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HISTORY OF PHYSICAL ASTRONOMY.

It is manifest that any two corresponding co-ordinates of either of tliotheories contained in the above table might have been employed with suc-cess in searching for the planet. Even twenty years before conjunction theerror of its position as assigned by Adams’ first approximation amounts tolittle more than 10°, a quantity which falls considerably within the range ofsearch proposed by the Astronomer Royal to Professor Challis, in the monthof July, 1846. The reader will not fail to remark, that the longitudes aregenerally represented with greater accuracy than the distances. This cir-cumstance admits of easy explanation. The intensity of the disturbing forcein any given configuration of the two planets depends on the mass and dis-tance of the disturbing planet. Now, if the distance be made too great,the disturbing force will be enfeebled in a corresponding degree ; but thiseffect may be obviated by a suitable increase of the mass. This is pre-cisely what happens in the theories of Le Verrier and Adams. The dis-tances are all too great in both theories ; but, on the other hand, the massin each case is considerably enlarged beyond its true value. The pertur-bations of Uranus may therefore be accounted for, in so far as the intensityof the disturbing force is concerned, even although the radius vector of thetheoretical planet should be considerably erroneous. The mass, however,exercises no influence in determining the direction of the disturbing force;and if the latter element be erroneous to any great extent, the perturba-tion will be necessarily erroneous also, since it cannot derive compensationfrom any other source. Hence arises the necessity of a comparativelyhigher degree of accuracy in the representation of the longitudes of thetheoretical planet.

When the elements of Neptune were determined with a degree of pre-cision sufficient to enable astronomers to trace its motion through theanterior part of its orbit, attempts were made to ascertain whether it hadbeen observed on any occasion previous to its discovery as a planet by Dr.Galle. It was soon found by Dr. Petersen, of Altona, and Mr. S. Walker,of Washington, thatja star in the Histoire Celeste of Lalande, observedMay 10, 1795, and since missing, could be no other than the planet Nep-tune. The place of the star being marked doubtful, the French astrono-mers were induced to examine the original manuscripts of the HistoireCeleste, which are deposited in the Royal Observatory of Paris. An in-spection of the observation established the identity of the planet with therecorded star, and disclosed an additional fact of extreme interest. Itappeared that the planet was also observed on the 8th May, 1795, andthat its right ascension and declination were regularly recorded, althoughthey were not subsequently inserted in the printed catalogue. The dis-cordance of the two positions May 8-10, in a case where identity waslooked for, beyond doubt suggested to Le Framjois Lalande a suspicion ofthe accuracy of his observations, and induced him to suppress altogetherthe observation of May 8. A comparison of the two observations clearly

investigation generally employed in physical astronomy. In his first solution, Mr. Adamsassumed that the mean distance of the hypothetic planet was equal to 38.4; in his secondsolution he made it 37.5; and in his communication to the Astronomer Royal, datedSeptember 2, 1846, he stated, as the result of further discussion, that 33.6 wouldprobably be a very near approximation. The actual mean distance in fact is 30.04.Thus we see that Mr. Adams was fairly cn the track of the true orbit. The methodemployed by M. Le Verrier is of a more ambitious character, but, unfortunately, it is notadequate to meet all the difficulties of such abstruse enquiries, and in the present instanceit had the effect of betraying M. Le Verrier into error with respect to the limits of themean distance and the other elements of the orbit.