﻿586 Mr. S. Butterworth on the Coefficients of 



Finally, the mutual induction between two solid coils of 

 radii a and b with their ends in contact is 



N.t 



6 



m.dh 



i/0 



= ^{17Kl4r 2 )E-r(14 + 37-)(l-^)K 



— 3m — 3^(f+«i)}. . (35; 

 in which r=b a. 

 When r=l, 



N=^|°(17-3 Ml ) = 2'4094a 5 (by (27)). . (36) 

 Inserting the series for E, K, m, y in (35) we find 



_N 

 where 



-^/ 1.3.5....2n+3 Y r 2 " 



f<VJ.4.6....2rc+4/ (2n+7)(2n + 3)(n+3)(n+l)' ^ } 



This result is identical with formula (D). 

 When r= 1. we find (to five figures) 



N= 2-4094 a 5 , 



which is in agreement with (36). 



9. By means of formulae (A), (B), (C), and (D) it is 

 possible to evaluate N for all values of z, and all values of r 

 up to unity. 



The formulas have the following ranges : — 



(A) z>3, (B) 4:>z>r, 



(C) r>z>0, (D) c = 0. 



Table I. shows the agreement of (A) and (B) when c = 4 ; 



Table II. shows the agreement of (B) and (C) when z=r ; 



N 



being: the numbers tabulated. 



2ttV n 



In Table III. are tabulated P = ,. 9 ., , for c<4, and 



ztt-v j 



in 



1 ~Nz 

 Table IV. are w~ n 5~^ 5 the forms £ and ?? being; 



J 7T V ' ■ 



chosen as being the most suitable for graphical interpolation. 

 For interpolation in 7} it is convenient to notice that i) is 

 almost linear in r 2 and in 1 : 2 . 



