COEFFICIENTS OF SOLENOIDS. 25 



we find by (17) 



^ - ^7iH&^\o,T,) \\ *,(o,r,) /r U^,t,) ) 27ti '""^ qj ""^ \ /r' Ji 



4 h 

 3;r // 



0= =- 



37T-/q,{l + q 



Expressing the ?9-functions by means of (/i-series, we find 



_i fffi . S(gl + 3ql±6ql+)\k^ 



For practical calculation, it is superfluous to retain terms beyond 

 (/i^ ; whence the simplified expression for S becomes 



+ 1 _ 1^''^^ — ^ A (22' ) 



It is needless to remark that the convergence is extremely rapid. 

 The slight inconvenience which is felt in the evaluation of the 



above expression is due to the presence of the term — := hg — . 



Vq, 1^ 



Even for small values of q^, it must be accurately known ; in fact, 

 we shall have to push the calculations for q^ to several decimal 

 23laces, which is quite unnecessary for finding the values of ä^ s, 

 for the simple reason that the expression contains terms multiplied 



by — = log — . It is convenient to calculate q^ from li, where 

 l/qi 'h 



7 _ l--/'^ ^-1 



l + y/k {l + ^Jcf{l + l:) 



