one in 1708 on the rectification of any curve, and lastly one in 1710 on the construction of logarithmic tables.

It is however much easier to obtain a lasting reputation by eccentricity than by merit; and hundreds who never heard of Craig's work on fluxions know of him as the author of Theologia Christianae principia mathematica published in 1699. He here starts with the hypothesis' that evidence transmitted through successive generations diminishes in credibility as the square of the time. The general idea was due to the Mahommedan apologists, who enunciated it as an axiom, and then argued that as the evidence for the Christian miracles daily grows weaker a time must come when they will have no evidential value, whence the necessity of another prophet. Curiously enough Craig's formulæ shew that the oral evidence would by itself have become worthless in the eighth century, which is not so very far removed from the date of Mahommed's death (632). He asserts that the gospel evidence will cease to have any value in the year 3150. He then quotes a text to shew that at the second coming faith will not be quite extinct among men : and hence the world must come to an end before 3150. This was reprinted abroad, and seriously answered by many divines; but most of his opponents were better theologians than mathematicians, and would have been wiser if they had contented themselves with denying his axioms.

I must not pass over this period without mentioning Flamsteed. John Flamsteed was born in Derbyshire in 1646. When at school he picked up a copy of Holywood's treatise on the sphere (see p. 5) and was so fascinated by it that he determined to study astronomy. It was intended to send him to Cambridge, but for some years he was too delicate to leave home. He however obtained copies of Street's Astronomy, Riccioli's Almagestum novum, and Kepler's Tables, which he read by himself. By the time he was twenty-two or three he 1 See pp. 77, 78 of A budget of paradoxes by A. De Morgan, London, 1872.

2 See his life, by R. F. Baily, London, 1835.

was already one of the best astronomers (both theoretical and practical) in Europe. He entered at Jesus College in 1670, and devoted himself to the study of mathematics, optics, and astronomy. He seems to have been in constant communication with Barrow and Newton. He took his B.A. in 1674, and in the following year was appointed to take charge of the national observatory then being erected at Greenwich. He is thus the earliest of the astronomer-royals. He gave Newton many of the data for the numerical calculations in the third book of the Principia, but in consequence of a quarrel, refused to give the additional ones required for the second edition. He died at Greenwich in 1719.

He invented the system (published in 1680) of drawing maps by projecting the surface of the sphere from the centre on an enveloping cone which can then be unwrapped. He wrote papers on various astronomical problems, but his great work, which is an enduring memorial of his skill and genius, is his Historia coelestis Brittanica, edited by Halley and published posthumously in three volumes in 1725.

By the beginning of the eighteenth century the immense reputation and great powers of Newton were everywhere recognized. The adoption of his methods and philosophy at Cambridge was however in no slight degree due to other than professed mathematicians. Of these the most eminent was Bentley, who invariably exerted his influence to make literature and mathematical science the distinctive features of a Cambridge training. Philosophy was also still read and was not unworthily represented by Bacon, Descartes, and Locke'. It was from

1 Francis Bacon, born in 1561, was educated at Trinity College, Cambridge, and died in 1626: the Novum organum was published in 1620. René Descartes was born in 1596 and died in 1650: his Discours was published in 1637, and his Meditations in 1641. John Locke, born in 1632, was educated at Christ Church, Oxford, and died in 1704: his Essay concerning human understanding was published in 1690.

Newton aided by Bentley that the Cambridge of the eighteenth century drew its inspiration, and it was their influence that made the intellectual life of the university during that time so much more active than that of Oxford.

Richard Bentley' was born in Yorkshire on Jan. 27, 1662, and died at Cambridge on July 14, 1742. He took his B.A. from St John's College in 1680 as third wrangler, but in consequence of the power of conferring honorary optime degrees (see p. 170) his name appears as sixth in the list. He was not eligible for a fellowship, and in 1682 went down.

In 1692 he was selected to deliver the first course of the Boyle lectures on theology, which had been founded by the will of Robert Boyle, who died in 1691. In the sixth, seventh, and eighth sermons he gave a sketch of the Newtonian discoveries this was expressed in non-technical language and excited considerable interest among those members of the general public who had been unable to follow the mathematical form in which Newton's arguments and investigations had been previously expressed.

