what  would  be  the  immediate  effects  of the  adoption  of  the  metric  system  in  mechanical  engineering  it is  interesting  to  study  the  experience  of  a  large  engine  works and  machine  shop  in  England — Messrs.  Willans  and  Robinson,  of Rugby — which  enjoys  a  reputation  for  extremely  accurate  work together  with  progressive  ideas  associated  with  the  best  engineer- ing practice.  This  firm  employs  in  its  works  the  metric  measures of  length,  and  not  only  are  they  preferred  by  their  draughtsmen and  engineers,  but  also  by  the  workmen  in  the  shops,  who  did not  experience  the  slightest  difficulty  in  accustoming  themselves to  the  new  system  or  to  employing  it  interchangeably  with  the customary  measures.  Inasmuch  as  this  shop  has  been  and  is now  experiencing  some  of  the  conditions  attendant  on  a  transition period  from  the  customary  to  the  metric  measures  its  experiences are  of  interest.  They  employ  bolts  whose  diameter  is  turned  to the  nearest  even  millimeter  larger  than  the  size  of  thread  and  on them  cut  a  thread  of  the  standard  Whitworth  pattern.  One  of their  engineers,  Mr.  Ernest  R.  Briggs,  in  describing  the  use  of  the metric  system  in  the  shop's  work  has  written:2  "I  have  seen  new machines  built  in  the  metric  system  side  by  side  with  existing lines  built  in  the  English  system,  and  I  have  seen  standard parts  of  one  set  of  machines  made  to  work  in  with  standard parts  of  the  other  set,  and  I  have  also  made  and  sent  into  the shops  drawings  in  which  a  single  large  and  complicated  casting has   been  figured  in  each  system.      I  can  make  no  defence  for 1  The  screw  of  this  lathe  is  six  feet  in  length,  and  is  made  of  compressed  steel, the  thread  being  cut  with  such  accuracy  that  it  is  said  to  be  correct  to  rjj^nr  of an  inch  at  60°  Fahrenheit.  The  lathe  is  installed  in  a  constant  temperature room  at  Bushy  House.     [Authors.] 2  Ernest  R.  Briggs,  p.  450,  vol.  xxv.  American  Machinist,  1902;  also  a  second jaaper  by  the  same  author  on  p.  1347  of  the  same  volume. 188     EVOLUTION   OF   WEIGHTS   AND   MEASURES this  latter,  but  it  shows  what  can  be  done  in  working  the  two systems  side  by  side  during  the  transition  period." In  England  there  is  at  present  the  beginning  of  a  lack  of uniformity,  as  during  recent  years  much  improved  machinery  has been  imported  from  the  United  States  and  from  Germany  and Switzerland.  The  former  has  screws  cut  to  the  Sellers  thread, while  in  the  latter  the  S.I.  system  is  being  widely  and  increas- ingly used.  Consequently,  so  long  as  English  engineers  will  go into  the  market  for  the  best  machinery  irrespective  of  its  source, as  is  now  the  tendency  of  the  best  and  most  progressive  manu- facturers, there  is  bound  to  be  an  increasing  lack  of  uniformity  in screws  and  screw-threads. As  to  the  effect  of  the  introduction  of  the  metric  system  into the  manufacture  of  machinery,  we  cannot  do  better  than  conclude by  quoting  from  the  remarks  of  Mr.  S.  M.  Vauclain,  the  superin- tendent of  the  Baldwin  Locomotive  Works  of  Philadelphia,  Pa. Mr.  Vauclain's  testimony  is  not  only  interesting  and  most valuable  from  his  high  reputation  as  a  mechanical  engineer,  but from  the  position  that  his  company  enjoys  in  the  manufacturing world.  Locomotives  from  its  works  have  been  shipped  all  over the  world,  while  the  actual  manufacture  has  been  systematized and  specialized  to  such  an  extent  that  unrivalled  speed  of  con- struction as  well  as  largeness  of  output  has  been  attained.  Mr, Yauclain  says  i1  "So  far  as  the  metric  system  is  concerned  from a  manufacturer's  standpoint,  it  certainly  should  have  no  terrors. Where — in  what  workshop — can  you  find  a  'dozen  men  who  will measure  the  same  piece  of  work  and  find  the  same  result  with the  ordinary  2-foot  rule,  or  such  scales  as  are  ordinarily  provided for  their  use  ?  Could  any  manufacturer  in  America  to-day  rely upon  the  accuracy  of  the  measurement  of  its  employees  in  its products  ?  Instead  of  having  first-class  fits  and  interchange- ability  he  would  have  first-class  misfits  and  ruination  of  his trade."  Eeferring  to  the  vast  amount  of  fitting  involved  at  the Baldwin  Works,  where  there  is  an  output  of  five  locomotives daily  and  a  force  of  workmen  aggregating  11,500,  Mr.  Yauclain goes  on  to  say,  " .  .  .  it  can  readily  be  understood  how  poorly these  locomotives  would  be  fitted  together  if  we  relied  upon  each and  every  one  of  these  11,500  men  to  do  the  measuring  necessary 1S.  M.  Vauclain,  p.  414,  vol.  cliii.  Journal  of  Franklin  Institute,  1902. THE   METRIC   SYSTEM   IN   MANUFACTURING     189 to  fit  these  parts  together  with  the  drawings  furnished  by  the draughtsmen  in  their  hands." Discussing  the  actual  relation  of  the  measures  to  the  work  of designing  and  construction,  he  says :  "  What  is  the  natural proceeding,  then,  in  a  workshop  of  this  kind  ;  you  receive  the drawings  from  the  drawing  room ;  they  are  all  made  to,  we  will say,  the  English  measure — 12  inches  to  the  foot,  3  feet  to the  yard,  or  whatever  you  please — no  matter  how  you  may  see  fit to  speak  of  it ;  but  really  and  truly  these  drawings  are  not  made to  the  ordinary  English  measure:  they  are  made  to  a  scale  which is  adopted,  and  which  represents  12  inches  to  the  foot,  or  3  feet to  the  yard,  or  so  many  sixteenths  inches  to  an  inch.  The  scale that  we  have  adopted  in  our  draughting  room  is  a  scale  of 2  inches  to  the  foot,  and  in  comparing  everything  that  we  look at,  we  do  not  consider  the  foot  at  all :  but  if  it  is  2  inches  long  it is  a  foot  long." "When  a  change  of  this  kind  would  commence  in  any  manu- facturing establishment,  it  would  first  commence  in  the  drawing- room  (because  unless  the  drawings  were  made  in  accordance  with the  metric  system,  the  men  in  the  shop  could  never  work  to  it), and  there  would  be  very  few  gauges  in  use  in  the  shop  that would  have  to  be  changed,  because  the  gauges  do  not  depend upon  the  figured  dimensions  on  the  drawings ;  the  drawings would  all  be  figured  for  the  gauges.  A  certain  gauge  would  be called  for  instead  of  a  certain  dimension.  In  our  works  to-day there  is  not  a  single  hole  drilled  in  a  connecting  rod  where  the straps  are  fitted  oh  the  stub  ends  of  the  rods,  that  is  drilled  to a  dimension  ;  the  drawings  do  not  refer  to  any  dimensions  ;  we have  no  use  for  dimensions,  but  we  have  for  gauges.  They  are marked  to  be  drilled  with  a  certain  gauge  and  a  certain  bushing piece.  You  could  not  use  an  inch  and  a  quarter  drill  in  a  inch and  an  eighth  bushing.  Whatever  bushing  you  use  determines the  size  of  the  drill  you  are  going  to  use ;  and  whatever  gauge you  use  determines  the  distance  apart  the  holes  may  be  and  the number  of  them,  and  the  distance  they  are  from  the  end  to  the stub.  The  workman  goes  ahead  and  drills  regardless  of  the consequences  in  accordance  with  the  gauge  that  is  ordered  on  the drawing ;  and  the  result  is  that  these  parts  are  perfectly  inter- changeable,   and    hundreds    and    thousands    of  these    parts    are 190     EVOLUTION   OF   WEIGHTS   AND   MEASURES duplicated  from  time  to  time  and  shipped  to  almost  every  country on  the  face  of  the  earth,  and  that  without  a  single  dimension either  metric  or  English  on  the  card — simply  the  gauge  number calling  for  that  part.  This  may  be  met  with  the  remark  that those  people  who  do  not  do  their  work  with  gauges  would  not find  it  so  easy  to  change ;  but  that  is  easily  confronted  by  stating that  no  first-class  shop,  or  any  shop,  no  matter  how  small  it might  be,  that  desired  to  enter  into  competition  with  the  world would  ever  do  its  work  in  any  other  way  and  expect  to  succeed; it  would  die  a  natural  death  sooner  from  the  fact  that  it  failed  to use  gauges  or  jigs  for  the  output  of  its  work — even  though  it  had only  one  of  a  kind  to  make — much  sooner  than  it  would  if  it undertook  to  use  the  metric  system."1 1  S.  M.  Vauclain,  p.  417,  vol.  cliii.  Journal  of  the  Franklin  Institute. CHAPTEE    VIII. METEIC  SYSTEM  IN   MEDICINE   AND  PHAEMACY. In  no  branches  of  scientific  work  is  there  greater  need  for uniformity  of  weights  and  measures  than  in  pharmacy  and medicine,  where  the  entire  world  is  drawn  upon  for  drugs  and chemicals  for  therapeutic  purposes,  and  where  the  latest  dis- coveries of  such  agents,  or  new  methods  of  their  use,  are  immedi- ately communicated  to  the  medical  profession  in  every  civilized country.  With  uniformity  of  measures  there  would  result  uniformity of  treatment,  and  the  ability  to  compare  various  methods  in different  cases.  In  fact,  there  is  no  reason  why  the  medical profession  should  not  be  able  to  write  and  speak  in  the  same language  as  concerns  their  weights  and  measures  throughout  the world  just  as  much  as  the  chemist  and  other  workers  in  pure  and applied  science;  such  a  condition  would  also  facilitate  the  exchange of  scientific  information,  which  in  the  case  of  medical  intelligence would  be  of  incalculable  value.  In  addition  to  this  must  be considered  the  commercial  advantages  to  the  general  wholesale drug  trade,  the  manufacturing  chemist,  and  the  retail  pharmacist, due  to  the  fact  that  many  drugs  are  produced  in  metric-using countries,  and  are  there  sold  and  exported  according  to  such measures.  These  same  drugs,  when  they  reach  English-speaking countries,  customarily  are  sold  according  to  avoirdupois  weight, and  are  then  compounded  according  to  apothecaries'  weight — a system  which  is  a  survival  from  mediaeval  times,  and  which  finds few,  if  any,  defenders  on  grounds  other  than  its  customary  usage. The  fact,  however,  must  be  considered  that  the  manufacture  and distribution  of  pharmaceutical  products  is  a  trade  that  is  self- 192     EVOLUTION   OF   WEIGHTS   AND   MEASURES contained,  as  it  were,  and  we  do  not  find  the  retail  consumption of  drugs  and  chemicals  save  for  medicinal  purposes,  where  the measurements  are  by  spoonfuls  or  similar  devices,  and  are  usually at  the  direction  of  a  physician,  a  matter  of  great  interest  in  the daily  life  of  the  public.  In  other  words,  the  buying,  selling,  and compounding  of  drugs  and  chemicals  concerns  the  physician  and pharmacist  rather  than  the  general  public,  who,  however,  are  the ultimate  consumers,  but  whose  wants  are  not  such  as  to  require the  use  of  any  particular  system  of  weights  and  measures,  much less  to  insist  upon  it.  The  use  of  the  metric  system  among  the manufacturers  and  dealers  in  drugs  and  chemicals  has  been constantly  on  the  increase,  in  fact  some  of  them  furnish  their products  altogether  according  to  metric  units.  On  the  other hand,  the  European  chemical  manufacturer  must  provide  special containers  for  all  of  his  products  intended  for  the  American market.  Therefore,  it  is  a  fact  that  manufacturers  and  dealers  in drugs  and  chemicals  are  more  than  willing  to  adopt  metric weights  and  measures  exclusively,  if  they  are  not  already  in  use. Furthermore,  we  know  that  the  pharmacist  is  convinced  of  the availability  of  the  metric  system  inasmuch  as  it  has  been  adopted universally  in  continental  Europe  (in  Germany  since  1858),  and figures  exclusively  in  the  United  States  Pharmacopoeia,  and  con- jointly in  the  British  Pharmacopoeia  of  1898.  This  brings  us  to the  medical  profession,  and  here  we  find  that  in  English-speaking countries  there  has  been  great  progress  in  the  use  of  metric weights  and  measures  in  writing  prescriptions,  but  that  owing  to the  conservative  tendencies  of  medical  colleges  it  is  by  no  means general,  and  while  the  majority  of  pharmacists  stand  ready  to compound  metric  prescriptions,  comparatively  few  American practitioners  write  them.  That  there  is  no  difficulty  involved  is shown  by  the  ease  with  which  the  system  was  adopted  by  the United  States  Marine  Hospital  Service,  the  Medical  Department of  the  United  States  Army,  and  the  Medical  Department  of  the United  States  Navy,  as  will  be  further  explained  below ;  while  the fact  that  it  is  eminently  desirable  is  demonstrated  not  only  from the  testimony  of  those  that  have  used  it,  but  from  resolutions adopted  at  various  times  by  representative  national  organizations of  physicians  and  surgeons.  Despite  the  fact  that  there  has  been no  active  campaign  in  behalf  of  the  metric  system  waged  among METRIC   SYSTEM   IN   MEDICINE  193 physicians  there  has  been  great  progress,  and  when  its  advantages -are  more  thoroughly  realized  it  is  believed  there  will  be  little opposition  to  completely  dropping  the  absurd  antiquated  apothe- caries' weights.  The  science  of  medicine  to-day  is  closely  con- nected with  chemistry,  physiology,  biology,  microscopy,  and  other sciences  in  which  measurement  plays  a  most  important  part.  For example,  in  all  experimental  medicine  the  doses  given  to  animals are  measured  in  metric  measures,  in  pathology  the  dimensions  of an  organ  or  any  part  of  it  are  always  stated  in  centimeters  or millimeters,  while  the  oculist  employs  metric  measures  in  all  his measures  of  focal  length.  In  short,  wherever  medicine  comes into  contact  with  natural  or  exact  science  we  find  that  the  metric system  is  employed,  and  there  is  no  reason  why  it  should  not  be used  universally.  The  only  excuse  advanced  is  that  the  practi- tioner has  learned  all  his  doses  on  the  basis  of  the  old  measures, and  that  any  change  not  only  might  result  in  inconvenience  but in  possible  danger  to  the  patient,  inasmuch  as  a  mistake  that might  prove  fatal  could  be  made  in  writing  out  the  quantities. This  is  indeed  a  very  weak  objection,  as  the  pharmacist  or  his clerk  is  constantly  on  the  lookout  for  errors  of  this  or  any  other kind  in  prescriptions.  Furthermore,  the  more  advanced  physician is  constantly  reading  in  medical  journals  of  new  methods  of  treat- ment employed  in  Europe,  where  of  course  the  metric  weights and  measures  are  altogether  employed,  and  desiring  to  adopt  such remedies  in  his  own  practice  he  must  either  employ  the  metric measures,  or  translate  them  into  English,  either  operation  requir- ing a  knowledge  of  the  metric  system. In  pharmacy  there  are  two  different  methods  of  compounding prescriptions  according  to  the  metric  system,  which,  while fundamentally  different,  in  their  actual  results  do  not  occasion any  very  serious  discrepancies.  In  Continental  Europe  and  in countries  where  the  metric  system  is  exclusively  used,  it  is  the practice  to  measure  all  substances  entering  into  a  prescription, whether  solid  or  liquid,  by  weight,  and  this  consequently  is known  as  the  gravimetric  method.  That  is,  the  quantities  are denoted  by  grams,  and  in  Germany  no  designation  of  the  unit follows  the  number,  grams  being  understood  in  every  case,  as no  other  units  are  employed  for  this  purpose.  This,  of  course, furnishes  a  very  accurate  method;  but  in  the  United  States  and N 194     EVOLUTION   OF   WEIGHTS   AND   MEASURES Great  Britain,  where  the  metric  system  is  used  it  is  customary  to employ  what  is  termed  the  volumetric  method,  where  the  fluids are  measured  by  volume  or  capacity  measure,  the  quantities being  indicated  in  cubic  centimeters.  The  solids,  of  course,  are weighed  in  grams,  and  it  is  usual  to  write  after  the  number  the abbreviation  gm.  to  distinguish  from  gr.  denoting  grains,  as  used in  the  older  system.  Inasmuch  as  the  specific  gravity  of  water is  taken  as  unity,  and  one  cubic  centimeter  of  water  at  its temperature  of  maximum  density  weighs  one  gram,  it  will  be seen  that  for  water  and  other  liquids  of  approximately  the  same specific  gravity  there  is  no  difference  between  the  two  methods, and  the  majority  of  the  liquids  used  in  compounding  prescrip- tions are  so  near  to  water  in  specific  gravity  that  little  trouble is  occasioned;  but  there  are  a  few  instances  in  which  this difference  is  material,  according  as  the  liquid  is  either  con- siderably lighter  or  heavier  than  water.  These  few  should  be borne  in  mind  in  comparing  formulae  on  the  gravimetric  system with  those  on  the  volumetric.  Of  the  substances  lighter  than water  the  most  important  are  ether,  whose  specific  gravity  is  '736 at  0°C.  and  spirits  of  nitrous  ether,  whose  specific  gravity  is  "837. Consequently,  speaking  approximately,  four  parts  by  weight  of these  liquids  will  occupy  an  equivalent  space  to  five  parts  by weight  of  water.  Alcohol  (proof  spirit)  sp.  gr.  0*79  at  20° Centigrade  is  another  substance  similar  in  this  respect.  On  the other  hand,  dealing  with  liquids  heavier  than  water,  we  find that  glycerin  stands  in  such  a  ratio  that  five  parts  by  weight of  it  occupy  the  same  space  as  four  parts  of  water,  while  with syrup  this  ratio  is  four  to  three,  and  with  chloroform  three to  two.  It  is,  of  course,  possible  to  indicate  on  the  prescription that  the  quantities  are  to  be  taken  by  weight;  but  except  in such  cases  as  above  noted,  or  in  those  of  an  extraordinary- character,  the  volumetric  method  is  employed,  and  not  only corresponds  more  closely  with  the  older  method,  but  also  is much  more  expeditious,  as  the  fluids  may  be  poured  from graduated  measuring  glasses  in  much  less  time  than  they  could be  weighed. The  profession  at  large  was  not  so  quick  to  see  the  advantages of  the  metric  system  as  the  medical  departments  of  the  United States  Government,  and  the  first  of  these  to  adopt  the  innovation METRIC   SYSTEM   IN   MEDICINE  195 was  the  Marine  Hospital  Service,  where,  in  accordance  with Department  Circular  39,  dated  April  27th,  1878,  it  was  ordered that  "  The  Medical  Officers  of  the  Marine  Hospital  Service  will hereafter,  for  all  official,  medical  and  pharmaceutical  purposes, make  use  of  the  Metric  System  of  Weights  and  Measures." This  action,  which  was  the  first  Government  order  issued  in the  United  States  to  make  the  use  of  the  metric  system  obli- gatory for  any  purpose  whatever,1  followed  the  report  made to  Surgeon-General  John  M.  Woodworth,  which  was  prepared by  Oscar  Oldberg,  Phar.D.,  then  Chief  Clerk  and  Acting  Medical Purveyor,  U.S.  Marine  Hospital  Service,  in  which  he  called attention  to  the  advantages  of  the  metric  system,  and  provided the  necessary  rules  for  expressing  quantities  in  that  system, and  also  described  the  necessary  methods  to  be  followed  in writing  metric  prescriptions. In  1881  the  Bureau  of  Medicine  and  Surgery  in  the  U.S. Navy  adopted  the  system,  as  on  April  15th  of  that  year  there was  approved  by  Secretary  William  H.  Hunt  a  small  volume entitled,  Instructions  for  Medical  Officers  of  the  United  States  Navy, prepared  by  Medical  Director  Philip  S.  Wales,  U.S.N".  On page  10,  Article  2,  Section  1,  was  the  official  direction  that  "the Metric  System  of  Weights  and  Measures  shall  hereafter  be employed  in  the  Medical  Department  of  the  Navy."  Accordingly, the  "  Supply  Table "  in  this  volume  was  prepared  on  a  metric basis,  and  supplies  have  since  been  issued  in  accordance  with this  system. In  1894  the  metric  system  was  adopted  by  the  medical department  of  the  United  States  Army,  and  was  put  into operation  under  the  provisions  of  the  accompanying  order. WAR  DEPARTMENT, Surgeon  General's  Office, Washington,  April  13,  1894. CIRCULAR  : Upon  the  publication  of  the  new  Supply  Table  and  receipt  of  the  new forms,  all  requisitions,  invoices,  receipts,  and  returns  pertaining  to  medical supplies  will  be  in  accordance  with  the  metric  system  of  weights  and measures. After   the  30th  day  of  June,  1894,  the  use   of  this  system  in  writing 1  See  Oldberg,  Weights,  Measures  and  Specific  Gravity,  Chicago,  1888,  p.  18. 196     EVOLUTION   OF  WEIGHTS   AND   MEASURES official  prescriptions  is  desired ;  on  and  after  the  1st  day  of  January,  1895, such  use  is  hereby  ordered. Metric  measures,  weights,  and  prescription  blanks  will  soon  be  issued to  all  posts  without  requisition. Until  medical  supplies  now  in  stock  in  troy  and  avoirdupois  weights are  exhausted,  the  following  approximate  values  may  be  considered  as equivalent  in  transferring  original  packages  : 1  ounce  =    30  grammes. 1  pound  =      \  kilogram. 1  fluid  ounce  =    30  cubic  centimeters. 1  pint  =  500  cubic  centimeters. 1  quart  =      1  liter. 1  yard  =      1  meter. GEO.  M.  STERNBERG, Burgeon  General,   U.S.  Army. Approved  : Daniel  S.  Lamont, Secretary  of  War. This  order  was  promptly  carried  out  on  the  dates  specified, and  all  supplies  were  not  only  handled  within  the  department, but  were  purchased  from  dealers  according  to  metric  weights  and dimensions.  In  addition,  the  army  surgeons  began  writing  their prescriptions  on  the  metric  basis  without  protest  or  difficulty, and  the  system  was  soon  in  successful  operation,  and  in  1902 was  pronounced  by  Surgeon-General  Sternberg  as  eminently satisfactory,  the  General  testifying  before  the  Committee  on Coinage,  Weights  and  Measures,  Congress,  February  15,  1902, when  asked  why  he  would  not  go  back  to  the  old  system  : "  Because  it  (the  metric  system)  is  so  decidedly  superior.  It  is working  smoothly,  and  we  have  no  difficulty  whatever — no protests  on  the  part  of  the  people  we  deal  with,  from  whom we  purchase.  The  wholesale  druggist  must  necessarily  be familiar  with  it." 1 General  Sternberg  also  said  that  the  principal  reason  for the  adoption  of  the  system  was  the  greater  simplicity  of  the decimal  system,  and  furthermore  it  was  successfully  used  in other  countries,  and  was  a  better  system  than  the  one  in  use. An  important  test  came  in  the  Spanish-American  War,  when  the 1  Page  83,  The  Metric  System  of  Weights  and  Measures.    Committee  on  Coinage, Weights  and  Measures  (Hearing),  February  15,  1902. METRIC   SYSTEM   IN   MEDICINE  197 medical  department  was  increased  by  a  number  of  volunteer  and contract  surgeons ;  but  the  latter  experienced  no  difficulty  in conforming  to  the  regulations. In  England  the  feeling  of  the  advanced  members  of  the medical  profession  has  been  most  favourable  to  the  metric  * system,  and  in  1904  the  General  Medical  Council  adopted the  following  resolution  in  reference  to  the  Bill  then  before the  House  of  Lords  :  "  That  the  President  (with  the  Chairman of  the  Pharmacopoean  Committee)  be  requested  to  inform  the Lord  President  of  the  Privy  Council  that  in  the  opinion  of the  Council  it  is  desirable  that,  after  a  sufficient  period  to be  fixed  by  law,  the  metric  system  of  weights  and  measures should  become  the  one  legal  system  for  the  preparation  and dispensing  of  drugs  and  medicines ;  that  the  Council  would view  with  favour  the  passing  into  law  of  a  Bill  such  as  that now  before  Parliament,  entitled  the  'Weights  and  Measures (Metric  System)  Bill ' ;  and  that  in  that  event  the  Council would  be  prepared  to  take  all  necessary  steps  to  give  effect to  the  law  by  making  the  proper  modifications  in  the  British Pharmacopoeia." The  correctness  of  the  prescription  when  written  in  metric units  is  much  more  likely  to  be  ensured,  as  there  is  no  possi- bility of  mistaking  the  various  units,  since  but  two  are  used — the  gram  for  solids,  and  the  cubic  centimeter  for  liquids. In  a  prescription  written  in  apothecaries'  weights  and  measures, on  the  other  hand,  not  only  are  there  numerous  units — as pounds,  ounces,  drachms,  scruples,  grains,  minims,  etc. — but these  are  denoted  by  alchemistic  characters  which,  at  least  in the  case  of  ounces  and  drachms,  are  susceptible  of  confusion. Thus,  not  only  is  there  the  danger  of  errors  in  figures  which is  common  to  both  methods,  but  in  the  case  of  the  older system  there  are  also  the  characters.  Furthermore,  with apothecaries'  weights  it  is  customary  to  denote  the  quantities by  Roman  figures  or  letters,  which  are  much  more  readily confused  than  the  Arabic  figures  employed  in  metric  prescrip- tions. If  the  decimal  line  is  used,  as  in  a  cash  account,  the danger  of  a  misplaced  decimal  point,  or  of  an  occasional  dot being  taken  as  a  point,  is  obviated.  In  fact,  these  possible errors    attributed    to    the    metric    system   have    been   found   by 198     EVOLUTION    OF  WEIGHTS   AND   MEASURES experience  to  be  altogether  imaginary,  for  a  misplaced  decimal point  decreases  or  increases  a  dose  ten-fold.  The  dispenser would  therefore  detect  the  error  at  a  glance.  Then  there  is the  further  advantage  that  it  is  possible  to  send  by  telegraph •  a  metric  prescription  with  far  greater  facility  than  one  where the  Eoman  characters  are  employed. While  the  gravimetric  method  may  be  the  most  scientific and  exact,  yet  it  must  be  remembered  that  the  dose  cannot be  administered  to  the  patient  in  the  great  majority  of  cases with  anything  like  scientific  accuracy,  and  it  is  usual  to employ  various  domestic  glasses  and  spoons,  which  of  course  give a  volumetric  measurement.  In  general  certain  rough  equivalents amply  suffice,  and  the  following  measurements  are  used  in  the United  States  and  France: A  tea-spoonful  =  1  fluid  drachm,  =      5  grams  of  water A  dessert-spoonful        =  2  fluid  drachms,  =    10 A  table-spoonful  =  J  fluid  ounce,  =    15 A  tumblerful  =  8  fluid  ounces,  =  240 A  wine  glass  (U.S.A.)  =  2     „         „  =60 A  wine  glass  (French)  =  5     „         „  =150 CHAPTER    IX. INTERNATIONAL  ELECTRICAL   UNITS. Beside  the  units  incident  to  our  every-day  life  which  we have  already  discussed,  it  is  possible  to  derive  from  the metric  system  in  connection  with  the  ordinary  unit  for  the measurement  of  time  employed  throughout  the  civilized  world, a  complete  system  of  units  that  will  answer  for  the  measure- ment of  any  and  all  physical  quantities.  For  such  a  system it  is  necessary  to  have  as  the  bases  certain  fundamental  units, and  with  them  we  may  build  up  and  extend  the  system  as occasion  demands.  It  has  been  found  that,  starting  with units  of  length,  mass,  and  time,  a  satisfactory  system  can  be evolved;  and  though  there  have  been  several  such  systems proposed,  yet  the  one  founded  on  the  centimeter  as  the  unit of  length,  the  gram  as  the  unit  of  mass,  and  the  second  as the  unit  of  time,  has  met  with  the  greatest  favour.  It  has for  many  years  been  the  only  one  employed  in  scientific work,  and  has  served  as  a  basis  for  other  and  practical units  when  such  have  been  required  or  desired.  As  the units  mentioned  have  been  adopted  for  most  scientific  work, being  as  small  as  were  convenient  to  employ  in  ordinary measuring  processes,  it  is  easy  to  see  why  they  were  chosen eventually  as  the  basis  of  a  system  of  units  that  should  be complete  and  symmetrical.  From  the  names  of  the  funda- mental units  this  system  is  known  as  the  C.G.S.  system, and  it  is  our  purpose  to  outline  briefly  its  development  in order  that  we  may  trace  the  derivation  of  some  of  the  ordi- nary   electrical    units    now    in    every-day    use,   and    which    are 200     EVOLUTION   OF   WEIGHTS   AND   MEASURES essentially  metric  in  their  origin.  The  first  suggestion  of such  a  system  of  units  was  due  to  Carl  Friedrich  Gauss,  who in  1832  proposed  a  system  of  so-called  absolute  units,  which. had  as  its  base  the  fundamental  units  of  length,  mass,  and time.  This  system  was  devised  by  Gauss  while  engaged  in the  study  of  terrestrial  magnetism,  in  which  the  intensity  of the  earth's  magnetism,  as  well  as  the  declination  and  dip, was  to  be  measured  at  different  points  in  Europe.  For  this purpose  a  German  Magnetic  Union  had  been  organized  by Gauss  and  Alexander  Von  Humboldt,  and  was  actively  engaged in  magnetic  studies  from  about  1834  to  1842.  Previously  there had  been  no  unit  for  the  intensity  of  magnetism,  and  English physicists  had  taken  the  intensity  at  London  as  the  standard. Gauss  believed  that  it  would  be  more  scientific,  as  well  as more  practical,  if  a  system  were  devised  which  would  be independent  of  season  or  place,  as  well  as  of  instruments  and external  conditions.  Accordingly,  as  the  system  which  he proposed  in  1832  was  based  merely  on  the  three  fundamental units  mentioned,  he  termed  it  the  Absolute  System.  In  this- system  it  was  possible  to  derive  all  necessary  units  from  the three  selected  as  fundamental ;  thus  a  unit  of  velocity  was obtained  by  defining  it  as  such  a  velocity  as  a  body  would have  in  travelling  unit  distance  in  unit  time.  Unit  accelera- tion was  the  acceleration  that  a  body  would  experience  when it  gained  or  lost  unit  velocity  in  unit  time.  Then,  for  the unit  of  force,  it  was  only  necessary  to  take  such  a  force  as would  impart  unit  velocity  to  unit  mass  in  unit  time — that is,  the  unit  acceleration.  Consequently,  when  it  came  to defining  a  unit  of  intensity  of  magnetism,  Gauss  took  such  a quantity  of  magnetism  as  would  exert  unit  force  on  a  similar quantity  at  unit  distance.1  Now,  as  magnetic  force  was  mani- fested by  the  attraction  or  repulsion  of  a  magnetic  pole  when placed  in  a  magnetic  fluid,  it  would  be  possible  to  measure- the  force  by  mechanical  methods,  and  for  this  he  deduced the  necessary  equations. In  this  way,  by  mathematical  processes  which  are  interesting  but. i  Resultate  aus  den  Beobachtungen  des  Magnetischen  Vereins,  1836-1842;  Soc. Gott.  viii.  1832-1837;  Pogg.  Ann.  xxviii.  §§  241,  591  (1833);  Gauss,  Werke,. v.  §  79-118. INTERNATIONAL   ELECTRICAL   UNITS  201 need  not  be  discussed  here,  it  was  possible  for  Gauss  to  determine the  intensity  of  the  earth's  magnetic  field  at  any  given  point  on its  surface.  While  the  process  of  derivation  was  the  same  as  for the  modern  C.G.S.  system,  yet  Gauss  employed  as  the  funda- mental units  in  his  Absolute  System  the  millimeter  as  the  unit of  length,  the  milligram  as  the  unit  of  mass,  and  the  second  as  the unit  of  time.  By  similar  reasoning,  it  was  possible  to  define  the unit  charge  of  electricity  as  such  a  charge  as  would  act  on  a similar  charge  at  unit  distance  with  unit  force.  So  useful  was this  idea  of  absolute  measurement  that  it  was  straightway adopted  by  Wilhelm  Weber,  (1804-1891)  and  found  application  in his  experiments  to  measure  the  intensity  of  an  electric  current,, the  intensity  of  electromotive  force  and  of  resistance ;  the  latter investigation  being  further  developed  by  Eudolf  Kohlrausch (1809-1858)  in  some  most  valuable  investigations.  Weber's  work1 is  remarkable  not  only  for  the  fact  that  he  applied  absolute measurements  in  electricity,  but  for  his  showing  that  electricity was  but  a  manifestation  of  mechanical  energy,  and  consequently could  be  measured  in  terms  of  length,  mass,  and  time.  There  was,, however,  an  important  difference,  in  that  it  was  not  possible  to measure  directly  quantities  of  electricity,  but  it  was  necessary  to make  such  measurements  by  the  effect  on  some  external  object. For  example,  when  Weber  came  to  determine  the  intensity  of  an electric  current  in  absolute  measurement,  he  found  three  ways open  to  him.  The  first  was  to  determine  the  strength  of  current by  its  chemical  or  electrolytic  effect.  In  other  words,  a  unit current  would  be  that  which  decomposed  a  unit  mass  of  water into  its  chemical  elements  in  unit  time.  Secondly,  the  magnetic effect  of  the  electric  current  also  served  as  a  basis  for  measuring a  current  of  electricity,  and  a  unit  of  intensity  of  current  he defined  as  such  a  current  as  would  exert,  upon  a  magnet  pole,  the same  force  as  an  infinitely  small  magnet  of  unit  moment,  placed at  the  center  of  a  closed  circuit  of  unit  area  around  which  the current  should  flow,  and  perpendicular  to  its  plane.  In  other words,  he  defined  his  unit  of  current  according  to  the  measure- ments which  could  be  made  with  a  tangent  galvanometer,  as  will be  described  below.     Then  thirdly,  the  intensity  of  current  could 1  Rosenberger,  Geschichte  der  Physik,  vol.  iii.  pp.  302,  514-519.     Braunschweig,. 1890.     Weber,  Pogg.  Ann.  xcix,  p.  11,  1855. 202     EVOLUTION   OF   WEIGHTS   AND   MEASURES --,& £5b     | O   v   9  0)  03 fl    fl    £  fl  S o  o  o  o  o fcfclz;  fe  to t:    to g  a o  o 03  a>       a> as       a o  o      © a o II C    fi 63 g OQ I a  ao  ~ o  o , £§  i tdQCO    . 3     fcfcS   4   £  Q 03    03 fl  a o  o toto 03    03  03 "Co      fl 03  fl 03  "-1 a  fi a  I fl  o 1  i 1* •3  °  ^ g  S.-S a  S  8  £ oca'-*3 •S.2.il ^2fl 1  £•»  ! -S§oS ==  ©  a  i 2  5       03 OS         -H H  _ ..  1 •3       .    03 .fl  ^  _ O    eg 8  s £  3 .KB a  ■  a 0<h   ci 9  0S 9&1 lS8 Boo e  P«  ■ e.8  *  fl &0  03<~    fl 03  4*     fclD  M •-•flag ill hOh §    s fl  fl o   >> 03    °  € 03  "^ CS    £  03 ^  a ,  03  e8  £ fl i  I •&   9 <   O 3  * I    8 CT1       03 03      'O rfl  C3 H        P3 fl T3 0,0.  