Page:Elektrische und Optische Erscheinungen (Lorentz) 061.jpg

 we can also introduce the distance l, so that $$\lambda/l$$ and $$l/a$$ become very great. The purpose of this assumption will become clear soon.

If the limiting surface $$\Sigma$$ is curved, then the radii of curvature shall be greater than $$\lambda$$, or at least of the same order.

§ 40. We already have spoken about the electric moment of a molecule in § 33. We want also now to retain the definition given there, and in similar manner call the vector

where the sum is extended over all ions in the interior of sphere I, the moment of unit volume. More precisely we say, that (47) may indicate the value of this moment in the center of the sphere. If we choose for this new vector the sign $$\mathfrak{M}$$, then

With this $$\mathfrak{M}$$, another magnitude is most closely connected. During the displacement of the ions from the equilibrium positions, a fixed surface will namely be interspersed, which we may call a "convection current through the surface". If $$d\sigma$$ is an element of surface, with P as its center and n as its perpendicular, then the charge $$\epsilon$$ that passed through it into the side designated by n, will depend on the location of P, if we specify the magnitude $$d\sigma$$ and the direction of n once and for all. Let $$d\sigma$$ be very small in relation to the molecular distances, but as great, so that we don't have to consider the cases in which an ion just is in contact with the borderline. Obviously some locations of P will exist, where the element won't intercept any ion at all, and others where it will intersect the path $$\mathfrak{q}$$ of an ion. In the first case $$\epsilon = 0$$, in the latter it is equal to the positive and negative calculated charge of the ion.

Since $$\epsilon$$ depends on the location of P, we can form the average $$\overline{\epsilon}$$ in the ordinary way; it is now, as it shall be shown in the next §,

$$\mathfrak{M}_{n}d\sigma$$.