in Rectangular Order upon a Medium. 

 which, as is well known, is the value of 



489 



12+ (_1)2 -22' 



111 



+ «• + 7—^ + 



Hence 



S 2 = 2tt 2 2 hm-Hrmr + Jtt 2 ; . . 



and in like manner 



S 4 = -p. -f 27r 4 2 { — § sin~ 2 z7?27r + sin -4 /w7r}, . 



0—.6 wi=oo 



Sf = 27735 + *>*£ \-h ™~ W 



— sin~ 4 zm7r + sin~ 6 m7r}. . 



(30) 

 (31) 



(32) 



We have seen already thnt S 6 = 0, and that S 2 = 7r. The 

 comparison of the latter with (30) gives 



2 sin" 



nmir- 



6 



(33) 



We will now apply (31) to the numerical calculation of 

 S 4 . We find: 



m. 



— sin 2 im7r. 



ein Hmir. 



1 

 2 

 3 



•007497G7 



1395 



3 



•0000562130 

 2 



Sum 



•00751166 



•0000562152 



so that 



S 4 =tt 4 x -03235020 (34) 



In the same way we may verify (33), and that (32) =0. 



If we introduce this value into (26), taking for example 

 the case where the cylinders are non-conductive (i/ = l), we 

 get 



1 "l+p--3058p 4 (35 > 



From the above example it appears that in the summation 

 with respect to m there is a high degree of convergency. 



