2 REPORT —1885. 
the expression for the kinetic energy of a moving particle there is the 
term : 
4inr? 6?, 
where ¢ is the distance of the particle from some fixed point, and @ the 
angle which the radius from this point to the particle makes with some 
fixed line; m is the mass of the particle. This term, by the above rule, 
will give rise to a force of type 7, i.e., along the radius vector equal to 
mre?, 
and this.is the ordinary centrifugal force. 
Now let us consider a moving electrified body. If it is symmetrical, 
and moves in an isotropic dielectric, it is evident that the electrification, 
if it enters at all, can only enter as a factor of the total velocity 4g, 
and cannot affect the separate components of the velocity differently. 
Let us suppose that the body is charged with a quantity of electricity 
denoted by e, then the kinetic energy, if it depends on the electrification, 
must be of the form 
amg” + fle)g’, 
‘where f(e¢) denotes some function of e. Now f(e) must be always 
positive, for if it were negative we could make 
dn + fle) 
negative, and then the electrified body would behave like one of negative 
mass. The simplest form satisfying this condition which we can take for 
_f(e) 18 ae”, where « is some positive constant; so that the form of ex- 
pression for the kinetic energy may be taken as 
din + ae?)q?. 
Now let us go on to the case where we have two electrified bodies present, 
with charges e and e’ of electricity ; let m and m’ be their masses, q, q’ 
their velocities, of which the components parallel to the axes of a, y, z 
are (u, v, w), (uv, v’, w’) respectively, the co-ordinates of the particles 
being (2, y, 2), (2, y’, 2’). 
If everything is symmetrical, the expression for the kinetic energy, 
if it only involves second powers of the charges of electricity, will be of 
the form 
Ling? + 4mq’? + ae?q? + fe? q?+ee' x. f {u, v, w, uv’, v', w} 
‘where f (u, v, w, wv’, v', w’) is a quadratic function of u, v, w, w, v', w’. 
By Lagrange’s equations we see that the last term will give rise to a 
‘force parallel to the axis of « on the particle whose charge is e equal to 
Sia { df _ a df i 
de dtduJ’ 
with similar expressions for the forces parallel to 7 and z. We can 
see, by substituting in this expression, that we get Weber’s law if we 
amake 
Bes reli 5% Ee; 2 
— “ww t ti" wv) +! Zw — wy’; 
rT Hi cf 