XI it  8 a  o«_ fl  J  o n   o   t< fe  .2  43 1-2  fl W   -O     03 Go  o  5 03    g OP ill .5      S 45    Mil    * C     D0+3     _, 2  2-2  o -§^^ M|jj 03  P4.S    O fl       *  A 03    fl fl w    fl fl o<l     *<     <3 O303O303O3C3O3  03  03  0303 flflflflflflfl  fl  fl  flfl OOOOOOO  O  O  OO &KK  %  tz;  %  &  m  ^  SziSz; 03    03    03  03  03 fl    fl    fl  fl  fl OOO  O  O 03 Is fl    eS B  E OO O    03    03  ,— ^^  03. 2       03  O  ©  03O  03O03  O  03 fl   fl   fl  sn&nfl    ^SflCfl  flfl  flflflflfl OO    >)(7*0     cj      O         O         O  OO  OOO         o         o ^3 fl 51 d^^ o II 03 fl INTERNATIONAL  ELECTRICAL    UNITS 203 &  m     M HS    ©© o   ©  ©  © fl    P.  0  0 o  o  o  o ££  ft  fc 0)       ©    gj o     o  o I        1 bo  ? cut e6       O i      g1       * OS  o T3 1 S  «2 o  ^  o s     2  © o       o   feS 3  © 8  >> ©  a a  o H3 a   £ © So b ©  -u> M   © ©  a bO bOcS •a Ikj © a o c3 °M    © m         © I  .  I "Sob *i  -^    Qj fc  P  © 5PP S£ ©       ©  S  9  ■ T3  Js  'w 13    n"  7= g    ©^ a  5  :s 1  c  •  S 3  >'3  3  3  g.s © 0  o o  © ©  © ©  <4;J o  o © £     <        £ El? (4H     © a  © "5  s J8  2 u  t3 53  © 0     &o .a  * ■^   >» ill M      cj1  © ©      w    S-i bo  's9 |  a| r1    s H    02 **«      ■ 2  -S  .-S  "S  © SJliil 5  I  g*  1  I _    ©    ©  ."5  ,J3    m E     ©     £     0     Q     B «8^    fl.S    fl    2 N|  a  a 2  >» n  §  9 ^   C71  S   ©    o   3 si!-!*8, Jnlfl ID fa     ^, K5 fc<      C3 ^ o © p      ©         ©         © \  %    %   § 5z5  !zs ©      © a     a o       o «m  >»      © ^3  2 Ills 204     EVOLUTION   OF   WEIGHTS   AND   MEASURES also  be  measured  by  the  effect  of  two  currents  flowing  along parallel  conductors  distant  from  each  other  by  a  unit  length. Following  out  these  three  methods,  Weber  made  a  series  of absolute  measurements  and  found  that  they  possessed  a  certain ratio  to  each  other.  He  also  found  that,  with  the  galvanometer, he  was  able  to  measure  the  quantity  of  electricity  with  which  a conductor  was  statically  charged,  by  allowing  it  to  be  discharged or  flow  to  the  earth  through  the  galvanometer.  Having  thus been  able  to  measure  the  intensity  of  current  in  absolute  units, which  (following  the  example  of  Gauss)  were  based  on  the millimeter,  milligram,  and  second,  Weber  then  proceeded  to  make absolute  measurements  of  electromotive  force.  The  absolute unit  of  electromotive  force  he  defined  as  that  induced  by  unit magnetic  force  in  a  circular  conductor  of  unit  area,  if  this circular  conductor  were  turned  from  a  position  parallel  to  the direction  of  the  magnetic  force  into  one  perpendicular  to  it  in  the time  of  one  second.1  Inasmuch  as  he  was  able  to  use  the magnetic  field  of  the  earth,  whose  intensity  could  be  measured accurately,  and  as  by  his  previous  experiments  he  was  able  to measure  the  intensity  of  the  current,  using  the  apparatus  known as  the  earth  inductor,  he  was  soon  able  to  make  a  direct measurement  of  electromotive  force.  The  earth  inductor,  it may  be  said  in  passing,  consisted  of  a  large  coil  of  wire  whose axis  of  revolution  was  perpendicular  to  the  lines  of  magnetic force,  so  that  when  the  coil  was  revolved  a  current  was  induced in  it  which  could  be  measured  by  the  galvanometer. With  methods  for  the  absolute  measurement  of  current  and electromotive  force  already  known  and  defined,  it  only  remained to  measure  the  resistance  in  absolute  units,  and  this,  of  course, followed  from  Ohm's  law,  which  had  been  known  since  1827. According  to  this  statement,  the  current  was  equal  to  the  electro- motive force  divided  by  the  resistance,  and  consequently  it  followed that  a  unit  of  resistance  would  be  that  through  which  unit electromotive  force  would  produce  unit  current.  This  determina- tion of  the  unit  of  resistance  involved  most  elaborate  experiments, 1  Rosenberger,  vol.  iii.  p.  517;  "  Electrodynamische  Massbestimmungen  ins besondere  Widertandsmessen, "  Abhandl.  der  K.  8.  Gesellsch.  I.  §  197,  1852;  Pogg. Ann.  lxxxii.  §  337.  Weber,  Abhandl.  bei  Begriindung  der  K.  S.  Gesellschaft  der Wissenschaft,  1846  ;  Abhandl.  der  K.  8.  Gesellschaft  d.  Wissenschaft,  I.  1852. INTERNATIONAL   ELECTRICAL   UNITS  205 which  are  among  the  most  celebrated  in  all  experimental  physics, and  their  result  was  firmly  to  establish  the  absolute  system  on  a thoroughly  scientific  basis. There  were,  previous  to  this,  various  arbitrary  electrical  units suggested,  and  in  more  or  less  limited  use.1  Thus  various lengths  of  copper,  iron,  or  German  silver  wire  of  specified  length, weight,  and  cross-section  were  suggested  and  employed  as  units. Perhaps  the  most  conspicuous  of  these  was  the  copper  wire  of prescribed  dimensions  and  weight  which  was  recommended  by Jacobi,2  of  St.  Petersburg,  in  1846,  to  the  physicists  of  Europe  as the  standard  of  normal  resistance.  This  standard  was  determined in  absolute  units  of  resistance  by  Weber,  but  it  did  not  prove entirely  acceptable,  owing  to  the  changes  taking  place  in  the copper  with  time,  and  owing  to  the  difficulties  experienced  in obtaining  standard  conditions.  Accordingly,  Werner  Siemens,  of Berlin,  proposed,  in  1860,  following  the  suggestion  of  Marie- Davy  made  in  1843,  to  use  mercury  in  defining  the  unit  of  resist- ance, and  as  a  standard,  a  column  of  this  substance  one  meter  in length  and  one  square  millimeter  in  cross-section,  measured  at 0°C.3  This  also  was  measured  by  Weber  in  1861,  and  later by  Kohlrausch. For  electromotive  force,  it  was  customary  at  this  time  to employ  the  electromotive  force  of  a  constant  battery,  such  as  the Daniell  cell,  and  in  the  case  of  a  current,  to  make  use  of  various arbitrary  units.  With  the  increase  in  the  scientific  knowledge  of electricity,  as  well  as  in  its  industrial  applications,  such  as  the telegraph  and  submarine  cable,  it  was  realized  that,  for  practical use,  there  should  be  a  systematic  and  comprehensive  system  of electrical  units,  which  would  be  based  on  certain  fixed  standards, and  would  be  universally  employed  by  electricians.  This  subject was  accordingly  taken  up  in  Great  Britain  by  the  British Association  for  the  Advancement  of  Science,  and  in  1861  a  strong committee,  composed  of  leading  physicists  and  electricians,  was appointed  to  investigate  the  subject  and  to  report  on  suitable units.     The  subject  was  discussed  in  all  its  many  bearings  by 1  For  a  list  with  bibliography,  see  Eosenberger,  Geschichte  der  Physik,  vol.  iii. pp.  519-520. 2  Jacobi,  Comptes  Rendus  (Paris),  p.  277,  vol.  xxxiii. 3W.  Siemens,  Poggendorff's  Annalen,  ex.  p.  1,  1860. 206     EVOLUTION   OF   WEIGHTS   AND   MEASURES this  committee,  Weber's  and  other  experiments  were  repeated,  and the  result  was  that  an  absolute  system  was  adopted,  only  the centimeter,  gram,  and  second  were  employed  as  the  fundamental units  in  place  of  the  millimeter,  milligram,  and  second  of  Gauss and  Weber.  This  committee  not  only  reported  in  favor  of  the establishment  of  the  C.G.S.  system,  but  also  fixed  a  certain number  of  so-called  practical  units,  which,  with  slight  modifica- tions, are  now  in  universal  use. The  reason  for  this  was  that  a  number  of  the  C.G.S.  absolute units  are  either  too  large  or  too  small  to  be  employed  in  practical work.  For  example,  the  electromotive  force  of  an  ordinary Daniell  cell  would  represent  about  108  absolute  units,  and  as  the electrician  of  that  time  dealt  with  electromotive  forces  of  this magnitude,  rather  than  with  those  represented  by  a  quantity  so much  smaller,  it  was  convenient  to  multiply  the  absolute  unit  by 108  to  obtain  a  convenient  practical  unit,  which  was  designated by  the  name  volt.  Likewise  with  the  ohm,  or  practical  unit  of resistance,  which  represented  109  absolute  units.  But  in  the  case of  the  ampere,  or  unit  of  current,  which,  as  we  have  seen,  must follow  from  Ohm's  law,  the  difference  was  not  so  large,  and  the absolute  unit  had  merely  to  be  divided  by  10  to  give  the  practical unit.  This  Commission  decided  on  the  coulomb  as  the  unit  of quantity,  being  10 _1  absolute  units,  and  being  the  quantity  of electricity  conveyed  by  one  ampere  in  one  second.  As  a  unit  of capacity,  the  farad,  or  10  ~9  absolute  units,  was  taken,  and  measured the  capacity  of  a  condenser  charged  to  a  potential  of  one  volt  by one  coulomb.  As  a  more  useful  unit  still,  the  micro-farad,  or  10 "& part  of  a  farad,  was  also  established.  For  work,  the  joule  was taken,  representing  107  ergs  or  absolute  units  of  work,  and equivalent  to  the  energy  expended  in  one  second  by  one  ampere flowing  through  a  resistance  of  one  ohm.  As  a  unit  of  power, the  watt,  or  107  ergs  per  second,  represented  the  power  of  a current  of  one  ampere  flowing  under  a  pressure  of  one  volt,  or one  joule  per  second,  and  when  multiplied  by  1000  it  gives  the kilowatt,  which  soon  became  common  in  electrical  work  in  place of  the  old  familiar  horse-power.1 i  For  an  interesting  historical  presentation  which  includes  the  text  of  recent legislation,  see  Wolff,  "  The  So-called  International  Electrical  Units,"  a  paper presented  at  the  International  Congresses  of  Electricians  at   St.   Louis,   1904. INTERNATIONAL   ELECTRICAL   UNITS  207 In  1865  this  committee  made  a  determination  of  the  ohm,  and constructed  a  standard  of  platinum-silver  to  represent  its  value. This  standard,  by  law,  represented  the  legal  unit  of  resistance  in Great  Britain,  and  was  also  known  for  many  years  as  the  B.A. (British  Association)  unit ;  in  fact,  holding  its  own,  especially  in English-speaking  countries,  until  the  adoption  of  the  international ohm  by  the  Chicago  Congress  of  1893. Soon  after  this,  the  invention  by  Latimer  Clark,  in  1873,  of  a constant  cell,  which  was  found  to  have,  under  certain  conditions, an  electromotive  force  of  1*434  volts,  furnished  a  standard  of electromotive  force  which,  while  not  legally  defined  until  some years  later,  became  widely  used,  and  figured  in  many  determina- tions. So  thoroughly  was  the  C.G.S.  system  thought  out  by  the British  Association  Committee,  and  so  systematically  were  the practical  units  determined  and  denned  that,  despite  minor  in- accuracies, as  shown  by  the  experiments  of  German  physicists,  the system  was  favorably  considered  at  the  International  Congress  of Electricians  held  in  Paris  in  1881,  and  resolutions  were  adopted in  which  the  C.G.S.  electro-magnetic  units  were  chosen  as  the fundamental  units  in  terms  of  which  the  practical  units  should  be defined.  At  a  meeting  held  in  1884  an  international  commis- sion decided  on  the  length  of  the  column  of  mercury  for  the standard  ohm,  and  the  legal  ohm  was  denned  as  the  resistance  of a  column  of  mercury  of  one  square  millimeter  section,  and  of  106 centimeters  length  at  a  temperature  of  melting  ice. The  ampere  was  defined  as  a  current  corresponding  to  10 -1 absolute  C.G.S.  electro-magnetic  units,  while  the  volt  was  defined as  an  electromotive  force  which  produced  a  current  of  one ampere  in  a  conductor  whose  resistance  was  a  legal  ohm.  This definition  of  the  ohm  did  not  carry  with  it  universal  acceptance, and  the  legal  ohm  was  not  made  legal  in  Great  Britain  or  in  the United  States ;  but  in  the  meantime  a  number  of  prominent physicists,  including  Professor  Henry  A.  Eowland  in  America  and Lord  Eayleigh  in  England,  carried  on  further  investigations  to evaluate  the  true  ohm,  with  the  result  that  the  length  of  the mercury  column  was  found  to  be  nearly  106*3  centimeters,  which Reprinted  in  Bulletin  No.  1,  Bureau  of  Standards,  Washington,  D.C.     See  British Association  Reports  on  Electrical  Standards  (London,  1873). 208     EVOLUTION   OF   WEIGHTS   AND   MEASURES accordingly  was  adopted  by  the  British  Association  Committee  in 1892,  together  with  the  definition  of  the  column  in  length  and mass,  rather  than  by  length  and  cross-section. Meanwhile,  in  1889,  another  international  congress  of  elec- tricians was  held  at  Paris,  at  which,  in  addition  to  a  number  of decisions  involving  nomenclature,  definitions  of  units  of  energy, power,  and  inductance  were  adopted.  The  joule  was  selected  as the  practical  unit  of  energy  and  was  defined  as  equal  to  107  C.G.S. units,  being  equivalent  to  the  energy  disengaged  as  heat  in  one second  by  a  current  of  one  ampere  flowing  through  a  resistance of  one  ohm.  As  a  practical  unit  of  power  the  watt  was  taken, and  was  equal  to  107  C.G.S.  units,  being  the  power  of  one  joule per  second.  For  inductance  the  quadrant  was  chosen  as  the practical  unit,  and  was  defined  as  equal  to  10d  centimeters.  This -congress  also  took  the  important  step  of  recommending  that  the power  of  various  electric  machines,  such  as  dynamos,  motors, transformers,  etc.,  should  be  rated  in  watts  and  kilowatts  instead of  horse-power,  and  this  practice  has  generally  prevailed  even  in non-metric  countries  such  as  Great  Britain  and  America. In  1893,  in  connection  with  the  World's  Columbian  Exposition at  Chicago,  an  International  Congress  of  Electricians  was  held, and  a  Chamber  of  Delegates,  composed  of  officials  appointed  by the  various  Governments,  proceeded  to  define  and  name  the various  electrical  units.  By  this  time,  owing  to  the  increased  use of  electric  lighting,  various  forms  of  power  transmission,  electric railways,  and  other  important  applications  of  electricity,  the subject  was  one  of  prime  interest,  and  required  the  most  careful oonsideration  of  the  Chamber  of  Delegates,  which  consisted  of many  of  the  world's  most  eminent  physicists  and  electrical engineers.  Its  deliberations  resulted  in  a  series  of  recom- mendations which  were  reported  to  the  Congress,  and  referred  to the  various  nations  of  the  world,  by  many  of  whom  they  were subsequently  embodied  to  a  greater  or  less  extent  in  legal ■enactments  making  the  use  of  the  new  units  obligatory.  In  the United  States  such  an  Act  was  passed  and  approved,  July  12,  1894.1 These  resolutions  contained  the  following  recommendations : "  Resolved, — That  the  several  Governments  represented  by  the delegates   of  this  International  Congress  of  Electricians  be,  and 1  Revised  Statutes  of  the  United  States,  Supplement,  vol.  ii.  chap.  131,  1894. INTERNATIONAL  ELECTRICAL  UNITS  209 they  are  hereby,  recommended  to  formally  adopt  as  legal  units  of electrical  measure  the  following:  As  a  unit  of  resistance,  the international  ohm,  which  is  based  upon  the  ohm,  equal  to  109 units  of  resistance  of  the  Centimeter-Gramme-Second  System  of electro- magnetic  units,  and  is  represented  by  the  resistance  offered to  an  unvarying  electric  current  by  a  column  of  mercury  at  the temperature  of  melting  ice  14*4521  grammes  in  mass,  of  a  constant cross-sectional  area,  and  of  the  length  of  106*3  centimeters. "  As  a  unit  of  current,  the  international  ampere,  which  is  one- tenth  of  the  unit  of  current  of  the  C.G.S.  system  of  electro- magnetic units,  and  which  is  represented  sufficiently  well  for practical  use  by  the  unvarying  current  which,  when  passed through  a  solution  of  nitrate  of  silver  in  water,  and  in  accordance with  accompanying  specifications  deposits  silver  at  the  rate  of 0*001118  of  a  gram  per  second. "  As  a  unit  of  electromotive  force,  the  international  volt,  which is  the  electromotive  force  that,  steadily  applied  to  a  conductor whose  resistance  is  one  international  ohm,  will  produce  a  current of  one  international  ampere,  and  which  is  represented  sufficiently well  for  practical  use  by  \^%  of  the  electromotive  force  between the  poles  or  electrodes  of  the  voltaic  cell  known  as  Clark's  cell, at  a  temperature  of  15°  C,  and  prepared  in  the  manner  described in  the  accompanying  specification.1 "  As  a  unit  of  quantity,  the  international  coulomb,  which  is  the quantity  of  electricity  transferred  by  a  current  of  one  international ampere  in  one  second. "  As  a  unit  of  capacity,  the  international  farad,  which  is  the capacity  of  a  condenser  charged  to  a  potential  of  one  international volt  by  one  international  coulomb  of  electricity. "  As  a  unit  of  work,  the  joule,  which  is  equal  to  107  units  of work  in  the  C.G.S.  system,  and  which  is  represented  sufficiently well  for  practical  use  by  the  energy  expended  in  one  second  by an  international  ampere  in  an  international  ohm. "  As  a  unit  of  power,  the  watt,  which  is  equal  to  107  units  of  power in  the  C.G.S.  system,  and  which  is  represented  sufficiently  well  for practical  use  by  work  done  at  the  rate  of  one  joule  per  second. 1  No  report  was  ever  made  by  the  committee  to  which  the  preparation  of  the specifications  was  entrusted.  Its  members  were  Professors  Helmholtz,  Ayrton, and  Carhart,  but  the  death  of  the  first  prevented  the  work. O 210    EVOLUTION   OF  WEIGHTS   AND   MEASURES "  As  a  unit  of  induction,  the  henry,  which  is  the  induction  in  a circuit  when  the  electromotive  force  induced  in  this  circuit  is one  international  volt,  while  the  inducing  current  varies  at  the rate  of  one  ampere  per  second." Specifications  for  Construction  and  Use  of  the  Silver  Voltameter. •  In  the  following  specifications  the  term  silver  voltameter means  the  arrangement  of  apparatus  by  means  of  which  an electric  current  is  passed  through  a  solution  of  nitrate  of  silver  in water.  The  silver  voltameter  measures  the  total  electrical quantity  which  has  passed  during  the  time  of  the  experiment, and  by  noting  this  time  the  time  average  of  the  current,  or  if  the current  has  been  kept  constant,  the  current  itself,  can  be  deduced. In  employing  the  silver  voltameter  to  measure  currents  of about  one  ampere  the  following  arrangements  should  be  adopted : The  kathode  on  which  the  silver  is  to  be  deposited  should  take the  form  of  a  platinum  bowl  not  less  than  10  cms.  in  diameter and  from  4  to  5  cms.  in  depth. The  anode  should  be  a  plate  of  pure  silver  some  30  sq.  cms.  in area  and  2  or  3  mms.  in  thickness. This  is  supported  horizontally  in  the  liquid  near  the  top  of  the solution  by  a  platinum  wire  passed  through  holes  in  the  plate  at opposite  corners.  To  prevent  the  disintegrated  silver  which  is formed  on  the  anode  from  falling  on  to  the  kathode,  the  anode should  be  wrapped  round  with  pure  filter  paper,  secured  at  the back  with  sealing  wax. The  liquid  should  consist  of  a  neutral  solution  of  pure  silver nitrate,  containing  about  15  parts  by  weight  of  the  nitrate  to  85 parts  of  water. The  resistance  of  the  voltameter  changes  somewhat  as  the current  passes.  To  prevent  these  changes  having  too  great  an effect  on  the  current,  some  resistance  besides  that  of  the  volta- meter should  be  inserted  in  the  circuit.  The  total  metallic resistance  of  the  circuit  should  not  be  less  than  10  ohms. In  the  United  States  the  foregoing  recommendations  were duly  given  force  of  law  by  an  Act  of  Congress  approved July  12,  1894,  one  section  of  which  provided  that  the  National INTERNATIONAL  ELECTRICAL   UNITS  211 Academy  of  Sciences  should  prepare  detailed  specifications  for the  practical  application  of  the  definitions  of  the  ampere  and volt.  Such  specifications  were  accordingly  prepared  by  a  com- mittee x  of  the  Academy,  and  were  adopted  by  that  body  on February  9,  1895.     They  are  given  in  full  below. REPORT. In  the  preparation  of  this  report,  in  order  to  have  the  specifications  accord with  international  usage,  free  use  has  been  made  of  the  English  Govern- ment specifications  and  of  certain  papers  prepared  by  Dr.  K.  Kahle  of Germany,  and  Prof.  H.  S.  Carhart  of  this  country. SPECIFICATIONS  FOR  THE  PRACTICAL  APPLICATION  OF  THE DEFINITIONS  OF  THE  AMPERE  AND  VOLT. Specification  A. — The  Ampere. In  employing  the  silver  voltameter  to  measure  currents  of  about  1  ampere, the  following  arrangements  shall  be  adopted : The  kathode  on  which  the  silver  is  to  be  deposited  shall  take  the  form  of a  platinum  bowl  not  less  than  10  centimeters  in  diameter,  and  from  4  to  5 centimeters  in  depth. The  anode  shall  be  a  disk  or  plate  of  pure  silver  some  30  square  centi- meters in  area  and  2  or  3  millimeters  in  thickness. This  shall  be  supported  horizontally  in  the  liquid  near  the  top  of  the solution  by  a  silver  rod  riveted  through  its  center.  To  prevent  the  dis- integrated silver  which  is  formed  on  the  anode  from  falling  upon  the kathode,  the  anode  shall  be  wrapped  around  with  pure  filter  paper,  secured at  the  back  by  suitable  folding. The  liquid  shall  consist  of  a  neutral  solution  of  pure  silver  nitrate,  con- taining about  15  parts  by  weight  of  the  nitrate  to  85  parts  of  water. The  resistance  of  the  voltameter  changes  somewhat  as  the  current  passes. To  prevent  these  changes  having  too  great  an  effect  on  the  current,  some resistance  besides  that  of  the  voltameter  should  be  inserted  in  the  circuit. The  total  metallic  resistance  of  the  circuit  should  not  be  less  than  10  ohms. Method  of  making  a  measurement. — The  platinum  bowl  is  to  be  washed consecutively  with  nitric  acid,  distilled  water,  and  absolute  alcohol ;  it is  then  to  be  dried  at  160°  C,  and  left  to  cool  in  a  desiccator.  When thoroughly  cool  it  is  to  be  weighed  carefully. It  is  to  be  nearly  filled  with  the  solution  and  connected  to  the  rest  of  the circuit  by  being  placed  on  a  clean  insulated  copper  support  to  which  a binding  screw  is  attached. 1  Henry  A.  Rowland,  Chairman ;  Henry  L.  Abbot,  George  F.  Barker,  Charles S.  Hastings,  Albert  A.  Michelson,  John  Trowbridge,  Carl  Barus. 212    EVOLUTION   OF  WEIGHTS   AND   MEASURES The  anode  is  then  to  be  immersed  in  the  solution  so  as  to  be  well  covered by  it  and  supported  in  that  position  ;  the  connections  to  the  rest  of  the circuit  are  then  to  be  made. Contact  is  to  be  made  at  the  key,  noting  the  time.  The  current  is  to be  allowed  to  pass  for  not  less  than  half  an  hour,  and  the  time  of  breaking contact  observed. The  solution  is  now  to  be  removed  from  the  bowl  and  the  deposit  washed with  distilled  water  and  left  to  soak  for  at  least  six  hours.  It  is  then to  be  rinsed  successively  with  distilled  water  and  absolute  alcohol  and dried  in  a  hot-air  bath  at  a  temperature  of  about  160°  C.  After  cooling in  a  desiccator  it  is  to  be  weighed  again.  The  gain  in  mass  gives  the  silver deposited. To  find  the  time  average  of  the  current  in  amperes,  this  mass,  expressed in  grams,  must  be  divided  by  the  number  of  seconds  during  which  the current  has  passed  and  by  0*001 11 8. In  determining  the  constant  of  an  instrument  by  this  method,  the  current should  be  kept  as  nearly  uniform  as  possible,  and  the  readings  of  the instrument  observed  at  frequent  intervals  of  time.  These  observations give  a  curve  from  which  the  reading  corresponding  to  the  mean  current (time-average  of  the  current)  can  be  found.  The  current,  as  calculated  from the  voltameter  results,  corresponds  to  this  reading. The  current  used  iu  this  experiment  must  be  obtained  from  a  battery, and  not  from  a  dynamo,  especially  when  the  instrument  to  be  calibrated  is an  electrodynamometer. Specification  B.— The  Volt. Definition  and  properties  of  the  cell. — The  cell  has  for  its  positive  electrode, mercury,  and  for  its  negative  electrode,  amalgamated  zinc ;  the  electrolyte consists  of  a  saturated  solution  of  zinc  sulphate  and  mercurous  sulphate. The  electromotive  force  is  1*434  volts  at  15°  C,  and  between  10°  C.  and  25°  C, by  the  increase  of  1°  C.  in  temperature,  the  electromotive  force  decreases  by 0*00115  of  a  volt. 1.  Preparation  of  the  mercury. — To  secure  purity,  it  should  be  first  treated with  acid  in  the  usual  manner  and  subsequently  distilled  in  vacuo. 2.  Preparation  of  the  zinc  amalgam. — The  zinc  designated  in  commerce as  "  commercially  pure  "  can  be  used  without  further  preparation.  For  the preparation  of  the  amalgam,  1  part  by  weight  of  zinc  is  to  be  added  to 9  parts  by  weight  of  mercury,  and  both  are  to  be  heated  in  a  porcelain  dish at  100°  C,  with  moderate  stirring  until  the  zinc  has  been  fully  dissolved  in the  mercury. 3.  Preparation  of  the  mercurous  sulphate. — Take  mercurous  sulphate,  pur- chased as  pure  ;  mix  with  it  a  small  quantity  of  pure  mercury,  and  wash  the whole  thoroughly  with  cold  distilled  water  by  agitation  in  a  bottle ;  drain off  the  water  and  repeat  the  process  at  least  twice.     After  the  last  washing, INTERNATIONAL   ELECTRICAL   UNITS  213 drain   off  as   much   of   the   water   as    possible.      (For    further    details    of purification,  see  Note  A.) 4.  Preparation  of  the  zinc  sulphate  solution. — Prepare  a  neutral  saturated solution  of  pure  recrystallized  zinc  sulphate,  free  from  iron,  by  mixing distilled  water  with  nearly  twice  its  weight  of  crystals  of  pure  zinc  sulphate and  adding  zinc  oxide  in  the  proportion  of  about  2  per  cent,  by  weight  of  the zinc  sulphate  crystals  to  neutralize  any  free  acid.  The  crystals  should be  dissolved  with  the  aid  of  gentle  heat,  but  the  temperature  to  which the  solution  is  raised  must  not  exceed  30°  C.  Mercurous  sulphate,  treated as  described  in  3,  shall  be  added  in  the  proportion  of  about  12  per  cent, by  weight  of  the  zinc  sulphate  crystals  to  neutralize  the  free  zinc  oxide remaining,  and  then  the  solution  filtered,  while  still  warm,  into  a  stock bottle.     Crystals  should  form  as  it  cools. 5.  Preparation  of  the  mercurous  sulphate  and  zinc  sulphate  paste. — For making  the  paste,  2  or  3  parts  by  weight  of  mercurous  sulphate  are  to be  added  to  1  by  weight  of  mercury.  If  the  sulphate  be  dry,  it  is  to be  mixed  with  a  paste  consisting  of  zinc  sulphate  crystals  and  a  con- centrated zinc  sulphate  solution,  so  that  the  whole  constitutes  a  stiff  mass, which  is  permeated  throughout  by  zinc  sulphate  crystals  and  globules of  mercury.  If  the  sulphate,  however,  be  moist,  only  zinc  sulphate  crystals are  to  be  added  ;  care  must,  however,  be  taken  that  these  occur  in  excess and  are  not  dissolved  after  continued  standing.  The  mercury  must,  in this  case  also,  permeate  the  paste  in  little  globules.  It  is  advantageous to  crush  the  zinc  sulphate  crystals  before  using,  since  the  paste  can  then  be better  manipulated. To  set  up  the  cell. — The  containing  glass  vessel,  .  .  .  shall  consist  of two  limbs  closed  at  the  bottom  and  joined  above  to  a  common  neck  fitted with  a  ground-glass  stopper.  The  diameter  of  the  limbs  should  be  at least  2  centimeters  and  their  length  at  least  3  centimeters.  The  neck should  be  not  less  than  1*5  centimeters  in  diameter.  At  the  bottom  of each  limb  a  platinum  wire  of  about  0*4  millimeter  diameter  is  sealed through  the  glass. To  set  up  the  cell,  place  in  one  limb  pure  mercury  and  in  the  other hot  liquid  amalgam,  containing  90  parts  mercury  and  10  parts  zinc.  The platinum  wires  at  the  bottom  must  be  completely  covered  by  the  mercury and  the  amalgam  respectively.  On  the  mercury  place  a  layer  1  centimeter thick  of  the  zinc  and  mercurous  sulphate  paste  described  in  5.  Both  this paste  and  the  zinc  amalgam  must  then  be  covered  with  a  layer  of  the neutral  zinc  sulphate  crystals  1  centimeter  thick.  The  whole  vessel  must then  be  filled  with  the  saturated  zinc  sulphate  solution,  and  the  stopper inserted  so  that  it  shall  just  touch  it,  leaving,  however,  a  small  bubble to  guard  against  breakage  when  the  temperature  rises. Before  finally  inserting  the  glass  stopper  it  is  to  be  brushed  around its  upper  edge  with  a  strong  alcoholic  solution  of  shellac  and  pressed  firmly in  place.     (For  details  of  filling  the  cell,  see  Note  B.) 214    EVOLUTION   OF  WEIGHTS   AND   MEASURES NOTES  TO  THE   SPECIFICATIONS. (A)  The  mercurous  sulphate. — The  treatment  of  the  mercurous  sulphate has  for  its  object  the  removal  of  any  mercuric  sulphate  which  is  often present  as  an  impurity. Mercuric  sulphate  decomposes  in  the  presence  of  water  into  an  acid  and a  basic  sulphate.  The  latter  is  a  yellow  substance — turpeth  mineral — practically  insoluble  in  water ;  its  presence,  at  any  rate  in  moderate quantities,  has  no  effect  on  the  cell.  If,  however,  it  be  formed,  the  acid sulphate  is  also  formed.  This  is  soluble  in  water,  and  the  acid  produced affects  the  electromotive  force.  The  object  of  the  washings  is  to  dissolve and  remove  this  acid  sulphate,  and  for  this  purpose  the  three  washings described  in  the  specification  will  suffice  in  nearly  all  cases.  If,  however, much  of  the  turpeth  mineral  be  formed,  it  shows  that  there  is  a  great deal  of  the  acid  sulphate  present,  and  it  will  then  be  wiser  to  obtain  a fresh  sample  of  mercurous  sulphate,  rather  than  to  try  by  repeated  washings to  get  rid  of  all  the  acid. The  free  mercury  helps  in  the  process  of  removing  the  acid,  for  the acid  mercuric  sulphate  attacks  it,  forming  mercurous  sulphate. Pure  mercurous  sulphate,  when  quite  free  from  acid,  shows  on  repeated washing  a  faint  yellow  tinge,  which  is  due  to  the  formation  of  a  basic mercurous  salt  distinct  from  the  turpeth  mineral,  or  basic  mercuric  sulphate. The  appearance  of  this  primrose-yellow  tint  may  be  taken  as  an  indication that  all  the  acid  has  been  removed ;  the  washing  may  with  advantage be  continued  until  this  tint  appears. (B)  Filling  the  cell. — After  thoroughly  cleaning  and  drying  the  glass vessel,  place  it  in  a  hot-water  bath.  Then  pass  through  the  neck  of  the vessel  a  thin  glass  tube  reaching  to  the  bottom,  to  serve  for  the  introduction of  the  amalgam.  This  tube  should  be  as  large  as  the  glass  vessel  will admit.  It  serves  to  protect  the  upper  part  of  the  cell  from  being  soiled with  the  amalgam.  To  fill  in  the  amalgam,  a  clean  dropping  tube  about 10  centimeters  long,  drawn  out  to  a  fine  point,  should  be  used.  Its  lower end  is  brought  under  the  surface  of  the  amalgam,  heated  in  a  porcelain dish,  and  some  of  the  amalgam  is  drawn  into  the  tube  by  means  of  the rubber  bulb.  The  point  is  then  quickly  cleaned  of  dross  with  filter  paper, and  is  passed  through  the  wider  tube  to  the  bottom  and  emptied  by  pressing the  bulb.  The  point  of  the  tube  must  be  so  fine  that  the  amalgam  will come  out  only  on  squeezing  the  bulb.  This  process  is  repeated  until  the limb  contains  the  desired  quantity  of  amalgam.  The  vessel  is  then removed  from  the  water  bath.  After  cooling,  the  amalgam  must  adhere to  the  glass,  and  must  show  a  clean  surface  with  a  metallic  luster. For  insertion  of  the  mercury,  a  dropping  tube  with  a  long  stem  will be  found  convenient.  The  paste  may  be  poured  in  through  a  wide  tube reaching  nearly  down  to  the  mercury  and  having  a  funnel-shaped  top. If  the  paste  does  not  move  down  freely  it  may  be  pushed  down  with  a INTERNATIONAL   ELECTRICAL   UNITS  215 small  glass  rod.  The  paste  and  the  amalgam  are  then  both  covered  with the  zinc  sulphate  crystals  before  the  concentrated  zinc  sulphate  solution is  poured  in.  This  should  be  added  through  a  small  funnel,  so  as  to leave  the  neck  of  the  vessel  clean  and  dry. For  convenience  and  security  in  handling,  the  cell  may  be  mounted  in a  suitable  case,  so  as  to  be  at  all  times  open  to  inspection. In  using  the  cell,  sudden  variations  of  temperature  should,  as  far  as possible,  be  avoided,  since  the  changes  in  electromotive  force  lag  behind those  of  temperature. Somewhat  similar  specifications  were  prepared  by  the  Board  of Trade  of  Great  Britain  and  were  promulgated  in  an  Order in  Council,  August  23,  1894.  The  chief  points  of  difference besides  phraseology  were  in  the  specifications  for  the  Clark  cell, but  these  were  in  no  way  radical.  Canada  also  adopted  regula- tions essentially  in  harmony  with  the  above,  as  did  France, Austria,  and  Belgium ;  while  in  Germany  the  measure  of  current was  made  of  prime  importance,  and  the  specifications  for  the silver  voltameter  and  the  method  of  measurement  are  somewhat modified.1 At  the  Paris  International  Electrical  Congress  of  1900  it  was decided  to  give  the  name  of  Gauss  to  the  C.G.S.  unit  of  magnetic field  intensity,  or  to  such  a  field  as  would  be  produced  by  the unit  of  magnetism  at  the  distance  of  one  centimeter,  or,  in  other words,  such  a  field  as  would  act  on  a  unit  pole  with  the  force  of one  dyne.  Likewise  the  same  congress  gave  sanction  to  the name  of  Maxwell  to  denote  the  C.G.S.  unit  of  magnetic  flux  or the  number  of  magnetic  lines  within  a  tube  of  force.  The magnetic  flux  would  consequently  be  equal  to  the  product  of  the intensity  of  the  field  by  the  area,  and  the  unit  would  be  a  single magnetic  line.  Thus  magnetic  flux  would  correspond  to  current, being  dependent  on  the  magnetomotive  force  and  the  magnetic reluctance.  This  step  was  taken  as  these  C.G.S.  units  were employed  in  actual  practice  and  apparatus  was  in  common  use by  means  of  which  field  intensities  could  be  measured  directly. The  name  Jcilogauss  is  also  employed  to  denote  a  thousand  times the  unit.  