The Royal Society at once awarded their highest honour, the Copley Medal, to Le Verrier (1846), and it was not till two years afterwards that it was awarded to Adams. Our Society was saved from expressing a similar preference by the bye-law requiring that the award of the medal should be confirmed by a majority of three-quarters of the Council. A sufficient minority were of opinion that " an award to M. Le Verrier, unaccompanied by another to Mr. Adams, would be drawing a greater distinction between the two than fairly represents the proper inference from facts, and would be an injustice to the latter."* It had been proposed that the General Meeting should be recommended to suspend the existing bye-law, so that more than one medal might be given, but the proposal was not carried on the Council. No medal of the Society has been awarded in connection with the discovery of Neptune, either at that time or subsequently.

Looking back now upon Adams's achievement, which, as has been truly said, belongs at once to the science and the romance of astronomy, there are several points that stand out as very remarkable: his extreme youth when he attacked, unaided, so difficult a problem, and steadily carried it through to success; his faith in the Newtonian law and in the results of his own mathematics; and his extreme modesty. As soon as he took his degree in 1843 he devoted his whole leisure, in term time at Cambridge, and in vacations in Cornwall, to the new planet's orbit, without assistance or encouragement from anyone. How quietly and unassumingly he pursued his investigations is shown by the fact that at the time of the finding of the planet his name was only known to Airy, Challis, Herschel,

among astronomers. In England at present the current runs the other way, and though I very much prefer this failing of the two, yet it is provoking too. I assure you that it was with difficulty that one could get a hearing, while pointing out the fact that Mr. Adams had deduced the elements and place of the planet in October 1845. I have been told repeatedly by those who should have known better that this was nothing at all, simply because the over-modest man communicated his results to Airy and Challis, that the planet might be looked for, instead of bringing his investigation before the world as he ought to have done. Surely it is a greater honour to science that two men should independently have come to the same conclusion from the same data than that one should have hit on it, as it were, accidentally. Thanks to Struve and Biot, &c. our anti-Adamites are calmer, and as there never was any opposition to Le Verrier, we are quite satisfied at present, and so I hope are the two discoverers. I think there is a hope that Mr. Adams will continue his astronomical researches. In any other country there could be no doubt of it, but in England there is no carrière for men of science. The Law or the Church seizes on all talent which is not independently rich or careless about wealth.” The principal contemporary publications relating to the new planet are to be found in vol. xvi. of the Memoirs, in the Comptes Rendus, in the Athenæum, in the Astronomische Nachrichten, and in vol. vii. (1847) of the North British Review, which contains an article by Brewster. Challis's report of December 12, 1846, to the Observatory Syndicate at Cambridge, which contains an account of his own proceedings relating to the new planet, was published in the Monthly Notices for 1883 (vol. xliii. pp. 165–172).

*Monthly Notices, vol. vii. p. 216.

Earnshaw, and a few intimate university friends of his own standing. The implicit reliance that he placed in the sufficiency of the Newtonian law to explain all the phenomena of the heavens is also noteworthy, as it was then considered much more likely than it is now that the true law might not be exactly that of the inverse square, or might be subject to other -modifications.* He was perfectly convinced of the reality of the planet and of the approximate accuracy of the place he had assigned to it; and in the paper which he placed in the hands of Challis in September, 1845, he used the words "the new planet." It is to be regretted that he should have refrained from publishing his results at the time (which he had been advised to do by some of his Cambridge friends), but he can scarcely be blamed for believing that the course he had taken would lead to a search being made for the planet at Greenwich or elsewhere.

A French translation of the memoir presented to the Society in 1846 was published in Liouville's Journal de Mathématiques Pures et Appliquées for 1875. The Editor, M. Résal, stated

