(Calvin of Farina, IL.2000-11-05) What are all of the metric prefixes? (Only 20 are official ones.)
(largest to smallest) and deprecated metric prefixes (obsolete or bogus)
SI
Value
Remarks
Obsolete
Bogus
1033
una, vendeka (V)
1030
dea, weka (W)
1027
nea, xenna (X)
yotta-
Y
1024
Adopted in 1991.
otta
zetta-
Z
1021
Adopted in 1991.
hepa
exa-
E
1018
Adopted in 1975.
peta-
P
1015
Adopted in 1975.
tera-
T
1012
Adopted in 1960.
megamega (MM)
giga-
G
109
Adopted in 1960.
kilomega (kM)
mega-
M
1000 000
CGS system since 1874. Legal in France since 1919.
100 000
hectokilo (hk)
10 000
myria (ma, my) 1795
kilo-
k
1000
Since 1793.
hecto-
h
100
Since 1793.
deca-
da
10
Since 1793. Alsodeka.
dk
1
Unprefixed.
deci-
d
1/10
Since 1793.
centi-
c
1/100
Since 1793.
milli-
m
1/1000
Since 1793.
1/10 000
decimilli, dimi (dm)
myrio (mo)
1/100 000
centimilli (cm)
micro-
,u
10-6
Within CGS system since 1874 (BAAS).
nano-
n
10-9
Adopted in 1960.
millimicro (m)
pico-
p
10-12
Adopted in 1960.
micromicro ()
femto-
f
10-15
Adopted in 1964.
atto-
a
10-18
Adopted in 1964.
zepto-
z
10-21
Adopted in 1991.
ento
yocto-
y
10-24
Adopted in 1991.
fito
10-27
syto, xenno (x)
10-30
tredo, weko (w)
10-33
revo, vendeko (v)
The use of metric prefixes dates back to the inception of the French metric system, in 1793.It was originally decided that thesubmultiples of all basic units would be prefixedwith aLatin root, corresponding to the decimal divisor(deci for 10,centi for 100,milli for 1000), whereas the decimalmultiples would be prefixed with aGreek root, corresponding to the decimalmultiplier (deca for 10,hecto for 100,kilo for 1000).In 1795, the Greek rootmyria for 10000 was added to the latter list(it's now officially obsolete, see below).
There was soon an obvious need to extend the system beyond its original limited range.The prefixmicro (from the Greekmikros, small) was introduced to denoteone millionth of the basic unit. The prefixmega(from the Greekmegas, great) appeared around 1870to denote a million times the basic unit.
It used to be acceptable to combine two prefixes (see above "obsolete" column).In 1960 however, it was decided to name only powers of 1000,not intermediary powers of 10, except for the original 1793 prefixes(the popularmyria prefix was thus deprecated in the process).Four additional prefixes were introduced at that time:pico (Spanishpico beak, small quantity),nano (Greeknanos, little old man, dwarf),giga (Greekgigas, giant),tera (Greekteras, monster).
It was then decided that the names of future prefixes should serve as reminders ofthe relevant power of 10.This started in 1964, with the introduction offemto andatto(Danish or Norwegian:femten for 15,atten for 18).The former prefix was particularly convenient, because it made the widespreadabbreviationfm (for "fermi") correspond correctly to thethe officially endorsedfemtometer.After that, however, it became clear (!?) that since only powers of 1000were to be named, the prefixes should reflect the ranks of the powers of 1000 involved.This is why, in 1975, the prefixexa (Greekhex, 6) was chosen for10=1000,whereaspeta (Greekpente, 5) was picked to represent10=1000.The four latest prefixes, which were made official in 1991, are also supposed to remindan international audience of the relevant powers of 1000:yocto(1000),zepto(1000),zetta(1000), andyotta(1000);the trend being that the ending "a" is used for large powers,while "o" is used for small ones.The 5 exceptions to this modern rule areall the 1793 prefixes, exceptdeca(for these 6 "low" prefixes,the long forgotten Greek/Latin distinction applies, as mentioned above).
The last column of the above table lists asbogus 10 extreme prefixes(revo, tredo, syto, fito, ento, hepa, otta, nea, dea, una).The larger of these follow theetymological pattern described above,and 4 of them "compete" with the latest official SI prefixes. These bogus prefixes have apparently not been used byanyone andare not endorsed byanybody, but they show upin tables which have been floating around in Cyberspace... This is probably the result of a minor hoax perpetrated sometimearound 1996. [2003-06-22 update:] Other dubious prefixes also appeared(vendeka, xenna, xenno, vendeko)which I discusselsewhere. Please,tell mewhatever you know about the issue...
Note (2002-05-01) :
In a 2002-01-14 post,Robi Buecheler plagiarized the abovetext...
On 2004-12-14,Robi Buechelerapologized: [edited summary]
I should have given you credit [and/or posted a] link. Sorry.
Bogus prefixes are no longer spreading out of control. However, at least one (careless) science-fiction writer has been fooled: In his 2003 novel entitled Schild's Ladder, Greg Egan usesthe two bogus prefixes xenno and vendeka as if theywere legitimate. (Thanks toTom Alcorn for pointing that out, 2007-12-05.)
(J. B. of New Lenox, IL.2001-02-09) How many kilobytes [kB or "K"] in 2 "megs" [megabytes, MB]?
For units of information that are multiples of the bit (andonly these),the multiplicative prefixes kilo- mega- giga- tera- etc. do not have their usualmeaning as powers of 1000. They're powers of 1024 (2 to the power of 10).
Thus, a kilobyte (kB) is 1024 bytes and a megabyte (MB) is 1024 times that(namely 1048576 bytes). Therefore, 2 "megs" is 2048 kilobytes.
A gigabyte (GB) is 1024 MB (1073741824 bytes) and a terabyte (TB)is 1024 GB (1099511627776 bytes). A petabyte (PB) would be1024 times as large, namely 1125899906842624 bytes (9007199254740992 bits or 86.2 nJ/K).
The situation may be quite confusing for several reasons. In particular, a few commercial designations havewronglyignored the above binary-based convention (powers of 1024)and used the standard decimal one (powers of 1000) insome cases. Even worse, the two have been mixed to create a special type ofdigital macaronicterms like the "megabyte of storage" which turns out to be worth 1024000 bytes,but is only used commercially forsome removable storage media. This came about (sadly) when the capacity ofthe so-called 3½" IBMmicrofloppiesdoubled from 720 kB to 1440 kBand the larger capacity was widely advertised as "1.44 MB"(instead of "1.40625 MB" or "1.4 MB").
In December 1998, theInternational Electrotechnical Commission (IEC) attempted to clear things up by introducing akilobinary system,in which we would no longer usekilobyte to designate 1024 bytes,butkibibyte (KiB).
The IEC proposal is slowlygaining some ground. However, it should only be a way to disambiguate the customary exception which has beenuniversally used for multiples of the bit (b) and the 8-bit byte (B),as far asaddressable computer memory is concerned. Ideally, acceptance of the IECproposal should only replace "kB" or "K" by "KiB" to mean 1024 bytes. It should never be construed as the permission to use "kB" concurrently to mean 1000 bytes. (Current usage does not allowunrestricted useof metric prefixes anyway: It's not permissible to use "kiloinch" for 25.4 m, is it?) Otherwise, ambiguity and confusion would be increased, not decreased. Arguably, manufacturers of digital storage who use the abbreviation "GB"for 1000 000 000 bytes would still be shortchanging their customers by 7.4%, even if the unambiguous IEC binary prefixes gain wider acceptance.
Warning: 1 kb/s = 1 Kib/s = 1.024 kbps
Be aware that the binary exceptiononlyapplies to multiples of the bit, notto derived units like the "bps" (bit per second),so that 56 kbps is exactly 56000 bps.This may not look so bad until you realize that a transfer speed of"1 kilobit per second" is actually equal to 1.024 kbps. The latter shouldonly be pronounced "kilo-bee-pee-ess"to avoid confusion with the former!
Likewise, the related baud rates have always used decimal prefixes: A kilobaud (kBd) is 1000 Bd. A megabaud (MBd) is 1000000 Bd.
That's the current mess we've built for ourselves. Careless standardization efforts could make the situation even worsebefore it gets better.
"Brontobyte" [ hoax alert ]
This unit is just ajoke (2004) nothing more! Unfortunately, the word caught thefancy ofmany unsuspecting webmastersand is now oftenlistedamong "serious" units of information (even more dubious is the geobyte of 1024 brontobytes).
