( 22 ) 
bepa gthqtea 
bep te ga ha—«@ 
Ww) == 
f having the same meaning as above. 
IL. When À and w are only dependent on z, y, z, the equation 
possesses two intermediate integrals only when 
XxX! 
N= yi? 
“a x” 9 x! x" ed 3 x" 9 vt mas y 2 
ne e+ wle, gy), 
where w(z,y) represents an arbitrary function of « and y, whilst 
X denotes a function of « and Y a function of y, of which the 
derivatives are indicated by dashes. 
In this case we find one of the intermediate integrals by 
eliminating y between 
KS Const 0 
and 
dv 3 ; Bu y' X'! 
mrt) VoD: 
where 
OA OA 
| fn) ie 2 ae ' 
= (= Me)? L 2A (p+ Aq) 
If we solve the integral of this linear differential equation accord- 
ing to the arbitrary constant C’ and if we replace this constant by 
an arbitrary function of C, the intermediate integral under research 
will be found if moreover we substitute X + Y for C. 
The second intermediate integral is determined in a similar way 
out of 
XS 
and 
fi " iV ! 
du 3 (Gp) rven 
where 
vG thijs +2 Ag) 
