352 Prof. J. J. Thomson on 
when the particles are moving with the same velocities they 
are acted on by couples whose moments round a, y, z are 
e of \ 
ae (lu+mv+nw)(mw—nr), 
/ 
7 (li + mv + nw) (nu—lw), 
/ 
a (lu+mv+nw)(lv—mu). 
These couples vanish if 
i. e., if the particies are moving along the line joining them ; 
and when 
lu-+mvt+ nw=(0), 
when the direction of motion is at right angles to the line, in 
all other cases there is a couple tending to twist the particles 
so that the line joining them gets parallel to the direction 
of motion if the charges are of the same sign, or per- 
pendicular to the direction of motion if the charges are of 
opposite signs. 
Kinetic Energy of a System consisting of two moving 
particles.—If T is the Kinetic Energy, 
=43(m4U,+%,V,;+%,W,+u.U,+0.Vo+ ee 
=3 Muto +r 2) 4 + 3M’ (uy + v2" + w,”) BS a? Hee (aut T UU. + WW) 
lt (a sik my 2) (os 2 ol 
2 (“G5 + Ge tgp, aia) ee eae JR. 
By Lagrange’s equations we have 
alt we 
re ee ea = force parallel to z, acting on the first particle, 
Hence the effect of the motion may be represented by a 
force parallel to x, equal to 
am _ ad 
dx, dt du, 
