As we know, mainly the phenomena of anomalous dispersion speak in favor of the assumption of co-oscillating masses. On the other hand, as regards the derivative with respect to x, y, z, it is the question, whether the terms in which they occur, are really great enough to exert a considerable influence. As we saw, the mentioned terms can only stem from the fact, that the electric moment doesn't have in all points of sphere I the same magnitude and direction. Since the radius is much smaller than the wave length, thus the differences are surely very insignificant, and we won't hesitate to neglect them, if it is about an action upon a distant point. Anyway, is would be premature to claim that also this small variation of couldn't have an influence on the phenomena in the interior of the sphere. The rotation of the polarization plane, to which we will return too, which presumable can't be understood without the aid of derivatives with respect to x, y, z, must prevent us from denying from the outset an influence of such terms on dispersion.
With more justification we can derive from the phenomena the insignificance of that influence. Namely, if we retain in equations (59) the derivatives with respect to x, y, z, and then simplify the equations, so far it is possible due to the known symmetry relations of crystals, then we are lead to laws for the motion of light, which are more complicated than the ones actually applied, and only go over into them by further simplification of the formulas, for which we cannot give any reason. For example, according to these laws the regular crystals wouldn't be isotropic, but must show a peculiar kind of birefringence.[1]
- ↑ See my earlier considerations (Over het verband tauchen de voortplantingsanelheid van het licht en de dichtheid en samenstelling der middenstoffen. Verhandelingen der Akad. van Wet. te Amsterdam, Deel 18, pp. 68—77; Wied. i., Bd. 9, p. 656).
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