Page:Elektrische und Optische Erscheinungen (Lorentz) 052.jpg

 where all occurring $$\rho\mathfrak{v}_{x}$$ are related to the same instant, namely to the instant when

is the local time of $$Q_0$$.

Since $$\mathfrak{v}_{x}$$ is equal for all points of an ion, then, if we write e for the charge of such a particle, the last integral transforms into

The sum is extending over all ions of the molecule.

Furthermore, if $$\mathfrak{q}$$ is now the displacement of an ion from its equilibrium position, then

and

This has a simple meaning. We can conveniently call the vector $$\Sigma e\mathfrak{q}$$ the electric moment of the molecule and denote it by $$\mathfrak{m}$$. Then it is

$$\Sigma e\mathfrak{q}_{x}=\mathfrak{m}_{x}{,}$$

$$\psi_{x}=-\frac{1}{r_{0}}\frac{d\mathfrak{m}_{x}}{dt}=-\frac{\partial}{\partial t}\left(\frac{\mathfrak{m}_{x}}{r_{0}}\right);$$

after the things said here, we have to take the value of the derivative for the instant when the local time in $$Q_0$$ is $$t'=\tfrac{r_{0}}{V}$$. Obviously we can also write

where $$\mathfrak{m}_{x}$$ means the first component of the electric moment in that very instant. After (by that and by two equations of the same from) we have found $$\psi_{x}$$, $$\psi_{y}$$, $$\psi_{z}$$ for the point (x, y, z) and the local time $$t'$$ at this place, the study of the propagating oscillations is very simple. The equations (37) give