Page:Elektrische und Optische Erscheinungen (Lorentz) 080.jpg

where j is a certain constant and which we want to add for resting bodies (65) to

$F_{1}({\mathfrak {M}})=\sigma {\mathfrak {M}}+j\ Rot\ {\mathfrak {M}}$

Now, we could introduce (into the term $F_{2}({\dot {\mathfrak {M}}},{\mathfrak {p}})$) derivatives with respect to x, y, z; however, we will omit this, since the things already said are sufficient for our purpose. By that we have (when we omit the prime over ${\mathfrak {E}}$ from now on) to put for isotropic, circular-polarizing media

${\mathfrak {E}}=\sigma {\mathfrak {M}}+j\ Rot\ {\mathfrak {M}}+k[{\mathfrak {{\dot {M}}.p}}]$

(68)

§ 55. It is not without interest, to consider for a moment the mirror image of a motion to which the found equation applies. The vectors that apply to this new motion, which may be called ${\mathfrak {E'}},{\mathfrak {M'}},{\dot {\mathfrak {M}}}'$ and ${\mathfrak {p}}'$, are mirror images of the vectors ${\mathfrak {E,M,{\dot {M}}}}$ and ${\mathfrak {p}}$. From that if follows, that the mirror images of $Rot\ {\mathfrak {M}}$ and $[{\mathfrak {{\dot {M}}.p}}]$ don't fall into $Rot{\mathfrak {\ M'}}$ and $[{\mathfrak {{\dot {M'}}.p'}}]$, but into $-Rot{\mathfrak {\ M'}}$ and $-[{\mathfrak {{\dot {M'}}.p'}}]$. Now, since the linear relation between four vectors expressed in (68), also then remains when we replace any of them by its mirror image, hence

${\mathfrak {E'}}=\sigma {\mathfrak {M'}}-j\ Rot\ {\mathfrak {M'}}-k[{\mathfrak {{\dot {M'}}.p'}}]$

By that we see, that the processes that can occur in the mirror image of the considered body, don't satisfy the relation (68) anymore, but a relation in which the terms with j and k have difference signs. Thus it is confirmed, that these terms are likely be connected with the fact, that body and its mirror image have different properties; we may expect, that a rotation of the polarization plane will actually be in agreement with them.

I postpone the details about this. Here, it only shall be remarked that the magnitude $j\ Rot\ {\mathfrak {M}}$ (we will make that the natural rotation of the polarization plane will depend on it) has much similarity with the terms, that were assumed by various physicists in the equations of motion of light,