Page:Elektrische und Optische Erscheinungen (Lorentz) 051.jpg



and thus have

a solution of (36). By that we have to imagine two points; first, the fixed point (x, y, z), for which we want to calculate $$\psi_{x}$$ and which we call P; second, a moving point Q, which has to traverse the whole space, where $$\rho\mathfrak{v}_{x}$$ is different from zero. r represents the distance QP, and $$t'$$ the local time of P at the instant for which we wish to calculate $$\psi_{x}$$; furthermore we have to understand by ξ, η, ζ, the coordinates of Q, and by dτ an element of the just mentioned space. The function $$\textstyle{f\left(\xi,\eta,\zeta,t'-\frac{r}{V}\right)}$$ is the value of $$\rho\mathfrak{v}_{x}$$ in this element, namely, if the local time that is valid at this place, is $$\textstyle{t'-\frac{r}{V}}$$.

A single luminous molecule.
§ 33. To excite electric oscillations, a single molecule with oscillating ions shall serve; let $$Q_0$$ be an arbitrary fixed point in it — for brevity, we say, "the molecule is present in $$Q_0$$" —, and for P a place is chosen, whose distance from $$Q_0$$ is much larger than the dimensions of the molecules. For distinction, $$Q_{0}P=r_{0}$$.

We now want to replace the various distances r, that are present in formula (38), by $$r_0$$ and also neglect the differences of local times at the various points of the molecule. In this way,