1892.] as affected by Stresses in Excited Dielectrics. G3 



also be illustrated by the following brief discusion, which has special 

 reference to the Mossotti-Helmholtz polarisation theory. In the 

 course of it reasons will appear that even the special limit of that 

 theory which coincides with Maxwell's as to form must be abandoned 

 as inconsistent with the dynamical phenomena, in favour of a 

 theory of pure contiguous action or strain of an incompressible 

 aether. 



Without entering here into detail as to the general characteristics 

 of this kind of polarisation, it will suffice to point out some of its 

 principal relations with regard to which misconception is easy, and 

 also to point out the modifications which are necessitated in its usual 

 form by the recognition of the discrete or molecular character of 

 the polarised elements. In the Poisson theory of induced magnetism 

 the magnetic potential is the potential not of the actual magnetism, 

 but of the continuous volume and surface distributions of ideal 

 magnetic matter which Poisson substitutes for it. The forces on a 

 magnetic molecule are therefore not to be derived from it.* But if 

 we imagine a very elongated cavity to be scooped out in the medium 

 along the direction of magnetisation, and the molecule to be placed 

 in the middle of the cavity, the forces of the remaining magnetised 

 matter will be correctly derived from this potential. This part of 

 the forcive will thus be derivable from a potential energy MF cos e, 

 where M is the moment of the molecule, F the resultant force derived 

 from the magnetic potential, and e the angle between their directions ; 

 we may thus consider a potential energy function IF cos e per unit 

 volume. We have to add to these forces the ones due to the rejected 

 magnetic molecules which lay in the elongated cavity. Now the 

 mutual action of contiguous magnetic molecules will be of the nature 

 of a tension along the lines of magnetisation and a pressure at right 

 angles to them, as Helmholtz remarked ;f but these stresses will not 

 necessarily be equal in intensity ; nor will they represent the Faraday- 

 Maxwell stress, since each component is proportional to the square of 

 the coefficient of magnetisation, not to its first power. In a fluid 

 medium these forces also must be derivable from an energy function, 

 for otherwise the medium could not be in equilibrium ; and the total 

 potential energy per unit volume with its sign changed is equal to the 

 fluid pressure. Thus in the polarised fluid the pressure is 



that is, J 



* In estimating these forces it is not allowable to replace the molecule by its 

 three components parallel to the axes in the usual manner. This procedure would 

 lead to error if there are electric currents in the field. Cf. Maxwell, ' Electricity,' 

 ed. 2, vol. 2, ch. xi, appendix 2, p. 2(52. 



f ' Wiedenmnn's Annalen,' yol. 13, 1881, p, 388. 



