1895.] loss of energy in Hysteresis. 3 



then measuring the area of the curve. Or again, since, if B is the 

 magnetic induction, we have B = H + 4tkI so that 



W = j Hdl=^- JHdB (1) 



(for JHdH vanishes when applied to a cyclic change), it follows 

 that the hysteresis loss may be determined by plotting and 

 measuring the curve given by simultaneous values of B and H. 

 To obtain any satisfactory curve at least a dozen simultaneous 

 observations of H and B are needed. 



I have striven to design a method which should enable the 

 hysteresis loss to be determined by a single observation of the 

 " throw " of a spot of light along a scale. The method was far 

 from being perfected when this communication was made to the 

 Society on 11 Nov. 1895, but it has been represented to me that 

 though at present imperfect it is of sufficient interest and promise 

 to justify its finding a place in the Society's pages. 



A bar of iron of cross section A is placed in a solenoid wound 

 with N turns of wire per cm. of its length. The current G which 

 flows round the solenoid and magnetizes the iron, also passes 

 round the fixed coils of a sensitive electrodynamometer. A se- 

 condary coil of n turns is wound over the iron and is connected in 

 series with the suspended coil of the electrodynamometer, the 

 resistance of the secondary circuit being R. When the primary 

 current C changes, the magnetic induction B changes and an 

 E.M.F. AndBjdt is set up in the secondary circuit. If the time- 

 constant of the secondary circuit is very small compared with 

 the time of a complete cycle, the effects of self-induction may be 

 neglected, and then there is a current 7 in the secondary circuit 



of amount 7 = -w -r- . Now the relation between C and H is 



R dt 

 expressed by H = k-rrNC, so that C = Hj^irN. Hence, if the 

 couple experienced by the suspended coil when a current \ flows 

 in it and a current i 2 flows in the fixed coil is qifo ergs, the couple 

 experienced by the suspended coil at any instant due to c and 7 is 

 qcy ergs, supposing that the deflection is not so large that the 

 value of q is appreciably different to its value in the equilibrium 

 position. 



Now if the time of vibration of the moving coil is so great 

 compared with the time occupied by the double-reversal of the 

 current that this process may be regarded as completed before the 

 coil has moved sensibly from its equilibrium position, the angular 

 momentum acquired by the coil for a single double-reversal of the 

 primary current is 



1—2 



