176 



Lord Rayleigh on the 



The 



accompanying curve 

 Fig. 1. 



called by Ewing hysteresis. 

 ABCDEFGA (fig. 1) is copied 

 from one given by him as appli- 

 cable to very soft iron, conducted 

 round a cycle from strong nega- 

 tive to strong positive magneti- 

 zation and back again. The 

 " residual magnetism " or " re- 

 tentiveness " (OE) amounts to a 

 large fraction (sometimes to 93 

 per cent.) of the maximum. 



The work spent in carrying 

 the iron round a magnetic cycle 

 is represented by — fid$, as 

 was first shown by Warburg*, 

 who supposes the magnetic force 

 operative upon the soft iron to 

 be due to permanent magnets, 

 and variable with their position. 

 The work required to carry the 

 permanent magnets through the 

 proposed cycle of motions is then 

 proved to have the above written value, applicable to the unit 

 of volume of the soft iron. If -3 were proportional to |), or 

 even related to it in any determinate manner, the integral 

 would vanish ; but on account of hysteresis it has a finite 

 value. 



So long as we limit our attention to complete cycles, we 



may write indifferently — j"-3*f£, or — j-fod§, since j§dg 

 vanishes. Again, under the same restriction, 



■ J3 d$= +j§ d3=^$ d®. 



When, however, we wish to consider incomplete cycles, espe- 

 cially with reference to the behaviour of soft iron, it is more 

 suitable to take 3 as independent variable. We are led 

 naturally to this form if we suppose that, as in the more im- 

 portant practical applications, the varying magnetizing force 

 is due to an electric current, upon which the magnetized iron 

 reacts inductively!* 



In order to avoid the question of free polarity, we may 



* Wied. Ann. xiii. p. 141 (1881). 

 t Hopkinson, I. c. p. 466. 



