Page:SahaElectrodynamics.djvu/33

 mass ; hence we see that we must proceed very carefully in comparing the different theories of the motion of the electron.

We remark that this result about the mass hold also for ponderable material mass ; for in our sense, a ponderable material point may be made into an electron by the addition of an electrical charge which may be as small as possible.

Let us now determine the kinetic energy of the electron. If the electron moves from the origin of co-ordinates of the system K with the initial velocity 0 steadily along the X-axis under the action of an electromotive force X, then it is clear that the energy drawn from the electrostatic field has the value $$\int eXdx$$. Since the electron is only slowly accelerated, and in consequence, no energy is given out in the form of radiation, therefore the energy drawn from the electro-static field may be put equal to the energy W of motion. Considering the whole process of motion in questions, the first of equations A) holds, we obtain :—

$$W=\int\ eXdx=\overset{v}{\underset{0}{\int}\ }m\beta^{3}vdv=mc^{2}\left[\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}-1\right]$$.

For v=c, W is infinitely great. As our former result shows, velocities exceeding that of light can have no possibility of existence.

In consequence of the arguments mentioned above, this expression for kinetic energy must also hold for ponderable masses.

We can now enumerate the characteristics of the motion of the electrons available for experimental verification, which follow from equations A).