642 Dr. C. V. Burton on the 



mechanical stress which may exist should be proportional to 

 the square of the electromotive intensity at each point, instead 

 of following a like linear law. 



3. To realize the nature of the assumption implicitly in- 

 volved in Maxwell's theory, consider first a body B (fig. 1) 



Fte. 1. 



bounded by a closed surface A of any form, and surrounded 

 by a medium C which may be treated as continuous. The 

 nature of the substances composing the body B and the 

 medium C need not be specified ; they may be identical in 

 nature or not. What must be understood here is that the 

 material, of whatever kind, contained within the surface A 

 is always the same identical portion ; that surface, however 

 its position and form may vary, being regarded as an im- 

 permeable barrier. In these circumstances, a given distri- 

 bution of stress in the medium C will give rise to determinate 

 forces acting upon the body B, the components of stress in 

 the medium at every point of the surface A being all that 

 we require to know in order to deduce those forces. In 

 particular, if at each point of the surface A the normal is a 

 principal axis of stress in the medium C, a specification of 

 the normal stress in the medium over the whole of A is 

 sufficient to determine the forces to which the body B is 

 subject. This corresponds in Maxwell's theory to the case 

 of a conducting body surrounded by a dielectric ; and from 

 the principle of virtual work it is evident that, in order to 

 apply directly the ordinary theory of stresses as Maxwell 

 does, we must assume the fulfilment of the conditions already 

 stated in this paragraph : the surface A, which is the bound- 

 ing surface of the conductor in question, must be regarded 

 as a boundary dividing that body from the medium C ; so 

 that wherever the surface of the conductor advances in the 

 direction of the outwardly drawn normal, the dielectric medium 

 recedes to the same extent, and vice versa. If the surface of 

 the conductor were in some degree permeable by the dielectric 

 medium, the force exerted on the body would be no longer 

 thus simply derivable from the stresses in the medium. If 



