Momentum in the Electric Field. 30a 
When the velocities of the particles are constant, this may 
be written as 
ce'4 x v dei La als R)- (" ee — w. is RY 
PN op aR) ON az Rae, RB) S 
d d d d 
SLL SE | dg a clea Sea 
2 Hee dit (ms day ae dy; wo.) Ht 
d d ig d Ne 
ree Ha M3 doe a duu de) Be 
The expressions in the first ii represent the usual ex- 
pressions for the force on the first particle due to its motion 
in the magnetic field produced by the motion of the second. 
The terms in the second and third lines reduce to 
a 
4 mee = Pe + v2" + w,”)(1 —3 cos? 8), 
where @ is the ag the direction of motion of the second 
particle makes with the line joining the two particles. Thus 
these terms represent a force acting = the line joining the 
particles and equal to 
ae pe (ue oF (ed -+ Wy ”/ (1— 3 Gos? Q). 
/ 
This radial force may be compounded with the force - due 
to the electrostatic attraction, and we take it into account by 
supposing that the attraction of the second particle on the 
first is not 
ee! ee! (tt5? + ie ae Wo”) 9 ) 
R” but f(t + ae ay ES cos? @) }, 
where V is the velocity of light. 
The difference between the electric forces due to a charge 
at rest and in motion is proportional to v?/V?, where v is the 
velocity of the particle and V that of light; and thus for any 
individual particle moving slowly compared with light is 
exceedingly small. Yet, on the view that the structure of the 
atoms is electrical, the number of charged particles is so 
enormous, and the ‘velocity of the negative particles so much 
greater than the positive, it might seem that if any order 
were to exist in the motion of the negative particles as in the 
case of a magnet, finite differences of electric force in dif- 
ferent directions might be produced: thus, for example, the 
magnet might behave as if it had a charge of negative 