Other  propositions  have  been  made  for  names  for  the C.G.S.  magnetic  units,  but  they  have  not  yet  been  adopted  legally 1  The  full  text  of  the  various  laws  and  regulations  will  be  found  in  the Appendix  to  Wolff's  paper  on  the  "So-called  International  Electrical  Units," Bulletin  of  the  Bureau  of  Standards  (Washington,  1901),  No.  1,  vol.  1,  pp.  61-76. 216    EVOLUTION   OF   WEIGHTS   AND   MEASURES as  they  have  not  been  considered  essential,  though  strenuously urged  by  many  prominent  electricians. After  the  adoption  of  the  resolution  defining  the  electrical units,  at  the  Electrical  Congress  held  at  Chicago  in  1893,  and their  subsequent  ratification,  either  in  whole  or  in  part,  by  various governments,  it  was  found  that  there  were  slight  errors  in  these definitions,  especially  in  the  electromotive  force  of  the  Clark cell,  which  has  been  found  to  be  nearer  1*433  volts  than  1*434  as defined.  It  was  stated  by  some  physicists  that  a  cadmium (Weston)  cell1  was  more  constant,  had  a  lower  temperature coefficient,  and  could  be  defined  with  greater  accuracy,  while further  researches  on  the  Clark  cell  itself  gave  a  value  for  its electromotive  force  somewhat  different  from  that  stated  in  the resolutions ;  and,  in  fact,  in  Germany  the  value  1*4328  volts  was adopted  as  corresponding  to  the  realized  value  of  the  ohm  and ampere.  There  was  also  a  demand  for  new  units,  and  for  changes in  the  nomenclature  in  the  existing  units.  Consequently,  at  the Electrical  Congress  held  in  connection  with  the  St.  Louis  Exposi- tion, 1904,  a  chamber  of  representatives  of  various  governments was  in  session  to  pass  upon  these  propositions.  It  was  the opinion  of  the  Chamber  of  Delegates  that  these  propositions  were of  sufficient  character  to  warrant  a  thorough  discussion,  but,  at the  same  time,  the  delegates  did  not  seem  to  be  of  the  opinion that  they  should  be  settled  at  such  a  meeting.  Accordingly,  they resolved  that  a  permanent  Commission,  consisting  of  representa- tives from  various  governments,  should  be  convened,  and  that  to such  an  International  Commission  should  be  entrusted  the  decision of  the  matter.  Such  an  international  body  would  have  much  the same  duties  as  the  International  Commission  of  Weights  and Measures,  and,  without  doubt,  its  deliberations  and  decisions would  be  equally  acceptable  and  important  to  electricians  and physicists. In  concluding  this  chapter  on  electrical  units  it  is  hardly necessary  to  more  than  call  attention  to  the  great  benefits  that 1  The  Weston  cell  has  for  its  electrodes  cadmium  amalgam  covered  with  a layer  of  crystals  of  cadmium  sulphate,  and  pure  mercury  in  contact  with  a  paste of  mercurous  sulphate,  cadmium  sulphate  crystals,  and  metallic  mercury,  while the  electrolyte  is  a  saturated  aqueous  solution  of  zinc  sulphate  and  mercurous sulphate. INTERNATIONAL  ELECTRICAL   UNITS  217 have  been  conferred  on  the  electrical  industry  throughout  the world  by  the  employment,  in  all  countries,  of  one  and  the  same system  of  units  of  measurement.  In  fact,  this  condition  has  been advanced  as  one  of  the  reasons  for  the  rapid  growth  of  the industry,  and  while  various  modifications  of  units  have  been demanded  and  discussed,  they  have  only  been  adopted  after  they have  been  determined  by  an  International  Congress.  No  nation or  group  of  electricians  or  engineers  has  ever  found  fault  with the  extensive  use  of  the  decimal  system,  and  by  the  close  con- nection of  electrical  units  with  the  metric  system  such  workers have  been  enabled  to  appreciate  the  advantages  of  the  latter,  so that  in  non-metric  countries  the  electrical  professions  unanimously are  found  eagerly  demanding  its  adoption.  In  fact,  it  has  been truly  said  by  a  British  electrical  engineer,1  than  whom  there  is no  one  more  competent  to  discuss  the  subject  in  its  many  aspects, that  "  so  far  as  I  am  aware  nobody  has  ever  suggested  that  it would  be  to  the  advantage  of  any  country  to  start  a  system  of electrical  units  of  its  own." 1  Alexander  Siemens,  Presidential  Address  before  the  Institution  of  Electrical Engineers  of  Great  Britain,  Nov.  10,  1904,  Electrician  (London),  Nov.  11,  1904, p.  149. CHAPTEE    X. STANDARDS  AND  COMPARISON. In  all  systems  of  weights  and  measures  based  on  one  or  more arbitrary  fundamental  units,  the  concrete  representation  of  the unit  in  the  form  of  a  standard  is  necessary,  and  the  construction and  preservation  of  such  a  standard  is  a  matter  of  primary importance.  The  reference  of  all  measures  to  an  original  standard is  essential  for  their  correctness,  and  such  a  standard  must  be maintained  and  preserved  in  its  integrity  for  purposes  of  com- parison by  some  responsible  authority,  which  is  thus  able  to provide  against  the  use  of  false  weights  and  measures.  Accord- ingly, from  earliest  times,  standards  were  constructed  and  pre- served under  the  direction  of  kings  and  priests,  and  the  temples were  a  favorite  place  for  their  deposit.  Later,  this  duty  was assumed  by  the  government,  and  to-day  in  addition  we  find  the integrity  of  standards  of  weights  and  measures  safeguarded  by international  agreement. The  progress  of  the  science  of  metrology  is  not  only  well exemplified  in  these  actual  representations  of  various  units,  but is  intimately  connected  with  the  construction  of  the  prototypes  of the  fundamental  standards.  The  mechanical  processes  and  other features  involved  in  their  construction  have  so  improved  with time  and  with  the  growth  of  physical  science,  especially  as  it involves  a  constantly  increasing  degree  of  exactness  in  measuring, that  the  subject  is  one  which  warrants  attention  in  even  a  brief treatise  on  weights  and  measures.  In  fact,  metrology  has  been defined  as :  "  That  part  of  the  science  of  measures  which  applies itself  specially  to  the  determinations  of  prototypes  representative of  the  fundamental  units  of  dimensions  and  of  mass,  of  the standards  of  the  first  order  which  are  derived  from  the  same,  and are    employed    in    experimental    researches,    aiming    at    a    high STANDARDS   AND   COMPARISON  219 exactitude,  as  well  as  to  the  operations  of  diverse  natures  which are  the  necessary  corollaries." 1 That  a  standard  should  exactly  represent  a  unit  is  of  course obvious,  and  what  is  usually  the  case,  the  definition  of  the  unit  is derived  from  the  standard,  as  is  the  definition  of  the  British imperial  yard  or  the  modern  definition  of  the  meter.  Therefore it  is  essential  that  the  standard  should  be  so  constructed  as  to  be as  nearly  permanent  and  invariable  as  human  ingenuity  can  con- trive. As  an  example  of  the  lack  of  permanence  experienced  in standards,  attention  might  be  called  to  the  fact  that  the  secondary standards  of  the  British  yard  of  1855,  which  were  distributed  to the  various  nations  and  laboratories,  have  since  undergone  careful comparisons  and  remeasurements,  and  it  is  believed  that  in  many cases  their  lengths  are  not  the  same  as  when  they  were  first constructed.2 While  it  is  physically  impossible  to  secure  absolute  invari- ability in  standards,  yet  in  their  construction  a  material  should  be chosen  whose  variations  are  well-determined  functions  of  one  or more  independent  variables  easy  to  measure.  In  practice,  these variations  themselves  ought  to  be  very  small,  and  the  variables upon  which  they  depend  susceptible  of  being  determined  with high  precision.  The  realization  of  these  conditions  represents essentially  what  has  been  accomplished  by  the  advance  of  metro- logical  science  so  far  as  exactness  in  standards  is  involved.  In the  past,  as  we  have  seen,  an  extreme  degree  of  precision  in measurement  was  not  essential,  nor  could  it  be  obtained  with  the means  at  the  disposal  of  the  scientist  or  mechanician,  but improvements  in  this  branch  of  science  have  been  made  to  such  an extent  that  within  two  centuries  the  precision  of  standards  of  length has  been  increased  nearly  a  thousand  fold.  With  the  growth  of knowledge,  it  was  realized  that  matter  varied  to  a  marked  degree under  the  influences  of  temperature,  pressure,  time,  and  other conditions,  so  that  in  consequence,  not  only  a  unit  must  be  defined precisely,  but  the  appropriate  standard  and  its  copies  be  so  con- 1J.  Rene  Benoit,  "  De  la  Precision  dans  la  Determination  des  Longuers  en Metrologie,"  p.  31,  Rapports  pre'sente's  au  Congres  International  de  Physique,  tome 1,  Paris,  1900. 2 See  Report,  Superintendent  U.S.  Coast  and  Geodetic  Survey,  1877.  Appendix 12,  pp.  180-181. 220    EVOLUTION   OF   WEIGHTS   AND   MEASURES structed  that  they  would  be  permanent,  invariable  and  exact.  In designing  and  constructing  a  standard  to  fill  these  demands  there would  be,  consequently,  a  number  of  conditions  to  be  satisfied. First,  there  would  be  the  natural  wear  of  time,  which  would  alter easily  the  length  of  a  measure  or  the  mass  of  a  weight,  and  could only  be  guarded  against  by  selecting  a  hard  and  durable  material which  would  resist  abrasion.  Then,  there  would  be  the  question of  temperature  effects,  most  important  in  all  metrological  work, but  hardly  realized  before  the  beginning  of  the  18th  century.  For it  will  be  remembered  that,  at  different  temperatures,  a  body varies  in  length  and  volume,  so  that  a  standard  of  length,  for example,  is  only  of  unit  length  at  one  stated  and  defined  tempera- ture, being  too  long  at  a  higher  temperature  and  too  short  at  a lower  temperature.  Consequently,  it  is  desirable  that  a  standard should  be  of  a  material  affected  as  little  as  possible  by  heat,  or, in  scientific  language,  having  a  low  and  regular  coefficient  of expansion,  and  it  is  essential  that  this  amount  of  expansion should  be  known  accurately,  so  that  in  case  the  standard  is  used at  other  temperatures  than  that  of  the  definition,  the  amount  that it  is  too  large  or  too  small  may  be  taken  into  consideration  and allowed  for,  as  by  knowing  accurately  and  applying  the  factor which  represents  the  variation  in  length,  a  measurement  may  be made  as  exact  as  the  original  measurement  on  which  the  standard is  based.  It  is  therefore  necessary  to  exclude  from  consideration materials  having  coefficients  of  expansion  which  vary  con- siderably at  different  temperatures,  or  which  expand  at  a different   rate  from  that  with  which  they  contract. The  prime  condition  of  a  standard  of  length,  and  the  same  is essentially  true  of  standards  of  mass,  is  that  it  should  consist  of  a single  bar,  or  piece  of  a  single  material,  avoiding  any  joining  of several  elements,  such  as  by  screws  or  by  soldering.  In  fact,  the method  used  at  the  beginning  of  the  19th  century,  whereby  a  strip of  silver  was  inlaid  on  a  brass  bar,  as  in  the  Troughton  scale,  after the  fashion  of  the  graduated  circles  of  various  modern  instruments, was  soon  found  unsuitable  for  the  standards  of  higher  precision which  were  demanded.  The  material  selected  should  not  only  be hard  and  highly  elastic,  but  should  have  a  surface  that  can  be polished  readily,  and  engraved  with  the  marks  of  terminal  limits, or  of  the  divisions  of  the  unit.     For  many  years  it  was  customary STANDARDS   AND   COMPARISON  221 to  construct  the  standards  of  iron  or  of  brass — materials  which were  easily  oxidizable,  and  which  were  with  difficulty  obtained  in a  pure  and  constant  condition.  For  the  standard  of  the  meter, known  as  the  Meter  of  the  Archives,  platinum  was  used  ;  but  later, the  material  best  suited  for  a  standard  was  found  to  be  an  alloy of  platinum  and  iridium,  and  such  was  used  for  the  international prototype  meter  and  kilogram  and  the  national  standards  copied therefrom.  This  material,  however,  being  extremely  expensive, cannot  be  used  generally  where  secondary  standards  for  ordinary exact  measurements  are  desired,  nor  can  rock  crystal  of  which  a few  standards  of  mass  have  been  constructed. A  recent  study  of  alloys,  however,  has  resulted  in  finding materials  which  possess  many  of  the  desired  properties,  such  as hardness  and  durability,  and  at  the  same  time  have  a  low coefficient  of  expansion.  One  of  the  most  recent  of  these,  known as  invar,  has  resulted  from  experiments  carried  on  at  the International  Bureau  of  Weights  and  Measures,  and  has  been developed  to  a  high  degree  of  usefulness  by  M.  Guillaume.  This metal,  which  consists  of  36  parts  of  nickel  to  64  of  steel,  has  been found  available  for  measuring  rods  and  wires  for  use  in  geodetic operations,  and  seems  destined  to  occupy  a  much  wider  field  in the  future.  Wires  for  measuring  base  lines  made  of  this  alloy have  been  found  to  possess  a  coefficient  of  expansion  in  some cases  as  low  as  '0000001  for  a  degree  centigrade.1  In  1900  invar standards  and  gauges  were  put  on  the  market,  and  for  all  prac- tical purposes  permitted  the  disregarding  of  temperature  effects. In  fact,  it  has  been  proposed  to  employ  a  heavy  bar  of  this material  as  the  support  of  the  observing  microscopes  in  a  com- parator. Invar,  however,  is  not  quite  steady  and  constant  and cannot  be  used  for  primary  standards.  In  accurate  surveying such  standards  should  be  determined  just  before  and  after  using in  the  field. From  the  early  standards  of  length  rectangular  or  cylindrical in  form,  much  improvement  has  been  made  and  care  is  now taken  that  the  cross-section  of  the  bar  shall  be  of  such  design 1See  Guillaume,  "  Les  Procedes  Rapides  de  la  Geodesie  Moderne,"  La  Nature (Paris),  1904,  No.  1640,  p.  339,  and  No.  1643,  p.  395;  id.,  Les  Applications  des Aciers  au  Nickel,  avec  un  Appendice  sur  la  The'orie  des  Aciers  au  Nickel  (Paris, 1904)  ;  id.,  La  Convention  du  Metre  (Paris,  1902),  pp.  127  and  233. 222    EVOLUTION   OF   WEIGHTS   AND   MEASURES that  not  only  it  shall  possess  maximum  strength,  but  especially that  it  will  resist  deformation  by  bending,  which  in  accurate measurements  may  cause  considerable  error.  Thus  in  a  linear scale  of  considerable  length  as  compared  with  its  breadth  and thickness  and,  let  us  say,  of  rectangular  section,  where  the divisions  are  on  the  upper  surface,  it  will  be  obvious  that  if  it  is so  supported  that  the  ends  hang  lower  than  the  centre,  the  upper surface  will  form  a  convex  curve,  and  the  particles  of  the  material lying  in  such  a  surface  will  be  stretched  apart,  and  the  distance  A to  B  will  be  greater  than  when  the  bar  is  straight  as  under normal  conditions. If  the  ends  of  the  scale  were  supported,  rather  than  the  centre, the  opposite  conditions  would  prevail,  and  the  marked  distance will  be  too  short.  This  was  recognised  by  Captain  Kater,  who proposed  the  employment  of  a  scale  of  small  thickness  which  was placed  on  a  base  whose  surface  was  perfectly  plane.1  A  better solution  of  the  difficulty  was  to  use  the  neutral  fibres,  as  shown by  the  dotted  line  CD,  and  for  this  purpose  the  British  standard of  1855  was  constructed,  as  shown  on  pages  245  and  246,  where  the unit  distance  is  measured  between  lines  on  polished  gold  plugs,  set in  two  holes  or  wells,  so  that  they  lie  in  this  so-called  neutral  plane. This  idea  was  more  perfectly  carried  out  in  the  standards  of the  International  Metric  Commission,  having  the  X-section  as shown  on  page  254,  where  the  construction  is  such  that  the  bar possesses  maximum  rigidity  with  the  minimum  material  and  the neutral  plane  in  the  line  standard  is  easily  accessible  for  measure- ments throughout  its  length.  In  standards  for  small  lengths,  such as  the  decimeter,  such  considerations  as  a  desirable  type  of  cross- section  and  the  placing  of  the  divisions  in  a  neutral  plane, naturally  do  not  require  careful  consideration  and  can  practically 1See  Kater,  "Investigation  of  the  Curvature  of  Bars,  produced  by  the  In- equalities of  the  supporting  surface,"  Phil.  Trans.,  1830,  p.  359.  See  also  W.  A. Rogers,  Proc.  Amer.  Acad.  Arts  and  Sciences,  vol.  xv.  1879-80,  p.  292. STANDARDS   AND   COMPARISON  223 be  neglected,  but  in  meter  or  yard  standards  it  is  an  important consideration. Then,  as  regards  the  actual  means  of  denoting  the  distance,  we may  have  end  standards  (Stalon  a  touts)  and  line  standards  (4talon a  traits).  The  end  standard  represents  the  given  unit  by  the distance  between  the  extreme  boundary  surfaces,  as  in  the  case  of any  ordinary  rule,  or  in  the  case  of  the  inside  measure, — the distance  between  the  interior  surfaces  of  two  extended  arms, — the object  being  to  secure  better  protection  for  the  surfaces  employed for  measurement,  and  at  the  same  time,  to  furnish  a  ready  means of  comparing  end  measures  with  a  standard,  by  simply  bringing them  within  the  space  included  between  the  terminal  arms. With  the  other  form  of  standard,  the  limits  of  the  distance  are indicated  by  lines  or  sometimes  dots.  The  line  standard,  of course,  can  be  used  with  a  microscope  with  cross-hairs,  or  a micrometer  microscope,  much  more  readily  than  an  end  standard, as  it  is  possible  to  effect  an  exact  setting  on  even  a  coarse line  with  much  greater  accuracy  than  on  an  edge,  which though  imperceptibly  worn  to  the  naked  eye,  would  appear rough  and  indistinct  when  magnified  by  the  microscope. The  line  standard  possesses  a  distinct  advantage,  where  it  is divided  throughout  its  whole  length,  as  is  usually  the  case,  since it  is  readily  comparable  with  its  own  sub-divisions  and  with smaller  standards.  On  the  other  hand,  the  end  standard  con- stitutes merely  a  standard  for  a  single  length,  and  does  not  lend itself  to  direct  comparisons  with  the  ordinary  standards  of  other lengths  in  the  laboratory  or  testing  bureau,  which  in  the  case  of metric  scales  are  usually  divided  into  millimeters,  with  the  centi- meters and  decimeters  suitably  marked.  With  a  standard  so divided,  standards  of  measure  for  other  distances  besides  the greatest  one  marked  on  its  surface  must  be  supplied. In  spite  of  the  general  tendency  to  use  a  line  standard,  rather than  an  end  standard,  Bessel,  in  1835,  when  he  was  preparing  a standard  based  on  the  seconds  pendulum  at  Koenigsberg,  used  a steel  bar  with  sapphires  set  in  its  ends,  to  form  a  standard  of  length. This  standard  of  Koenigsberg  was  used  as  a  basis  for  numerous measurements  of  base  lines  in  geodetic  surveys  in  Europe.1 Though   the  line   standard   forms   the   most   suitable,  and   in 1  P.  9,  Guillaume,  La  Convention  du  Metre. 224    EVOLUTION   OF  WEIGHTS   AND   MEASURES fact  the  only,  standard  for  a  modern  prototype,  and  even  for secondary  purposes,  there  are  nevertheless  occasions  where  stan- dards of  the  end  type  can  be  conveniently  used.  Especially  is this  the  case  in  mechanical  engineering,  where  various  gauges and  shop  standards  must  be  constructed  so  as  to  be  used  readily in  the  tool-room  or  machine  shop  for  accurate  measurements. The  methods  of  comparison  are  essentially  similar  to  those employed  in  comparing  line  standards.  However,  certain variations  of  methods  have  been  introduced,  since  it  is necessary  to  consider  the  terminal  faces,  which  are  susceptible of  wear  and  must  be  protected  carefully.  In  addition  to  the use  of  the  microscope  comparator,  which  is  described  below, in  connection  with  line  standards,  there  are  three  methods which  can  be  used  for  this  purpose,  as  follows : First,  the  method  of  direct  contact,  which,  while  the  simplest, can  also  be  made  very  accurate  if  properly  used. Second,  by  reflection  of  an  object  at  the  terminal  surface. Third,  by  interference  fringes  which  are  produced  at  the ends  of  the  scale  to  be  measured. In  the  method  of  contact,  which  is  ordinarily  employed where  a  high  degree  of  precision  is  unnecessary,  it  is  usual to  employ  such  simple  measuring  devices  as  a  screw  micro- meter, or  a  spherometer,  or  some  less  accurate  form  of  instru- ment, such  as  calipers  or  a  beam  compass.  The  second  and third  methods  are  optical,  and  must  be  executed  by  a  trained physicist ;  but  they  increase  materially  the  range  of  precision, and  can  afford  results  more  accurate  than  are  obtained  in comparing  line  standards. The  method  of  reflection  was  employed  in  comparing  the Meter  of  the  Archives,  an  end  standard,  with  the  provisional meter  for  the  construction  of  the  international  prototype,  and also  subsequently  in  the  standardizing  of  certain  end  standards of  platinum-iridium,  which  were  given  to  such  nations  as  had ordered  them.  This  method  consisted  in  observing  the  dis- placement of  the  reflection  of  a  line  at  the  terminal  surface of  the  bar;  and  while  under  certain  circumstances  it  was exact,  it  required  a  study  of  the  objectives  of  the  microscope and  other  features  in  order  to  insure  its  accuracy. Employing   this   method,  in  1881-82,  a  series  of  comparisons STANDARDS   AND   COMPARISON  225 of  the  new  standards  was  made  at  the  Conservatoire  des  Arts ot  Metiers  with  the  Meter  of  the  Archives,  taking  into  con- sideration most  carefully  the  question  of  temperature.  It  was found  that  these  comparisons,  when  reduced  to  0  degrees  C, gave  an  accuracy  of  *6   of  a  micron  for  each  standard. In  the  method  of  interference  use  is  made  of  the  phenomenon •of  Newton's  rings,  whereby  interference  of  light  follows  differ- ences in  the  path  of  a  beam,  such  as  may  be  produced  by reflection  from  two  different  surfaces.  It  is  necessary  to  have ■a  fixed  and  determined  surface  as  a  plane  of  reference,  and  then to  consider  the  difference  in  the  fringes  that  are  produced by  light  falling  on  two  other  surfaces  at  different  times. Considering  now  a  line  standard  constructed,  of  approved material  and  cross-section,  it  is  naturally  of  primary  import- ance to  provide  the  marks  accurately  limiting  the  distance. These  marks  or  traces  are  usually  made  with  a  diamond,  and are  transverse  to  the  axis  of  the  bar.  The  method  employed is  to  place  the  bar,  with  the  standard  by  which  it  is  graduated, •on  the  carriage  of  a  special  piece  of  apparatus,  such  as  a  com- parator or  dividing  engine,  which  will  be  described  below  more fully,  with  the  cross-hairs  of  one  of  the  microscopes  accurately •over  the  line  of  the  standard  scale.  After  a  mark  is  made on  the  scale  to  be  graduated,  both  scales  are  moved  until  the second  mark  of  the  standard  scale  is  under  the  cross-hairs, and  another  ruling  is  then  made  by  the  diamond.  Or  the scales  may  remain  stationary  and  the  microscope  and  tracing device  be  moved. To  divide  a  scale  into  millimeters  or  other  divisions  the dividing  engine  is  employed,  an  instrument  in  which  the •essential  feature  consists  of  an  accurately  constructed  screw, whose  pitch  (i.e.  distance  between  threads),  as  well  as  its oonstant  and  periodic  errors,  are  known  to  a  high  degree  of precision.  This  screw,  working  in  a  suitable  nut,  moves  a table  along  a  heavy  metal  supporting  bench,  and  a  metal  or glass  bar  on  this  table  can  be  moved  forward  by  regular  and successive  intervals  of  length.  Above  the  table  is  a  tracing device  operating  in  a  fixed  vertical  plane,  and  by  this  means the  desired  divisions  may  be  inscribed  on  the  bar.  Apparatus of  this  kind  has   been  constructed  which  is  entirely  automatic p 226    EVOLUTION   OF   WEIGHTS   AND   MEASURES in  its  movements,  and  which  is  able  to  mark  the  divisions in  millimeters  on  a  scale  a  meter  in  length.  Such  machines have  means  of  correcting  the  errors  in  the  screw,  whether they  are  constant  or  occur  at  different  intervals  of  its  length, and  also  devices  permitting  corrections  for  temperature.  Often these  machines  are  driven  by  an  electric  motor,  and  even  the differences  in  length  of  the  marks  denoting  divisions  of  the scale — as,  for  example,  at  every  tenth  millimeter — are  made longer  automatically.  A  meter  scale  divided  into  millimeters can  be  ruled  with  a  machine  of  this  description  in  the  Inter- national Bureau  of  Weights  and  Measures,  in  about  sixteen  hours,, with  an  accuracy  of  two  or  three  microns  for  each  division.1 With  the  dividing  engine  or  ruling  machine  of  the  late  Pro- fessor H.  A.  Eowland  of  the  Johns  Hopkins  University,  designed for  constructing  diffraction  gratings  for  spectroscopic  work  rather than  for  making  linear  scales,  as  many  as  20,000  lines  to  the  inch,. 787*5  to  the  millimeter,  could  be  ruled  on  speculum  metal,  and gratings  having  as  many  as  120,000  lines  have  been  made  where- the  estimated  error  between  any  two  lines  was  not  thought  to exceed  2000000  °^  an  mcn>  or  nearly  the  80q0q  of  a  millimeter.2 To  secure  the  best  results,  the  surface  of  the  standard  or  scale on  which  the  lines  are  traced  should  be  highly  polished,  and  great care  should  be  taken,  not  only  in  the  choice  of  the  diamond  or tracing-tool,  but  in  the  actual  operation.  The  line  made  should be  clear  and  sharp,  not  broader  than  is  absolutely  necessary,  and not  appearing  rough  and  indistinct  when  seen  under  the  micro- scope. In  the  national  standard  prototypes  of  the  meter  this  line- measures  from  6  to  8  microns  in  width,  but  after  it  had  been ruled,  it  was  thought  that  a  much  narrower  line,  say  2  or  & microns,  could  have  been  used  with  advantage, — securing,  of course,  a  sufficient  depth  to  insure  the  permanent  preservation  of the  line.  On  both  sides  of  the  line  at  a  distance  of  *5  mm. are   two  parallel   and   similar  lines,  the   distance   between  them 1M.  Guillaume  says,  "It  is  essential  in  order  to  get  very  good  lines  to  trace very  slowly,  and  in  the  studies  made  at  the  Bureau  International  it  has  been found  useful  to  trace  the  1000  lines  of  the  meter  in  millimeters  in  about  16  hours. The  inaccuracy  in  the  position  of  either  end  line  does  not  exceed  two  or  three microns,  but  of  course  the  error  of  every  interval  of  1  mm.  is  much  smaller." 2  See  The  Physical  Papers  of  Henry  A.  Rowland  (Baltimore,  1902),  pp.  506-51 1„ 691-697. STANDARDS   AND   COMPARISON  227 forming  a  standard  millimeter  at  each  end  of  the  scale,  which furnishes  a  check  on  the  micrometer  of  the  microscopes  of  the comparator  used  to  compare  the  scales.  These  transverse  lines are  crossed  by  two  longitudinal  lines  parallel  to  the  axis  of  the bar,  and  distant  from  each  other  *2  of  a  millimeter.  Between the  intersections  of  these  lines  with  the  transverse  lines  is  where the  standard  distance  is  measured. The  important  part  played  by  temperature  in  exact  determina- tions and  comparisons  of  standards  of  length,  as  well  as  of  mass, of  course  involves  a  means  of  measuring  such  temperatures.  This subject  has  received  increasing  attention  in  the  course  of  time, and  it  has  been  realized  that  exactitude  in  constructing  standards of  length  is  only  possible  where  the  most  accurate  methods  of temperature  measurements  are  employed,  as  the  changes  in  length or  volume  with  temperature  of  course  produces  marked  variations from  the  standard  unit.  Since  a  linear  unit  is  represented  by  the length  of  a  standard  or  bar  of  metal  at  a  fixed  and  defined  temper- ature, at  no  other  temperature  will  this  bar  have  the  standard length,  and  consequently  its  exact  length  at  such  other  tempera- ture can  only  be  ascertained  by  knowing  the  amount  that  it expands  for  a  unit  (degree)  of  temperature,  and  the  precise temperature  at  which  the  measurement  is  made.  Accordingly, two  thermometric  measurements  of  great  precision  are  involved, one  in  determining  the  expansion  of  the  material  forming  the standard,  or  obtaining  the  coefficient  of  expansion  of  the  bar, and  the  other,  in  measuring  the  temperature  at  which  the  bar  is used.  Now  as  the  coefficient  of  expansion  enters  as  a  direct factor  in  determining  the  exact  length  of  a  standard,  it  is necessary  to  consider  how  far  we  can  depend  upon  its  accuracy, and  to  realize  that  if  this  factor  cannot  be  trusted  beyond  a certain  figure  of  decimals,  then  refinement  of  measuring  with  the micrometer  is  quite  superfluous. In  the  first  attempts  at  accurate  measurement  and  comparison of  standards,  as  soon  as  temperature  effects  began  to  be  considered, mercury-in-glass  thermometers  were  used,  and  in  them  for  many years  a  confidence  was  placed,  which  has  been  since  found entirely  unwarranted.  The  gravity  of  this  matter  was  realized by  physicists  toward  the  middle  of  the  19th  century,  and  at  the time  of  the  construction  of  the  international  standards,  it  was 228    EVOLUTION   OF  WEIGHTS   AND   MEASURES considered  necessary  to  undertake  a  complete  study  of  the mercury-in -glass  thermometer,  and  find  within  what  limits  its accuracy  could  be  trusted.  So  many  sources  of  error  were  found in  the  instruments  as  then  constructed,  due  to  the  material  used, and  to  differences  in  its  behaviour  at  different  temperatures,  as well  as  to  the  difference  in  the  coefficient  of  expansion  of  mercury at  different  temperatures,  that  it  was  found  necessary,  after  a most  thorough  investigation,  to  adopt  a  gas  thermometer  in  which hydrogen  was  used  as  the  expanding  fluid.  In  this  the  expansion of  the  gas  indicates  the  temperature,  and  within  certain  limits  it is  far  more  accurate  than  the  mercurial  thermometer.  The  latter, however,  when  carefully  studied  and  calibrated,  can  be  referred  to the  hydrogen  scale  with  sufficient  exactness  for  use  at  ordinary temperatures.  For  purposes  of  standardizing,  it  has  been  found necessary  to  refer  all  temperature  measurements  to  the  hydrogen thermometer,  and  the  study  of  exact  thermometry  made  at  the International  Bureau  of  Weights  and  Measures,  has  been  one  of its  most  important  scientific  works.  It  has  served  to  increase  the accuracy  of  the  present  standard  of  length  and  of  mass,  as  well  as to  raise  materially  the  degree  of  precision  in  all  measurements  in science  in  which  temperature  enters  as  a  factor.1 Fundamental  standards  or  prototypes  are  of  course  not  avail- able for  general  work,  even  where  high  precision  is  demanded, but  they  must  serve  only  as  a  basis  for  the  construction  and testing  of  secondary  standards  which  are  divided  throughout  their entire  length.  These  are  necessary  for  many  purposes,  and  can be  used  under  conditions  involving  more  or  less  wear. The  question  of  the  permanence  of  these  fundamental standards,  or  more  particularly  that  of  the  international  prototype meter  is  of  primary  importance.  New  methods  involving  greater exactness  in  measurements  and  comparisons  would  avail  little  if 1  Good  modern  mercury  thermometers  made  of  hard  glass  alloy  are  of  great accuracy  at  moderately  high  temperatui'es,  but  their  scale  though  very  well defined  and  reproducible  is  an  arbitrary  one  and  has  no  fixed  relation  with theoretical  phenomena,  as  is  the  case  with  the  gas  thermometer — Guillaume. See  Benoit,  p.  75,  Rapports  Congres  International  de  Physique,  tome  i.  Paris, 1900.  Guillaume,  La  Convention  du  Metre,  Paris,  1902,  p.  26,  etc.,  for  resume of  thermometric  studies  at  the  International  Bureau  of  Weights  and  Measures  ; Traite  de  la  Thermome'trie  de  Precision.  Paris,  1889.  Travaux  et  Me'moires, Bureau  International  des  Poids  et  Mesures,  vol.  i.-vi.,  x.,  xii.,  xiii. STANDARDS   AND   COMPARISON  229 changes  were  taking  place  in  the  material  of  the  standard  bar which  would  produce  variations  in  its  length.  Evidence  that has  accumulated  in  almost  twenty  years'  experience  with  the national  standard  meter  bars  does  not  indicate  any  substantial changes  that  should  give  cause  for  anxiety  in  this  respect,  but  at the  same  time,  the  physicist  is  hardly  in  a  position  to  guarantee this  permanence  for  a  longer  period  of  time,  such  as  a  century. Recourse  must  be  had,  therefore,  to  a  series  of  comparisons of  other  standards  among  themselves  and  of  providing  new  means by  which  the  integrity  of  the  standard  may  be  safeguarded. The  most  satisfactory  of  these  auxiliary  means  of  protection  is the  reference  of  the  standard  meter  to  a  wave-length  of  light, according  to  the  method  devised  by  Professor  A.  A.  Michelson and  applied  at  the  Bureau  International  des  Poids  et  Mesures,  to which  reference  will  be  made  in  the  course  of  a  few  pages.  Thus to-day  the  permanence  of  the  meter  is  assured  in  that  it  is  defined in  terms  of  a  wave-length  of  cadmium  light,  with  an  exactitude of  one  part  in  1,000,000  or,  in  other  words,  of  a  micron.1 In  comparing  standards  of  length  the  earliest  scientific  device employed  was  the  use  of  some  form  of  calipers  or  beam  compass. Thus  in  comparing  an  outside  end  standard  with  an  inside  end standard,  by  placing  the  former  between  the  projecting  ends  of the  latter,  a  measurement  could  readily  be  made.  For  com- parisons of  this  kind,  the  inside  end  standards  constructed  of metal  were  frequently  embedded  in  a  masonry  wall  at  some central  and  convenient  point  in  a  city.  