AND THE THEORY OF A QUASI-LABILE ETHER 241 



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

 equation of the form 



_ 

 ' = 



I 2 4 p z 



B is an absolute constant (the rigidity of the ether, previously 

 represented by the same letter), A' and 6 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 motion will vary more or less, and A' and b will 

 vary more or less. 



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

 trical 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 ponderable molecules, as well as to 

 such motions of the ponderable particles themselves as may some- 

 times occur. These parts of the kinetic energy may be represented 

 respectively by 



7TFW , 7T 2 /^ 2 



- and -. 



Their sum equated to the potential energy gives 



irWh* 7T*fh?_Gh Z 



~JT f T' 



Here F is the constant of electrodynamic induction, which is unity if 

 we use the electromagnetic system of units, / and G (like A 7 and 6) 

 vary only so far as the type of motion varies. 



We have the means of forming a very exact numerical estimate 

 of the ratio of the two parts into which the statical energy is thus 

 divided on the elastic theory, or the kinetic energy 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-length will also vary, and presumably to some 

 extent the type of vibration. But, by the principle just stated, if the 

 ether or the electricity could be constrained to vibrate in the original 

 type, the variations of I and p would be the same as in the actual 



* See page 182 of this volume. 



t 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. 

 G. II. Q 



