He paid another visit to Cambridge with the object of learning more with regard to the mathematical methods which had already conducted Newton to such sublime truths, and he again encouraged the latter both to pursue his investigations, and to give some account of them to the world. In December of the same year Halley had the gratification of announcing to the Royal Society that Newton had promised to send that body a paper containing his researches on Gravitation.
It seems that at this epoch the finances of the Royal Society were at a very low ebb. This impecuniosity was due to the fact that a book by Willoughby, entitled "De Historia Piscium," had been recently printed by the society at great expense. In fact, the coffers were so low that they had some difficulty in paying the salaries of their permanent officials. It appears that the public did not care about the history of fishes, or at all events the volume did not meet with the ready demand which was expected for it. Indeed, it has been recorded that when Halley had undertaken to measure the length of a degree of the earth's surface, at the request of the Royal Society, it was ordered that his expenses be defrayed either in 50 pounds sterling, or in fifty books of fishes. Thus it happened that On June 2nd, the Council, after due consideration of ways and means in connection with the issue of the Principia, "ordered that Halley should undertake the business of looking after the book and printing it at his own charge," which he engaged to do.
It was, as we have elsewhere mentioned, characteristic of Newton that he detested controversies, and he was, in fact, inclined to suppress the third book of the "Principia" altogether rather than have any conflict with Hooke with respect to the discoveries there enunciated. He also thought of changing the name of the work to De Motu Corporum Libri Duo, but upon second thoughts, he retained the original title, remarking, as he wrote to Halley, "It will help the sale of the book, which I ought not to diminish, now it is yours," a sentence which shows conclusively, if further proof were necessary, that Halley had assumed the responsibility of its publication.
Halley spared no pains in pushing forward the publication of his illustrious friend's great work, so that in the same year he was in a position to present a complete copy to King James II., with a proper discourse of his own. Halley also wrote a set of Latin hexameters in praise of Newton's genius, which he printed at the beginning of the work. The last line of this specimen of Halley's poetic muse may be thus rendered: "Nor mortals nearer may approach the gods."The intimate friendship between the two greatest astronomers of the time continued without interruption till the death of Newton. It has, indeed, been alleged that some serious cause of estrangement arose between them. There is, however, no satisfactory ground for this statement; indeed, it may be regarded as effectually disposed of by the fact that, in the year 1727, Halley took up the defence of his friend, and wrote two learned papers in support of Newton's "System of Chronology," which had been seriously attacked by a certain ecclesiastic. It is quite evident to any one who has studied these papers that Halley's friendship for Newton was as ardent as ever.
The generous zeal with which Halley adopted and defended the doctrines of Newton with regard to the movements of the celestial bodies was presently rewarded by a brilliant discovery, which has more than any of his other researches rendered his name a familiar one to astronomers. Newton, having explained the movement of the planets, was naturally led to turn his attention to comets. He perceived that their journeyings could be completely accounted for as consequences of the attraction of the sun, and he laid down the principles by which the orbit of a comet could be determined, provided that observations of its positions were obtained at three different dates. The importance of these principles was by no one more quickly recognised than by Halley, who saw at once that it provided the means of detecting something like order in the movements of these strange wanderers. The doctrine of Gravitation seemed to show that just as the planets revolved around the sun in ellipses, so also must the comets. The orbit, however, in the case of the comet, is so extremely elongated that the very small part of the elliptic path within which the comet is both near enough and bright enough to be seen from the earth, is indistinguishable from a parabola.
Applying these principles, Halley thought it would be instructive to study the movements of certain bright comets, concerning which reliable observations could be obtained. At the expense of much labour, he laid down the paths pursued by twenty-four of these bodies, which had appeared between the years 1337 and 1698. Amongst them he noticed three, which followed tracks so closely resembling each other, that he was led to conclude the so called three comets could only have been three different appearances of the same body.
The first of these occurred in 1531, the second was seen by Kepler in 1607, and the third by Halley himself in 1682. These dates suggested that the observed phenomena might be due to the successive returns of one and the same comet after intervals of seventy-five or seventy-six years. On the further examination of ancient records, Halley found that a comet had been seen in the year 1456, a date, it will be observed, seventy-five years before 1531. Another had been observed seventy-six years earlier than 1456, viz., in 1380, and another seventy-five years before that, in 1305.