248 Prof. J. W. Gibbs's Comparison of the Electric Theory 



B is an absolute constant (the rigidity of the sether, pre- 

 viously represented by the same letter), A' and h 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 

 Eether distributes itself between the ponderable molecules, and 

 the degree in which these take part in the motion, may un- 

 dergo a change. When the period of vibration varies, the 

 type of motion will vary more or less, and A' and h 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 irregu- 

 larities in the fluxes which are caused by the presence of the 

 ponderable molecules, as well as to such motions of the pon- 

 derable particles themselves, as may sometimes occur. These 

 parts of the kinetic energy may be represented respectively by 



5- and -^^^ 



Their sum equated to the potential energy gives 



2 1 2 — — ~~r~ (■^3j 



^-^ ^^ 4 



Here F is the constant of electrodynamic induction, which is 

 unity if we use the electromagnetic system of units ; /and G 

 (hke A' and V) 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 

 b}"^ any constraint f. 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 gether or the electricity could be constrained to vibrate in 

 the original type, the variations of / and p would be the same 

 as in the actual case. Therefore, in finding the differential 

 equation between I and ^, we may treat h and A' in (24) and 



* See Amer. Journ. Sci. vol. xxii. p. 262. 



t See Lord Rayleigli's ' Theory of Sound,' vol. i. p. 84. The applica- 

 tion of the principle is most simple in the case of stationary waves. 



