( 214 ) 
e' = e’y, + w, - e'x, + vS, = ie* (r, + x,) + k V ( n , + & 
so that we can write: 
V '(r-x,) = i P * ( r,+l 1 )<r 4 -i,)+i^+g,). - - ft,-g.) = 
= W,*-x. , )-KV-i’). 
by which (11) passes into 
t-’K n - | - I X,*)! - |ft, - 
(12) 
The second member of (12) must now be brought by means of 
the differential equation of y — tp (x) into the form 
q* m*f&) .i- . 0 ? 
from this can easily be found that <P (y) must be of the form io(y) :/'* (y); 
the transformation of the second member of (12) takes place as follows 
If now the given function y- 
of the third order 
t co(y) o>(*)l 
|/ r %) /»v 
: <f{x) satisfies the differential equation 
(^l^)-(?-^) + ‘ o(y)J ' ,, - <o( * y ' =0 ’ ’ (1S) 
then f{x ) resp. f{y) is found out of 
|/'"(y) 3 /'”(y)) _ (/» 3 /"»(»)> = _ j**L, 
\f"(y) -/"(y) i j/'■(*> 2/»l f"W 
so out of 
/V) _ % f'\y) _ °>( x ) __ c . . . . ( 14 ) 
f\x) 2 f\x) f"{x) ’' 
and then here too we are able to build up <p{x) by means of infinitesi 
iteration. 
By putting t equal to x (13) passes into 
The 
F\x) ~ 
thus a 
—7 .—-r y -% + «Ky)y"-«>(*) = °- 
y 2 y 
integration furnishes if we introduce fo 
the symbo1 yW 
ag(x) + 0 
.... ( 15 > 
the integral of 
1 standard form ivith three independent arbitrary consta 
