316 FOURTH REPORT— 1834. 



their frequency. Mr. Challis has adopted and developed this 

 hypothesis. According to this author, it has been ah-eady ob- 

 served, the diminished velocity of transmission in the denser 

 medium may be explained by the obstacle which the solid 

 particles of the medium offer to the free movement of the 

 ethereal particles. If the former be supposed to be immoveable, 

 the ratio of the velocities of propagation, in free space and in 

 the medium, will be a simple function of the density of the 

 latter, and in a given 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 there- 

 fore vary with the colour of the light *. 



The solution suggested by Professor Airy is more closely 

 connected with received principles. It is now generally admitted 

 that part of the velocity of sound depends on a change of elas- 

 ticity, which the air undergoes during its vibrations, in conse- 

 quence of the development of latent heat by compression. If 

 this heat required time for its development, the quantity de- 

 veloped, 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 diiferent for waves of different 

 lengths. Professor 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 

 simplest and most natural. The conclusion of analysis — that 

 the velocity of wave-propagation is constant in the same homo- 

 geneous medium, — is deduced on the particular supposition that 

 the sphere of action of the molecules of the medium is inde- 

 finitely small compared with the length of a wave. If this re- 

 striction be removed, we have no longer any ground for con-^ 

 eluding 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 wavef. Here then 



• " 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 hy the author, as con- 

 tained in a note appended to his memoir on double refraction. The note how- 

 ever, probably by some oversight, has never been printed. 



