HISTORY OF PHYSICAL ASTRONOMY.

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to its discovery in 1781, and on the anterior observations of Bradley,Lemonuier, and Mayer. The actual motion of the planet was representedbetter by them than by the tables constructed in 1821, but the residualerrors were still, in many instances, too great to be accounted for by anyprobable errors of observation. This was candidly admitted by the authorof the tables, who intimated also his belief that the errors were of such anature as to give countenance to the opinion entertained by his uncle thatthey were due to the perturbations produced by another planet*.

The failure of this laborious attempt to correct the tables of Uranus without the introduction of any new hypothesis, beyond doubt produced astrong impression on the minds of the French astronomers; and it wasprobably this circumstance which induced M. Arago to propose to hisfriend, M. Le Verrier, the theory of Uranus as a subject eminentlyworthy of attention. We have already had frequent occasions to alludeto the labours of this talented mathematician. He had recently beenoccupied with the theory of comets ; but, at the suggestion of the illustriousphilosopher just mentioned, he temporarily laid aside his researches onthat subject, and resolved to institute a searching scrutiny into all thecircumstances affecting the motion of Uranus . An account of the firstpart of his researches appeared in the Comptes Rendus of the Academyof Sciences , for the 10th of November, 1845. It contained the result of arigorous examination of the motion of the planet according to the princi-ples of the actual theory. The only interior planets which produce sen-sible perturbations in the motion of Uranus are Jupiter and Saturn , andof these the latter exercises the more powerful influence, on account ofhis comparative proximity to the disturbed planet. Le Verrier deter-mined the value of every inequality depending on the action of Saturn ,that exceeded the twentieth part of a second, employing two distinctmethods of calculation, in order to assure greater accuracy to his resultsf.He also computed all the perturbations occasioned by the action of Jupiter .Nor did he confine his researches to the inequalities of the first order ofmagnitude. All the principal inequalities depending on the squares ofthe disturbing forces were also taken into account by him J. A greatnumber of small terms were thus introduced, for the first time, into the

* In a letter from Eugene Bouvard to Mr. Airy, dated the 6th October, 1837, wefind also an allusion to the opinion entertained by his uncle, Alexis Bouvard , that the ir-regularities of Uranus were occasioned by a disturbing planet. After adverting to theinconsistency of the tables with observation, he then proceeds thus: “ Cela tient-il a uneperturbation inconnue apportee dans le mouvement de cet astre par un corps situe au-dela? Je ne sais, mais e’est du moinsTidee de mon oncle.”—Airy’s Hist. Statement, No. 3.

+ One of these methods is that to which allusion has been made in page 115 of this work.

I When the mutual action of two planets is considered, their perturbations are firstcomputed by supposing them to move in ellipses, and the resulting inequalities are of thefirst order with respect to the disturbing forces. In a second approximation the perturba-tions consequent upon the derangements of the motions of the two planets, as assigned bythe first approximation, are taken into account, and the inequalities hence derived are of thesecond order with respect to the disturbing forces. It is important to remark that theinequalities of the second order may be materially modified by the derangements of bothplanets depending upon the action of a third planet. This happens when the theory ofUranus and Saturn is considered, the action of Jupiter exercising a very sensible influ-ence on the mutual perturbations of those bodies. On account of his great mass and hiscomparative proximity to Saturn, Jupiter produces very extensive perturbations in themotion of that planet. Le Verrier, who resolved to verify everything by actual calcula-tion, was induced by this circumstance to investigate a great part of the theory of Saturn ,even although, in the present case, it was only with the ulterior view of computing theaction of that planet upon Uranus .