These elements represent the observations of the planet with a remarkable degree of precision. It will be seen that they differ in several respects very considerably from the corresponding results obtained by Mr. Adams and M. Le Verrier. This circumstance pre sented a difficulty to the minds of several persons, who even went so far as to assert that the planet Neptune did not represent the theo retical planet indicated by the researches of those geometers, and that Its discovery was the result of a happy accident ! But any such diffi culty will vanish when it is borne in mind that the object proposed by M. Le Verrier and Mr. Adams wan not to determine rigorously the elements of the disturbing planet, which could only result from the discussion of a series of its oterved position, but merely to ascertain its whereabouts during the period when its perturbations were sensible. For this purpose, any combination of elements varying within consider able limits will be sufficient. During the whole of the period comprised between the year 1090 and the beginning of the present century, the disturbing action of Neptune was incapable of exercising any appre ciable influence on the motion of Uranus. During the present century, however, the perturbations have been of sensible magnitude. It was therefore necessary that throughout this period the intensity and direction of the disturbing force, and consequently the position of the disturbing body, should be represented with considerable precision by the theoretical results of M. Le Ferrier and Mr. Adams. That this object was effected by both of the geometers just mentioned may 1 e readily seen by the following numbers, which exhibit a comparison between the heliocentric longitude and radius vector of Neptune for every ten years since the year 1800, and the corresponding values of the co-ordinates, as deduciblo from the researches of M. Le Verrier and Mr. Adams Shortly after the discovery of Neptune, Mr. Lease]] discovered that it was attended by a satellite. M. Otto Struve found from his own obser
vations, made with the great refractoi of Pulkowa, that the semi-major axis of its apparent orbit is l7"'89, and that it revolvers round the planet in a period of 21"l 5•*. These elements give for the mass of the planet the value the sun's mass being represented by unity. Professor Peirce, of Harvard College, Cambridge, U.S., determined the mass of the planet from observations of the satellite made by the late Mr. Bond, Director of the Cambrid,e Observatory, and found it to amount to in terms of the same unit. Adopting this value of the mass, Professor Peirce calculated the perturbations produced by the planet in the motion of Uranus, and he obtained results which on the whole repre sent very satisfactorily the irregularities in the motion of the latter planet which so much perplexed astronomers previously to the dis covery of Neptune. It will be seen that tho masa of Neptune, as deduced from the observations of the satellite either by M. Otto Struve or Mr. Bond, Is considerately leas than the value of the same element assigned by Mr. Adams or M. Le Vcrricr. It is to be borne in mind, however, that, on the other hand, the researches of both these geometers make the distance of the planet from the sun greater than the true distance. A compensation is thus effected, so that the intensity of the disturbing force presents a satisfactory agreement in all three cases: How nearly the direction of the disturbing force agrees in so far na regards the real end the theoretical planets, has been shown by the table just given.
31. Kowalski has recently published tables of Neptune, which are used in the' Nautical Almanac' for computing the ephemeris of the planet. Mr. Arlains's researches on the theory of Uranus aro to be found in the Supplement to the Nautical Almanac for 1851 ; those of M. Le Verrier on the same subject are published in the 'Connaisaance des Temps' for 1849.