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 ∫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:—
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)].
1. From the second of equations [A)], it follows that an electrical force Y, and a magnetic force N produce equal deflexions of an electron moving with the velocity v, when Y = Nv/c. Therefore we see that according to our theory, it is possible to obtain the velocity of an electron from the ratio of the magnetic deflexion Am, and the electric deflexion Ae, by applying the law:—
This relation can be tested by means of experiments because the velocity of the electron can be directly measured by means of rapidly oscillating electric and magnetic fields.
2. From the value which is deduced for the kinetic energy of the electron, it follows that when the electron falls through a potential difference of P, the velocity v which is acquired is given by the following relation:—
