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The equations of motion of light for ponderable bodies.

Equations for the aether enclosed in ponderable bodies.

§ 39. Let us now turn to the motion of light in ponderable, dielectric, and completely transparent bodies. It shall be assumed, that they are moving with velocity ${\mathfrak {p}}$ in an arbitrary direction, and that, as already said, the molecules contain ions that are connected with certain equilibrium position.

For one of these particles we again denote the charge by e, and the displacement from the equilibrium position by ${\mathfrak {q}}$. The components ${\mathfrak {q}}_{x}$,${\mathfrak {q}}_{y}$,${\mathfrak {q}}_{z}$, as well as the velocities ${\dot {\mathfrak {q}}}_{x}$,${\dot {\mathfrak {q}}}_{y}$,${\dot {\mathfrak {q}}}_{z}$ we consider as infinitely small; i.e. besides magnitudes that only contain one of these components as factor, we neglect terms in which two such factors occur.

Any of the considered bodies shall be homogeneous. However, for that the cases of reflexion and refraction are not excluded, we imagine two different bodies, they may (Fig. 1) either sharply mutually separated at a surface $\Sigma$, or steadily go into one another at a thin limiting layer, such as