240 COMPARISON OF THE ELECTRIC THEORY OF LIGHT 



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 

 the missing wave) certainly 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 deviations 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 principal indices of refraction of a crystal are 

 given, the intermediate values for oblique wave-planes will be less if 

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

 tesimal, and will be greater if the velocity of the missing wave is very 

 great than if it is infinite.* Hence, if the velocity of the missing 

 wave is small but finite, the intermediate 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 

 Fresnel's law. But the recent experiments of Professor Hastings on 

 the law of double refraction in Iceland spar do not encourage us to 

 look in this direction for the decision of the question.! 



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 ether which is repre- 

 sented 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 

 (estimated per unit of volume for a space including many wave- 

 lengths) may be represented respectively by 



, 



and 



* 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 change that the potential energy of a given configur- 

 ation 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. 



t Am. Jour. Sci., ser 3, vol. xxxv, p. 60. 



