ceeded those of his contemporaries, and such as he was he has left a permanent impress on the history of Cambridge.

The interest that Bentley felt in the Newtonian philosophy arose from the nature of the conclusions and of the irrefutable logic by which they were proved. He was not however capable of appreciating the mathematical analysis by which they had been attained. Of those who were urged by him to take up the study of mathematics, one of the earliest was Whiston. William Whiston1 was born in Leicestershire on Dec. 9, 1667. He entered in 1685 at Clare, and mentions in his biography that he attended Newton's lectures. He took his B.A. in the Lent term of 1690, in the same year was elected a fellow, and for some time subsequently took pupils. In 1696 he published his celebrated Theory of the earth. The fanciful manner in which he accounted for the deluge by means of the tail of a comet is well known; but Bentley's criticism that Whiston had forgotten to provide any means for getting rid of the water with which he had covered the earth, and that it was of little use to explain the origin of the deluge by natural means if it were necessary to invoke the aid of the Almighty to finish the operation, is a sound one.

When in 1699 Newton was appointed master of the mint he asked Whiston to act as his deputy in the Lucasian chair. As such Whiston lectured on the Principia. In 1703 Newton resigned his professorship and Whiston was chosen as his successor.

In 1702 Whiston brought out an edition of Tacquet's2

1 Whiston wrote an autobiography, published at London in 1749, but many of the events related are not described accurately: see Monk's Life of Bentley, vol. i. pp. 133, 151, 215, 290, and vol. ii. p. 18. An account of his life is given in the Biographia Britannica, first edition, 6 vols., London, 1747-66.

2 Andrew Tacquet, who was born at Antwerp in 1611 and died in 1660, was one of the best known Jesuit mathematicians and teachers of the seventeenth century. His translation of Euclid's Elements was published in 1655, and remained a standard text-book on the continent until superseded by Legendre's Géometrie. Tacquet also wrote on optics and astronomy. His collected works were republished in two volumes at Antwerp in 1669.

Euclid which remained the standard English text-book on elementary geometry until displaced by the edition of Robert Simson issued in 1756. A year or so later Whiston asked Newton to be allowed to print the Universal arithmetic, manuscript copies of which were circulating in the university in much the same way as manuscripts containing matter which has not yet got incorporated into text-books do at the present time. Newton gave a reluctant consent, and it was published by Whiston in 1707.

Whiston seems to have been an honest and well-meaning man but narrow, dogmatic, and intolerant; and having adopted certain religious opinions he not only preached them on all occasions, but he questioned the honesty of those who differed from him. The following account of the beginning of the controversy is taken from a letter of William Reneu of Jesus, an undergraduate of the time.

I have a peice of very ill news to send you i.e. viz. yt one Whiston our Mathematicall Professor, a very learned (and as we thought pious) man has written a Book concerning ye Trinity and designs to print it, wherein he sides wth ye Arrians; he has showed it to severall of his freinds, who tell him it is a damnable, heretical Book and that, if he prints it, he'll Lose his Professorship, be suspended ab officio et beneficio, but all won't do, he saies, he can't satisfy his Conscience, unless he informs ye world better as he thinks than it is at present, concerning ye Trinity.

It is characteristic of the tolerancy of the Cambridge of the time that, although Whiston's opinions were contrary to the oath he had taken on commencing his M.A., yet no public notice was taken of them until he began to attack individuals who did not agree with him. It was impossible to allow the scandal thus occasioned to continue indefinitely. Whiston was warned and as he persisted in going on he was in 1711 expelled from his chair. The details of his opinions are now of no

interest.

After leaving the university Whiston wrote several books on astronomy and theology, but they are not material to my purpose. A list of them will be found in his life. His trans

lation of Josephus is still in common use.

He and Desaguliers

gave lectures on experimental physics illustrated by experiments in or about 1714: these are said to have been the earliest of the kind delivered in London.

