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Summary of the equations.
§ 52. Neglecting the primes over the letters — since was continue to only speak about averages — we summarize the equations of motion now in the following way.

In the interior of any body it is given

{{MathForm2|$$(V_c)$$|$$\left.\begin{array}{c} \varkappa_{1}\mathfrak{E}_{x}=4\pi V^{2}\mathfrak{D}_{x}+[\mathfrak{p.H}]_{x},\ \varkappa_{2}\mathfrak{E}_{y}=4\pi V^{2}\mathfrak{D}_{y}+[\mathfrak{p.H}]_{y}\\ \varkappa_{3}\mathfrak{E}_{z}=4\pi V^{2}\mathfrak{D}_{z}+[\mathfrak{p.H}]_{z}\end{array}\right\}$$}}

and

since, neglecting magnitudes of second order, we may replace, by the relation (53), $$4\pi\overline{\mathfrak{d}}$$ by $$\mathfrak{E}/V^{2}$$ in equation (54).

At the borderline the conditions apply

If there is no translation, then $$\mathfrak{H}'$$ falls into $$\mathfrak{H}$$; then the equations ($$III_c$$) and ($$V_c$$) go over into

and the last of the limiting conditions ($$VIII_c$$) into

Thus for this case, the known equations of motion and limiting conditions of the electromagnetic theory of light are given. From formulas $$(I_c), (II_c), (III'_c), (IV_c)$$ and $$(V'_c)$$ we derive (when $$\varkappa_1, \varkappa_2, \varkappa_3$$ are different from each other) the laws of light motion in crystals of two axes, while the assumption $$\varkappa_1=\varkappa_2=\varkappa_3$$ leads back to isotropic bodies. Besides, since $$\varkappa_1, \varkappa_2$$ and $$\varkappa_3$$ depend on the