( 742 ) 
where U A represents a homogeneous function of degree 4 in q x and 
q 2 . Furthermore we find : 
T=\q x ' +4 q 2 ' 4- \ ?;* 4- p* ftft 4- 4 p , ft*; 
where: 
p i = «i ft 2 4 ft ft ft 4 «. ft% 
p * = ft* 4 6 s ft ft 4 ft 2 * 
p 3 = «> ft 2 4 ft ft ? 2 + f, 
the a’s, d’s, and c’s being constants. 
The equations of Lagrange become : 
. dP, • 
ft 4 «i- s ft = - 
.j.-P.ft- 
2 d^ 
d ft 
ft 4- V ft = — P* ft — A g, 4- 
dP. dP, 
/I dP, dP 2 \ . 
/ 1 dP, dP\ . dP, . . 1 dP, . 
1 2 d ?> d ? , J ?1 dq, ' h ?2 
dP, 
In the same way as was done in §15 we may replace ft, ft, 
g x *, and . ft 2 in the terms of order h 9 by others. 
Now in the first equation a term — a 2 q x ft q 2 appears which 
we must consider separately (in the second equation also there are 
terms containing ft ft, but these are not disturbing). 
We introduce for this a new variable q\ in such a way that: 
Then we find : 
1 .. 1 ... 
91 — 4 -j ft ft g* 4 y «2 q* (ft ft 4- ft*) 4-«, ft ft ft* 
where ft and q 2 in the terms of order h 3 may again be simplified. 
Of the terms now appearing in the equations of motion the following 
are disturbing, in the first equation those with frq^ ft*, q*q 2 and ftft 8 , 
in the second those with A*ft, q*> q 2 and ft*ft. Now just as in $ 15 
the terms with ftft 2 in the first equation, those with q x q s in the 
second equation may still be simplified. 
If we perform these calculations the result proves that the terms 
of order h * to be inserted in the equations may be put in this form; 
Ptyi 4 «ft*ft 4" <ft* in the first equation. 
Q h ~ ( h 4- /ft 3 ‘ 4- „ „ second „ 
