Relation of Mass to Energy, 17 
Here (V) is the density of the total electromagnetic energy, 
S z , S y , Sz are the components of the Poynting vector, $ Xi ^, 
<^z are the components of the total electromagnetic force on 
unit charge, (p) is the density of electrification at the given 
point, and v x , v y , v z represent the velocity through space of 
this electrification. Thus 
iv= ~ { (X 2 + Y 2 +Z 2 ) + (V+/3 2 + r 2 )}, 
where X, Y, Z, and a, /3, 7, are the electric and magnetic 
force intensities respectively, and 
$r=X + (tyy— v z 0), 
<^y = Y + {V;a — v x y), 
Equation (23) states merely that the rate of increase of 
energy in an elementary volume is equal to the activity of any 
foreign (i. e., non-electrical) forces which may act therein 
minus the outward flow of energy. 
Now suppose we consider an electromagnetic system 
bounded by a rigid surface (AB), which moves uniformly 
through space with the velocity (vj) along the axis of (a:) ; 
and further suppose that the volume inside this closed surface 
is divided into two parts by the plane partition (CD) which 
is perpendicular to the #-axis and which, although fixed in 
the moving system, coincides at a given instant with the 
plane (CD') fixed in space. If this system be considered as 
isolated, then no disturbance passes through the bounding 
surface (AB). 
In equation (23) the time derivative of the energy density 
Phil. Mag. S. 6. Vol. 15. No. 85. Jan. 1908. C 
