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
