the Planet exterior to Uranus. 523 



his second memoir on the theory of Uranus. The first part 

 contains the results of a new reduction of nearly all the exist- 

 ing observations of Uranus, and their treatment with reference 

 to the theory of perturbations, as amended in the former 

 memoir. After concluding from this reduction that the ob- 

 servations are absolutely irreconcilable with the theory, M. Le 

 Verrier considers in the second part all the possible explana- 

 tions of the discordance, and concludes that none is admissible 

 except that of a disturbing planet exterior to Uranus. He 

 then proceeds to investigate the elements of the orbit of such 

 a planet, assuming that its mean distance is double that of 

 Uranus, and that its orbit is in the plane of the ecliptic. The 

 value of the mean distance, it is to be remarked, is not fixed 

 entirely by Bode's law, although suggested by it: several 

 considerations are stated which compel us to take a mean di- 

 stance, not very greatly differing from that suggested by the 

 law, but which, nevertheless, without the suggestions of that 

 law, would leave the mean distance in a most troublesome 

 uncertainty. The peculiarity of the form which the investi- 

 gation takes is then explained. Finally, M. Le Verrier gives 

 as the most probable result of his investigations, that the true 

 longitude of the disturbing planet for the beginning of 1847 

 must be about 325°, and that an error of 10° in this place is 

 not probable. No elements of the orbit or mass of the planet 

 are given. 



This memoir reached me about the 23rd or 24th of June. 

 I cannot sufficiently express the feeling of delight and satis- 

 faction which I received from it. The place which it assigned 

 to the disturbing planet was the same to one degree as that given 

 by Mr. Adams's calculations, which I had perused seven 

 months earlier. To this time I had considered that there was 

 still room for doubt of the accuracy of Mr. Adams's investi- 

 gations ; for I think that the results of algebraic and nume- 

 rical computations, so long and so complicated as those of an 

 inverse problem of perturbations, are liable to many risks of 

 error in the details of the process : I know that there are im- 

 portant numerical errors in the Mecanique Celeste of Laplace ; 

 in the Theorie de la Lune of Plana ; above all, in Bouvard's 

 first tables of Jupiter and Saturn ; and to express it in a word, 

 I have always considered the correctness of a distant mathe- 

 matical result to be a subject rather of moral than of mathe- 

 matical evidence. But now I felt no doubt of the accuracy of 

 both calculations, as applied to the perturbation in longitude. 

 I was however still desirous, as before, of learning whether 

 the perturbation in radius vector was fully explained. I there- 

 fore addressed to M. Le Verrier the following letter: — 



2 N 2 



