Page:LorentzRelatieveBeweging.djvu/4

 molecular forces, but then it can make make a difference, whether the connecting line of two particles, which move together through the ether, is moving parallel to the direction of motion or perpendicular to it. One can easily see, that an effect of order $$\tfrac{p}{v}$$ is not expected, but an effect of order $$\tfrac{p^{2}}{V^{2}}$$ is not excluded and that is exactly what we need.

Since we know nothing about the nature of molecular forces, it is impossible to verify the hypothesis. We only can - of course by introducing more or less plausible assumptions - calculate the influence of the motion of ponderable matter on electric and magnetic forces. Perhaps it is worth mentioning, that when the result obtained for the electric forces is transferred to molecular forces, it exactly gives the value of $$\alpha$$ given above.

Let $$A$$ be a system of material points, which bear certain electrical charges and which are at rest relative to the aether, and $$B$$ is the system of the same points, when they are moving in the direction of the $$x$$-axis by the collective velocity $$p$$ through the aether. From the equations developed by me one can deduce, by which forces the particles in the system act on each other. The result can be expressed in the most simple way, if one introduces a third system $$C$$ that is at rest like $$A$$, but differs from the latter system by the mutual position of the points. System $$C$$ can be obtained from $$A$$ by a mutual expansion, by which all dimensions in the direction of the $$x$$-axis are $$1+\tfrac{p^{2}}{2V^{2}}$$ times larger, while the perpendicular dimensions remain unchanged.

Concerning the relation between the forces in $$B$$ and $$C$$ it follows, that the components in the direction of the $$x$$-axis are the same as in $$C$$, while the components perpendicular to the $$x$$-axis are $$1-\tfrac{p^{2}}{2V^{2}}$$ times larger as in $$C$$.

We want to transfer this to the molecular forces, and imagine a solid body as a system of material points, in equilibrium by the influence of their mutual attractions and repulsions. The system $$B$$ shall be a body moving