138 J. W. Gibhs — Comparison of the Electric Theory of 



missing wave is so small that the quantities on which it de- 

 pends may be set equal to zero in the equations which repre- 

 sent the phenomena of optics. But the mental processes by 

 which we satisfy ourselves of the validity of our results (if we 

 do not work out the whole problem in the general case of no 

 assumption in regard to the velocity of th.e missing wave) cer- 

 tainly involve conceptions of a higher degree of difficulty on 

 account of the circumstances mentioned. Perhaps this ought 

 not to affect our judgment with respect to the question of the 

 truth of the hypothesis. 



Although the two theories give laws of exactly the same 

 form for monochromatic light in the limiting case, their devi- 

 ations 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 experimentum crucis to decide between the two theories. 

 A little consideration will make it evident, that when the prin- 

 cipal indices of refraction of a crystal are given, the interme- 

 diate values for oblique wave-planes will be less if the velocity 

 of the missing wave is small but finite, than if it is infinitesi- 

 mal, 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 interme- 

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

 given by Fresnel's 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 encour- 

 age us to look in this direction for the decision of the ques- 

 tion, f 



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

 tential energy, on the elastic theory, may be divided into two 

 parts, of which one is due to that general deformation of the 

 ether 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 ether. 

 If we write h for the amplitude, I for the wave-length, and 

 p for the period, these two parts of the statical energy (esti- 



* This may be more clear if we consider the stationary waves formed by two 

 trains of waves moving in opposite directions. The case then comes under the 

 following theorem : 



" If the system undergo such a chaDge that the potential energy of a given con- 

 figuration 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 

 Rayleigh's Theory of Sound, vol. i, p. 85. 



f This Journal, vol. xxxiii, p. 60. 



