Page:Elektrische und Optische Erscheinungen (Lorentz) 066.jpg

 § 45. Equation ($$IV_b$$) admits of a similar application. Before, I give the remark that no magnetic forces exists, as long the ions are at rest, thus that $$\mathfrak{H}$$ is of same order as the velocities $$\mathfrak{v}$$. In ($$VII_b$$) we can consequently neglect the last term; it becomes $$\mathfrak{F}=\mathfrak{E}$$, consequently by ($$IV_b$$) for the interior of a body

$$Rot\ \mathfrak{\overline{E}}=-\dot{\overline{\mathfrak{H}}}$$,

and for the borderline

$$\overline{\mathfrak{E}}_{h(1)}=\overline{\mathfrak{E}}_{h(2)}$$.

At last it still follows from ($$V_b$$) and ($$VI_b$$)

and

The equations of motion for ions.
§ 46. So far everything was quite simple. Yet great difficulties arise, when we also want to form the equations of motion for the oscillating ions themselves. To express in these equations the relations, which are the basis for dispersion, birefringence, and circular polarization, it would be required an understanding of molecular processes that wasn't achieved by us by far. We want to restrict ourselves, to derive from a very simple presupposition the most probable shape of the sought relations, and then help on ourselves as good as possible. It is of course an advantage, that for this task we have to consider the interior of the homogeneous body, since (regarding the borderlines) the already derived equations enclose all required conditions.

The mentioned assumption is now, that any of the mutual completely equal molecules, only contains a single movable ion, while all others are fixed.

Let m be the mass of a movable ion, $$\mathfrak{K}$$ the total