William Brouncker, 2nd Viscount Brouncker

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The Right Honourable
The Viscount Brouncker
President of the Royal Society
In office
1662–1677
Preceded byOffice established
Succeeded byJoseph Williamson
Personal details
Bornc. 1620
civil servant
InstitutionsSaint Catherine's Hospital
Academic advisorsJohn Wallis
Brouncker's signature as president, signing off the 1667 accounts of the Royal Society, from the minutes book

William Brouncker, 2nd Viscount Brouncker

civil servant, serving as a commissioner in the Royal Navy. Brouncker was a friend and colleague of Samuel Pepys, and features prominently in the Pepys' diary
.

Biography

Brouncker was born c. 1620 in

William Brouncker (1585–1649), 1st Viscount Brouncker and Winifred, daughter of Sir William Leigh of Newnham. His family came originally from Melksham in Wiltshire. His grandfather Sir Henry Brouncker (died 1607) had been Lord President of Munster 1603–1607, and settled his family in Ireland. His father was created a viscount in the Peerage 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 a

Diary of Samuel Pepys; despite their frequent disagreements, Samuel Pepys
on the whole respected Brouncker more than most of his other colleagues, writing in 1668 that "in truth he is the best of them".

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 of

Lord High Admiral of England from 1679.[1]

Abigail Williams

Brouncker never married, but lived for many years with the

Sir Oliver Cromwell, and first cousin to the renowned Oliver 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 Samuel Pepys
, whose private apartments were also destroyed in the blaze.

On Brouncker's death in 1684, his title passed to his brother Henry, 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".

Mathematical works

His mathematical work concerned in particular the calculations of the lengths of the

infinite series.[3] He was the first European to solve what is now known as Pell's equation. He was the first in England to take interest in generalized continued fractions and, following the work of John Wallis, he provided development in the generalized continued fraction of pi
.

Brouncker's formula

This formula provides a development of π/4 in a generalized continued fraction:

The convergents are related to the

Leibniz 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]

See Euler's continued fraction formula.

See also

References

  1. ^ "No. 1485". The London Gazette. 9 February 1679. p. 2.
  2. Philosophical Transactions of the Royal Society of London, abridged edition 1809, v. i, pp 233–6, link form Biodiversity Heritage Library
  3. ^ Julian Coolidge Mathematics of Great Amateurs, chapter 11, pp. 136–46
  4. ^ John Wallis, Arithmetica Infinitorum, ... (Oxford, England: Leon Lichfield, 1656), page 182. Brouncker expressed, as a continued fraction, the ratio of the area of a circle to the area of the circumscribed square (i.e., 4/π). The continued fraction appears at the top of page 182 (roughly) as: ☐ = 1 1/2 9/2 25/2 49/2 81/2 &c , where the square denotes the ratio that is sought. (Note: On the preceding page, Wallis names Brouncker as: "Dom. Guliel. Vicecon, & Barone Brouncher" (Lord William Viscount and Baron Brouncker).)

External links

Peerage of Ireland
Preceded by
William Brouncker
 Viscount Brouncker
1645–1684 		Succeeded by
Professional and academic associations
First 1st President of the Royal Society
1662–1677 		Succeeded by
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