1296 



).i , Il , Gi, Hi. 



We can choose a unit of time so tliat / =; t. This unit is about 

 9/8 of a day. 

 Then we have 



dli__^i* bSi dXi_^i* 05/ 



dr'~L?~dHi ' lh~Ü'~'bGi' 



As a general rule I will denote by [A'] the non-periodic part 

 of a function A'. We must have 



This can be realised in two ways. We can take 



or 





06/" 



= 



(^) 



{B) 



Now the perturbative function is given as a development (e.g. 

 by Newcomb's method) in terms of Xi, li, ai and ei, and we have 



bS- _ 2 bSi' cos*<pi 1 dSi' 

 dHi~ ^ [/ai ' da,- (i \/ai ei dei ' 



dSi' 2 dSi' cos (fi tan ^ (fi dSi' 

 a;- 



dGi ^ \/ai 'ö«j- 

 where Ave have put e; =^ sin (fi 



^ y ai dei 



dSi' ,. 



In the case (A) we thus find that a, ^~ is of the order of x, in 



Oat 



dSi' . 

 the case (B) it is of the order of x . ei*, in both cases — - is of the 



dei 

 order of x . ei It thus appears that the method (B) is preferable. 

 Instead of Hi=^ 2 Lisin" \(fi I now introduce 



i]i ^ 2 sin ^ (fi. 

 We have 



dai 2 



ai /Ji |/a, 



(ci^,- + dG-), 



1 /cos y \ 



drii = dHi — ^ r^i dGi • 



We find everywhere the denominator /?j l/a/. We can thus simplify 

 our formulas by putting 



