( 539 ) 
yy = Wi (*1) 
and with the aid of this equation: 
ty =P [1 (%)s Yrs “J 
from which 7; may be solved. Here #, and z, are again the limits 
between which y may be represented by wi (2). 
From the two equations: 
w&=oply' ge) and y= wie) 
we may eliminate y and then solve « as function of y' and 2’, 
Let us represent this by: 
smile, gy) thn y=w[ry)] 
and 
dy amily (2,4) 1 
de dz (ey) 
eis dy . 
By substituting these values of z, y and an the given equation ; 
v 
dij digs 
(=. pews vy, ») = 0 
we get a differential equation : 
U 
Bree 
Fy (Shays #') =0 
; nt dal s:, oud 
in which only Edd and 2’ occur. If the solution of this equation 1s: 
v 
y= We, ©); 
we may represent y by (e) between the limits vy and 23, which 
vz may be again calculated from #9 by means of the formulae: 
= P (Y3s Yas a) 
Yo = Wz (#2) and Y3 = We (#3) 
wa contains a constant c, of which we may still dispose. We 
determine it in such a way that: 
Yo = Wiler) = y' = Yo (Yas ©) + 
39* 
