144 PROCEEDTNGS OF THE AMERICAN ACADEMY 



done to the doctrine of similar triangles and the science of trigonom- 

 etry is too evident to require any comment." 



Two hundred and ninety-fifth Meeting, 



May 4, 1847. — Monthly Meeting. 



The Vice-President in the chair. 



Professor Peirce announced that he had continued and near- 

 ly completed his researches into the irregularities of motion 

 exhibited by Uranus, and was more strongly than ever of the 

 opinion that they were not to be attributed to the influence 

 of the newly discovered planet Neptune. He had obtained 

 several possible solutions of the problem, which are diflJerent 

 from those of Leverrier and Adams, and which are published 

 in a communication to the Boston Courier^ dated April 29, 

 1847, and which he now proposes to lay before the Academy. 



" The problem of the perturbations of Uranus admits of three solu- 

 tions, which are decidedly different from each other, and from those 

 of Leverrier and Adams, and equally complete with theirs. The 

 present place of the theoretical planet, which might have caused the 

 observed irregularities in the motions of Uranus, would, in two of 

 them, be about one hundred and twenty degrees from that of Neptune, 

 the one being behind, and the other before, this planet. If the above 

 geometers had fallen upon either of these solutions instead of that 

 which was obtained, Neptune would not have been discovered in con- 

 sequence of geometrical prediction. The following are the approxi- 

 mate elements for the three solutions at the epoch of Jan. 1, 1847. 



I. II. III. 



Mean Longitude, . . . 319° 79° 199° 



Longitude of Perihelion, . . 148 219 188 



Eccentricity, . . .0.12 0.07 0.16 



In each of them (the mass of the sun being unity) 



The mass is 0.0001187 



" The period of sidereal revolution is double that of Uranus. It will 

 be observed that the mean distance in all these cases is the same with 

 that of Neptune, and that, in the first* of them, the present direction 



* The first of these solutions is corrected from the one which was published in 



