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stood, capable of reformation for the better in divers things, yet to engage indefinitely against all prelacy, they would not agree. After many days debate on this point (as I understood from those who were then present) some of the parliament, who then pressed it, suggested this expedient, that by prelacy they did not understand all manner of episcopacy or superiority, but only the present episcopacy, as it now stood in England, consisting of archbishops, bishops, and their several courts and subordinate officers, &c. And that if any considerable alteration were made in any part of this whole frame, it was an abolition of the present prelacy, and as much as was here intended in these words; and that no more was in. tended but a reformation of the present episcopacy in England. And in pursuance of this it was agreed to be expressed with this interpretation; prelacy, that is, church government by archbishops, bishops, their chancellors and commissaries, deans, deans and chapters, arch-deacons, and all other ecclesiastical officers depending on that hierarchy. And with this interpretation at length it passed; and the Scots commissioners in behalf of their church agreed to those amendments. I know some have been apt to put another sense upon that interpretation; but this was the true intendnient of the assembly, and upon this occasion.”

Some of these sentiments belong not only to the assembly, but to our author; and, as he retained them to the last, were probably the cause of his having so little preferment afterwards when he was a favourite at court, and much em, ployed as a decypherer.

In March of this year, 1644, he married Susanna, daughter of John and Rachel Glyde of Northiam, Northamptonshire. In 1645, the weekly meetings, which gave birth to the Royal Society, being proposed, he attended them along with Dr. John Wilkins (afterwards bishop of Chester), Dr. Jonathan Goddard, Dr. George Ent, Dr. Glisson, Dr. Merret, doctors in physic, Mr. Samuel Foster, then professor of astronomy at Gresham college, Theodore Haak, a German of the palatinate, and then resident in London, who is said to have first suggested those meetings, and many others. These meetings were held sometimes at Dr. Goddard's lodgings in Wood-street, sometimes in Cheapside, and sometimes at Gresham college, or some place near adjoining.

In 1647, he happened to meet with Oughtred's “Clavis," of which be made himself master in a few weeks, and dis-,

mate, aveled the ti somes in Chi

covered a new method of resolving cúbic equations, which he communicated to Mr. Smith, professor of mathematics at Cambridge, with whom he held a literary correspondence upon mathematical subjects for some years. The Independents having now acquired the superiority, our author joined with some other ministers of London, in subscribing a paper, entitled “A testimony to the truth of Jesus Christ, and to the solemn league and covenant: as also against the errors, heresies, and blasphemies of these times, and the toleration of them.” Not long after this, he exchanged St. Gabriel Fenchurch-street, for St. Martin's Ironmonger-lane; and in 1643, subscribed, as minister of that church, to the remonstrance against putting the king to death; and to a paper entitled “A curious and faithful representation of the judgments of ministers of the Gospel within the province of London, in a letter from them to the General and his Council of War.” Dated Jan. 17, 1648. .

Notwithstanding this opposition to the ruling powers, he was in June following appointed by the parliamentary visitors, Savilian professor of geometry at Oxford, in room of Dr. Peter Turner, who was ejected; and now quitting his church, he went to that university, entered of Exeter college, and was incorporated master of arts. Acceptable as this preferment was, he was not an inattentive observer of the theological disputes of the time; and when Baxter published his “ Aphorisms of Justification and the Covenant,” our author published some animadversions on them, which Baxter acknowledged were very judicious and moderate. Before the end of this year, Wallis, in perusing the mathematical works of Torricelli, was particularly struck with what he found there of Cavalleri’s method of indivisibles, this being the first time he had heard or seen any thing of that method, and conceived bopes of attaining by it some assistance in the problem concerning the quadrature of the circle. He accordingly spent a very considerable time in studying it, but found some insuperable difficulties, which, with what he had accomplished, he communicated to Mr. Seth Ward, then Savilian professor of astronomy, Rook, professor of astronomy at Gresham college, and Christopher Wren, then fellow of All Souls, and several other eminent mathematicians at that time in Oxford, but not meeting with the assistance he wished, he desisted from the farther pursuit.

In 1653, he published a grammar of the English tongue, for the use of foreigners in Latin, under this title: “Grammatica Linguæ Anglicanæ, cum Tractatu de Loquela seu Sonorum Formatione,” in 8vo. In the piece “ De Loquela,” &c. he tells us, that “he has philosophically considered the formation of all sounds used in articulate speech, as well of our own as of any other language that he knew; by what organs, and in what position, each sound was formed; with the nice distinctions of each, which in some letters of the same organ are very subtle : so that by such organs, in such position, the breath issuing from the lungs wiil form such sounds, whether the person do or do not hear himself speak." This we shall find he afterwards endeavoured to turn to an important practical use. In 1654, he was admitted to the degree of D.D. after per. forming the regular exercise, which he printed afterwards, and in August of that year, made some observations on the solar eclipse, which happened about that time. About Easter, 1655, the proposition in his “Arithmetica Infinitorum,” containing the quadrature of the circle, being printed, he sent it to Mr. Oughtred; and soon after, in the same year, be published that treatise in 4to, dedicated to the same eminent mathematician. To this he prefixed a treatise on conic sections, which he set in a new light, considering them as absolute planes, constituted of an infinite number of parallelograms, without any relation to the cone, and demonstrated their properties from his new method of infinites.