An attempt to prosecute him was made in London by some clergymen; but the courts deemed it vindictive, and strained the law to delay the sentence till 1715, when all past heresy was pardoned by an act of grace. Whiston rather cleverly made use of these proceedings to push his opinions and in particular his theory of the deluge into general notice: on one occasion he put an account of the latter instead of a petition into the legal pleadings and the judges discussed it with great gravity and bewilderment until they found it had nothing to do with the suit. As so often happened in similar cases the prosecution only served to disseminate his opinions and excite sympathy for his undoubted honesty and candour. Queen Caroline who liked to see celebrated heretics ordered him to preach before her, and after the sermon in talking to him said she wished he would tell her of any faults in her character, to which he replied that talking in public worship was certainly a prominent one, and on her asking whether there were any others he refused to tell her till she had amended that one. He died in London on Aug. 22, 1752.

Intolerant, narrow, vain, and with no idea of social proprieties' he was yet honest and courageous; and though not a specially distinguished mathematician himself, his services in disseminating the discoveries of others were considerable. His tenure of the professorship was marked by the publication of Newton's writings on algebra and theory of equations (the Universal arithmetic), analytical geometry (cubic curves), the fluxional calculus, and optics. Copies of lectures and papers in the transactions of learned societies are and always will be inaccessible to many students. Henceforth Newton's mathematical works were open to all readers, and the credit of that is partly due to Whiston.

1 See e.g. p. 183 of his memoirs.

Whiston was succeeded in the Lucasian chair by Saunderson. Nicholas Saunderson' was born in Yorkshire in 1682, and became blind a few months after his birth. Nevertheless he acquired considerable proficiency in mathematics, and was also a good classical scholar. When he grew up he determined to make an effort to support himself by teaching, and attracted by the growing reputation of the Cambridge school he moved to Cambridge, residing in Christ's College. There with the permission of Whiston he gave lectures on the Universal arithmetic, Optics, and Principia of Newton, and drew considerable audiences. His blindness, poverty, and zeal for the study of mathematics procured him many friends and pupils; and among the former are to be reckoned Newton and Whiston.

When in 1711 Whiston was expelled from the Lucasian chair, queen Anne conferred the degree of M.A. by special patent on Saunderson so as to qualify him to hold that professorship, and he continued to occupy it till his death on April 19, 1739.

His lectures on algebra and fluxions were embodied in text-books published posthumously in 1740 and 1756. The algebra contains a description of the board and pegs by the use of which he was enabled to represent numbers and perform numerical calculations. The work on fluxions contains his illustrations of the Principia and of Cotes's Logometria; and probably gives a fair idea of how the subject was treated in the Cambridge lecture-rooms of the time.

He is described by one of his pupils as "justly famous not only for the display he made of the several methods of reasoning, for the improvement of the mind, and the application of mathematics to natural philosophy; but by the reverential regard for Truth as the great law of the God of truth, with which he endeavoured to inspire his scholars, and that peculiar felicity in teaching whereby he made his subject familiar to

1 An account of his life is prefixed to his Algebra published in two volumes at Cambridge in 1740.

their minds." He was passionate, outspoken, and truthful, and seems to be fairly described as "better qualified to inspire admiration than to make or preserve friends."

I notice references to two other mathematicians of this time as having taken a prominent part in the introduction of the Newtonian philosophy, but I can find no particulars of their lives or works. The first of these is Thomas Byrdall, of King's College, who died in 1721, and is said to have not only assisted Newton in preparing the Principia for the press, but to have checked most of the numerical calculations. Contemporary rumour is not to be lightly rejected, but I have never seen any evidence for the statement. The second of these writers is James Jurin, a fellow of Trinity College, who was born in 1684, graduated as B.A. in 1705, and died in 1750. He wrote in 1732 on the theory of vision, and was one of the earliest philosophers who tried to apply mathematics to physiology. He took a prominent part in the controversies between the followers of Newton and Leibnitz, and in particular engaged in a long dispute1 with Michelotti on a question connected with the momentum of running water.

During this time the Newtonian philosophy had become dominant in the mathematical schools at Oxford: the Savilian professors of astronomy being David Gregory from 1691 to 1708, and John Keill from 1708 to 1721; and the Savilian professors of geometry being Wallis (see p. 42) till 1703, and thence till 1720 Edmund Halley; but mathematics was still an exotic study there, and the majority of the residents regarded mathematics and puritanism as allied and equally unholy subjects. In London the Newtonian philosophy was worthily represented by Abraham de Moivre and by Brook Taylor, while Newton himself regularly presided at the meetings of the Royal Society.

1 See Philosophical transactions vols. LX. to LXVI.