Properties of the Electric Field. 165 



that sphere, substituting the values of /, g, h in this equation 

 in terms of yfr we find, if 10/V < 1, 



A = eY VV 2 -w 2 . 

 Thus the electrostatic potential </> is given by the equation 



ilr: 



« 2 +y 9 + 



Thus the tubes of induction are no longer uniformly distributed, 

 but are, in consequence of the electrical inertia, crowded 

 towards the region in proximity to the equatorial plane of the 

 sphere, where the displacements do not vary so quickly as 

 along the axis. 



The displacements are radial and are given by 



The components a and /3 of the magnetic force are given by 

 ewy 1 



{'-« 



x*+f + 



V 2 / 



0= 



ewx 



y i~T? 



V 2 , 



(See Heaviside, Phil. Mag. April 1889 ; J. J. Thomson, Phil. 

 Mag. July 1889.) 



The momentum in the medium is at right angles to the 

 displacement and the magnetic force, and is therefore at 

 right angles to the radius in the plane containing the radius 

 and the direction of motion ; its magnitude per unit volume is 

 by equation (2), 



w e 2 a 2 +y 2 



Let us now suppose that the sphere is moving in a uniform 

 Phil. Mag. S. 5. Vol. 31. No. 190. Mar. 1891. 