In terms ofentropy,this huge amount of information is only 1.7668 J/K.
( L. K. of Owen, WI.2000-10-10) What has a density of 1 ?
Proper units (g/cc, lb/ft 3, etc.)are used to express anabsolute density.
Arelative density is the ratioof an absolute density to the absolute density of "water". For the utmost precision,it's important to specify what kind of "water" is meant.
However, the universally accepted conversion factorbetween "absolute" and "relative" density is 0.999972 g/cc ! This is one number which has acquired theunofficial status of a defined exact conversion factor, which has ultimately little to do with actual water or SMOW.
In other words, the short answer to this question is:"Water." A more precise (somewhat cynical) long answer is: "Anything with an absolute density of exactly 0.999972 g/cc."
(Michael of United Kingdom.2001-02-12) What's the difference between normal [1N] and molar [1M] solutions in acid chemistry?Particularly for sulfuric acid.
Each liter of a molar solution (1M or 1000mM) contains a mole of a given compound(a mole of HSOis about 98.08 grams of it).A normal acid (1N), on the other hand, contains the solute(s)thatcould produce a mole of H ions.
In the case of sulfuric acid, you'd have 2 Hions per molecule,so that a normal (1N) solution of sulfuric acid is actually a 1/2 molar solution(0.5M or 500mM).
per mole.[Here, the parenthesized 27 indicates an uncertainty whose standard deviation is27 times the weight of the last decimal position shown.]
Free protons (H+ ions) in water are mostly a convenient fiction, since such ions would quickly combine with nearby molecules ofwater to form hydronium ions. The dissociation of water molecules into ionsis thus best described by the following reversible chemical reaction:
2 H2O H3O+ + OH
(J. M. of College Station, TX.2001-02-11) How much energy is required to raise the temperatureof one kilogram of water [by] one degree Celsius?
If the calorie was still defined as the energy required to raisea gram of water by 1°C,the answer would be "1000 calories" (or 1 kcal).
However, that definition of the calorie was dependent on the starting temperatureand wasn't good enough for metrological purposes.
Several more precise definitions have been given (see table below) including the fifteen degree calorie which is still defined as the energy that raises a gram of water from14.5°C to 15.5°C. This type of calorie must be measured to be equal to 4.1855 J at a fairly modest level of precision (an uncertainty of about 0.0003 J). It's only good for casual use...
Since 1935, the current (thermochemical)calorie has been defined asexactly equivalent to 4.184 J. No other conversion factor should be used in Science. The recommendation is to use joules primarily.
The energy which raises a kg of water by 1°C (under 1 atm = 101325 Pa) is a function of temperature which features a minimum of about 4178 J around 34.5°C. It's about the same at the ice point (4218 J at 0°C) and the steam point (4216 J at 100°C). All valuesbetween 4178 J and 4216 J arecorrect for two temperatures (one below 34.5°C, one above that).
Various "calories" competing with the thermochemical calorie of 4.184 J
The dubious "IST calorie" (or "steam tables calorie") was created merely for compatibilitywith the official definition of theBtu, discussed next.
British Thermal Unit (Btu) Therm and Quad :
The Btu itself is never used in Scienceand it seems to be utterly unknown outside of the US and UK. So is the obscure unit dubbed therm, defined as 100000 Btu. (Warning: The name "therm" was used to denotethe 4° calorie between 1888 and 1899, as mentioned in the above table.)
Other definitions of the Btu are still floating around/ and the ensuing confusion extend to the therm of 100000 Btu and the quad of 1015 Btu.
Definitions of the Btu competing with the standard one (1055.05585262 J)
Value (J)
Qualifier
Remarks
1055.206
778.28 foot-pounds
1055.056
EC
ISO
1055.05585262
IT
IST definition (1956)
1055.05585257348
UK
1054.804
59°F
US (1 cal = 4.1858 J)
1054.68
Canada
1054.350264488888...
Thermochemical (unused)
cdw239(2001-08-23) What is the equation for converting horsepowers to watts?
Thehorsepower and thewatt are both units of power;there's just aconversion factor between them. The way power is delivered (voltage, etc.) is completely irrelevant.
Ahorsepower (hp) is about 745.7watts (W),but many metric countries use another closely related unit [best abbreviated "ch"] of nearly 735.5 W.
The horsepower unit (hp) was originally defined byJames Watt (1736-1819)as exactly equal to 550 ft-lbf per second (lbf = "pound-force") .Since January 1, 1959,the foot and the pound have been defined in metric terms(1 ft = 0.3048 m and1 lb = 0.45359237 kg, bothexactly).
Furthermore, since the third CGPM of 1901, thestandard(orconventional)acceleration of gravity has been defined as exactly equal to 9.80665 m/s2. That's the proper "conversion factor" to use to transform (not "convert", please) a unit of masslike the pound (lb) into theunit of force best called pound-force (lbf). The resulting exact conversion factor has 12 digits:
1 lbf = (0.45359237 kg) (9.80665 N/kg) = 4.4482216152605 N
Multiply this by the length corresponding to 550 ft(exactly 167.64 m) and you have the equivalence of ahorsepower in watts (as a watt "W" is simply ameter-newton per second). This gives an exact modern conversion factorwhich requires no fewer than 17 digits:
1 hp = 745.69987158227022 W
Needless to say thateverybodyusually rounds this up in the most obvious way (which is appropriate except in computerized conversion tables):
1 hp 745.7 W
In countries where the metric system has been around for a while,thehorsepower (ch) is a 1.37%smaller unit,calledPferdestärke (PS) in German,paardekracht (pk) in Dutch,hästkraft (hk) in Swedish,caballo de vapor (CV) in Spanish,cavalo-vapor in Portuguese andcavalli vapore in Italian. The French call itcheval-vapeur (ch)orcheval (plural ischevaux).
This "metric" horsepower (ch) is defined as75 kgf-m/s, whichengineers used to abbreviate as 75 kgm/s, using the obsolete symbolkgmfor a "technical" unit of energy calledkilogrammetre orkilogram-meter and worth 9.80665 J (that same unit of energy was also called kilopond-meter and abbreviated kpm ). A metric horsepower (ch) is thus exactly :
1 ch = (75 kg) (9.80665 N/kg) (1 m/s) = 735.49875 W
Adding to the confusion, a so-calledelectric horsepoweris defined as exactly equal to 746 W (it's clearly a rounded-up version of the "hp").
Finally, there's an unrelated unit of power called theboiler horsepower,defined in 1884 as the power it takes to boil 34.5 lb of water per hour(under 1 atm, when water is already at 100°C = 212°F). So defined, theboiler horsepower is approximately9809.91 W, or about 13.155 hp. However, this is so close to1000 kgf-m/s(which is 9806.65 W) that I suspectsuch a "metric" definition of theboiler horsepower may have been given... (The quotes around "metric" are a reminder that "technical" units of force,named after units of mass, arenot official SI units.) I'd be grateful if anyone couldtell meif this is so...
(2001-05-04) Why is 9.80665 m/s2 [1 G] the standard acceleration of gravity?
To an actual measurement of 9.80991 m/s2 in Paris,a theoretical correction factor of 1.0003322 was applied which givesa sea-level equivalent at 45° of latitude. The result (9.80665223...) was rounded to five decimalsto obtain the value officially enacted by the third CGPM, in 1901.
(9.82025 m/s2 ) / (1+z/R) 2
(2018-02-27) One is expressed inhertz (Hz) or rad/s, the other in becquerels (Bq).
Any periodic quantity is only a function of its phase. Phases add up like circular angles do; returning to the same position after a whole number of turns. They are naturally measured in angular units, the most obvious of whichis variously called turn, cycle or revolution.
For a metronome or a pendulum (only) the beat has been historically defined as half of the period in time (the motion is composed of two symmetrical halves). The beat of a simple pendulum of length L = 1 m is nearly equal to one second. More precisely, its period T in a standard gravitational field g = 9.80665 N/kg is equal to:
T = 2
L
= 2.006409292589... s
g
In all other cases, a beat is equal to a complete time period. Thus, beat and period are almost always synonymous. (This general definition does applies to the sound made bya symmetrical pendulum or a symmetrical metronome, albeit not to their visual appearances.)
Musicians express a tempo in beats per minute (bpm) in reference tothe sound of a metronome. The same unit outside of music is called a revolution per minute (rpm). Notably in the automotive industry.
