Self-Demagnetizing Factor of Bar Magnets. 731 



reaction of the magnetism of this piece is equal to the mag- 

 netizing action of the whole of the rest of the bar, less the 

 demagnetizing reaction of the bar as a whole. The inevitable 

 result is a distributed pole. It cannot remain concentrated 

 at one point, on the end ; it must redistribute itself along the 

 bar with a distribution determined by the conditions of 

 equilibrium at every point. 



Also the middle piece of the bar will not be exempt from 

 influence, it, too, must diminish its inherent magnetism, 

 because even in weak fields the magnetism of the hardest 

 steel is subject to cyclical changes ; and because any retro- 

 cession of the poles is, 'pro tanto, productive of an increase in 

 the self-demagnetizing force at the middle. Only in cases 

 where this self -demagnetizing force at the middle is less than 

 that which suffices to produce an irreversible change in the 

 magnetism of the steel, that is only in cases where the bar is 

 very long in proportion to its cross- section, can the action at 

 the middle be regarded as negligible. 



It is clear then, in general, that for every bar-magnet there 

 will be a self-demagnetizing action the value of which, at the 

 middle of the bar, depends, for a given intensity of magneti- 

 zation, on the length of the bar relatively to its cross-section, 

 on the permeability of its parts, and on the distribution of 

 its surface-magnetism. Owing to the circumstance that with 

 every kind of steel the permeability is neither constant, nor 

 stands in any simple or even single- valued relation to the 

 flux-density, any calculation of the actual polar distribution 

 for rods or bars is exceedingly complicated and indeed 

 impracticable. 



As is well-known, the one and only form of magnet that 

 is practicable for calculation is that of the ellipsoid, the 

 properties of which are that for any and eveiy value of the 

 permeability, and when placed in any uniform field, the 

 surface magnetism is so distributed that the magnetic force 

 which this distribution of polarity exerts in the interior 

 is uniform at every point within. Hence the internal 

 demagnetizing force everywhere within is constant ; the 

 resultant field at every point of the interior (if the structure 

 is homogeneous and isotropic) is also constant, and the 

 internal flux-density cannot but be uniform. 



Du Bois and others have determined by experiment the 

 demagnetizing actions of cylindrical rods of various dimen- 

 sions, and have compared them with ellipsoids of revolution 

 of similar dimensional proportions. 



In the case of ellipsoids, it is natural to compare the value 

 of the intensity of the self-demagnetizing force with the value 



