branch is also known as Bronkard, Brounkard, and Brunkard.
Young Brouncker studied mathematics in his youth at Oxford, and became proficient in many languages. On 23 Feb. 1646-7 he was created doctor of medicine at Oxford. In April 1660 he subscribed the declaration acknowledging General Monk the restorer of the laws and privileges of the nation.
Brouncker chiefly employed himself during the Commonwealth in literary work. In 1653 he published, under the pseudonym of 'A Person of Honour,' a translation of Descartes's 'Musical Compendium,' with criticisms of his own (cf. Pepys's Diary, 25 Dec. 1668). He prepared a new division of the 'diapason by sixteen mean proportionals into seventeen equal semitones, the method of which is exhibited by him in an algebraical process, and also in logarithms' (Hawkins, History of Music, iv. 181). Descartes declined to accept this scheme. In 1657 and 1658 Brouncker was corresponding on mathematical topics with Dr. John Wallis, who printed the letters in 1658 in 'Commercium Epistolicum.' Brouncker made two mathematical discoveries of importance. He was the first to introduce continued fractions, and to give a series for the quadrature of a portion of the equilateral hyperbola.
After the Restoration Brouncker took part in the meetings of scientific students in London out of which sprang the Royal Society. The association was incorporated under royal charter, first on 15 July 1662, and again on 15 April 1663. From the date of the society's first incorporation till 30 Nov. 1677, when he resigned, and was succeeded by Sir Joseph Williamson, Brouncker held the office of president, to which he was elected annually. John Evelyn, the diarist, was his intimate friend, and the two often discussed scientific questions with Charles II. In August 1662 Brouncker built a yacht for the king, 'which Mr. Pitt,' says Pepys, 'cries up mightily ' (Diary, 14 Aug. and 3 Sept. 1662). He was president of Gresham College from 1664 to 1667. Brouncker, Boyle, and Sir R. Murray, Evelyn writes, 'were the persons to whom the world stands obliged for the promoting of that generous and real knowledge which gave the ferment that has ever since obtained and surmounted all those many discouragements which it at first encountered' (Evelyn to Mr. Wotton, 30 March 1696, in Diary, edited by Bray and Wheatley, iii. 481).
Brouncker was appointed chancellor of Queen Catherine on 18 April 1662, and was commissioner for executing the office of lord high admiral from 12 Nov. 1664 (Luttrell, Relation, and Savile Correspondence, Camd. Soc. p. 256). Pepys has much to say of him in this office, and appears to have lived on terms of great intimacy with him. In 1681 Brouncker became, after much litigation with Sir Robert Atkyns, master of St. Catherine's Hospital, near the Tower of London. He died at his house, in St. James's Street, Westminster, on 5 April 1684, and was buried nine days later in the chapel of St. Catherine's Hospital.
Brouncker was the author of the following scientific papers: 'Experiments of the Recoiling of Forces' (Spratt, History of the Royal Society, 233 et seq.); 'An Algebraical Paper upon the Squaring of the Hyperbola,' and 'On the Proportion of a Curved Line of a Paraboloid to a Straight Line, and of the Finding a Straight Line equal to that of a Cycloid' (Philosophical Transactions, iii. 645, viii. 649).
A series of letters from Brouncker to Archbishop Ussher are printed at the close of Parr's 'Life of Ussher.' Sir Peter Lely painted Brouncker's portrait, which is still in the possession of the Royal Society.
Brouncker was succeeded in the peerage by his brother Henry, cofferer to Charles II, and gentleman of the bedchamber to the Duke of York, who was created doctor of medicine at Oxford on 23 June 1646, took part in the siege of Colchester in 1648, was one of the commissioners of trade and plantations in 1671, and died on 4 Jan. 1687-8. He lived at Sheen Abbey, and was buried at Richmond, Surrey. Evelyn says of him that he 'was ever noted for a hard, covetous, vicious man; but for his worldly craft and skill in gaming few exceeded him.' Pepys's friend, Captain Cocke, described him as 'one of the shrewdest fellows for parts in England, and a dangerous man' (Diary, 17 Feb. 1667-8). It is certain that he pandered to all the Duke of York's vices. He presumed so much on his intimacy with the duke that in August 1667 he was dismissed the court, to the delight (according to Pepys) of all honest men. The Comte de Grammont describes him in his 'Mémoires' (chap, xii.) as 'le premier joueur d'échecs du royaume.' He married Rebecca Rodway, widow of Thomas Jermyn, brother to the Earl of St. Albans. With his death the title became extinct.
[Biog. Brit. (Kippis); Wood's Fasti Oxon. (Bliss); Notes and Queries, 5th ser. xi. 344; Pepys's Diary, passim; Kennett's Register; Birch's Hist. Royal Society; Burke's Extinct Peerage; Weld's Hist. Royal Society; Button's Mathematical Dictionary; Evelyn's Diary; Luttrell's Relation of State Papers, s. v. 'Brunkard.']
