182 ■ I" THE AMERICAS ACADEMY. 



ciable. Of course this statement does not apply to the case of an 



alternate current of very great frequency. 



* 



In the problem just considered the electromotive force was suddenly 



shunted out of the solenoid circuit after a steady current had been 



^Wished in it, and, on the assumption that the permeability of the 



iron was fixed, the value of the magnetic field within the core was 



determined as a function [H Q /(t, r)] of the time and the space i 



ordinates. The function / satisfies (65) and (G.s), vanishes when ( 



is infinite, and is initially equal to unity. If the solenoid circuit 



containing an applied electromotive force E be suddenly closed at the 



time t = 0, and if the ultimate value {4&NE/w) of the magnetic field 



in the core be denoted by H^ , the value of the field at any time will 



be given by the equation 



H=H ao [l-f(t,r)l (in;,, 



The function defined by this equation vanishes, when / = <», for all 

 values of r, and when t is infinite is equal to H x . It satisfies at all 

 times the equation (65) and the surface equation 



Hs+ —( A -" B) l!F + -^-JJjF (lvd y = — L > (1,M " 



and such a function is evidently unique. 



Although in practice the permeability is not fixed, the analysis of 

 this section enables us to shut in between narrow limits the effects of 

 eddy currents in many cases, and to assert, when this is the truth, that 

 in a given instance the effects of such currents will be negligible, if the 

 pieces of which the core is built are properly varnished. 



It is sometimes possible to get interesting information about the 

 magnetic properties of the core of a transformer which has several coils, 

 and about the excellence of the insulation of the sheets of which it is 

 made, by observing the sudden changes in the currents in the coils when 

 the inductances of the system are impulsively changed, or by stud} 

 the rate of propagation of the induction flux into the core, but these 

 subjects must be left for the next instalment of this paper. 



The Jefferson Phtbioax Laboratort, 



HaRVARI, 1'viVl RSITY, 



Cambridge, Mass 



