142 Mr. A. R. McLeod on the Lags of 



4. Steady Lag for a Sphere in a Medium whose 1 emperature 

 changes at a Uniform Rate, the Surface Conductivity 

 being Finite. 



We require a solution of (1) which satisfies the con- 

 ditions 



u = 0, for t = 0, 

 k|? « h(Qt-u), for r = e (13) 



The temperature of the medium is Grt, and h is the 

 (constants surface conductivity. Let the lag at any point 

 in the sphere distant r from the centre be 0, and write 

 u = Gt-e in (1). Then we get 



G 



t ~ a V r 2 r'dr)' 



and for the steady lag o&/ot = 0. 



Hence the equation for the lag, when it has reached its 

 steady value, is 



d 2 2 dO G ' 

 dr z r dr a* 



The solution of (14) is 



'- a +?-t£ (15 > 



Since 6 is finite for r = 0, we must have B = 0. 

 The mean lag for the sphere is 



If there is a temperature lag, C , at the surface, it is 

 given by 



K~= h(Gt — u\ where r — c. 

 or 



This becomes 



-K 



&L-*- • — (17 > 



