Page:Elektrische und Optische Erscheinungen (Lorentz) 091.jpg

 was present in the instant when the light was emitted. Now the motion of Earth causes, that we observe the star not at this place P, but at another place $$P'$$, namely the displacement from P to P'  can be derived by the ordinary rule for aberration. By the consideration of § 61 its prove is at hand.

Eventually a simple figure shows, that P' falls into the true place at the time of observation, as soon as the velocity of the light source agrees in magnitude and direction with that of earth.

Experiments with terrestrial light sources.
§ 64. From the results previously obtained it directly follows, that we will see a distant terrestrial object always in the direction, where it is actually located. We also have already seen, that for a light sources rigidly connected with earth, no difference exists between the true and the observed oscillation period.

In general, the motion of Earth will never have an influence of first order on the experiments with terrestrial light sources.

To justify this theorem, we want at first (by application of the superposition principle (§ 7)) derive from the formulas of § 33 other ones, which are valid for an arbitrary system of luminous molecules. On that occasion we assume, that they have the common translation $$\mathfrak{p}$$, and we choose the local time $$t'$$ specified by (34), and the relative coordinates (§ 19), as independent variables.

Let

be the locations of the molecules, and

{{MathForm2|(72)|$$\left.\begin{array}{c} \mathfrak{m}_{x(1)}=f_{1}(t'),\ \mathfrak{m}_{y(1)}=g_{1}(t'),\ \mathfrak{m}_{z(1)}=h_{1}(t'),\\ \mathfrak{m}_{x(2)}=f_{2}(t'),\ \mathfrak{m}_{y(2)}=g_{2}(t'),\ \mathfrak{m}_{z(2)}=h_{2}(t'),\\ \mathrm{etc.}\end{array}\right\} $$}}