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HISTORY OF PHYSICAL ASTRONOMY.

The theory of Uranus was now about to be submitted to a severeexamination by a young mathematician of England. Mr. J. C. Adams ,while still pursuing his studies at St. John’s College, Cambridge, had pur-posed investigating the cause of the strange irregularities in the motion ofthe planet. His attention was first drawn to the subject by Mr. Airy’sallusion to those anomalies in his valuable account of the progress ofastronomy in the nineteenth century, contained in the Report of theBritish Association for 1832. Mr. Adams , on referring to bis note-bookat a subsequent period, found the following memorandum inserted in itunder the date of the 3rd July, 1841 :—“ Formed a design, in the begin-ning of this week, of investigating, as soon as possible after taking mydegree, the irregularities in the motion of Uranus which are yet unac-counted for; in order to find whether they may he attributed to the actionof an undiscovered planet beyond it, and if possible, thence to determineapproximately the elements of its orbit, &c., which would probably leadto its discovery.”*

Mr. Adams having taken his degree in January, 1843, proceeded toconsider the subject of his future researches. The problem which offereditself to him for solution maybe stated in the following terms :—Assumingthat Uranus was disturbed by some unknown body, to determine the posi-tion of the latter, its mass, and the elements of its orbit, by means of theirregularities it produces in the motion of the disturbed planet. Thisproblem being the inverse case of the ordinary problem of planetary per-turbation, is manifestly of a very intricate character, and demands theresources of a very refined analysis for its successful treatment. Nay, it iseven more complicated than at first it appears to he, for the elements ofUranus , which form the basis of the geometer’s researches, are vitiatedby the action of the unknown planet, and their rectification, howeverdesirable, can only he effected by the actual solution of the problem. Inorder to acquire clear ideas upon this point, the reader must bear in mindthat the fundamental or mean orbit of Uranus is an ellipse, in which itwould constantly revolve if it was exposed solely to the attractive influenceof the sun, and that the action of the other bodies of the system tendsmerely to occasion minute excursions of the planet now on one side andnow on the other side of this orbit. It is manifest, then, that in deter-mining the elliptic elements of a planet’s motion by means of its positionsas assigned by observation, the effects of perturbation must be subductedfrom the co-ordinates of each position, in order that the planet may he reducedto the place which it would occupy in the mean elliptic orbit. Now whenDelambreand Bouvard were severally engaged in determining the elementsof Uranus, they applied the perturbations due to Jupiter and Saturn as cor-rections to the positions derived from observation; but, as they did not takeinto account the action of the unknown planet, it is manifest that, if thelatter really existed, the final values of the heliocentric co-ordinates, as de-termined by each of these astronomers, must have failed to represent theelliptic positions of the planet. Hence, the elements deduced from theseerroneous data were necessarily inaccurate, and it is manifest that thiscircumstance alone would have the effect of distorting the orbit of theplanet, and thereby occasioning discordances between the observed andcomputed values of the longitude, latitude, and radius vector. The errorsof the tables of Uranus were, therefore, attributable to two distinct causes,being due partly to the errors in the elements of the planet’s own orbit,

* Mem. Ast. Soc., vol. xvi.; see also the Nautical Almanac for 1851 {Appendix ).