COEFFICIENTS OF SOEENOIDS. 



13 



(A-af + o- , 



4^a 



__.cpp-a") 



2Aa 

 By simple substitution 



Silice ir« = '(^/^"^f + -.^ ^o, and ^/ct;^, = 0, ^/<:(;.; = 0, 



0)2 Wo 



—- — -f (1 - ß' — 2a ßiju - a-irv) | — f- 



pv—'pii 



Again 



1-3'- 



«T/2 



i / r/2 



-p-v 



ß'- -j^^ - « (pv - c) (a pu + 2ß) = «•' ^ ^ 



1 — ß^ — 2aßjw - (/rp-u = — a: {pv — c.) (j><y — ^3) . 

 Thus by integration 



This expression for / is to be substituted for /i, L, l^ and 

 /i in (7), for evaluating the mutual inductance 31 of coaxal 

 solenoids. 



§ 8. Evidently the first two terms of / 



and p'^-'fji 



are easily expressed by means of complete elliptic integrals of 



