1900. No. SE ON PARTIAL DIFFERENTIAL EQUATIONS, ETC. 25 
Gu 
gn +65 
0 a) 
—G (S| tur =o IH. 
Da = Gz) +125 = 
where A and w must satisfy the condition 
AD — HG 
ar 
and 
Ou Ou Ou 
25 ane apr ER Gr 
Gå Ou De 
FE G(s, | or 
Go Ou A% 
Cet lay AG =9, 
where Å and w must satisfy the condition 
AD — HG 
uh = ad rc ae ’ 
and these two systems are equivalent. We have then only to consider 
the systems (III). 
That these systems are relevant to the solution of the problem under 
consideration may be shown by eliminating from (II), by means of the 
system 
ei eo 474 = 
Er 
