[ in ] 



XL. On Hysteresis Loops and IAssajous* Figures, and on 

 the Energy wasted in a Hysteresis Loop. By Professor 

 Silvanus P. Thompson, D.8c., F.R.S. * 



[Plate VI.] 



§ 1. ~P)KOBABLY many physicists have attempted to find 

 I an explanation of the forms of the looped curves 

 which express the hysteresis exhibited by iron and steel when 

 subjected to cycles of magnetization. Physical explanations 

 to account for their general shape have indeed been given by 

 Ewing and by Hopkinson. Neither of these pioneers, how- 

 ever, offered any mathematical equations to express their 

 forms ; nor, so far as appears, has any other person yet found 

 any, though M. Pierre Weiss has put forward an electronic 

 theory to account for the principal features. 



According to Ewing's molecular hypothesis of magnetism, 

 the act of magnetization consists in the orientation into a 

 common direction of the axes of the elementary magnets 

 constituted by the iron molecules which, when the mass of 

 iron is in the unmagnetized state, are miscellaneous in their 

 directions, the molecules being then arranged in groups 

 within which the individuals are so oriented as to satisfy 

 amongst themselves their various polarities in a more or less 

 stable equilibrium. When a small magnetizing force is 

 applied and gradually increased, the individual elementary 

 magnets are at first merely slightly deflected towards the 

 line of the magnetizing force, but still remain in their various 

 groups. With larger magnetizing forces and increased 

 deflexions of individual elements, the groupings, or some of 

 them, become unstable, and break up as instability is reached ; 

 the elements of the group then suddenly swinging round 

 into a new configuration more nearly in alignment with the 

 impressed magnetic force. The less stable groups will be 

 first affected, the more stable afterwards, and the most stable 

 will be the last to swing into alignment. When all or nearly 

 all the groups have thus been broken up, any further increase 

 in the magnetizing forces can produce but little effect, though 

 an infinite magnetizing force might be needed to produce 

 absolute alignment of every element. To deduce from this 

 hypothesis an expression for the ascending curve of magneti- 

 zation, it might be possible to apply the statistical method, 

 under the assumption that the number and variety of the 

 groupings is enormously great. The ratio dffi/dlk would 

 represent at each stage the differential permeability of the 



* Communicated by the Physical Society : read July 8, 1910. 

 Phil. Mag. S. 6. Vol. 20. No. 117. Sept. 1910. 2 F 



