Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/469

NEWTON 439 of bachelor of arts. The persons appointed (in conjunction with the proctors, John Slade of Catharine Hall, and Benjamin Pulleyn of Trinity College, Newton s tutor) _ to examine the questionists were John Eachard of Catharine Hall and Thomas Gipps of Trinity College. It is a curious accident that we have no information about the respective merits of the candidates for a degree in this year, as the "ordo senioritatis " of the bachelors of arts for the year is omitted in the " Grace Book." It is supposed that it was in 1665 that the method of fluxions first occurred to Newton s mind. There are several papers still existing in Newton s handwriting bearing dates 1665 and 1666 in which the method is described, in some of which dotted or dashed letters are used to represent fluxions, and in some of which the method is explained without the use of dotted letters. Both in 1665 and in 1666 Trinity College was dismissed on account of the plague. On each occasion it was agreed, as appears by entries in the " Conclusion Book" of the col lege, bearing dates August 7, 1665, and June 22, 1666, and signed by the master of the college, Dr Pearson, that all fellows and scholars who were dismissed on account of the pestilence be allowed one month s commons. Newton must have left college before August 1665, as his name does not appear in the list of those who received extra commons on that occasion, and he tells us himself in the extract from his commonplace book already quoted that he was "forced from Cambridge by the plague" in the summer of that year. Newton was elected a fellow of his college on October 1, 1667. There were nine vacancies, one of which was caused by the death of Cowley in the previous summer, and the nine successful candidates were all of the same academical standing. A few weeks after his election to a fellowship Newton went to Lincolnshire, and did not return to Cambridge till the February following. On the 16th of March 1668 he took his degree of M.A. During the years 1666 to 1669 Newton s studies were of a very varied kind. It is known that he purchased prisms and lenses on two or three several occasions, and also chemicals and a furnace, apparently for chemical experiments ; but he also employed part of his time on the theory of fluxions and other branches of pure mathe matics. He wrote a paper Analysis per Equationes Numero Terminorum Infinitas, which he put, probably in June 1669, into the hands of Isaac Barrow (then a fellow of Trinity College, and the first occupant of the Lucasian chair of mathematics), at the same time giving him per mission to communicate the contents to their common friend Mr John Collins, a mathematician of no mean order, and a correspondent of many of the eminent men of his time. Barrow did this on the 31st of July 1669, but kept the name of the author a secret, and merely told Collins that he was a friend staying at Cambridge, who had a powerful genius for such matters, and ex pressed a hope that the paper would not a little delight him. In a subsequent letter on the 20th of August, Barrow expressed his pleasure at hearing the favourable opinion which Collins had formed of the paper, and added, "the name of the author is Newton, a fellow of our college, and a young man, who is only in his second year since he took the degree of master of arts, and who, with an unparalleled genius (eximio quo est acumine), has made very great progress in this branch of mathematics." Shortly afterwards Barrow, who had resolved to devote his attention to theological in preference to mathematical studies, resigned the Lucasian chair, and was instrumental in securing Newton s election as his successor. Newton was elected Lucasian professor on the 29th of October 1669. It was his duty as professor to lecture at least once a week in term time on some portion of geometry, arithmetic, astronomy, geography, optics, statics, or some other mathematical subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had met with. The subject which Newton chose for his lectures was optics. He gave courses of lectures on this subject, and the success which attended his researches in optics must have been great. The results of his investi gations, however, were known only through his own oral lectures, and were not published until he presented an account of them to the Royal Society in the spring of 1672. On December 21, 1671, he was proposed as a candidate for admission into the Royal Society by Dr Seth Ward, bishop of Salisbury, and on January 11, 1672, he was elected a fellow of the Society. At the meeting at which Newton was elected a description of a reflecting telescope which he had invented was read, and " it was ordered that a letter should be written by the secretary to Mr Newton to acquaint him of his election into the Society, and to thank him for the communication of his telescope, and to assure him that the Society would take care that all right should be done him with respect to this invention." In his reply to the secretary on January 18, 1672, Newton writes : " 1 desire that in your next letter you would inform me for what time the society continue their weekly meetings ; because, if they continue them for any time, I am purposing them to be considered of and examined an account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt not but will prove much more grateful than the communication of that instrument, being in my judgment the oddest if not the most considerable detection which hath hitherto been made into the operations of nature. " The promise here made was fulfilled in a communica tion which Newton addressed to Oldenburg, the secretary of the Royal Society, on February 6, 1672, and which was read before the Society two days afterwards. The whole is printed in No. 80 of the Philosophical Transactions, and the first part of it has been already printed in the article LIGHT, vol. xiv. p. 590. After explaining his discovery of the composition of white light, he proceeds: " When I understood this, I left off my aforesaid Glass works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescrip tions of Optick Authors (which all men have hitherto imagined), as because that Light it self is a Heterogeneous mixture of differently refrangible PMIJS. So that, were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which having the same Incidence upon the same Medium are apt to suffer a different refraction. Nay, I wondered, that seeing the difference of refrangibility was so great, as I found it, Telescopes should arrive to that perfection they are now at." He then points out why "The object-glass of any Telescope cannot collect all the rays which come from one point of an object, so as to make them con vene at its focus in less room than in a circular space, whose diameter is the 50th part of the Diameter of its Aperture: which is an irregularity some hundreds of times greater, than a circularly figured Lens, of so small a section as the Object-glasses of long Telescopes are, would cause by the unfitness of its figure, were Light uniform"; and he adds "This made me take reflections into consideration, and finding them regular, so that the Angle of Reflection of all sorts of Kays was equal to their Angle of Incidence; I understood, that by their mediation Optick instruments might be brought to any degree of perfection imaginable, provided a Reflecting substance could be found, which would polish as finely as Glass, and reflect as much light, as glass transmits, and the art of communicating to it a Parabolick figure be also attained. But these seemed very great difficulties, and I have almost thought them insuperable, when I further considered, that every irregularity in a reflecting super ficies makes the rays stray 5 or 6 times more out of their due course, than the like irregularities in a refracting one ; so that a much greater curiosity would be here requisite, than in figuring glasses for Refraction.