In  comparing  the  toise of  Peru  with  that  of  the  Grand  Chatelet,  we  are  told  by  the Astronomer  Lalande  that  the  microscope,  in  connection  with  a beam  compass  having  very  fine  points,  was  used  as  early  as 1735,  and  we  also  know  that  a  similar  device  where  the jaws  or  points  were  moved  by  micrometer  screws  with  divided heads  was  employed  in  England  by  Graham,  in  1742,  in making  his  comparison  of  standards  of  length.2  In  the  earliest comparisons  involved  in  the  original  determination  of  the  meter and   the  construction   of  the  standard   bars   used  for  measuring 1  Benoit,  p.  68,  Rapports  Congres  International  de  Physique,  vol.  i.    Paris,  1900. 2 See  "Description  of  Standards  and  Use  of  Beam  Compasses,"  Philosophical Transactions,  1742-1743,  vol.  xlii.     London. 230    EVOLUTION   OF   WEIGHTS   AND   MEASURES the  bases,  the  various  scales  to  be  measured  and  compared were  placed  on  a  long  plate  of  brass,  having  a  fixed  terminal piece  at  one  end,  with  which  the  ends  of  the  scales  were  placed in  contact.  Differences  of  length  were  determined  by  means  of  a moving  contact  block  and  a  small  scale  carefully  divided.  This device,  known  as  the  rule  of  comparison,  or  the  comparator  of Borda  and  also  of  Lenoir,  which  was  believed  for  many  years  to have  been  lost,  was  discovered  by  M.  Wolf,1  and  is  now  preserved in  the  Observatory  of  Paris.  It  consists  of  a  heavy  strip  of copper,  some  13  pieds  (4*225  meters)  long,  30  lignes  (6*78  centi- meters) in  width,  and  4  lignes  (-9  centimeter)  in  thickness.  The movable  piece  is  a  smaller  scale  of  copper,  about  6  feet  in  length, and  divided  into  ten  thousandths  of  a  toise.  It  was  movable along  the  copper  bar,  and  with  it  an  exact  reading  of  the  length of  the  scales  to  be  compared  could  be  made.  There  were  verniers ruled  on  the  copper  bar  at  different  points,  such  as  12  pieds  from the  extremity,  for  the  comparison  of  geodetic  base  bars  of  2  toises length ;  at  6  pieds  for  the  comparison  of  toise  standards ;  at  3 pieds  for  the  comparison  of  meters,  etc.  The  verniers  were divided  to  read  to  tenths,  so  that  it  was  possible  to  obtain  the Y^j  part  of  the  length  of  a  toise.2 In  this  way  a  degree  of  precision  equal  to  about  ^tro  °f  a ligne  ('01  mm.)  was  obtained,  which  was  practically  ten  times  that attained  in  the  comparisons  of  the  toise  of  Peru  and  that  of  the Grand  Chatelet  half  a  century  before.  However,  even  greater precision  was  demanded  at  this  time,  and  accordingly,  a  lever comparator  was  constructed  by  Lenoir,  in  which  the  long  arm  of a  lever  magnified  the  distance  traversed  by  a  movable  contact  piece in  connection  with  a  shorter  arm,  with  the  result  that  it  was  pos- sible to  read  even  smaller  differences  than  those  mentioned  above.3 The  next  step  marking  progress  and  increased  accuracy  in  the comparison  of  standards  was  the  use  of  the  micrometer-microscope which  was  devised  by  Troughton,  of  London,  and  was  first  em- ployed by  Sir  George  Shuckburgh,  in  1796-8,  in  the  measurement of  some  line  standards,  which  were  then  beginning  to  be  employed 1  See  Annates  de  VObservatoire  de  Paris;  Me'moires,  vol.  17,  p.  C  32. 2Bigourdan,  p.  86,  Le  Systtme  Me'trique,  Paris,  1901. 3  Benoit,  p.  34,  Rapports  pre'sentts  au  Gongres  International  de  Physique,  vol.  i. Paris,  1900. STANDARDS   AND   COMPARISON  231 in  metrology.1  This  device  has  since  played  an  important  part in  all  such  comparisons,  and  the  micrometer-microscope,  in improved  form,  figures  in  many  instruments  for  this  purpose.  In •Shuckburgh's  comparator,  the  two  microscopes  were  arranged vertically  on  a  metallic  bar,  and  in  one  there  were  fixed  cross- hairs, and  in  the  other,  a  movable  system  of  cross-hairs  connected with  the  screw  of  a  micrometer.  The  divisions  of  the  head  of this  screw  corresponded  to  ten  thousandths  of  an  English  inch. The  method  of  operating  was  to  adjust  one  of  the  scales  so  that the  image  of  its  line  should  appear  at  the  cross-hairs  of  one  of  the microscopes,  the  cross-hairs  being  set  at  the  focus  of  the  objective. The  other  microscope  would  be  so  adjusted  that  its  cross-hairs would  coincide  with  the  image  of  the  line  at  the  opposite  end  of the  scale,  or  in  case  of  a  comparison  with  end  standards,  the  cross- hair would  be  set  on  the  ends  themselves.  In  making  a  com- parison, a  second  scale  was  substituted  for  the  first,  and  was placed  under  the  microscopes  in  the  same  position,  one  of  the lines,  or  the  extremity  of  the  scale  (in  case  it  were  an  end standard)  being  made  to  take  a  position  so  that  its  image  would ■correspond  with  the  cross-hairs  of  the  first  microscope.  If  the •other  division  were  exactly  equivalent  to  that  of  the  first  scale,  it would  occupy  the  same  position  in  the  field  of  the  second  micro- scope, but,  in  case  there  was  a  difference,  this  difference  could  be measured  by  moving  the  movable  cross-hairs  with  the  micrometer screw.  The  micrometer-microscope  of  Sir  George  Shuckburgh was  capable  of  reading  to  '0001  of  an  inch,  or  the  -^  of  a  milli- meter, and  with  this  apparatus  he  made,  in  1802,  a  comparison between  the  British  and  French  standards. This  idea  for  a  comparator  underwent  subsequent  improvements about  1804  at  the  hands  of  Baily,  also  of  England,  who  employed in  his  apparatus,  two  microscopes,  each  provided  with  a  micro- meter and  with  an  achromatic  objective,  by  means  of  which the  image  was  made  clearer  and  the  magnification  increased. He  also  devised  a  method  whereby  the  scales  could  be  slid under  the  microscopes,  without  touching  them  with  the  hands, by  arranging  a  carriage  on  a  frame  independent  of  the  microscopes. While  this  apparatus  contained  important  improvements,  never- theless, in   its  construction,   it  lacked  in    solidity,  and    at    the 1  Philosophical  Transactions  (London),  1798,  p.  137. 232    EVOLUTION   OF  WEIGHTS   AND   MEASURES same  time  was  without  adequate  means  of  preserving  the* temperature  of  the  rules  constant.  Accordingly,  the  commission charged  with  the  construction  of  the  British  Imperial  Standards,, in  1843,  made  important  improvements  in  the  comparator^ supplying  the  desired  rigidity  and  strength  by  means  of  a solid  foundation  for  the  microscopes,  and  providing  for  enclosing the  rules  to  be  compared  in  a  double-lined  box,  whose  tempera- ture was  maintained  constant  at  the  desired  temperature  by a  circulation  of  water. In  France,  also,  the  work  of  constructing  and  comparing standards  of  length  developed,  and  the  progress  towards  exact- ness made  in  that  country  during  the  nineteenth  century,  was due  in  large  part  to  the  placing  the  service  of  weights  and measures  in  charge  of  the  Conservatoire  des  Arts  et  Metiers- There  was  constructed  for  this  institution,  by  Gambey,  a  com- parator with  longitudinal  displacement,  which  permitted  the comparison  of  both  end  and  line  standards,  and  at  the  same- time  allowed  the  defining  lines  to  be  marked  upon  them.  The result  of  improvements  and  the  activity  of  this  establishment, was  that  much  was  accomplished  in  the  semi-scientific  and industrial  application  of  exact  measurements,  and  the  weights and  measures  of  France  were  brought  to  a  higher  degree  of precision. In  the  United  States,  also,  important  comparisons  were  made of  the  various  scales  presented  by  the  French  and  British Governments,  with  those  in  the  Coast  and  Geodetic  Survey.. But  neither  instruments  nor  methods  represented  any  striking departures  from  European  practice,  though  the  work  itself  was. up  to  the  high  scientific  standard  maintained  by  this  bureau and  was  favorably  commented  on  abroad.  A  useful  and accurate  comparator,  still  in  use,  was  constructed  by  Saxton and  was  employed  in  making  the  early  standards  of  length.1 While  there  have  been  no  fundamental  improvements  in the  idea  underlying  the  operation  of  comparing  standards,, within  the  last  half-century,  nevertheless  by  various  mechanical improvements  and  refinements,  the  range  of  accuracy  has  been notably  increased,  so  that  to-day  the  modern  comparator represents   an   instrument  susceptible   of   great  precision  in  the 1  Executive  Doc.  27,  34th  Congress,  3rd  Session. STANDARDS   AND   COMPARISON  233 hands  of  a  competent  observer.  The  prime  requisite  of  a  com- parator designed  for  such  purposes  as  the  comparison  of  a prototype  with  national  or  other  standards,  is  its  stability,  and for  that  purpose  the  instrument  is  generally  mounted  on  piers of  solid  masonry,  which  are  independent  of  the  structural  walls of  the  building  in  which  it  is  placed.  It  is  essential  that  such  a building  should  be  located  in  a  place  free  from  vibrations  and disturbances,  such  as  would  be  produced  by  the  traffic  of  a  busy street,  or  by  machinery,  or  by  a  railway.  The  micrometer- microscopes  are  mounted  on  heavy  castings,  set  on  separate  piers placed  at  approximate  distances,  if  the  comparator  is  to  be  used for  the  comparison  of  standards  of  a  single  unit,  as,  for  example,, meter-bars.  If,  on  the  other  hand,  the  comparator  is  of  a universal  character,  and  must  be  used  in  the  comparison  of various  lengths,  then  the  microscopes  must  be  mounted  on solid  carriages,  which  are  capable  of  being  moved  along  some sort  of  a  solid  frame-work  or  firmly  mounted  beam.  Equally important  with  the  microscopes  is  the  arrangement  for  carrying the  scales  which  are  to  be  compared.  Some  means  must  be- provided  to  place  them  successively  in  the  same  position  beneath the  microscopes,  so  that  the  difference  in  their  length  may  be- determined  by  means  of  the  micrometers.  These  scales  must  be maintained  at  the  same  temperature,  and  must  be  examined under  practically  the  same  conditions.  This  involves,  first,  the absolute  uniformity  of  the  temperature  of  the  apparatus  itself, and  for  this  purpose  it  should  be  installed  in  a  room  where direct  sunlight  cannot  penetrate  and  be  surrounded  by  corridors, enabling  a  constant  temperature  to  be  maintained.  This  requires, naturally,  an  apartment  of  a  considerable  extent,  provided  with thick  walls,  and  specially  designed  doors  and  windows,  as  well as  various  devices  for  maintaining  automatically  the  desired degree  of  temperature.  The  entire  instrument  may  be  surrounded by  a  box  through  which  penetrate  only  the  eye-pieces  of  the microscopes  and  the  handles  controlling  the  various  parts  of  the mechanism. To  keep  the  scales  at  the  same  temperature  there  is  a  movable carriage  which  carries  a  double-walled  box  containing  water. In  this  box  the  scales  are  placed  and  the  water  is  kept  in constant    circulation    by    means    of    small  agitators    electrically 234    EVOLUTION   OF  WEIGHTS   AND   MEASURES driven  and  in  motion  except  at  the  moment  of  reading.  A number  of  thermometers  arranged  in  close  proximity  to  the  scales enable  a  series  of  accurate  readings  of  the  temperature  to  be  made with  microscopes  placed  above  for  that  purpose.  It  will  readily be  seen  that  by  changing  the  temperature  of  the  surrounding water,  the  amount  of  expansion  of  a  scale  can  be  measured.1 Improvements  have  been  made  in  the  micrometer-microscope as  well  as  in  the  rest  of  the  apparatus,  and  particularly  in  the screws  which  form  the  basis  for  moving  the  cross-hairs  and for  measuring  the  amount  of  motion.  These  improvements consist  essentially  of  a  frame  carrying  several  sets  of  cross-wires in  pairs,  which  occupy  a  vertical  position  in  the  field  of  view of  the  microscope.  This  frame  is  set  at  the  focal  plane  of the  objective,  and  can  be  moved  laterally  by  means  of  a  screw with  a  graduated  head  and  handle.  Such  screws  are  so  con- structed that  they  are  practically  free  from  constant  or  periodic error,  and  by  means  of  a  spring,  any  "  back-lash  "  or  lost  motion between  the  screw  and  nut  is  guarded  against.  The  head  of the  screw  is  graduated  to  a  certain  number  of  divisions,  usually 100,  so  that  a  fractional  part  of  the  revolution  of  the  screw can  be  determined  accurately.  For  example,  if  a  pair  of  cross- wires  are  focussed  over  a  line  of  a  scale,  it  is  possible,  by  noting the  number  of  revolutions  of  the  screw,  to  bring  those  cross- wires  over  the  next  line,  to  determine  the  value  of  a  single revolution  of  the  screw,  and  by  means  of  its  divided  head  and  a vernier,  of  minute  fractions  of  a  single  revolution.  Where  cross- wires  of  the  ordinary  or  X  type  were  once  employed  and  a  setting made  on  the  centre  of  the  magnified  division,  it  is  now  usual  to employ  two  vertical  cross- wires,  following  a  plan  proposed  by Kupffer  when  preparing  the  Eussian  standards,  and  to  arrange the  setting  with  respect  to  the  edges  of  the  engraved  line.  This lends  itself  to  greater  accuracy,  as  by  means  of  the  bright  borders of  the  image  of  the  line  a  much  sharper  setting  can  be  made than  where  the  magnified  line  was  bisected  by  a  single  cross- wire.  The  magnifying  power  of  the  microscope  for  accurate comparisons  ranges  from  80  to  250  times,  and  in  some  few  rare cases  even  higher,  the  most  serviceable  power  being  determined XA  description  of  the  Brunner  Comparator  of  the  International  Bureau  will  be found  in  Travaux  et  Mdmoires  du  Bureau  International  des  Poids  et  Mesures,  vol.  4. STANDARDS   AND   COMPARISON  235 after  considering  the  conditions,  as,  under  many  circumstances, increased  magnification  introduces  errors  and  does  not  result in  as  satisfactory  results  as  with  the  use  of  a  lower  power.1 There  must  also  be  considered  the  illumination  of  the  face  of the  rule,  and  it  is  now  usual  to  provide  direct  illumination,  rather than  oblique.  This  is  accomplished  by  the  use  of  a  prism  which will  reflect  light  from  a  distant  source,  such  as  an  incandescent lamp  with  a  ground  glass  globe,  to  the  scale  and  then  to  the objective  of  the  microscope.  A  transparent  plate  of  plane  glass placed  in  the  tube  of  the  microscope  at  an  angle  of  45  degrees  to the  axis,  will  also  produce  the  same  result,  and  is  preferred  by some  observers. As  regards  the  manner  in  which  the  adjustment  of  the  scale  is •accomplished,  two  main  divisions  of  comparators  can  be  made, — those  which  give  the  transverse  movement  of  the  scales,  and  those in  which  the  scales  are  moved  longitudinally.  A  longitudinal comparator  is  so  arranged  that  the  divisions  of  a  standard  can  be studied  accurately ;  for  example,  throughout  the  entire  length ;  or standards  of  different  lengths,  whose  differences  exceed  the diameter  of  the  field  of  the  microscopes,  can  be  measured  with facility.  Thus  from  a  standard  meter,  a  bar  or  tape  of  several times  this  length  for  use  in  measuring  a  base  line  or  in  surveying, •can  be  standardized.  In  a  comparator  of  this  kind  the  scales must  be  so  adjusted  that  they  lie  with  their  axis  either  in  a perfectly  straight  line  or  exactly  parallel. In  the  comparators  where  the  scales  have  a  transverse  move- ment, as  is  the  case  with  an  instrument  designed  for  comparing two  scales  of  the  same  length,  the  microscopes  are  mounted  at  a fixed  distance,  and  the  scales  are  adjusted  so  that  their  axes  are parallel  to  a  line  connecting  the  two  microscopes.  The  two scales  should  rest  in  a  carriage  protected  from  changes  of temperature  by  means  already  described,  and  so  arranged  that after  being  adjusted  parallel  to  each  other,  they  can  be  moved under  the  two  microscopes.  Such  an  arrangement  enables  one  to study  the  relative  expansion  of  scales  of  different  materials,  as  the measurement  of  the  differences  of  length  at  a  certain  temperature 1  See  W.  A.  Rogers,  "  On  the  Present  State  of  the  Question  of  Standards  of Length,"  Proceedings  American  Academy  of  Arts  and  Sciences,  vol.  xv.  1879-80, pp.  290-291. 236    EVOLUTION   OF   WEIGHTS   AND   MEASURES can  be  made,  and  then,  at  a  second  temperature,  obtained  by varying  the  warmth  of  the  circulating  water. With  standards  of  mass,  the  material  of  which  they  are  com- posed is  of  primary  importance.  Not  only  must  the  standard  be of  a  permanent  character,  hard  and  able  to  resist  abrasion  in  actual use,  but  it  must  be  such  that  it  will  not  be  affected  by  the  oxygen of  the  air,  or,  in  other  words,  have  its  surface  oxidized  and  the weight  increased.  Other  and  more  subtle  chemical  changes  must also  be  provided  against.  On  this  account,  platinum  and  rock crystal  have  been  found  to  be  the  most  useful  materials,  and  the former  posesses  the  merit  of  having  a  high  specific  gravity,  so that  when  weighed  in  air  the  amount  displaced  is  a  minimum. Furthermore,  the  shape  must  be  such  that  the  volume  can  be measured  with  a  high  degree  of  exactitude,  as  on  the  volume depends  the  effect  of  buoyancy,  and  of  temperature.  Such  cor- rections are  often  very  small ;  in  fact,  much  less  than  in  the case  of  a  standard  of  length,  but  in  constructing  and  using  a standard  of  mass,  the  barometric  pressure,  temperature,  and  the humidity  should  be  determined,  as  the  density  of  the  air  must be  known  accurately  and  duly  considered. In  addition  to  possessing  a  geometrical  figure  easily  measured, the  standard  should  be  so  designed  that  there  are  no  grooves  or cavities  to  collect  dust,  and  that  when  used  in  a  balance  it  will conform  to  the  needs  of  the  mechanism  used  for  changing  the weights  in  the  scale-pans.  Taking  all  things  into  considera- tion, the  cylindrical  shape  with  round  edges  serves  the  best, and  such  is  the  form  of  the  Kilogram  of  the  Archives  and  of the  International  Prototype  and  its  copies. For  determining  standards  of  mass,  the  modern  physicist has  recourse  to  the  same  instrument  which  was  employed  thou- sands of  years  ago  by  the  ancients,  viz.  the  balance  with  equal arms.  But  he  has  effected  such  improvements  in  its  mechanical construction  and  operation  that  this  instrument  is  now  entitled  to rank  with  the  apparatus  of  precision  of  the  first  order.  For accurate  weighing,  the  balance  must  be  of  the  finest  and  most accurate  workmanship,  and  also  there  must  be  employed  various methods  and  corrections  evolved  largely  from  mathematical considerations. In  comparing  standards  of  mass,  and  in  all  accurate  weighings- STANDARDS   AND   COMPARISON  237 with  a  balance,  it  is  necessary  to  take  into  consideration  the buoyant  effect  of  the  displaced  air,  as  conditions  are  quite •different  from  those  obtained  when  a  body  is  weighed  in  a vacuum.  This  correction  is  especially  necessary  in  making  an ■absolute  determination,  but  in  cases  where  the  standard  and the  weights  with  which  it  is  compared  are  of  the  same  material, the  effect  is  the  same  in  both  cases  and  does  not  enter  into consideration  at  all. For  accurate  weighing  it  is  possible  to  employ  the  method of  double  weighing  of  Borda,  where  the  two  objects  whose  masses are  to  be  compared  are  successively  placed  in  the  same  scale- pan  and  are  counterpoised  by  weights  on  the  opposite  side,  or the  interchange  of  the  weights  on  the  scale-pans,  as  devised  by Gauss.  There  must  be  considered,  also,  the  effect  of  temperature, which  can  change  the  condition  of  balances  and  weights,  just  as much  as  in  other  physical  operations,  and  it  is  accordingly necessary  to  have  such  a  balance  placed  in  a  room  with  constant temperature,  and  to  provide  against  currents  of  air,  by  means  of  a suitable  case.  Even  the  influence  of  the  temperature  of  the •observer's  body  has  its  effect,  and  he  must  be  placed  as  far  as possible  from  the  balance,  observing  the  oscillation  of  the  beam with  a  small  telescope,  and  changing  the  weights,  setting  the beam  in  motion  and  bringing  it  to  rest,  and  performing  other necessary  operations  by  suitable  mechanical  devices,  which  can be  operated  at  a  distance,  without  opening  the  casing  of  the balance. These  conditions  are  realized  in  the  balances  used  at  the Bureau  International,  as  well  as  at  various  governmental Bureaus  of  Standards,  physical  laboratories  and  like  institutions. Typical,  perhaps,  as  involving  the  greatest  refinements,  are  the balances  of  the  Bureau  International,  two  forms  of  which  are •described  in  outline  below. Of  these  perhaps  the  simplest  is  the  Ruprecht  type  of  balance, which  consists  of  a  balance  with  equal  arms  carrying  two  scale- pans  in  which  an  opening  is  cut  in  the  form  of  a  cross,  the  edge being  cut  away  at  one  of  the  branches.  Beneath  this  is  an  axis carrying  a  cross-shaped  piece  of  somewhat  smaller  dimensions than  the  opening  in  the  scale-pan.  Two  supports  similar  in shape   to   the    scale-pans   and   provided  with   like  openings   are 238    EVOLUTION   OF   WEIGHTS   AND   MEASURES attached  to  the  central  column  supporting  the  balance.  When a  weight  is  placed  on  the  scale-pan  by  means  of  mechanism operated  from  a  distance  of  over  four  meters,  it  is  possible  for  the cross-shaped  piece  below  to  be  raised,  thus  carrying  the  weight clear  of  the  scale-pan,  and  then  to  be  swung  out  through  the opening  clear  of  the  latter,  and  into  the  plate  placed  on  the central  column  where  the  weight  may  be  deposited.  The standard  carrying  the  cross-shaped  piece  is  then  lowered and  the  weight  is  left  on  the  rest.  The  weights  can  then  be revolved  around  the  central  column  carrying  the  beam  and  by  the apparatus  just  mentioned  placed  on  opposite  pans  from  their original  position.  This  operation  is  accomplished  by  means  of gears  and  shafts,  and  is  carried  on  simultaneously  for  both  pans of  the  balance.  Mechanism  is  also  provided,  so  that  the  observer may  release  the  pans  and  also  the  beam,  by  turning  suitable cranks,  and  there  is  a  telescope,  whereby  he  may  observe  the deflections  of  the  beam  by  means  of  a  mirror  and  divided  scale.1 The  Bunge  balance,  at  the  Bureau  International  des  Poids  et Mesures,  contains  several  features  leading  to  further  refinements. It  is  enclosed  in  a  copper  case,  from  which  the  air  may  be exhausted,  so  that  the  weights  may  be  compared  in  vacuo.  In addition  to  the  means  of  changing  the  weights,  and  for  releasing and  arresting  the  scale-pans  and  beam,  mechanism  is  provided whereby  small  additional  weights  can  be  added  to  one  side  or  the other  of  the  beam,  as  is  found  necessary.  All  of  the  controlling devices  are  so  arranged  that  they  may  be  operated  by  the observer  from  a  distance  of  several  meters,  and  with  this  balance the  most  accurate  results  may  be  obtained. In  the  determination  of  standards  of  mass,  it  is  necessary  to determine  their  specific  gravity  and  the  amount  of  water  that they  displace  when  immersed.  For  this  hydrostatic  balances are  used,  which,  in  their  essential  features,  correspond  with  the balances  of  precision  just  described.  The  vessel  containing  the water  in  which  the  weight  is  immersed  is  placed  directly  below 1  Guillaume's  La  Convention  du  Metre,  p.  111.  The  balances  have  been  pro- vided with  suitable  mechanism  to  add  small  differential  weights,  i.e.  at  the  same time  two  weights  say  of  100  and  100*5  milligrams  respectively,  which  give  a  new position  of  equilibrium  and  allow  the  determination  of  the  sensitiveness.  This- addition  of  small  weights  can  be  made  without  arresting  the  balance  which  con- stitutes a  great  saving  of  time. — Ch.  Ed.  Guillaume. STANDARDS   AND    COMPARISON  239 the  point  of  support  of  one  of  the  arms  of  the  balance.  There is  also  provided  a  scale-pan,  in  which  the  body  to  be  measured is  placed,  and  connected  with  it — a  device  by  which  it  can  be supported  when  immersed  in  water — the  whole  forming  a  con- tinuous arrangement  supported  from  one  arm.  The  body  is  first placed  in  the  upper  pan  and  counterbalanced  by  weights  on  the opposite  side  of  the  balance.  It  is  then  removed  and  weights are  added  in  its  place  until  the  equilibrium  of  the  balance  is secured.  The  sum  of  the  weights  so  added  gives,  of  course,  the actual  weight  of  the  body.  It  is  then  immersed  in  water,  and the  same  process  is  gone  through  with,  the  temperature  of  the water  being  noted  by  a  carefully  calibrated  thermometer.  Various devices  are  employed  to  secure  a  uniform  temperature  of  the water,  to  diminish  the  effects  of  friction  and  capillarity,  and  to facilitate  the  handling  of  the  body  when  immersed. The  sensibility  of  an  accurate  balance  depends  on  the  load, and  in  making  a  weighing,  this  factor  must  be  determined accurately,  and  it  is  likely  to  vary  under  different  conditions. With  the  balances  employed  in  comparing  the  standard  kilo- grams, it  is  usual  to  have  the  sensibility  equal  to  25  to  50 divisions  for  a  milligram,  or,  in  other  words,  an  addition  of weight  equal  to  a  milligram  produces  a  deflection  of  the  beam corresponding  to  this  amount.  This  is  useful,  inasmuch  as  the differences  of  weight  between  the  two  standards  compared  are usually  so  small  as  to  be  measured  only  by  the  deflection,  and  not requiring  the  addition  of  the  smaller  weights  to  either  scale-pan. In  some  cases,  a  reading  of  a  tenth  of  a  division  of  the deflection  in  either  direction  may  correspond  to  some  thousandths of  a  milligram.  Thus,  in  comparisons  of  standard  kilograms,  the •01  of  a  milligram  would  be  equal  to  a  '000,000,01  of  the  mass measured,  but  other  considerations  do  not  permit  this  degree  of precision  to  be  maintained.  Nevertheless,  this  represents  a substantial  gain  in  accuracy,  as  the  fine  balance  used  at  the London  Mint  by  Harris  in  1743  was  able  to  indicate  only  ^  of a  grain  on  a  Troy  pound,  or  about  one  part  in  50,000,  while  in adjusting  the  Kilogram  of  the  Archives  in  1779,  Fortin  employed a  balance  sensitive  to  one  part  in  a  million. As  units  of  capacity  are  defined  in  terms  either  of  linear measures  or  of  mass,  the  construction  of  suitable  standards  does 240    EVOLUTION   OF  WEIGHTS   AND   MEASURES not  present  any  particular  difficulty,  nor  is  any  high  degree  of precision  required,  save  in  a  few  cases.  In  fact,  standard measures  of  capacity  are  usually  adjusted  by  means  of  the weight  of  a  liquid  such  as  water,  taken  at  a  certain  temperature. As  these  measures  are  used  in  few  experiments  or  determina- tions where  extreme  accuracy  is  called  for,  there  is  no  need of  observing  particular  precautions,  either  in  their  construction or  their  calibration.  The  standards  are  usually  of  some  metal, such  as  bronze  or  gun-metal,  of  a  regular  geometrical  shape, and  are  adjusted  with  water  at  a  certain  temperature.  The purpose  for  which  a  measure  of  capacity  is  to  be  used  is  borne in  mind  in  determining  its  shape,  as  with  liquids  it  is  not necessary  to  take  into  consideration  the  question,  of  compres- sibility or  of  heaping  the  measure  which  would  be  involved  in the  measurement  of  grain  or  vegetables.  This,  of  course,  does not  affect  the  actual  cubical  contents  of  the  measure,  but  merely considers  its  actual  application  in  commerce.  Thus,  in  Great Britain  there  have  been  various  shapes  adopted  for  standards  for the  liquid  and  dry  gallon,  and  for  the  coal  bushel,  and  for  other measures,  the  exact  dimensions  of  which  are  defined.  In  view of  the  great  inaccuracy  in  measuring  goods  by  capacity  measures being  unavoidable,  it  is  the  present  tendency  of  metrology  to use  capacity  measures  as  little  as  possible,  and  to  recommend the  use  of  weights,  especially  in  business  dealings.  In  Europe this  practice  is  rapidly  increasing  among  the  metric  countries, and  in  some  of  them  nearly  all  articles  of  food  and  other necessities  for  daily  life,  even  liquids  such  as  oil,  are  bought  and sold  by  weight. There  is,  however,  one  kind  of  standard  of  capacity  where accuracy  is  important,  namely,  flasks,  burettes,  or  other  vessels  of glass  employed  in  physical  or  chemical  experiments.  These  are calibrated  carefully  with  water  or  mercury,  whose  volume  at  any specified  temperature  is  known  with  exactness.  Such  standards, however,  are  not  specially  and  exclusively  maintained  by  national bureaus  and  direct  comparisons  made  with  them,  but  as  their  cali- bration involves  little  difficulty  to  the  trained  physicist  or  chemist,1 1  The  calibration  of  chemical  and  other  graduated  glass-ware  is  one  of  the regular  routine  duties  of  the  National  Bureau  of  Standards  at  Washington,  and is  done  for  the  technical  public  at  reasonable  and  established  fees. STANDARDS   AND   COMPARISON  241 they  are  usually  constructed  in  any  laboratory  where  their  use is  desired. In  the  case  of  other  standards,  such  as  those  of  electricity,  the most  important  are  the  ohm  and  the  standard  cell,  which  involve the  realization  of  the  international  definitions1  by  careful  scientific work.  These  definitions  for  practical  purposes  are  so  exact  and the  modes  of  construction  so  well  understood  by  physicists  that such  standards  can  be  constructed  at  national  or  other  physical laboratories  and  bureaus  of  standards  by  trained  investigators, and  the  results  represent  refined  methods  of  manipulation  and  the use  of  specific  apparatus  rather  than  scientific  work  of  such character  as  was  involved  in  the  construction  of  the  international standards  of  length  and  mass.  It  should  not  be  understood, however,  that  from  the  purely  scientific  point  of  view  that electrical  engineers  and  physicists  are  altogether  satisfied  with the  present  definitions.  Consequently  there  is  at  present  much important  investigation  in  progress  which  has  as  its  object  the determination  of  new  standards  or  new  definitions,  and  at  the Electrical  Congress  held  at  St.  Louis  in  1904  it  was  decided  that steps  should  be  taken  to  form  an  international  electrical  com- mission composed  of  official  representatives,  much  after  the  fashion of  the  International  Commission  of  Weights  and  Measures.  The call  for  a  preliminary  meeting  of  delegates  has  been  issued  and the  formation  of  this  international  commission  in  the  near  future is  probable.  From  the  discussion  of  the  electrical  units  in  the  last chapter  their  independence  on  each  other  will  be  appreciated,  so that  it  is  necessary  to  determine  whether  the  voltameter  operating under  standard  conditions  shall  give  the  unit  of  current  from which,  with  the  ohm,  may  be  derived  the  unit  of  electromotive force,  or  whether  the  unit  of  electromotive  force  as  given  by  a standard  cell  shall  be  considered  the  fundamental  source  of  the standards. There  have  been  constructed  by  the  Physikalisch-Technische Reichsanstalt  at  Berlin  and  the  English  National  Physical Laboratory,  primary  mercurial  standards  of  resistance  in  which the  international  definition  of  the  ohm  has  been  realized  and the  apparatus  of  these  two  laboratories  shows  substantial agreement  of  measurement,  being  in  harmony  to  a  few  parts  in 1  See  chapter  ix.  ante. Q 242    EVOLUTION   OF   WEIGHTS   AND   MEASURES IOOjOOO.1  Furthermore  there  are  in  England,  preserved  at  the Board  of  Trade  Electrical  Standardizing  Laboratory  in  London, actual  standards  of  resistance,  current  and  electrical  pressure which  have  been  duly  legalized  (Order  in  Council,  August  23, 1894). Thus  the  standard  ohm  is  the  resistance  between  the  copper  ter- minals of  the  platinum-silver  coil  marked  "  Board  of  Trade  Ohm Standard,  verified  1894,"  to  the  passage  of  an  unvarying  electrical current,  when  the  coil  of  insulated  wire  forming  part  of  the aforesaid  instrument  and  connected  to  the  aforesaid  terminals  is in  all  parts  at  a  temperature  of  15*4  degrees  Centigrade. The  standard  ampere  is  the  current  which  passes  in  and  through the  coils  of  wire  of  the  standard  ampere  balance,  marked  "  Board of  Trade  Ampere  Standard,  verified  1894,"  when  on  reversing  the current  in  the  fixed  coils  the  change  in  the  forces  acting  upon the  suspended  coil  in  its  sighted  position  is  exactly  balanced  by the  force  exerted  by  gravity  in  Westminster  upon  the  iridio- platinum  weight  marked  "  A"  and  forming  part  of  said  instrument. The  British  standard  volt  is  one-hundredth  part  of  the  pressure which,  when  applied  between  the  terminals  of  a  Kelvin  electro- static voltmeter  of  the  multicellular  type  marked  "  Board  of  Trade Standard,  verified  1894,"  causes  a  certain  exactly  specified  amount of  rotation  of  the  suspended  part  of  the  instrument. While  various  other  standards  are  of  course  possessed  by  the different  national  laboratories  and  testing  bureaus,  yet  they  aim rather  at  representing  specifically  the  definitions  of  the  various units,  than,  as  in  the  case  of  the  British  Board  of  Trade,  employing as  national  standards  the  mere  concrete  apparatus.  