CHAP. II., 5.] PHYSICAL ASTRONOMY. M. LEVERRIER MR ADAMS. 



31 



amounted to two minutes of longitude. M. Bouvard 

 to his latest years, perhaps his latest hours, 1 che- 

 rished the hope of extricating this theory from its 

 difficulties. He also engaged his nephew M. Eugene 

 Bouvard in the same career, who appears to have 

 followed it with much zeal and intelligence, and 

 in 1845 constructed new tables of Uranus. But by 

 this time two geometers had separately and inde- 

 pendently undertaken the problem, with the deter- 

 mination of finding, if possible, a physical solution 

 of all this perplexity. The earliest in point of date 

 was Mr Adams, a young graduate of Cambridge ; the 

 other was M. Leverrier of Paris, whose attention 

 was directed to the subject by .M. Arago. As the 

 researches of M. Leverrier, though second in point of 

 time, occasioned the actual recognition of the planet, 

 and thus stamped the correctness of the solution with 

 success, we shall consider them in the first instance. 

 (133.) M. LEVERKIER is, we believe, a native of St Lo 

 M. Lever- i n Normandy, a province which has been singularly 

 ; 8 ~ productive of eminent men (Laplace and Fresnel 

 were of the number). With no advantages, but the 

 reverse, he won a high position at entering the 

 polytechnic school, which he constantly maintained. 

 He at first, we believe, attached himself to chemis- 

 try, but his taste for physical astronomy was soon 

 developed, and was advanced entirely by his private 

 efforts. It is a peculiarity of the mode of culti- 

 vating the sciences in Paris, that such abstruse 

 and difficult studies are not merely engaged in tem- 

 porarily for purposes of academial distinction, but that 

 they actually become a " carriere" or calling, and are 

 pursued in that methodical manner for which the 

 French are distinguished. In 1845, when he com- 

 menced the careful examination of the theory of 

 Uranus, M. Leverrier was already favourably known 

 by his researches on comets, and on the orbit of 

 Mercury, but especially by immense calculations, con- 

 nected with the secular inequalities of the planets, by 

 which his ability and hardihood in computation had 

 been thoroughly exercised. He began his new en- 

 quiry with the method and intrepidity of calculation 

 which distinguish him. He revised with the most 

 minute care the observations of Uranus, and 

 computed afresh every sensible perturbation which 

 theory recognised as arising from known planets. 

 This done, and having compared the most probable 

 orbit with observations which he collected from 

 authentic sources, and especially from the Greenwich 

 observations which were communicated to him for 

 this purpose, the result was, that even confining 

 himself to observations since 1781, arranged in 

 eleven convenient groups (each resulting from many 

 observed places), and attributing to each group the 



largest error which could be in reason allowed, 

 and even admitting that all these errors were in the 

 direction most favourable to the assumption, it was 

 still impossible to account for more than one-fourth 

 part of the observed discordances. 



M. Leverrier then assumed that a perturbing 

 planet existed beyond the orbit of Uranus, and at 

 nearly double its distance from the sun, in conformity 

 with the empirical law, (usually attributed to Bode 

 the German astronomer,) which expresses with gene- 

 ral accuracy, thus far, the arrangement of the planetary 

 system. The law is, that the distances of the planetary 

 orbits from Mercury are successively doubled. This 

 assumption (it was absolutely necessary to assume 

 some distance to begin with) was ingeniously con- 

 firmed by other considerations. 



Leaving the perturbations in latitude out of ac- 

 count, he now considered each error of Uranus in 

 longitude as the expression of a perturbation due 

 to the action of the unknown planet, and capable 

 therefore of algebraic expression in terms of the ele- 

 ments of that planet, namely its excentricity, longi- 

 tude of perihelion, epoch in its orbit, and mass ; but, 

 as we have already remarked, the first three of these 

 elements must be considered as incorrectly assumed 

 for Uranus itself, as well as the mean distance of that 

 planet, and, therefore, there are four unknown correc- 

 tions for its elliptic elements, making in all eight quan- 

 tities to be eliminated from the discordances of theory 

 and obserYation. So complex an elimination cannot 

 be directly effected ; and even if it could, the result 

 could not be depended on, as the possible error of 

 each observation involves a fresh and important 

 source of doubt in the conclusion. M. Leverrier 

 proceeded, by a series of gradually restricted assump- 

 tions, to find within what limits the more important 

 elements might be made to vary without producing 

 effects incompatible with observation, and his atten- 

 tion was at first confined to the approximate mean 

 longitude of the planet. He obtained a result after 

 a prodigious amount of tentative calculation. The 

 excentricity and position of the perihelion were then 

 inferred. On the 1st June 1846 he announced to 

 the Academy of Sciences that the true longitude of 

 the expected planet for 1st January 1847 was 325, 

 with a probable error of 10. This result was im- 

 mediately published in the Comptes Rendus. 



Between the 1st June and 31st August 1846, 

 when his third memoir on the perturbations of 

 Uranus appeared, M. Leverrier busied himself in ob- 

 taining a farther approximation to the elements and 

 place of the suspected planet. He now assumed the 

 correction of the mean distance amongst the other 

 quantities to be sought. By a fresh calculation he 



(134.) 



(135.) 

 how con- 

 ducted : 



Their re- 

 sult. 



(136. 

 M. Lever- 

 rier's final 

 announce- 

 ment; 



1 M. Bouvard was born in 1767. He performed almost all of the numerical calculations required by Laplace in his great 

 work, and was associated with that eminent man by the most friendly ties. He " ceased to calculate and to live" 7th June 

 1843. 



