580 OPTICAL PHENOMENA. 



599. Whatever be the cause which modifies the circular vibra- 

 tions, it is to be foreseen that the effects, being very small, become 

 equal and of opposite signs on the two inverse rays, and that they 

 are proportional to the magnetic force X. 



Hence, if U is the velocity, and T the period of the ray in 

 question, if the magnetic field were suppressed, and if n is the 

 refractive index corresponding to the velocity U, 



(5) 



and 



The rotation of the plane of polarization becomes, in that case, 



The field being supposed uniform, the product ^X represents the 

 difference of potential at the entrance and emergence of the ray ; 

 we shall have then 



For ordinary rotation, Fresnel assumes that the period does not 

 change. If this be admitted, the coefficient ft is null ; if n' and n" 

 are the refractive indices of the two circular rays, we have simply 



_.. V V\ 27T72 -H 47772 



(8) o> = - / =- = a 



600. This would be the rotation if the velocity of propagation 

 were independent of the wave length ; but it must still be observed 

 that the rotatory polarization brings about a dispersion between the 

 two circular rays. 



