1900. No.5. ON PARTIAL DIFFERENTIAL EQUATIONS, ETC. 33 
Reasoning as above, we see that this equation may assume the fol- 
lowing form: 
ae ew ee amy (cla un 
[2 Gi) a >) A | 12) Be TE Å EL 
where À is to be determined by the equation of the second degree, 
A21— ABA+ CA + EH=o. 
If A, and A, be the values of A thus found, our given system becomes 
of 
Ts 
DUREE aaa. 
po 2 [PD + aa 
Now these equations can only be simultaneously satisfied by equating 
to zero one factor in the first member of each of the last two equations; 
and the different combinations which are thus possible give rise to four 
systems of linear equations. 
If we equate to zero the first linear factors, we have 
Po 
ot 
a +22 
+) 
whence, by subtraction, 
2 
eae) S| =o. 
This combination must therefore be rejected. In like manner the 
combination formed by equating to zero the second linear factors in the 
Vid.-Selsk. Skrifter. M.-N. KL 1900. No. 5. 3 
