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 planets or satellites of the solar system. The most noteworthy feature connected with the satellite is a secular change which is going on in the position of its orbital plane. Were the planet spherical in form, no such change could occur, except an extremely slow one produced by the action of the sun. The change is therefore attributed to a considerable ellipticity of the planet, which is thus inferred to be in rapid rotation. It will ultimately be possible to determine from this motion the position of the axis of rotation of Neptune with much greater precision than it could possibly be directly observed.

The following elements of the satellite were determined by H. Struve from all the observations available up to 1892:

The eccentricity, if any, is too small to be certainly determined. From the above mean distance is derived as the mass of Neptune . The motion of Uranus gives a mass.

Discovery of Neptune.—The detection of Neptune through its action upon Uranus before its existence had been made known by observation is a striking example of the precision reached by the theory of the celestial motions. So many agencies were concerned in the final discovery that the whole forms one of the most interesting chapters in the history of astronomy. The planet Uranus, before its actual discovery by Sir William Herschel in 1781, had been observed as a fixed star on at least 17 other occasions, beginning with Flamsteed in 1690. In 1820 Alexis Bouvard of Paris constructed tables of the motion of Jupiter, Saturn and Uranus, based upon a discussion of observations up to that year. Using the mutual perturbations of these planets as developed by Laplace in the Mécanique Céleste, he was enabled satisfactorily to represent the observed positions of Jupiter and Saturn; but the case was entirely different with. Uranus. It was found impossible to represent all the observations within admissible limits of error, the outstanding differences between theory and observation exceeding 1′. In these circumstances one of two courses had to be adopted, either to obtain the best general representation of all the observations, which would result in the tables being certainly erroneous, or to reject the older observations which might be affected with errors, and base the tables only on those made since the discovery by Herschel. A few years of observation showed that Uranus was deviating from the new tables to an extent greater than could be attributed to legitimate errors of theory of observation, and the question of the cause thus became of growing interest. Among the investigators of the question was F. W. Bessel who tried to reconcile the difficulty by an increase of the mass of Saturn, but found that he could do so only by assigning a mass not otherwise admissible. Although the idea that the deviations were probably due to the action of an ultra-Uranian planet was entertained by Bouvard, Bessel and doubtless others, it would seem that the first clear statement of a conviction that such was the case, and that it was advisable to reach some conclusion as to the position of the disturbing body, was expressed by the Rev. T. J. Hussey, an English amateur astronomer. In a letter to Sir George B. Airy in 1834 he inquired Airy’s views of the subject, and offered to search for the planet with his own equatorial if the required estimate of its position could be supplied. Airy expressed himself as not fully satisfied that the deviation might not arise from errors in the perturbations. He therefore was not certain of any extraneous action; but even if there was, he doubted the possibility of determining the place of a planet which might produce it. In 1837 Bouvard, in conjunction with his nephew Eugene, was again working on the problem; but it does not seem that they went farther than to collect observations and to compare the results with Bouvard’s tables.

In 1835 F. B. G. Nicolai, director of the observatory at Mannheim, in discussing the motion of Halley’s comet, considered the possibility that it was acted upon by an ultra-Uranian planet, the existence of which was made probable by the disagreement between the older and more recent observations.

In 1838 Airy showed in a letter to the Astronomische Nachrichten that not only the heliocentric longitude, but the tabulated radius vector of Uranus was largely in error, but made no suggestions as to the cause.

In 1843 the Royal Society of Sciences of Göttingen offered a prize of 50 ducats for a satisfactory working. up of the whole theory of the motions of Uranus, assigning September 1846 as the time within which competing papers should be presented.

It is also recorded that Bessel, during a visit to England in 1842, in a conversation with Sir John Herschel, expressed the conviction that Uranus was disturbed by an unknown planet, and announced his intention of taking up the subject. He went so far as to set his assistant Fleming at the work of reducing the observations, but died before more was done.

The question had now reached a stage when it needed only a vigorous effort by an able mathematician to solve the problem. Such a man was found in John Couch Adams, then a student of St John’s College, Cambridge, who seriously attacked the problem in 1843, the year in which he took his bachelor’s degree. He soon found that the observations of Uranus could be fairly well represented by the action of a planet moving in a radius of twice the mean distance of Uranus, which would closely correspond to Bode’s law. During the two following years he investigated the possible eccentricity of the orbit, and in September 1845 communicated his results to Professor James Challis. In 1845, about the 1st of November, Adams also sent his completed elements to Airy, stating that according to his calculations the observed irregularities in the motion of Uranus could be accounted for by the action of an exterior planet, of which the motions and orbital elements, were given. It is worthy of note that the heliocentric longitude of the unknown body as derived from these elements is only between one and two degrees in error, while the planet was within half a degree of the ecliptic. Two or three evenings assiduously devoted to the search could not therefore have failed to make the planet known. Adams’s paper was accompanied by a comparison of his theory with the observations of Uranus from 1780, showing an excellent agreement. Airy in replying to this letter inquired whether the assumed perturbation would also explain the error of the radius-Vector of Uranus, which he seemed to consider the crucial test of correctness. It does not seem that any categorical reply to this question was made by Adams.

Meanwhile, at the suggestion of Arago, the investigation had been taken up by U. J. J. Leverrier, who had published some excellent work in theoretical astronomy. Leverrier’s first published communication on the subject was made to the French Academy on the 10th of November 1845, a few days after Adams’s results were in the hands of Airy and Challis. A second memoir was presented by Leverrier in 1846 (June 1). His investigation was more thorough than that of Adams. He first showed that the observations of Uranus could not be accounted for by the attraction of known bodies. Considering in succession various explanations, he found none admissible except that of a planet exterior to Uranus. Considering the distances to be double that of Uranus he then investigated the other elements of the orbit. He also attempted, but by a faulty method, to determine the limits within which the elements must be contained.

The following are the elements found by Adams and Leverrier: