Page:Elektrische und Optische Erscheinungen (Lorentz) 053.jpg

 and because we seek the value of $$\mathfrak{d}$$ outside the molecule, (IIIb) is transformed into

or, due to (35), it is transformed into

If we bring the last two terms on the left side, then we just obtain $$\textstyle{\frac{1}{V^{2}}\dot{\mathfrak{F}}_{x}}$$ or $$\textstyle{\frac{1}{V^{2}}\frac{\partial\mathfrak{F}_{x}}{\partial t'}}$$, as it can be seen by (Vb); since $$\mathfrak{H}$$ and $$\mathfrak{H}'$$ only differ by magnitudes of order $$\mathfrak{p}$$, we may replace the vector product (Vb) by $$[\mathfrak{p.H'}]$$.

From

we obtain $$\mathfrak{F}$$ by integration; constants were omitted by us, since we are only dealing with vibrations.

We substitute the values (39) and put

It is then

and namely, $$\mathfrak{m}_{x}$$, $$\mathfrak{m}_{y}$$, $$\mathfrak{m}_{z}$$ are still related to the instant given above.

As to how the other magnitudes occurring in (Ib)-(VIIb) can be determined, can immediately be seen.

§ 34. Just some words on the error committed in the above calculation. That in (38) the factor $$\tfrac{1}{r}$$ was replaced by $$\tfrac{1}{r_{0}}$$, needs surely no justification. But we also haven't taken the values of $$\rho\mathfrak{v}$$ for the function f at the the correct times. Once we have replaced $$t'-\tfrac{r}{V}$$ by $$t'-\tfrac{r_{0}}{V}$$ in (38), then in the time when l is one of the