226 Journal of the Asiatic Soctety of Bengal. [June, 1912.] 
(2). Changing the equation into polars and noting that v 
is independent of angular co-ordinates, (writing k? for k) 
6v de 2) Oe 
we have 5 = *(se+: ah 
A(rv) rv) 
a 2 eee <a 
with the condition, rv =/(t), r=a. 
The solution is 
; (r—a)2 
J r—q — 4kt—a) 
we= abe : Cs ee (3) 
es heap hes " 

To verify this, we may put as usual, 
(r—a)". a he. 
4k(t —a) 
2 aD sain 2 
T= a J rs. (: is at) dx. 
9 


= 
pater je e . dd f(t) whenr =a 
mn ss : 
cE A, ee 
le as ff) =f. 
And the resultant tem 
perature due to the two surface 
conditions superposed will b 
e the sum of these, ie. (4) and (5). 
