Iron under Small Periodic Magnetizing Forces. 233 



iron, the permeability over the range H = 0'04 to H — 0-00004: 

 was appreciably constant, while for values of H greater than 

 0*04: the expression 



fx, = a + bH 



agreed well with experiment up to H = l*2. The value of a 

 for hard iron was 90 or 100. Similar results held for steel ; 

 but for soft iron a complication arose due to the time-lag of 

 the magnetization. The effect of this time-lag in soft iron 

 has been further investigated by Ewing *, who found that up 

 to H = 0"1 any change of EL instantaneously produced an 

 induction proportional to the change in H, and that then 

 the induction gradually changed (in the same direction as 

 the instantaneous effect) for some seconds afterwards. In 

 the experiments, a description of which is given later, it 

 will be found that when a bundle of wires (in which the 

 eddy-currents are small) is subjected to cyclic variations of 

 magnetic intensity, the hysteresis loop is practically a straight 

 line at the lowest inductions over the whole range of fre- 

 quencies used (50 to 8*5). This would show that the amount 

 of creeping of the induction that had time to occur was 

 negligible for these frequencies. The iron, however, was 

 not very soft. 



2. The relation between the amplitude and phase of the 

 harmonics of the intensity of an alternating magnetic field 

 and of the corresponding magnetic induction produced in 

 iron have been investigated for different frequencies by 

 Lyle t ; the amplitude of the first harmonic of the intensity 

 varying from 04 to 5" 6 7 for approximately sinusoidal waves, 

 and to 14 for waves not sinusoidal. The total amount of 

 energy lost in the iron per c.c. per cycle was also calculated 

 from the Fourier expressions for the allied current and flux 

 waves, and was found to be given with considerable accuracy 

 s within the limits B = 1000 and B = 12,000 (when the mag- 

 netizing current wave was approximately sinusoidal) by the 

 formula 



I = (a + hn)?8 x , 



where I is the total iron loss, 



a, b, t c are constants for any particular specimen, 

 n the frequency. ^/^ 



and 2) the " effective induction," which is -r— - times the 



square root ot mean square or — . 



* J. A. Ewing, p roc . Roy. Soc. vol. xlvi. p. 269 (1889) ; Magnetic 

 Induction in Iron and other Metals, 3rd edition, p. 127. 

 t T. R. Lyle, Phil. Mag-. [6] vol. ix. p. 104 (1905). 



