Page:SahaElectrodynamics.djvu/30

 our kinematical principle as the basis, the electromagnetic basis of Lorentz's theory of electrodynamics of moving bodies correspond to the relativity-postulate. It can be briefly remarked here that the following important law follows easily from the equations developed in the present section :— if an electrically charged body moves in any manner in space, and if its charge does not change thereby, when regarded from a system moving along with it, then the charge remains constant even when it is regarded from the stationary system K.

§ 10. Dynamics of the Electron (slowly accelerated).
Let us suppose that a point-shaped particle, having the electrical charge e (to be called henceforth the electron) moves in the electromagnetic field ; we assume the following about its law of motion.

If the electron be at rest at any definite epoch, then in the next "particle of time," the motion takes place according to the equations

$$m\frac{d^{2}x}{dt^{2}}=eX,\ m\frac{d^{2}y}{dt^{2}}=eY,\ m\frac{d^{2}z}{dt^{2}}=eZ$$

Where $$(x, y, z)$$ are the co-ordinates of the electron, and m is its mass.

Let the electron possess the velocity v at a certain epoch of time. Let us now investigate the laws according to which the electron will move in the 'particle of time' immediately following this epoch.

Without influencing the generality of treatment, we can and we will assume that, at the moment we are considering,