Magnetic Hysteresis with Frequency. 103 



work in a more accurate way. It is hoped that the experi- 

 mental results given below will be of sufficient interest to 

 merit publication now. 



1. The experiments were made on two rings of laminated 

 annealed iron, in one of which the radial breadth of the iron 

 was considerable relative to its mean radius. These rings 

 were magnetized by alternating currents of different strengths 

 and periods ; both the magnetizing-current wave and the 

 magnetic-flux wave were quantitatively determined by the 

 wave-tracer, using the galvanometer method described in 

 the paper already quoted, and the wave-forms so obtained 

 were subjected to harmonic analysis. 



The experiments were divided into series in which the 

 period and wave-form of the magnetizing current were kept 

 as nearly constant as possible throughout any one series, 

 while its strength was varied. The analytic expressions for 

 the associated current and flux waves for a few series are 

 given in tabular form, and some of their more interesting 

 amplitude and phase relations are shown by means of curves. 



From the analytic expressions for each pair of associated 

 waves the total iron loss (I, say) per cubic centimetre per 

 cycle was calculated, and it was found, when the magnetizing 

 current is approximately sinusoidal, that I is given with 

 considerable accuracy by the formula 



I = (-00180 + -000026 n)*B™ 

 for ring I., 



and by 



1= (-001684 + -0000272 n) S 1 ' 57 

 for ring II., 



where n is the number of periods per second and 3} (called 

 the effective induction) is \/2 times the root of mean square 

 of dB/dt, for all values of u. and for all values of the induction 

 between 1000 and 12.000. 



When from the total iron loss I per cm. 3 per cycle the 

 sum of the statical hysteresis (U, say) previously obtained 

 by Ewing and Klaasen's method, and E the value that theory 

 assigns to eddy-current loss, was subtracted, a considerable 

 quantity (I — U — E) remained, which increased both when 

 the frequency and when the flux-density increased. This 

 quantity, called by Fleming the kinetic hysteresis, has been 

 obtained for each experiment, and is given in the table- that 

 are to follow, and curves are also given which show how it 

 varies with the frequency and flux-density. That such a 