Physicist most often use the ratio of two lengths to quantify an angle (the ratio of a subtended circular arc to the radius of the circle involved). Thus, an angle looks superfically like a dimensionless number because itseems to be just the ratio of two quantity having the same dimensionality. However, this ain't quite so. What makes all the difference is that one of the twoaforementioned lines is curved.
There are two ways to curve (to the left or to the right). Angles can be negative or positive, ultimately depending ona conventional orientation of the Euclidean plane (theuniversal convention todayis that counterclockwise is positive and clockwise is negative).
An angle (planar angle or solid angle) measures a quantity with axial symmetry, whereas so-called pure numbers only measure quantities with radial symmetry (which is the technical way to state that theirs signs do not depend on the orientation of the frame of reference).
Frequency or Pulsatance :
The rate at which phase changes with time is called frequency, especiallywhen the angular unit of phase is the cycle (turn or revolution, same thing). Otherwise the more precise terms of pulsatance or angular frequency are preferrable.
All those termes denote strictly the same physical thing. This is clear only if the hertz (Hz, the official SI unit of frequency) is properly defined as one cycle per second and not as "the reciprocal of the second" (the absence of any reference to angularphase in the latter definition would make it better suited for the becquerel, as discussed next).
Activity of a random phenomenon. Radioactivity.
A stochastic process which occurs at irregular time intervals (as opposed to a regular period) is characterized by a quantity called activity, which is the expected (average) number of events occuring per unit of time.
Such phenomena have no phase, which is to say that the time it will take until the next event doesn't depend on the time elapsed since the last one. Radioactive decay is the prime example of this.
As a result the unit of activity (the SI unit is the becquerel, symbol Bq) is just the reciprocal of the unit of time (1 Bq is one event per second, on average). It's fundamentally different from the aforementioned unitsof frequency which ultimately measure a rateof change of phase. In spite of a superficial similarity, one random event per second and one cycle per second are two very different things!
Time
(Bob J.of Clarksville, TN.2000-09-28) What is the term for 1/1000 of an attosecond? (This would be 10-21 s.)
That's one zeptosecond (zs). One thousandth of that is a yoctosecond : 1 ys = 10-24 s Both terms were officially adopted by the CGPM in 1991.
Fred Berman,Ph.D., P.E. (2002-11-29; e-mail) Is a jiffy really the time for light to travel one centimeter in a vacuum?
A formal definition of the jiffy as a light-centimeter (roughly equal to 33.3564 picoseconds) was first proposed, in physical chemistry, byGilbert Newton Lewis (1875-1946),the American chemist who isolated heavy water and defined a Lewis acid as an acceptor of electron pairs (1916).
Informally, a jiffy can be any short period of time, though. The word was commonly used before1785. Jiffy meant "lightning" in thieves' cant (possibly as early as 1530) but its early etymology is otherwise unknown. The jiffy has been given several definitions in various contexts:
In the quaint context of computer engineering, a jiffy may denote the period of the system's main clock (e.g., 10 ns for a 100 MHz clock) but it can also be the interval between two regular timer interrupts, which is usually something between 1 ms and 20 ms (most commonly 4 ms).
In electrical engineering, a jiffy used to be the period of the electrical power grid, namely: 20 ms in Europe (50 Hz) or about 16.6667 ms in the US (60 Hz). Nowadays, this flavor of jiffy has all but disappeared; a modern jiffy is usually equal to 10 ms (the resolution of an ordinarystopwatch).
On 2008-12-30, Dr.Robin Whitty wrote: [edited summary]
I love it! Where but Numericana could you find something so minute given suchJohnsonian treatment?
A much smaller obsolete unit [about 9.3996392(13) 10-24 s] isrelated to the above jiffy of physical chemists: The tempon is defined as the time required for light to travela distance of oneclassical electron radius.
The smallest recognized unit of time is called chronon, orPlanck time:
(2014-11-28) That's one informal nuclear time unit coined for the Manhattan Project.
The saying two shakes of a lamb's tail denotes any short time interval...
The typical time required for each step in anuclearchain reaction is roughly one shake. A nuclear explosion takes less than 100 shakes (1 us).
(B. D. of Australia.2000-05-01) How long is one second? (J. F. of Memphis, TN.2000-10-20) Who determined the length of a second?
The "SI second" (formerly called "atomic second") is now defined as equal to9192631770 periods of the radiationcorresponding to the transition between the two hyperfine levels of Cesium-133.(Until recently, surprisingly, nobody seemed to care aboutgeneral relativistic effects,which are becoming relevant: Are we talking about cesium atoms in free fall or not?)
In 1967, this replaced officially the "Ephemeris Second", which was based on theorbital motion of the Earth around the Sun. An earlier definition was based on themean solar day instead,and was thus tied to the Earth'srotation around its own polar axis,although fluctuations in this rotation make it a poor basis for the definitionof a precise unit of time (as was first shown by Simon Newcomb).
The Full Story:
Originally, thesecond was defined as 1/86400 of themean solar day. In other words, there are 24 hours of 3600 seconds in a day. It is necessary to specify "mean" solar day because the length of the day varies throughoutthe year,as the angular speed of the Earth varies in its elliptical motion around the Sun. (It is this angular speed which determines how soon the Sun will be seen again at the samelongitude in the sky, afterroughly one revolution of the Earth on its axis.)
Thismean solar second came under international scrutiny by the CGPM in 1954,and the BIPM proposed (in 1956) a new official definition of the second: The definition of the so-calledephemeris second is based entirely on theorbital period of the Earth, which is steadier than its spin. It is specified, as explained below, by equatingto 31 556 925.9747ephemeris seconds theinstantaneous valueatepoch 1900.0 of thetropical year. This definition was ratified by the CGPM in 1960, but it originated in the 19th century:
The American astronomer Simon Newcomb (1835-1909) discovered that there are significantirregularities in the rotation of the Earth on its own axis(this was apparent to him when he analyzed the ephemerides of the Moon published by Hansenin 1857). Newcomb came up with a famous equation giving L,the so-called "meangeometrical longitude of the Sun",as a function of the time T expressed in the number of centuries[of exactly 31 557 600 000 seconds each]elapsed since "January 0.5 1900" [this is either 24:00 GMT on 1899-12-31 or 0:00 GMT on 1900-01-01]. That "longitude" is measured against thevernal point [which means it integratesthe wobbling of the Earth's spin which influences the length of thetropical year and causes theprecession of equinoxes]. The qualifier "geometrical" is a reminder that the equation gives theimmediateposition of the Sun, not itsapparent location,as perceived from solar light emitted about 499 seconds before. Finally, the qualifier "mean" is a reminder of the averaging made necessaryby the variable angular speed of the Earth, in its elliptical orbit around the Sun.
L = 279° 41' 48.04" + 129602768.13" T + 1.089" T 2
Atropical year is the time it takes for L to increase by a full turn(360° or 1296000"),we may thus state that theinstantaneous tropical yearat time T is a full turn divided by dL/dT. To obtain the duration Y of this year expressed in seconds(rather than Juliancenturies),we simply multiply by3155760000. This boils down to:
Y(T)
= 227214720000000000 / ( 7200153785 + 121 T )
= 31556925.9747415242... - (0.5303203455...) T + O( T 2)
It turns out that Newcomb's equation can be usedbackwardsto define the unit of time with fargreater precision than anything based on the rotation of the Earth. By specifying the value of Y(0) in some unit of time,that unit is very precisely definedin terms of the orbital motion of the Earth around the Sun,rather than on the less precise rotation of the Earth about its own axis. This is precisely how the so-calledephemeris second was defined,by making exactde jure Newcomb's value of Y(0) rounded [down]at the fourth position after the decimal point:
Y(0) 31556925.9747ephemeris seconds
This definition makes theephemeris second very slightly longer than whateverwe may call the "second" used by Newcomb himself to establish his equation.
(roughly 50microseconds per year). This is lower than the combined precision of the observations used by Newcomb,which were made between 1750 and 1892. Thesolar second and theephemeris second were identical around 1820 or 1826.Since then, themean solar day has been slightlylonger than86 400 ephemeris seconds, as the rotation of the Earth is slowingdown under the braking effect of the tides. It may be amusing to record that, according to Newcomb's original equation,theinstantaneous tropical year was exactly 31556925.9747 "seconds"about 247097 seconds after T=0: January 3, 1900, at 20:38:17 GMT.
