42 Proceedings of the Royal Irish Academy, 



These equations can now be solved by approximation. 

 Por this purpose, we must calculate the numbers e^^,, e^^. 



^^ow, ^ 



fjL having all positive integer values. 

 Now, 



V ^ ^ f 2 ^ _ ^ _Jt \ 



Now, u 1/1 1 



+ 



6-2 - 4/^2 4 \2/t - 5 2fjL + s J' 

 '^52-4/^2 4 ( VI 3 5 



1 n \2fia-i)-.f:.^JL)i (42) 



4(s'2_s2) (s' s \ 3 sj V 3 

 Again, 



Now, 



16 256 ^ 64aA/€i3 4aA 



16 4ah 

 16 4aA 

 75 = 



Now, integrating our original expression for v over disk, and 

 remembering that Ji{a„,) = 0, we find 



7 4 A ^ 1 



, 4h I 16/1 1 \\ 16a/i"- ^ ,,,, 



where ^ , 1 1 



or, nearly, 



