536 Prof. J. J. Thomson on 
the pole at A, a couple acting on the charged sphere whose 
components along the axes of x, y, z are respectively 
Lyf, eee pet gt ae 
a ("das  dady r dadzr J’ 
p? 2 Sree ap 1 
gens ae ay ee 
Z 2 SE cae Lee 
5 CMa | Uae agdes aed 
where w, v, w are the components of the velocity of the centre 
of the sphere relative to the pole. 
The moment of momentum remains unaltered when the 
charged sphere is rotated about a diameter: thus rotation of 
the sphere leaves the momentum in the electromagnetic field 
unaltered. Hence the momentum of the material systems in 
the field must remain unchanged, or the forces between the 
point and the rotating sphere must be equal and opposite. 
Momentum due to Moving Charges.—If a charge eis moving 
with uniform velocity w parallel to the axis of z, then, if a, 8, y 
are the components of the magnetic force, 7, g, h the com- 
ponents of the polarization in the dielectric, then, when the 
field has become steady, if we neglect squares and higher 
powers of w/V, where V is the velocity of light, we have 
fae oi i @ al ee 
. idee? dor dy dar dz’ 
a=4rwa, p= —A4rvyf, y=0; 
therefore 
Tf ge 0 det OL nee 
Here x, y, z are the coordinates of the point at which the 
magnetic force is (a, 8, y) and the dielectric polarization 
f, 9, h. Hence by the rule the components p, g, r of the 
momentum per unit volume at P are given by the equations 
ew Lz 
Det: [ag | ale ee aD 
eS, Se a, Ba 
eee A eae do po” 
ay (poaaee 
r=ag —Bf= ew (x ty) 
