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The Viscount Brouncker | |
|---|---|
 | |
| President of the Royal Society | |
| In office 1662–1677 | |
| Preceded by | Office established |
| Succeeded by | Joseph Williamson |
| Personal details | |
| Born | c. 1620 Castlelyons, Ireland |
| Died | 5 April 1684(1684-04-05) (aged 64) Westminster, London |
| Residence | England |
| Scientific career | |
| Alma mater | University of Oxford |
| Known for | Brouncker's formula, leadership ofRoyal Society |
| Fields | Mathematician,civil servant |
| Institutions | Saint Catherine's Hospital |
| Academic advisors | John Wallis |
William Brouncker, 2nd Viscount Brouncker,FRS (c. 1620 – 5 April 1684) was an Anglo-Irish peer and mathematician who served as thepresident of the Royal Society from 1662 to 1677. Best known for introducing Brouncker's formula, he also worked as acivil servant, serving as acommissioner in theRoyal Navy. Brouncker was a friend and colleague ofSamuel Pepys, and features prominently in thePepys' diary.
Brouncker was bornc. 1620 inCastlelyons,County Cork, the elder son ofWilliam Brouncker (1585–1649), 1stViscount Brouncker and Winifred, daughter of Sir William Leigh of Newnham. His family came originally fromMelksham inWiltshire. His grandfather SirHenry Brouncker (died 1607) had beenLord President of Munster 1603–1607, and settled his family in Ireland. His father was created aviscount in thePeerage of Ireland in 1645 for his services to the Crown. Although the first viscount had fought for the Crown in the Anglo-Scots war of 1639, malicious gossip said that he paid the then enormous sum of £1200 for the title and was almost ruined as a result. He died only a few months afterwards.
William obtained aDM at theUniversity of Oxford in 1647. Until 1660 he played no part in public life: being a staunch Royalist, he felt it best to live quietly and devote himself to his mathematical studies. He was one of the founders and the firstpresident of the Royal Society. In 1662, he becamechancellor toQueen Catherine, then head of theSaint Catherine's Hospital. He was appointed one of the commissioners of theRoyal Navy in 1664, and his career thereafter can be traced in theDiary of Samuel Pepys; despite their frequent disagreements,Samuel Pepys on the whole respected Brouncker more than most of his other colleagues, writing on 25 August 1668 that "the truth is, he is the best man of them all".[1]
Although his attendance at the Royal Society had become infrequent, and he had quarrelled with some of his fellow members, he was nonetheless greatly displeased to be deprived of the presidency in 1677. He was commissioner for executing the office ofLord High Admiral of England from 1679.[1]
Brouncker never married, but lived for many years with theactress Abigail Williams (much to Samuel Pepys' disgust) and left most of his property to her. She was the daughter of Sir Henry Clere (died 1622), first and last of theClere Baronets, and the estranged wife of John Williams, otherwise Cromwell, second son ofSir Oliver Cromwell, and first cousin to the renownedOliver Cromwell. She and John had a son and a daughter. The fire of 1673 which destroyed the Royal Navy Office started in her private closet: this is unlikely to have improved her relations with Pepys, whose private apartments were also destroyed in the blaze.
On Brouncker's death in 1684, his title passed to his brotherHenry, one of the most detested men of the era. William left him almost nothing in his will "for reasons I think not fit to mention".
His mathematical work concerned in particular the calculations of the lengths of theparabola andcycloid, and thequadrature of thehyperbola,[2] which requires approximation of thenatural logarithm function byinfinite series.[3] He was the first European to solve what is now known asPell's equation. He was the first in England to take interest ingeneralized continued fractions and, following the work ofJohn Wallis, he provided development in the generalized continued fraction ofpi.
This formula provides a development of π/4 in a generalized continued fraction:
The convergents are related to theLeibniz formula for pi: for instance
and
Because of its slow convergence, Brouncker's formula is not useful for practical computations of π.
Brouncker's formula can also be expressed as[4]
SeeEuler's continued fraction formula.
| Peerage of Ireland | ||
|---|---|---|
| Preceded by | Viscount Brouncker 1645–1684 | Succeeded by |
| Professional and academic associations | ||
| First | 1st President of theRoyal Society 1662–1677 | Succeeded by |
