228 ELASTIC AND ELECTRICAL THEORIES OF LIGHT. 



connected with the period), because the wave-length is enormously 

 great compared with the size of the molecules and the distances 

 between them. 



The potential energy on the elastic theory must be increased by 

 a term of the form 6 D /i 2 , where & D is a quadratic function of the 

 direction-cosines of the displacement. For the ponderable particles 

 must oppose a certain elastic resistance to the displacement of the 

 ether, which in seolotropic bodies will presumably be different in 

 different directions. The potential energy on the electric theory will 

 be represented by a single term of the same form, say G D /i 2 , where 

 a quadratic function of the direction-cosines of the displacement, G D , 

 takes the place of the constant G, which was sufficient when the 

 ponderable particles were absent. Both G D and 6 D will vary to some 

 extent with the period, like A D and / D , and for the same reason. 



In regard to that potential energy, which on the elastic theory is 

 independent of the direct action of the ponderable molecules, it has 

 been supposed that in seolotropic bodies the effect of the molecules is 

 such as to produce an aeolotropic state in the ether, so that the energy 

 of a distortion varies with its orientation. This part of the potential 



h 2 

 energy will then be represented by B ND - , where B ND is a function of 



the directions of the wave-normal and the displacement. It may 

 easily be shown that it is a quadratic function both of the direction- 

 cosines of the wave-normal and of those of the displacement. Also, 

 that if the ether in the body when undisturbed is not in a state of 

 stress due to forces at the surface of the body, or if its stress is 

 uniform in all directions, like a hydrostatic pressure, the function B ND 

 must be symmetrical with respect to the two sets of direction -cosines. 

 The equation of energies for the elastic theory is therefore 



h 2 h 2 



A D -2 = B ND7 2 

 P 



which gives V 2 = - 2 = A B ,. (6) 



* - 2 



The equation of energies for the electrical theory is 



2 > 2 



G^, (7) 





which gives V *=|=<|5-A. (8) 



It is evident at once that the electrical theory gives exactly the 

 form that we want. For any constant period the square of the 

 wave-velocity is a quadratic function of the direction-cosines of 

 the displacement. When the period varies, this function varies, 



