Page:Elektrische und Optische Erscheinungen (Lorentz) 074.jpg

The things said may justify, that we, while preliminarily the circular-polarizing media remain excluded, assume for the other transparent bodies that the relation (62) contains no derivative with respect to x, y, z. We thus put

${\begin{cases}{\overline {\mathfrak {E}}}_{x}=\sigma _{1.1}{\mathfrak {M}}_{x}+&\sigma _{1.2}{\mathfrak {M}}_{y}+\sigma _{1.3}{\mathfrak {M}}_{z}+({\mathfrak {{\dot {M}},p}})_{x},\\{\overline {\mathfrak {E}}}_{y}=\sigma _{2.1}{\mathfrak {M}}_{x}+&\sigma _{2.2}{\mathfrak {M}}_{y}+\sigma _{2.3}{\mathfrak {M}}_{z}+({\mathfrak {{\dot {M}},p}})_{y},\\{\overline {\mathfrak {E}}}_{z}=\sigma _{3.1}{\mathfrak {M}}_{x}+&\sigma _{3.2}{\mathfrak {M}}_{y}+\sigma _{3.3}{\mathfrak {M}}_{z}+({\mathfrak {{\dot {M}},p}})_{z},\end{cases}}$

(63)

and here we understand by $({\mathfrak {{\dot {M}},p}})_{x},\ ({\mathfrak {{\dot {M}},p}})_{y},\ ({\mathfrak {{\dot {M}},p}})_{z}$ expressions, which are linear and homogeneous with respect to ${\dot {\mathfrak {M}}}_{x},\ {\dot {\mathfrak {M}}}_{y},\ {\dot {\mathfrak {M}}}_{z}$ as well as to ${\mathfrak {p}}_{x},{\mathfrak {p}}_{y},{\mathfrak {p}}_{z}$. The coefficients in these expressions, as well as the factors $\sigma$ are to be viewed as functions of T.

Now I will prove, that for a very general class of bodies, the terms $({\mathfrak {{\dot {M}},p}})_{x}$, etc. will vanish; at the same time we reach on that occasion also a simplification of the terms independent from ${\mathfrak {p}}$.

Bodies with three mutually perpendicular planes of symmetry.

§ 51. Let A be an arbitrary body, and $A'$ a second body that is the mirror image of the first one with respect to a certain plane E, and namely down to the smallest parts, thus also for the distribution of the smallest particles. If the molecular forces depend in such way from the configurations, that the vectors, by which they were represented in A and $A'$, behave like objects and their mirror images, then ion motions can occur in the two bodies in connection with state changes of aether (§ 18), so that also regarding these phenomena, one system is forever the mirror image of the other one. When passing from the first system to the second, the vectors ${\mathfrak {{\overline {E}},M}}$ and ${\mathfrak {p}}$ are transformed into their mirror images.

The inner construction of body A can only be such, by appropriate choice of the plane E, so that A and $A'$ with respect