OF ARTS AND SCIENCES. 341 



plicable to the theory of the mutual perturbations of Uranus and Nep- 

 tune. The successive periods of conjunction and opposition, occurring 

 at intervals of eighty-four years, that is, in about the time of revolution 

 of Uranus, this planet is always at the same part of its orbit when it is 

 most affected by the action of Neptune. The action of Neptune, con- 

 sequently, assumes a fixed, permanent, undisturbed character, so that 

 it can hardly be recognized as perturbation by the practical observer. 

 It is far otherwise with the ordinary class of perturbations, where the 

 place of greatest disturbance varies from point to point of the orbit ; 

 thus the place of greatest disturbance in the case of the theoretical 

 planet would not have remained stationary, but have varied 80° upon 

 the orbit of Uranus at each successive conjunction and opposition ; so 

 that the disturbance could not in this case be disguised to any great extent 

 under the fixed laws of ordinary elliptic motion. In the case of Nep- 

 tune, its action on Uranus is to be detected in the comparatively small 

 differences between its character and that of an elliptic motion, and the 

 difference between the influence at opposition and that at conjunction. 

 In undertaking, therefore, anew the solution of the problem of the 

 perturbations of Uranus, with the assumption of the actual period of 

 Neptune, instead of that adopted in the former theories, I found at 

 once that I could not profit by the previous researches of Adams and 

 Leverrier. The problem now presented, instead of being of the usual 

 character, assumed a differential form by the disguise of the primary 

 perturbations under the aspect of elliptic motions, and the whole ques- 

 tion now rested upon the secondary perturbations, which were compar- 

 atively unimportant in the previous theories.' 



" There is a popular notion, which hardly deserves to be refuted be- 

 fore a scientific body, that the less distance of Neptune than the planet 

 of geometry is compensated by its smaller mass, so that its action upon 

 Uranus is the same with that which was predicted. But the fallacy of 

 this view of the subject, which takes no cognizance of the chief diffi- 

 culty of the problem arising from the unknown orbit of Uranus, is ob- 

 vious enough from a simple inspection of the following table, in which 

 no one can fail to perceive the difference between the actions of the 

 two planets. The second column of this table, which comprises the 

 action of the theoretical planet of Adams's second hypothesis, is copied 

 from page 27 of Adams's memoir. 



