Wallis, John

, an eminent English mathematician, was born Nov. 2S, 1616, at Ashford in Kent, of which place his father of the same names was then minister,*


Mr. Wallis was son of Robert Ellen Wallis of Thingdon (or, as it is usually proounced, Fyenden) in the county of Northampton, and was born there in January 1587, and baptized the 18th of that month. He was educated in Trinity college in Cambridge, where he took the degrees of B. A. and M. A. and about the same time entered into holy orders, in the reign of queen Elizabeth. Toward the end of that queen’s reign he was made minister of Ashford, a market-town in Kent, where he continued the remainder of his life in great esteem and reputation, not only in that town and parish, but with the clergy, gentry, and nobility, round about. “He was,” says Dr. Wallis, “a pious, prudent, learned, and orthodox divine, an emiBent and diligent preacher; and with his prudent carriage kept that great town in very good order, and promoted piety to a great degree. Beside his preaching twice on the Lord’s Day, and and other occasional sermons, and his catechising and otherwise instructing: the younger sort, he did, with some of the most eminent neighbouring ministers, maintain a week-day lecture, on Saturday, their market-day which was much frequented, beside a numerous auditory of others, by very many of the neighbour-ministers, the justices of the peace, and others of the gentry who after sermon did use to dine at an. ordinary, and there confer, as there was occasion, about such affairs as might concern the welfare and good government of that town and the parts adjacent, wherein they ere respeclively concerned.” He died at Ashford November 30, and was buried December 3, 1622. By his wife Joanna, daughter of Henry and Sarah Chapman of fJodmersham in Kent, he had three sons: John, the eldest, the subject of this article, Henry and William; and two daughters, Sarah and Ellen.

but did not survive the birth of this his eldest son above six years. He was now left to the care of his mother, who purchased a house at Ashford for the sake of the education of her children, and placed him at school there, until the plague, which broke out in 1625, obliged her to remove him to Ley Green, in the parish of Tenterden, under the tuition of one James Movat or Mouat, a native of Scotland, who instructed him in grammar. Mr. Movat, says Dr. Wallis, “was a very good schoolmaster, and his | scholar I continued for divers years, and was by him well grounded in the technical part of grammar, so as to understand the rules and the grounds and reasons of such rules, with the use of them in such authors, as are usually read in grammar schools: for it was always my affectation even from a child, in all parts of learning or knowledge, not merely to learn by rote, which is soon forgotten, but to know the grounds or reasons of what I learn, to inform my judgment as well as furnish my memory, and thereby make a better impression on both.” In 1630 he lost this instructor, who was engaged to attend two young gentlemen on their travels, and would gladly have taken his pupil Wallis with them; but his mother not consenting on account of his youth, he was sent to Felsted school in Essex, of which the learned Mr. Martin Holbeach was then master. During the Christmas holidays in 1631, he went home to his mother at Ashford, where finding that one of his brothers had been learning to cypher, he was inquisitive to know what that meant, and applying diligently was enabled to go through all the rules with success, and prosecuted this study at spare hours on his return to Felsted, where also he was instructed in the Latin, Greek, and Hebrew tongues, and in the rudiments of logic, music, and the French language.

