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can be reversed, in case all molecular forces are determined by the configurations and not, for example, depending on the velocities.

During the inversion of motions all velocities obtain an opposite direction, thus also the translation ${\mathfrak {p}}$. Furthermore we can easily see, — look at formulas of §§ 43 and 44 —, that in the new state at time t, the vectors

${\mathfrak {M}},\ {\overline {\mathfrak {H}}}$ und ${\overline {\mathfrak {E}}}$

have the same direction and magnitude, as the vectors

${\mathfrak {M}},\ -{\overline {\mathfrak {H}}}$ und ${\overline {\mathfrak {E}}}$

in the original state at time -t.

Obviously, the transparent bodies, namely only those,^[1] in which the light motions are reversible in the alluded sense, and it may be clearly emphasized, that the circular polarizing substances form no exception from this rule.^[2]

We now want to see, which simplification of equation (58) is obtained from this reversibility; there, terms without and with ${\mathfrak {p}}$ shall be considered separately.

§ 49. If ${\mathfrak {p}}=0$, then it must be possible to express ${\overline {\mathfrak {E}}}_{x},{\overline {\mathfrak {E}}}_{y},{\overline {\mathfrak {E}}}_{z}$ as homogeneous, linear functions of the magnitudes ${\mathfrak {M}}_{x},{\dot {\mathfrak {M}}}_{x},{\ddot {{\mathfrak {M}}_{x}}}$, etc., and their derivatives with respect to the coordinates; the relations that serve for this, must stay unchanged, when we pass to the inverse motion. As to this motion we now have (at time t) ${\overline {\mathfrak {E}}}_{x},{\overline {\mathfrak {E}}}_{y},{\overline {\mathfrak {E}}}_{z}$, and also the components ${\mathfrak {M}}_{x},{\mathfrak {M}}_{y},{\mathfrak {M}}_{z}$, as well as their derivatives with respect to the coordinates, have the same value and the same sign as with the original motion (at time -t). The same is true for all even derivatives with respect to time. The uneven derivatives with respect to t have, however, the same magnitude as regards the two motions, but opposite signs, and thus these derivatives

1. If we would reverse the motions in an absorbing medium, then a state would arise, at which the amplitude would be increased in the direction of propagation.
2. The magnetic rotation of the polarization plane remains excluded from our considerations