Page:Elektrische und Optische Erscheinungen (Lorentz) 069.jpg

remains undecided for now. In any case, since we neglect magnitudes of second order, only the first powers of ${\mathfrak {p}}_{x},{\mathfrak {p}}_{y},{\mathfrak {p}}_{z}$ will occur. If we also consider now, that in formulas (57) the magnitudes $eN{\overline {\overline {{\mathfrak {q}}_{x}}}}$, etc., could be replaced by ${\mathfrak {M}}_{x}$, etc., and if we think of these equations as solved with respect to ${\overline {{\mathfrak {E}}_{x}}}$, etc., then we can see, that these components of the electric force can be represented as linear, homogeneous functions of ${\mathfrak {M}}_{x},{\mathfrak {M}}_{y},{\mathfrak {M}}_{z}$ and their derivatives with respect x, y, z, t, and that the coefficients in these functions can linearly contain the velocities ${\mathfrak {p}}_{x},{\mathfrak {p}}_{y},{\mathfrak {p}}_{z}$.

For brevity, the equations that would result in a completely developed theory for ${\overline {{\mathfrak {E}}_{x}}},{\overline {{\mathfrak {E}}_{y}}},{\overline {{\mathfrak {E}}_{z}}}$, may be summarized in the formula

${\overline {\mathfrak {E}}}=F({\mathfrak {M,{\dot {M}},{\ddot {M}}}},\ldots ,{\mathfrak {p}})$

(58)

As regards any of the vectors ${\mathfrak {M,{\dot {M}},{\ddot {M}}}}$, ..., we also have to consider the derivatives of its components with respect to the coordinates.

If we now eventually let fall our simplifying presupposition, and consider any molecule as a formation of, maybe, very complicated structure that contains several movable ions, then it is near at hand to assume, that still a relation like the one represented in (58) does exist. Our next task shall be, to simplify as much as possible the relation by means of certain, general considerations.

Simplification for transparent bodies.

§ 48. If a certain motion exists in a system, then, as it was shown in § 18, also the inverse motion is possible, as soon as forces of non-electric origin are the same for a certain location of the ions as well, as in the original case. From this it directly follows, that all motions in a body, that besides ions also contain uncharged mass particles,