tried to his friends, who now were desirous to bring the matter to the test. Accordingly he was persuaded to employ his skill on one Daniel Whalley of Northampton, who had been deaf and dumb from a child. About January, 1661-2, he began to teach this person, and with such success, that in little more than a year, he taught him to pronounce distinctly even the most difficult words, and to express his mind in writing. He was likewise able to read distinctly the greater part of the Bible, could express himself intelligibly in ordinary affairs, understand letters written to him, and write answers to them, if not elegantly, yet so as to be understood. This being known, attracted the curiosity of the public in no common degree. Whalley was brought to the Royal Society, May the 21st, 1662, and to their great satisfaction, pronounced distinctly enough such words as were proposed to him by the company; and though not altogether with the usual tone or accent, yet so as easily to be understood. He did the like several times at Whitehall in the presence of his majesty, prince Rupert, and others of the nobility; and the doctor was desired to try his skill on Alexander Popham, esq. a son of lady Wharton, by her former husband, admiral Popham. His mother, it is said, when she was big with him, received a sudden fright, in consequence of which his head and face were a little distorted, the whole right side being somewhat elevated, and the left depressed, so that the passage of his left ear was quite shut up, and that of the right ear proportionally distended and too open. However Dr. Holder says, that he was not so deaf, but that he could hear the sound of a lute string, holding one end of it in his teeth; and when a drum was beat fast and loud by him, he could hear those, who stood behind him, calling him gently by his name. When he was of the age of ten or eleven years, he was recommended to the care of Dr. William Holder, then rector of Blechindon in Oxfordshire, and taken by him into his house in 1659, where he learned to speak and pronounce his name, and some other words. Of this Wood gives us the following account; that Dr. Holder "obtained a great name for his most wonderful art in making a young gentleman, Alexander Popham, who was born deaf and dumb, to speak; that he was the first that is remembered ever to have succeeded therein in England, or perhaps in the world; and because it was a wonderful matter, many curious scholars went from Ox

ford to see and hear the person speak," However this be, three years after, viz. in 1662, this young gentleman was sent by his relations to Dr. Wallis, for him to teach him to speak, as he had taught Mr. Whalley. Wood owns, that Mr. Popham being called home by his friends, he began to lose what he had been taught by Dr. Holder. And Dr. Wallis observes, that both Mr. Whalley and Mr. Popham, notwithstanding the proficiency they had made under him in learning to speak, were apt to forget, after their departing from him, much of that nicety, which before they had, in the distinct pronouncing some letters, which they would recover, when he had been occasionally with them to set them right, they wanting the help of an ear to direct their speaking, as that of the eye directs the hand in writing. "For which reason," says he, "a man, who writes a good hand, would soon forget so to do, if grown blind. And therefore one, who thus learns to speak, will, for the continuance and improvement of it, need somebody continually with him, who may prompt him, when he mistakes." Dr. Wallis remarks likewise, that Dr. Holder had attempted to teach Mr. Popham to speak, "but gave it over.". This seems very likely to be true, because his friends did not send him again to Dr. Holder, but desired Dr. Wallis to teach him. However that be, a dispute took place between the two doctors. A letter of Dr. Wallis concerning this cure was inserted in the "Philosophical Transactions" of July 1670. This was represented, as if he had vainly assumed to himself the glory of teaching this young gentleman to speak, without taking any notice of what had been before done to him by Dr. Holder, who therefore published in 1678 at London in 4to, "A Supplement to the Philosophical Transactions of July 1670, with some Reflections op Dr. Wallis's Letter there inserted." To this Dr. Wallis replied the very same year, entitling his papers, which were directed to the lord viscount Brouncker, president of the Royal Society, "A Defence of the Royal Society, and the Philosophical Transactions, particularly those of July 1670, in answer to the Cavils of Dr. William Holder," London, 1678, in 4to. To this Dr. Holder made no reply. The reverend and learned Mr. John Lewis of Mergate observes, in a MS life by him of Dr. Wallis, communicated to the authors of the General Dictionary, "that without lessening Dr. Holder's great abilities, it is a plain and certain fact, that Dr. Wallis had, in his tract

De Loquela,' discovered the theory of this by considering very exactly, what few attended to, the accurate formation of all sounds in speaking; without which it were in vain to set about this task. This tract was printed no less than six years before Dr. Holder undertook to try his skill of teaching a dumb man to speak on Mr. Popham. And it is no disingenuous reflection to suppose, that Dr. Holder had seen it, and profited by it; whereas it does not appear, that Dr. Wallis could have the least hint from him, when he at first taught Mr. Whalley. But Wood, to shew how just and equitable a judge he was of this difference, tells us, that he knew full well, that Dr. Wallis at any time could make black white, and white black, for his own ends, and had a ready knack of sophistical evasions. Base reflections, which confute themselves, and expose their inventor!" However, Dr. Wallis published his method of instructing persons deaf and dumb to speak and understand a language, which was printed in the Philosophical Transactions. And "I have," says he, "since that time, upon the same account, taught divers persons (and some of them very considerable) to speak plain and distinctly, who did before hesitate and stutter very much; and others to pronounce such words or letters, as before they thought impossible for them to do, by teaching them how to rectify such mistakes in the formation, as by some impediment or acquired customs they had been subject to."