The  same holds  true  for  standard  barometers,  thermometers,  polariscopes, and  other  instruments  of  precision  which  are  used  for  standardizing similar  instruments  used  in  science  and  industry. Having  considered  the  general  principles  underlying  standards and  their  construction  and  comparison,  it  may  be  advantageous  to discuss  briefly  the  weights  and  measures  that  have  served  this purpose  in  France  and  England,  as  well  as  the  present  metric standards.  While  it  was  legally  possible  to  establish  the  inch  by taking  "  three  barley  corns  round  and  dry  "  as  was  provided  by the  statute  of  Edward  II.  and  to  raise  a  pound  from  7680  grains xThe  first  standard  ohm  was   constructed   privately   by   M.    Benoit  of   the Bureau  International. STANDARDS   AND   COMPARISON  243 of  wheat  as  was  enacted  by  the  statute  of  the  Assize  of  Bread  and Ale  (51  Henry  III.,  stat.  1,  1266),  yet  such  means  on  their  very face  were  manifestly  lacking  in  accuracy,  as  there  was  nothing  to ensure  that  the  corns  or  grains  would  conform  to  a  uniform standard.  Consequently  as  early  as  the  fourteenth  year  of  the reign  of  Edward  III.  (1340)  a  royal  edict  was  published  ordering "  standard  weights  and  measures  to  be  made  of  brass,  and  sent into  every  city  and  town  in  the  kingdom."  This  necessary  and excellent  law,  however,  merely  followed  the  precedent  made  by Eichard  I.,  who  ordered  that  standard  measures  of  length  should be  made  of  iron  and  that  those  for  capacity  should  have  iron brims,  and  that  standard  measures  of  every  kind  should  be  kept by  the  sheriffs  and  magistrates  of  towns.  While  it  cannot  be said  that  this  law  was  enforced,  yet  it  shows  that  the  government was  alive  to  the  necessity  of  proper  standards  in  order  to secure  the  desired  uniformity  and  that  their  construction  was constantly  in  mind. The  earliest  English  standard  of  length  extant  is  the  Exchequer standard  yard  of  Henry  VII.,  which  dates  back  to  1496.  It  is  a brass  bar  of  octagonal  cross  section  whose  length  furnished  the standard  distance,  and  which  is  divided  both  into  inches  and  also into  sixteen  equal  parts  on  the  basis  of  binary  division.  It  was used  until  1588,  when  in  the  reign  of  Queen  Elizabeth  a  new standard  yard,  also  of  brass,  was  constructed,  which  is  still  in existence  after  having  served  for  a  long  period  as  an  original standard.  It  is  a  rectangular  bar  one  yard  in  length,  on  which are  indicated  the  divisions  of  a  yard  and  also  a  similar  bar  forming an  ell  of  45  inches  (exact  length  45*04  inches),  there  being  a third  and  larger  bar  with  two  beds  or  matrixes  into  which  both of  the  end  standard  bars  could  fit,  and  having  at  one  end  of  the yard  bed  a  subdivision  into  inches  and  half  inches.  It  may  be said  in  passing  that  both  the  standards  of  Henry  VII.  and  of Elizabeth  are  essentially  of  the  same  length,  and  they  are  only about  '01  inch  shorter  than  the  present  British  imperial  standard. The  Elizabethan  standard  did  duty  until  well  into  the  nineteenth century,  in  spite  of  the  fact  that  some  time  between  1760  and 1819  it  had  been  broken  and  mended  by  means  of  a  dovetail joint  in  a  rather  crude  fashion.  In  fact  this  ancient  standard  has been  spoken  of  most  contemptuously  by  F.  Baily,  who  examined 244    EVOLUTION   OF   WEIGHTS   AND   MEASURES it  in  1836,  he  even  going  as  far  as  to  call  it  disgraceful  for  the British  government  to  issue  certificates  and  construct  copies based  on  it  as  representing  the  English  standard.1 A  line  standard  constructed  by  Bird  in  1760,  under  the authorization  of  the  Committee  on  Weights  and  Measures  of the  House  of  Commons,  was  based  upon  a  standard  made  by the  same  maker  in  1742  for  the  Royal  Society,  and  on  a  line standard  which  he  constructed  in  1758.  The  former  has  been pronounced  by  H.  W.  Chisholm,  an  authority  on  British metrology,  to  be  "  the  first  scientifically  constructed  measure of  length  in  this  country "  (England).2  The  Bird  standard  of 1760  was  approved  by  the  Committee,  and,  though  not  at  that time  legally  established,  formed  a  basis  for  a  number  of secondary  standards.  It  was  eventually  adopted  as  the  legal standard  of  Great  Britain  by  an  Act  of  Parliament  promulgated June  17,  1824,  and  served  as  such  until  its  destruction  in  the  fire which  consumed  the  Houses  of  Parliament  in  1834.  The  adop- tion of  this  standard,  however,  at  this  time  was  hardly  warranted in  view  of  the  state  of  scientific  knowledge,  or  by  the  actual character  of  the  standard  itself.  It  was  a  brass  bar,  1*05  inch square  and  39'73  inches  in  length,  with  gold  plugs  near  the  ends, on  which  were  points  or  dots,  the  distance  between  which  at  the temperature  of  62  degrees  Fahrenheit  (16*7  degrees  Centigrade) represented  the  standard  yard.  This  standard  bar,  however,  in addition  to  being  of  comparatively  crude  construction,  even  at the  time  of  its  legal  adoption  had  become  badly  worn  by  rough treatment.  By  the  use  of  beam-compasses,  and  in  various  rough comparisons,  the  dots  had  become  worn,  so  that  under  the  micro- scope they  were  seen  to  appear  like  the  craters  of  small  volcanoes, and  consequently  rendered  the  bar  quite  unsuitable  for  exact scientific  work.  In  the  Act  by  which  this  standard  was  estab- lished it  is  clear  that  the  idea  of  a  natural  standard  was  still cherished,  since  it  provided  that  in  the  event  of  the  loss  of the  standard  yard  it  should  be  restored  by  means  of  a  reference 1  See  H.  W.  Chisholm,  ' '  Seventh  Annual  Report  of  the  Warden  of  the  Standards, " 1872-3,  English  Parliamentary  Papers,  Reports  from  Commissioners,  1873,  vol. xxxviii.  pp.  25  and  34;  also  id.  "Weighing  and  Measuring"  (London,  1877),  pp. 50-54.     See  also  footnote,  p.  36,  ante. 2  See  Chisholm  in  same  Report,  p.  10,  for  full  description  of  this  and  other standards. STANDARDS   AND   COMPARISON 245 to  a  pendulum  beating  seconds  in  a vacuum,  at  the  latitude  of  London and  reduced  to  sea  level,  which  would have  the  relation  to  the  yard  of 391393  to  36;  but  in  spite  of  this statutory  provision,  when  the  standard yard  was  destroyed  ten  years  later  no recourse  was  had  to  the  seconds' pendulum,  as  that  method  seemed  then incapable  of  furnishing  the  standard with  sufficient  exactness,  and  the  stan- dard yard  was  reconstructed  from  other standards  in  the  possession  of  the Government  and  scientific  societies which  had  been  compared  with  the standard  of  1760.  These  included  the five-foot  brass  standard  scale  of  Sir George  Shuckburgh  which  was  made by  Trough  ton,  of  London,  in  1796,  two iron  standards  made  for  the  Ordnance Survey  in  1826-7,  the  brass  tubular  scale of  the  Royal  Astronomical  Society,  and the  standard  yard  of  the  Royal  Society constructed  under  Captain  Kater's direction  in  1831.  The  Shuckburgh scale  was  based  on  a  five-foot  scale made  and  used  by  Troughton,  which  in turn  was  constructed  from  an  accurate 90-inch  brass  scale  made  by  Bird.1 This  imperial  standard  yard,  as  well as  the  imperial  standard  prepared under  the  direction  of  a  Parliamentary Committee    appointed    in    1843,    were xSee  W.  Harkness,  "Progress  of  Science  as Exemplified  in  the  Art  of  Weighing  and Measuring,"  Bulletin,  Philosophical  Society  of Washington,  D.C.,  vol.  x. ;  Smithsonian  Miscell- aneous Collection,  vol.  xxxiii.  1888,  pp.  43  et  seq. Present  State  of  the  Question  of  Standards  of  Length,"  Proceedings,  American Academy  of  Arts  and  Sciences,  vol.  xv.  1879-80,  pp.  273  et  seq. British  Imperial  Yard. Also  W.  A.  Rogers,   "  On  the o 246    EVOLUTION   OF   WEIGHTS   AND   MEASURES duly  legalized  in  1855  (18  and  19  Vict.  c.  72)  by  an  A.ct known  as  the  Standards  Acts,  whose  provisions  as  regards these  standards  were  re-enacted  in    the  Weights  and  Measures British  Imperial  Standard  Yard.     Cross-section.    (Exact  size.) 1. — Section  of  Bar.  2. — Section  through  holes. Act  of  1878.  These  standards,  as  they  represent  the  best practice  of  the  time  of  their  construction,  and  as  they  are the  present  standards  of  Great  Britain,  may  be  briefly  de- scribed.1 The  imperial  standard  yard  is  a  solid  square  bar of  a  special  bronze  or  gun-metal  known  as  Baily's  metal, composed   of    copper    16    parts   by  weight,  tin  2  J,  and    zinc   1. Diagram  Showing  British  Imperial  Standard  Yard  from  above,     a— a=l  yard. It  is  38  inches  in  length,  with  a  cross  section  one  inch  square, and  has  near  its  ends  two  circular  holes  or  wells  sunk  to  a point  midway  the  depth  of  the  bar.  In  these  wells  are  inserted two  gold  studs,  on  which  the  fiducial  lines  are  engraved,  the distance  between  them  forming  the  imperial  standard  yard  of  36 inches  at  a  temperature  of  62  degrees  Fahrenheit  (16j-°  C).  This imperial  standard,  as  also  the  imperial  standard  pound,  is  pre- served in  a  strong  fire-proof  room  at  the  Standards  Office  in Old    Palace    Yard,    Westminster,   and    copies    are    deposited    at 1 G.  Airy,  ' '  Account  of  the  Construction  of  the  New  National  Standards  of Length,  and  of  its  Principal  Copies,"  Philosophical  Transactions  (London),  18th June,  1857. STANDARDS   AND   COMPARISON  247 the  Royal  Observatory,  Greenwich,  the  Royal  Mint,  the  Royal Society,  and  the  Houses  of  Parliament.  The  latter  are  specially designated  by  statute  as  Parliamentary  copies,  and  must  be  com- pared with  the  imperial  standard  once  in  every  ten  years,  since in  the  event  of  the  possible  destruction  of  the  latter  they  would furnish  the  source  from  which  a  new  standard  would  be  derived. There  were  in  addition  thirty-five  other  standards  made  of  the same  size  and  of  the  same  material,  which  were  duly  compared with  the  prototype,  and  were  distributed  to  the  various  nations  of the  world  and  to  scientific  institutions  in  Great  Britain  and  else- where. One  of  these  standard  bars,  by  Act  of  Parliament,  June 30,  1855,  was  presented  to  the  United  States  Government,  and was  known  as  "Bronze  Standard  No.  11."  It  is  '000088  inch shorter  than  Bronze  Standard  No.  1,  which  was  chosen  as  the imperial  standard.  It  was  accompanied  by  a  malleable  (Low Moor)  iron  standard  of  length,  No.  57,  and  standard  weight  No.  5, the  correction  for  each  standard  being  given  over  the  signature  of G.  B.  Airy,  Astronomer-Royal.1 These  two  yards,  particularly  the  bronze  standard,  were  so much  superior  to  the  Troughton  scale  that  they  were  accepted by  the  United  States  Office  of  Weights  and  Measures  as  the standards  of  the  United  States,  and  in  this  way  comparisons of  American  measures  of  length  were  made  with  the  imperial yard.  In  1876,  and  again  in  1888,  they  were  taken  to  England and  were  compared  with  the  British  standards. In  1904,  the  late  H.  J.  Chany,  Warden  of  the  Standards,  caused to  be  constructed  and  standardized  at  the  International  Bureau  a platinum-iridium  bar  similar  in  composition  and  section  to  the  inter- national meter,  and  while  this  has  not  as  yet  any  legal  standing, it  is  perhaps  the  best  representative  of  the  British  yard. The  oldest  authenticated  British  standards  of  weight  date  from the  reign  of  Queen  Elizabeth,  and  consist  of  three  distinct  sets. The  first  of  these  are  bell-shaped  standards  of  bronze  for  the heavier  weights,  and  range  from  56  lbs.  to  1  lb.  inclusive.  They are  of  importance,  as  from  the  time  of  their  construction  in  1588 until  1824  they  were  the  standards  of  the  kingdom.      Then  there 1  See  Report,  Superintendent  U.S.  Coast  and  Geodetic  Survey,  1877,  Appendix 12,  p.  154,  for  description  of  these  standards  of  length.  See  also  Executive Document  27,  34th  Congress,  3rd  Session,  p.  17. 248    EVOLUTION   OF   WEIGHTS   AND   MEASURES is  a  series  of  flat  circular  avoirdupois  weights  from  8  lbs.  to  T^ of  an  ounce,  and  a  set  of  cup-shaped  Troy  weights  which,  with  the exception  of  the  very  small  weights,  fitted  into  each  other.  These standards  had  been  prepared  under  the  direction  of  a  committee of  merchants  and  goldsmiths,  who  employed  as  the  basis  for avoirdupois  weight  a  56  lb.  standard  of  the  Exchequer  dating  from Edward  III.,  and  for  Troy  weight  the ancient  standard  of  the  Goldsmiths'  Hall. About  1758  the  Parliamentary  Com- mittee, to  which  we  have  before  referred, caused  to  be  constructed  three  standard Troy  pound  weights,  but  like  the  yard  of the  same  period  none  of  these  was  legalized until  1824,  when  one  of  the  weights  was chosen  as  the  government  standard,  only to  be  destroyed  by  the  fire  of  ten  years later.  On  the  recommendation  of  the Standards  Committee  of  Parliament,  made in  a  report  submitted  December  21,  1841, the  British  imperial  standard  of  weight was  changed  from  a  Troy  pound  of  5760 grains  to  an  avoirdupois  pound  of  7000 grains,  and  a  standard  representing  the- latter  was  constructed  in  1844  and  duly legalized  in  1855.  After  much  discussion and  a  careful  examination  of  existing standards  it  was  found  necessary  to  use almost  exclusively  two  platinum  weights,  one  belonging  to  the Eoyal  Society  and  the  other  to  Professor  Schumacher,  whose values  were  accurately  known  in  terms  of  the  lost  standard. The  new  standard,  which  is  indeed  the  present  imperial  standard, is  of  platinum,  cylindrical  in  form,  1*35  inches  in  height,  and 1*15  inches  in  diameter.  Its  density  as  compared  with  distilled water  is  21*1572,  and  it  displaces  *403  grains  of  air  under standard  conditions.1  It  has  a  slight  groove  or  channel  near  its upper  surface  by  which  it  may  be  moved  with  a  fork  of  ivory,  and 1W.  H.  Miller,  "On  the  Construction  of  the  New  Imperial  Standard  Pound, etc.,"  Philosophical  Transactions  (London),  1st  June,  1856.  H.  W.  Chisholm,. Weighing  and  Measuring  (London,  1877). British  Imperial  Standard Pound.    (Exact  size.) STANDARDS   AND   COMPARISON  249 bears  on  its  upper  surface  the  inscription  "P.S.I 844, 1  lb.,"  the  letters signifying  Parliamentary  Standard.  Copy  No.  5  was  presented  to the  United  States  in  1856.  The  British  units  of  capacity,  the gallon  and  the  bushel,  are  based  on  the  fact  that  an  imperial gallon  represents  the  volume  occupied  by  ten  imperial  pounds  of distilled  water  at  62  degrees  Fahrenheit  and  a  barometric  pressure of  30  inches,  while  the  bushel  is  eight  gallons,1  The  imperial standard  gallon  bears  the  date  of  1828  and  is  of  brass,  with  a diameter  equal  to  its  depth.  The  imperial  bushel  standard  is  of gun-metal,  with  a  diameter  twice  that  of  the  depth,  these  latter dimensions  being  selected  on  account  of  the  applicability  to  the use  for  the  measure  of  grain.  It  dates  from  1824,  and  was verified  in  the  following  year. The  French  standard  of  length  previous  to  the  completion  of the  Meter  of  the  Archives  was  the  Toise  de  Perou,  to  which reference  has  already  been  made.  It  was  constructed  for  use  in making  the  base  measurements  for  determining  the  length  of  the Peruvian  arc  of  the  meridian  and  the  verification  of  the  arc passing  through  Paris,  being  derived  from  the  Toise  du  Grand Chatelet,  which  dated  back  to  1668.  This  latter  standard  was  a bar  of  iron  which  was  fixed  in  the  wall  of  the  Grand  Chatelet, forming  an  inside  end  standard  by  which  all  scales  could  be  tested by  simply  placing  them  between  the  limiting  ends.  This  naturally deteriorated  from  exposure  and  wear,  and,  as  a  result,  the  Toise de  Perou  was  substituted  for  the  Toise  du  Grand  Chatelet,  as  the French  standard  of  length,  in  1766,  and  is  now  preserved  at  the Observatory  in  Paris.  It  is  an  end  standard  of  polished  iron, somewhat  greater  than  a  toise  in  length  and  of  rectangular section,  17  lignes  in  breadth  and  4-^  lignes  in  thickness.  At  each end  of  the  bar  a  rectangular  portion  extending  to  a  line  midway of  the  breadth  was  removed,  and  the  standard  distance  was  taken between  the  edges  of  the  remaining  portion  of  the  bar,  at  a  point about  one  ligne  from  the  median  line.  On  the  longer  part  of  the bar  two  lines  were  traced,  with  points  marked  at  their  centers,  so that  the  distance  between  them  was  exactly  a  toise,  with  the  result that  an  end  standard  was  combined  in  the  same  metal  bar  with the  more  exact  line  standard, — there  being,  however,  a  difference 1  Henry  Kater,  "Verification  of  Standard  Gallon,"  Philosophical  Transactions (London),  1826. 250    EVOLUTION   OF   WEIGHTS   AND   MEASURES between  the  two  scales  of  about  "1  of  a  millimeter,  a  quantity which  was  readily  negligible  in  the  metrology  of  those  days. The  bar  was  standard  at  a  temperature  of  13°  Reaumur  (16°*25  C. or  61°'25  F.)  and  has  been  found  equal  to  1-949036  meter  at  0°  C. The  French  standards  of  weight  were  a  series  of  weights known  as  the  Pile  of  Charlemagne,  and  dating  back  to  the  reign of  that  king  (about  789).  Together  they  aggregated  50  marcs, as  the  unit  of  the  series  was  termed,  or  25  livres  poids  de  marc (pounds),  and  in  standardizing  weights  the  sum  of  the  pile  was usually  taken  as  the  standard.  These  weights  are  now  preserved in  the  Conservatoire  des  Arts  et  Metiers  at  Paris,  and  have figured  in  many  comparisons.1 With  the  experience  which  the  French  scientists  had  gained in  their  brilliant  geodetic  work  during  the  18th  century,  it  was possible  to  employ  new  and  more  accurate  standards  of  length in  the  measurements  of  the  base  lines.  Accordingly,  for  the purpose  of  making  this  fundamental  measurement  in  determining the  length  of  the  earth's  quadrant,  four  compound  standard  bars of  novel  form  were  designed  and  constructed  by  Borda,  each of  which  was  two  toises  in  length,  six  lignes  in  width  and  almost one  ligne  in  thickness.2  Each  bar  consisted  of  a  strip  of  platinum connected  permanently  at  one  end  with  a  strip  of  copper,  which otherwise  was  free  to  move  longitudinally  as  it  expanded  or contracted.  At  the  opposite  end  the  copper  was  cut  away  for a  short  distance  and  a  movable  rod  of  platinum  was  provided,  so that  an  exact  and  variable  setting  could  be  made  by  means  of a  divided  scale  and  vernier.  As  the  two  metals  had  unequal coefficients  of  expansion,  it  was  possible,  by  determining  their relative  expansion,  as  indicated  by  a  graduated  scale  and  vernier, to  obtain  not  only  a  true  measure  of  length,  but  also  the temperature  of  the  bar.  This  was  accomplished  by  first  standard- izing the  bars  in  the  laboratory  and  measuring  the  relative expansion  corresponding  to  a  certain  number    of  degrees.3     In 1  See  C.  Mauss,  La  Pile  de  Charlemagne  (Paris,  1897).  A  mathematical discussion  of  these  weights. 2  See  Borda,  "  Experiences  sur  les  regies  destinees  a  la  mesure  des  bases  de  l'arc terrestre,"  Delambre  and  M^chain,  Base  du  Systeme  Me'trique,  vol.  iii.  p.  313. 3  These  bars  of  Borda  were  studied  and  standardized  by  Lavoisier.  See  Chisholm in  Nature  (London),  vol.  ix.  p.  185,  Jan.  8,  1874.  See  also  Dumas,  Works  of Lavoisier,  vol.  v. STANDARDS   AND   COMPARISON  251 use  in  the  field,  these  bars  were  placed  end  to  end  and  were carefully  levelled.  One  of  them  was  considered  as  a  standard, and  to  this  all  measurements  were  referred,  including  that  of the  seconds'  pendulum,  and  when  the  length  of  the  meter  was evaluated,  it  was  obtained  in  terms  of  the  fraction  ('256537) of  this  modulus.1 Compensated  bars  of  this  form  found  increased  use  in  the measurement  of  base  lines  in  geodetic  surveys  until  well  into the  19th  century,  though  they  have  been  largely  displaced  by  the employment  of  bars  of  a  single  material,  or  steel  tapes  or  wires whose  temperature  coefficients  are  accurately  known.  In  the  case of  the  metallic  bars,  in  one  of  the  most  accurate  base  measurements to  which  reference  has  already  been  made,  viz.,  that  at  Holton, Mich.,  which  was  made  in  connection  with  the  transcontinental survey  of  the  United  States,  the  distance  was  measured  by  means of  a  bar  carried  in  a  trough  of  melting  ice.2 In  passing  from  these  standards  of  Borda  to  the  meter,  use was  made  of  the  comparator  of  the  Committee,  and  that  of Lenoir,  already  described.  A  provisional  standard  of  brass,  first constructed,  served  as  a  means  of  connecting  the  two  measure- ments. Finally,  when  sufficient  data  had  been  obtained  and computed  to  justify  the  construction  of  a  definite  standard,  it was  made  from  a  mass  of  platinum  as  nearly  pure  as  possible and  of  a  rectangular  section.  It  was  an  end  standard  4  milli- meters in  thickness  and  25  millimeters  in  breadth  becoming  the Meter  of  the  Archives.3  From  the  same  material  and  at  the same  time  were  constructed  two  other  standards,  which  differed only  in  having  a  thickness  of  35  millimeters.  These  have  since been  known  as  the  Meter  of  the  Conservatory  and  the  Meter of  the  Observatory.4 1Benoit,  "  Dela  Precision  dans  la  Determination  des  Longueurs  en  Metrologie," Rapports  presented  au  Congres  International  de  Physique  (Paris,  1900),  vol.  i. p.  34.  Bigourdan,  Le  Systeme  Metrique  (Paris,  1900),  p.  83.  C.  Wolf,  "  Recherches historiques  sur  les  etalons  des  poids  et  mesures  de  l'Observatoire,"  Annales  de I'Observatoire  {Memoires),  Paris,  vol.  xvii.  p.  C  36  et  seq. 2  See  note  ante,  p.  141,  chapter  v. 3  For  Cross-section  see  illustration  on  p.  252.  No.  1  is  the  Meter  of  the Archives. 4C.  Wolf,  "Recherches  historiques  sur  les  etalons  des  poids  et  mesures  de l'Observatoire,"  Annales  de  V Observatoire  (Me'moires),  vol.  xvii.  p.  52. 252    EVOLUTION   OF   WEIGHTS   AND   MEASURES The  construction  of  the  actual  meter  was  accomplished  by- using  a  number  of  auxiliary  rules,  which  being  placed  end  to end  and  compared  both  among  themselves  and  with  the  modulus, enabled  the  true  length  of  the  meter  to  be  obtained.  This proceeding  involved  considerable  careful  mathematical  work  as well  as  manipulative  skill,  and  was  accomplished  with  a  remark- able degree  of  precision,  considering  the  apparatus  at  the  disposal of  the  investigators.  In  fact,  it  is  fair  to  say  that  modern  work of  this  character  is  more  exact  only  through  the  improved  instru- ments that  an  advance  in  mechanical  and  scientific  knowledge has  made  possible,  rather  than  in  any  greater  skill  and  carefulness on  the  part  of  the  observers. Although  a  large  number  of  standards  of  a  secondary  character were  constructed  by  the  different  bureaus  established  for  this purpose  by  the  French  Government  as  well  as  by  instrument makers,  but  little  advance  was  made  as  regards  their  form  and general  character.  In  most  of  them  the  rectangular  shape  was preserved,  and  though,  by  the  use  of  the  microscope,  a  more accurate  division  was  possible,  yet  no  standards  of  high  precision were  attempted.  When,  however,  the  custody  of  the  standards and  their  verification  was  assigned  to  the  Conservatoire  des  Arts et  Metiers,  more  interest  was  taken  in  this  work,  and  with  the installation  of  new  comparators,  the  scientific  staff  of  that  institu- tion began  researches  which  led  to  substantial  improvements. It  was  due  to  M.  Tresca,  who  was  Assistant  Director,  that  a thorough  study  of  the  shape  and  material  of  standards  was undertaken,  the  results  of  which  were  placed  at  the  service  of the  International  Commission,  when  it  assembled  in  1870.1 The  French  Committee,  of  which  he  was  a  member,  recom- mended in  preparing  the  specification  for  the  international  meter, that  the  new  standard  should  be  a  line  standard,  having  a  cross- section  sufficient  in  form  and  dimensions  to  preserve  accurately the  shape  of  the  bar,  and  that  its  coefficient  of  expansion  should^ be  as  nearly  as  possible  that  of  the  meter  of  the  Archives.  The platinum  which  went  to  make  up  this  original  standard  contained also  iridium,  together  with  a  small  amount  of  palladium,  and it  was  deemed   desirable,  in    constructing   a  new   prototype,  to 1See  Tresca,   Appendix   7,   Annates  du  Conservatoire    des    Arts  et   Mi '.tiers > vol.  x.  1873. STANDARDS   AND   COMPARISON 253 employ  an  alloy  of  platinum,  with  one-tenth  part  of  iridium,  as devised  by  H.  Sainte- Claire  Deville,  since  as  such  a  combination filled    the    required    conditions    of    inalterability,    homogeneity, r R u n H CI rj 12 df~ b Cross-Sections  of  Standards  (Studied  by  Tresca). 1. — Meter  of  the  Archives.  8. — Provisional  Standard  of  Platinum  Iridium. 9,  10,  12.— H  Standards.  13,  14,  15.— X  Standards. durability,  and  small  expansibility  under  the  influence  of  tem- perature. In  addition,  it  was  susceptible  of  taking  a  high  polish, and  possessed  numerous  other  physical  and  chemical  advantages which  made  it  particularly  suitable  for  this  purpose.1 1  Bigourdan,  Le  Systeme  M&rique,  p.  274. 254    EVOLUTION   OF   WEIGHTS   AND   MEASURES In  preparing  the  standards  of  length,  it  was  realized  by  the Commission  at  the  outset  that  two  essential  conditions  must be  fulfilled,  viz.,  that  the  metal  bars  should  be  as  rigid  as  pos- sible, without  employing  such  a  quantity  of  the  platinum  alloy as  would  make  their  cost  prohibitive,  and,  secondly,  that  the lines  marking  the  divisions  must  be  placed  in  the  plane  of  the neutral  fibres.  M.  Tresca,  who  had  given  the  subject  of standards  careful  study,  reported  to  the  Commission  on  their form,  and  stated  the  essentials  which  must  be  observed  in  the construction  of  a  new  standard  meter.  He  called  attention  to the  fact  that  it  was  necessary  that  the  distance  between  the two  limiting  lines  should  lie  entirely  in  a  plane  which  would contain  the  various  centres  of  gravity,  and  this  condition  could only  be  obtained  by  making  the  bar  of  such  cross-section  that it  would  have  the  greatest  rigidity.  He  also  deemed  it  essential that  the  cross-section  should  be  uniform  throughout  the  length of  the  bar,  and  that  the  median  plane  on  which  the  lines  were traced  should  be  available  for  tracing  the  necessary  divisions, and  for  observation  with  the  microscope  of  the  comparator.  M. Tresca  carried  on  a  series  of  experiments  and  investigations  with bars  of  different  cross-sections  for  which  he  calculated  the mechanical  constants,  and,  as  a  result  of  the  studies,  he  came to  the  conclusion  that  the  most  suitable  form  for  the  standards of  length  was  the  bar  of  X  section,  as  shown  in  the  accompany- ing figures. «.,, zom™. „  m 2omri m I I  \ Li  I I  \ Li 1  2 Cross-Section  of  Standard  Meter  Bars.    (Exact  size.) 1.— Line  Standard.  2.— End  Standard. It  will  be  seen  from  the  illustration  that  the  median  plane, or  plane  of  the  neutral  fibres,  lies  exactly  in  the  center  of  the bar,  and  is  available  for  marking  any  necessary  lines  or divisions.     This  is  the  case  with  the  line  standard.     For  the  end STANDARDS   AND   COMPARISON  255 standard  he  adopted  a  somewhat  similar  section,  but  with  the cross-bar  relatively  higher,  so  that  the  median  plane  passed through  its  center  instead  of  being  situated  in  its  upper  surface, as  in  the  case  of  the  line  standard.  The  section  in  either  case would  be  included  in  a  square  20  mm.  on  each  side,  and  the diagram  represents  accurately  the  actual  size  and  figure  of  the section.1 As  compared  with  the  Meter  of  the  Archives,  the  new  stan- dard proposed  by  Tresca  had  a  profile  1*509  times  as  great, so  that  the  actual  quantity  of  material  involved  was  but  slightly more  than  a  third,  but  the  form  of  construction  made  possible far  greater  strength  and  rigidity,  while  at  the  same  time  the standard  distance  was  measured  in  the  neutral  plane.  These recommendations  were  duly  adopted,  the  material  was  prepared according  to  the  above  specifications,  and  the  bars  were  delivered to  the  Conservatoire  des  Arts  et  Metiers,  where  the  standards were  constructed  by  the  French  section  under  the  terms  of  the international  agreement. In  the  comparison  of  the  prototype  meters  among  themselves and  with  the  international  standard,  the  first  step  was  to  con- struct a  provisional  meter,  whose  constants  were  determined directly  in  terms  of  the  Meter  of  the  Archives.  For  this  purpose a  comparator  with  a  transverse  movement  was  employed,  while for  making  the  definitive  marks  on  the  bars  a  longitudinal comparator  was  used.  The  comparisons  between  the  Meter  of the  Archives  and  the  provisional  meter  were  made  at  the  Conser- vatoire des  Arts  et  Metiers.  The  standard  bars  were  taken  to  the Bureau  International,  where  was  made  a  series  of  comparisons which  established  their  relations  to  each  other,  as  well  as  to  the international  prototype.2  Of  the  thirty  bars  thus  examined,  the one  that  approached  most  nearly  the  length  of  the  Meter  of the  Archives  was  selected  as  the  international  prototype,  and a  new  scale  was    chosen    to    take    its    place    in    the    series    of ^uillaume,  La  Convention  du  Metre  (Paris,  1902),  pp.  15-18;  Benoit,  "  De la  Precision  dans  la  Determination  des  Longueurs  en  Metrologie,"  JRapports, Congres  de  Physique  (Paris,  1900),  tome  i.  p.  48. 2 See  U.S.  Coast  and  Geodetic  Survey  Report,  1890,  Appendix  18,  pp.  743  et  seq.y for  a  description  of  the  construction  of  the  standard  meter  bars  ;  also  Bigourdan, Le  Systeme  Me'trique. 256    EVOLUTION   OF   WEIGHTS   AND   MEASURES comparisons.  As  a  result  of  these  comparisons,  the  probable  error of  a  single  comparison  was  stated  at  ±0-12  /a — the  probable  error in  the  length  of  any  one  of  the  standards  being  stated  at ±0"04  jii}  From  the  result  of  many  years  of  comparison  at  the Bureau  International,  the  conclusion  is  reached  that  the  length of  a  standard  can  be  absolutely  guaranteed  to  an  exactitude  of about  *2  micron  at  all  usual  temperatures.2 In  the  construction  of  standards  of  weights,  the  instrument makers  of  the  eighteenth  century  had  gradually  become  more proficient,  and  their  work  partook  of  greater  precision,  both  in the  weights  themselves  and  in  the  balances.  Nevertheless,  no particular  features  are  worthy  of  note  until  the  kilogram  of  the Archives  was  constructed.  This  unit  of  weight,  as  we  have  seen, was  defined  as  the  "weight  of  a  cubic  decimeter  of  distilled  water, taken  at  its  maximum  density  and  weighed  in  a  vacuum."  To realize  such  a  definition  in  a  standard  would  apparently  involve the  construction  of  a  cubic  vessel  whose  side  was  exactly  a decimeter,  and  then  ascertaining  the  weight  of  water  contained therein.  A  measurement  of  this  kind  could  be  made  by  taking a  vessel  of  regular  form  and  known  interior  dimensions,  but  to determine  its  volume  accurately  by  any  process  of  measuring was  a  difficult,  if  not  an  impossible  proceeding.  Eecourse  was had,  accordingly,  to  the  law  of  Archimedes,  which  states  that  a body  immersed  in  a  fluid  loses  an  amount  of  weight  equal  to the  weight  of  the  volume  of  the  fluid  which  it  displaces.  Con- sequently, in  order  to  determine  the  weight  of  the  displaced water,  it  was  necessary  to  weigh  a  solid  body  of  regular  form, first  in  air,  reducing  to  vacuum,  and  then  in  water,  making suitable  provision  or  correction  for  its  temperature.  *  In  order to  determine  exactly  the  volume  of  such  a  body,  it  must  be constructed  in  a  regular  geometric  form,  such  as  a  cube  or  a cylinder.  The  latter  form  was  adopted  in  making  the  standard of  weight  by  the  Committee  of  the  Meter,  and  Lefevre-Gineau, with  the  assistance  of  Fabbroni,  standardized  a  hollow  cylinder of  brass,  which  was  constructed  for  them  by  Lenoir.  It  was 243*5  millimeters  in  height  and  diameter,  and  thus  had  a  volume 1  Benoit,    Rapports,    Congres  International  de  Physique  (Paris,   1900),   vol.  i. p.  63. Ubid.  p.  66. STANDARDS   AND    COMPARISON  257 slightly  in  excess  of  eleven  cubic  decimeters,  and  had  a  weight  in water  of  about  200  grams.1  The  dimensions  of  the  cylinder  were •obtained  with  a  lever  comparator  from  a  scale  equal  to  the  ^ part  of  the  modulus  (the  double  toise  standard  of  Borda).  As  a result  of  these  experiments,  a  theoretical  value  of  18827*15  grains {poids  de  marc)  was  assigned  to  the  kilogram,  and  such  a  weight was  constructed  in  pure  platinum  to  be  the  prototype  standard.2 Unfortunately,  no  record  has  been  left  to  us  of  the  methods employed  in  constructing  such  a  standard.  It  is  known,  how- ever, that  at  the  time  when  the  platinum  was  prepared  for  the four  standard  meter  bars,  material  was  made  ready  for  four cylinders  destined  for  the  standard  kilogram.  After  adjustment, one  of  these  was  taken,  and  has  since  survived  as  the  Kilogram of  the  Archives.  It  is  unquestionable,  however,  that  the  same balance  and  weights  employed  in  determining  the  weight  of  a cubic  decimeter  of  water  were  used  in  these  latter  operations.3 During  the  first  half  of  the  19th  century,  with  the  growth of  experimental  physics  and  with  improvements  of  apparatus, new  methods  giving  a  high  degree  of  precision  were  available  for use  with  the  balance.  