In 1632 he was sent to Cambridge, and admitted of Emanuel college, under the tuition first of Mr. Anthony Burgess, afterwards rector of Sutton Colfield; next of Thomas Horton, afterwards master of Queen’s college, and lastly of the celebrated Benjamin Whichcot. It is not improbable that he had his divinity from the first two, and somewhat of his style from the last of these tutors. At his first entrance upon academical studies, he was reconciled to having staid a year or two longer at school than appeared necessary, or than he liked, since he found that owing to the knowledge he had accumulated in that time, he was now able to keep pace with those who were some years his seniors. “I found,” he says, “that beside the improvement of what skill I had in Latin, Greek, and Hebrew languages (which I pursued with diligence) and other philologic studies, my first business was to be the study of logic. In this I soon became master of a syllogism, as to its structure and the reason of its consequences, however cryptically proposed, so as not easily to be imposed on by fallacious or false syllogisms, when I was to answer or defend; | and to manage an argument with good advantage, when I was to argue or oppose; and to distinguish ambiguous words or sentences, as there was occasion; and was able to hold pace with those, who were some years my seniors, and had obtained the reputation of a good disputant. And indeed I had the good hap all along, both at school and in the university, to be reputed (if not equal) not much inferior to those of the best of my rank. From logic I proceeded to ethics, physics, and metaphysics (consulting the schoolmen on such points), according to the methods of philosophy then in fashion in that university. And I took into the speculative part of physic and anatomy, as parts of natural philosophy; and, as Dr. Glisson (then public professor of physic in that university) hath since told me, I was the first of his sons, who, in a public disputation, maintained the circulation of the blood, which was then a new doctrine, though I had no design of practising physic. And I had then imbibed the principles of what they now call the new philosophy; for I made no scruple of diverting from the common road of studies then in fashion to any part of useful learning; presuming that knowledge is no burthen; and, if of any part thereof I should afterwards have no occasion to make use, it would at least do me no hurt; and what of it I might or might not have occasion for, I could not then foresee. On the same account I diverted also to astronomy and geography, as parts of natural philosophy, and to other parts of mathematics; though at that time they were scarce looked upon with us as academical studies then in fashion. As to divinity, on which I had an eye from the first, I had the happiness of a strict and religious education all along from a child. Whereby I was not only preserved from vicious courses, and acquainted with religious exercises, but was early instructed in the principles of religion and catechetical divinity, and the frequent reading of scripture and other good books, and diligent attendance on sermons: and whatever other studies I followed, I was careful not to neglect this: and became timely acquainted with systematic and polemic divinity, and had the repute of a good proficient therein.” The length of this extract we trust will be excused, as it is but seldom we attain that interesting part of biography, the progress of early studies.

Soon after his admittance into Emanuel college, he was chosen of the foundation, and admitted a scholar of the | house, but by the statutes he was incapable of a fellowship, it being provided that there should not be more than one fellow of the same county at the same time, and there was already one of the county of Kent, Mr. Wellar, who continued in the college long after Mr. Wallis left it. Wallis, however, was so highly esteemed by the society, that when he declared his design of leaving the college, Dr. Richard Holdsworth, then master, and the fellows, had a consultation about founding a new fellowship on his account, that he might not remove from them. But the times growing confused, there was no room for executing such a design, and Mr. Wail is removed to Queen’s college in Cambridge, where he was chosen fellow, and continued so, till by his marriage he vacated his fellowship. In Hilary term 1636-7, he took the degree of bachelor of arts, and about four years after that of master; and then removed to Queen’s, probably in consequence of the interest of Dr. Horton, his former tutor, and now master of that college.

Being designed for the church, he had studied divinily with great care, and now was admitted to holy orders by Dr. Walter Curie, bishop of Winchester. In 1641 he left college to be chaplain to sir William Darley, at Bustercramb in Yorkshire. In the following year he acted in the same capacity to lady Vere, widow of sir Horatio Vere. It was during her occasional residence in London that he was enabled to discover his surprising talent in decypheringj and as this had an important effect on his future life and fame, it may be necessary to give his own account of the discovery. “About the beginning of our civil wars, in th* year 1642, a chaplain of sir William Waller’s, one evening as we were sitting down to supper at the lady Vere’s in London, with whom I then dwelt, shewed me an intercepted letter written in cypher. He shevyed it me as a curiosity (and it was indeed the first thing I had ever seen written in cyphers), and asked me, between jest and earnest, whether I could make any tiling of it; and he was surprized, when I said, upon the first view, perhaps I might, if it proved no more but a new alphabet. It was about ten o’clock, when we rose from supper. I then withdrew to my chamber to consider it; and by the number of different characters therein (not above 22 or 23) I judged, that it could not be more than a new alphabet, and in about two hours time, before I went to bed, I had decyphered it; and I sent a copy of it. so decyphered the next morning to | him from whom I had it. And this was my first attempt at decyphering. This unexpected success on an easy cypher was then looked upon as a great matter; and I was somewhile after pressed to attempt one of another nature, which was a letter of Mr. secretary Windebank, then in France, to his son in England, in a cypher hard enough, and not unbecoming a secretary of state. It was in numeral figures, extending in number to above seven hundred, with many other characters intermixed; but not so hard as many that I have since met with. I was backward at first to attempt it, and after I had spent some time upon it, threw it by as desperate; but after some months resumed it again, and had the good hap to master it. Being encouraged by this success beyond expectation, I afterwards ventured on many others, some of more, some of less difficulty; and scarce missed of any that I undertook for many years, during our civil wars, and afterwards. But of late years the French, methods of cypher are grown so intricate beyond what it was wont to be, that I have failed of many, tho‘ I have mastered divers of them. Of such decyphered letters there be copies of divers remaining in the archives of the Bodleian library in Oxford, and many more in my own custody, and with the secretaries of state.” The copies of decyphered letters, mentioned by Dr. Wallis to be in the archives of the Bodleian library, were reposited by him there in 1653, and are in the doctor’s own hand-writing, with a memorandum at the beginning, to this purpose: “A collection of several letters and other papers, which were at several times intercepted, written in cypher,’ decyphered by John Wallis, professor of geometry in the university of Oxford; given to the public library there,” anno domin‘t 1653. This part of our author’s skill gave him afterwards no small trouble, and might possibly have been of very bad consequences to him, had he not had some friends in power, particularly the earl of Clarendon and sir Edward Nicholas secretary of state, who valued him for his great learning and integrity, and were sensible of his affection for the royal family, and his loyalty to the king, and the many good services he had done his majesty before the restoration. The doctor’s enemies soon after the restoration eiH deavoured to represent him as an avowed enemy to the royal family; and to prove this they reported, that he had during the civil wars decyphered king Charles I.’s letters taken in his cabinet at Naseby; and that the letters so | decyphered by him were to be seen in the books of cyphers, which our author had given to the university. This report being revived upon the accession of king James II. to the crown, the doctor wrote a letter in his own vindication to his great friend Dr. John Fell, bishop of Oxford/dated April 8, 1685 which was as follows

