MAGNUSSON — ANOMALOUS DISPERSION OF CYANIN. 259 



refraction if all colors were deviated the same amount, but for 

 dispersion, or the difference in the velocity of transmission of 

 light of various wave lengths they offer no solution. 



To explain the fact that in material media light waves, dif- 

 fering in wave length, are propagated with different velocities, 

 while in free space all light waves are transmitted with the 

 same velocity, Cauchy 1 made the following assumptions : 



1st. That the ether is of a granular structure. 



2nd. That there is a certain attractive force between ether and 



matter so that inside a material body the ether is very much 



denser than in free space. 

 3rd. That the distance between the ether particles inside the 



body is comparable to the wave length of light, while in free 



space it is of a different order. 

 4th. That the period of vibration of a wave is constant, and 



hence, that the wave length varies with the velocity of 



transmission. 



From these assumptions Cauchy developed the following ex- 

 pression for the velocity of transmission of light in terms of the 

 wave length in the medium : 



*&' 



V» = A, + A 2 (?£)"+ A 3 (2£) 4 + &ct. (7). 



where A 1} A 2 , A 3 , etc., are constants depending upon the nature 

 of the medium. While calculating the values of these con- 

 stants he observed that this series is rapidly converging and that 

 for all practical purposes it may be sufficient to use the first two 

 terms, thus: 



(¥)' . (8) ' 



V'^A. + A, 



From his 4th assumption there results : a : a' : : v : / where A is 

 the wave length in free space and v the velocity. Combining 

 this with equation (8), making a series of transformations, and 



1 Canchy, Memoire sur la dispersion de la lumiere. Prag. 1836. Beer:— Einleitung in 

 der hoheren Optik, p. 209, Braunschweig, 1853. 



