436 Hysteresis Loops and Lissajous' Figures. 



§ 13. Hysteresis is commonly regarded as an irreversible 

 process, and as such involving a degradation o£ energy into 

 heat. But in view of the present analysis of the hysteresis 

 loop it is necessary to revise this opinion. In the first place, 

 no energy is wasted in producing any cosine component of 

 the loop. In the case of the first cosine term — the oblique 

 line — the distortion is a mere shear. True energy is spent in 

 half the cycle in producing the magnetic flux, but that energy 

 is returned to the magnetizing circuit during the other half 

 of the cycle, exactly as it is in the case of the production of a 

 magnetic flux in a solenoid devoid of iron. The like is true 

 of the higher cosine-components. Also the sine-components 

 higher than the first represent reversible processes. The 

 only component which represents an irreversible process is 

 the fundamental sine-component, the ellipse, itself due to that 

 component of current which is in phase with the voltage. 

 This irreversible part is due in detail to an energy-waste 

 which at every instant is proportional to the square of the 

 magnetizing current, and is in phase with it. True hysteresis 

 waste accompanies the current, and does not either lag 

 behind it nor precede it. True hysteresis does not cause any 

 lag in the current, being necessarily simultaneous with it. 

 True, the curve of the flux-density always lags 90° behind 

 the voltage curve, and therefore 90° behind the effective 

 component of the current curve. Of the reversible com- 

 ponents, it is the first cosine term which is concerned in 

 the lag of the current, and the lagging component of 

 current is wattless. The higher cosine-components conjointly 

 produce additional lags, and are also wattless. The higher 

 sine-components, also wattless, do not cause any lag of the 

 current as a whole. The name " hysteresis " was originally 

 given * to the phenomenon to connote an effect which lagged 

 behind its cause. The term is now usually restricted to the 

 phenomenon of energy-waste. But the energy-waste does 

 not involve or produce any phenomenon of lag. On the 

 contrary, as it is a simultaneous phenomenon, its presence 

 actually produces an advance in the phase of an otherwise 

 lagging current. The greater the reluctance of the mag- 

 netic circuit, the greater the angle of lag. The less the 

 permeability which enters into that reluctance the greater 

 is tne angle of lag. The lagging components, that is the 

 cosine-components of the loop, so far as they are not due to 

 eddy-currents, depend solely upon the reduction of the per- 

 meability of the iron during the process of the cycle of mag- 

 netization. The lag is in fact due to components other than the 

 fundamental component which represents the true hysteresis. 



* Ewing, Phil. Trans. 1885, pt. ii. p. 524. 



