512 ON PHYSICAL LINES OF FORCE. 



These are the equations of an undulation consisting of a plane vibration 



O_ n 



whose periodic time is : - , and wave-length : - = X, propagated in the direction 



of z with a velocity - = v, while the plane of the vibration revolves about the 



2?r 

 axis of z in the positive direction so as to complete a revolution when z = . 



Now let us suppose c 1 small, then we may write 



ra nV 



1 T 



and remembering that c 1 = - py, we find 



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 



/> = * .................................... (159), 



where i is the index of refraction. 



On the theory of MacCullagh and Neumann, 



p = s .................................... (160) 



in all bodies. 



\L is the coefficient of magnetic induction, which is unity in empty space 

 or in air. 



y is the velocity of the vortices at their circumference estimated 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 



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 



y=j= z 



Jirs 



