Perkins — Telocity of the Propagation of Magnetism. 171 



ing that circuit similar to that of B. The result, as expected, 

 was no deflection, although so sensitive was the apparatus that 

 a change of one millimeter in the position of B overthrew the 

 equilibrium. This at least showed that the velocity must be 

 exceedingly great as compared to that in the steel bar. 



It only remains to show that the mathematical theory predicts 

 results similar to that observed. In an article by J. Zennech,* 

 the author develops the theory of the propagation of magnetism, 

 which, though it takes no account of hysteresis, should give at 

 least approximate values when properly used. The fundamental 

 equation is similar to that for variable currents : 



(i) Q—^-^l. 



where Q = flux, 



w m = reluctance, 



Y m = magnetic potential, 



p m = coefficient of self-induction of the core. 



By applying the law that the rate of leakage is proportional to 



where C m is the magnetic analogue of capacity, and combining 

 (1) and (2), the equation (3) is obtained : 



(3) C mP JQ + C m w m Q = g, 



whose solution must be of the form : 



(4) Q = Q e ~ P* ■ e i( ^ nt ~ * x \ 



where /3 is the damping factor, n = twice the frequency and 7 = 



7T7? 



- — , v being the desired velocity. This solution satisfies the 

 equation when 



(5) j £ 2 - y 2 = C m ■ w m 



(6) ( and 2^y = C m -irnp m . 



To find v it is necessary to know three of the quantities, /3, C m , 

 w m and p m . As p m presents the greatest difficulty, the first 

 three were selected by the author of this article. /3 was deter- 



* Drude's Ann., 1903, No. 4, p. 845. 



