where denotes the electric force. In this manner, we have obtained the first and second law of motion of Newton.
Because when no external force is acting, the law of inertia is simply the law of conservation of electromagnetic energy, and the second law of Newton says here, that the work expended by the force during , is equal to the corresponding change of electromagnetic energy.
The third law of Newton, that maintains the equality of action and reaction, holds for all electrostatic forces between electric quanta. The mechanical forces must, for our stand point, identified with such forces. Since we make the assumption of a resting aether, this law doesn't hold for the general electromagnetic forces.
The theorem of parallelogram of forces is contained in our foundations in so far, as it holds for electric polarizations and for the forces acting between two electric quanta.
At last, as regards the rigid connections that can exist between several electric masses, those actually wouldn't exist from stand point. Only forces can arise, that are mutually in equilibrium. For example, if a pendulum swings, gravity is acting in a stretching way on the pendulum string, until the electric forces produced became equally great. Such forces expending no work, are to be introduced into the known Lagrangian form.
One can describe the foundation of mechanics sketched here, as diametrically opposed to that of Hertz. The rigid connections, belonging to the presuppositions according to Hertz, here show up as the action of complicated individual forces. Also the law of inertia is a comparably late consequence from the electromagnetic presuppositions. While Hertz's mechanics is obviously aimed at presenting the electromagnetic equations as consequences, the relation is directly reversed here. With respect to
