LE VERRIER AND ADAMS PLANET. 



There were not wanting, some who, viewing these discordances, 

 did not hesitate to declare that the discovery of the planet was 

 the result of chance, and not, as was claimed, of mathematical 

 reasoning, since, in fact, the planet discovered was not identical 

 with either of the two planets predicted. 



To draw such a conclusion from such premises, however, betrays 

 a total misapprehension of the nature and conditions of the 

 problem. If the problem had been determinate, and, conse- 

 quently, one which admits of but one solution, then it must have 

 been inferred, either that some error had been committed in the 

 calculations which caused the discordance between the observed 

 and computed elements, or that the discovered planet was not 

 that which was sought, and which was the physical cause of the 

 observed disturbances of Uranus. But the problem, as has been 

 already explained, being more or less indeterminate, admits of 

 more than one, nay, of an indefinite number of different solu- 

 tions, so that many different planets might be assigned which 

 would equally produce the disturbances which had been observed; 

 and this being so, the discordance between the two sets of pre- 

 dicted elements, and between both of them and the actual elements, 

 are nothing more than might have been anticipated, and which, 

 except by a chance, against which the probabilities were millions 

 to one, were, in fact, inevitable. 



So far as depended on reasoning, the prediction was verified ; 

 so far as depended on chance it failed. Two planets were 

 assigned, both of which lay within the limits which fulfilled the 

 conditions of the problem. Both, however, differed from the 

 true planet in particulars which did not affect the conditions of 

 the problem. All three were circumscribed within those limits, 

 and subject to such conditions as would make them produce 

 those deviations or disturbances which were observed in the 

 motions of Uranus, and which formed the immediate subject of 

 the problem. 



14. It may be satisfactory to render this still more clear, by 

 exhibiting in immediate juxtaposition the motions of the hypo- 

 thetical planets of MM. Le Verrier and Adams and the planet 

 actually discovered, so as to make it apparent that any one of the 

 three, under the supposed conditions, would produce the observed 

 disturbances. We have accordingly attempted this in fig. 4, 

 where the orbits of Uranus, of Neptune, and of the planets 

 assigned by MM. Le Yerrier and Adams are laid down, with the 

 positions of the planets respectively in them for every fifth year, 

 from 1800 to 1845 inclusively. This plan is, of course, only 

 roughly made ; but it is sufficiently exact for the purposes of the 

 present illustration. The places of Uranus are marked by Q 

 182 



