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the oscillation direction of the transmitted light is independent of the translation.

Here, it is to be noticed, that for the plane of incidence, as well as for the component polarized perpendicularly to the plane of incidence, we have to assume the dragging coefficient of Fresnel. Thus both are propagating with the same velocity, by which a phase difference between them and an elliptic polarization of the transmitted light is excluded.

§ 101. If the direction of translation is, as it was assumed in the last paragraph, not parallel to the marginal surface, but parallel to it, thus it must be distinguished, whether it lies in the plane of incidence, or perpendicular to it. We only want to consider the first case, and additionally restrict ourselves to the plane of incidence of polarized light.

At first it should be remembered, as to how we arrive to the value of the reflected amplitude for such light. If we choose the marginal surface with respect to y z-, and the plane of incidence with respect to the x z-plane, and we argue on the basis of the electromagnetic theory, then we have to put ${\mathfrak {E}}_{x}={\mathfrak {E}}_{z}=0$, and also ${\mathfrak {H}}_{y}=0$, while the marginal conditions consist of the continuity ${\mathfrak {E}}_{y,}\ {\mathfrak {H}}_{x}$ and ${\mathfrak {H}}_{z}$. Since in every of both media it is given by equation ($IV_{c}$) (§ 52)

${\frac {\partial {\mathfrak {H}}_{x}}{\partial t}}={\frac {\partial {\mathfrak {E}}_{y}}{\partial z}}$, und ${\frac {\partial {\mathfrak {H}}_{z}}{\partial t}}=-{\frac {\partial {\mathfrak {E}}_{y}}{\partial x}}$,

the the continuity of ${\mathfrak {H}}_{x}$ and ${\mathfrak {H}}_{z}$ has the same meaning as the continuity of $\partial {\mathfrak {E}}_{y}/\partial z$ and $\partial {\mathfrak {E}}_{y}/\partial x$. The first of those derivatives, however, will be steady, as soon as ${\mathfrak {E}}_{y}$ has this property itself, and at the end we are only dealing with ${\mathfrak {E}}_{y}$ and ${\frac {\partial {\mathfrak {E}}_{y}}{\partial x}}$.

Indeed — and this remark is true for every light theory — the known formula of Fresnel is given, when we assume, that this or that magnitude that come into consideration as regards to oscillations, and simultaneously its derivative with respect to the normal of the marginal surface, is steady.

As regards plane waves, the differentiation with respect to x amounts to the same, as if we would differentiate with respect to t, and then multiply by a factor m dependent on the direction and velocity of the waves.