The ephemeris second was theofficial definition of the second from 1960 to 1967. During that period, the credit for determining the "length of a second"would clearly have gone toSimon Newcomb...
Since 1967, the official definition of the second has been in "absolute"atomic terms rather than astronomical ones. It was decided to define the second in termsof a number of standard transitions of the Cesium atom.
In 1958, it had been determined that there were9192631770 such transitions (give or take 20) in an ephemeris second. This was the result of a three-year collaboration between William Markowitz atUSNO(U.S. Naval Observatory, in Washington, DC)andLouis Essen (1908-1997)atNPL(National Physical Laboratory, in Teddington, England). USNO contributed accurate astronomical time measurements,using a dual-rate Moon camera (invented by Markowitz in 1951)which was compensating simultaneously for sidereal and lunar motions. Occultations of stars by the Moon provided the best estimate of Ephemeris Time. On the other hand, NPL provided theWorld'sfirst caesium clock standard, which had been perfected by Louis Essen and Jack Parry since 1953. (The two clocks were compared using synchronizing radio transmissions from theWWV stationoperated by the National Bureau of Standards, now calledNIST.)
This value of 9192631770 Cesium transitions per second was ultimately accepted as thede jure value. Therefore, the guys who really determined"the length of a second" are the authors of that particular measurement. It was a team effort, by Markowitz, Hall, Essen and Parry[See "Frequency of Cesium in Terms of Ephemeris Time"by W. Markowitz, R. Glenn Hall, L. Essen, and J.V.L. Parry inPhysical Review Letters, Volume 1, pp. 105-106 (1958)]. That's our final answer, as long as the "Cesium standard" remains the basisfor the official definition of the second.
The international body which is responsible for making such definitionsofficialis the CGPM. However, the CGPM should not be credited for the work on which its decisions are based. Instead, we ought to remember the accomplishments of great scholars likeSimon Newcomb, Louis Essen, or William Markowitz...
(C. V. of Indianapolis, IN.2000-10-23) How many seconds in a day?
The short answer is 86400 (24 hours of 3600 seconds).
At a higher level of accuracy,it may be useful to point out that there are 3 kinds ofstandard days,but we may still say that there areexactly 86400 "solar" secondsin a "mean solar day" and 86400 "ephemeris" seconds in an ephemeris day. The "day" used in modern science is also defined as exactly equal to86400 SI seconds (officially defined in terms of the cesium atomic standard).
When the "day" of one system is expressed in terms of the "second" of another,the numbers are slightly off. For example, the mean solar day "at epoch 2000.0" isabout 86400.002 SI seconds.
Now, the so-called "sidereal day" is another matter entirely because it is significantlydifferent from the above 3 "standard" days and hasnever been used as a standard unitof time. A sidereal day is about 86164.09 SI seconds.
It is interesting to notice a weird point of etymology about "sidereal"(which is often misspelled "sideral", as would be correct in French and/or a few otherlanguages)."Sidereal"should mean that a "sidereal day" refers to the rotation of the Earthwith respect to the fixed stars (as is the case with other "sidereal" motions, by the way). This is the definition most dictionaries will give you. However, that's not quite so. Historically, astronomers have most often usedthe term "sidereal day" to refer to the rotation with respect to the slowly moving"vernal point" (which rotates a full turn in about 25772 years, the period of "precessionof the equinoxes").
When motion with respect to the fixed stars is meant, the unambiguous term "Galilean day"should be used. In other words, the Earth rotates on its axis once per Galilean day(i.e., once in each period of 86164.1 s). The Galilean day is longer than the sidereal day by 0.0084 s. The Galilean day increasesby about 0.00164 s per century because of the braking effects of tides. Both the sidereal day and the mean solar day also increase at almost exactly the same rate(so the differences between these three remain roughly constant). The drift rates are almost exactly the same because all the other relevant astronomicalmotions are far more stable than the spin of the Earth on its axis. The SI "atomic" day, on the other hand, is absolutely stablein principle(assuming only that the laws of physics themselves do not change over time).
(2000-11-03) (P. H. of Concord, CA.2000-11-03and I. I. of Canada.2001-02-05) How many seconds in a year? (John of Springville, AL.2000-10-08) What is a "scientific year" ? jwill123 (2002-05-05)A light-year is the distance that light travels in one year. How many seconds in [such] a "year"?
The only recognized "year" unit in scientific practice is a year ofexactly 365.25 days, based on a day of exactly 86400 seconds(these are standard SI seconds, formerly known as "atomic seconds"). Therefore:
The number of seconds in a year is exactly 31557600.
This is the number you should use, for instance, to compute precisely the number of metersin a light-year (which isexactly 9460730472580800).
1 light-year = (299792458 m/s)× (31557600 s) = 9460730472580800 m = (9460730472580800 /149597870700) au = 63241.07708426628... au
Some scientists like to memorize the duration of a year in seconds as approximately equalto " times ten to the seventh".
Thisscientific year is longer than the average calendar year,theGregorian year of 365.2425mean solar days,and it's extremely close to theJulian year of 365.25mean solar days. As themean solar day slowly drifts in duration, so do both the Gregorian yearand the Julian year. The relatedtropical year is more stable than either of thesecalendar years,because it is based on the orbital motion of the Earth, which is steadier than its spin. The wobbling period of the Earth's axis(responsible for the precession of equinoxes) affects thistropical year but notthesidereal year which is measured with respect to the "fixed stars"(more precisely, the background of galactical nebulae). However, even thissidereal year is not absolutely stable,since the orbit of the Earth does decay...
By contrast, the scientific year of 31557600 seconds is rock stable[more stable than any rock will ever be, actually];it's atrue unit of time. It will never change, unless the laws of physics themselves change. Finally, it is properly based on a local [atomic] definition, as any unit of timeshould be: According to Special and GeneralRelativity,there is not such thing as an absolute time which would "flow" the same for allobservers, irrespective of their motions and/or surrounding gravitational fields.
Length
nara(2000-04-11) How long is a meter? I know it is not the same system, but how many inches are in a meter?
There are (very) sligthly more than 39.37 inches in a meter (a more precise numberis 39.37007874).
Since January 1, 1959,the International inch has beendefined to be exactly equal to 25.4 mm(0.0254 meter).Now, the inch and the meter are thusalmost part of the same system (well, kinda)...
Since 1866, theUS Coast and Geodetic Survey has been usinganother metric definition of the inch,equating a meter to 39.37 inches. This "US Survey" inch (of about 25.4000508 mm)was confirmed for general use by the Mendenhall ordinance of April 5, 1893,but it's been restricted to US surveying since 1959.
There's a noteworthy numerical coincidence concerning the ratio of these two different"types" of inches, since (254/10000)/(100/3937) turns out to be exactly 999998/1000000,so that it can be stated that the modern International inch isexactly 2 ppm lessthan the 1893 "US Survey" inch, whose value in mm has the following expansion: 25.400050800101600203200406400812801625603...
The 1824Imperial inch was based on the actualBritish standard yard,which keptshrinking (the 1760 brass artifact was lost in an 1834 fire;new ones were made ofBaily's Metal, after 1841). Thisobsolete inch was "calibrated"to be:
25.399978 mm in 1895.
25.399956 mm in 1922.
25.399950 mm in 1932.
25.399931 mm in 1947.
The 1895 and 1922 calibrations are still quotedtoday in an historical context, whereas the others are all but forgotten. The preliminary1819 equivalence of 39.3694" to the meterdescribes a larger inch (of about 25.400438 mm)whichmay best match the yard made by Bird in 1760(after an oldTower standard).
(2007-05-22) The typographer's point is exactly 0.013837" = 0.3514598 mm.
Typographers use several specific traditional units of length.
The ATA point and its spinoffs
The typographer's point was defined in term of the inch in 1886. Thus, when the inch evolved and was redefined in terms of the meter in 1959,so was thetypographer's point.
The point is exactly 0.013837 inches. That's precisely 0.01 ppm below what is implied by the conversion factor of 72.27 points to the inch,which has been advocated by Donald Knuth in connectionwith his "TeX"computerized typesetting system. The difference between thegenuine typographical point and the "TeX point"is so minute that the two are interchangeable, even in themost exacting typographical work. (There are 72.2700007227... points to the inch.)
