54 Mr. A. R. McLeod on the 



Substituting in (11), we find, since the series are uniformly 

 convergent, 



1+ Ji(y3» 3 +ff)j (A)L «W ' 



Taking the mean temperature, we get for the mean lag 



l - V£,i \\ z 4H 2 r(G^V r «, tfW 



■ a 2 V8 + 2H/ + ^AW + H 2 ) L a 2 A 2 



-("o+Si)-^ 2 ]- • (*» 



3. Cas# o/*a Spherical Bulb. 



To preserve the analogy, the solution will be obtained by 

 the use of Bessel functions. We require a solution, satis- 

 fying conditions (5) and (6) (in which c is now the radius of 

 the sphere) of the equation 



1 <^ _ 2 ^ u . ^ /.20\ 



a 2 d* ~ r ~dr * ~dr 2 K ' 



Substituting u = r~he~ a2an * t/c2 , x = a n r[c, we get 



cPv ldv / _1\ _ () 



dx 2 x dx \ 4^ 2 / 



Hence the general solution of (20) of the type required is 

 u= g A / -^(«//c)r a V^, . . . (21) 



n«=l 



To determine the constants «„, we arrive at the condition 

 «*J*'W + {H-i)Jj(«J=0, . . . (22) 



or (1 — H) tana M = «„. 



The basic expansion is 



/© - S G J*(^/«)fr- — , (23) 



j o 2 «J*(--0Wf 



