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 alternately at Castle Hedingham, Essex, and in London. Here, one evening at supper, a letter in cipher was brought in, relating to the capture of Chichester on 27 Dec. 1642, which Wallis within two hours succeeded in deciphering. The feat made his fortune. He became an adept in the cryptologic art, until then almost unknown, and exercised it on behalf of the parliamentary party. He was rewarded in 1643 with the sequestrated living of St. Gabriel, Fenchurch Street, which he exchanged in 1647 for that of St. Martin in Ironmonger Lane. In 1644 he acted as secretary to the assembly of divines at Westminster, and obtained by parliamentary decree a fellowship in Queens' College, Cambridge. This, however, he speedily vacated by his marriage, on 14 March 1645, with Susanna, daughter of John and Rachel Glyde of Northiam, Sussex. He now came to live in London. Already zealous for the ‘new’ or experimental philosophy, he associated there with Robert Boyle [q. v.] and other reformers of scientific method, whose weekly meetings, divided after 1649 between Oxford and London, led to the incorporation, in 1663, of the Royal Society (for Wallis's account of its origin, see History of the Royal Society, i. 30, 36). Having contributed effectively to found it, he long helped to sustain its reputation by imparting his own inventions and expounding those of others.

He was well off, his mother at her death in 1643 having left him a substantial estate in Kent, and the course pursued by him in politics, although devious, does not appear to have been dishonest. He gave evidence against Archbishop Laud in 1644 (, Canterburies Doome, 1646, p. 73), but in 1648 signed the remonstrance against the king's execution, and in 1649 the ‘Serious and Faithful Representation.’ ‘Oliver had a great respect for him,’ according to Anthony Wood, and he showed it by appointing him in 1649 Savilian professor of geometry in the university of Oxford, of which he was incorporated M.A. from Exeter College in the same year. He further took a degree of D.D. on 31 May 1654, confirmed by diploma on 25 June 1662. His succession in 1658 to Gerard Langbaine the elder [q. v.] as keeper of the university archives, elicited Henry Stubbe's hostile protest, ‘The Savilian Professor's Case stated’ [see or, (1632–1676)]. In 1653 Wallis deposited in the Bodleian Library a partial collection of the letters deciphered by him, with an historical preface, published by John Davys in 1737 in his ‘Essay on the Art of Decyphering.’ Wallis was afterwards accused by Prynne and Wood of having interpreted the correspondence of Charles I captured at Naseby; but ‘he had this in him of a good subject, that at this time, in 1645, he discovered nothing to the rebels which much concerned the public safety, though he satisfied some of the king's friends that he could have discovered a great deal’ (Life of Dr. John Barwick, p. 251). That this was his plan of action he himself expressly states in a letter to Dr. John Fell [q. v.], dated 8 April 1685; and the details of the services rendered by him in this line to the royal cause during some years before the Restoration were doubtless authentically known to Charles II. He was accordingly confirmed in his posts in 1660, was nominated a royal chaplain, and obtained an appointment among the divines commissioned in 1661 to revise the prayer-book.

Wallis published, in 1643, ‘Truth Tried; or Animadversions on the Lord Brooke's Treatise on the Nature of Truth.’ The perusal in 1647 of Oughtred's ‘Clavis Mathematicæ’ may be said to have started his mathematical career, and his genius took its special bent from Torricelli's writings on the method of indivisibles. Applying to it the Cartesian analysis, Wallis arrived at the new and suggestive results embodied in his ‘Arithmetica Infinitorum’ (Oxford, 1655), the most stimulating mathematical work so far published in England. Newton read it with delight when an undergraduate, and derived immediately from it his binomial theorem. It contained the germs of the differential calculus, and gave, ‘in everything but form, advanced specimens of the integral calculus’ (, in the Penny Cyclopædia). The famous value for π, here made known, was arrived at by the interpolation (the word was of his invention) of terms in infinite series. In the matter of quadratures, first by him investigated analytically, Wallis generalised with consummate skill what Descartes and Cavalieri had already done. The book promptly became famous, and raised its author to a leading position in the scientific world.

He prefixed to the ‘Arithmetica Infinitorum’ a treatise in which analysis was first applied to conic sections as curves of the second degree. In a long-drawn controversy, begun in 1655, he exposed the geometrical imbecility of Thomas Hobbes [q. v.] It excited much public interest; but after the death of his adversary, Wallis declined to reprint the scathing pamphlets he had directed against him while alive (cf. Works, ed. Molesworth, 1839–45, passim). A numerical problem sent to him by the