About the same time, Hobbes published his “Elementorum Philosophiæ sectio prima, de corpore,” in which he pretended to give an absolute quadrature of the circle. This pretence Dr. Wallis confuted the same year, in a Latin tract, entitled “ Elenchus Geometria liobbianæ;" which being written with some asperity, so provoked Hobbes, that in 1656 he published it in Englisb, with the addition of what be called “Sir Lessons to the Professors of Mathematics in Oxford,” 4to. Upon this Dr. Wallis wrote an answer in English, entitled, “ Due Correction for Mr. Hobbes; or, School Discipline for not saying his Lessons right," 1656, in 8vo; to which Mr. Hobbes replied in a pamphlet, with the title of “ ETILMAI, &c. or, Marks of the absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms, of John Wallis,” &c. 1657, 4to. This was immediately rejoined to by Dr. Wallis in “ Hobbiani Puncti Dispunctio,” 1657; and here this controversy seems to have ended at this time : but four years after, 1661, Mr. Hobbes printed “ Examinatio & emendatio Mathematicorum hodiernorum, in sex Dialogis ;" which occasioned Dr. Wallis to publish, the next year, “ Hobbius Heautontimorumenos," in 8vo, addressed to Mr. Boyle. Although Dr. Wallis was universally allowed to have the best of the argument in this controversy, Hobbes being notoriously deficient in mathematical science, yet none of his answers to Hobbes were inserted in the collection of his mathematical works, published in 1699, 3 vols. fol. because, as he says bimself, he had no inclination to trample on the ashes of the dead, although it was his duty to expose the fallacious reasoning of Hobbes when alive *.

In 1656 he published a work on the angle of contact, in which he exposes the opinion of Peletarius. In the following year, having completed his plan of lectures, he published the whole, in two parts, under the title of “Mathesis Universalis, sive Opus Arithmeticum.” While this was in the press, he received a challenge from Mr. Fermat of Toulouse, which engaged him in an epistolary dispute with that gentleman, as well as with Mr. Frenicle of Paris. The problem was “ Invenire cubum, qui additis omnibus suis partibus aliquotis conficiat quadratum.” This chal. lenge had been sent by Fermat to Frenicle, Schooten, and Huygens. Dr. Wallis sent a solution of it before the end of March, which being objected to both by Frenicle and Fermat, occasioned a dispute which was carried on this year and part of the dext, after which both these gentlemen acknowledged the sufficiency of Wallis's solution, with the encomium of being the greatest mathematician in Europe. Wallis, however, having heard that Frenicle was about to publish the correspondence, and being, from some circumstances in his conduct, a little suspicious of misrepresentation, requested sir Kevelm Digby, then at Paris, through whose hands the whole had passed, to give his consent to the publication of it by the doctor himself, which being readily granted, it appeared in 1658, under the title of Commercium Epistolicum.”

In the same year, on the death of Dr. Gerard Langbaine, Dr. Wallis was chosen to succeed him in the place of

* See an amusing account of this controversy in Mr. D'Israeli's “Quarrels of Authors," vol. II.

“ Custos Archivorum” to the university. But he was not elected to this office without some struggle. Dr. Richard Zouch, a learned civilian, who, as his friend Mr. Henry Stubbe represents the case, had been an assessor in the vice chancellor's court for thirty years and more, and was well versed in the statutes, liberties, and privileges of the University, stood in opposition to our author. But the election being carried for Dr. Wallis, provoked Mr. Stubbe, a great admirer of Mr. Hobbes, to publish a pamphlet entitled, “ The Savilian Professor's Case stated :" London, 1658, in 4to. Dr. Wallis replied to this; and Mr. Stubbe republished his case with enlargements, and a vindication of it against the exceptions of Dr. Wallis. Anthony Wood, who is inveterately prejudiced against Dr. Wallis *, gives a suitable misrepresentation of this affair. In July of the same year (1658) he received a letter from sir Kenelm Digby, in which were contained two prize questions proposed by M. Pascal, for squaring and finding the gravity of some sections of the cycloid; and though he had never before considered that curve, yet he sent a solution to both the questions, but too late, it would appear, according to the time fixed at Paris, for him to receive the prizes. This however occasioned his publishing in 1659, a letter “ De Cissoide et corporibus inde genitis."

It appears that just before the restoration, he had done considerable service to the royal caụse by his art of decyphering, and on that event, Charles II. received him very graciously, and he was not only confirmed in both his places, of Savilian professor, and keeper of the archives, but likewise was made one of the king's chaplains in ordinary.. In 1661 he was one of the divines who were appointed to review the book of Common Prayer. He afterwards complied with the terms of the act of uniformity, and continued a steady conformist to the church of England until bis death.

We have already mentioned his Grammar of the English tongue, published in 1653. By some observations in that work, he had been led to suppose it possible to teach the deaf and dumb to speak. On this it is probable he had made many experiments; and communicated what he had

* This appears to have been the case with Aubrey too, who gives some very ill-founded reports of Dr. Wallis. Slubbe's pamphlet, it may be added,

gave such general dislike, that he was compelled to write and pronounce a sort of recantation in the convocation,

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