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PELL, JOHN (1611–1685), mathematician, was born at Southwick in Sussex on 1 March 1611. His father, John Pell, was incumbent of that place, whither his grandfather, another John Pell, had migrated from Lincolnshire. He came of a good old family, one of his ancestors having been lord of a manor in Lincolnshire in 1368. He married Mary Holland of Halden, Kent, and died at Southwick in 1616, one year before his wife. His daughter, Bathsua Makin [q. v.], is separately noticed.

Pell, the younger of his two sons, was educated at the free school of Steyning in Sussex, and progressed so rapidly that he was admitted to Trinity College, Cambridge, at the age of thirteen, being then, Wood relates, ‘as good a scholar as some masters of arts.’ He worked indefatigably. A ‘strong and good habit of body’ enabling him to dispense with recreations, ‘he plied his studies while others played.’ Yet he never became a candidate for college honours. He graduated B.A. in 1628, proceeded M.A. in 1630, and in 1631 was incorporated of the university of Oxford. By this time, at the age of twenty, he was already ‘in great reputation and esteem for his literary accomplishments,’ which included the mastery, not only of Hebrew, Greek, and Latin, but of Arabic, Italian, French, Spanish, High and Low Dutch. He was ‘also much talked of for his skill in the mathematics,’ the taste for which continually grew upon him. He was, moreover, remarkably handsome, with dark hair and eyes, and a good voice. In 1628 he corresponded with Henry Briggs [q. v.] about logarithms, and drew up papers on the use of the quadrant and on sundials, which, however, remained unpublished. Lansberg's ‘Everlasting Tables’ were translated by him from the Latin in 1634. His ‘Eclipse Prognosticator’ was written about the same time. On 3 July 1632 he married Ithumaria, daughter of Henry Reginolles of London, by whom he had four sons and four daughters; and in 1643, through the interest of Sir William Boswell [q. v.], he became the successor of Hortensius in the chair of mathematics at Amsterdam. A course of lectures on Diophantus, delivered by him there, excited much applause, and his colleague, Gerard John Vossius, styled him ‘a person of various erudition and a most acute mathematician’ (De Scientiis Mathematicis, cap. x.) In 1646 he was induced by the Prince of Orange to remove to the new college of Breda, where he enjoyed a salary of one thousand guilders; and, returning to England in 1652, was appointed by Cromwell to lecture on mathematics at 200l. a year. Two years later he was despatched as Cromwell's political agent to the protestant cantons of Switzerland, in which capacity he acquitted himself so well that he was continued as resident at Zürich with a yearly salary of 600l. The real object of his mission was to detach the cantons from France, and to draw them into a continental protestant league headed by England. Interminable negotiations ensued. ‘They move so slowly here,’ Pell wrote to Thurloe from the Swiss Baden in May 1656, ‘that it is hard to discern whether they go forward or backward’ (Vaughan, Protectorate of Cromwell, i. 396). Recalled in 1658, he reached London on 13 Aug., three weeks before Cromwell's death. Some obscure services, however, rendered by him to the royalist party and to the church of England secured his position at the Restoration. Having taken orders, he was presented by Charles II in 1661 to the rectory of Fobbing in Essex, and by Dr. Sheldon, bishop of London, in 1663, to the vicarage of Laindon with Basildon in the same county. Both preferments were held by him till his death. Assisted by William Sancroft [q. v.], he introduced on 5 Dec. 1661 a scheme for a reform of the calendar into the upper house of convocation; his name was included in the first list of fellows of the Royal Society chosen on 20 May 1663; and, having been nominated domestic chaplain to Dr. Sheldon on his elevation to the see of Canterbury, he took the degree of D.D. at Lambeth on 7 Oct. 1663 (‘Graduati Lambethani’ in Gent. Mag. 1864, i. 636). A bishopric was expected for him; but he drifted off the highroad to promotion into hopeless insolvency. ‘He was a shiftless man as to worldly affairs,’ Wood testifies, ‘and his tenants and relatives dealt so unkindly with him that they cozened him out of the profits of his parsonages, and kept him so indigent that he wanted necessaries, even paper and ink, to his dying day.’ He resided for some years at Brereton Hall, Cheshire, as the guest of William, third lord Brereton, who had been his pupil at Breda; and his children were in 1671 living in the same neighbourhood, as we learn from Thomas Brancker's mention of an unpaid loan for their support (Rigaud, Correspondence of Scientific Men, i. 166). Pell was also in debt to John Collins (1625–1683) [q. v.], having boarded long at his house. Collins nevertheless respected him as ‘a very learned man, more knowing in algebra, in some respects, than any other.’ ‘But to incite him to publish anything,’ he added, ‘seems to be as vain an endeavour as to think of grasping the Italian Alps in order to their removal. He hath been a man accounted incommunicable’ (ib. pp. 196–7). His hints of new methods led to nothing. ‘We have been fed with vain hopes from Dr. Pell about twenty or thirty years,’ Collins wrote to James Gregory in or near 1674 (ib. ii. 195). But for this reticence he would, it was thought, have been recommended by the Royal Society to the king of France for a pension. His embarrassments meantime increasing, he was twice thrown into the king's bench; then, in March 1682, Dr. Daniel Whistler [q. v.] afforded him, when utterly destitute, an asylum in the College of Physicians. A failure of health, however, soon compelled his removal to the house in St. Margaret's, Westminster, of one of his grandchildren, whence he was transferred to the lodging in Dyot Street of Mr. Cothorne, reader in the church of St. Giles-in-the-Fields. There, on 12 Dec. 1685, he died, and was buried in the rector's vault.

