Relation of Mass to Energy. 11 
motion causes in the velocity of propagation through the 
system of electrical disturbances. This is seen in the simple 
case of a moving electron where the crowding of the lines 
towards the equator with increase of velocity is only partly 
due to the added energy. It is evident, therefore, that for 
velocities so great that the second order terms cannot be 
neglected, the mass depends on complicated terms which vary 
with the internal structure and motions of the system, and 
it does not appear as if a general expression for the mass of 
a system for such high velocities could be found. 
The second order terms may in the future make themselves 
experimentally manifest through an increase of mass of 
rapidly moving a-par tides. 
9. Expression (18) may readily be verified for simple 
symmetrical systems. For a single charged conducting 
sphere of radius (a) the mass for slow velocities is well- 
known to be 
21r 2 e e 4 1. ^ , ,. n 4 w 
3Fa = 3W« = 3P2 (e ' P ° tential)= W^' 
An interesting verification of equation (16) for the special 
case of a general, rigid, electrostatic system in translator}" 
motion has been furnished me privately by Mr. Gr. F. C. 
Searle. He obtains for such a system (Phil. Mag. Jan. 1907,, 
p. 129) the expression 
M,=ff. ( 19 > 
where M x is the momentum of the entire system along the 
direction (a*) of motion, (T) is the total magnetic energy due 
to this motion, and (vj) is the common translatory velocity 
possessed by all parts of the system. 
Now it is well known that where the Faraday tubes move 
through space uniformly, as in the present case, the magnetic 
force (H) is given in terms of the electric force (E) by the 
expression 
H=^Esin<9, 
(6) representing the angle between (E) and the velocity of 
motion (vj), and (H) being in a direction perpendicular both 
to (E) and (rj). In the present notation 
and hence we have 
87T 8*7T V 
= ^=^^(E/ + E/). . . . (20) 
