338 Prof. J. J. Thomson on 
Since the components f, g, 4 of the electric polarization are 
given by the equations 
we see that p, g, 7 the components of the density of the 
momentum are given by 
a’e’wy ae? wu 
P= 3 xd I~ 3 xd 73 
thus the momentum at any point is parallel to the direction 
in which that point would move if the point were rigidly 
connected with the sphere. 
The moment of momentum in the field about the axis of 
either w or y vanishes ; about the axis of ¢ it is equal to 
2 are’w 
4 Oe 
If the shell had a mass M, the moment of momentum of 
the shell would be 5 PoM. Thus when the charge is 
2 
. . . . . i eé . ¥ 
rotating, the effective mass is 3a While when the motion 
is translatory the effective mass is, @/a, i.e, twice that for 
rotatory motion. In the case of an ellipsoid charged with 
electricity, the moment of momentum in the field correspond- 
ing to rotations w,, w,, @, about the axes of a, y, z, would be 
of the form A’w,, Blw,, Clo, where A’, B!, C! are different. 
Thus, unless the axis of rotation coincided with one of the 
principal axes, the axis of the moment of momentum would 
not coincide with the axis of rotation and the motion could 
not be steady. 
Momentum in the Field before the Steady State is reached.— 
Hitherto we have considered the momentum when the field 
due to the moving charged particle has reached a steady 
state; we shall now consider the distribution of momentum 
before the steady state is reached. Let us suppose that a 
charged sphere is suddenly set in motion by an impulse 
parallel to the axis of <, then at a time ¢ after the impulse 
has ceased to act, the distribution of magnetic force is as 
follows. Let O be the point from which the centre of the 
charged sphere starts. With centre O and radii Vt, Vi+6, 
where 6 is small, describe two spherical surfaces ; then out- 
side the outer of these surfaces there is no magnetic force, 