"My Lord,

I understand there have of late been complaints made of me, that I decyphered the late king’s letters, meaning those taken in the late king’s cabinet at Naseby- fight, and after printed. As to this, without saying any thing, whether it be now proper to repeat what was done above forty years ago, the thing is quite otherwise. Of those letters and papers (whatever they were) I never saw any one of them but in print; nor did those papers, as I have been told, need any decyphering at all, either by me or anybody else, being taken in words at length just as they were printed, save that some of them were, I know not by whom, translated out of French into English. ‘Tis true, that afterwards some other letters of other persons, which had been occasionally intercepted, were brought to my han’ds; some of which 1 did decypher, and some of them I did not think fit to do, to the displeasing of some, who were then great men. And I managed my selfe in that whole busi^ ness by such measures, as your lordship, I think, would not bee displeased with. I did his majesty who then was (king Charles the first) and his ‘friends many good offices, as I had opportunity both before and after that king’s death; and ventured farther to do them service, than perhaps some, of those, who now complaine of mee, would have had the courage to do, had they been in my circumstances. And I did tp his late majesty, k. Charles the second, many good services both before and since his restauration, which himselfe has been pleased divers times to profess to mee with great kindnes. And if either my lord chancellor Clarendon, or Mr. secretary Nicholas, or his late majesty, were now alive, they would give mee a very different character from what, it seemes, some others have done. And I thinke his majesty that now is kn<Mves somewhat of it, and some other persons of honour yet -alive, &c.

