WALLIS, Rev. JOHN, D.D., a very eminent English mathematician, was the eldest son of the rev. John Wallis, incumbent of Ashford in Kent, and was born there, Nov. .23, 1616. He was brought up with a view to the church, and was educated for his pro fession, to the strict exclusion of all other branches of knowledge, in accordance with the prevailing practice of the time, which was in his case carried to such an extent that even ordinary arithmetic was wholly neglected. Wallis never saw a hook of arithmetic till he was 15 years old, and then only by accident, At the age of 16, lie was entered at Emmanuel college, Cambridge, where at that time mathematics found no place in the course of study, being esteemed merely mechanical. After a brilliant career, he took his degree, was chosen a fellow of queen's, and took orders in 1640. On the outbreak of the civil war, he sided with the parliament, and was of great use to his party in deciphering intercepted correspondence, an art in which like Vita (q.v.) and Battista in Porta, he was eminent. In 1644, he was one of the secretaries of the assembly of divines at Westminster, holding at that time the living of St. Gabriel, Fenehurch street; and. in the following year, he joined with other eminent men in the establishment of the meetings for mutual instruction, which,' 17 years afterward, developed into the royal society. It was not till 1647 that he commenced the study of mathematics; and, in 1649, he was chosen Savilian professor of geometry'at Oxford. The rapid progress he had made in his mathematical studies was evidenced by the publication of his greatest work, the Arithmetica. Infinitorum, with a treatise on conic sections prefixed, in 1655 In the .samcycar commenced his well-known controversy with Hobbes—regarding a qualrature of the circle, which the latter believed he had effected—which was contin ued at intervals till 1663, and was marked by the usual quaint caustic satire of the time. Wallis had, of course, the right side of the dispute; but unfortunately for posterity, his manly feeling of forbearance toward a deceased antagonist (Hobbes died in 1679) pre vented him from admitting his polemical treatises into the collection of his works, which was published 1693-99. Numerous other mathematical works, as the MUthesis Unirer sails (1657). Commercium Epistolicum (1658), Cane-GI/tams (1663), De Proportionitms (1663), De 2Estu Mains (1668), a treatise on mechanics (1669, 1670, 1671), editions of the works of Horrocks (1673), of the arenarius and quadrature of Archimedes (1676), and of Ptolemy's harmonics (1680), a treatise on algebra (1685), and edition of Aristarchus and of Pappus (1f88), etc., were the products of his originality and industry. We have besides numer
ous minor theological works, polemical and expository, from his pen, none of which, however, are important enough to call for mention... Of his other works, the treatise on logic (1687) is of the highest excellence, and even at the present day is well worthy of perusal; and his English grammar (1653), written in Latin for the use of foreigners, has only of recent years, when the true principles of grammar are becoming better under stood, received the attention it merits. About 1658, Wallis joined the party who were in favor of it restoration of kingly government, and his talent for deciphering was now put in practice against his former friends, an act for which he has been abused with vir ulent injustice. At the restoration he was confirmed in his professorship, was appointed keeper of the archives at Oxford, and royal chaplain. In 1692, he was consulted as to the adoption of the Gregorian calendar, and his strong disapproval decided the govern ment to retain the old style. He died Oct. 28, 1703.
It is exclusively as a mathematician that 1Vallis's name has obtained pemanently a niche in the temple of fame; though as an expositor of the cardinal doctrines of Chris tianity he was fully on a par with Ninth and Sherlock; but his eminence in the former character has thrown into shade even his services as a scholar, and few at the present time remember that it was he who first edited the musical works of Ptolemy, Porphy rius, Aristarchus of Samos, and the later work of Briennius, though the manner in which these labors were effected indicates unquestionably an immense expenditure of labor, and a high degree of scholarship. His Arithmetica Infinitorum is a successful attempt to solve, by means of the suminatiou of series to infinity, a number of the more simple problems of the calculus, such as the evaluation of all cases e.the; and, in extension, to discover the limit which the quadrature of the circle is a particular case. There are numerous other results, which are, at the present time, con sidered to belong to the more advanced stages of the calculus; and, in fact, Wallis is another example of the strange blindness which, in full possession of a principle, neg lects to suit it with a generalized form of expression. The best known of WAWA results is his formula for it, which gives 2.4.4.6.6.8..• ad infinitum, 3.3.5,5.7.7....