1900. No.5. ON PARTIAL DIFFERENTIAL EQUATIONS, ETC. 23 
Multiplying this equation by an indeterminate quantity uw, and adding 
the result to the second equation of (Il), we obtain 
ou)? ÆD[au]? (ED+ CG)u+ HG du ou Ou\ Ou 
nals EG [>| GA Voy UG | | 
ou 
Her) + Agel ge + PU a AG) - 
Reasoning as before, we are led to assume, as an equivalent of the first 
member of our equation, an expression of the form 
(arme 
Multiplying the factors of this expression together, and then equating 
the coefficients with those of the first member of the proposed equation, 
we obtain 
uA=uA 
a2 aes 72 
Ber a oa 
(ED + OUT A+ my 
u.G=—m.u 
uF=n.m 
G=—m.m 
Den) 
all 7 
From the last four equations, we find 
oe =? AND 
values which will be found to satisfy the second and fourth equations, 
and which reduce the third equation to the form 
FGu? + (ED + CG) u + AG — AD =o. (u) 