Pell's mathematical performance entirely failed to justify his reputation. He is remembered chiefly by his invention of the sign ÷ for division, and of a mode of marginally registering the successive steps in the reduction of equations. These novelties were contained in Brancker's translation of Rhonius's ‘Algebra,’ published, with additions and corrections by Pell, at London in 1668. Among his few and slight original printed works may be mentioned: 1. ‘A Refutation of Longomontanus's pretended Quadrature of the Circle,’ Amsterdam, 1646; in Latin, 1647. 2. ‘Easter not mistimed,’ a letter to Haak in favour of the new style, 1664. 3. ‘An Idea of Mathematics,’ written about 1639, and sent by Hartlib to Mersenne and Descartes. It was published as an appendix to Durie's ‘Reformed Library-keeper,’ London, 1650, and included by Hooke, with Mersenne's and Descartes's comments, in the ‘Philosophical Collections,’ 1679, p. 127. It sketched the outline of a comprehensive but visionary plan for the promotion of mathematical studies. 4. ‘On the Day Fatality of Rome,’ printed in 1721 among Aubrey's ‘Miscellanies.’ 5. ‘A Table of Ten Thousand Square Numbers,’ London, 1672. An ‘Antilogarithmic Table,’ the first of its kind, computed by Pell and Walter Warner [q. v.] between 1630 and 1640, was soon afterwards lost or destroyed. Pell had an edition of Diophantus nearly ready for the press in 1647, but it never saw the light. He demonstrated the second and tenth books of Euclid, and only laid aside Apollonius at the request of Golius in 1645. He left large deposits of manuscripts wherever he lodged. Most of these are now in the British Museum, occupying nearly forty volumes of the Birch collection. Among them are tracts entitled: ‘Tabulæ Directoriæ ad Praxin Mathematicam conferentes,’ 1628; ‘The Eclipse Prognosticator,’ 1634; ‘Apologia pro Francisco Vietâ’ (Sloane MS. 4397). Pell's loose mathematical papers occupy fourteen volumes of the same collection (Nos. 4418–31), while in three more (Nos. 4278–80) his correspondence with his scientific contemporaries is preserved. One of those with whom he was in frequent communication from 1641 to 1650 was Sir Charles Cavendish, brother of William, marquis of Newcastle. Cavendish unremittingly urged the publication of ‘a large volume concerning Analyticks.’ Pell replied from Amsterdam on 18 Feb. 1645: ‘I fear it will be long ere I find leisure to finish such a volume for the press, adding: ‘You have here some of the heads of that multitude of thoughts that I would willingly be delivered of; but it may be somebody else must bring them forth’ (Harleian MS. 6796, f. 294). Eleven volumes of the Lansdowne manuscripts (Nos. 745–55) are composed of Pell's further remains. Thence, as well as from one volume of the Sloane series (No. 4365), Dr. Robert Vaughan took the materials for ‘The Protectorate of Cromwell’ (London, 1638). The bulk of his two volumes consists of Pell's official reports to Thurloe and Sir Samuel Morland [q. v.] on the progress of his Swiss mission (1654–8). They are of great historical importance. His philosophical correspondence during the same interval with Sir William Petty, Hartlib, Brereton, Brancker, and others, is printed in an appendix, together with his letters to his wife. These last are harsh and contemptuous in tone, and suggest that Ithumaria was a foolish woman, though a devoted wife. She died on 11 Sept. 1661, and Pell remarried before 1669. His eldest daughter was married to Captain Raven on 3 Feb. 1656.

His only brother, Thomas Pell, a gentleman of the bedchamber to Charles I, went to America about 1635, and acted as a surgeon in the Pequot war. He settled later at Fairfield, Connecticut, and secured from the Indians in 1654 a large part of Westchester County, in the State of New York. A patent from the Duke of York converted this tract in 1666 into the lordship and manor of Pelham, and it passed by will in 1669, on the death without heirs of the first owner, to his nephew John (born on 3 Feb. 1643), the only surviving son of the mathematician. He was drowned in a boating accident in 1702, and his sons, John and Thomas, became the ancestors of all the American branches of the family.

[Wood's Fasti Oxon. i. 461 (Bliss); Biogr. Brit. 1760 vol. v.; Gen. Dict. 1739, viii. 250; Birch's Hist. Royal Soc. iv. 444; Phil. Trans. Abridged, Hutton, ii. 527; Hutton's Mathematical Dict., 1815; Foster's Alumni Oxon.; Rigaud's Correspondence of Scientific Men, passim; Robert Boyle's Works, 1744, i. 35; Martin's Biogr. Phil. p. 334; Aikin's Gen. Biography, vol. viii.; Newcourt's Repertorium, ii. 269; Halliwell's Brief Account of Sir Samuel Morland, p. 27; Sherburn's Sphere of Manilius, p. 102; Kennett's Register, i. 574; Alfred Stern in Sybel's Hist. Zeitschrift, xi. 52; Poggendorff's Biogr. Lit. Handwörterbuch; Watt's Bibl. Brit.; Lansdowne MS. 987, f. 77 (notice of Pell in Bishop Kennett's Collections); Sloane MS. 4223, f. 120 (copy of a biographical account of Pell by Hooke, derived from Aubrey); information from Mr. W. C. Pell, U.S.A.; Bolton's Hist. of Westchester County, ii. 39, 44; O'Callaghan's Hist. of New Netherland, ii. 283; Notes and Queries, 8th ser. viii. 444.]

A. M. C.