of Light and the Theory of a Quasi-labile y^ther. 247 



tions from this limit are in opposite directions ; so that if the 

 phenomena of optics differed in any marked degree from what 

 we would have in the limiting case, it would be easy to find 

 an experiinentum crucis to decide between the two theories. 

 A little consideration will make it evident that, when the 

 principal indices of refraction of a crystal are given, the inter- 

 mediate values for oblique wave-planes will be less if the 

 velocity of the missing wave is small but finite than if it is 

 infinitesimal^ and will be greater if the velocity of the missing 

 wave is very great but finite than if it is infinite*. Hence, if 

 the velocity of the missing wave is small but finite, the inter- 

 mediate values of the indices of refraction will be less than are 

 given by FresneFs law ; but if the velocity of the missing 

 wave is very great but finite, the intermediate values of the 

 indices of refraction will be greater than are given by Fres- 

 nel's law. But the recent experiments of Professor Hastings 

 on the law of double refraction in Iceland spar do not en- 

 courage us to look in this direction for the decision of the 

 question f. 



In a simple train of waves in a transparent medium, the 

 potential energy, on the elastic theory, may be divided into 

 two parts ; of which one is due to that general deformation 

 of the sether which is represented by the equations of wave- 

 motion, and the other to those deformations which are caused 

 by the interference of the ponderable particles with the wave- 

 motion, and to such displacements of the ponderable matter 

 as may be caused, in some cases at least, by the motion of the 

 aether. If we write h for the amplitude, I for the wave- 

 length, and p for the period, these two parts of the statical 

 energy (estimated per unit volume for a space including 

 many wave-lengths) may be represented respectively by 



-TT^B/i^ . bm 

 -72— and ^• 



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

 an equation of the form 



~ir--^T = -Y~ ' ^ 



* This may be more clear if we consider tlie stationaiy waves formed 

 by two trains of waves moving in opposite directions. The case then 

 come? under the following theorem : — 



" If the system imdergo such a change that the potential energy of a 

 given configuration is diminished, while the kinetic energy of a given 

 motion is unaltered, the periods of the free vibrations are all increased, 

 and conversely." See Lord Eayleigh's 'Theory of Sound,' vol. i. p. 85. 



t Amer. Joum. Sci. vol. xxxiii. p. GO. 