Consequently,  in  the  construction  of weights  and  in  their  reference  to  standards,  much  more  precision was  obtained  than  ever  previously.  This,  however,  did  not  cause any  marked  demand  for  new  metric  standards,  although  various physicists  were  of  the  opinion  that  the  kilogram  did  not  repre- sent accurately  the  mass  of  a  cubic  decimeter  of  water.  These determinations,  however,  varying  as  they  did — being  both  greater and  smaller  than  the  Kilogram  of  the  Archives — did  not  inspire any  greater  degree  of  confidence.  Accordingly,  when  it  was proposed  to  construct  new  standards  for  the  meter  and  the kilogram,  it  was  decided  to  use  the  Kilogram  of  the  Archives as  the  basis,  and  then  by  subsequent  experiments  determine its  relation  to  the  mass  of  a  cubic  decimeter  of  water  at  its  tem- perature of  maximum  density.  Accordingly,  the  International Commission     made     arrangements    for     such     an    investigation. ^uillaume,  La  Convention  du  Metre,  p.  5. 2  For  full  description  of  the  determination  of  the  standard  of  mass,  see Delambre  and  Mechain,  Base  du  Systeme  Me'trique,  vol.  iii.  pp.  579-638 ; Bigourdan,  Le  Systeme  Me'trique,  p.  107. 3Bigourdan,  Le  Systeme  Me'trique,  p.  159. R 258     EVOLUTION  OF   WEIGHTS  AND  MEASURES To  this  body,  in  1879,  three  cylinders  of  platinum-iridium alloy,  designed  for  standard  kilograms,  were  delivered,  and were  then  compressed  in  a  powerful  coining-press  of  the Paris  Mint.  They  were  then  given  to  an  instrument  maker for  approximate  adjustment,  and  samples  of  the  material  were submitted  to  chemical  analysis  by  Stas  and  Sainte-Claire Deville,  it  having  been  found  by  experiments  at  the  Ecole Normale  that  the  final  density  was  21*55.  The  first  adjustment was  made  with  the  kilograms  of  the  Paris  Observatory,  which were  copied  from  that  of  the  Archives,  and  for  this  purpose a  balance  of  the  Ecole  Normale  Superieure  was  employed.  After the  three  standards  had  received  their  final  adjustment  at  the hands  of  M.  A.  Collet,  they  were  then  compared  with  the  Kilo- gram of  the  Archives,  with  the  standards  of  the  Observatory  and the  Conservatoire,  and  with  the  standard  kilogram  of  Belgium,, and  then  final  comparisons  were  made  at  the  Paris  Observatory, both  the  French  section  and  the  International  Committee  being duly  represented.1 The  volume  of  these  three  new  standards  was  determined by  hydrostatic  weighings,  and  compared  with  that  of  the  standard of  the  Archives,  which,  however,  was  determined  by  other  methods, as  it  was  not  deemed  advisable  to  place  it  in  water.2  The  work was  finished  October  18,  1880,  when  the  Committee  submitted  a report  covering  other  duties. After  a  careful  examination  of  these  three  kilograms  among themselves,  and  with  the  standard  kilogram  of  the  Archives,  the committee  deemed  it  wise  to  select  one  which  was  known  as Kill  as  the  standard  kilogram,  rather  than  to  make  a  series  of additional  comparisons  with  the  other  kilograms,  to  be  constructed as  national  standards,  in  the  course  of  which  the  platinum-iridium cylinder  would  doubtless  experience  a  certain  amount  of  injury. Accordingly,  this  was  adopted  in  a  formal  resolution,  at  a  meet- ing held  October  3,  1883,  and  that  kilogram  has  since  been designated  by  |Ji,  although  it  bears  no  mark.3 In  the  following  year,  after  several  attempts  had  been  made  to secure    an   alloy    of  the  necessary    purity,   satisfactory  material 1  Guillaume,  La  Convention  du  Metre  (Paris,  1902),  p.  123. 2  Ibid.  p.  124. 3Bigourdan,  Le  Systeme  Me'trique  des  Poids  et  Mesures  (Paris,  1901),  p.  365. STANDARDS   AND    COMPARISON  259 suitable  for  the  national  prototypes  was  delivered  in  the  form  of forty  cylinders.  These  were  worked  down  to  approximately  the exact  weight,  and  finished  under  the  direction  of  the  members  of the  commission  and  an  elaborate  series  of  comparisons  was  under- taken.1 The  weighings  were  effected  by  means  of  the  Rueprecht  and Bunge  balances  already  described,  the  latter  being  employed when  comparisons  were  made  with  the  international  prototype, which,  of  course,  was  preserved  most  carefully  from  any  deterio- rating influences.  The  constants  were  calculated  separately  for each  standard,  and  they  were  found  to  agree  within  a  limit  of one  milligram,  and  were  accepted  by  the  International  Committee, this  decision  being  formally  sanctioned  at  the  International  Con- ference in  1889.  Originally  it  had  been  determined  to  insist  on an  accuracy  of  '2  of  a  milligram  for  each  kilogram,  but  in  certain cases  it  was  found  that  the  polishing  had  been  carried  on  too vigorously,  and  it  was  accordingly  found  necessary  to  fix  the  limit of  accuracy  at  one  milligram,  within  which  limits  the  forty standards  all  fell.  For  example,  those  given  to  the  United States,  in  the  drawing  by  lot  (Nos.  4  and  20)  were  found  to  have an   error  of  —  '075  milligram  and  —  '039  milligram  respectively.2 The  permanence  of  the  national  standards  of  mass  is  no  less important  than  that  of  the  standards  of  length.  After  about ten  years  there  was  made  at  the  Bureau  International  a  com- parison of  eight  standards  from  seven  different  nations  with  the working  standards  of  the  Bureau,  and  it  was  found  that  the deterioration  experienced  was  barely  appreciable,  ranging  as  it did  from  '027  milligram  in  the  case  of  one  of  the  Belgian standards,  to  '001  of  a  milligram  in  the  case  of  that  from Roumania.  It  was  possible  that  the  deterioration  in  the  case of  some  of  the  kilograms  which  had  experienced  considerable usage,  was  as  much  as  '04  of  a  milligram,  but  it  was  believed  that the  future  would  not  show  as  great  an  amount  of  change.3 The  idea  of  the  founders  of  the  Metric  System  to  establish  a unit  of  length  which  would  be  absolutely  invariable,  by  means  of its  reference  to  the  dimensions  of  the  earth,  and  also  by  reference 1Guillaume,  La  Convention  du  Metre,  p.  125.  2  Ibid.  p.  126. 3  Ibid.  p.  127.     Also  Report  by  M.  Benoit  in  Proces-Verbaux  des  Seances  de 1900,  ComiUs  International  des  Poids  et  Mesures.     See  also  Proces-  Verbaux,  1905. 260     EVOLUTION  OF  WEIGHTS  AND  MEASURES to  the  seconds'  pendulum,  was  not  destined  to  survive.  It  soon was  seen,  in  view  of  subsequent  researches,  that  the  trigono- metrical operations  on  which  the  length  of  the  meter  was  based were  not  carried  on  with  an  exactitude  required  by  modern methods  of  geodetic  work,  and  that,  as  a  result,  the  standard  was in  error  by  about  *1  millimeter.  This  did  not  detract  from  the usefulness  of  the  system,  but  it  did  require  the  abandonment  of the  idea  of  referring  the  meter  to  the  ten-millionth  of  the  earth's quadrant  as  a  natural  standard.  A  century  after  the  Metric System  was  established,  it  was  found  possible  to  realize  the condition  of  reference  to  a  natural  and  invariable  standard,  which was  at  that  time  thought  so  fundamental,  and  the  meter  was defined  in  terms  of  wave-length  of  light,  after  a  series  of  most elaborate  experiments  carried  on  at  the  International  Bureau  of Weights  and  Measures  by  Professor  A.  A.  Michelson,  later  of  the University  of  Chicago,  who  had  previously  distinguished  himself by  his  accurate  determination  of  the  velocity  of  light. The  fundamental  idea  of  using  a  wave-length  of  light  was  by no  means  new,  as  a  unit  of  this  nature  had  been  proposed  by J.  Clerk  Maxwell,1  who  suggested  that  a  system  of  absolute units  could  be  founded  on  the  following  basis : As  a  unit  of  length,  the  wave-length  of  some  determined  kind of  light  in  vacuo, As  a  unit  of  time,  the  period  of  vibration  of  this  light, As  a  unit  of  mass,  the  mass  of  a  single  molecule  of  a  specified substance. By  determining  a  unit  of  length  in  terms  of  wave-lengths  of light,  a  standard  would  be  obtained  independent  of  any  gradual contraction  of  the  terrestrial  globe,  which  naturally  would  produce a  change  in  the  length  of  the  meridian,  or  other  terrestrial disturbance.  Likewise,  it  would  be  independent  of  molecular changes  occurring  in  a  metallic  bar,  and  naturally  affecting  its dimensions.  The  length  of  a  wave  of  light  would  under  all conditions  be  most  invariable,  as  it  depends  solely  on  the elasticity  of  the  ether.  Such  a  unit,  then,  gives  us  a  means  of establishing  the  permanent  values  of  the  meter,  as  by  determining its  length  in  these  minute  distances  represented  by  the  vibration of  particles  producing  one  kind  of  light,  we  have  a  much  better 1  Maxwell,  Electricity  and  Magnetism  (third  edition,  Oxford,  1891),  vol.  i.  pp.  3,  4. STANDARDS    AND    COMPARISON  261 means  of  fixing  its  invariability  than  by  comparing  it  with  the length  of  a  meridian  or  with  the  seconds'  pendulum. In  order  to  define  the  standard  of  length  in  terms  of  the wave-length  of  light,  a  study  of  different  sources  of  light  was essential,  and  was  carried  on  by  Professor  Michelson  with  great thoroughness.  For  this  purpose,  he  used  the  luminous  vapors  of metals  produced  by  the  passage  of  an  electric  current  from  the induction  coil  through  a  vacuum  tube.  By  a  process  of  elimina- tion, he  found  that  the  most  suitable  source  of  light  was  the spectrum  furnished  by  the  metal  cadmium,  which  gave  a  series  of lines  valuable  for  his  purpose.  The  visible  spectrum  of  this metal  consisted  of  four  groups  of  lines, — one  red,  which  was  single and  also  fine ;  the  second,  a  series  of  fine  green  lines ;  the  third, a  blue  line ;  the  fourth,  a  violet  line.  In  his  early  experiments, Professor  Michelson  used  the  green  rays,  but  in  later  work, especially  by  M.  Hamy  and  M.  Chappuis,  the  others  were employed  and  greater  precision  was  attained.1 Professor  Michelson's  method  is  based  on  the  fact  that  inter- ference is  produced  in  a  beam  of  light  after  two  of  its  component parts  are  compelled  by  means  of  reflection  to  travel  distances slightly  unequal.  The  earliest  application  of  this  principle  of interference  in  metrology  was  when  Fizeau  endeavored  to determine  accurately  the  coefficients  of  expansion  of  samples  of various  substances.  By  placing  a  plano-convex  lens  over  and very  close  to  the  terminal  surface  of  the  body  to  be  studied,  and causing  a  beam  of  sodium  (yellow)  light  to  fall  from  above  on  the lens,  he  was  able  to  obtain  the  optical  phenomenon  known  as interference  by  observing  the  reflected  beam.  This  was  similar in  nature  to  the  well-known  experiment  called  Newton's  rings, where  the  difference  in  path  of  the  rays  of  light  reflected  from the  surface  of  a  body  and  those  reflected  from  the  surface  of  the lens  produces  interference.  The  reason  for  this  is  found  in  the fact  that  waves  of  monochromatic  light,  when  so  impeded  that  a part  of  them  lose  a  half-wave  length  or  some  odd  number  of half-wave  lengths,  will  neutralize  each  other,  and  consequently produce  darkness  when  they  reach  a  certain  point.  This  is  due to  the  particles  at  this  point  being  under  the  influence  of  waves in  opposite  phases.     If,  on  the  other  hand,  where  they  meet,  the 1  Guillaume,  La  Convention  du  Metre,  p.  147. 262     EVOLUTION  OF  WEIGHTS  AND  MEASURES number  of  half-wave  lengths  is  even,  there  is  increased  effect, which  is  manifested  by  greater  brightness.  In  the  case  of  a  lens, arranged  as  above,  there  would  be  a  series  of  alternate  light  and dark  concentric  rings.  If  white  light  is  used,  these  rings  will show  spectral  colors,  which  become  complex  with  an  increase  in distance  from  the  center.  With  such  an  arrangement,  Fizeau  was able  only  to  measure  short  distances,  which  did  not  exceed  12  or 15  mm.  in  length.  His  method  was  useful,  however,  in  measuring accurately  the  screw  of  the  micrometer  of  the  comparators.1 Using  the  same  idea,  but  developing  it  practically,  Professor Michelson  was  able  to  measure  the  length  of  the  meter  in  terms of  waves  of  light.  Part  of  the  difficulty  was  solved  by  the American  physicist  when  he  found  a  suitable  source  of  light,  as has  been  described  above,  but  it  was  largely  due  to  his  ingenious methods  and  apparatus,  as  well  as  to  his  manipulative  skill,  that he  was  able  to  carry  his  plan  to  so  successful  a  conclusion.2  His arrangement  was,  in  substance,  as  follows :  Light  from  the  given source,  S,  was  allowed  to  fall  on  a  glass  plate  at  A,  ground  so that  the  surfaces  were  perfectly  plane  and  parallel.  This  plate was  placed  obliquely  to  the  axis  of  the  beam  and  on  the  side  A was  silvered,  so  that  it  formed  a  semi-transparent  reflector.  The beam  falling  on  this  silvered  surface  was  divided  into  two  parts, one  of  which  passed  through  the  silver  film  and  glass,  and  after reflection  at  E  in  the  mirror  B  to  a  mirror,  Nt  from  which  it was  reflected  back  through  the  glass  plate  to  the  interior surface  of  the  film,  where  it  underwent  reflection  again, back  through  the  glass  and  to  a  telescope,  T,  so  arranged  as  to enable  the  fringes  produced  in  its  field  to  be  observed.  The  other part  of  the  beam  was  reflected  at  the  silvered  surface  and  trans- mitted through  a  second  glass  plate,  Q,  whose  thickness  was  equal to  the  first,  to  a  mirror,  M,  where  it  was  reflected  back  through the  first  plate  in   the  same  direction  as  the  first  beam.     Both 1J.  Rene  Benoit,  "Etudes  sur  l'appareil  de  M.  Fizeau  pour  la  mesure  des dilatations  appartenant  au  Bureau  International  des  Poids  et  Mesures,"  vol.  ii. Travaux  et  M6moires,  Bureau  International  des  Poids  et  Mesures,  Paris. 2  Guillaume,  La  Convention  du  Metre  (Paris,  1902),  pp.  146-169.  A.  A.  Michelson, "Determination  expe>imentale  de  la  valeur  du  metre  en  longueurs  d'ondes lumineuses,"  vol.  xi.  Travaux  et  Mdmoires,  Bureau  International  des  Poids  et Mesures,  Paris. STANDARDS    AND   COMPARISON  263 H A V 264     EVOLUTION  OF  WEIGHTS  AND  MEASURES beams  meeting  at  the  telescope,  interference  phenomena  would appear  if  there  were  any  difference  in  the  length  of  their  respective paths,  ADFEFDAC  and  ABAC.  By  displacing  one  of  the  mirrors by  a  small  amount  through  the  agency  of  a  screw,  this  difference of  position  could  be  measured  in  terms  of  wave-length.  The  first task  of  the  investigator  was  to  determine  the  length  of  a  very  short standard  by  displacing  the  fringes  for  a  counted  number  of  wave- lengths. Then  with  this  as  a  standard,  he  would  be  able  to  construct a  standard  twice  as  long  and  derive  its  length  in  wave-lengths.  In this  way  Professor  Michelson  prepared  a  number  of  standards  of lengths,  each  double  the  length  of  another,  so  that  he  was  able  to step  from  one  to  the  other  and  at  the  same  time  preserve  the original  accuracy,  Finally  he  standardized  a  piece  one  decimeter in  length,  and  with  this  he  made  a  comparison  with  the  inter- national meter,  displacing  it  ten  times  and  measuring  the  displace- ment by  interference  methods  so  as  to  start  from  the  first  line  of the  meter  and  then  reach  the  second,  and  so  on ;  using  three different  kinds  of  light,  viz.  the  red,  green,  and  blue  of  the cadmium  spectrum,  he  determined  the  wave-length  of  each  or the  number  of  times  this  wave-length  was  contained  in  the standard  meter.  The  wave-lengths  for  each  color  were  as follows : Red  radiations     1  meter  =15531 63 '6  \R,   of  which   kR  =  -64384722  /x. Green  radiations 1  meter  =  1966249*7  Xv,   of  which   AF=  "50858240  /x. Blue  radiations    1  meter  =  2083372-1  XB,   of  which   AB=  -47999107  /x. The  accuracy  of  this  work  is  almost  incredible,  as  the variation  in  the  measurements  was  only  about  one  part  in  ten million.  In  fact,  where  a  precision  of  from  one-fourth  to one-fifth  of  a  micron  is  possible  in  the  case  of  determining the  relative  length  of  two  standards,  here  is  an  absolute measurement  which  gives  the  length  of  a  standard  in  terms of  a  natural  unit,  under  conditions  reproducible  at  any  time.  This, of  course,  gives  a  permanent  check  on  the  integrity  of  the  meter, as  in  the  event  of  the  international  prototype  being  damaged or  destroyed,  sufficient  data  is  at  hand  to  enable  such  physicists as  may  be  found  at  any  international  laboratory  or  bureau  of standards  to  redetermine  this  fundamental  unit.  The  apparatus  of Professor  Michelson  represented  the  highest  skill  of  the  instrument STANDARDS    AND   COMPARISON  265 maker,  as  mirrors  and  optical  planes  were  finished  to  a  high degree  of  exactitude,  reaching  in  some  cases  an  accuracy  as great  as  40^00  of  a  millimeter,  or  the  -^  of  the  mean  wave- length of  light. Just  what  this  work  of  determining  standards  of  length  in terms  of  the  wave-length  of  light  means  to  science  can  be  readily understood  if  a  moment's  consideration  be  given  to  the  enormous mass  of  scientific  and  technical  literature  and  knowledge,  to  the numberless  instruments  of  measurement  and  tools  and  appliances of  trade.  At  first  thought  it  would  seem  that  if  some  cataclysm should  suddenly  destroy  all  these  evidences  of  advancement,  then the  poor  individual  who  might  have  survived  would  be  compelled to  begin  all  over  again,  and  his  standards  and  units  would have  to  be  new,  and  he  would  have  no  means  of  connect- ing his  system  with  the  past.  All  the  observations  on matters  astronomical  or  terrestrial,  all  that  mass  of  information which  it  has  taken  centuries  and  centuries  to  accumulate,  would be  hopelessly  lost  because  of  the  break  in  the  standards  of measurement.  The  meter  would  be  gone,  the  quadrant  of  the earth  no  longer  the  same,  and  apparently  our  last  tie  broken. ISTot  all  the  ties,  for  one,  a  little  one,  remains,  like  hope  in  the bottom  of  Pandora's  box.  A  wave  of  light  so  small  that  a thousand  would  scarcely  reach  across  the  eye  of  a  needle,  this is  the  key  to  the  restoration  of  our  system  of  most  complicated and  complete  units.  So  long  as  the  earth  has  a  material  exist- ence, so  long  as  there  is  light  and  heat,  so  long  is  man  in the  position  to  rebuild  his  system  of  units  and  standards. The  work  of  Michelson  in  comparing  the  international  meter with  the  wave-lengths  of  light  has  put  our  system  upon  a foundation  that  is  as  permanent  as  the  universe.  If  man  were transported  to  the  uttermost  confines  of  the  universe,  he  would still  have  the  little  waves  of  light,  and  they  would  be  just  the same  as  here. If  some  day  we  are  able  to  communicate  with  the  dwellers upon  some  other  planet,  it  will  be  a  simple  thing  to  communicate to  them  our  standard  of  length  and  time  and  mass,  and  with  the little  waves  of  light  to  convey  our  message  we  may  ultimately impart  our  exact  knowledge  to  them,  and  receive  theirs  in return.     The  laws  of  light  motion,  of  gravitation,  of  electricity 266     EVOLUTION  OF  WEIGHTS  AND  MEASURES are  undoubtedly  identical  for  the  whole  universe,  and  given the  first  communication  of  another  world  we  would  be able  to  establish  a  truly  universal  system  of  units  and  stan- dards. By  this  means  inter-planetary  communication  would be  placed  upon  a  quantitative  basis,  and  the  omnipresent,  ever- lasting, but  ultra-microscopic  wave  of  light  would  be  the universal,  unchanging  standard. APPENDIX. TABLES  OF   CONVERSION  FEOM   COMMON  TO  METRIC MEASURES,   USEFUL  CONSTANTS  AND EQUIVALENTS. NOTE. Unless  otherwise  specified,  the  following  tables  are  based on  the  U.S.  Legal  Equivalents.  They  are  derived  for  the most  part  from  the  Tables  of  Equivalents  published  by  the National  Bureau  of  Standards  of  the  U.S.  Department of  Commerce  and  Labor. LEGAL  EQUIVALENTS   OF   THE   UNITED   STATES. Act  of  July  28,  1866.     Revised  Statutes  3570. MEASURES  OF  LENGTH. Metric  Denominations  and  Values. Equivalents  in  Denominations  in  Use. Myriameter, . 10,000  meters. 6-2137  miles. Kilometer, - 1,000  meters. 0-62137  miles  or  3,280  feet  and  10  inches. Hectometer, - 100  meters. 328  feet  and  1  inch. Dekameter, - 10  meters. 393-7  inches. Meter, - 1  meter. 39-37  inches. Decimeter, - y  (7  of  a  meter. 3-937  inches. Centimeter, - y^jTj-  of  a  meter. 0-3937  inch. Millimeter, - ToVo"  °f  a  meter. 0-0394  inch. MEASURES   OF  CAPACITY. Metric  Denominations  and  Values. Equivalents  in  Denominations  in  Use. Names. Number of  Liters. Cubic  Measure. Dry  Measure. Liquor  or Wine  Measure. Kiloliter  \ or  Stere J Hectoliter Dekaliter Liter Deciliter Centiliter Milliliter 1000 100 10 1 1 TO" 1 TTT0" TO-TRF 1  cubic  meter YX7  of  cubic  meter 10  cubic  decimeters 1  cubic  decimeter To-  cubic  decimeter 10  cubic  centimeters 1  cubic  centimeter 1  -308  cub.  yards /  2  bushels  and  \ \     3  35  pecks     J 9-08  quarts 0-908  quart 6 -1022  cub.  inches 0-6102  cub.  inch 0-061  cub.  inch 264-17  gallons. 26-417  gallons. 2-6417  gallons. 1  -0567  quarts. 0-845  gill. 0-338  fluid  ounce. 0-27  fluid  dram. MEASURES  OF  SURFACE. Metric  Denominations  and  Values. Equivalents  in  Denominations  in  Use. Hectare, Are, Centare, 10,000  square  meters. 100  square  meters. 1  square  meter. 2-471  acres. 119  "6  square  yards. 1,550  square  inches. 270     EVOLUTION  OF  WEIGHTS  AND  MEASURES WEIGHTS. Metric  Denominations  and  Values. Equivalents  in  De- nominations in  Use. Names. Number  of Grams. Weight  of  what Quantity  of  Water  at Maximum  Density. Avoirdupois  Weight. Millier  or  Tonneau Quintal Myriagram Kilogram  or  Kilo Hectogram Dekagram Gram Decigram Centigram Milligram 1,000,000 100,000 10,000 1,000 100 10 1 1 To" TTTO 1 1  cubic  meter 1  hectoliter 10  liters 1  liter 1  deciliter 10  cubic  centimeters 1  cubic  centimeter jjy  cubic  centimeter 10  cubic  milliliters 1  cubic  milliliter 2204-6  pounds. 220-46  pounds. 22-046  pounds. 2-2046  pounds. 3-5274  ounces. •3527  ounce. 15*432  grains. 1  -5432  grains. 0-1543  grain. 0-0154  grain. 1000 BRITISH  LEGAL   (BOARD   OF  TRADE)  EQUIVALENTS. May,  1898. LINEAR  MEASURE. Metric. 1  Millimeter  (mm. )  (t  o~Vo"  m- ) 1  Centimeter  (y^xj  m-) 1  Decimeter  \y$  m.) 1  Meter  (m. ) 1  Dekameter  (10  m.) 1  Hectometer  (100  m.) 1  Kilometer 003937  Ins. 0-3937  Ins. 3-937  Ins. '  39-370113  Ins. 3-280843  Ft. .     10936143  Yds. 10-936  Yds. 109-36  Yds. •62137  Mile. 1  Inch 1  Foot  (12  ins.) 1  Yard  (3  ft.) 1  Fathom  (6  ft.) 1  Pole  (54  yds.) Imperial. =  25-400  Millimeters. 0-30480  Meter. 0-914399  Meter. 1-8288  Meters. 5-0272  Meters. 1  Chain  (22  yds.)    =  20-1168  Meters. 1  Furlong :  201  168  Meters. 1  Mile  (8  furlongs)  =     1-6093  Kilometers. BRITISH   LEGAL   EQUIVALENTS  271 SQUARE  MEASURE. Metric. 1  Square  Centimeter  =        0*15500  Sq.  In. 1  Sq.  Decimeter  (100  sq.  centimeters)       =      15*500  Sq.  In. 1  Sq.  Meter  (100  sq.  decimeter,)  =  {  ™™  g;  ^ 1  Are  (100  sq.  meters)  =    119*60  Sq.  Yds. 1  Hectare  (100  ares  or  10,000  sq.  meters)  =        2*4711  Acres. Imperial. 1  Square  Inch  =     6*4516  Sq.  Centimeters. 1  Sq.  Ft.  (144  sq.  ins.)=     9*2903  Sq.  Decimeters. 1  Sq.  Yard  (9  sq.  ft.)    =       "836126  Sq.  Meter. 1  Perch  (30£  sq.  yds.)  =  25*293  Sq.  Meters. 1  Rood  (40  perches)      =   10*117  Ares. 1  Acre  (4840  sq.  yds.)  =     0*40468  Hectare. 1  Sq.  Mile  (640  acres)  =259  Hectares. CUBIC  MEASURE. Metric. 1  Cubic  Centimeter  =        '0610  Cubic  In. 1  Cubic  Decimeter  (c.d.)  (1000  cubic  centimeters)  =    61*624  Cubic  Ins. .  «  . .    .,  t     /1AAA      ..     ,     .      .      >  f  35*3148  Cubic  Ft. 1  Cubic  Meter  (1000  cubic  decimeters)  =■{       nrvf,neA  ~  ,  .    «.. I   1*307954  Cubic  Yds. Imperial. 1  Cubic  Inch  =  16*387  Cubic  Centimeter. 1  Cubic  Foot  (1728  cub.  ins.)  =  0*028317  Cubic  Meter. 1  Cubic  Yard  (27  cub.  ft.)      =  0*764553  Cubic  Meter. CAPACITY. Metric. 1  Centiliter  (TJ<j  liter)  =  *670  Gill. 1  Deciliter  (TV  liter)  =  *176  Pint. 1  Litre  =  1  *75980  Pints. 1  Dekaliter  (10  liters)     =2*200  Gallons. 1  Hectoliter  (100  liters)  =  2*75  Bushels. Imperial. 1  Gill  =  1  *42  Deciliter. 1  Pint  (4  gills)  =    *568  Liters. 1  Quart  (2  pints)         =  1  *136  Liters. 1  Gallon  (4  quarts)     =4*5459631  Liters. 1  Peck  (2  gallons)       =9*092  Liters. 1  Bushel  (8  gallons)    =3*637  Dekaliters. 1  Quarter  (8  bushels)  =  2*909  Hectoliters. 272     EVOLUTION  OF  WEIGHTS  AND  MEASURES WEIGHT. Metric. 1  Milligram  (iijjyjj  grm.)  = 1  Centigram  (T J^  grm. )  = 1  Decigram  (y o  grm- )  = 1  Gramme  (1  grm.)  = 1  Dekagram  (10  grm.)  — 1  Hectogram  (100  grm.)     = 1  Kilogram  (1000  grm.)     = 1  Myriagram  (10  kilog.)    = 1  Quintal  (100  kilog.) 1  Tonne  (1000  kilog.) 1  Gramme  (1  grm.)  = 1  Gramme  (1  grm.)  ==■ Imperial. Avoirdupois. 1  Grain  : 1  Dram 1  Oz.  (16  drams) 1  Pound  (16  oz.  or  7000  grains)     = 1  Stone  (14  lb.) 1  Quarter  (28  lb.) 1  Hundredweight  (cwt.)  (112  lb.)  =  { lTon(20cwt.) Troy. 1  Grain 1  Pennyweight  (24  grains) 1  Troy  ounce  (120  pennyweights): Apothecaries'  Weight. 1  Grain  : 1  Scruple  (20  grains)  : 1  Drachm  (3  scruples)  -. 1  Oz.  (8  drachms)  : Avoirdupois. 0-015  Grain. 0-154  Grain. 1  -543  Grains. 15-432  Grains. 5-664  Drams. 3-527  Oz. f         2-2046223  Lb.  oz. 115432-3564  Grains. 22-046  Lb. 1-968  Cwt. 0-984  Ton. Troy. /         0-03215  Oz.  Troy, t       15-432  Grains. Apothecaries'  Weight. (        0-2572  Drachm. |         0-7716  Scruple. I       15-432  Grains. 0-0648  Gramme. 1  -772  Grammes. 28-350  Grammes. 0-45359243  Kilogram. 6  "350  Kilograms. 12-70  Kilograms. 50-80  Kilograms. 0-5080  Quintal. /   1-0160  Tonnes  or U016  Kilograms. 0  0648  Gramme. 1  "5552  Grammes. 31-1035  Grammes. 0-0648  Gramme. 1  -296  Grammes. 3-888  Grammes. 31-1035  Grammes. APOTHECARIES'  MEASURE. 1  Minim 1  Fluid  Scruple 1  Fluid  Drachm  (60  minims) 1  Fluid  Ounce  (8  drachms) 1  Pint =  0-059  Milliliter. =  1-184  Milliliters. =  3-552  Milliliters. =  2-84123  Centiliters. =  0-568  Liter. 1  Gallon  (8  pints  or  160  fluid  oz.)  =  4-5459631  Liters. EQUIVALENTS   OF   UNITS   OF   LENGTH 273 0 l-H Eh Q pfl p H s o OS     i-« 9m o IS S3 'HH      ^ ^    » OS    O o  « l-H      OT o ^  o 9  § o  9 2  9 S3 3 -—I   eo co   S~ ©  'H ©Ico ©  io ©  «o IO     » CM    t- ©  s? ^  IN os  9 4*  <=> §« §  S o Th o IO on IO 00 00 oo o> os 5 cq ^h <N s, IS o  io eo IO    t- 9 53 1    eo ©  IS o  9 6i« ^  o CM CO    00 GO    o 9  S ©  * O  en CO      T-l co  oo n IP S3  «o ©   io co  oo oo  en O   »o CO    w OS     00 I— I  en §1 £:  9 CO    r-l CO    o CO    oo S2  w co  io ©IrH _,  t- £g co  en os  io co  ^ tf J M P Q n HH Eh 5s r-l Eh 3 Em a 9 274    EVOLUTION   OF   WEIGHTS   AND   MEASURES 1 o o <i o > < w >3 c o  o o S8 a CO    t- 55  «o oi* I! OJ  IO CO  Oi 1  1 P  lea IS 3   to 1'* SI o  » 00    O o ©3 o  £ 30 M 9i« £ OS    so io  <o cc   »o 8eo .  leo O s  8 ?  3! g  » 61" CO    g 1—1      «N1 CC    £ OS 00    t- Ci    iO t^  1-1 CO     <» P  IW co  io cs  io oo  2*: cc  t- OS   o 9  § cc  «o 15 3  s SI  « y  i-i W  Ah o > < 5 5 Seh- §   1 n  o o  o 3  m EH    C LENGTHS 275 K H H I— I a E  I .  §  g 0      rH    g ^5 5g o  * W  Ph H Q H P Oi cococococo    ©  ©  ©  ©  © GO  CM  ©  ©  r*     00  CM  ©  ©  ■<* CMcpcp©TH     ©  ip  ©  cp  iH CM<tfi>.©CM    -^r-©CM»b i— i      i— i  i— i  CM  CM  CM 00 CM  CM  CM  CM  CM     CM  CM  CM  CM  CM COt^iHlOOl     COI>HiOOi ©  ip  rH  ©  p-h     ^-CMOOCOOO CM  rt<  t~  ©  CM     r*  t^  ©  CM  "* rH       MrHH(MCM fr- 00 00  CO  00  00      00  GO  00  00  00 i^fhioosco    t^i-Hioosco r-  co  00  cp  os    t»<  ©  >p  ©  cp ph  tJ<  CO  OS  h     4*  t~  ©  CM  ■* i—t        rH   rH   rH  CM  CM ee 1-524 4  064 6-604 9-144 11-684 14-224 16-764 19-304 21-844 24-384 ta ©©©©©    ©©©©© !>.  rH   l<0  ©  CO       t^  rH   O  ©  CO CM   GO   CO  GO   T*       OS   lO  ©   ip   r-H rH  CO   CO  00   rH       CO  ©OS   rH   4* PH        pH   rH   rH  CM   CM tH cococococo    cococococo hioo5coi>    Hioa«t> ©   lO   ©   CO   rH        I^CMt-CpOO rH   CO  CO   00   rH       CO  CO  00   -H  CO I-,       rH   rH   rH  CM   CM 00 CM  CM  CM  CM  CM     CM  CM  CM  CM  CM ©  ©  -<*  00  CM     ©  ©  t*  GO  CM i_-»  CO  GO  CO  OS     hh  p  "p  ©  CO co  »b  00  ©    co  cb  00  rH  i-o r_<       _   pH   rH  CM  CM <M 00X00  00  00     0000000000 ©TjiOOCM©     ©  t*  00  CM  © ip  ©  ip  Htp     CMt^CMOOCO coiooo©    cb  «b  oo  ©  cb pH       pH   rH   rH  CM  CM rH lO  ©  CO  t-  rH       lO  ©  CO  t—  rH CMt^COOO"*       p  T*  ©   lO  rH cm  »b  fr-  ©    cm  »b  oo  ©  cb ^        rH   rH   rH   CM  CM O ©©©©©   ©©©©© tP  00  CM  ©     ©  hh  00  CM  © ip  ©  cp  p-i     r-  CM  r-  cp  op CM  K5  t<-  ©     CM  >b  t^  ©  CM rH       rH   rH   rH   CM  CM 3rd IS rHCMCO'cH     lOCOfr-OOOi OS •35433 •74803 114173 1  -53543 1-92913 2-32283 2-71653 3-11023 3  50393 3-89763 00 ©©co©co    co  ©  ©  ©  © 05©CC©t^        HH    rH   O0   O   CM -*  GO  CM  CO  ©     C0t^©^00 rH  O  ©©  00       00t^t>»CO»O C0  ^-  rH   HH   00       CM   p  ©  HH   00 H  ^H  ^     CM  CM  CO  CO  CO fr- ©ososos©   OS'  os  ©  ©  © lO  CM  OS  CO  CO      ©t^T*r-,CO O  ©  CM  ©  ©     Tft^rHiOOO NtOtOOlO      t*  CO  CO  CM  pH CM  ©  ©  tH  00     CM  ©  ©  rt<  op _l  ^  ^     CM  CM  CO  CO  CO w Q ee CM  CM  CM  CM  CM     CMCMCMCMCM CM   ©©CO©        t^TjHrHOOO ©OSCOt-rH        T*H   GO  CM   lO  © COCMCMrHrH       ©  OS  ©  00   l>» CM  ©  ©  tP  Cp     CM  >p  OS  CC  fr» rllrHrH       CM  CM  CM  00  CO O    go H SI 1-^ 10 lO  lO  »C  «3  lO     UO  lfj  lO  lO  »0 00  lO  CM  ©  ©       00  ©  l^»  T*  i-H COO-*I>h     10  ©  CM  ©  © cs©oor-t-    ©  10  10  t)h  ■<* rH   lO  P  C0  I>»       r-<   lO  ©  C0  fr» rH  rH     CMCM  CMC0C0 tH QOO0GOO0O0      0000000000 •*  H  00  IQ  CI      OS  ©  CO  ©  !>• t-  rH   -^   CO  CM        UO  ©  CO  t-  © O  O   HH  CO  CO       CM   rH   rH  O  © rH   ip  p  CC  t-       rHippCOt^. ^•^     CM  Ol  CM  CO  cb P5  w H 00 rH00»OCMOS     ©co©t^co GO  i-H   lO   ©   CM       ©©T^t^rH <—t^<OGiGi     OOQOlr^©© rH   ip  p  CM   ©       ©   T*<   00  CM  © ,1,  ^     CMCMCM  cbcb a rJ 1— 1 9 CM t^-^HOOiO      CM  OS  ©  CO  © 00  CM  ©©  CO      t^©-*O0CM !>•  t-  ©  >C  10     tJi  hh  CO  CM  (M ©•^OOpi©        ©TfOOCM© ^^     CM  CM  CM  cb  cb 1— 1 CO©t^HHrH       OOiCiCM©© ©  CO  ©  ©   "#       t^rHlOOOCM CO  CO  CM  CM  fh     ©©©0000 ©■*Op6l©       ©THl^rHip ^-,^    cm  c>i  cm  cb  cb O 0 •39370 •78740 1-18110 1-57480 1-96850 2-36220 2-75590 3-14960 3  54330 5 <u a 3 9 THCMCOrH     lOCOfr-OOOS 276     EVOLUTION   OF  WEIGHTS   AND   MEASURES o o o 1 H       9 rt   cc^   o H^ '■  ^_ H « i— i 11 <U  c3 515625 53125 546875 5625 578125 59375 609375 625 640625 65625 671875 6875 703125 71875 734375 75 765625 78125 796875 8125 828125 84375 859375 875 890625 90625 921875 9375 953125 96875 984375 000 i-i aa t-  •*»  rH  CO      TtdHOOlO      CM  OS  CO  CO OSOSOSCO      CO  00  t~  t-      NO»tO ©  rH  00  CM      CO  O  •*  00      CM  ©  ©  i* co  co  co  4t<    4t<  io  io  >o    cb  ©  t- t- OS  CO  CO  O     N-^HOO >0<OOtfS      •**  i*t  rH  CO CO  CM  ©  ©      Tf  00  CM  CO t- CO  CO  OS      0  0)00 >*  rH  00  lO CO  CO  CM  CM ©  Tf  00  CM CM  CM  <M  CM CM  OS  ©  CO CM  rH  rH  rH CO  ©  ^f  CO CM  CO  CO  CO CM  CM  CM  CM II     II     II     II OS  ©  CO  © ©©o  © CM  CO©  7* 4ti  4ji  o  >b CM  CM  CM  CM II     II     II     II II  II  II  II    II  II  II  II    II  II  II  II II     II     II     II        II     II     II     II DO r*l to CO-JmcO     NOOSSO      rH  CM  CO  rj< cococoeo    eococo^    ■>*<"*•«*(•*« lO  CC  t~  00      OS  O  rH  CM ■<*•*•<*<■<*<      Tfl  2  lO  MS co  «*  >o  © "OiSflifl t-00  OS© lO  IO  »0  © 1-h  CM  CO  Ttl ©  ©  ©  © GO § CM CO i~         CO            OS         O            i-l         (N rH         rH            rH         CM            CM         CM CO          •»*              lO          CO CM         CM             CM         CM t»      oo CM         CM OS           © CM         CO r-i         CM CO          CO CO ,3 § .-i os                o                 H M                     co ->* lO © oo a 00 >o © t~ 00 CO - Hn CM o - oo^3 Z  c« 5«a lO         >0            >0         lO            lO         iO CM  >0  i-            WON            CM  IO  t— ©  CM  CO  >0      HSMO     CO  CM  CO  it} Or 1  CO  CM      CO  CO  OS  O      OOH1- i-icotjico    r-  os  ©  cm    -h<  >o  t~  co OOOO      OOi-lT-l      r-tr-ir+r* lO       lO          >o       »o NK3N            CHON HNWO      ©  CM  00  O CO  CO  -h  ©      lO  i— 1  CD  CM o  —  co  95    co  oo  os -h CM  <M  CM  CM      CMCMCMCO »o       IO l-HJt-  CO  © cc  co  os  >o CM  -*  lO  t— CO  CO  CO  CO io      *o CM  IO  t- CO  CM  cc  »o OS  ©  CM  CO CO  rfl  rH  ^ >o      >o CM  iO  t- CO  CO  -H< iO  ©00 Ttl  ^ji  tH  IO •     00 §1 sa t~  *  — '  00      MIHOOiO      CM  OS  CO  CO OSOSOSCO      CO  CO  t-  t-     NO<Dffl CO  t-  rH  >p      OS  CO  t-  rH      ipOSCOb- ^  ^-t      rH  CM  CM  CO      CO  CO  4*  4tl II     II     II     II        II     II     II     II        II     II     II     II OS  CO  CO  O     N<*H0O OiO"0  0      •*  -Hi  -H<  CO I-H  IO  OS  CO      t^rHVOOS >o  io  io  cb    ©.t-t-t- -*  rH  CO  lO CO  CO  CM  <M CO  t-  rH  ip CO  00  OS  OS II  II  II  II CM  OS  CO  CO CM  rH  l-H  rH OS  CO  t-rH OS  ©  ©  rH n1i"ii"ii OS  ©  CO  © ©©©© >p  OS  CO  t- rH  rH  Cd  CM H » u  i © pH  CM  CO  rjt      iO©t-00      OS  O  i-l  CM CO  •>*<  lO  ©     *-  CO  OS  © rH  CM  CO  'tl CM  <M  CM  CM iO  ©  i-  00 CM  CM  CM  CM OS  ©  rH  CXI CM  CO  CO  CO Pi <M co rH         CM            CO         ■*            lO         CO 1^        CO            OS        o r^         CM CO         r* iO         © 00 ,2 to rH                          CM                          CO -*                        io CO 1~ CO 00 M CO h CM CO rH 00 - CM oo HCQ 1 rH COMPARISON   OF   PRICES 277 COMPARISON  OF  PRICES. FRENCH  AND  GERMAN  PRICES  FOR  METRIC  UNITS,  BRITISH  PRICES FOR  IMPERIAL  UNITS,  AND  UNITED  STATES  PRICES  FOR  UNITED STATES  STANDARD  WEIGHTS  AND  MEASURES. [Based  upon  the  circular  of  the  Secretary  of  the  Treasury  dated  October  1,  1902, fixing  the  legal  equivalent  of  the  (German)  mark  at  23 '8  cents,  of  the  (French) franc  at  19*3  cents,  and  the  British  pound  sterling  at  $4  '8665.  ] Francs       D°llara Francs        Dollars Francs     D^rs Francs       Dollars Shillings     Dollars per per             per meter.          yard. Per           $g llter-    liquid  gal. per             per hectoliter,    bushel. per             per British         U.S. imp.  gal.  liquid  gal. 1        =   -088 1        =   -176 1        =  -731 1        =   -068 1        =   -203 2        =  '175 2        =   -353 2        =1-461 2        =   -136 2        =   -405 3        =   -263 3        =   -529 3        =2-192 3        =   -204 3        =   -608 4        =   -350 4        =   -705 4        =2-922 4        =  -272 4        =   -810 5        -   '438 5        =   '882 5        =3-653 5        =  -340 5        =1-013 6        =   -525 6        =1-058 6        =4-384 6        =   -408 6        =1-216 7        =   '613 7        =1-234 7        =5-114 7        =   -476 7        =1-418 8        =   '700 8       =1-411 8        =5-844 8        =   '544 8        =1-621 9        =   -788 9        =1-587 9        =6*575 9        =   -612 9        =1-824 11-423=1 5-667  =  1 1-369=1 14-703=1 4-935  =  1 22*846=2 11-334  =  2 2-738=2 29-407=2 9-871=2 34-269  =  3 17-000  =  3 4-106  =  3 44-110  =  3 14-806=3 45-691=4 22-667=4 5-475=4 58-813=4 19-742  =  4 57-115=5 28-334=5 6-844  =  5 73-517=5 24-677=5 68-537=6 34-001  =  6 8-213=6 88-220=6 29-612=6 79-960  =  7 39-668=7 9-581=7 102-923  =  7 34-548=7 91-383=8 45-334=8 10-950=8 117-627=8 39-483=8 102-806=9 51-001  =  9 12-319=9 132-330=9 44-419=9 Marks        Walters Marks        Dollars Marks     Do"f8 Marks        Dollars Shillings       Dollars ,  „  Per             avoir kilogram.     pound per             per meter.         yard. ner            per •                U.S liter-    liquid  gal. per             per hectoliter,    bushel. per              per British          U.S. bus.             bus. 1        =   -108 1        =   '218 1        =   -901 1        =   -084 1        =   -236 2        =   -216 2        =   -435 2        =1-802 2        =   -168 2        =   -472 3        =   -324 3        =   -653 3        =2-730 3        =   -252 3        =  '707 4        =   -432 4        =   -871 4        =3-604 4        =   -335 4        =   -943 5        =   -540 5        =1-088 5        =4-505 5        =   -419 5       =1-179 6        =   -648 6        =1-306 6        =5-406 6        =   -503 6        =1-415 7        =  -756 7        =1-523 7        =6-307 7        =   -587 7        =1-650 8        =   -864 8        =1-741 8        =7-207 8        =  -671 8        =1-886 9        =  -972 9        =1-959 9        =8-108 9        =  -755 9        =2-122 9-263=1 4-595  =  1 1-110=1 11-923=1 4-241=1 18-526  =  2 9-190=2 2-220  =  2 23-847=2 8-483  =  2 .27-789  =  3 13-785=3 3-330  =  3 35-770  =  3 12-724=3 37-052=4 18-380=4 4*440=4 47-693  =  4 16-965  =  4 46-316  =  5 22-975  =  5 5  550=5 59-616  =  5 21-207  =  5 55-579=6 27-570  =  6 6-660=6 71-540=6 25-448=6 64-842=7 32-165=7 7-770=7 83-463=7 29-689  =  7 74-105=8 36-760=8 8-880=8 95-386=8 33-931  =  8 83-368=9 41-355=9 9-990=9 107-310  =  9 38-172=9 278     EVOLUTION   OF   WEIGHTS   AND   MEASURES LENGTH. INCHES  AND  CENTIMETERS.— EQUIVALENTS  FROM  1  to  100. Inches  to  Centimeters. Inches  to  Centimeters. Centimeters  to  Inches. Centimeters  to  Inches. 0 50 127  000 0 50 19-6850 1 2  540 51 129  540 1 •3937 51 20-0787 2 5-080 52 132  080 2 •7874 52 20-4724 3 7-620 53 134-620 3 1-1811 53 20-8661 4 10-160 54 137-160 4 1-5748 54 21-2598 5 12-700 55 139-700 5 1*9685 55 21-6535 6 15-240 56 142-240 6 2-3622 56 22  0472 7 17-780 57 144  780 7 2-7559 57 22-4409 8 20  320 58 147  320 8 3-1496 58 22-8346 9 22-860 59 149-860 9 3  5433 59 23  2283 10 25  400 60 152-400 10 3-9370 60 23  6220 11 27  940 61 154-940 11 4-3307 61 24-0157 12 30-480 62 157-480 12 4-7244 62 24-4094 13 33  020 63 160020 13 5-1181 63 24-8031 14 35-560 64 162-560 14 5-5118 64 25-1968 15 38-100 65 165-100 15 5-9055 65 25-5905 16 40-640 66 167-640 16 6-2992 66 25-9842 17 43-180 67 170-180 17 6-6929 67 26-3779 18 45-720 68 172-720 18 7-0866 68 26-7716 19 48-260 69 175-260 19 7-4803 69 27-1653 20 50-800 70 177-800 20 7-8740 70 27-5590 21 53  340 71 180-340 21 8-2677 71 27-9527 22 55-880 72 182-880 22 8-6614 72 28-3464 23 58-420 73 185-420 23 9-0551 73 28-7401 24 60-960 74 187-960 24 9-4488 74 29-1338 25 63-500 75 190-500 25 9-8425 75 29-5275 26 66-040 76 193-040 26 10-2362 76 29-9212 27 68-580 77 195-580 27 10-6299 77 30-3149 28 71-120 78 198-120 28 11-0236 78 30-7086 29 73-660 79 200-660 29 11-4173 79 31-1023 30 76-200 80 203-200 30 11-8110 80 31-4960 31 78-740 81 205-740 31 12-2047 81 31-8897 32 81-280 82 208-280 32 12-5984 82 32-2834 33 83-820 83 210-820 33 12-9921 83 32-6771 34 86  360 84 213-360 34 13-3858 84 33-0708 35 88-900 85 215-900 35 13-7795 85 33-4645 36 91  '440 86 218-440 36 14-1732 86 33-8582 37 93-980 87 220-980 37 14-5669 87 34-2519 38 96-520 88 223-520 38 14-9606 88 34-6456 39 99-060 89 226-060 39 15-3543 89 35  0393 40 101-600 90 228-600 40 15-7480 90 35-4330 41 104-140 91 231-140 41 16-1417 91 35-8267 42 106-680 92 233-680 42 16-5354 92 36-2204 43 109-220 93 236-220 43 16-9291 93 36-6141 44 111-760 94 238-760 44 17-3228 94 37-0078 45 114-300 95 241-300 45 17-7165 95 37-4015 46 116-840 96 243-840 46 18-1102 96 37-7952 47 119-380 97 246-380 47 18-5039 97 38-1889 48 121  -920 98 248-920 48 18-8976 98 38-5826 49 124-460 99 251-460 49 19-2913 99 38-9763 LENGTH:    FEET   AND   METERS 279 LENGTH. FEET  AND  METERS.— EQUIVALENTS  FROM  1  to  100. Feet Meters. Feet Meters. Meten s.    Feet. Meters.    Feet. 0 50 15  24003 0 50  164  04167 1 •30480 l 15-54483 1 3-28083 1  167  32250 2 •60960 2 15-84963 2 6-56167 2  170-60333 3 •91440 3 16-15443 3 9  84250 3  173-88417 4 1-21920 4 16-45923 4 13-12333 4  177-16500 5 1-52400 5 16-76403 5 16-40417 5  ISO -44583 6 1  -82880 6 17-06883 6 19-68500 6  183-72667 7 2-13360 7 17  37363 7 22-96583 7  187-00750 8 2-43840 8 17-67844 8 26-24667 8  190-28833 9 274321 9 17-98324 9 29-52750 9  193  56917 10 3-04801 60 18-28804 10 32-80833 60  196-85000 1 3-35281 1 18-59284 1 36-08917 1  200-13083 2 3  65761 2 18-89764 2 39-37000 2  203-41167 3 3-96241 3 19-20244 3 42-65083 3  206-69250 4 4-26721 4 19-50724 4 45-93167 4  209-97333 5 4-57201 5 19-81204 5 49-21250 5  21325417 6 4-87681 6 20-11684 6 52-49333 6  216-53500 7 5-18161 7 20-42164 7 5577417 7  219-81583 8 5-48641 8 20-72644 8 59-05500 8  223  09667 9 5-79121 9 21-03124 9 62-33583 9  226-37750 20 6-09601 70 21-33604 20 65-61667 70  229-65833 1 6-40081 1 21-61084 1 6S -89750 1  232-93917 2 6-70561 2 21-94564 2 72-17833 2  236-22000 3 7-01041 3 22-25044 3 75-45917 3  239-50083 4 7-31521 4 22-55525 4 78-74000 4  242-78167 5 7-62002 5 22-86005 5 82-02083 5  246  06250 6 7-92482 6 23-16485 6 85-30167 6  249  34333 7 8-22962 7 23-46965 7 88-58250 7  252-62417 8 8-53442 8 23-77445 8 91-86333 8  255-90500 9 8-83922 9 24-07925 9 95-14417 9  259-18583 30 9-14402 80 24-38405 30 98-42500 80  262-46667 1 9-44882 1 24-68885 1 101-70583 1  265  74750 2 9-75362 2 24-99365 2 104-98667 2  269  02833 3 10-05842 3 25-29845 3 108-26750 3  272-30917 4 10-36322 4 25-60325 4 111-54833 4  275-59000 5 10-66803 5 25-90805 5 114-82917 5  278-87083 € 10-97282 6 26-21285 6 118-11000 6  282-15167 7 11-27762 7 26-51765 7 121-39083 7  285-43250 8 11-58242 8 26  82245 8 124-67167 8  288-71333 9 11-88722 9 27  12725 9 127  95250 9  291-99417 40 12-19202 90 27-43205 40 131-23333 90  295-27500 1 12-49682 1 27-73686 1 134-51417 1  298-55583 2 12-80163 2 28-04166 2 137-79500 2  301-83667 3 13-10643 3 28-34646 3 141-07583 3  305-11750 4 13-41123 4 28-65126 4 144-35667 4  308-39833 5 13-71603 5 28-95606 5 147-63750 5  311-67917 6 14-02083 6 29-26086 6 150-91833 6  314-96000 7 14-32563 7 29-56566 7 154-19917 7  318-24083 8 14-63043 8 29-87046 8 157-48000 8  321-52167 9 14-93523 9 30-17526 9 160-76083 9  324-80250 280     EVOLUTION   OF   WEIGHTS   AND   MEASURES LENGTH. YARDS  AND  METERS.— EQUIVALENTS  FROM  1  to  100. Yards Meters. Yards Meters. Meter? Yards. Meters Yards. 0 50 45-72009 0 50 54-68056 1 •91440 51 46-63449 1 1-09361 51 55-77417 2 1-82880 52 47-54889 2 2-18722 52 56-86778 3 2  74321 53 48-46330 3 3-28083 53 57-96139 4 3-65761 54 49-37770 4 4-37444 54 59-05500 5 4-57201 55 50-29210 5 5-46806 55 60-14861 6 5-48641 56 51-20650 6 6-56167 56 61-24222 7 6-40081 57 52-12090 7 7-65528 57 62  33583 8 7  31521 58 53-03530 8 8-74889 58 63  42944 9 8-22962 59 53-94971 9 9-84250 59 64-52306 10 9-14402 60 54-86411 10 10-93611 60 65-61667 11 10-05842 61 55-77851 11 12  02972 61 66-71028 12 10-97282 62 56-69291 12 13-12333 62 67-80389 13 11-88722 63 57  60731 13 14-21694 63 68-89750 14 12-80163 64 58-52172 14 15-31056 64 69-99111 15 1371603 65 59-43612 15 16-40417 65 71  08472 16 14-63043 66 60-35052 16 17-49778 66 72-17833 17 15-54483 67 61-26492 17 18-92139 67 73-27194 18 16-45923 68 62-17932 18 19-68500 68 74-36556 19 17-37363 69 63-09372 19 20-77861 69 75-45917 20 18-28804 70 64-00813 20 21-87222 70 76-55278 21 19-20244 71 64-92253 21 22-96583 71 77-64639 22 20-11684 72 65-83693 22 24-05944 72 78-74000 23 21  03124 73 66-75133 23 25-15306 73 79-83361 24 21-94564 74 67-66573 24 26-24667 74 80-92722 25 22-86005 75 68-58014 25 27-34028 75 82-02083 26 23-77445 76 69-49454 26 28-43389 76 83-11444 27 24-68885 77 70-40894 27 29-52750 77 84-20806 28 25-60325 78 71-32334 28 30-62111 78 85-30167 29 26-51765 79 72-23774 29 31-71472 79 86-39528 30 27  43205 80 7315214 30 32-80833 80 87-48889 31 28-34646 81 74-06655 31 33-90194 81 88-58250 32 29-26086 82 74-98095 32 34-99556 82 89-67611 33 30-17526 83 75-89535 33 36-08917 83 90-76972 34 31-08966 84 76-80975 34 37-18278 84 91  -86333 35 32-00406 85 77  72415 35 38-27639 85 92-95694 36 32-91846 86 78-63855 36 39-37000 86 94-05056 37 33-83287 87 79-55296 37 40-46361 87 95-14417 38 34-74727 88 80-46736 38 41  -55722 88 96-23778 39 35-66167 89 81-38176 39 42-65083 89 97-33139 40 36-57607 90 82-29616 40 43  74444 90 98-42500 41 37-49047 91 83-21056 41 44-83806 91 99-51861 42 38-40488 92 84-12497 42 45-93167 92 100-61222 43 39-31928 93 85-03937 43 47-02528 93 101-70583 44 40-23368 94 85-95377 44 48-11889 94 102-79944 45 41-14808 95 86-86817 45 49-21250 95 103-89306 46 42-06248 96 87-78257 46 50-30611 96 104-98667 47 42-97688 97 88-69697 47 51-39972 97 106-08028 48 43  89129 98 89-61138 48 52-49333 98 107-17389 49 44-80569 99 90-52578 49 53-58694 99 108-26750 LENGTH:    MILES   AND  KILOMETERS 281 LENGTH. MILES  AND  KILOMETERS.— EQUIVALENTS  FROM  1  to  100. Miles. Kilometers. Miles. Kilometers. Kilometers.  Miles. Kilometers.  Miles. 0 50 80-4674 0 50 3106850 1 1-6093 l 82-0767 1 •62137 l 31-68987 2 3  2187 2 836861 2 1-24274 2 32-31124 3 4-8280 3 85-2954 3 1-86411 3 32-93261 4 6-4374 4 86  9047 4 2-48548 4 33-55398 5 8-0467 5 88-5141 5 3-10685 5 34-17535 6 9-6561 6 90  1234 6 3-72822 6 34-79672 7 11-2654 7 91  -7328 7 4-34959 7 35-41809 8 12*8748 8 93-3421 8 4-97096 8 36-03946 9 14-4841 9 94-9515 9 5  59233 9 36-66083 10 16  0935 60 96-5608 10 6-21370 60 37-28220 1 17  7028 1 981702 1 6-83507 1 37-90357 2 19-3122 2 99-7795 2 7-45644 2 38-52494 3 20-9215 3 101  -3889 3 8-07781 3 39-14631 4 22-5309 4 102-9982 4 8-69918 4 39-76768 5 24-1402 5 104-6076 5 9-32055 5 40-38905 6 25-7496 6 106-2169 6 9-94192 6 41  01042 7 27  3589 7 107-8263 7 10-56329 7 41-63179 8 28-9682 8 109-4356 8 11-18466 8 4225316 9 30-5776 9 111  0450 9 11-80603 9 42-87453 20 32-1869 70 112-6543 20 12-42740 70 43-49590' 1 33-7963 1 114  2637 1 13-04S77 1 44-11727 2 35-4056 2 115-8730 2 13-67014 2 44-73864 3 37-0150 3 117-4823 3 14-29151 3 45-36001 4 38-6243 4 119-0917 4 14-91288 4 45-98138 5 40-2337 5 120-7010 5 15-53425 5 46-60275 6 41-8430 6 122-3104 6 1615562 6 47  22412 7 43  4524 7 123  9197 7 16-77699 7 47-84549 8 45-0617 8 125-5291 8 17-39836 8 48-46686 9 46-6711 9 127  1384 9 18-01973 9 49-08823 30 48-2804 80 128-7478 30 18-64110 80 49-70960 1 49-8898 1 130-3571 1 19-26247 1 50-33097 2 51-4991 2 131-9665 2 19-88384 2 50-95234 3 53-1085 3 133-5758 3 20-50521 3 51-57371 4 54-7178 4 135-1852 4 21-12658 4 52-19508 5 56-3272 5 136-7945 5 21  -74795 5 52 -81 645 6 57-9365 6 138-4039 6 22-36932 6 53-43782 7 59-5458 7 1400132 7 22-99069 7 54-05919 8 61-1552 8 141  -6226 8 23-61206 8 54-68056 9 62-7645 9 143-2319 9 24-23343 9 55-30193 40 64-3739 90 144-8412 40 24-85480 90 55-92330 1 65-9832 1 146-4506 1 25-47617 1 56-54467 2 67-5926 2 148-0599 2 26-09754 2 57-16604 3 69-2019 3 149-6693 3 26-71891 3 57-78741 4 70-8113 4 151-2786 4 27-34028 4 58-40878 5 72-4206 5 152-8880 5 27-96165 5 59  03015 6 74-0300 6 154-4973 6 28-58302 6 59-65152 7 75  6393 7 156-1067 7 29-20439 7 60-27289 8 77-24S7 8 157-7160 8 29-82576 8 60-89426 9 78-8580 9 159-3254 9 3044713 9 61-51562 282     EVOLUTION   OF   WEIGHTS   AND   MEASURES AREAS. ACRES  AND   HECTARES.— EQUIVALENTS   FROM  1  to  100. Acres Hectares. Acres Hectares. Hectares.   Acres. Hectares.   Acres. 0 50 20-23436 0 50 123-55220 1 0-40469 l 20-63905 1 2-47104 l 126  02324 2 0-80937 2 21  -04374 2 4-94209 2 128-49428 3 1-21406 3 21  -44842 3 7-41313 3 130-96533 4 1-61875 4 21-85311 4 9-88418 4 133-43637 5 2-02344 5 22-25780 5 12-35522 5 135-90742 6 2-42812 6 22-66249 6 14-82626 6 138-37846 7 2-83281 7 23-06717 7 17-29731 7 140-84950 8 3-23750 8 23-47186 8 19-76835 8 143-32055 9 3-64219 9 23-87655 9 22-23940 9 145-79159 10 4-04687 60 24-28124 10 24-71044 60 148-26264 1 4-45156 1 24-68592 1 27-18148 1 150  73368 2 4-85625 2 25-09061 2 29-65253 2 153-20472 3 5  26093 3 25-49530 3 32-12357 3 155-67577 4 5-66562 4 25-89998 4 34-59462 4 158-14681 5 6-07031 5 26-30467 5 37-06566 5 160-61786 6 6-47500 6 26-70936 6 39-53670 6 163-08890 7 6-87968 7 27-11405 7 42  00775 7 165-55994 8 7-28437 8 27*51873 8 44-47879 8 168  03099 9 7-68906 9 27-92342 9 46  94983 9 170-50203 20 8-09375 70 28  32811 20 49-42088 70 172-97308 1 8-49843 1 28-73280 1 51-89192 1 175-44412 2 8-90312 2 29-13748 2 54  36297 2 177-91516 3 9-30781 3 29-54217 3 56-83401 3 180-38621 4 9-71249 4 29-94686 4 59-30505 4 182-85725 5 1011718 5 30-35154 5 61-77610 5 185-32829 6 10-52187 6 30-75623 6 64-24714 6 187-79934 7 10-92656 7 31-16092 7 66-71819 7 190-27038 8 11-33124 8 31-56561 8 69  18923 8 192-74143 9 11-73593 9 31-97029 9 71-66027 9 195-21247 30 12  14062 80 32  37498 30 74-13132 80 197-6S351 1 1254531 1 32-77967 1 76-60236 1 200  15456 2 12-94999 2 33-18436 2 79-07341 2 202-62560 3 13-35468 3 33-58904 3 81-54445 3 205-09665 4 13-75937 4 33-99373 4 84-01549 4 207-56769 5 14-16405 5 34-39842 5 86-48654 5 210-03873 6 14-56874 6 34-80310 6 88-95758 6 212-50978 7 14-97343 7 35  20779 7 91-42863 7 214-98082 8 15-37812 8 35-61248 8 93-89967 8 217-45187 9 15-78280 9 36-01717 9 96-37071 9 219-92291 40 1618749 90 36-42185 40 98-84176 90 222-39395 1 16-59218 1 36-82654 1 10131280 1 224-86500 2 16-99686 2 37  23123 2 103  78385 2 227  33604 3 17-40155 3 37-63592 3 106-25489 3 229-80709 4 17-80624 4 38-04060 4 108-72593 4 232-27813 5 18  21093 5 38-44529 5 111-19698 5 234-74917 6 18-61561 6 38-8499S 6 113-66802 6 237  22022 7 19-02030 7 39-25466 7 116-13906 7 239-69126 8 19-42499 8 39-65935 8 118-61011 8 242-16231 9 19-82968 9 40  06404 9 121  08115 9 244-63335 CAPACITY  :  LIQUID    QUARTS   TO   LITERS        283 CAPACITY. LIQUID  QUARTS  TO  LITERS.— EQUIVALENTS   FROM  1  to  100. Quarts.   Liters. Quarts.   Liters. Liters Quarts. Liters. Quarts. 0 50 47*31793 0 50 52-83409 1 •94636 l 48-26429 1 1-05668 l 53-89077 2 1-89272 2 49-21065 2 2-11336 2 54-94746 3 2-83908 3 50-15701 3 3-17005 3 56  00414 4 3-78543 4 51-10337 4 4-22673 4 57  06082 5 4-73179 5 52-04972 5 5-28341 5 58-11750 6 5-67815 6 52-99608 6 6  34009 6 59-17418 7 6-62451 7 53-94244 7 7-39677 7 60  23086 8 7-57087 8 54-88880 8 8-45345 8 61  -28755 9 8-51723 9 55-83516 9 9-51014 9 62-34423 10 9-46359 60 56-78152 10 10-56682 60 63-40091 1 10-40994 1 57-72788 1 11-62350 1 64-45759 2 11-35630 2 58-67423 2 12-68018 2 65-51428 3 12-30266 3 59-62059 3 13-73686 3 66-57096 4 13-24902 4 60-56695 4 14-79355 4 67  62764 5 14-19538 5 6151331 5 15-85023 5 68-68432 6 15-14174 6 62-45967 6 16-90691 6 69-74100 7 16-08810 7 63-40603 7 17-96359 7 70-79768 8 17-03446 8 64-35239 8 19-02027 8 71-85437 9 17-98081 9 65  29875 9 20-07696 9 72-91105 20 18-92717 70 66-24510 20 21-13364 70 73-96773 1 19-87353 1 67-19146 1 22-19032 1 75-02441 2 20-81989 2 68-13782 2 23-24700 2 76-08109 3 21-76625 3 69-08418 3 24-30368 3 77-13778 4 22-71261 4 70-03054 4 25-36036 4 78-19446 5 23-65897 5 70-97690 5 26-41705 5 79-25114 6 24-60532 6 71-92326 6 27-47373 6 80-30782 7 25-55168 7 72-86961 7 28-53041 7 81-36450 8 26-49804 8 73-81597 8 29-58709 8 82-42119 9 27-44440 9 74-76233 9 3061377 9 83-47787 30 28-39076 80 75-70869 30 31-70046 80 84-53455 1 29-33712 1 76-65505 1 32  75714 1 85-59123 2 30-28348 2 77-60141 2 3381382 2 86-64791 3 31  -22983 3 78-54777 3 34-87050 3 87 '70459 4 32-17619 4 79-49412 4 35-92718 4 88-76128 5 33-12255 5 80-44048 5 36-98387 5 89-81796 6 34-06891 6 81-38684 6 38-04055 6 90-87464 7 35-01527 7 82-33320 7 39-09723 7 91-93132 8 35-96163 8 83  27956 8 40-15391 8 92-98800 9 36-90799 9 84-22592 9 41-21059 9 94-04469 40 37-85436 90 85  17228 40 42-26727 90 95-10137 1 38-80070 1 86-11863 1 43-32396 1 96-15805 2 39-74706 2 87-06499 2 44-38064 2 97-21473 3 40-69342 3 88-01135 3 45-43732 3 98-27141 4 41-63978 4 88*95771 4 46-49400 4 99-32809 5 42-58614 5 89-90407 5 47-55068 5 100-38478 6 43-53250 6 90-85043 6 48-60737 6 101-44146 7 44-47886 7 91-79679 7 49-66405 7 102-49814 8 45-42521 8 92-74315 8 50-72073 8 103-55482 9 46-37157 9 93-68950 9 51-77741 9 104-61150 284     EVOLUTION   OF   WEIGHTS   AND   MEASURES CAPACITY. GALLONS  AND  LITERS.— EQUIVALENTS  FROM   1  to  100. Gallons Liters. Gallons.   Liters. Liters Gallons. Liters Gallons. 0 50 189  2717 0 50 13-20852 1 3  7854 l 193-0572 1 •26417 l 13-47269 2 7-5709 2 196-8426 2 •52834 2 13-73686 3 11-3563 3 200-6280 3 •79251 3 14-00103 4 15-1417 4 204-4135 4 1  -05668 4 14-26521 5 18-9272 5 208-1989 5 1-32085 5 14-52938 6 22-7126 6 211-9843 6 1  -58502 6 14-79355 7 26  4980 7 215-7698 7 1  -84919 7 15-05772 8 30-2835 8 219-5552 8 2-11336 8 15-32189 9 34-0689 9 223-3406 9 2  37753 9 15-58606 10 37-8543 60 227-1261 10 2-64170 60 15-85023 1 41-6398 1 230-9115 1 2-90588 1 16-11440 2 45-4252 2 234-6969 2 3-17005 2 16-37857 3 49-2106 3 238-4824 3 3-43422 3 16-64274 4 52-9961 4 242-2678 4 3-69839 4 16-90691 5 56-7815 5 246-0532 5 3-96256 5 17-17108 6 60-5670 6 249-8387 6 4-22673 6 17-43525 7 64-3524 7 253-6241 7 4-49090 7 17-69942 8 68-1378 8 257-4095 8 4-75507 8 17-96359 9 71-9233 9 261-1950 9 5  01924 9 18-22776 20 75-7087 70 264-9804 20 5-28341 70 18-49193 1 79  4941 1 268-7658 1 5-54758 1 18-75610 2 83  2796 2 272-5513 2 5-81175 2 19-02027 3 87-0650 3 276-3367 3 6-07592 3 19-28444 4 90-8504 4 280-1222 4 6-34009 4 19-54861 5 94  6359 5 283-9076 5 6-60426 5 19-81279 6 98-4213 6 287-6930 6 6-86843 6 20  07696 7 102-2067 7 291-4785 7 7-13260 7 20-34113 8 105-9922 8 295-2639 8 7-39677 8 20-60530 9 109-7776 9 299  0493 9 7-66094 9 20-86947 30 113-5630 80 302-8348 30 7-92511 80 21-13364 1 117-3485 1 306-6202 1 8-18928 1 21  -39781 2 121-1339 2 310-4056 2 8-45345 2 21-66198 3 124-9193 3 314-1911 3 8-71763 3 21-92615 4 128-7048 4 317-9765 4 8-98180 4 22-19032 5 132-4902 5 321-7619 5 9  24597 5 22-45449 6 136-2756 6 325-5474 6 9-51014 6 2271866 7 140  0611 7 329-3328 7 9-77431 7 22-98283 8 143  8465 8 333-1182 8 10-03848 8 23-24700 9 147  6319 9 336-9037 9 10-30265 9 23-51117 40 151-4174 90 340-6891 40 10-56682 90 23-77534 1 155-2028 1 344-4745 1 1083099 1 24  03951 2 158-9882 2 348-2600 2 11-09516 2 24-30368 3 162-7737 3 352-0454 3 11-35933 3 24-56785 4 166-5591 4 355-8308 4 11-62350 4 24-83202 5 170-3446 5 359-6163 5 11-88767 5 25-09619 6 174-1300 6 363-4017 6 12-15184 6 25  36036 7 177-9154 7 367-1871 7 12-41601 7 25-62454 8 181  -7009 8 370-9726 8 12-68018 8 25-88871 9 185-4863 9 374-7580 9 12-94435 9 26-15288 MASSES :  AVOIRDUPOIS  POUND  AND  KILOGRAM  285 MASSES. AVOIRDUPOIS  POUND  &  KILOGRAM.— EQUIVALENTS  FROM  1  to  100. Pounds Kilos. Pounds Kilos. Kilos. Pounds. Kilos. Pounds. 0 50 22-67962 0 50 110-2311 1 •45359 l 23  13321 1 2-2046 l 112-4357 2 •90718 2 23-58681 2 4-4092 2 114-6404 3 1-36078 3 24-04040 3 6  6139 3 116-8450 4 1-81437 4 24-49399 4 8-8185 4 119-0496 5 2-26796 5 24-94758 5 11-0231 5 121-2542 6 2-72155 6 25-40118 6 13-2277 6 123-4589 7 317515 7 25-85477 7 15  4324 7 125  6635 8 3-62874 8 26-30836 8 17  6370 8 127-8681 9 4  08233 9 26-76195 9 19-8416 9 1300727 10 4-53592 60 27  21555 10 22  0462 60 132-2773 1 4-98952 1 27  66914 1 24-2508 1 134-4820 2 5-44311 2 28  12273 2 26  4555 2 136-6866 3 5-89670 3 28-57632 3 28-6601 3 138-8912 4 6-35029 4 29  02992 4 30-8647 4 141-0958 5 6-80389 5 29-48351 5 33  0693 5 143-3005 6 7-25748 6 29-93710 6 35-2740 6 145  5051 7 7-71107 7 30-39069 7 37  4786 7 147-7097 8 8-16466 8 30-84429 8 39-6832 8 149-9143 9 8-61826 9 31-29788 9 41-8878 9 152-1189 20 9-07185 70 31-75147 20 44  0924 70 154-3236 1 9-52544 1 32-20506 l 46  2971 1 156-5282 2 9  97903 2 32-65865 2 48-5017 2 158-7328 3 10-43263 3 33  11225 3 50  7063 3 160-9374 4 10-88622 4 33-56584 4 52-9109 4 163  1421 5 11-33981 5 34-01943 5 55-1156 5 165-3467 6 11-79340 6 34-47302 6 57  3202 6 167-5513 7 12-24700 7 34-92662 7 59-5248 7 169-7559 8 12-70059 8 35-38021 8 61-7294 8 171-9605 9 13-15418 9 35-83380 9 63  9340 9 1741652 30 13-60777 80 36-28739 30 66-1387 80 176-3698 1 14-06137 1 36-74099 l 68  3433 1 178-5744 2 14-51496 2 37-19458 2 70-5479 2 180-7790 3 14-96855 3 37-64817 3 72-7525 3 182-9837 4 15-42214 4 3810176 4 74-9572 4 185-1883 5 15-87573 5 38-55536 5 77*1618 5 187  3929 6 16-32933 6 39-00895 6 79-3664 6 189-5975 7 16-78292 7 39  46254 7 81-5710 7 191-8021 8 17  23651 8 39-91613 8 83  7756 8 194-0068 9 17-69010 9 40-36973 9 85-9803 9 196-2011 40 18-14370 90 40  82332 40 88'1849 90 198  4160 1 18-59729 1 41-27691 1 90-3895 1 200-6206 2 19-05088 2 41-73050 2 92-5941 2 202-8253 3 19-50447 3 42  18410 3 94-7988 3 205  0299 4 19-95807 4 42-63769 4 97  0034 4 207  2345 5 20  41166 5 43  09128 5 99-2080 5 209-4391 6 20-86525 6 43  54487 6 1014126 6 211-6437 7 21-31884 7 43-99847 7 103-6172 7 213-8484 8 21  -77244 8 44-45206 8 105-8219 8 216  0530 9 22-22603 9 44-90565 9 108-0265 9 218  2576 286     EVOLUTION   OF   WEIGHTS   AND   MEASURES COMPARISON   OF   THE   VARIOUS   TONS   AND    POUNDS IN   USE  IN   THE  UNITED   STATES. FROM  1  to  10  UNITS. Long  Tons. Short  Tons. Metric  Tons. Kilograms. Avoirdupois Pounds. Troy  Pounds. •00036735 •00044643 •00073469 •00089286 •00098421 •00041143 •00050000 •00082286 •00100000 •00110231 •00037324 •00045359 •00074648 •00090718 •00100000 •37324 •45359 •74648 •90718 1 ■822857 1 1-64571 2 2-20462 1 1-21528 2 2-43056 2-67923 •00110204 •00133929 •00146939 •00178571 •00183673 •00123429 •00150000 •00164571 •00200000 •00205714 •00111973 •00136078 •00149297 •00181437 •00186621 1-11973 1-36078 1  -49297 1-81437 1-86621 2-46857 3 3-29143 4 4-11429 3 3-645S3 4 4-86111 5 •00196841 •00220408 •00223214 •00257143 •00267857 •00220462 •00246857 •00250000 •00288000 •00300000 •00200000 •00223945 •00226796 •00261269 •00272155 2 2-23945 2-26796 2-61269 2-72155 4-40924 4-93714 5 5-76000 6 5-35846- 6 6-07639 7 7-29167 •00293S78 •00295262 •00312500 •00330612 •00357143 •00329143 •00330693 •00350000 •00370286 •00400000 •00298593 •00300000 •00317515 •00335918 •00362874 2-98593 3 3-17515 3-35918 3-62874 6-582S6 6-61387 7 7-40571 8 8 8-03769 8-50694 9 9-72222 •00393683 •00401786 •00492103 •00590524 •006S8944 •00440924 •00450000 •00551156 •00661387 •00771618 •00400000 •00408233 •00500000 •00600000 •00780000 4 4-08233 5 6 7 8-81849 9 11-0231 13-2277 15-4324 10-71691 10-93750 13-39614 16-07537 18-75460 •00787365 •00885786 •89287 •98421 1 •00881849 •009920S0 1 1-10231 1-12000 •00800000 •0090000 •90718 1 1-01605 8 9 907-18 1,000-00 1,016-05 17-6370 19-8416 2,000-00 2,204-62 2,240-00 21-43383 24-11306 2,430-56 2,679-23 2,722-22 1-78571 1-96841 2 2-67857 2-95262 2 2-20462 2-24000 3 3-30693 1-81437 2 2-03209 2-72155 3 1,814-37 2,000-00 2,032-09 2,721-55 3,000-00 4,000-00 4,409-24 4,480-00 6,000-00 6,613-87 4,861-11 5,358-46 5,444-44 7,291-67 8,037-69 3 3-57143 3-93683 4 4-46429 3-36000 4 4-40924 4-48000 5 3-04814 3-62874 4 4-06419 4  53592 3,048-14 3,628-74 4,000-00 4,064-19 4,535-92 6,720-00 8,000-00 8,818-49 8,960-00 10,000-00 8,166-67 9,722-22 10,716-91 10,888-89 12,152-78 4-92103 5 5-35714 6-90524 6 5-51156 5-60000 6 6-61387 6-72000 5 5-08024 6-44311 6 6-09628 5,000-00 5,080-24 5,443-11 6,000-00 6,096-28 11,023-11 11,200-00 12,000-00 13,227-73 13,440-00 13,396-14 13,611'H 14.5S3-33 16,075-37 16,333-33 6-25000 6-88944 7 7-14286 7-87365 7 7-71618 7-84000 8 8-81849 6-35029 7 7-11232 7-25748 8 6,350-29 7,000-00 7,112-32 7,257-48 8.000-00 14,000-00 15,432-36 15,680-00 16,000-00 17,636-98 17,013-89 18,754  60 19,055-56 19,444-44 21,433-83 8 8-03571 8-85786 9 8-96000 9 9-92080 10-08000 8-12838 8-16466 9 9-14442 8,128-38 8,164-66 9,000-00 9,144-42 17,920-00 18,000-00 19,841-60 20,160-00 21,777-78 21,875-00 24,113-06 24,500-00 MEASURES   OF   CAPACITY 287 MEASURES   OF   CAPACITY. EQUIVALENTS  FROM  1  to  10. Milli-         U.S. liters.       Liquid (c.c.)      Ounces. (c-c,)        Drams. U.S. Apothe- caries' Scruples. Milli- liters, (c.c.) U.S. Liquid       Liters. Quarts. U.S. Liquid       Liters. Gallons. 1        =0-03381 1         =0-2705 0-8115  = 1 1            =0-94636 0-26417=  1 2        =0-06763 2          =0-5410 1 1-2322 1-05668=1 0-52834=  2 3        =0-10144 3          =0-8115 1-6231  = 2 2            =1-89272 0-79251=  3 4        =0-13526 3-6967=1 2 2-4645 2-11336=2 1            =  3-7S543 5  =0-16907 6  =0-20288 7  =0-23670 8  =0-27051 9  =0-30432 4  =1-0820 5  =1-3525 6  =1-6231 7  =1-8936 7-3934=2 2-4346  = 3 3-2461  = 4 4-0577  = 4-8692  = 3 3-6967 4 4-9290 5 6 3  =2-83908 3-17005  =  3 4  =3-78543 4-22673=4 5  =4-73179 1-05668=  4 1-32085=  5 1-58502=  6 1-84919=  7 2           =  7-57087 29-574=1 8          =2-1641 5 5-6S07  = 6-1612 7 5-28341=5 2-11336=  8 59-147=2 9          =2-4346 6 7-3934 6            =5  67815 2-37753=  9 8S-721  =  3 11-0901  =  3 6-4923  = 8 6-34009=6 3            =11 -3563a 118-295=4 14-7869=4 7 8-6257 7            =6-62451 4            =15-14174 147-869=5 18-4836=5 7-3038  = 9 7-39677=7 5            =18-92717 177-442=6 22-1803=6 8 9-8579 8           =7-5708S 6            =22-71261 207-016=7 .25-8770=7 9 11-0901 8-45345=8 7            =26-49804 236-590=8 29-5737=8 9            =8-51723 8            =30-28348 266-163  =  9 33-2704  =  9 9-51014=9 9            =34-06891 U.S. Dry          Liters. Quarts. Pack's.        Liters- Deka- liters. U.S. Pecks. U.S.          Hecto- Bushels.       liters. U.S.     Hectolitres Bushels         per per  Acre.    Hectare. 0-9081=1 0-11351=  1 0-8S10  = 1 1            =0-35239 1            =0-S707S 1          =1-1012 0-22702=  2 1 1-1351 2            =0-70479 1-14840  =  1 1-8162=2 0-34053=  3 1-7620  = 2 2-83774  =  1 2            =1-74156 2          =2-2025 0-45404=  4 2 2-2702 3            =1-05718 2-29680  =  2 2-7242=3 3  =3-3037 3-6323=4 4  =4-4049 4-5404=5 5  =5-5061 0-56755=  5 0-68106=  6 0-79457=  7 0-90808=  8 1            =  8-80982 2-6429  = 3 3-5239  = 4 4-4049  = 5 3 3-4053 4 4-5404 5 5-6755 4  =1-40957 5  =1-76196 5-67548=2 6  =2-11436 7  =2-46675 3  =2-61233 3-44519=3 4  =3-48311 4-59359=4 5  =4-353S9- 5-4485  =  6 6  =6-6074 6-3565=7 7  =7-7086 7-2646  =  8 1-02157=  9 2  =17-61964 3  =26-42946 4  =35-23928 5-2859  = 6 6-1669  = 7 7-0479  = 6 6-8106 7 7-9457 8 8  =2-81914 8-51323=3 9  =3-17154 11-35097=4 5-74199=5 6  =5-22467 6-S9039=6 7  =6-09545 8          =8-8098 5            =44-04910 7-9288  = 9 14-18871  =  5 8            =6-96622 8-1727  =  9 6            =52-85892 8 9-0808 17-02645=6 8-03879=7 9         =9-9110 7            =61-66874 9 10-2159 19-S6420=7 9            =7-83700 8            =70-47856 22-70194=8 9-18719=8 9           =79-28838 25-53968=9 10-33558=9 288     EVOLUTION   OF   WEIGHTS   AND   MEASURES MEASURES  OF  MASS. EQUIVALENTS  FROM  1  to  10. Grains. Grams. Avoir- dupois Ounces. Grams. Ounces.      Grams- Avoir-         Kilo- dupois       _ZZfI Pounds.      ^ams- Troy           Kilo- Pounds,      grams. 1 =  0-06480 0-03527  = 1 0-03215=     1 1            =0-45359 1            =0-37324 2 =  0-12960 0-07055  = 2 0-06430=     2 2            =0-90718 2            =0-74648 3 =  0-19440 0-10582  = 3 0-09645=     3 2-20462=1 2-67923  =  1 4 =  0-25920 0-14110  = 4 0-12860=     4 3            =1-36078 3            =1-11973 5 =  0-32399 0-17637  = 5 016075=     5 4           =1-81437 4            =1-49297 6 =  0-38879 0-21164  = 6 0-19290=     6 4-40924=2 5            =1-86621 7 =  0-45359 0-24692  = 7 0-22506=     7 5           =2-26796 5-35846  =  2 8 =  0-51839 0-28219  = 8 0-25721=     8 6            =2-72155 6            =2-23945 9 =  0-58319 0-31747  = 9 0-28936=     9 6-61387=3 7            =2-61269 15-4324 =  1 1 28-3495 1            =  31-10348 7           =3-17515 8            =2-98593 30-8647 =  2 2 56-6991 2            =  62-20696 8            =3-62874 8-03769  =  3 46-2971 =  3 3 85-0486 3           =  93-31044 8-81849=4 9            =3-35918 31-7294 =4 4 113-3981 4            =124-41392 9           =4-08233 10-71691=4 77-1618 =5 5 141-7476 5            =155-51740 11-02311=5 13-39614=5 92-5941 =6 6 170-0972 6            =186-62088 13-22773=6 16-07537=6 108-0265 =  7 7 198-4467 7           =217-72437 15-43236=7 18-75460=7 123-4589 =8 8 226-7962 8            =248-82785 17-63698=8 21-43383=8 138-8912 =  9 9 255-1457 9            =279-93133 19-S4160=9 24-11306=9 APOTHECARIES'   AND   METRIC   WEIGHT 289 £ s 5 < s M « S O 5 0 3 0 2 s «s< to J 5s o 3 M fc> H n P5 Q O 3 O ft o 6  s ►J  <! CO    S OS  00 t?  iH 00  fr- re  g ~'  CO co  o> £  o •    leo C5     00 o  le* GO  eo £:  oo iC  IO OS  <N Ol  rH co  oo O Id 5  2 ft  s '•?    00 J?  en co  S3 co  c* o l« z  < C5     CO §3 Sg 00 CO     00 Ci     rH ^  S3 «     CO o r  § i§ ^  52 »o  2 oi  . r-l  eo co  2 CO  t~ s  s ^-i  CJ> CO  ^ o 2  § c-  o CO CO  to 9  o Ol    oo 9     r-i ©     « ICO II 2  s CM  2 co   £ i  § •  l*« oi   p 8.p 8.1 oi  S 3  5 o O    o 0  rH 01  00 SS8 §  3 Pico CO  O O  rH O    00 SI 9|« co   3 •O    53 P    § 5  51 oi  « ©  ^ t>    rH 3  ># rj<     OS CO iH IO 3  2 "*    00 i  $ <*     00 IO     00 •      IrH 3d 290     EVOLUTION   OF   WEIGHTS   AND   MEASURES TABLE   GIVING DENSITY   (SPECIFIC   GRAVITY),   MELTING  POINT AND  BOILING  POINT MISCELLANEOUS  ELEMENTS  AND  SOLIDS. Density. Melting  Point. Centigrade. Boiling  Point. Centigrade. Aluminium Amber Antimony  - Asbestos    - Asphaltum Bismuth     ■ Bone Brass Bronze Butter Cadmium  - Calcite Chalk Cobalt Constantan Copper Cork- Feldspar    - German  silver  - Glass,  common  - ,,       plate,  crown  - ,,       flint,  light ,,  ,,      heavy     - Gold  ---         - Granite Graphite    - Gutta  percha     - Gypsum     - Ice     .... Iron,  cast  - ,,      wrought  - ,,      wire ,,      cast  steel Ivory Lard  - Lead  - Lime,  burned    - Magnesium Manganese Manganin  - Marble Mica  -         -         -         . Nickel Paraffin Platinum    - Porcelain    - Potassium  - Quartz Rubber,  unvulcanised ,,         hard     - 2-60—  (270) 1-078 6-71 2-0—2-8 1-07—1-2 9-8 1-7—2-0 8-1—8-6 8-7 0-86 8-6 2-7 2-25—2-69 8-6 8-8 8-5—8-9 0-2 2-55 8-5 2-50—2-70 2-45—2-72 3-15—3-4 3-6-3-9 19-2—19-3 2-5—2-9 1-8—2-24 0-96—0-98 2-32 0-9167 7-1—7-7 7-8 7-7 7-8 1-9 0-93 11*3 2-3—3-2 1-7 7  4 8-4     • 2-65-2-8 2-65—2-93 8-8—8-9 0-87 21-4—21-5 2-2—2-5 0-87 2-65 0-92-0-95 1*2 600-850 425—450 267—268 900—920 31—315 315—320 1500—1800 1000—1150 1000 800 to 1400 1065 0 1200—1400 1300—1400 41—42 325—327 630 1900? 1450—1600 38—56 1800 62 2000 1400— 1700 1400—1700 760-770 100 1450—1600 About  1100 350— 430 687—731 MISCELLANEOUS   ELEMENTS   AND   SOLIDS      291 MISCELLANEOUS   ELEMENTS   AND   SOLIDS— Continued. Density. Melting  Point. Centigrade. Boiling  Point. Centigrade. Sandstone  - Serpentine Silver Slate  - Sodium Spermaceti Sulphur Tallow,  beef       - ,,         mutton Tin     - Wax,  Japanese ,,       white ,,       yellow Wood,  beech , ,        box ,,        elm , ,        oak ,,        poplar    - yellow  pine Zinc 2  2— 2  5 2-4—2-7 10-5 2-6-2-7 0-98 0-8S— 0-94 2  07 0-97 0-92 7  3 0-99 0-96—0-97 0-96-0-97 0-85 1-33 0-80 0-7—0-8 0-40 0-66 715 960 95-6—97-6 44 114 43 47—50 227—232 54 63 62 412—420 740 448 1450—1600 930—950 LIQUIDS. Acid,  hydrochloric    - 1-24 ,,       nitric        - 1-42 ,,       sulphuric 1-84 Alcohol,  ethyl    - 0-7911 -130 78-3 ,,         methyl,  wood 0-80 66 Amyl  acetate     - 0-90 140 Aniline,  oil 1-02 185 Benzol, 0-881 5 80-3 Carbon  di sulphide     - 1-265 -113 46 Chloroform         .... 1-53 -70 61-2 Ether,  sulphuric 0-717 -118 34-9 Glycerine  ----- 1-24—1-26 -20 290 Mercury     ----- 13  596 -38-8 357 Oil,  linseed        - 0  93 ,,     olive 0-91 Petroleum,  crude 1-75—1-84 ,,            refined     - 0-84 ,.            rhigolene 0-65—0-66 40—70 ,,            gasolene - 0-66—0-69 70—90 ,,            benzene  - 0-69  -0-70 90—110 Phenol,  carbolic  acid 1-08 40 180 Turpentine,  oil  - 0-87 GASES. Air 0-001293 -200 Carbonic  acid    - 1865 -57? -  78  to  -  80 Hydrogen  ----- 0901 -250 -256 Nitrogen    ----- 1251 -203  to  -214 -194 Oxygen      1429 -  181  to  -  184 Water  vapor      - 0804 0 100 292     EVOLUTION   OF  WEIGHTS   AND   MEASURES THERMOMETER   SCALES. CENTIGRADE  AND  FAHRENHEIT  EQUIVALENTS. For  Absolute  Temperatures  add  273°  to  Centigrade  Scale. Centigrade. Fahrenheit. Remarks. Centigrade. Fahrenheit. Remarks. -273 -549-4 ' '  Absolute  zero. " -6-1 21 -250 -418 Hydrogen  boils. -6 212 -200 -328 Temp,  liquid  air. -56 22 -190 -310 Nitrogen  boils. -5 23 -180 -292 Oxygen  boils. -4-4 24 -170 -274 -4 24-8 -160 -256 -39 25 -150 -238 -  3  3 26 -140 -220 -3 26  6 -130 -202 Alcohol  freezes. -2-8 27 -120 -184 -22 28 -110 -166 -2 28-4 -100 -148 -1-7 29 -80 -112 Carbonic  acid  gas -1-1 30 -60 -76 boils. -1 30-2 -40 -40 Mercury  melts. -06 31 -30 -22 Ammonia  boils. 0 32 Water  freezes. -25 -13 06 33 -20 -4 1 33-8 -19 -22 1-1 34 -18 -0-4 1-7 35 -17'8 0 2 35-6 -17  2 1 2  2 36 -17 1-4 2-8 37 -16-7 2 3 37  4 -161 3 3  3 38 -16 3  2 3  9 39 -15-6 4 4 39-2 Maximum  density -15 5 4-4 40 of  water. -14-4 6 5 41 -14 6-8 5  6 42 -13-9 7 6 42-8 - 13\3 8 61 43 -13 8-6 6  7 44 -12-8 9 7 44  6 -122 10 7-2 45 -12 10-4 7-8 46 -11*7 11 8 464 -li-i 12 8-4 47 -11 122 8-9 48 -10-6 13 9 48-2 -10 14 9  5 49 -94 15 10 50 -9 15-8 106 51 -8-9 16 11 51-8 -8-3 17 11-2 52 -8 17'6 11-7 53 -7'8 18 12 53-6 -7'2 19 12-3 54 -7 19-4 12-8 55 -6-7 20 13 55-4 THERMOMETER   SCALES 293 THERMOMETER   SCALES. CENTIGRADE  AND  FAHRENHEIT   EQUIVALENTS. For  Absolute  Temperatures  add  273°  to  Centigrade  Scale. Centigrade. Fahrenheit. Remarks. Centigrade. Fahrenheit. Remarks. 133 56 33 91-4 13-9 57 33  3 92 14 57  2 33-9 93 14-4 58 34 93  2 15 59 34-4 94 Ether  boils. 15'6 60 35 95 16 60-8 35  6 96 16-1 61 36 96-8 167 62 36-1 97 17 62  6 36-7 98 172 63 37 98-6 Human  blood  tem- 17-8 64 37  2 99 perature. 18 64  4 37-8 100 18-3 65 38 100-6 18-9 66 38-3 101 19 66-2 38-9 102 19-4 67 39 102-4 20 68 Proper  room  tem- 39-4 103 20-6 69 perature. 40 104 21 69-8 43  3 110 211 70 45 113 21-7 71 48  9 120 22 71'6 50 122 22  2 72 54  4 130 22-8 73 55 131 23 73-4 60 140 Chloroform  boils,  62*. 23-3 74 65 149 Potassium  melts,  62°. 23  9 75 65-6 150 Methyl  alcohol  bis., 66*. 24 75  2 70 158 Woods  alloy  melts,  65°. 24  4 76 71-1 160 25 77 75 167 25-6 78 76-7 170 26 78-8 80 176 Ethyl  alcohol  boils,  79°. 26-1 79 82-2 180 26-7 80 85 185 27 80-6 87-8 190 27  2 81 90 194 27-8 82 93-3 200 28 82-4 95 203 Sodium  melts,  96°. 28-3 83 98-9 210 28-9 84 99 210-2 29 84-2 99-4 211 29-4 85 100 212 Water  boils,  under 30 86 125 257 76  cm.  pressure. 30  6 87 150 302 31 87'8 Critical   tempera- 175 347 311 88 ture  of  carbonic 200 392 Solder  melts,  183°. 317 89 acid. 250 482 Tin  melts,  227°. 32 89-6 300 725 Lead  melts,  335°. 32-2 90 350 662 Mercury  boils, 32-8 91 400 752 357°  3. 294     EVOLUTION   OF  WEIGHTS   AND   MEASURES MISCELLANEOUS   CONSTANTS  AND  EQUIVALENTS. tt  =  3*1416.  tt2  =  9*8696.  1/tt  =  0"31831.  4tt=  12*566. 1/4*-  =  0*07958.  Jog7r= -49715.  log tt2= -99430.  log  l/7r=f*50285. log  4tt=  1-09921.  