Not so with the coarse equivalence of 72 points to the inch,which was part of the original specification of PostScript, the pagedescription language championed by the Adobe Corporation, which wasinstrumental in launching the "DeskTop Publishing" (DTP) industry in the mid1980's. This rough equivalence gave birth to a new set of "DTP" units forcomputerized typography: There are, for example, exactly 6 DTP picas to theinch, and 72 DTP points to the inch.
Other points. 155520 Didot points to the arpent...
Although the above now dominates computerized publishing worldwide,some typographic systems are based on other unrelated "point" units.
Most notably, the Didot point was introduced by François Ambroise Didot (1730-1804) with the system of font measurements that we still use today (regardless of a slight difference in scale). Didot's father (also named François, 1689-1757) was the founder of the printingand publishing enterprise which survives to this day (in Paris, France)under the name of Firmin-Didot & Cie.
The originalDidot point was defined as the 72nd part of theFrench Royal inch (pouce). Thefoot corresponding to 12pouceswas the pied de roi.
Two (very close) metric equivalences can be given for thepied de roi. The earlier one goes back to the very inception of the metric system itself,since the French scientists who conceived the new system were actuallyusing the toise of 6 pieds de roi in their preliminary work. The metrological equivalence they gave now stands as a metric definitionof the old unit: 0.513074 toise to the meter. (That would make atoise approximately equal to 1.9490366 m.)
However, the Canadians can be considered to be the rightful heirs to theancient French system, as they still use the arpent of 30 toises. The modern Canadian definition is thusjust as relevant as the current definition of theInternationalinch (of exactly 25.4 mm) regardless of previous definitions... The Canadian arpent is nowdefined to be 191.835 ft or 50.471308 m. This makes the toise exactly equal to 1.9490436 m. The pied de roi is 0.3248406 m and the pouce is exactly 27.07005 mm, Theproleptic value of theDidot point is 72 times smaller than that, namely:
1 Didot point = 0.3759729166666... mm 1 Cicéro (12 Didot points) = 4.511675 mm (exactly )
The French Imprimerie nationale (IN) now uses a metric point of exactly 0.4 mm. The obsolete Truchet point was exactly half of a Didot point.
Other traditional units of lengthpertaining to newsprint include the line (theagate line of 1/14 in, called a "ruby" in the UK) and the "SAU column width" of 36/16 in (i.e., 2-1/16inches of print and a 1/8" gutter space between columns).
cheftell(Wilmington.2001-02-11) How far in miles is 20000 leagues? One league equals how many miles?
A (land) league used to be defined as an hour's walk. It's now defined as exactly 3 statute miles (4828.032 m).
However, anautical league is 3nautical miles(5556 m, or about 3.452 miles),and that's the league Jules Vernes refers to in the title of his book"20000 Leagues under the Sea".So, if you are a fan of Jules Vernes and Captain Nemo,20000 nautical leagues is 60000nautical miles.That's about 69047statute miles, 111120 km or almost3 times around the Globe [at the Equator].
(D.W. of Orangevale, CA.2000-10-07) What is the circumference of the Earth at the equator? (D.N. of Grass Valley, CA.2000-10-09) What is the radius of the Earth?
The irregularities of the Earth are charted with respect to a perfect ellipsoid whosedimensions were preciselydefined (not measured) once and for all in 1980, by theIUGG (International Union of Geodesy and Geophysics).The equatorial radius of that ellipsoid isexactly 6378137 meters,which makes the circumference at the equator equal to40075016.685578486...mdown to the nearest (ludicrous) nanometer. That's about 24901.46 statute miles(these are "land miles" of 1609.344 m; the circumference may also be expressed as21638.7779 "nautical miles", the modernnautical mile being exactly 1852 m).
Theconventional "radius of the Earth" is a unitdefined to be 6371000 m.This isalmost the radius of a sphere having thesame volume as the reference ellipsoid (6371000.79 m)or the radius of a sphere with the same area as the ellipsoid(6371007.181 m).
(Michael of Nashville, TN.2000-10-03) [2012 update] Are there any units longer than a lightyear, or shorter than an ångström?
A list of extreme units of lengththat haveactually been used, largest first:
Big ones :
gigaparsec (Gpc). Over 3 thousand million light-years.
hubble. A thousand million light-years, by definition,
megaparsec (Mpc).
kiloparsec (kpc).
parsec (pc) = 3.261563378 light-years.
light-year (exactly 9460730472580800 m).
Theparsec(pc) is actually a very specific (irrational) multiple of theastronomical unit (au) since it's defined as the radius of a circlefor which an arc of one second has alength of one astronomical unit (au). In other words, a parsec is exactly648000/au (about 206265 au).
The radius of the observable Universe itself is about 4 Gpc,so there is no need for units larger than the gigaparsec.
Small ones :
ångström (Å). 10-10 m = 0.1 nm.
picometer (pm). 1/100 of an ångström. Formerly known as a micromicron, bicron, or stigma.
femtometer or fermi (fm). 1/100000 ångström.
microångström. 1/1000000 ångström.
Only the picometer (pm) and femtometer (fm) are official SI units. The ångström and its submultiples aren't.
Well below all of these is a truly minuscule "unit", the Planck length, which is about1.616 10-35 m and describes a scale at which space itself is thought to lack any kind of smoothness. At the Planck scale, the very concept of length measurement becomes meaningless.
Surface Area
robster(2001-04-15) How many square inches in one acre?
An acre [Greekagros, field] is precisely 1/10 of a square furlong. A furlong being 660 feet,a square furlong is 6602 = 435600 square feetand an acre is 43560 square feet. There are 122 = 144 square inches in a square foot,so an acre is 43560 times 144 square inches, or exactly 6272640 square inches.
1 acre = 0.1 fur2 = 43560 ft2 = 4046.8564224 m2
A (Gunter) chain is 66 ft (1/10 of a furlong). The chain is itself divided into 100 Gunter links (each of those is 0.001 fur, 7.92 in or 20.1168 cm). An acre is thus the area of a rectangle whose length is one furlongand whose width is one chain.
Historically, the relation is reversed: Thefurlong ["furrow-long"] was a basic unit so strongly favored by the Tudorsthat they redefined the mile so that it would be exactly 8 furlongs. Thisstatute mile of 8 furlongs or 5280 ft thus displaced the previousLondon mile of 5000 ft, which had a definition similar to that of theRoman mile of 1000 strides (double-paces)of 5 Roman feet each. The acre was thus defined to be 1/10 of a square furlong well before Edmund Gunterintroduced thechain (in 1620) as the "width" of an acre. Gunter's invention of thechain[divided into 100 links ofexactly 7.92 inches]actually made itmuch easier to work out land areas expressed in acres.
A lot of the bizarre conversion factors which are now floating aroundwere once perfectly sensible. The way to (numerical) hell is paved with good intentions...
Volume, Capacity
( Lacy of Fort Walton Beach, FL.2000-12-03) Why is the abbreviation for liter "L" instead of [a lowercase] "l" ?
This is theonly metric symbol which you maychoose to capitalize or not.
For all other metric units, the symbol is capitalized if, and only if, it has been namedin honor of a person,whereas the unit name isnever capitalized:V for volt, Hz for hertz, A for ampere,E for erlang..., butm for meter and g for gram because these two werenot namedafter anybody!
Up until a few years ago, the recommendation was indeed a lowercase "l"for liter, according to the common rule, but cursive script became commonlyused to make a clear distinction between a lowercase""and the numeral "1". When typing, a cursive""may not be an option and a capital "L" became acceptable.
(Joan of Norwell, MA.2000-11-05) What are the formulas for changing ounces or teaspoons into drops? (T.S. of Clarksboro, NJ.2001-01-25) How many drops are in a milliliter?
In either the US (Winchester) or the UK (Imperial) system of liquid measures, adropis another name for aminim and there are 480 of these in afluid ounce. Thus, if you have a volume inounces, multiply by 480 to have thenumber ofdrops in it.
However, since the US and UK ounces are slightly different, a drop isabout 0.0616 cc in the US and only 0.0592 cc in the UK.
The metric drop is exactly 0.05 cc. Nowadays, this is the conventional value worldwide: 20metric dropsto a cubic centimeter (ormilliliter).
Similar distinctions hold forteaspoons : Ateaspoon is 1/6 of a fl oz (about 4.929 cc in the US and 4.7355 cc in the UK). So, there are exactly 80drops in ateaspoon(in either the Imperial or the Winchester system).
