French mathematician Fermat led to a correspondence, in which Lord Brouncker, Sir Kenelm Digby, Frénicle, and Schooten took part, published under the title ‘Commercium Epistolicum’ (Oxford, 1658). In a tract, ‘De Cycloide,’ issued in 1659, Wallis gave correct answers to two questions proposed by Pascal, and treated incidentally of the rectification of curves. His ‘Mathesis Universalis’ (Oxford, 1657) embodied the substance of his professorial lectures.
In 1655 Christian Huygens sent to the Royal Society a cryptographic announcement of his discovery of Titan. Wallis retorted with an ingenious pseudo-anagram, capable of interpretation in many senses, which eventually enabled him to claim for Sir Paul Neile and Sir Christopher Wren anticipatory observations of the new Saturnian satellite. Huygens surrendered his priority in all good faith, but was irritated to find that he had been taken in by a practical joke. ‘Decepisse me puto si potuisset,’ was his private note on Wallis's letter to him of 17 April 1656. One dated 1 Jan. 1659 gave at last the requisite explanation (Œuvres Complètes de Christiaan Huygens, i. 335, 396, 401, ii. 306). Wallis was partial to his countrymen. In his ‘History of Algebra’ he attributed to Thomas Harriot [q. v.] much that belonged to Vieta. This narration, the first of its kind, made part of his ‘Treatise on Algebra’ (London, 1685). Roger Cotes [q. v.] said of the volume: ‘In my mind there are many pretty things in that book worth looking into’ (Correspondence of Newton and Cotes, ed. Edleston, p. 191).
Wallis's ‘Grammatica Linguæ Anglicanæ’ (Oxford, November 1652) has been tacitly commended by many imitators, and often reprinted. To it was appended a remarkable tract, ‘De Loquela,’ describing in detail the various modes of production of articulate sounds. The study led him to the invention of a method for imparting to deaf-mutes the art of speech. ‘I am now upon another work,’ he wrote to Robert Boyle on 30 Dec. 1661, ‘as hard almost as to make Mr. Hobbes understand a demonstration. It is to teach a person deaf and dumb to speak’ (Boyle, Works, vi. 453). His patient was a youth named Daniel Whalley, exhibited in 1663 as a triumph of the novel curative process before Charles II, Prince Rupert, and the Royal Society. His next success was with Alexander, son of Admiral Edward Popham [q. v.], previously experimented upon by Dr. William Holder [q. v.] Their respective shares in his instruction occasioned some dispute.
On 26 Nov. 1668 Wallis laid before the Royal Society a correct theory of the impacts of inelastic bodies, based upon the principle of the conservation of momentum (Phil. Trans. iii. 864). It was more fully expounded in his ‘Mechanica,’ issued in three parts, 1669–71, the most comprehensive work on the subject then existing. Wallis's ‘De Æstu Maris Hypothesis Nova,’ appeared in 1668. The essential part of the tract had been communicated to the Royal Society on 6 Aug. 1666 (ib. ii. 263, see also iii. 652, v. 2061, 2068). It is worth remembering chiefly for the sagacious assumption made in it that the earth and moon may, for purposes of calculation, be regarded as a single body concentrated at their common centre of gravity.
After the Revolution, Wallis was employed as decipherer, on behalf of William III, by Daniel Finch, second earl of Nottingham [q. v.] Some of the correspondence submitted to him related to the alleged supposititious birth of the Prince of Wales (James III). On one of these letters he toiled for three months, on another for ten weeks; and he wrote piteously to Nottingham asking for ‘some better recompense than a few good words; for really, my lord, it is a hard service, requiring much labour as well as skill’ (Monthly Magazine, 1802, vols. xiii. xiv.). Consulted in 1692 about the adoption of the Gregorian calendar, he strongly discountenanced the step, mainly on the ground that it would imply subserviency to Rome; and his authority prevailed.
At Sir Paul Neile's on 16 Dec. 1666, Samuel Pepys met ‘Dr. Wallis, the famous scholar and mathematician; but he promises little.’ The acquaintance, however, continued, and Wallis wrote to Pepys, after the lapse of thirty-five years: ‘Till I was past fourscore years of age, I could pretty well bear up under the weight of those years; but since that time, it hath been too late to dissemble my being an old man. My sight, my hearing, my strength, are not as they were wont to be’ (Pepys, Diary, ed. Braybrooke, v. 399). He died at Oxford on 28 Oct. 1703, aged 86, and was buried in St. Mary's Church, where his son placed a mural monument in his honour.
A full-length portrait of him in his robes was painted in 1701 by Kneller, who was sent to Oxford by Pepys for the purpose. Designed as a gift to the university, it was hung in the gallery of the schools, where it remains. Kneller declared to Pepys: ‘I never did a better picture, nor so good an one in my life, which is the opinion of all as has seen it.’ Wallis expressed his gratitude
