﻿Self and Mutual Induction of Coaxial Coils. 582 



Using this method for the lower limit of (16), and com- 

 bining with (11), 



1/1 21 2 1 A r 2 /i 2 1\ 



— = -( ~Z"LOg ^Z" — -rjrK log — - | 



2tt 2 >' 3 3\2 °-r 3 / 40\ °r 20/ 



r 2 fl*_i^ Is 

 " f "2 l3r Sr^Gr 



4 1 c 5 A 2r 77\ 

 i~30?V° g T + 60j 



(—)» l£»-3 «a»/r*« 



2 a 2 2 '- 2 7 t -Tl |n + l (2n 



(2;i + l)(2n + 3) j 



(19) 



Using this to replace (12), we have instead of (B), 



i=(?-S) , °4 +A '-( B '-' 3 )" 2+cv4 - u " 6 - (°> 



in which 

 3A'=^ 2 log2(l + ?) + i?~e-i^ 



40B'=log2(l + 0-j-+20» 



„ z (I lz 2 , l* 3 1 «*/i 2r . 77 \ 

 ^ = 27.{3-3? + 6^-"30M lo -T + 60; 



^ (C) 



(_)« |2ai 



9»_ 



y 2« A«2n 



r2 4 2 2 2 »~ 2 [n-1 |n + l (2n + 1) ( 

 6. When s = 0, (19) becomes 



n ?' 2 /i 2 1\ 



Hence by (6) and (11), 



S 1 r» A 4 , 9 \ , 1 4 



27+3yl 



N 



(20) 

 (I>) 



her 



0"= S 



3 \2n 



„2»-s4 



:2 2 4 »- 2 (2rc + 3) |w \n [ n-1 [ n + 1 

 1,3.5 2n+3\ 2 



» / 1..3.D gn + g V 



: o V2.4.6 2n-r4/ 



«8» 



(2n+7)(2n + 3).(n + 3)(n + l) 



7. As a check on this result, the case of c = will now he 

 treated by another method, involving elliptic integrals. The 

 method is to start with the known elliptic integral formula 

 for the mutual induction between two coaxial solenoids and. 