In our authorities are other proofs of his innocence in this matter; but we presume it cannot be denied that he had been of service to the republican government by this peculiar talent. He had always joined with them, and in 1653 he had | the sequestered living of St. Gabriel, Fenchurch- street, granted to him. The same year he published in 4to, Truth tried; or, Animadversions on the Lord Brooke’s Treatise of the nature of Truth’.“His mother dying this year, he became possessed of a handsome fortune. In 1644 he was appointed one of the scribes or secretaries to the assembly of divines at Westminster, to whose conduct and views he gives a very different colouring from what we meet with in most of the publications of that time.” The parliament,“he asserts,” had a great displeasure against the order of bishops, or rather not so much against the order, as the men, and against the order for their sakes; and had resolved upon the abolition of episcopacy as it then stood, before they were agreed what to put instead of it; and did then convene this assembly to consult of some other form to be suggested to the parliament, to be by them set up, if they liked it, or so far as they should like it. The divines of this assembly were, for the generality of them, conformable, episcopal men, and had generally the reputation of pious, orthodox, and religious protestants; and (excepting the seven independents, or, as they were called dissenting brethren) I do not know of any nonconformist among them as to the legal conformity then required. Many of them were professedly episcopal, and, I think, all of them so episcopal, as to account a well-regulated episcopacy to be at least allowable, if not desirable and advisable; yet so as they thought the present constitution capable of reformation for the better. When I name the divines of this assembly, I do not include the Scots commissioners, who, though they were permitted to be present there, and did interpose in the debates, as they saw occasion, yet were no members of that assembly, nor did vote with them, but acted separately in behalf of the church of Scotland, and were zealous enough for the Scots presbytery, but could never prevail with the assembly to declare for it. On the other hand, the independents were against all united church government of more than one single congregation, holding that each single congregation, voluntarily agreeing to make themselves a church, and choose their own officers, were of themselves independent, and not accountable to any other ecclesiastical government, but only the civil magistrate, as to the public peace; admitting indeed that messengers from several churches might meet to consult in common, as there might | be occasion, but without any authoritative jurisdiction* Against these, the rest of the assembly was unanimous, (and the Scots commissioners with them) that it was lawful by the word of God for divers particular congregations (beside the inspection of their own pastor and other officers) to be united under the same common government; and such communities to be further subordinate to provincial and national assemblies; which is equally consistent with episcopal and presbyterian principles. But whether with or without a bishop or standing president of such assemblies, was not determined or debated by them. When any such point chanced to be suggested, the common answer was, that this point was not before them, but was precluded by the ordinance by which they sat; which did first declare the abolition of episcopacy (not refer it to their declaration), and they only to suggest to the parliament somewhat in the room of that so abolished, And this is a true account of that assembly as to this point (and when as they were called presbyterians, it was not in the sense of anti-episcopal, but anti-independents), which I have the more largely insisted on, because there are not many now living who can give a better account of that assembly than I can. To this may be objected their agreement to the covenant, which was before I was amongst them. But this, if rightly understood, makes nothing against what I have said. The covenant, as it came from Scotland, and was sent from the parliament to the assembly, seemed directly against all episcopacy, and for setting up the Scots presbytery just as among them. But the assembly could not be brought to assent to it in those terms, being so worded as, to preserve the government of the church of Scotland, and to reform that of England, and so to reduce it to the nearest uniformity. But before the assembly could agree to it, it was thus mollified, to preserve that of Scotland (not absolutely, but) against the common enemy; and to reform that of England (not so as it is in Scotland, but) according to the word of God, and the exarnpleof the best reformed churches; and to endeavour the nearest uniformity; which might be as well by reforming that of Scotland, as that of England, or of both. And whereas the covenant, as first brought to them, was against popery, prelacy, heresy, schism, profaneness, &c. they would by no means be persuaded to admit the word prelacy, as thus standing absolute. For though they thought the English episcopacy, as it then | 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 intended 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 intendment 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 employed as a decypherer.

In March of this year, 1644, he married Susanna, daughter of John and Rachel Clyde 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. Giisson, 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 he made himself master in a few weeks, and | discovered a new method of resolving cubic 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 1648, 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 hopes 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 Linguse Anglicanae, 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 will 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 performing 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, he published that treatise in 4to, dedicated to the same eminent mathematician. To this he prefixed a treatise on conic sections, which he sdtin 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 Philosophise 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 Geometrise Hobbianse; 17 which being written with some asperity, so provoked Hobbes, that in 1656 he published it in English, with the addjtion of what he called” Six 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” 2TIFMAI, &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” Hob* | biani Puncti Dispunctio,“1657; and here this controversy seems to have ended at this time: but four years after, 1661, Mr. Hobbes printed” Examinatio & emendatio Matheoiaticorum 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 or* his answers to Hobbes were inserted in the collection of his mathematical works, published in 1699, 3 vols.‘fol. because, as he says himself, 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 foU lowing 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 confieiat quadratum.” This challenge 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 next, 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 Kenelm 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.

| Gustos 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 Universit3 T 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,*

This appears to have been the case with Aubrey too, who gives some very ill-founded reports of Dr. Wallis. Stubbe’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.

gives a suitable misrepresentation of this affair. In July of the same year (1658) he received a letter from sir Kenelrn 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 solutiorr 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 hi& 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 cause 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 SaviMan 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 his 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 wade many experiments; and communicated what he had | 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 Bib!e, 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 | Oxford 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. 14 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 on 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 Roya.1 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, 1673, in 4to. To this Dr. Holder made no reply. The reverend and learned Mr. John Lewis of ?crgate 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 1“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. AndI 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-cunseus, 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 phaenoinena of the tide, of which no tolerable account had then appeared. This, after further investigation, he published in 1668, under the title of “De ystu 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 “Mechanic*, sive de motu tractatus geometric us.” In 1673, he published in Latin “Horqccii 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 t Dimensio Circuli.” This he printed in 1676, at dean Fell’s request, to-convince the public of the necessity of publish! tig 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 fjnally determined in favour of the university. In 168O, he published, from the best manuscripts, “Glaudii Ptolemsei opus harmonicum,” Gr. et Lat. with -notes; to which he afterwards added an appendix, “.De veterum harmonica ad hodiernum comparata *,” as also “P.orphyrii in harmonica Ptoleimei 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 lunae,” with “Pappi libri secundi collectionum inathematicorum 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 conhrmed. (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. Barney, in one of the most Competent judges of his Hi to; y of Music, vol. 1. p. 125.
| letter, subscribed W. 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 doctors 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 xviL 3. and afterwards an eighth letter, dated November the 23d, 139 1

