Momentum in the Electric Field. 351 
that the deflexion of the velocity of the particle struck from 
the line of impulse is not so marked as the motion imparted 
to the charged particle in its neighbourhood. The deflexion 
of the first particle may be supposed to occur as follows : 
when the particle is first acted on by the impulse it starts 
parallel to the impulse with a velocity P/M; a pulse of strong 
electric force spreads out from the particle, after a time this 
reaches the second particle and starts it impulsively; the 
sudden starting of the second particle produces pulses of 
electric force which travel on and strike the first particle 
deflecting it from the original direction. 
The momenta of the particles may be expressed in the follow- 
ing way. U,, V;, W,, Us, Ve, We being the components of 
the momenta of the first and second particles ; ww, 7, wy, 
Uz, Voy Wy the components of their velocities :— 
ee’ eeu, 
U, = My, + sR tat Fhe Ulett mvs + nw), 
ee! 
V,= Mo, + ok” -+ SUE (lets + mete + NWs) y 
! 
! 
W,= Mw, + ne au Sy let + mvz+nuvy), 
! ! 
U,= M'u. + open Se Spellha + mv, + nw), 
V,=Mw+ ee pry + ee pom (ly + mez, + NW), 
7 Bier OR 
ee 
W, = Mw.+ a5 mw + ah” (lu + mv, +n). 
ee! 
2R 
Take the case when the particles are moving with the same 
velocity ; then, unless the momentum of the system is in the 
direction of the velocity, the line of action of the resultant 
momentum will change : thus the moment of momentum in 
the field about axes of x, y, z will be changing at the rate 
(W, =r W,)v— (V, = V.)w 3 (U, + U,)w— (W, + W,) Uw 3 
: (V, a V3) UU (ui, aie U,) UV. 
Since the momentum of the system consisting of the field and 
particle remains constant, the particle must be acted on by 
couples about the axes of x, y, z, equal and opposite to the 
rate of increase of the moment of momentum in the field. 
Hence, substituting for the values of U, V, W, we find that 
