266 Dr. J. W. Nicholson on the 



If he is not too great 



1 l6 8i _ log h' 2 ae—fjiJolkaJ f 

 a log ha — /uJ /kaJ ' ' 



and has the value 2 for a small value of h. 



l+^T- {**£+•. + %}/***. • (65) 

 to the same order, where 



e 1 = fiJ (Jcoi)/kaJo (ka), .... (66) 

 and e 2 is the same function of (k 1 , 6), 



&l _ i _ o 2 

 a ~ log! " ' 



and e x reduces practically, under the present circumstances, 

 to 



2^/Fa 2 {l-^}, 



and quoting the value of k, the real part is J/li, and the self- 

 induction becomes 



L=21og^ + i( M +v), .... (67) 



in accord with the results deduced from a distribution 

 assumed uniform. 



Case of two equal wires. 

 When the wires are equal, iL is the imaginary part of 



t(>-*J> 



When h 2 c 2 and h 2 a 2 are both neglected, this leads to 



T , , c All ber a ber' ^r + bei tfbei' x //>ON 



L = 41 °ga + ¥ (ber'*)'+(boi'*)» ' ' (68) 



where, if — is the frequency of alternation per second, 



v^ayJW" (69) 



The functions ber a/, bei #, are those introduced by Lord 

 Kelvin*, and subsequently tabulated. 



* Loc. cit. ante. 



