4!)9 



WALLIS, JOHN. 



WALLIS, JOHN. 



500 



are universally admitted to display a genius for that class of composi- 

 tion of a rare order. As in the case of our own Dr. Watts, the poet's other 

 verses may be said to be forgotten, while his hymns are the delight of 

 thousands. They have been adopted in the authorised Swedish 

 Psalm and Hymn-Book, of which they form the principal ornament, 

 though several other contributions from modern poets have assisted 

 to raise the collection to the rank which it now takes of one of the 

 best in Europe. Wallin, who in 1812, began to occupy a pulpit in 

 Stockholm, soon became a popular preacher and was selected to impart 

 theological instruction to Prince Oscar, now (1857) king of Sweden. 

 After filling various ecclesiastical dignities, he was appointed in 1833 

 archbishop of Upsal, the highest post in the Swedish church. He 

 died on the 30th of June 1839, universally respected and admired. 

 Three volumes of 'Religious Discourses on various occasions,' 'Reli- 

 gions-Tal vid atskilliga Tillfallen' (Stockholm 1827-31), and three of 

 sermons, ' Predikninger,' published after his death, are unsurpassed in 

 Swedish literature as specimens of pulpit eloquence. His literary 

 works ' Witterhets Arbeten,' were published in two volumes at Stock- 

 holm in 1848. 



WALLIS, JOHN, was the eldest son of the Rev. John Wallis, in- 

 cumbent of Ashford in Kent, where he was born November 23, 1616. 

 The life of this eminent mathematician is very fully given in the 

 ' Biographia Britannica,' which is our sole authority for the facts now 

 to be stated respecting him. 



The father of Wallis died when he was six years old, leaving five 

 children to the care of his widow. As he died wealthy, his eldest son was 

 brought up with great care and intended for a learned profession. In 

 that day mathematical studies were rarely preparatory to the higher 

 kind of pursuits; in the case of Wallis, even common arithmetic seems 

 to have been neglected. Ho was fifteen years old when his curiosity 

 was excited by seeing a book of arithmetic in the hands of his younger 

 brother, who was preparing for trade. On his showing some curiosity 

 to know what it meant, his brother went through the rules with him, 

 and in a fortnight he had mastered the whole. At the age of sixteen, 

 which was rather late at that time, he was entered at Emmanuel 

 College in Cambridge, where he soon obtained reputation. Among his 

 other studies, anatomy found a place ; and he is said to have been the 

 first student who maintained, in a public disputation, the doctrine of 

 the circulation of the blood, which had been promulgated by Harvey 

 four or five years before. There were no mathematical studies at that 

 time in Cambridge, and none to give even so much as advice what 

 books to read : the best mathematicians were in London, and the science 

 was esteemed no better than mechanical. This account is confirmed 

 by his contemporary Horrocks, who was also of Emmanuel, and whose 

 works Wallis afterwards edited. After taking the degree of master of 

 arts, the county of Kent not being vacant in his own college, he was 

 chosen fellow of Queen's, and took orders, in 1640. He was then 

 chapl dn in one and another private family, residing partly in London, 

 till the breaking out of the civil war, in which he took the side of the 

 Parliament He made himself useful to his party by deciphering 

 intercepted letters, an art in which he was eminent. Vieta, as we have 

 seen [ VIETA, FRANCIS, vol. vi. col. 361.], had deciphered, and Baptista 

 Porta had written something on the subject, but only with reference 

 to simple ciphers. In 1643, the sequestered living of St. Gabriel, 

 Feuchurch Street, was given to him ; and in the same year he published 

 ' Truth Tried, or Animadversions on the Lord Brooke's Treatise on the 

 Nature of Truth.' In this year also he came into a handsome fortune by 

 the death of his mother. In 1644 he was appointed one of the secre- 

 taries of the Assembly of Divines at Westminster. He has given a 

 succinct account of the proceedings of this body. (See the 'Biographia 

 Britannica.') In this year also he married. In 1645 he was among the 

 first who joined those meetings which afterwards gave rise to the Koyal 

 Society : but we do not hear of any particular attention to mathe- 

 matics on his part till 1647, when he met with Oughtred's ' Clavis,' 

 at which time he says he was a very young algebraist, being then 

 more than thirty years old. He and James Bernoulli are alike in this, 

 and differ from most others of the same celebrity, that they showed no 

 strong tendency to mathematical pursuits at a very early age. When 

 the Independents began to prevail, Wallis joined with others of the 

 clergy in opposing them ; and in 1648 subscribed a remonstrance 

 against the execution of Charles I. He was then rector of St. Martin's 

 Church in Ironmonger Lane, but in 1649 he was appointed Savilian 

 professor of geometry at Oxford by the Parliamentary visitors, his 

 predecessor, Dr. Turner, having been ejected. He now removed to 

 Oxford, and applied himself diligently to mathematics. In 1650 ap- 

 peared his 'Animadversions' on the celebrated Richard Baxter's 

 ' Aphorisms of Justification and the Covenant/ a moderate piece of theo- 

 logical controversy, undertaken, Wood supposes, at the desire of Baxter 

 himself. At the end of 1650 he first met with the method of indivisibles 

 in the writings of Torricelli, and from this time the researches begin, 

 of which we shall presently have to speak. In 1653 he published, in 

 Latin, an English grammar for the use of foreigners, with a treatise on 

 the formation of articulate sounds prefixed. In the same year he 

 deposited in the Bodleian Library a collection of deciphered letters, 

 which afterwards caused some controversy. In 1654 he took the 

 degree of doctor of divinity, and in the following year he published 

 his ' Arithmetica Ittfinitornm,' with a treatise on Conic Sections pre- 

 fixed, lu 1655 ho began his controversy with Hobbes, who, in his 



' Elementorum Philosophise Sectio Prima,' had given a quadrature of 

 the circle. Wallis answered this in a tract entitled ' Elenchus Geo- 

 metrke Hobbianse.' Hobbes replied in ' Six Lessons to the Professor 

 of Mathematics at Oxford :' on which Wallis published ' Due Correction 

 for Mr. Hobbes, or School Discipline for not saying his Lesson right,' 

