(11) 



410 Dr. T. J. Fa. Bromwicb : Examples of 



Thus F(a) 6V 



A'(a) c 2 



Hence we have the interpretation of (8) : 



V 15a" or a a- / 



= e { i ./, + ^sV" , '* ! ] 1 • (12) 

 t 15a 2 Tra » =i n 4 J v y 



and this result agrees with that calculated by A. R. McLeod 

 (see p. 13b' of the paper quoted). 



(/3) The same problem as (a), allowing for 

 surface-conductivity. 



The surface-condition is then 



K^ = A(Gi — w), at r=c, 



where A is the surface-conductivity, supposed to be the same 

 at all points on the surface of the spherical boundary. 

 Substituting in this condition the symbolic solution 



ru = sinh (qr/c)A, 



where A is independent of r, we deduce the formula 



ru _ eh sinh (qr/c) ^ . ^ 



c K(g cosh q— sinh q) + cii sinh q ^ '' ^ 



Then the mean temperature is given by the symbolic 

 formula 



:k% cosh q- sinh q) 



U ~~ q*{K(q cosh q- sinh q) + cA sinh ?} V ^ ' l ; 



and it will be noted that the formula (14) reduces to (8) 

 if cA/K-*co. 



To obtain the interpretation of (14), we note that 



g cosh ^ - sinh ? = (i- 1 l)q d + (i^-jho)g 5 + ■■■ 



Thus we find, on substituting in (14), and reducing 

 FQQ cA(l + T W + ...) 



A( jP )"" C A(H-k 2 +---) + K(k 2 +...) 



~ V15 + 3caJ a 2 ■"' 



