IN PHYSICAL ASTRONOMY. 
47 
and 6i j0 = 2T80214, which differs but slightly from the value of b\, 0 given by 
Laplace, viz. 2* 1802348. 
The equation 
A = ifl _i 
r 2 L hjd\ J 
or S a = — S _L — A /*lL? d* 
r r r 2 ,/ dA 
appears to me to give numerical results more simply than that made use of 
by Laplace, 
2rJr + dr£r 
a- n d t 
+ 
V 1 — e' 1 
See Theor. Anal. vol. i. p. 491. 
When, however, that part of the inequality only is wanted which has a small 
coefficient in the denominator, as in the great inequality of Jupiter, the latter 
equation seems preferable, which thus reduces itself to 
?A = 
dtd’R 
The apparent difference between the value of the coefficient given by this 
equation and the former, (see Phil. Trans. 1831, p. 290,) arises, no doubt, from 
part of the expression given by the former containing implicitly the same 
small quantity in the numerator. 
It appears from the last Number of the Bulletin des Sciences Math6matiques, 
that M. Cauchy, in a Memoir read before the Academy of Turin, has given 
“ definite integrals which represent the coefficient of any given cosine in the 
development of R ,” by which means the calculation of any given inequality 
depending on a high power of the eccentricity is much facilitated. A similar 
method is alluded to by M. Poisson, Memoires de l’lnstitut, vol. i. p. 50. 
