OF HEAT IN ELLIPSOIDS OF REVOLUTION. 
151 
where 9 and 12 are determined by the equations 
d 2 9 . , n d9 m?9 0 „ n , . 
A s+ co ~ kx ~ 008 .< 79 > 
/720 r/O 
Vf + tanh af- + = -X 2 c a sinh® a.O+LQ. 
dor da. cosh- a 
The latter of these equations, on putting £=kc cosh a, becomes converted into 
, >* , x „ 0 \d 2 n odX2 X 2 c 2 r/fi 7>i 2 X 2 c 2 f2 />o \o o\ , 7 
(f-+x-c-)—+2£— +——+ — _ — (£-—\-c~)n+£n . . . (so) 
These two equations (79) and (80) are of precisely the same form as (18,) and (19) 
which we have been discussing, and differ from them only in having — \~c 2 instead of 
+\ s c 2 . The subsequent formulae will, therefore, be the same almost in every instance, 
and the investigation need not therefore be repeated. 
