Properties of the Electric Field. 1(33 



the left than from the right, because some of those which would 

 have come from the right if B had been absent will be absorbed 

 by B ; thus in unit time more momentum having the direction 

 of left to right will enter A than that having the opposite 

 direction ; thus A will move towards the right, that is, to wards 

 B, while for a similar reason B will move towards A. 



We have now shown that we can explain the properties of 

 the electromagnetic field if we suppose that throughout that 

 field tubes of electrostatic induction in rapid motion are dis- 

 tributed, and that we can obtain the ordinary equations of the 

 electromagnetic field if we start with the principle that the 

 line-integral of the magnetic force round a closed curve is 

 equal to the rate of increase of the number of tubes of electro- 

 static induction passing through that curve. 



We shall now proceed to discuss some special problems by 

 the light of this theory. The first we shall take is that of a 

 sphere charged with electricity, and moving with the velocity 

 w parallel to the axis of z. When things have reached a 

 steady state, we may suppose that the sphere and the tubes of 

 electrostatic induction emanating from it move like a solid 

 body: we shall now consider the effect produced by pushing 

 these tubes of force through the sether. Thus, if a, /3, 7 are 

 the components of the magnetic force at any point, /, g, h 

 those of the electric displacement at the same point, we have, 

 by equation (1), 



a = — 4:7rwg, 



/3 = 477-10/, 



7=0. 



If X x , Y 1? Zj are the components of the electromotive 

 intensities due to the motion of the tubes of electrostatic in- 

 duction, we have, by equation (3), 



Y 1 = —wet, 

 Zi=0. 



The total electromotive intensity, whose components are 

 X, Y, Z, will be given bv the equations 



*--— $ 



where yjr is a function which we must proceed to determine. 