Themetric teaspoon is slightly larger (5 cc)and themetric drop slightly smaller (0.05 cc) than the nonmetric counterparts,so there are exactly 100metric drops in ametric teaspoon.
In a cubic centimeter or milliliter (cc, ml, or mL), there are exactly 20 metric dropsand about 16 Winchester drops or 17 Imperial drops (more precise values being16.23 and 16.89 respectively).
Note that all of the above are conventional values,which are only loosely related to the results you would actually get by using athin dropper. So, don't be disappointed at the lack of "accuracy" if you do.
dbsafe(2001-06-21) How do I convert milliliters into ounces?
Roughly speaking, divide a number of milliliter by about 30 to express thatvolume in fluid ounces (fl oz). For example,300 mL is about 10 fl oz.
Actually, thefluid ounce has differentvalues in the Winchester (US) system and in the Imperial (UK) system. The US ounce is about 4% larger than the British ounce (the ratio is 1.04084273078623608419542947895884...); about 29.6 mL (29.6 cc) to the US fl oz and 28.4 mL to the UK fl oz.
More precisely:
There are exactly29.5735295625 milliliters in a US ounce. In the US, the Winchester system is used and the basic unit of capacity for fluidsis the US gallon, defined to beexactly 231 cubic inches.Since 1959, the inch has been defined to be exactly 2.54 cm, and the number ofmilliters in a cubic inch is thus 2.543=16.387064.Now, there are 128 US ounces in a US gallon,so the number of milliliters in a US ounce isexactly(i.e., legally) 231/128 multiplied by 16.387064, which is the number advertised above.
There are exactly28.4130625 milliliters in a UK ounce (Imperial fl oz). The BritishImperial gallon wasfirst introduced in 1824as the volume occupied by 10 pounds of water at 62°F. Unlike the US gallon, it is divided into 160 fluid ounces. (Since there are also 160 ounces of mass in 10avoirdupois pounds,this equated afluid ounce with the volume ofone avoirdupois ounce of water at 62°F.) TheImperial gallon was later redefined in metric terms as 4.54609 L,making the number of milliliters in a fluid ounceexactly equal to4546.09/160 = 28.4130625, as advertised.
Since 1963, the Imperial gallon has ben defined purely in metric terms. The 1963 definition merely translate a metrological renovation of the 1824 naivedefinition (volume of 10 pounds of water at 62°F ) according to which an Imperial gallon ought to be equal to the space occupied by 10 lb of distilled water of density 0.998859 g/mL,weighed in air of density 0.001217 g/mL against weights of density 8.136 g/mL.
4.545964591 L from 1963 to 1976.
4.546092 L from 1976 to 1985.
4.54609 L since 1985.
4.53608 L future reform (?) to enforce: 1 fl oz = 28.413 mL
( A. B. of Saint George, UT.2000-05-02) How many milliliters [ml or mL] in a gallon?
The US gallon is the Winchester gallon,now defined asexactly equal to 231 cubic inches (this odd value comes from rounding up thevolume of a cylindrical measure 7 inches in diameter and 6 inches in height,which dates back to the days of theMagna Carta). Since 1959, the inch isexactly 25.4 mm.Therefore, there are exactly 3785.411784 ml in a US gallon.
If the British Gallon is meant, the answer is 4546.09 ml, also an exact valueaccording to the 1985 British "Weights and Measures Act" (in 1963,the British Parliament had decided to redefine all British units in metric terms). There areabout 277.42 cubic inches in this modern Imperial gallon.
Originally (in1819),theImperial gallon was meant to be the volume occupied by10 pounds of water at 62°F. It was thus intermediate in value between the two British units it replaced in 1824,namely the corn gallon of 272¼ cubic inches (4461.378174 ml)and the ale gallon of 282 cubic inches (4621.152048 ml). The old British wine gallon of 231 cu in survives as theUS gallon (see above).
Finally, a USdry gallon is defined as 1/8 of a US bushel(orWinchester bushel, seebelow) and isthusexactly equal to 268.8025 cu in (4404.88377086 ml). This unit was once known in England as theWinchester corn gallon.
(Gérard Michon.2000-11-2) A US bushel (bu) is defined to be exactly 2150.42 cubic inches. How many bushels in a cylindrical container74 inches in diameter and 50 inches deep? Explain the "curious" numerical result...
With ludicrous precision: 100.000007969708869510499316219846+ bu. There are very nearly 100 bushels in such a container! Here's why:
The US system of capacity is based on the Winchester system whose two basic units arethegallon for liquids and thebushel for dry goods.
The ancient Celtic city of Winchester was once an important Roman community,and it became the capital of England in the 9th century, whenthe kings of Wessex ruled the country. Itseemsthat theWinchester bushel was originally equivalent to 4 Roman modii (or 4/3 of a Roman cubic foot).
8.8 L)of 16sextarii was the largest dry measure unit. In other words, there were 3modii to theamphora,but the modius was not used at all for liquids. Unlike larger units, the submultiples of thesextarius were used forboth liquids and dry goods: hemina (1/2 of a sextarius),quartarius (1/4),cyathus (1/12),cochlear ("spoonful"; 48cochlearia to thesextarius). Note that the Romantalentwas the mass of an amphora of water and was divided into 80librae (Roman pounds).
Henry VII [Tudor] reigned from 1485 to 1509. In 1495, the Winchester bushel was legally defined as the capacity ofactualstandard bushels bearing his seal and kept at the Exchequer. In 1696, these were measured to be about 2145.6 cubic inches,under the supervision of members of the British House of Commonswho were discussing some excise duty onmalt. It was then suggested that thebushel itself be defined asa simple circular measure roughly equivalent to this.
This was enacted in1701(during the reign of William III of Orange) when the Winchester bushel was legally redefined, under the name ofcorn bushel,as the capacity of"any round measure with a plain and even bottom,being 18½ inches wide throughout and 8 inches deep"(there would have been exactly 100 of these in the above container). Sometime before 1795, this volume was rounded down from 2150.420171...to exactly 2150.42 cubic inches, which is how the so-calledmalt bushel was normally defined. (I couldn't determine theexact point at which the oldercylindrical definition of thisbushel faded from view. Please,tell mewhatever you may know. Thanks.)
The same thing happened to theUS gallon, which is a descendant of the oldWinchester wine gallon, a cylindrical measurefrom the days of the Magna Carta: 7" in diameter and 6" deep,or about 230.90706 cubic inches. This capacity wasstatutorily rounded to 231 cubic inches in 1707,by Anne Stuart (it was thus once known as the Queen Anne wine gallon).
Both Winchester units are thus tied to the inch and have, in effect,been redefined every time the inch was. The current units of capacity are based on the 1959 international inch,which is nowforever defined in metric terms(1" = 25.4 mm).
The US adopted the Winchester system for capacities in 1836, using the above equivalences.The British had adopted the competing Imperial system in 1824,on the totally different basis of anImperial gallonthen introduced as the volume occupied by 10 lb of water at 62°F (later redefined in metric terms, as exactly equal to 4.54609 L) and an Imperial bushel equal toexactly 8 of these gallons (36.36872 L).
jlj3394(2001-01-15) How many 12 oz beers are in a keg?
The US government defines (for tax purposes and such) a barrel of beer as exactly equalto 31 US gallons (these are Winchester gallons of exactly 231 cubic inches,not the Imperial gallons used in the UK).
The US brewing industry calls a [full] keg a quantity of beer equal to half of sucha barrel, namely 15.5 gallons (half a keg is called a "pony-keg" and equals7.75 US gallons).A US gallon being divided into 128 oz, the above implies that a keg equals 1984 oz,or 165 and 1/3 times a "12 oz beer".
The 12 oz size (can or bottle) is most commonlysold in "packs" of 6 or 12 ("6 pack" or "12 pack"), but retail packs of18, 20, 24 or 30 are also widely available. Traditionally, acase of beer consistsof 24 cans or 24 bottles.There are thus almost 7 cases of beer(which would be 168 cans) to the keg.
Mass, "Weight"
(C. B. of Philadelphia, PA.2000-10-25) Is there a [unit of] measurement smaller than a milligram?
Here's a list of the smaller official units of mass in "concrete" terms:
gram (g): A paper clip.
milligram (mg): Cubic millimeter of water. Mass of a typical ant.
microgram or gamma: Dust mite (dermatophagoides pteronyssinus).
nanogram (ng)
picogram (pg): A typical bacterium (Escherichia coli).
femtogram (fg)
attogram (ag): A typical virus, or 20 prions.
zeptogram (zg, g): 3 gold atoms, or 33 water molecules.
