1900. No. GE ON PARTIAL DIFFERENTIAL EQUATIONS, ETC. 
c. Let now G=0, E +0, F +o. System (II) (p. 16) becomes 
Ou Ou Ou du 
A(; ie Tage lee or Er a 
Ou Ou Ou Ou au |? ou ou _ 
oe oe 
ou]? cu Ou Ou du Ou\ Ou 
a B CES an ae > 2 (3) spe 
If we substitute the value of 2 * drawn from the first equation, 
the three other equations, we å re 
ou ou ou 
ar) DE, + HEZ=0 
Ou u 
AR: å + (EBF + ED) + EP (Z) =o 
AZ cn) 2 a DE 27 BE 
in 
Multiplying the first by ##?, the second by ZD, and the third by 
AF?, we obtain 
[4?7° + E?F?H + D2E® + ACEF? + BDE?F) pe 0, 
Ou 
or, when DE ENO) 
A2F3 + E2F2H + DE? 4 ACEF? + BDE?F=0; 
and when this relation exists, only two of the last three equations of our 
system are independent of each other. 
