732 Dr. S. P. Thompson and Mr. E. W, Moss on the 



of the internal magnetization c/, because both of these are 

 uniform throughout the interior. For an ellipsoid of 

 revolution of given axial proportions, whether highly or only 

 slightly magnetized, both £& d the self-demagnetizing force, 

 and c/, are proportional to one another. By definition J- is 

 the quotient of the magnetic moment by the volume. For a 

 given size of equatoreal cross-section of the prolate ellipsoid, 

 the magnetic moment and the volume are both proportional 

 to the axial length. But for ellipsoids of given equatoreal 

 section and of different lengths, the self - demagnetizing 

 force <%o d (for a given c/, or a given m) does not follow any 

 simple function of the axial length. For small changes of 

 length it is nearly proportional to the inverse square of the 

 axial length, but is accurately expressible only in terms 

 deducible from a rather troublesome elliptic integral. Max- 

 well and Du Bois (following F. Neumann) have given the 

 general formulBe. But because both <!/<o d and / are for an 

 ellipsoid of given ellipticity proportional to one another, it 

 was quite natural to regard the quotient of the former by the 

 latter — that is to say the amount of self -demagnetizing force 

 per unit of intrinsic magnetization — as a sort of natural 

 coefficient, and to recognize it as a self-demagnetizing factor. 

 Du Bois (following Maxwell) assigns to it the symbol N. 

 It has a definite value for ellipsoids of revolution of any 

 assigned ellipticity. Thus for an ellipsoid of equatoreal 

 diameter 1 and axial length 10, the value of i^is 0'2549 

 whatever the degree of magnetization. Thus if an ellipsoid 

 of this form be magnetized so that c/has the value 100 c.G.S. 

 units, the self-demagnetizing force within the ellipsoid will 

 everywhere have the value of 25*49 gauss. Denoting the 

 dimension-ratio of axial length I to equatoreal diameter d by 

 the symbol IU = I -r- d (in Du Bois' notation), then ttt 2 iV r 

 varies from 25*49, when m = 10, to 80 when m = 1000. 

 (See Du Bois, The Magnetic Circuit, p. 4.1.) 



But, if we now compare the case of the ellipsoid with that 

 of the cylindrical bar, we find that the matter is not so simple. 

 For with the bar, as stated above, £& d is by no means uniform 

 throughout the interior, neither is c/. The former has its 

 minimum at the middle point of the axis, while the latter has 

 its maximum at the equatoreal section of the bar. To com- 

 pute the value of 2& d at the middle point (or at any other) is 

 impossible without knowing the law of surface distribution, 

 and this depends on too many conditions to be of service. 

 But the nett value of <?<o d for the entire bar can be easily 

 determined by comparing the 3S~^o curve of the bar (found 



