162 Prof. J.J. Thomson on the 



When the tubes of electrostatic induction enter a conductor, 

 their ends, as we have seen, get attached to atoms of the con- 

 ductor, and the momentum of the tube gets transferred to the 

 conductor. Let us consider a small portion of a conductor 

 conveying a current, the area of the portion being so small 

 that we may consider the magnetic force over it to be con- 

 stant. The momentum parallel to x of a tube entering it is 



thus the momentum parallel to x which enters the element in 

 unit time is 



J J 2 { (gy — h/3) (lu + mv + nw)dS, 



where dS is an element of the surface of the element, and I, 

 m, n the direction-cosines of the normal to this surface. The 

 above expression may be written in the form 



7 JJ*2{ g (lu + mv+nw)} dS—/3§§t{h(lu + mv + nw)}d$. 



Now 



f (X{g(lu + mv + nw)d$, 

 and 



f f 2 { h(lu + mv + nw)d$ 



are the number of tubes of force parallel to x and y respec- 

 tively which enter the element in unit time, that is, they are 

 the components q and r of the current parallel to y and z 

 respectively. Thus the momentum parallel to x communi- 

 cated in unit time to the conductor, in other words, the force 

 parallel to x acting on the conductor, is equal to 



yq— j3r. 



Similarly, the forces parallel to y and z are respectively 



ur— <yp, 



/3p — *q. 



These are the ordinary expressions for the force acting on a 

 conductor carrying a current in a magnetic field. 



When, as in the above investigation, we regard the force 

 on a conductor carrying a current as due to the tubes of 

 electrostatic induction which enter the circuit giving up their 

 momentum to it, the origin of the force between two currents 

 will be very much the same as that of the attraction between 

 two bodies on Le Sage's theory of gravitation. Thus, for 

 example, let us take the case of two straight parallel currents, 

 A and B, flowing in the same direction, and let us suppose that 

 A is to the left of B ; then more tubes of force will enter A from 