* The words in the text were in type before the writer saw a private letter from Adams to Professor James Thomson, dated November 26, 1846, from which the following very interesting sentences relating to this subject are extracted:" On considering the subject it appeared to me that by far the most probable hypothesis that could be formed to account for these irregularities was that of the existence of an exterior undiscovered planet whose action on Uranus produced the disturbances in question. None of the other hypotheses that had been thrown out seemed to possess the slightest claims to attention, as they were all improbable in themselves, and incapable of being tested by any exact calculation. Some had even supposed that, at the great distance of Uranus from the Sun, the law of attraction became different from that of the inverse square of the distance, but the law of gravitation was too firmly established for this to be admitted till every other hypothesis had failed to account for the observed irregularities; and I felt convinced that in this, as in all previous instances of the kind, the discrepancies which had for a time thrown doubts on the truth of the law, would eventually afford it the most striking confirmation. In contrast with all these vague hypotheses, the supposition that the irregularities were caused by the action of an unknown planet appeared to be thoroughly in accordance with the present state of our knowledge, could be tested by calculation, and would probably lead to important practical results-viz. the approximate determination of the position of the disturbing body." After quoting the memorandum of July 3, 1841, he proceeds:" Accordingly, in 1843, I commenced my calculations, and in the course of that year I arrived at a first solution of the problem, which, though incomplete in itself, fully convinced me that the hypothesis which I had formed was quite adequate to account for the observed irregularities, and that the place of the disturbing body might be very approximately determined by a more extended investigation. Having received from the Astronomer Royal, in February 1844, the whole of the Greenwich observations of Uranus, I accordingly attacked the problem afresh, and in a much more complete manner than before, and, after obtaining several solutions, differing little from each other, by gradually taking into account more and more terms in the series expressing the perturbations, I communicated my final results to Professor Challis in September 1845, and the same, slightly corrected, to the Astronomer Royal in the following month. The near agreement of the several solutions which I had obtained gave me great confidence in my results, which included a determination of the mass, position, and elements of the orbit of the supposed planet."

In

that he had been led to undertake this republication by the pressing solicitations of several eminent mathematicians. introducing the memoir he writes:-" Le problème fut résolu simultanément, en Angleterre par M. Adams, et en France par M. Leverrier, qui, ainsi que le reconnaît M. Adams, a publié le premier les résultats de ses recherches. Il est impossible de rencontrer, dans l'histoire des sciences, une découverte qui fasse plus d'honneur au génie humain. Les lois de Newton recevaient ainsi la plus éclatante des confirmations, et l'Astronomie, désormais indiscutable dans ses principes, était arrivée à l'état de science parfaite. Le Mémoire de M. Adams a valu, à juste titre, à son auteur la plus glorieuse célébrité : il est digne, en effet, de figurer à côté des plus beaux mémoires de Laplace et Lagrange.' This republication of the memoir, after an interval of thirty years, in a purely mathematical journal, derives additional interest from the fact that the author himself has added a few notes at the end, some of which relate to the objections made by Professor Benjamin Peirce to the legitimacy of the methods pursued by both Adams and Le Verrier. In Peirce's paper, which was published in 1847, he contended that the period of Neptune differed so considerably from that of the hypothetical planets that the modes of procedure adopted were unreliable, so that the finding of the planet was partly due to a happy accident. In reply to this, Adams points out that the objection would be valid if the object in view had been to represent the perturbations of Uranus during two or three synodic periods, but that the case is different when, as in this instance, it is only required to represent the perturbations for a fraction of a synodic period.

The honours so freely and deservedly bestowed upon Le Verrier in France and other countries form a striking contrast to the general want of appreciation with which Adams's work was at first received. But there were conspicuous exceptions. In 1847, on the occasion of the Queen's visit to Cambridge, the honour of knighthood was offered to Adams, but this offer he felt obliged to decline. The members of St. John's College, also, were not slow in showing their sense of the honour he had conferred on his college and the University, for in a very short time a fund, producing about 8ol. per annum, was raised for establishing a prize to be connected with his name. This fund was offered to the University, and accepted on April 7, 1848. The Adams Prize, which is biennial, is awarded for the best essay on some subject of pure mathematics, astronomy, or other branch of natural philosophy. It was awarded in 1857 to Clerk Maxwell for his well-known essay on the stability of Saturn's rings.

Before leaving the subject of Neptune, it should be stated that Adams always expressed the warmest appreciation of Le Verrier's work. It was a great pleasure to him when they met at Oxford in 1847. In the same year Le Verrier visited Adams at

Cambridge. The honorary degree of LL.D. was conferred upon Le Verrier in 1874 by the University of Cambridge, and it cannot be doubted that this was owing to the action of Adams.

In 1847 he communicated to the Society a paper on an important error in Bouvard's tables of Saturn. Having been engaged upon a comparison of the theory of Saturn with the Greenwich observations, he was struck with the magnitude of the tabular errors in heliocentric latitude, which could not be attributed to imperfections in the theory. He found that the error was one of computation, two terms of different arguments having been, in effect, united into one.

