the Planet exterior to Uranus. 533 



arrive here, at the earliest, before the third or fourth week in 

 September; and it does not appear that any earlier notice of 

 its contents was received in England. 



It is not my design here to give a complete analysis of this 

 remarkable paper; but I may advert to some of its principal 

 points. M. Le Verrier states that, considering the extreme 

 difficulty of attempting to solve the problem in all its gene- 

 rality, and considering that the mean distance and the epoch 

 of the disturbing planet were determined approximately by 

 his former investigations, he adopted the corrections to these 

 elements as two of the unknown quantities to be investigated. 

 Besides these, there are the planet's mass, and two quantities 

 from which the excentricity and the longitude of perihelion may 

 be inferred ; making in all, five unknown quantities depending 

 solely on the orbit and mass of the disturbing planet. Then 

 there are the possible corrections to the mean distance of Ura- 

 nus, to its epoch of longitude, to its longitude of perihelion, 

 and to its excentricity ; making, in all, nine unknown quan- 

 tities. To obtain these, M. Le Verrier groups all the ob- 

 servations into thirty-three equations. He then explains the 

 peculiar method by which he derives the values of the un- 

 known quantities from these equations. The elements ob- 

 tained are, — 



Semi-axis major 36*154 (or — =-.0*531. ) 



Periodic time 217 y *387 



Excentricity 010761 



Longitude of perihelion 284° 45' 



Mean longitude, 1 Jan. 1847 ... 318 47 



Mass -J-— 0-0001075 

 9300 



True heliocentric longitude, 1 Jan. 1847 326° 32' 

 Distance from the sun 33*06 



It is interesting to compare these elements with those ob- 

 tained by Mr. Adams. The difference between each of these 

 and the corresponding element obtained by Mr. Adams in his 

 second hypothesis is, in every instance, of that kind which 

 corresponds to the further change in the assumed mean di- 

 stance recommended by Mr. Adams. The agreement with 

 observations does not appear to be better than that obtained 

 from Mr. Adams's elements, with the exception of Flamsteed's 

 first observation of 1690, for which (contrary to Mr. Adams's 

 expectation) the discordance is considerably diminished. 



M. Le Verrier then enters into a most ingenious computation 

 of the limits between which the planet must be sought. The 

 principle is this : assuming a time of revolution, all the other 

 unknown quantities may be varied in such a manner, that 



