of the Electric and Luminiferous Medium. 



281 



when a fluid medium is in equilibrium there must exist in it a hydro- 

 static pressure \i'dF, and in addition on each interface a traction 

 27m" 1 + ^i'dF along the normal towards each side, arising from other 

 than electric causes and balancing the electric forcive : so that to 

 maintain mechanical equilibrium, an extraneous normal traction 

 27tm /2 towards each side of each interface is alone required. 



6. This result differs from that of von Helmholtz's investigation, 

 also based on the method of energy : the origin of the discrepancy is 

 traced to the circumstance that a single continuous energy-function 

 cannot serve for the complex medium aether plus matter. This 

 difference goes to the root of things, especially in optical theory, even 

 in cases where the resulting expressions present no difference in 

 form. Variation of the physical constants of the medium arising from 

 the strain involved in the virtual displacement is also included by 

 von Helmholtz in the deduction of the mechanical forcive, thus intro- 

 ducing effects which are here held to be more consistently explained as 

 physical changes arising from the molecular action of the polarisation. 



Of the purely local part of the total energy of a molecular medium, 

 there is a regular or organised portion depending on the deformation 

 of the material in bulk, which is the energy of the mechanical stress 

 that compensates the applied mechanical forces: the remaining, 

 usually wholly irregular, part finds its compensation in other inter- 

 actions between neighbouring molecules, which may reveal themselves 

 in the aggregate in alterations of the local physical constants of the 

 material as well as of its volume and other dimensions. 



But in the circumstances of a medium electrically polarised this 

 residuum itself involves a part which is regular in each element of 

 volume, arising from the regularity in the orientation of the molecules 

 which act on each other in that element. The mutual forcive thence 

 originating may be expressed, though there is not much object in 

 doing so, as regards the interior of an isotropic medium, as an in- 

 ternal molecular stress related to the lines of polarisation. When 

 the distance between the effective poles of a molecule is small com- 

 pared with that between neighbouring molecules this stress is a 

 tension \tti' 1 along the lines of polarisation together with a pressure 

 f .%tt% 2 uniform in all directions at right angles to them : it is to be 

 considered as balanced locally by cohesive reaction. 



Under all circumstances, the forces between neighbouring mole- 

 cules produce and are compensated by change of the relative con- 

 figuration of these molecules ; they thus produce change of the local 

 physical constants of the material, and also local intrinsic change of 

 volume and other dimensions, all which are proportional to the 

 square of the polarisation ; but they contribute nothing directly to 

 the mechanical stress transmitted by the material in bulk. In a 

 solid material, however, these intrinsic changes of configuration of 



VOL. lxi. x 



