1900. No. 5. ON PARTIAL DIFFERENTIAL EQUATIONS, ETC. 
35 
Case II. Let F=o, G=o, E +0, and suppose A~o. 
case I, we are led to assume that D — 0. 
assumes the form 
As in 
The given system (p. 31) then 
Of es 
a 
ie) 
CUS 
The second equation reduces to one equation, or breaks up into two 
equations of the form 
0 
DAN SZ of of 
I) or ts ap 
À being determined by the quadratic equation 
fj? — BL + E=o. 
Making is À ai in the third equation of our system, we get 
> er oy q y S 
(+e wt] 
which breaks up into 
JAN of VA of 
(2) ar 2 (Å) + CZ 14 =o. 
But if we combine the first of these with the two other equations of 
our system, we obtain a combination which must be rejected as irrelevant 
to the solution of our problem. There remains then the combination 
GLE 
SP 
BP) +f m =o 
ox 
0 