In 1699 Bentley was appointed master of Trinity College, and from that time to his death an account of his life is the history of Cambridge. It is almost impossible to overrate his services to literature and scientific criticism, and his influence on the intellectual life of the university was of the best. It is however indisputable that many of his acts were illegal, and the fact that he wished to promote the interests of learning is no excuse for the arrogance, injustice, and tyranny which characterized his rule.

One reform of undoubted wisdom which he introduced may

1 See the Life of Bentley by W. H. Monk, 2 vols., London, 1833: see also the volume by R. C. Jebb in the series of English men of letters, London, 1882; the latter on the whole is eulogistic, and it must be remembered that most of Bentley's Cambridge contemporaries would not have taken so favourable a view of his character. Another brilliant monograph on Bentley from the pen of Hartley Coleridge will be found in the Worthies of Yorkshire and Lancashire, London, 1836.

be here mentioned. Elections to scholarships and fellowships at that time took place on the result of a viva voce examination by the master and seniors in the chapel. To give an opportunity for written exercises and time for discussion by the electors of the merits of the candidates, Bentley arranged that every candidate should be first examined by each elector. In practice part of the examination was always oral and part written. He also made the award of scholarships annual instead of biennial, and admitted freshmen to compete for them. In 1789 the examination was made the same for all candidates and conducted openly. A survival of the old practice after nearly two hundred years-exists in the fact that the electors to fellowships and scholarships still always adjourn to the chapel to make the technical election and declaration.

The following account of the scholarship examination for 1709 taken from a letter1 of one of the candidates (John Byrom) to his father may interest the reader, as it is the earliest account of such an examination which I have seen. In that year there were apparently ten vacancies, and nineteen students "sat" for them. At the end of April every candidate sent a letter in Latin to the master and each of the seniors announcing that he should present himself for the examination. On May 7 Byrom was examined by the vice-master, on the following Monday and Tuesday he was examined by Bentley, Stubbs, and Smith in their respective rooms, and on Wednesday he went to the lodge and while there wrote an essay: the other seniors seem to have shirked taking part in the examination. "On Thursday," writes Byrom, "the master and seniors met in the chapel for the election; Dr Smith had the gout and was not there. They stayed consulting about an hour and a half, and then the master wrote the names of the elect, who (sic) shewed me mine in the list. Fifteen were chosen. [The

1 See p. 6 of the Remains of John Byrom, Chetham Society Publications, Manchester, 1854.

five lowest being pre-elected to the next vacancies]...... Friday noon we went to the master's lodge, where we were sworn in in great solemnity, the senior Westminster reading the oath in Latin, all of us kissing the Greek Testament. Then we

kneeled down before the master, who took our hands in his and admitted us scholars in the name of the Father, Son, &c. Then we went and wrote our names in the book and came away, and to-day gave in our epistle of thanks to the master. We took our places at the scholars' table last night. To-day the new scholars began to read the lessons in chapel and wait [i.e. to read grace] in the hall, which offices will come to me presently."

In appearance Bentley was tall and powerful, the forehead was high and not very broad, but the great development and rather coarse lines of the lower part of the face and cheeks seem to me the most prominent features and always strike me as indicative of cruelty and selfishness. The hair was brown and the hands small. Of his appearance Prof. Jebb says, "The pose of the head is haughty, almost defiant; the eyes, which are large, prominent, and full of bold vivacity, have a light in them as if Bentley were looking straight at an impostor whom he detected, but who still amused him; the nose, strong and slightly tip-tilted, is moulded as if nature had wished to shew what a nose can do for the combined expression of scorn and sagacity; and the general effect of the countenance, at a first glance, is one which suggests power-frank, self-assured, sarcastic, and I fear we must add insolent."

In character he was warm-hearted, impulsive, and no doubt well-intentioned; and separated from him by a century and a half we may give him credit for the reforms he made-in spite of the illegal manner in which they were introduced, and of his injustice and petty meanness against those who opposed him. Even his apologists admit that he was grasping, arrogant, arbitrary, intolerant, and at any rate in manner not a gentleman, while in the latter part of his life he neglected the duties of his office. But his abilities immeasurably ex