346 Mr J. Brill, On Solutions of Differential [May 6, 
the integral being taken along the boundary. 
R 4 Q 
Nee (3) 
: P 
If we apply this theorem to the region PQAS in figure (1) 
we have 
20u Ow Ou 
e meet (Fay a 
Sou Ou Ou 
pecans sal, (5 WU ~ 5, &) = 95 
and therefore 
tigate + | (5) dy — 5a ar) = 0, u +f (5,2 ~ ae 2): 
If we now make PQ and SR approach indefinitely near to 
each other, we obtain 
(Fae +rdy) + (Gedy 5u ae), 
? 
0 oy Oy Ox 
Ou re Ow Ow 
= (qe de+ = dy) + (5, dy ~5, de) | 
, Ow Ou 
v.€. le dy) = (ay dy) 
If we apply our theorem to the region PQRS in figure (2), we 
have 
2 jou Ou Rou Sou Ou Pow 
and therefore 
up Uy [| (jw- oe de) = uy U +] dy ~ 5 da). 
If we make PS and QR approach indefinitely near to each 
other, we obtain 
