150 



IDENTITY OF THE PLANET LEVEJtRIER 



Hypothesis I 



«— v— ' 



Mean longitude of the planet 1st October, 1846, 325°8' 



Longitude of the Perihelion 315°.57 



Eccentricity 0.16103 



Mass, (that of the sun being 1) 0.00016563 



Hypothesis II. 

 G = 0.515) 



' V ' 



323 c 2' 



292°. 11 



0.12062 



0.00015003 



" The investigation has been conducted in the same manner in both cases, so that the 

 differences between the two sets of elements may be considered as wholly due to the variation of 

 the fundamental hypothesis. 



"The errors given by the Greenwich observations of 1843, are very sensible, being, for 

 the first hypothesis + 6" .48, and for the second, + 5". 50. By comparing these errors, 

 it may be inferred that the agreement of theory and observation would be rendered very 

 close by assuming " = 0.57, and the corresponding mean longitude on the 1st of October 



would be about 315° 20', which I am inclined to think is not far from the truth. It is 

 plain also that the eccentricity corresponding to this value of % would be very small." 



This letter of Mr. Adams's is exceedingly valuable in the present inquiry. His most 

 probable value of % == 0.57 gives 33.6842 for the mean distance. The variation of the 

 eccentricity, according to Adams's Elements I. and II. for a variation of about one-thirtieth 

 of the primitive mean distance of 38.4, in —Yrjths of the eccentricity when the primitive 

 value is 0.16103. From this proportion between the variations of the mean distance and 

 eccentricity, the value of e, of the latter may be derived from any assumed value a, of the 

 former by the formula 



0.12062 1 ^ [ J 



-««-x[gB] ^ c 



03 



With the mean distance a, == 30.200585 of my Elements II., formula V. gives for the 

 eccentricity e, = 0.01538825. I am thus enabled to complete Elements II. without any 

 assumption respecting the missing star of Lalande, with one deficiency only, and that is 

 the want of knowledge of the fact whether the radius vector is now increasing or 

 diminishing. The complete elements for the only two possible cases are, 



