( 634 ) 
In case the relation n i = 2n x is strictly satisfied or nearly so, the 
disturbing terms are: 
in the first equation those with q t q x , q x q t , q x q 2 ,q x q„ 
„ „ second „ „ „ q t * , q x q x q x *. 
If at first approximation we try to satisfy the equations by : 
q l -S=s Ah cos (n x t -f X) , q % ~Bh cos (n 2 t -j- p) 
where A, B, X and p are functions of t, however in such a manner that 
A, B, X, p are of order li or smaller, we may replace in the 
second member of the equations: 
</\ by n* (4 Vi 2 — g 2 ,), q* by n* (B'h? — q , 2 ), | 
'/. by — q, by — n.’q,. 
If we take this into account for the disturbing terms and if we 
omit the non-disturbing terms, the equations become: 
<h + — (K* + W,’ -f 2 p) q t q , — hq x q t , : 
) 
The terms %pq 1 q i in the first equation and pq* x in the second 
originate from a term —pq\q 2 , appearing in U % . 
To get rid of the term with q x q 2 we use the new variable q' 
so that: 
tit + ^ b 9i q t - 
* b q 1 + - hq x q 2 4- < 
. . » t 7~ ?• + 4 ?1 ?* - 2 1 (*.* + «,’) ?, ?»• 
Therefore: 
" , i- • 1 
9i + b 9i q 2 = q 1 ■+ - b («!* -f n *) q x q 2 . 
The equations now pass into: 
\ + V *’> = (iB >’ + «*■’ — \ t> a,* + 2 p) q\ q t , 
J fc + V«,■»=(« 
rt w* 01 WG - ma ^ re P^ ace second members q x by q /, as their 
difference is of order hr. * 
