Til K O U151T OF I i: A N US 17 



The following are special \alm s of y/_ and q t , developed to tne sixth power of 

 the eccentricities, as derived from the preceding formula-: 



3 :> 7 



1*1 ~~ * a e I ici.) C ooi<:^ 



1 11 

 l>2- 2 e - 3 - \- l( .c 



_3 I.'. 



m* 



-. , 4375 

 -384 -" 



. 

 46080 C 



27 

 80 



16807 



(16)' 



1 1 4 1 



~^ ~ " 



1 1,1 



_3 27 243 



3 ~ ~ C r e 



4 



I-'/ 



125 4 _3125 

 *~ C "9216 



27 , 

 *=8(/ 



_ 16807 

 27 = ~ 46080 



Having the developed and >? in terms of time, let us resume the equation (13). 

 As only purely linear operations are performed on Q in this equation, it follows 

 that if we represent its several parts by Q t , Q t , etc., and by fy>,, ip^ etc., the values 

 <*p obtained by putting Q = Q lt Q = Q t , etc., we shall have 



fy = fy, + fy, + etc. 



^'' liave, therefore, only to find the separate values of r *fy> corresponding to the 

 different terms of Q, and to take their sum. Let us then represent, as before, by 



h cos (W + a +/u' + jb) 

 i 

 any one term of R. 



3 April. 1873. 



