denotes 4π times the density of electricity, and (_u__{_x_}, _u__{_y_}, _u__{_z_}) are the velocity-components of electricity. If we now suppose that the electrical-masses are bound unchangeably to small, rigid bodies (Ions, electrons), then these equations form the electromagnetic basis of Lorentz’s electrodynamics and optics for moving bodies. If these equations which hold in the system K, are transformed to the system _k_ with the aid of the transformation-equations given in § 3 and § 6, then we obtain the equations:— $$ \frac{1}{c} (\rho' u_{\xi} + \frac{\partial X'}{\partial \tau}) = \frac{\partial N'}{\partial \eta} - \frac{\partial M'}{\partial \zeta} $$ , $$ \frac{\partial L'}{\partial \tau} = \frac{\partial Y'}{\partial \zeta} - \frac{\partial Z'}{\partial \eta} $$ , $$ \frac{1}{c} (\rho' u_{\eta} + \frac{\partial Y'}{\partial \tau}) = \frac{\partial L'}{\partial \zeta} - \frac{\partial N'}{\partial \xi} $$ , $$ \frac{\partial M'}{\partial \tau} = \frac{\partial Z'}{\partial \xi} - \frac{\partial X'}{\partial \zeta} $$ , $$ \frac{1}{c} (\rho' u_{\zeta} + \frac{\partial Z'}{\partial \tau}) = \frac{\partial M'}{\partial \xi} - \frac{\partial L'}{\partial \eta} $$ , $$ \frac{\partial N'}{\partial \tau} = \frac{\partial X'}{\partial \eta} - \frac{\partial Y'}{\partial \xi} $$ , where $$ \frac{u_{x} - v}{1 - \frac{u_{x}v}{c}} = u_{\xi} $$ , $$ \frac{u_{y}}{\beta(1 - \frac{vu_{x}}{c^2})} = u_{\eta} $$ , $$ \rho' = \frac{\partial X'}{\partial \xi} + \frac{\partial Y'}{\partial \eta} + \frac{\partial Z'}{\partial \xi} = \beta(1 - \frac{vu_{x}}{c^2}) \rho $$ , $$ \frac{u_{x}}{\beta(1 - \frac{vu_{x}}{c^2})} = u_{\zeta} $$ , 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