20 Relation of Mass to Energy. 
the average, integrating along (#) throughout the entire 
system, 
§{(V 2 + v 1 2 )m x -2v 1 w t }dT=;0. . . . (29) 
This gives, using the former notation, and remembering that 
on the average the internal structure is assumed to remain 
the same, 
*--*S = 4^ • • • (30) 
Y 2 + Vl 
V 2 
M*) 
which, since fa) is here along (or), is precisely the result o£ 
equation (16), and becomes (17) on differentiation. 
Conclusion. 
It has been shown in the foregoing that the electromagnetic 
mass of an isolated, symmetrical, purely electric system 
possessing any structure which on the average remains the 
same, and any internal motions or constraints, is expressible 
in terms of its velocity as a whole through space together 
with its " transverse energy " and the derivative of the latter 
with respect to the velocity. If second-order terms in the 
velocity be neglected, the mass is a simple constant multiplied 
by the total included electromagnetic energy. 
If the mass of ponderable bodies has an electromagnetic 
origin, then the inertia of matter is to be considered merely 
as a manifestation of confined energy. From this point of 
view, matter and energy are thus very closely related and the 
laws of the conservation of mass and energy become practically 
identical. 
It has been pointed out that the loss of mass, inevitable 
on this view, which takes place when energy is lost to the 
system, is large enough to be detected in the case of radio- 
active changes. If we assume the disintegration theory of 
the elements, this loss of mass affords a ready explanation of 
the general, small irregularities to be found in the list of 
atomic weights, and thus removes a serious difficulty from the 
path of the disintegration theory. For this loss of mass to 
take place however, it is not necessary that the whole of the 
mass be electromagnetic. 
It has been shown that if material mass be electromagnetic 
and if lighter elements are formed from heavier ones through 
violent energy changes, it follows that gravity acts between 
quantities of confined energy and not between masses in any 
other sense. Several speculations are indulged in as to the 
results of assuming gravitation between quantities of energy. 
