The Principle of Relativity · Albert Einstein
II.—ELECTRODYNAMICAL PART.
Since the vector (_u__{ξ}, _u__{η}, _u__{ζ}) is nothing but the velocity of the electrical mass measured in the system _k_, as can be easily seen from the addition-theorem of velocities in § 4—so it is hereby shown, that by taking 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 _d²x_ _d²y_ _d²z_ _m_ ----- = _e_X, _m_ ----- = _e_Y, _m_ ----- = _e_Z _dt²_ _dt²_ _dt²_ Where (_x_, _y_, _z_) are the co-ordinates of the electron, and _m_ is its mass.
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