( 737 ) 
To transform the equations to such a form that the disturbing 
terms may be regarded as derivatives of one and the same function 
resp. to x and y, let us consider the term with xy 2 in the first and 
that with x 2 y in the second equation. If we substitute the expressions 
found above as first approximation for x and y in these terms, after 
the development of the products and powers of the cosines among 
others terms will appear, differing only in coefficient from the 
expressions indicated for x and y ; the remaining terms which appear 
are not disturbing. From this ensues that we may replace: 
in the first equation: xy 2 by 
in the second equation: x-y by ~ ~ y. 
Accordingly the equations may be written : 
We thus see that they take the form of: 
$ 16. We must now write R as function of the «’s and p’s by 
substituting for x and y, in the expressions obtained, the expressions 
by which they are represented at first approximation, and by retaining 
only those terms in which t does not appear explicitly. Thus we 
arrive at: 
aa, a -f ba t a, — ea* -\- y h * «* -f- m i 2 2 cos tp , 
