( 745 ) 
where we must take 
- R = e x x* + e 2 x'y -|- e t x'y* -f e t xy* + e#* -f 
+ $(“■ +«•)(*’+*>- J <** + **>■• 
§22. If we substitute in the function R for x and y the expressions 
assumed at first approximation and if we retain only those terms 
not containing t explicitly, we arrive at 
~^=Y<4- ~ cor, 2 -|- /«!«, sin' <p -f/, (o t -f « 3 ) | /a^ cos <p, 
where 
.= 5^+' 
4n« ^ 8 g* 
. 3* g «’ 
- sr* + ^ -’ 
Jl 8n** 
<p = 2n(p l -p i ). 
The system of differential equations indicating the time-variability 
of the a’s and ps becomes: 
~ — Infect, sin rp cos <p -f 2 nf x -f a s ) Va x a^ . sin <p 
= -f infant sin <pcos<p - 2nf, (a, -f «,) <p, 
? = °“‘ + 6 “* +/a ’ sin ' v ( 3V ^+ a '\/t) ms '' 
?=*••+«.+m «»■ * + 1/. (». + 8 
It appears at once from the system that: 
*1 + ^ = 0. 
*!+«* = ' 
50 * 