In 1848 he was occupied with the determination of the constants in Gauss's theory of terrestrial magnetism. This investigation he afterwards resumed, and the calculations connected with it, with which he was occupied in the later years of his life, were left unfinished at the time of death. When failing health prevented him from any longer giving his personal attention to the work, he placed the manuscripts in the hands of his brother, Professor W. G. Adams, for completion.

In 1851 he was elected President of our Society, and held the office for the usual term of two years, during which he delivered the addresses on the presentation of the medal to Peters and to Hind. In 1852 he communicated to the Society_new tables of the Moon's parallax, to be substituted for those of Burckhardt. Henderson had compared the parallaxes deduced from observation with those derived by calculation from the tables both of Damoiseau and of Burckhardt, finding a difference of no less than 13, according as one set of tables or the other was employed. The parallax in Damoiseau's tables is given at once in the form in which it is furnished by theory, but that in Burckhardt's tables is adapted to his peculiar form of the arguments, and requires transformation in order to be compared with the former. When this was done, Adams found that several of the minor equations of parallax deduced from Burckhardt differed completely from their theoretical values as given by Damoiseau. He discovered that these errors were due to Burckhardt's transformations of Laplace's formula, and he succeeded in tracing them to their sources. He also examined carefully the theories of Damoiseau, Plana, and Pontécoulant, with respect to the same subject, and supplied a number of defects and omissions. Burckhardt's value of the parallax having been employed in the Nautical Almanac, Adams gave, in addition to the new tables, a table of corrections to be applied to the values in the Nautical Almanac for every day of the year from 1840 to 1855 inclusive. This contribution to astronomy is very characteristic of its author. It contains the results of an immense amount of intricate and elaborate mathematical investigation, carried out with great skill and accuracy in all its details, both analytical and numerical, but no part of the work itself is given. The method of procedure is briefly sketched, and the final conclusions are stated in the fewest words and simplest manner possible. No

one unacquainted with the subject would imagine how much difficult and laborious research was represented by these few pages of results. The tables were printed as a supplement to the Nautical Almanac for 1856.

As Adams had not taken holy orders, his Fellowship at St. John's College came to an end in 1852, but he continued to reside in the college until February 1853, when he was elected to a Fellowship at Pembroke College, which he retained till his death. In the autumn of 1858 he was appointed Professor of Mathematics in the University of St. Andrews, and shortly afterwards, in the same year, he was elected Lowndean Professor of Astronomy and Geometry at Cambridge, in succession to Peacock. He continued his lectures at St. Andrews, however, until the end of the session in May 1859. In 1861 he succeeded Challis as Director of the Cambridge Observatory.

In 1853 Adams communicated to the Royal Society his celebrated memoir on the secular acceleration of the Moon's mean motion. Halley was the first to detect this acceleration by comparing the Babylonian observations of eclipses with those of Albategnius and of modern times, and Newton referred to his discovery in the second edition of the "Principia." The first numerical determination of the value of the acceleration is due to Dunthorne, who found it to be about 10" in a century. Tobias Mayer obtained the value 6"7, which he afterwards increased to 9". Lalande's value was nearly 10". The discrepancies were due to the eclipses selected, the results derived from the different eclipses being inconsistent with one another. The history of the theoretical investigations relating to the acceleration may be summed up as follows:-In 1762 the French Academy proposed as the subject of their prize the influence of a resisting medium upon the movements of the planets. The prize was won by Bossut, who showed that the principal effect of such a medium would be an acceleration in their motions, which would be much more sensible in the case of the Moon than in that of the planets. In 1770 the question proposed was whether the theory of gravitation could alone explain the acceleration. Euler obtained the prize, but he was unable to discover any term of a secular character, and concluded that the force of gravitation would not account for this inequality. The subject was proposed again in 1772, Euler and Lagrange sharing the prize between them. The former came to the same conclusion as before, attributing the acceleration to a resisting medium; the latter did not carry the application of his formulæ so far as to complete the investigation. The prize was again offered for the same subject in 1774, the competitors being required to examine whether the fact that the Moon appeared to have a secular acceleration, while there was no sensible effect of this kind in the case of the Earth, could be explained by the theory of gravitation alone, taking into account not only the action of the Sun and the Earth upon the Moon, but also the action of the other