﻿590 



Mr. S. BuUerworfch on the Coefficients of 



(~ ^ x 0-03652+ ^ x 0-03077) 



Therefore by (41) and (42), using the notation f of the 

 Tables and putting 



&2 for ?(~> >'<?)> £'m f ° r f(V» V) 



*-fliKri' 8 (ru + ra-Fti-^-^(?ii+P»-f«--F«) 



-/ 4 3 "2 3 \ 



- lO'Y - ~ X 0-02820+ ^ x 0-02978) 



43 



10 3 " '"" ' 103 



= -104-4. 



.-. M=M 1 +M 2 =27rV*2(74G-7- 104-4) =-12,680rti??2. 



12. Self-inductances. 



Since the self-induction of a coil is the same as the mutual 

 induction between two coincident coils, we have by the 

 method of section 10, 



L = L x + L,, 

 in which L : is the self-induction calculated by assuming the 

 ■coil to be part of an infinite coil and L 2 are the linkages due 

 to the polar field of the coil. 



If the coil has length e, outer radius a, inner radius b, 

 winding density n, 



L 1 = $n*n*a*z(i-r)\l + 2r+3r*), . . (44) 



in which z — c/a, r = b/a, and no allowance is made for the 

 space occupied by insulation. 



Also L 2 is given by the M 2 of (4 2 c) in which (41 a) holds, 

 so that, using the present notation, 



L 2 =2{M(c)-M(0)} (45) 



M (0)/n»==a 8 { (l + r 5 )N(0, 1)-2N(0, r) } 3 



-or using the notation f, 77 of the tables, 



M(e)/2irW=ft*,l)-&*e(* > r) + r*f0, l) 



when ~<4, 



M 



(c)*/wVo*=£(l-^ ^. (47) 



wJien £>4, 

 and 

 M(0)/27r 2 ?i 2 a 5 = (l + r s )f(0, l)-2y- :; f(o : ,j. 