log  1/4tt  =  2*90079. Base  of  the  natural  system  of  logarithms,  e  =  2*7183,     log  e=  -43429  (Briggs). Modulus      „  „  „         M=  l/loge  =  2-3026,  log M=  -36222  (Briggs). Radian  =  angle  where  the  arc  equals  the  radius  =  57° '2958  =  3437' '75  =  206265". log  radian  (in  degrees)  =  1  "75812,         (in  minutes)  =  3  "53628, (in  seconds)  =  5 "31443. Steradian  =  the  solid  angle  at  the  center  of  a  sphere  of  unit  radius  which  is  sub- tended by  the  unit  area.     Total  angle  at  a  point  equals  Air  steradians. Earth's  radius  in  kilometers — equatorial  =  6378  "2,  polar  =  6356  "5,  mean  =  6367  "4, log  equatorial  =  3  "80469,         log  polar  =  3  "80321 ,         log  mean  =  3  "80396. Mean  solar  year  =  365  "2422  days  =  8765  "8 13  hours  =  525948  "8  min.  =31556928  sec. Stellar  day  is  3  min.  55  "9  sec.  shorter  than  the  mean  solar  day,  =0*99727  day. Velocity  of  sound  in  dry  air  at  0°C.  is  331  meters  per  second. Coefficient  of  expansion  of  gases  =  1/273  =  *003665. Acceleration  of  gravity  at  poles  =  983  *2 ;  at  equator  =  978  *0 ;  at  45°  =  980  *6 ;  at  New York  =  980*2  ;  at  Greenwich  =  981*2  ;  at  <f>°  latitude  =  978(1  +0*0052  sin20). 1  gram  of  water  1°C.  =  minor  calorie  =  4*2  x  107  ergs  =  4  "2  joules. Latent  heat  of  water  =  80;  of  steam  =  539. Specific,  heat  of  air  at  constant  pressure  =  0 "237.     Ratio  of  specific  heats  =1*40. Capillary  constant  of  water  =  7  "7,  of  alcohol  =  2  "3,  of  mercury  =  50  rng./mm. Velocity  of  light  in  vacuo  =  3  x  1010  cm.  /sec. Wave  length  of  sodium  light  =  0 "0005893  mm. Length  of  the  meter  in  wave  lengths  of  red  cadmium  light  =  1553163  "5. 1  ampere  of  current  deposits  1  "118  mgr.  of  silver  per  second  =  0"1740c.c.  (H.  and  0. ). A  plate  of  quartz  1  mm.  thick  at  18°  C.  rotates  the  plane  of  polarization  21° '71. Ohm  =  resistance  of  a  column  of  mercury  1  sq.  mm.  cross-section,  106 "3  cm.  long. E.M.F.  of  Latimer  Clark  cell  at  18°  is  1-434,  of  cadmium  (Weston)  cell  at  4°  is 1-0190. The  solar  constant  =  3  gram-calories  per  sq.  cm.  per  minute. The  mass  of  the  hydrogen  atom  is  =  10-24  gram  ;  of  the  electron  is  =  10-27  gram. Value  of  e/m  =  4*5  x  1017  electrostatic  =  1 *5  x  107  electromagnetic. Velocity  of  the  electrons — beta  particles  =  2-7  x  1010,  alpha  particles  =  3  x  109. Probable  speed  of  a  molecule  of  oxygen  at  0°  C.  =376*6  m./sec. ,  of  hydrogen  =  1500*9. Mean  free  path  of  a  molecule  of  air  at  a  pressure  of  76  cm.  and  at  0°  C.  =9*6  x  10~6. Number  of  molecules  of  air  in  a  c.c.  at  0°  C.  and  76  cm.  =6  x  1019. One  atmosphere  pressure  =  76  cm.  of  mercury  =1*0132  megadynes  per  sq.  cm. A  knot  is  a  speed  of  one  nautical  mile  per  hour  =1*1515  statute  miles  or  1S53'25 meters  per  hour. A  miner's  inch  of  water  is  from  1*20  to  1*76  cu.  ft.  per  min.  =0*708  liter  per  sec. Ratio  of  the  probable  error  to  the  mean  error  is  0*6745  (2/3). Light  year  is  the  distance  travelled  by  light  in  one  year  =  9*467  x  1012  kilometers =  5*8825  x  10»  miles. INDEX. PACE Abbot.  Gen.  Henry  L.  -         -     21 1 Abraham 4,  19 Absolute  measurements         -         -     204 Absolute  system  -  200 Academy  of  Sciences,  Paris,  47,  48,  65 Academy  of  Sciences,  Paris,  Sup- pression of     -         -         -         -       52 Academy    of    Sciences,   National, U.S.       -        -        -      127,  129,  210 Academy  of  Sciences,  St.  Peters- burg        71 Acts  of  Congress 119,  121,  127,  128,  129,  131,  132,  210 Actus    -         -         -         -         -         -       26 Adams,  John  Quincy 109,  115,  116,  117,  118 Aeginetan  talent  and  mina  -  27,  28 Airy,  Sir  G.  B.     -         -         -     100,  247 Ale  gallon 35 Alexandrian  talent  -  -  25,  32,  33 Alloys,  Nickel  steel  -  -  -  221 Amenoemopht  ...  -  22 American  Geographical  and  Statis- tical Society  -  -  -  -  125 American  Metrological  Society  -  129 Ampere        -       206,  207,  208,  209,  211 Amphora 28 Angle,  Measurement  of  -  -  2<  12 Anglo-Saxon  measures  of  length  -  36 Angular  acceleration  -  -  -  202 Angular  velocity  -  -  -  -  202 Anti-Metric  argument  of  American Society  Mechanical  Engineers 145-162 Apothecaries'  pound  32 Ar 142 Arabs,  Measures  of       -         -  29,  38 Arago 100 Arbitrary  units    -         -         -         -         5 Arbuthnot 10 Arc  of  Meridian,  Measurement  of       55 Archinne 94 Are 54 Argentine  confederation        -         -  76 Ark,  Dimensions  of       -         -         -  11 Aroura           -         -         -         -         20,  23 Arpent 45 Articles  of  confederation,  Weights and  measures  in     -         -         -  109 As,  Roman  unit  of  weight    -         -  26 Assize  of  bread  and  ale           32,  35,  242 Association  geodesique          -         -  71 Assyrian     documents,     Measures in 16 Astronomy,  Babylonian         -         -  12 Ater 23 Athena,  Temple  of  25 Athenian  talent  27 Attic  foot 25 Aulne,  Derivation  of     -         -         -  26 Aune  des  marchands    -         -         -  38 Aune  of  Paris        -         -         -         -  38 Aune,  Swiss  97 Australia  and  the  metric  system  -  102 Austria  adopts  metric  system       -  90 Austria- Hungary      signs     metric treaty 75 Autun,  Talleyrand,  Bishop  of       -  46 Avoirdupois  pound 33,  34,  35,  122,  123,  248 Babylonia,  Measures  of  8,  9,  11,  12,  13, 14,  15,  16,  17,  18,  19,  22 Bache,  Professor  A.  D.  122,  123,  124 Baden  adopts  decimal  measures  -  82 Baily,  F.  -  -  -  -  231,  243 Balance  -  24,  236,  237,  238,  239 Baldwin  locomotive  works  -  -  188 Bancroft,  George  -  -  -  -  125 Barcelona  -  -  -  -  49,  56 Barker,  Geo.  F.  -  -  -  -  211 Barley  corn  as  a  unit  -  -  -  8,  29 Barnard,  Prof.  F.  A.  P.  -  -  129 Barus,  Carl 211 296 INDEX Base  measurement PAGE -      55 Bassot -       41 Bath -      20 Beal 6 Belgic  foot    - -       31 Belgium  adopts  metric  system -       91 Belhaven  and  Stenton,  Lord  101 Benoit,  J.  Rene  -  -  69,  219,  251 Berthollet     -        -         -         -         54,  99 Bessel 40,  223 Bigourdan,  M.       -         -         -  41 Binary  subdivision  -  -  -  179 Bird  standard  ....  244 Bismer-pund  96 Black  cubit 29 Blaine,  James  G.  -         -         -         -     159 Board  of  Trade  British  specifica- tions       215 Board   of   Trade   electrical   stan- dards      242 Body  measures  6 Boeckh  -         -         -         -  11,  29,  30 Boisseau 66 Borda  -         -         -    47,  48,  54,  250,  251 Brandis,  J. 11 Brazil  and  metric  treaty  -  -  75 Briggs,  Ernest  B.  -         -         -     187 Brighton  railway,  England  -         -     168 Brisson 54 British  Association  committee  on units      -         -         -               205,  207 British  Association  unit  of  resist- ance        207 British  engineers  in  Egypt  -  -  92 British  imperial  gallon  -         -       36 British  imperial  standards 245,  246,  247,  248,  249 British  imperial  standard  yard  -  246 British  pharmacopoeia  -      192,  197 British  standards  of  length  and weight  -       245,  246,  247,  248,  249 British    Weights     and    Measures Association    -  163 Brix 69 Bronze  standard  No.  11        -         -    247 Brumaire 53 Brumer  comparator  -  -  -  234 Bunge  balance  ...  -  238 Bureau  International  des  Poids  et Mesures  established       -         -       76 Bureau  of  Standards,  U.S.  -      131,  132 Cadmium  spectrum,  Lines  of  -  261 Calendar,  French  reforms  in  52,  53 Caliph-Al-Mamum  29 Calipers  for  standards  of  length 224,  229 Canaan,  Civilization  of  -         -       19 Capacity,  Electrical      -         -     203,  209 Capacity,  Measures  of 5,  27,  28,  35,  144,  240 Carat 3,  25 Cassini  -         -         -         -  44,  49,  54 Cattle  standard    -         -         -         -         3 Centesima 43 Centigram  -  -  -  146,  147,  148 Centiliter  -----  144 Centime        -         -         -         -         -       45 Centimeter 139 Centner 86 Centuria 43 C.G.S.  or  centimeter-gram-second- system  -         -       102,  199,  205,  206 C.G.S.  electro-magnetic  units     -       207 Chambers  of   Agriculture  favour metric  svstem  -  -  -  102 Chaney,  H.  J.       -         -  30,  37,  247 Chappuis,  M.  -  -  -  -  261 Charlemagne  37 Charlemagne,  "  Pile  de "  -  -  39 Chase,  Salmon  P.  126 Chicago  congress  -  208 Chisholm,  H.  W.  -         -   25,  32,  33,  244 Clark  cell 207 Clark,  Capt.  A.  R.  -  -  -  69 Clarke's  spheroid-  62 Coast  and  Geodetic  Survey  stand- ards      -         -         -      114,  121,  122 Colles,  Geo.  W.    -         -         -         -     133 Collet,  M.  A.        -         -         -         -     258 Cologne,  Mark  of  -         -         32,  40 Colonial  Governors,  British,  favour metric  system  -  -  -  159 Commemorative  medal  for  metric system  -  -  -  -  63,  64 Commercial  pound  (libra  mercatoria)  33 Committee   on    coinage,    weights and  measures  reports       73,  75,  87, 90,  91,  120,  121,  128,  130,  133 Committee  of  weights  and  measures and  of  moneys  of  Paris  Ex- position of  1867     -         -         -       85 Comparison  of  standards  of  length     229 Comparator  of  Borda    -         -         -     230 Comparator  of  Lenoir  -         -         -     230 Compensated  bars         -         -         -     251 Conder,  C.  R.        -         -         -         -       22 Condorcet     -         -         -         -         47,  48 Conference    of    British     Colonial Premiers        -         -         -         -     159 Congius 28 Congress,  U.S.,  considers  weights and  measures  -         -      113,  127 Congress,  Acts  of 119,  127,  128,  131,  132 Conservatoire  des  Arts  et  Metiers 69,  250,  251,  252 Conservatory,  Meter  of         -         -       73 INDEX 297 Continental  Congress,  legislation on  weights  and  measures,       -     109 Corinth,  Units  of  weight  in  -         -       27 Corn  bushel 35 Corn  gallon 35 Corps  Legislatif  receives  standard meter  and  kilogram       -         -       63 Cotton  values  quoted  decimally    -     167 Coulomb 54 Coulomb,  unit  of  quantity  203,  206,  207 Cross- wires  -  -  -  -  231,  234 Crypt  chapel  30 Crystal  standards  -         -         -     236 Cubit  -  -  6,  13,  14,  15,  20,  22,  26 Cunin-Gridaine  83 Currency,  Decimal  -  -  85,  110 Curvature,  Unit  of  202 Dagobert 37 Daniell  cell 205 Deben  or  uten  24 De  Bonnay,  Marquis  46 Decagrams    -  146,  148 Decaliter       -  144,  145 Decameter    -  138,  139 Decigrams     -         -         -         -      146,  148 Deciliter 144 Deciina 43 Decimal  Association  -  -  -  101 Decimal  clocks  ...  -  168 Decimal  hour  ....  168 Decimal  multiplication  -         -     167 Decimal  system  of  coinage  -  85,110 Decimal  system  of  Jefferson  -     111 Decimal    system    of    money   pro- posed in  France  45 Decimes 45 Decimeter  -  -  -  -  138,  139 Decistere      -         -         -         -         -     144 Decuria 43 Didrachms 25 Delambre  ....  54,  60 Delambre  and  Mechain,  Base  du Systeme  MUrique  -         -         -       41 De  Luc 99 Denier 38 Denmark  signs  metric  treaty  -  76 De  Puvy,  Charles  A.  -  -  -  168 De  Sarzec,  E.        -         -         -  14 De  Schubert,  Gen.  T.  F.  -  -  69 Dessert-spoonful  ...         -     198 Digit 6 Directive  force  ....  202 Dividing  engine    -  225 Domesday  book    -         -         -  31 Double  weighing  -  237 Drachmas 27 Draughting  room,  Metric  system in 181 )rusus,  Foot  of     - PAGE -       26 )unkirk 49,  56 )u  Vernois,  Prieur -       44 Sarth  inductor -     204 3dgar,  Laws  of     - -      30 3d  ward  L,  Laws  of -       34 fid  ward  II. .  Laws  of    - -       36,  242 Mward  III.,  Laws  of  - -    243 Sgypt,  metric  measures -       92 Egyptian  measures,  Ancient 11,  20,  22,  23,  24 Ehalkus 27 Electrical  congress,  Chicago  208,  216 Electrical  congress,  Paris  -  -  215 Electrical  congress  (St.  Louis)  216,  241 Electrical  measure,  U.S.  units  of  131 Electromotive  force  -  -  -  204 Elephantis,  Cubit  of     -  22 Elizabeth,  Standards  of         34,  36,  243 Ell 26,  36,  89 Elle 83 End  standard  (metre  a  bouts)  -  74 End  standards  (e talon  a  bouts)  -  223 Energy,  Unit  of  -  -  -  -  202 Engineering,  Metric  system  in  -  172 England,      Progress     of      metric system  in       -         -         -         -       98 English  Bible,  Weights  and  meas- ures in 20 English    parliamentary    accounts and  papers  91 English  yard 3,  31,  36,  243,  244,  245,  246 Ephah 20 Eratosthenes  29 Erg 202,  206 Euboic  talent  27 Everest,  Col.  George  69 Exchequer,  Standards  of  -  34,  109 Exodus,  Weights  and  measures  at time  of 20 Export     business     and     uniform measures        ....     133 Ezekiel  ....         20,  23 Fabbroni 256 Farad 203,  206 Farmers'      Associations      favour metric  system        -         -         -  102 Fathom 6 Federal  constitution,  Weights  and measures  in    -         -         -         -  109 Finland,  metric  system  adopted  -  95 Fizeau 261 Fleetwood,  Bishop        -         -         -  30 Floreal 53 Foerster,  W.          ....  87 Foot      6,  25,  26,  31,  37,  38,  44,  89,  112 298 INDEX PAGE Force,  Units  of    -  200,  202 Forney,  M.  N.  -  -  -  -  185 Foster,  Secretary  of  State  -  -  159 France,  Measures  of     -         -  37,  43 French  Academy  99 French  foot 38 French  standards  of  length  -  37,  249 French    standards    presented    to various  nations       -         -         -       83 French  standards  of  weight         38,  250 Fructidor 53 Fundamental  units  -  -  S,  200 Fuss 83 42,  55 -  164 -  43 -  200 8,  89,  90 9,  22,  24 -  15 Galileo 15 Gallatin,  Albert,  Minister  -  119,121 Gambey,  Comparator  of        -        69,  232 Gan 15 Gar 15 Garden 15 Gas  thermometer  -         -         -     228 Gauges  -         -         -      176,  177,  178 Gauss,  Carl  Friedrich  -  -  200,  201 Gauss  (unit)  ....     215 Genesis         ....  11-19 Geodetic  or  trigonometrical  survey "  Geometrical "  inch     - Geometric  foot German  Magnetic  Union Germany,  Metric  system  in 86,  87, Ghizeh,  Pyramid  of Gin Gird 30 Godin  and  Bouguer  44 Goldsmith's  Hall,  Standard  of      -     248 Gore,  J.  H. 43 Gouon  and  Penin  64 Gradus 26 Graham,  George  36 Gram 54,  146 Gratings,  Diffraction  -  -  -  226 Gravimetric  method  -  -  -  193 Great  circle  42,  48 Great  rnina 16 Great  pyramid  -  -  7,  9,  22,  24 Greaves,  John  -  -  -  29,  30 Greece,  Measures  of  ancient  -       25 Greece,  Metric  system  in  -  -  92 Greek  cubit  -  -  -  -  22,  25 Greek  foot  -----  25 Gregorian    calendar    resumed    in France 53 Griffiths,  F.  L.      -         -         -         -      23 Gros 39,  66 Gudea  scale  -  -  -  -  13,  14 Gunter,  Edmund-  9S Gur 16 Guillaume,  Ch.  Ed. vii.,  35,  39,  221,  223,  228 Guizot 83 Halsey    and    Dale,     The    Metric Fallacy 134 Hamy,  M. 261 Hand-breadth       -         -         -         -  6,  13 Harpham,  F.  E.   -         -         -  41 Harris  ------       34 Harrison,  President  Benjamin  -  131 Hassler  -  -  114,  121,  122,  123 Hastings,  Charles  S.  -  -  -  211 Haute-Guyenne  45 Haiiy 54,  62 Hebrew  weights  and  measures 19,  20,  21 Hectar(e)  -  -  -  -  51,  142 Hectogram  -  51,  148 Hectoliter  -  -  -  -  51,  145 Hectometer  -  -  -  -  51,  139 Hekatompedos  25 Hekt 23 Henry  (unit)  -  -  -  -  210 Henry  L,  Yard  of  -  -  -  3,  31 Henry  III.,  Statutes. of    -    32, Henry  IV. Henry  VII.  34, Henry  VIII.,  Statutes  of     - Henry,  Prof.  Joseph     - Henu Herschel,  Sir  John        -         -         7, Hilgard,  J.  E.       - Hin Hindus,  Weights  and  measures  of Hiuen-Tsiang        - Holland,  Metric  system  in   -  82,  93, Hoi  ton,  Michigan,  Base  at  -         -     141 Homer 21 Hommel  -  -  -  -  11,  12,  13 House    of    Commons    Committee report    -         -         -         - House  of  Deputies,  France,  bill Hultsch         .... Hundredweight    - Hungary,  Metric  system  in  - Hunt,  Wm.  H.     -         -         - Huygens       - Hydrogen  scale     - Hydrogen  thermometer 33 33 35 34 129 23 164 129 21 18 6 94 100 67 25 156 91 195 43 228 228 Ibanez,  General  77 Iced  bar  base  apparatus         -         -     141 Ideler,  L. 12 Imperial  bushel    -         -         -       35,  249 Imperial  standards 245,  246,  247,  248,  249 Inch 26,  36 India,  Ancient  measures  of  -         -         6 INDEX 299 PAGE -    208 120,  121 186 181 200 216 208 216 75 209 Inductance,  Unit  of Ingham,  S.  D.       - Institution  of  Electrical  Engineers Instruments  of  precision,  Use  of metric  system  in    - Intensity  of  magnetism,  Measure- ment of  International  American  Conference of  1890  -  103,  159 International  ampere  -  -  -  209 International  Bureau  of  Weights and  Measures        -  75,  76,  77,  129, 221,  226,  260 International  Commission 61,  72,  9 International  Congress  of  Elec- tricians (Chicago)  - International    Congress   of    Elec- tricians (Paris)       -         -     207,  208 International   Congress    of    Elec- tricians (St.  Louis) International       Convention       of Weights  and  Measures International  Coulomb International  electrical  units 131,  199,  209 International  farad  -  -  -  209 International  Geodetic  Association  71 International  kilogram,  Definition of  -         -         -         -        ."   .     "       78 International  metric  commission 72,  73,  74,  75,  76,  77,  78 International    metric     prototype standards  -  76,  77,  252,  254,  255, 256,  257,  258,  259 International  ohm  -  -  207-209 International  Postal  Convention  127 International  Postal  Union  -  -  151 International  prototype  meter 130,  136,  221,  252,  255 International   standard   kilogram 78,  258,  259 International  Statistical  Congress  126 International  volt  -         -         -     209 Invariability  of  standards  -  219,  260 Israelites,  measures  -  -  19,  20,  21 Italy,  Metric  system  in         -         -       93 Jacobi 205 Japanese  weights  and  measures  -  93 Jefferson,  Thomas 110,  111,  112,  113,  114,  115 Jeremiah 23 Jews,  Weights  and  measures  of  -  19 Johns,  Rev.  C.  H.  U.  -         -  16,  17,  18 Josephus 10 Jomard  -  -  -  -  10,  30 Joule  ----  206,  208,  209 Jugerum 26 Ka Kab      - Karsten Kasbu  - Kat  or  Kiti  - Kater,  Captain  Henry 99,  100,  119,  120, Keith,  Rev.  George  Skene Kelly    - Kelvin  - Kennedy,  A.  R.  S. Khar     -         -         - Khet     ---         - Kilogauss Kilogram     50,  62,  63,  73, 147,  256, Kilogram  of  the  Archives 73,  74,  75,  147, Kilometer     - Kilowatt King  Edgar  - Kirwan Kiti  or  Kat  - Koenigsberg  standard  - Kohlrausch,  Rudolf Kor       .... Korn-Tonde- Kupffer PAGE -  16 16,  21 -  40 -  15 -  24 122,  222,  245 -  99 31,  37 -  101 -  20 -  23 -  23 -  215 74-146, 257,  258,  259 256,  257,  258 -  50,  138 -  206 -  30 -  98 -  24 -  223 -  201,  205 -  21 -  96 -  234 47: Lacaille La  Condamine Lagrange Lalande Laplace         -         -47,  48, Larsam  or  Larsa  - Lathes  - Latin  prefixes Latin  Union Latitude,  Determination  of 56,  57,  58,  59 Lavoisier  ....  62,  98,  99 Leading  screw  of  lathes         -         -     187 ■   49 -  44 48,  54 -  229 54,  65,  98,  99 -  13 -  182 -  137 -  85 Lefevre-Gineau Lehmann Lenoir  - Lepsius Leroux,  Alfred Lever  comparator Le  Verrier    - Libbrae  metrica    - Libra    - Libra  mercatoria Library  catalogue  cards Lieue    - Lignes  - Line  and  reel Line  standards  (etalon  a Linnard,  J.  H. Liter     .... 62,  256 15,  18 14,  230,  251,  256 13,  22 -  71 -  230 -  69 -  82 -  28 -  33 -  140 -  97 44,  45 -  23 -       223 -  134 54,  145 traits) 300 INDEX PAGE Liverpool  Cotton  Association        -     167 Livre 39,  45,  97 Livre  de  Troyes   -  33 Livre  Esterlin  ...  32,  38 Livre  poid  de  marc  39 London  Exposition  of  1851  -          83,  84 Longitude 59 Long  ton 168 Louis  XVI. 45 Lumber,  Measurement  of      -         -     178 Maass  concordats  -         -         83,  97 Machine  shop,  Metric  system  in  -  182 Madison,  President  James  -  -  115 Magna     Charta,     Weights     and measures  in    -         -         -         -       32 Magnetic  field,  Unit  of  -         -     203 Magnetic  pole,  Unit  of  -         -     202 Maine  approves  metric  system  -  122 Mairan,  Toise  of  -         -         -  61 Marc 39 Marc  de  Troyes  -  -  -  -  33 Marine  Hospital  Service  -  192-195 Mark  of  Cologne  32,  40 Mass,  Measures  of  146 Master  Car  Builders'  Association 173,  185 Mauss,  C. 250 Maxwell,  (unit)  -  -  -  203,  215 Maxwell,  J.  Clark  -  -  -  260 Measures  of  capacity  -  -  144,  240 Mechain  -  -  -  41,  54,  60,  61 Mechanical  engineering  and  manu- facturing, Metric  system  in  -  172 Mechanical   engineers,    American Society  of      -  145-162 Medical  department  of  the  army 192,  195,  196 Medical  department  of  the  navy 192,  195 Medical  papyri  24 Medicine  and  pharmacy,   Metric system  in  191 Medimnus 23 Megameter 138 Memphis,  Necropolis  at  -  -  22 Memphis-Faium  road  -  -  -  23 Mendenhall,  J.  C.  -         -         -     164 Mesures  usuelles  -         -  65,  66,  67 Meter        -         -  49-54,  62-63,  139 Meter  of  the  Archives  62,  71,  73,  75, 221,  225,  249,  251 Meter  of  the  conservatory  -  63,  251 Meter  of  the  observatory  -  -  251 Method  of  interference  for  measur- ing differences  of  length  -  225 Metre  a  bouts  74 Metre  a  traits  -  -  -  72,  73,  74 Metric  measures  of  capacity       144,  240 PAGE Metric  measures  of  length  -  -  138 Metric  measures  of  mass  -  -  146 Metric  measures  of  surface  -  -  142 Metric  measures  of  volume  -  -  143 Metric  prescriptions  -  -  -  192 Metric  standard    of    U.S.    Coast Survey 114 Metric  standard  of  United  States  130 Metric  system  -  -  39,  41,  61,  63 Metric  system  in  U.S.   Congress 133,  134 Metric  thread       ....     183 Metric  ton 147 Metric  wire  gauges  -  -  -  178 Metrological  Society,  American  -  129 Mexico,  Metric  system  in  -  -  103 Michelson,  Prof.  A. 211,  260,  261,  262,  263,  264,  265 Micro-farad 206 Micrometer-microscope 230,  231,  233,  234 Micrometer  screws        -         -         -     229 Micron 140 Milan,  Metric  system  introduced in 82 Mile 26,  31 Milia  pasuum  -  -  -  26,  31 Miller,  W.  H.  -  -  -  35,  248 Miller,  Sir  John  Riggs  -       99,  163 Milligram     -         -         .  146,  148 Milligram  weights         -         -         -     148 Milliliter 144 Millimeter    -  138;  140 Millimicron  -  138^  140 Mina  -  -  -16,21,25,27,28,32 Mina,  Babylonian  16 Mina,  heavy  -         -         -         -       16 Mina,  light 16 Mina,  Phoenician  16 Mint,  U.S.,  standard  troy  pound      119 M'Leod 99 Modius 28 Moment  of  rotation,  Unit  of  -  202 Momentum,  Unit  of     -  202 Monge 48,  54,  99 Moore,  Dr. 123 Morin,  General  A.         -         -  41,  69 Morris,  Robert  -  -  -  -  110 Mouton,  Gabriel  -  -  -  -  43 Miinzpfund  -         -         -      •  -         -       86 Myriameter 138 Myriagram  -         •         -         -      146,  147 Napoleon  I.  -  -  -  65,  77,  82,  92 Napoleon  III.  -  -  -  -  71 National  Academy  of  France  -  49 National    Academy   of    Sciences, U.S.       -         -         -      127,129,211 National  Assembly  (French)         -       46 INDEX 301 PAOE National  Bureau  of  Standards  -  132 National  Institute  of  Sciences  and Arts  (French)  -  -  53,  63 National      Physical     Laboratory (England)  -  -  -  152,  241 National  prototype  meter  of  the United  States  -  -  -  130 Natural  standards  5 Natural  units  -  -  -  -  5 Neutral  plane  ....  222 New  Hampshire  approves  metric system 125 Newton's  rings     -  261 New  Zealand  adopts  metric  system  102 Nickel  five  cent,  piece-  -  -  128 Noak,  Ark  of  -  -  -  -  11 Normal-Aichungs-Kommission  87,  90 North  German  Confederation  -  87 Norway         -         -         -         -         95,  96 Oboles  - . 38,  39 Ohm      -         -        ,- . -     206 Ohm's  law    - . -     204,  206 Oke       - . -         -       92 Oldberg,  Oscar - -     195 Old     Testament,     Weights     and measures  of  -         -         -  19,  20,  21 Olympian  foot  25 Oner 21 Opticians'  use  of  metric  system    -     181 Orguia,  or  fathom         -         -         -       25 Origin  of  weights  and  measures    -         1    i Ounce  -         -         -         -     25,  26,  32,  33 Pace 2,  6 Palestine       Exploration       Fund, Quarterly  statement,  1902     -       22 Palm     - 6 Palm,  Babylonian  -         -         -       14 Palmipes  or  foot  26 Parasang  -  -  -  -  -  15 Paris  Academy  of  Sciences  46,  47,  71 Paris  Exposition  -  -  70,  84,  85,  129 Paris     International      Electrical Congress         -         -      207,  208,  215 Parliamentary  reports  91 Parliament,  Burning  of  Houses  of, 1834 35 Parliamentary  standard        -         -     249 Parthenon 25 Par  value 167 Passus  ------       26 Paucton        -         -         -         -     7,  10,  37 Pavilion  Breteuil  -         -         -       77 Pence 32 Pendulum  as  a  unit  of  length 15,  37,  42,  44,  46,  48,  49,  111,  245 Penny,  or  sterling  -  -  -  32 Pennyweight         -         -         -         -       32 Perch    ...         - PAGE -       45 Perche  - -       97 Perpignan,  Base  at -       55 Pertica  or  Decempeda  - -       26 Peru,  Toise  de 44,  249 Petrie,  Flinders    - -  18,  23,  24 Pfund  - -  82,  83,  86 Philippine  Tariff  Act,  1901  -  -  132 Philosophical  drachm,  ounce,  and pound 98 Phoenician  weights  and  measures  18,  21 Physicalisch  Technische  Reich  san- stalt 152 Picard 43 Pied  de  roi 37 Pied  geometrique  44 Pied  (Swiss)  ....       97 Pile  of  Charlemagne  -  -  39,  250 Pinte  (French)      -  145 Platinum  for  standards  -  236,  257 Platinum  Iridium  standards 74,  77,  148,  221,  252 Platinum  metres  •         -         -        62,  251 Pliny 26 Plumb-line 15 Plutarch 25 Pluviose 53 Polar  axis  -----  164 Polar  flattening    -         -         -  48,  59,  62 Polaris 39 Polar  radius  -         -         -         -     164 Polybius 26 Polychrome  Bible  -         -         -       14 Porto  Rico,  Metric  measures  in  -  132 Portugal,  Metric  system  in  -  -  94 Postal  Congress  of  1863         -         -     126 Pot  (Swiss) 97 Potential  difference,  Unit  of  -  203 Pound  -  27,  32,  33,  34,  38.  119,  248 Power,  Unit  of  -  -  -  -  202 Pratt  &  Whitney  Co.    -         -         -     185 Prairial 53 Prescriptions,  Metric  -  -  -  197 Priestley,  Dr.        -         -         -         -       98 Prony 54 Ptolemy  Lagos  24 Pyx  chapel 30 Quadrant  (unit  of  inductance)  -  208 Quantity  of  electricity,  Unit  203,  209 Quarteron  -----  39 Quarteron  (Swiss  unit  of  capacity)  97 Queen  Anne,  Gallon  of  -         -       35 Queen  Elizabeth,  Standards  of 35,  36,  243,  247 Quintal  ...  -  146,  147 Quito,  arc 44 Railway  shares 167 302 INDEX Rawlinson    - Rayleigh,  Lord     • Rayon  astronomique Reed     - Regnault Reichsanstalt Resistance    - Retail  Trades  Associations  favour metric  system Rhine  countries,  Measures  in Rhine  foot  - Richard  L,  Laws  of      -         - Riders Ridge  way  3 PAGE -  13 -  207 -  43 -  15 -  69 152,  241 203,  204,  205 102 26 40 31 148 4,  18 Rock  crystal  standards  148,  236 Rogers,  Wm.  A.  -  -  -  185,  235 Rome,  Weights  and  measures  of  -  26 Rosenberger  -         -         -     204,  205 Rosebery,  Lord    -  101 Rowland,  Henry  A.  -  207,  211,  226 Royal  foot  (French)  ...  37 Royal  Society  (British) 46,  47,  84,  99,  101 Ruggles,  Samuel  B.  -  -  -  126 Ruprecht  balance  -  -  -  237 Russia,  Weights  and  measures  of  94 Ruthe 82 Salces,  Base  at      -         -         - Sagene Sar Sauvage,  Ed. Saxon  weights  and  measures  30, Schoenus       .... 31 55 94 15 183 ,32 23 Schools,  Metric  system  in  125,  129,  165 Schiraz,  Anania  de Schumacher,  Professor Screws,  Cutting  of Screw-cutting  lathe Screw  threads      182,  183,  184,  185 Seah     - Second's  pendulum 15,  36,  37 48,  49, 44 25 248 182 186 186 21 46, Sellers,  Dr.  Coleman Sellers,  Wm. Seller's  standard  - Seller's  thread Senkereh  tablet    - Sensibility  of  balance   - Sexagesimal  system Sextarii Shaku  - Shaw-Caldecott,  W.  - She  -  -  -  - Sheet   and  plate  iron  and U.S.  standard  scale Shekel,  Babylonian Shekels  of  the  Hebrews Shilling         -         - 111,  245 -  161 -  183 -  183 -  185 13,  17 -  239 -  12 -  28 -  93 13,  17 -  15 steel, 131 16 21 32 PAGE Shoppen 83 Short  ton 168 Shuckburgh,  Sir  George 120,  230,  231,  245 Shuckburgh  scale  -         -         -     100 Shuckburgh's  comparator     -     230,  231 Siemens,  Alex.      -         -       186,  216,  217 Siemens,  Werner  -  205 Silver  coinage  by  metric  weight    -     128 Silver  voltameter  -      210,211,212 Sizes  of  screw  threads  - Skaal-Pund Smith,  Prof.  R.  H. Smyth,  Piazzi       - Societe     d'Eneouragement     pour l'lndustrie  Nationale Solid  angle  unit    - Solive Solon    -         -         -         - Sols Solvay  Process  Company South    America,    Metric    system used  in South  and  Central  America,  Metric system  employed  in      103,  107 Spain,  Adoption  of  metric  system in Span Spanish  Geographical  and  Statis- tical Institute Spartan    States    use    Babylonian talent     - Specific  gravity  of  standard 184 96 135 10 183 -  202 -  65 -  27 38,  39 -  168 Specific  gravity  tables 160 108 95 6 158 27 -  238 290,  291 Specifications  for  ampere  and  volt  211 Spencer  -  -  -  -  -  102 Square  measures  -  142 Stadion 25 Standard  avoirdupois  pound  -     248 Standard  bars  for  base  measure- ments    - Standard  kilogram  and  meter Standard  cell       212,  213,  214 Standard  gauges  - Standardization    - Standards  of  capacity  - Standard  sizes Standard  troy  pound  of  1758 Standard  troy  pound,  U.S.  Mint Standard  yard  (Elizabeth)    - Standard  yard  (Henry  VII.) Standard  yard,  British 244,  245,  246,  247 Standard  yards  of  United  States  114, 247 Standards  and  comparison  -  -  218 Standards  Commission,  British  35,  100 Standards  office  - Standards  of  mass Standards  of  the  Netherlands 215 141 254 216 176 154 240 175 34 119 36,  243 36,  243 246 236 93 INDEX 303 PAGE Standards  of  the  United  States  -  122 Standards  of  resistance  -  -  241 Standards   of  resistance,  current and  electrical  pressure  -  -  242 Standards,  Permanence  of  -  -  228 State  standards     -         -         -      121,  122 Steel  tape 140 Stere 54,  144 Sternberg,  Gen.  Geo.  M.       -         -     196 Strabo 23,  26 St.  Louis  Exposition  -  -  -  216 St.       Petersburg      Academy      of Sciences  71 Sweden,  Metric  system  adopted  -  95 Switzerland,  Metric  system  in  82,  97 Syrian  standard  21 Systeme    International,    S.I.    or S.J. 183 Table-spoonful  -  -  -  -  198 Talent,  Alexandrian     -         -         -       25 Talleyrand 46 Taps  and  dies  ....  183 Teachers'     Associations     endorse metric  system         -         -         -     102 Teaspoonful 198 Tel-el-Amarna  correspondence  -  19 Temperature  measurements  -         -     227 Thermidor 53 Thermometers,  thermometric  meas- urements       ...         .     227 Thermometer  scales,  Table  of       -     290 Tillet 47 Tittman,  0.  H.     -         -         -         -     120 Toise 38,  44,  97 Toise  de  macons  38 Toise  de  Perou      -         -  38,  54,  249 Toise  du  Grand  Chatelet  -  38,  249 Torque,  Unit  of  -  -  -  -  202 Tortuosity,  Unit  of  -  -  -  202 Totten,  C.  A.  S.  -  -  -  -  10 Tours,  Standards  of  -         -       39 Tower  Pound  -  -  -  32,  33,  34 Tralles-         -         -         -    62,  81,  82,  114 Transits 58 Treasury  Department,  U.S.,  Stan- dards of  -     123 Treaty,  Metric  75 Tresca  -         -         74,  252,  253,  254,  255 Trigonometrical  survey         -         -       55 Troughton 230 Troughton  scale  -  114,  121,  122,  247 Troy  pound  -  -  25,  33,  34,  119,  248 Troyes,  Standards  of    -         -  33,  39 Trowbridge,  John         -         -         -     211 Tumblerful 198 Tungri,  Belgic  foot  of  -  -  -  31 Turkey,  Measures  of  -  -  -  97 Tweedmouth         -         -         -         -     102    I PAGE Ulna     -         -         -         -         -         -  26 Ulna  or  Aulne       -         -         -         -  31 Unit  acceleration           -         -         -  200' United  States,  Weights  and  meas- ures of  -         -         -         -     103,  109 United  States  Army,  Med.  Dept.  195 United  States  Bureau  of  Standards  131 United  States  Navy,  Med.  Dept.  195 United  States  Pharmacopoeia       -  192 Unit  of  Intensity  of  Magnetism    -  200 Units 1 Unit  velocity         -         -         -         -  200 Units,  Absolute    -         -         -         -  200 Units,  Arbitrary  5 Units,  Fundamental  8 Units,  Natural      ...         -  5 Upton,  J.  K.         -         -         -         -  91 Ush 15 Usuelle         -         -         -         -  65,  66,  67 Vauclain,  S.  M.    - Vandermonde Van  Swinden Vendemiaire Vernet,  Base  near Vienna  coin  treaty Virga  or  Verge     - Virga    -         -         -         - Virgula  geometrica Volt      -         -         - Volume,  Measures  of    - Von  Humboldt,  Alex.  - -  188 -  54 -  61,  80,  82, -  53 -  55 -  85 -  31 -  43 -  43 206,  209,  212 -  143 -  200 Wales,  Philip  S.  -  -  -  -  195 Warren,  Gen.  Charles  10 Washburne,  E.  B.  -  -  -  130 Washington,  President  -  111,  113 Watchmakers  use  of  metric  threads    181 Water  clock 12 Watt  (unit)  -  -  202,  206,  208,  209 Watt,  James  98 Wave  length  of  light  -  229,260,261, 262,  263,  264,  265,  266 Weber,  Wilhelm  -  -  201,204,205 Weighing,  Earliest  -  -  -  4 Weights      and      Measures      Act (British,  1878)        -         -         -     101 Westminster  Abbey      -         -         -       30 Weston  cell 216 Wheat  bushels  -  -  -  -  156 Whitworth  standard  -  -  183,  186 Willans  &  Robinson,  Messrs.  -  187 William  the  Conqueror,  Decree  of  30 Williams,  R.  P.  -  -  -  -  125 Winchester  standards  -  -  -  30 Winchester  bushel  -  -  35,  122 Winchester  corn  gallon  -  -  35 Wine  gallon  -         -         -         -       35 304 INDEX PAGE Wine  glass   -         -         -         -         -     198 Windom,  Secretary  of  the  Treasury   159 Wire  and  sheet  metals Wolf,  C.        - Wolf,  M.      - Wolff,  F.  A. Wollaston,  Wm.  H. Wood  worth,  John  M. Work,  Unit  of      - 176 62,  230,  251 -  230 -     206,  215 -  99 -  195 202,  206 World's  Columbian  Exposition     -    208 Wrottesley,  Sir  John PAGE 99 Yard  or  gird  30,  31 Yard  standards    -         36,  1 14,  243,  247 Yates,  James  84 Young,  Dr.  Thomas  99 Yusdrumin  pound  of  Charlemagne       29 Zollpfund Zollverein 86,  89 -       86 GLASGOW:     PRINTED   AT   THE   UNIVERSITY   PRESS   BY   ROBERT   MAOLEHOSE   AND   CO.    LTD. PLEASE  DO  NOT  REMOVE CARDS  OR  SLIPS  FROM  THIS  POCKET UNIVERSITY  OF  TORONTO  LIBRARY QC  Hallock,  William &3  Outlines  of  the H28  evolution  of  weights  and measures  and  the  metric Physical  *         SyStem Applied  ScL