Page:Elektrische und Optische Erscheinungen (Lorentz) 104.jpg

then (by the referred theorem) the integral for the light ray is a minimum.

However, I neither want to dwell more closely on these considerations, nor on further applications of formulas (82) and (87), since we have solved the question concerning the influence of Earth's motion in different cases, already above in a much simpler way.

Closer consideration of light bundles of plane waves.

§ 74. In the application of the general theorem found in § 59, I was as brief as possible and I didn't dwell more into the details, as it just was required. For further explanation is seems justified, however, to show by some examples, as to how all details of the light motions are given from that theorem as well.

At first, we consider a light bundle of plane waves, that propagates in the aether, after it went through an additional opening in a non-transparent screen which is connected to Earth. For a moment we neglect the motion of Earth. Let:

l, m, n the direction constants of the wave normal,

q a constant,

f, g, h the direction constants of the dielectric displacement,

a the "amplitude" of the latter.

Consequently, the light motion can be represented by the equations

${\mathfrak {d}}_{x}=af\ \cos \psi ,\ {\mathfrak {d}}_{y}=ag\ \cos \psi ,\ {\mathfrak {d}}_{z}=ah\ \cos \psi$,

(92)

${\mathfrak {H}}_{x}=4\pi aV(mh-ng)\cos \psi ,\ {\mathfrak {H}}_{y}=4\pi aV(nf-lh)\cos \psi$, ${\mathfrak {H}}_{z}=4\pi aV(lg-mf)\cos \psi$,

(93)

$\psi ={\frac {2\pi }{T}}\left(t-{\frac {lx+my+nz}{V}}+q\right)$,

(94)