94 On the Action of Magnetism on Polarized Light, 



9 9_. 



vibration whose periodic time is — , and wave-length — =X, 



....... n n P 



propagated in the direction of z with a velocity - =v, while the 



plane of the vibration revolves about the axis of z in the positive 



direction so as to complete a revolution when g?= 



? 

 Now let us suppose c 2 small, then we may write 



^ anil?= S ; - • • • • < 157) 



1 r 



and remembering that c 2 = yu/y, we find 



g =Y-g. .... . .... (158) 



Here r is the radius of the vortices, an unknown quantity, 

 p is the density of the luminiferous medium in the body, which 

 is also unknown ; but if we adopt the theory of Fresnel, and 

 make s the density in space devoid of gross matter, then 



p=si*, (159) 



where i is the index of refraction. 



On the theory of MacCullagh and Neumann, 



p=s . . . (160) 



in all bodies. 



/M is the coefficient of magnetic induction, which is unity in 

 empty space or in air. 



7 is the velocity of the vortices at their circumference esti- 

 mated in the ordinary units. Its value is unknown, but it is 

 proportional to the intensity of the magnetic force. 



Let Z be the magnetic intensity of the field, measured as in 

 the case of terrestrial magnetism, then the intrinsic energy in air 

 per unit of volume is 



" 8tt' 8tt ' 



where s is the density of the magnetic medium in air, which we 

 have reason to believe the same as that of the luminiferous 

 medium. We therefore put 



7=-i=Z (161) 



VTTS 



X is the wave-length of the undulation in the substance. Now 

 if A be the wave-length for the same ray in air, and i the index 



