﻿580 Mr. 8. Butterworth on the Coefficients of 



Inserting (9) in (6) and rearranging so as to express K 

 in inverse powers of: c, 



. . . (10) 

 or on expansion 



irV it (2-)Al5 15/ ' (Ss) 4 121^25 + 21 / 



C2-)A27 + 7 7 + 27 7 





1 /14 28 , , 40 , 28 . , 14 A 



- (A) 



From this formula, N (which represents the mutual in- 

 duction between the two solid coils) can be obtained to 1 in 

 100,000 if z> 3. 



4. When z is small (7) may be expanded in direct powers 

 of z giving 



wQo 1 1 . ( n 2 , 1\ 



5=100 f_V |9«_ 3 



s=2 _J 



Iii this formula the factor — -^ 2 log z requires special 

 treatment. Denoting it by a>[27r, 



1 d 2 «> /. 3\ 1 dzna 2n~Z 



2 7 r^ = ~l 1()gC+ 2> ^rd^ = ~^' 



Hence by (6), if rc represents the number of linkages due 



to &>, 



;: 1 , , _,_ r 2 / 3\ 



2ttV -, " 40 V * : 27 



2 "=°° (__)« 2^-3 /_r\ai 

 + ~n= 2 (2^ + 3) \n \n+l\2z) ' ' ' (12) 



This converges so long as z >r. 



For the remaining portion of D. it is preferable to retain 

 the finite form (7) because of the slow convergence of (11). 



