446 Mr. J. Larmor. A Dynamical Theory of [Dec. 7, 



which, are to be surmounted, not by logical argument or any clear 

 representation, but by the physical intuition of a mind saturated with 

 this aspect of the phenomena. Many of these obstacles may, I think, 

 be removed by beginning at the other end, by explaining electric 

 actions on the basis of a mechanical theory of radiation, instead of 

 radiation on the basis of electric actions. The strong point of Max- 

 well's theory is the electromotive part, which gives an account of 

 electric radiation and of the phenomena of electromagnetic induction 

 in fixed conductors; and this is in keeping with the remark just 

 made. The nature of electric displacement, of electric and magnetic 

 forces on matter, of what Maxwell calls the electrostatic and the 

 magnetic stress in the medium, of electrochemical phenomena, are 

 all left obscure. 



We shall plunge into the subject at once from the optical side, if 

 we assume that dielectric polarisation consists in a strain in the aether, 

 of the rotational character contemplated above. The conditions of 

 internal equilibrium of a medium so strained are easily worked out 

 from MacCullagh's expression for W, its potential energy. If the 

 vector (/, , Ti) denote the curl or vorticity of the actual linear dis- 

 placement of the medium, or twice the absolute rotation of the portion 

 of the medium at the point considered, and the medium is supposed 

 of crystalline quality and referred to its principal axes, so that 



where dr is an element of volume, it follows easily that for internal 

 equilibrium we must have 



a z fdx + tfgdy + c*hdz = dV, 



a complete differential, and that over any boundary enclosing a region 

 devoid of elasticity the value of Y must be constant. Such a boundary 

 is the surface of a conductor ; V is the electric potential in the field 

 due to charges on the conductors ; (/, gr, h) is the electric displace- 

 ment in the field, circuital by its very nature as a rotation, and 

 (a 2 /, 6 2 <7, c^Ti) is the electric force derived from the electric potential Y. 

 The charge on a conductor is the integral of (/, </, h) over any 

 surface enclosing it, and cannot be altered except by opening up a 

 channel devoid of elasticity, in the medium, between this conductor 

 and some other one ; in other words, electric discharge can take place 

 only by rupture of the elastic quality of the ssthereal medium. 



[At the interface between two dielectric media, taken to be crystal- 

 line as above, the condition comes out to be that the tangential 

 electric force is continuous. When the circumstances are those of 

 equilibrium, and therefore an electric potential may be introduced, this 

 condition allows discontinuity in the value of the potential in crossing 



