62 THE ORBIT OF URANUS. 



Perturbations produced by Jupiter. 



The series in which these perturbations are expressed converge so rapidly that 

 I deem it unnecessary to present the details of the computation. They have been 

 computed by both methods, and the separate and independent results are given in 

 the following table, where <H represents the perturbations computed by the method 

 developed in Chapter I, and iv 2 those computed by the method of variation of 

 elements. 



The apparently large discrepancy between the coefficients multiplied by the time 

 arises from the circumstances that in the form of development the mean motion, 

 and hence the mean anomaly, appears affected by the perturbation 31".2tf. Accord- 

 ingly when we enter the table which gives the true longitude in terms of the mean 

 anomaly in the form 



v = I 4- 2e sin (I n) -f- etc., 



we may consider this quantity 3l".2t as a secular variation of? n producing inv 

 the term 



lv GVAet cos (7 n). 



In dv l this term is left in its primitive form, while in fe 2 the value of I is supposed 

 to include this term, and the secular terms are only those which arise from the 

 secular variation of the eccentricity and perihelion. 



It is also to be remarked that the terms which are independent of the mean 

 longitude of Jupiter, or those in which i' = 0, are not comparable, as they corre- 

 spond to slightly different elliptic elements in the two theories. 



