340 _ Prof. J. J. Thomson on 
where a is the radius of the charged sphere. Thus the total 
momentum, viz., the sum of that inside the inner surface of 
the shell and the shell itself, is equal to 
rae a | El eee 
3° a OB t3°MOB= 3 a 
thus it is constant and equal to that in the field when the 
steady state is reached and the pulse has passed off to an 
infinite distance ; the pulse in passing over any region 
leaving part of its momentum behind it. 
When a particle which has been in uniform motion is 
suddenly stopped, then the state of things at a time ¢ after 
the stoppage is as follows :—Let O be the centre of the sphere 
now at rest; describe two spheres centre O, radii Vt, V¢+6; 
then inside the inner sphere there is no magnetic force ; in 
the space between the spheres the magnetic force is given by 
the equations 
ewy CWL 
—3.0p» 2= 5 Ope ¥=% 
while outside the outer sphere the magnetic force is the same 
as that before the stoppage of the particle and is given by 
C— 
ewy _ . ewe 
OP” aK OP 
We can easily see that the momentum in the shell is in 
this case equal and opposite to that in the space surrounding 
it, so that the total momentum in the field vanishes as soon 
as the charged point is reduced to rest. 
Let us now consider the case of a charged particle sud- 
denly set in motion in an extcrnal magnetic field. Suppose 
that this field is uniform and parallel to the axis of «, let it 
be due to two parallel plates of positive and negative 
magnetism, the plates being infinite and parallel to yz. Let 
us find the momentum due to the external magnetic field 
before the pulse started by the sudden movement of the 
sphere has reached the layers of magnetism. To calculate 
this momentum, we have to know the distribution of the di- 
electric polarization after the sphere has been started. Now 
in the pulse there is an additional polarization whose com- 
ponents 7’, g’, h’ are 
vy =0, 
f! Piecing Ohiew’ yz —ew (a?+y’) 
=" Ve? 2 ind?” stele 
where V is the velocity of light. The components of mo- 
mentum due to a field H parallel to « and this polarization 
