42 REPORT ON PHYSICAL OPTICS. 



a simple function of the density of the latter, and in a 



gven medium its value will be constant; but when the particles 

 of the medium vibrate, the value of this ratio will depend also on 

 the length of the wave, and will therefore vary with the colour o 



the light.* 



The solution suggested by Professor Airy is more closely con- 

 nected with received principles. It is now generally admitted 

 that part of the velocity of sound depends on a change of elasticity 

 which the air undergoes during its vibrations, in consequence of 

 the development of latent heat by compression. If this heat 

 required time for its development, the quantity developed, and 

 therefore the elastic force, must vary with the time of vibration. 

 Consequently, the velocity of propagation should also vary with 

 the time, and be different for waves of different lengths. Pro- 

 fessor Airy imagines something similar to this in the case of light ; 

 and conceives that the elasticity of the ether, in refracting media, 

 may consequently undergo a change whose amount depends on 

 the time of vibration. 



But the explanation offered by Fresnel seems to be the sim- 

 plest and most natural. The conclusion of analysis that the 

 velocity of wave-propagation is constant in the same homogeneous 

 medium is deduced on the particular supposition that the sphere 

 of action of the molecules of the medium is indefinitely small 

 compared with the length of a wave. If this restriction be re- 

 moved, we have no longer any ground for concluding that waves 

 of different lengths will be propagated with the same velocity. 

 Fresnel states that he has demonstrated that, when the mutual 

 action of the ethereal molecules extends to a sensible distance as 

 compared with the length of a wave, the waves of different lengths 

 will be propagated with different velocities ; the elasticity of the 

 medium, and therefore also the velocity, increasing with the length 

 of the wave.f Here, then, the constancy of the velocity of wave- 

 propagation is regarded but as the approximate result of an 

 incomplete analysis. The problem presented itself to M. Cauchy 

 in a similar point of view. In the profound researches of this 



* " An attempt to explain theoretically the different Refrangibility of the Rays of 

 Light, according to the hypothesis of Undulations." Phil. Mag., New Series, vol. viii. 



t This demonstration is more than once referred to by the author, as contained in 

 a note appended to his memoir on double refraction. The note, however, probably by 

 some oversight, h*s never been printed. 