Dr. Wallis had become one of the first members of the Royal Society, and was a very considerable contributor to their early stock of papers, particularly on mathematical subjects. In 1663, at the request of sir Robert Moray, he wrote his "Cono-cunæus, or Shipwright's circular wedge," and a treatise "De Proportionibus," in vindication of Euclid's definition in the fifth book of his Elements. This he dedicated to lord Brouncker, with whom he lived in the most friendly communication of studies till his lordship's death. In the same year, he gave the first demonstration of that most important and useful problem, concerning "the laws of motion in the collision of bodies." In 1666, he framed a new hypothesis to solve the phænomena of the tide, of which no tolerable account had then appeared. This, after further investigation, he published in 1668, under the title of "De Estu maris hypothesis nova;" and the next year, the first part of his treatise "De motu," which was generally esteemed his master-piece. The whole

was completed in 1671, under the title of "Mechanica, sive de motu tractatus geometricus." In 1673, he published in Latin "Horoccii opera posthuma" (see HORROX), to which he subjoined Flamsteed's "Discourse of the equation of time." He also employed some of his leisure hours in correcting, for his own private use, and supplying the defects found in all the manuscript copies of Archimedes's "Arenarius et Dimensio Circuli." This he printed in 1676, at dean Fell's request, to convince the public of the necessity of publishing a collection of the ancient mathematicians; a scheme which, a few years before, had been dropped for want of encouragement.

About this time, the university having determined to publish an Oxford Almanack, their right to do so was disputed by the Company of Stationers. Dr. Wallis was entrusted with the management of the suit, which was finally determined in favour of the university. In 1680, he published, from the best manuscripts, "Claudii Ptolemæi opus harmonicum," Gr. et Lat. with notes; to which he afterwards added an appendix, "De veterum harmonica ad hodiernum comparata," as also "Porphyrii in harmonica Ptolemæi Commentarius," &c. In 1684, he published his "Algebra," in English, containing the history of that art, and the successive improvements, from its first appearance in Europe to his own invention of the "Arithmetic of Infinites ;" to which he afterwards added the infinitesimal method of Leibnitz, and that of fluxions by sir Isaac Newton. In the following year he published three dissertations, on Melchisedeck, Job, and the titles of the Psalms. In 1687, his "Institutio Logica" appeared; and nearly about the same time he edited "Aristarchus Samius de magnitudine solis et lunæ," with "Pappi libri secundi collectionum mathematicorum hactenus desiderati fragmentum.' In the same year, 1689, he wrote a letter to sir Samuel Morland at Utrecht, proving, in at least fifty instances, how much Des Cartes borrowed his pretended improvements in Algebra from our countryman Harriot; and this charge, our readers may recollect, has been more recently confirmed. (See HARRIOT.)

In 1690, he published "The doctrine of the Blessed Trinity briefly explained;" on which he received a written

This work is highly praised by the subject, the late Dr. Burney, in one of the most competent judges of his History of Music, vol. I. p. 126.

letter, subscribed IV. J. with the post-mark September 23, returning him thanks for his book. This letter he printed, and in answer to it published a second letter dated September 27, 1690, and afterwards a third, dated October 28, 1690. Before this third letter was published there came out a pamphlet, entitled "Dr. Wallis's Letter touching the doctrine of the Blessed Trinity answered by his Friend." This occasioned the doctor to add a postscript dated November the 15th, 1690. Soon after came out a tract, entitled "An Answer to Dr. Wallis's three letters," and another entitled "The Arian's Vindication of himself against Dr. Wallis's fourth letter on the Trinity." This produced a fifth letter of the doctor's on the same subject, dated February 14, 1690-1. "Observations" were likewise made on these four letters concerning the Trinity and Creed of Athanasius. This induced the doctor to write a sixth letter, dated March the 14th, 1690-1. W. J. wrote the doctor a second letter, which was answered by the doctor in a seventh letter, who likewise published three sermons, on John xvii. 3. and afterwards an eighth letter, dated November the 23d, 1691.

He had also a controversy on infant-baptism, which occasioned his writing a tract "De Pædobaptismo"; and another on the Sabbath, with Thomas Bampfield, a counsellor at law, who, in 1691, published a work to prove that the Sabbath should be observed on Saturday rather than on Sunday. In answer to this Dr. Wallis produced his "Defence of the Christian Sabbath," 1692, two editions of which were quickly sold. Bampfield wrote a reply, to which Dr. Wallis rejoined, and there the dispute ended.

The last affair in which Dr. Wallis appears to have been consulted was on the scheme for altering the style, which he opposed on various reasons, and it was accordingly laid aside; but has since been established without any of the inconveniences either in astronomical calculations, or otherwise, of which he was afraid. Towards the end of his life the curators of the university-press made a collection of his mathematical works, which were printed at Oxford 1699, in three volumes in folio, with this title, "Johannis Wallis S. T. P. Geometriæ Professoris Saviliani in celeberrimâ Academiâ Oxoniensi, Opera Mathematica, tribus Voluminibus contenta." This edition was dedicated to king William III.