224 Prof. J. Perry on a Formula for Calculating 



value of a or c but for the same values of — , the magnetic 

 resistance is inversely proportional to a, say that it is — y 



Fig. 2. 



Fig. 1. 



p being a function of - . Now the remaining part of the coil 



(fig. 1) may be considered made up of coils of square section 

 c x c and of mean radius a ; and the additional magnetic 

 resistance introduced by each of these is inversely proportional 



to a if - is constant. There are of them, and the total 



a c 



magnetic resistance, irrespective of the ends, is proportional 



to — if - remains constant. Say that it is (b — 2se) -^-, 



ca a c J y J a 2J 



where q is a function of — . The whole magnetic resistance is 



then 



l + ^(b-2sc). 

 a a 2 v 



And the inductance L for one winding is the reciprocal of this. 

 If there are n windings, 



L = 



(1) 



pa + qb—2sqc 



As sc is comparable with the axial distance inside a coil 

 from the end, at which the lines of force are no longer per- 

 ceptibly curved, s may be supposed to be a proper fraction. 

 In finding the values of p, q, and s, p and q being functions 



of -, and s being nearly constant, it is evident that if we, 



experimentally or by calculation, find L for various values of 



