\(\ AKT. G. — II. NAGAOKA : THE INDUCTANCE 



easily calculated from the known dimensions and position o( tlie 

 coils, and 



1/62-63 



2-/6, - f 3 



and 



or = J" (1-2^ + 2^^-2^''+...)'^ 



2yei — e2 



ê,"(o) ^ _ 87r(q + 4q'+9q') 

 ^?„(o) l+2q+2q' + 2q' ' 



_^o>I ^ 8n%q-4q' + 9q'+. ..) 

 âo{o) l-2q+2q'-2q'+... 



For long coils, direct calculation of ih involves c\ which is 

 inconveniently large ; but in the above form, there only remains 

 c^A" or c-a-, and the expression becomes free of one source of error. 



Another advantage of the above transformation is that we can 

 check the result of calculation for the termsi -^Q--p'vj co, +2^^' -V^ 

 by taking either form requires little labour as soon as jw—e^, 

 2w—e.,2)v-€. are once calculated. By summing these quantities 

 and noticing that ^1 + ^2+ 63=0, we find j^v ; mutual subtraction 

 gives e^—e.y, e-^—Cs, eo—cn; this again leads to the evaluation of î'i 

 which is generally very small. These being known, Wj and con- 

 sequently y^/i is calculated by means of the formuhe already given. 



It is also worthy of remark that 



b 

 or -^^-ly'v-e^pv , 



can be expressed in terms of '^-functions by utilizing the formula 



