Page:ComstockInertia.djvu/20

the average, integrating along ($x$) throughout the entire system,

$\int \{(V^{2}+v_{1}^{2})m_{x}-2v_{1}w_{t}\}d\tau =0\,$,

(29)

This gives, using the former notation, and remembering that on the average the internal structure is assumed to remain the same,

$M_{x}={\frac {2v_{1}W_{T}}{V^{2}+v_{1}^{2}}}={\frac {2v_{1}W_{T}}{V^{2}\left(1+{\frac {v_{1}^{2}}{V^{2}}}\right)}}$

(30)

which, since ($v_{1}$) is here along ($x$), is precisely the result of 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 radioactive 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.