Electromagnet and the Law of the Dynamo. 5 



Substituting for ra/B, its equivalent i/M, Frolich then obtained 

 from the law of the dynamo the following expression for 

 the " effective magnetism ": — 



M = 



a + bi 



an expression which he himself appears, in his original paper, 

 to have considered as a mere interpolation-formula. It is, 

 however, this expression which is generally referred to as 

 Frolich's formula for the electromagnet. 



It was in 1883 that the author of this paper, in working at 

 the problem of the dynamo, realized the significance of this 

 result of Frolich's. He had been using as the fundamental law 



E = 4rcAH 



to express the average value of the electromotive force de- 

 veloped by rotating in a uniform magnetic field of intensity 

 H, an armature whose total effective area was A ; and requiring 

 a formula to connect H with the exciting current, he was 

 considering the various equations of Miiller, Weber, and 

 others when he became aware that Frolich's expression fur- 

 nished what was needed ; and, finding it necessary for the 

 case of compound-wound machines to express the excitation 

 in terms of ampere-turns rather than of amperes, he rewrote 

 the formula in the following way : — 



h = gs; *, ., 



where, as before, Si is the number of ampere-turns, G a geo- 

 metrical coefficient, k the coefficient of magnetic permeability 

 in the initial stage, and a a small saturation-coefficient de- 

 pendent on the quantity and form as well as on the quality 

 of the iron of the core. 



Writing similarly Zi s for the ampere-turns of a shunt- 

 winding, the expressions for H became 



H = G& 



for shunt-wound machines, and 



for compound-wound machines. 



Inserting these values in the fundamental equation at once 

 gave the following expressions : — 



