* Light and the Theory of a Quasi-labile Ether. 139 



mated per unit of volume for a space including many wave- 

 lengths) may be represented respectively by 



and 



r 4 



The sum of these may be equated to the kinetic energy, giving 

 an equation of the form 



tt'BA 8 __ bh* _. tt 2 A'A 2 , 24) 



r 4 p* 



B is an absolute constant (the rigidity of the ether, previ- 

 ously represented by the same letter), A' and b will be constant 

 (for the same medium and the same direction of the wave- 

 normal) except so far as the type of the motion changes, i. e., 

 except so far as the manner in which the motion of the ether 

 distributes itself between the ponderable molecules, and the 

 degree in which these take part in the motion, may undergo a 

 change. When the period of vibration varies, the type of mo- 

 tion will vary more or less, and A 7 and b will vary more or less. 

 In a manner entirely analogous,* the kinetic energy, on the 

 electrical theory, may be divided into two parts, of which one 

 is due to those general fluxes which are represented by the 

 equations of wave-motions, and the other to those irregularities 

 in the fluxes which are caused by the presence of the ponder- 

 able molecules, as well as to such motions of the ponderable par- 

 ticles themselves, as may sometimes occur. These parts of the 

 kinetic energy may be represented respectively by 



and -sL. . 



p p* 



Their sum equated to the potential energy gives 



~V + -p~ = T- (25) 



Here F is the constant of electrodynamic induction, which 

 is^ unity if we use the electromagnetic system of units, /"and G 

 (like A/ and b) vary only so far as the type of motion varies. 



We have the means of forming a very exact numerical esti- 

 mate of the ratio of the two parts into which the statical en- 

 ergy is thus divided on the elastic theory, or the kinetic en- 

 ergy on the electric theory. The means for this estimate is 

 afforded by the principle that the period of a natural vibration 

 is stationary when its type is infinitesimally altered by any 

 constraint.-^ Let us consider a case of simple wave motion, 

 and suppose the period to be infinitesimally varied, the wave- 



* See this Journal, vol. xxii, p. 262. 



f See Lord Rayleigh's Theory of Sound, vol. i, p. 84. The application of the 

 principle is most simple in the case of stationary waves. 