He had also a controversy on infant-baptism, which occasioned his writing a tract “De Pgedobaptismo” 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. Gedmetriae Professoris Saviliani in celeberrima Academia Oxoniensi, Opera Mathematica, tribus Voluminibus -contenta.” This edition was dedicated to king William III. | Dr. Wallis died at the Savilian professor’s house in New" college lane, Oxford, Oct. 28, 1703, in his eighty-eighth year, and was interred in St. Mary’s, where a monument was erected by his son, John Wallis, esq. a barrister. This son was born December the 26th, 1650, and placed by his father in Trinity college, in Oxford, and afterwards admitted of the Inner Temple, London, where he proceeded barrister-at-law February 1, 1681-2. He married Elizabeth daughter of John and Mary Harris, of Soundels, or Soundess, by Nettlebed, in Oxfordshire, afterwards heiress to her brother Taverner Harris, whose mother descended from Richard Taverner, a learned lawyer in king Henry VlII/s time, and high sheriff of the county of Oxford. By this match Mr. Wallis became possessed of a good estate called Soundess. His wife died August the 8th, 1693, leaving three children surviving her, viz. John, Mary, and Elizabeth.

Anne, the doctor’s eldest daughter, was born June 4, 1656, and married, December 23, 1675, to John Blencow, of an ancient family at Marston St. Laurence, in Northamptonshire, then barrister-at-law, and afterwards knighted, and promoted to be one of the barons of the exchequer, and afterwards one of the justices of the king’s bench. It has been said, that the promotion of this gentleman to these honourable posts was owing to the doctor, who having excused himself on account of his age from accepting the offer of a bishopric, told his friends that he had a son-inlaw a barrister-at-law and that if they would promote him, he should be as much obliged as if he was promoted himself. The doctors daughter had by sir John seven children, viz. John, Mary, Anne, Thomas, William, Elizabeth, and Susanna, who were all living in 1696,

Elizabeth, the doctor’s youngest daughter, was born September 23, 1658, and married February 21, 1681, to William Benson, son to George and Mary Benson, of Towcester, in Northamptonshire, who dying on November 5, 1691, left her a widow without any children.

Mr. Lewis observes, that the doctor “was happy in the enjoyment of a vigorous constitution of body, and of a mind, which was strong, serene, and calm, and not soon ruffled and discomposed;” and that, “though whilst he Jived he was looked on by the most rigid and zealous partymen in the university with a jealous eye, and suspected as not thoroughly well affected to the Monarchy and Church | of England, he was yet very much honoured and esteemed by others of a better temper and judgment, and of more knowledge and larger thoughts. By these, both at home and abroad, was he reckoned the glory and ornament of his country, and of the university in particular.” In this character his talents are certainly not over-rated. It is therefore with some surprize that we perceive him slightly noticed by a late mathematical biographer, as “distinguished more by industry and judgment than genius,” Surely higher praise is due to the man whose discoveries “constituted the germ from which some of the most important of the Newtonian discoveries originated.

During his latter years he was much employed as a decypherer for government, but the very great services he performed by means of this uncommon faculty, were very ill rewarded. Indeed, he seldom received more than the pay of a copyist, when he certainly might have secured his own terms, and made his fortune at once. But it is among the best parts of his character that, in all situations, he was unambitious and independent. Courtiers’ promises, as he shrewdly observes, are like certain medicines, if they do not operate quickly, it is not ifkely they will at all. The elector of Brandenburgh sent him a gold chain and medal of great value, which the editor of his sermons, published 1791, disposed of some years ago, as old gold, but not without first offering it for sale to the Oxford and British museums, and to several antiquaries. In 1700 king William granted Dr. Wallis an annuity of 100l. per annum, with survivorship to his grandson, Mr. William Blencoe, on condition of his teaching the latter his art of decyphering. 1

1 Life prefixed to Sermons, V791. Gen. Dict. Biog. Brit. Thompson’s History of the Royal Society. rreface to —Hearne’s Langtoft’s Chronicle."