.315 



For c = 1.00 



V = ±90.0 







2.8 

 1.8 

 2.4 



For e = 0.06 

 For e = 0.05 



V = ± 87.2 



V = ± 85.4 



For e = 0.04 



V = ±83.0 



T s 



For e = 0.03 



V = ±79.2 



o.o 

 7.0 



For e = 0.02 



» = ±72.2 



221 



For e = O.OI 



V = ±50.1 



50.1 



For e = 0.006474 



V = 0.0 





72.2 



Hence the a priori probability that e falls below 0.02 is —— , and 



50.1 

 that it falls below 0.01 is — - , and this probability is based on a 



theory that has for its probable discrepancy from observation for 5^ 

 months ±0".49. 



The next inquiry is, how far this small period and small eccentri- 

 city may be reconciled with the conditional equations obtained by 

 Leverrier and Adams, between its perturbations of Herschel and the 

 residual perturbations of that body. 



In the supplement to the Nautical Almanac for 1852, Mr. Adams 

 states that a mean distance of about 32, and small eccentricity, agrees 

 with his computation better than the two hypotheses of a mean distance 

 much greater; and that the small mean distance and eccentricity are 

 in accordance with the planet's present place in the heavens. 



From the results of Mr. Adams' two hypotheses, Mr. Walker de- 

 rives the formula, — 



e = 0.16103 [Si] ^'"■^^' 

 This gives e = 0.0153883 for a = 30.20058. 



It remains to consider M. Leverrier's paper in the Additions to the 

 Connaissance des Temps for 1849. 



He there fixes the place of the planet at 240° ± 5° in 1840, for the 

 longitude of the epoch. Mr. Walker's Elements II. would give with 

 eccentricity < 0.06, the epoch = 226° nearly. Hence the limit of 

 M. Leverrier would be required to be doubled to include Mr. Walker's 

 solution. 



This limit of M. Leverrier may be readily extended to double his 

 assigned value, if we do not require this one disturbing planet to ex- 



VOL. IV. — 2 T 