Thus, the ratio of the mass of the Sun to that of the Earth (atmosphere included) is known with excellentprecision, namely: 332946.0438.
Although the Sun loses millions of tons per second,it will take more than 2000 years for this to affect the least significant digit of that last ratio. This is good enough to use the changing mass of the Sunas a very practical unit which allows the mass oflarge celestial bodies in the solar systemto be expressed with much more precision than SI units (kilograms) would allow, using the values of their relative gravitational constants, as defined above.
Body
Mass
Reciprocal
Sun
1
1
Jupiter
9.5479194 10-4
1047.3486
Earth + Moon
3.040432685 10-6
328900.5558
Earth
3.003489661 10-6
332946.0438
Moon
3.69430242 10-8
27068710
The Earth is 81.30059 times as massive as the Moon.
("Biker" of Jerome, ID.2000-10-09) What is a slug, in the [engineering] weight measurement system?
Theslug is a unit of mass. The word was coined in a 1902 textbook by the British physicistA.M. Worthingtonto designate theBritish engineer's unit of mass, which appearedin engineering calculations late in the 19th century.
Theslug is defined as the mass which would accelerateat a rate of 1 ft/s2 under a force of one pound-force (lbf). Since 1 lbf is the force exerted on a mass of one pound by astandard gravitational field (of exactly 9.80665 meters per square second),a slug is thusexactly equal to 196133/6096 pounds(about 32.1740485564 lb or 14.593902937206 kg).
It's worth making a few technical points about this:
Theslug is the unit of mass in a coherent system called either"British engineering system" or "English gravitational system". On the other hand, the Imperial (formerly "English") unit of mass is the pound (lb),which is nowdefined in metric terms(0.45359237 kgexactly).
The "metric equivalent" of the slugis the hyl of exactly 9.80665 kg which is the unit of mass of the so-called "metric-technical system". The hyl is also called "metric slug" ordesignated by the German acronym TME (Technische Mass Einheit ). A mass of one hyl gets accelerated at a rate of one meter per square secondby a force of one kilogram-force (namely, 9.80665 N).
The SI unit of mass is thekilogram,not the gram or the hyl.
Both the pound and the slug are units ofmass. The latterweighs about 32 times as much as the former,even on the surface of the moon. On the moon, however theweight of a pound-mass(lb or lbm) is only about one sixth of a pound-force (lbf).
(2007-05-13) What are the units of mass available on modern electronic balances?
The customary units listed below are mostly kept alive bygold traders.
A common feature of electronic analytical and/or precision balancesis the ability to use various customary units of mass. Copying each other over the years(often misspelling "baht" and/or "mesghal") manufacturers have picked from thefollowing limited catalog of units, which caters to all international traders.
In East Asia, the catty is to the tael (TL) what the pound (lb) is to the ounce (oz). There are 16 taels to the catty... The Taiwanese tael (37½ g) thus corresponds to a catty of 600 g, whereas the "tael of Singapore" (defined as 1/12 lb or 4/3 oz) corresponds to a catty of 4/3 lb (about 604.79 g).
1000 grams (g) to the kilogram (kg). 7000 grains (gn) to theavoidupois pound (lb). Note that the abbreviation "gr" is best shunned (asit could stand for either grams or grains).
The word troy is so strongly associated with the goldtrade that it's now employed (as a suffix) for the unrelatedAsian units used to trade gold in Hong-Kong and elsewhere (manufacturers of electronic scales use the term tael of Hong-Kong for the tael troy):
The proper British troy system itself is fully compatible withthe deprecated apothecaries' weight system of pharmacists, which has been illegal for trade in the UK since 1985. This is to say that units with the same name (pound, ounce, grain) have identical values in both system. However, there are units which are used in only one of those two systems:
Units of the Troy System and Apothecaries' Weights
Apothecaries' weight was used for dispensing medicine in the UKuntil the Medical Act of 1858 adopted the avoirdupois system, which could then be used for everything but precious metals, pearls and gemstones.
Units of the Avoirdupois System of Weights (avdp)
Name
Symbol
Avoirdupois
Grains
Metric
(Long) ton
t
20 cwt
15680000
1016.0469088 kg
(Short) ton
t (US)
20 cwt (US)
2000 lb
907.18474 kg
Hundredweight
cwt
4 qr
784000
50.80234544 kg
Short hundredweight
cwt (US)
100 lb
700000
45.359237 kg
Quarter
qr
2 st
196000
12.70058636 kg
Stone
st
14 lb
98000
6.35029318 kg
Pound
lb
16 oz
7000
453.59237 g
Ounce
oz
16 dm
437.5
28.349523125 g
Drachm
dm (dr)
27.34375
1.7718451953125 g
Grain
gn (or gr)
1
64.79891 mg
In the US, the stone (14 lb) and its multiples nevercaught on and larger units are not multiple of that. Thus, Americans use short versions of the hundredweight (100 lb instead of 112 lb) and the ton (2000 lb instead of 2240 lb). Whenever there is a risk of confusion, the proper qualifiers short and long should be used forthose units. Be aware that many otherton units are in use!
The grain unit of 64.79891 mg is shared by all of the above systems.
(2007-06-03) The ancient livre de Charlemagne and the poids de marc system.
From the early definitions of the kilogramsurvives only an exact equivalence between the old French units of masspoids de marc and the metric system;there are exactly18827.15 French grains to the kilogram.
Once it had been realized that a definition of the kilogram as the mass of acubic decimeter of water was not satisfying (by the metrological standards of the late 18th century) the kilogram was evaluated using the best system ofweights then available. In pre-revolutionary France, that was based on afamous artifact known as thepile de Charlemagne,which is still preserved in the Musée National des Techniques in Paris, France.
When the kilogram (then called thegrave)was first defined (on August 1, 1793), it was equated to 18841 grains ofthe above poids de marc system,from a single measurement byLavoisier andHaüy. Early in 1799, an accurate equivalence of 18827.15 grains to the kilogram was established...
The new determination was enacted on May 30, 1799, and it became the final legalequivalence between the kilogram and the "old" French units.
Since the newer equivalence was quite different from Lavoisier's original one (13.85grains is about 3/4 of a gram) the standard weights that had been sent to all departmental chef-lieus had to be recalled. New ones were made.
The old French system of 18onces to thelivre had been introduced in the wake of Charlemagne'smonetary reform. The once was understood to be exactly the same as the Roman uncia but there were 18 of those toCharlemagne's livre (French pound, poids de marc ) as opposed to 12 unciae to the libra (Roman pound). So, a French pound was exactly 1½ Roman pounds.
The above thus provides a paper trail to what may be construed as a "legal" value of the ancient Romanpound in metric terms, namely:
1 Roman pound (libra) = 12onces (of 512 grains) = 0.326337231... kg
(J. W. of Tustin, CA.2001-02-07) How many pounds was a talent? How many ounces was a shekel?
Atalent was the mass of a cubicfoot of water. The exact value of the talent thus depended on whatfoot was in usein a specific part of the world at a certain period in history. If there was such a thing as a modern Imperial talent (based on water at 62°F) it would be about 62.288 lb (or 28.25 kg).
The Roman talent was also defined as 80Roman pounds("librae", plural of "libra"). Theabove value of thelibra,from the days of Charlemagne, makes the Roman talent equal to about 26.107 kg.
The ancient Sumerian talent is estimated at about 28.8 kg (about 63.5 lb)from the mass of survivingstandard weights (basalt statuettes in the form ofsleeping ducks). Outside of Rome, thetalent was normally divided into 60 minas;a mina (ormaneh) was thus roughly equal to a modern avoirdupois pound.
Theshekel was always somesubmultiple of this mina: The Babylonian shekel was 1/60 mina, the Phoenician shekel was 1/25 mina,the Egyptian shekel was 1/100 mina,whereas the "modern" Palestinian or Syrian shekel is 1/50 of a mina.
Solomon'smina of gold (1 Kings 10:17) was divided into100 units (unnamed in the Hebrew text of 2 Chr. 9:16)not necessarilyrelated to the Biblicalshekel of the sanctuary or holy shekel (cf. bishekel hakodesh) whose value ought to be determined by the last words of Ezekiel 45:12. Unfortunately, Bible scholars have been advocatingat leasttwo contradictory renditions of that verse, namely:
50 shekels to a mina(Septuagint, according toWalther Zimmerli): "[...] 5 shekels are to be 5, and 10 shekels are to be 10,and 50 shekels are to amount to amina with you."