 Oxford, 1656. Hobbes defended himself in Srry/xas, or ' The Mark? of 

 the absurd Geometry, Ac. of Dr. Wallis,' London, 1657. Wallis 

 answered in ' Hobbiani Puncti Dispunctio, in answer to Mr. Hobbea's 

 2T7juas,' Oxford, 1657. The controversy was renewed by Mr. Hobbes 

 in 1661, in ' Examinatio et Emendatio Mathematicorum hodiernorum,' 

 to which Wallis replied in'Hobbius Heautontimoreumenos,' Oxford, 

 1663. Wallis, as may be supposed, had the right ou his side; and 

 we are disposed to regret that he did not allow his part of the con- 

 troversy to appear in the collection of his works, though we cannot 

 but respect the motive, namely, the desire not to attack an opponent 

 after his death. In 1656 he published his treatise on the angle of 

 contact, and a defence of it in 1685. 



In 1657 Wallis published his'Mathesis Universalis,' and in 1658 

 appeared, under the title of 'Commercium Epistolicum,' a corres- 

 pondence arising out of a problem proposed to him by Format : also a 

 sermon, 'Mens sobria serio commendata," and a commentary on the 

 Epistle to Titus. In 1658 the questions of Pascal on the cycloid 

 appeared, which were answered by Wallis, and led to a controversy. 

 About this time Wallis, who with others desired the restoration of the 

 kingly power, employed his art of diciphering on the side of the 

 Royalists ; so that at the Restoration he was received with favour by 

 Charles II., confirmed in his professorship and in the place of keeper 

 of the archives at Oxford, and was made one of the royal chaplains. 

 In 1661 he was one of the clergy appointed to review the Book of 

 Common Prayer. He was of course one of the first members of the 

 Royal Society, and from this to his death his life is little more than 

 the list of his works. His tract on the Cuno-cuneus, or circular wedge, 

 was published in 1663; his tract 'De Proportionibus,' and his treatise 

 on the laws of collision, in the same year : his new hypothesis on the 

 tides, 'De -iEstu Maris,' in 1668; and the treatise on mechanics at 

 different times, in 1669, 1670, and 1671. In 1673 he edited the works 

 of Horrocks ; the Areuarius and quadrature of Archimedes appeared 

 in 1676 ; his edition of Ptolemy's Harmonics (to which other ancient 

 musicians were afterwards added) in 1680. His algebra appeared in 

 English in 1685, and was translated into Latin with additions in the 

 collection of hia works ; in the same year also, his treatise on Angular 

 Sections and on the Cuno-cuneus. In 1685 he wrote theological 

 pieces on Melchisedec, Job, and the titles of the Psalms. In 1687 

 appeared his celebrated work on logic. In 1688 he edited Aristarchus 

 and fragments of Pappus. In 1691 he published his pieces on the 

 Trinity, and on the baptism of infants; and, in 1692, his defence of 

 the Christian sabbath against the Sabbatarians, or observers of Satur- 

 day. The collection of his works by the curators of the University 

 press began to be made in 1692; the three volumes bear the disordered 

 dates of 1695, 1693, and 1699. In 1692 he was consulted upon the 

 adoption of the Gregorian calendar, or new style, against which he 

 gave a strong opinion, and the design was abandoned. In 1696, when 

 the first two volumes of his works appeared, he was the remote occa- 

 sion of beginning the controversy between the followers of Newton 

 and Leibnitz. Some remarks were made on his assertions as to the 

 origin of the differential calculus in the Leipsic Acts, which produced 

 a correspondence, and this correspondence was published in the third 

 volume. He died October 28, 1703, in his 88th year. 



The character of Wallis as a man was attacked upon one occasion 

 only, in which it was asserted that he had deciphered the king's letters 

 after the battle of Naseby, to the great detriment of the royal cause 

 and its followers. It was also said that the collection of deciphered 

 letters which he gave to the University had some of its contents 

 withdrawn by him when the Restoration was approaching. Wallis 

 himself denied that he had deciphered the king's letters on that occa- 

 sion, though had he done so, it would, granting his adherence to the 

 parliament to be justifiable, have been no more than his duty. A sort 

 of repugnance exists to a decipherer, though common sense tells us 

 that those who intercept and open an enemy's letter which, being 

 written in common language, is in some sort confided to those into 

 whose hands it may fall, are much more obnoxious to any charge than 

 the decipherer of a letter which, being written in cipher, more 

 resembles a defiance. 



All that can be said against Wallis, if it amounts to anything, is just 

 this, that when he desired the downfall of the kingly power, he used 

 his talents against the king, and then, when, at another time and 

 under very different circumstances, he wanted the restoration, he used 

 his talents for it. And as to the charge of withdrawing the letters 

 from the Bodleian, it ought to have been added, that when he pre- 

 sented them, it was with a written reservation to add or withdraw. 

 The best testimony to the general character of Wallis is as follows : 

 He was exceedingly obnoxious to the high church party at Oxford, 

 both from his low church principles, and from his haviug been forced 

 upon the University by external and democratic power. But all that 

 his contemporary Wood, who will not admit him into the ' Athena? 

 Oxonienses ' as an Oxford writer*, can say or hint against him, amounts 

 to as much as we have mentioned. And yet there was no want of 

 disposition to disparage a presbyterian ia Wood, as witness the follow- 



