364 Mr. Yngve Bjornstahl on Magnetic 



becomes uniform like the induced intensity of magnetization 

 I, components along- the principal axes of the ellipsoid I aj 

 lb, and I c : 



L a — 5 -Lb — 5 J-c — 5 



(a « + X )L ; 



B =W TZTfTiL' C=ia6 C | 



(a-' + X) 

 dK 



The potential energy of the ellipsoid, the work that is 

 necessary to introduce the ellipsoid into the field, is repre- 

 sented by the scalar product iu= — J\ (I, H )fi?r, where dv is 

 an element of volume. 



If the ellipsoid can be turned about the axis e, the axis a 

 forming an angle a with the external field H 0; the couple 

 of rotation is 



which can also be written 



-^ _ /^qHq 2 sin 2aQ — A6 ) 2 (A — B> 



2 [/a + B(yu— ,u )] [^ + A(yu,-^ )] ' 



As a>b>c, we must have B>A. 



Hence the expression for R is constantly negative, and is 

 not influenced by the sign of the permeability of the body 

 nor by that of the surrounding medium. Thus the ellipsoid 

 tends to turn its major axis parallel to the direction of the 

 given field *. 



An seolotropic substance shows quite a different action f. 

 The permeability is here represented by a tensor triple, the 

 intensity of the magnetization varying with the direction. 

 Yet it is not the shape that determines the orientation. We 

 obtain for the potential energy w the expression 



* "When the susceptibility is small, the couple is exceedinglj- small. 

 t Cp. Lord Kelvin: 'Papers on Electrostatics and Magnetism,' 

 Macmillan & Co., London, p. 479 (1872). 