60 shekels to a mina (King James and other English versions, alsosupported by Rabbi Nosson Scherman, in the Stone Edition Tanach):"[...] 20 shekels, 25 shekels, and 15 shekels shall be your mina."
The latter may have exhorted traders to check their minas against smallerstandard weights... If you know for sure, pleasetell me.
There are many different kinds of tons. In the US, you're most likely to encounter the short ton(2000 lb, or about 907.185 kg) unless you're primarily concerned with ships,for which thedisplacement ton and thegross ton are in fact units ofmass both equivalent to the Britishlong ton of 160stones(2240 lb, or about 1016 kg). Thelong ton is retained in this international contextbecause it's almost exactly equal to the mass of acubic meter of seawater. This is a prime example of crossbreeding between the metric and Imperial systems.
A troy ounce (ozt)per ton is a milligram (mg) per assay ton.
Ton, in lb
Assay ton, in g
short ton
2000 lb
175 / 6
29.16666... g
long ton
2240 lb
98 / 3
32.66666... g
troy ton
2016 lb
147 / 5
29.4 g
Other types oftons include the very importantmetric ton(better spelledtonne, which corresponds to 1000 kg or about 2204.62 lb)and the totally unimportant and unusedtroy ton of 144stones(2450 lbt = 2016 lb = 914.44221792 kg).
As if this were not bad enough, a fewunits of volumeare also calledtons: This includes, most notably, the internationalregister tonof 100cubic feet (2831.6846592 L). Of lesser importance is the Britishwater ton of (exactly) 224 Imperial gallons,which originally corresponded to the volume occupied by a long ton (2240 lb)of distilled water at 62°F, when the Imperial gallon was still defined in liketerms as a "10 pound gallon". (Under the modern definition of the Imperialgallon, in metric terms, the British water ton is exactly 1018.32416 L.)On the other hand, the unit variously calledshipping ton,freight tonormarine ton is 40 cubic feet (1132.67386368 L),which happens to be equal to the so-calledton of timber (of 480 board feet). There's alsoa fluid ton of 32 cubic feet (906.139090944 L),a corn ton of 32 bushels(which means exactly 1127.65024534016 L in the US and 1163.79904 L in the UK),and a Britishtun, spelled with a "U", of two pipes or 252 Imperial gallons(1145.61468 L).
I just wanted to drop you a line to tell you that I enjoyed your treatise on the "ton"(s).[above] For completeness, it would be interesting if you were to also mention and/ordescribe the origination/relation of the "refrigeration ton" and/or the "explosion ton" units.
Regards,Darren Finck
Thanks for the kind words, Darren.
First a general remark: The adjective "extensive" qualifies (loosely speaking) physical quantities forwhich the measure of the whole is the sum of the measures of the parts. Volume and mass are examples of extensive quantities (pressure and temperature are not). Choosing some "stuff" of reference, like water under normal conditions, establishesa "conversion factor" (coefficient of proportionality)between any pair ofextensive quantities and/orthe units which measure them. New "practical" units may thus be createdad nauseam, including many flavors oftons which correspond to variousextensive properties of aton of "stuff".
This is how some of the "tons" mentioned above as unitsofmass gave rise to units ofvolume(avolume of oneton being the volume occupied under standardconditions by amass of oneton of water). This is also how a unit ofmass may become a unit offorce(the correspondingweight in astandard gravitational field,equal to 9.80665 m/s).In particular, theton of thrust is a unit offorce equal to the standardweight of ametric ton/tonne, namely 9806.65 N. [The newton (N) is the SI unit of force. Applying for 1 second a force of 1 Nto a mass of 1 kg, initially at rest, will make it move at a speed of 1 m/s.]
Theton unit pertaining to nuclear explosionsis a unit ofenergy equal to 1000 000 000thermochemicalcalories (of exactly 4.184 J)and is thusexactly equal to 4184 000 000 joules. (Thekiloton andmegaton are a thousand and a million times as large.)
Detonating1000 kg ofTNT (227.134 g/mol) yieldsonly 64% of such aton:
The carbon (C) produced appears asblack smoke. Some residues may subsequentlyburn in air to givemore energy (393.51 kJ per mole of carbon,241.826 kJ per mole of hydrogen gas,282.98 kJ per mole of CO). The totalheatof combustion of TNT is thus about 3305 kJ/mol, whichtranslates into 3½ of the abovetons of energyfor 1000 kg of TNT (227.13 g/mol)... What's wrong? Well, to optimize the energy of the initial blast, anoxidizer(ammonium nitrate = AN) must be added to TNTto form abalanced high explosive, calledamatol. The optimal proportion for agiven total weight is 78.7% AN and 21.3% TNT,matching the stoichiometry of the following reaction. (A slight excess of AN seems better for dynamic reasons,so the usual mix is 80/20.)
This yields 1.0174tons of energy when 1000 kg of the mix are detonated,which justifies quantitatively the term "ton of TNT "commonly used for the aboveton of energy,although "ton ofamatol" would have been more proper...
Other types of "tons" are used to measure energy in a more peaceful context:Burning a ton of crude oil releasesabout 10 times as much energy as exploding a ton of TNT/amatol. On the other hand, the best grade of coal (anthracite) issupposedto be about 30% less efficient than oil.
This gave rise to two other "ton" units for measuring energy,theton oil equivalent (toe) and theton coal equivalent (tce):1 tce = 0.7 toe. Both refer to metric tons (1000 kg) but, unlike theton of TNT,they are usually defined as round multiples of theIT calorie(International Steam Tablecalorieof exactly 4.1868 J instead of 4.184 J):
1 tce = 29 307 600 000 J 1 toe = 41 868 000 000 J
Now, theton of refrigerationorton of cooling is a unit ofpower(which can't be compared with any of the above units ofenergy). It was first defined as the power released by a ton (2000 lb) of water when it freezesin one day (86400 seconds) or, conversely,the power absorbed by a ton of ice which melts in a day. This would be about 3502.6 W (watts),but theton of cooling is now conventionally defined asexactly 12000 Btu/h (about 3516.852842 W),based on the rounded value of 144 Btu/lb for the latent heat of fusion of water. In the United Sates,air conditioning unitsare now rated using theBtu of cooling, which is a unit ofpower simplyequal to a Btu per hour(about 0.293 W, more precisely 0.2930710701722222...W). The labeling of A/C units is in terms of thousands of Btu [per hour](typically: 024, 030, 036, 042, 048, or 060), butbetrays its origin in terms of tons of cooling(2, 2½, 3, 3½, 4, or 5tons of refrigeration).
Last, and probablyleast, we're told that the "ton" is also aninformalBritish unit ofspeed equal to 100 mph (160.9344 km/h or 44.704 m/s). [Colloquially, in the UK, a ton can be 100 timesas large asany commonly understood unit.]
(2023-09-29) Burning various types of natural gas at room temperature.
As natural gas is an important source of energy, thetoe hasbeen given the following standard equivalences in term of gas quantities,using the different units of volume preferred in various regions of the Globe(these values are, unfortunately,slightly incompatible with each otherand with theabove):
USA : 42900 cubic feet (about 1214.8 cubic meters).
Europe : 1270 cubic meters.
Japan : 0.855 metric tons of LNG ("Liquefied Natural Gas").
When natural gas is used for heating, it's measured by volume atroom temperature (the meter is typically located inside a room around 21°C).
Frenchresidential customers are billed for natural gas in units of energy (1 kWh = 3600 000 J) using gas meters measuring volume at room temperature.
The altitudes at which the meters are permanently located is on record and servesto compute gas quantities per volume using the ideal gas law. Two main gas ratings are defined according to their origin. B-gas is being phased out but still represents 10% of the NG didtributed in France (mostly Northern France).
B-gas or L-gas (fromGroningen,with high-levels of nitrogen): 10.0 kWh/m3
H -gas (from North See, Russia and Algeria): 11.2 kWh/m3
Natural gas is odorless but is distributed with a THT additive (Tetra Hydro Thiophene)which gives it a characteristic odor which makes leaks noticeable.
TheLacq gas fieldwas exploited by Total from 1957 to 2013. It was noted for a very high concentrationinhydrogen sulfide (H2S).
robster(
"and the numeral "1". When typing, a cursive"
On 2001-10-26,