Page:Elektrische und Optische Erscheinungen (Lorentz) 088.jpg

the deviation from equilibrium is a function of

$t-{\frac {b_{x}x+b_{y}y+b_{z}z}{W}}$

then for the moving system, similar functions of

$t'-{\frac {b_{x}x+b_{y}y+b_{z}z}{W}}=t-\left\{\left({\frac {b_{x}}{W}}+{\frac {{\mathfrak {p}}_{x}}{V^{2}}}\right)x+\left({\frac {b_{y}}{W}}+{\frac {{\mathfrak {p}}_{y}}{V^{2}}}\right)y+\left({\frac {b_{z}}{W}}+{\frac {{\mathfrak {p}}_{z}}{V^{2}}}\right)z\right\}$

occur. The direction constants $b'_{x},b'_{y},b'_{z}$ of the wave normal will thus be determined for this system by the condition

$b'_{x}:b'_{y}:b'_{z}=\left(b_{x}+{\frac {W\ {\mathfrak {p}}_{x}}{V^{2}}}\right):\left(b_{y}+{\frac {W\ {\mathfrak {p}}_{y}}{V^{2}}}\right):\left(b_{z}+{\frac {W\ {\mathfrak {p}}_{z}}{V^{2}}}\right)$,

or, in the case of a propagation in pure aether, by

$b'_{x}:b'_{y}:b'_{z}=\left(b_{x}+{\frac {{\mathfrak {p}}_{x}}{V}}\right):\left(b_{y}+{\frac {{\mathfrak {p}}_{y}}{V}}\right):\left(b_{z}+{\frac {{\mathfrak {p}}_{z}}{V}}\right)$.

From this equation is is given in reverse

$b{}_{x}:b{}_{y}:b{}_{z}=\left(b'_{x}-{\frac {{\mathfrak {p}}_{x}}{V}}\right):\left(b'_{y}-{\frac {{\mathfrak {p}}_{y}}{V}}\right):\left(b'_{z}-{\frac {{\mathfrak {p}}_{z}}{V}}\right)$.

(71)

The aberration of light.

§ 61. Let $b'_{x},b'_{y},b'_{z}$ be the direction constants of the line drawn from a stationary celestial body to earth, thus also the direction constants of the perpendicular with respect to the plane waves that arrive in the vicinity of earth. So when we, to investigate the following path of propagation, relate the motion of light to a coordinate system, that shares the motion of earth, then of course the direction constants of the wave normal remain $b'_{x},b'_{y},b'_{z}$, while that one comes into play as the relative oscillation period $T'$ (§ 37), which was modified by Doppler's law. As we have seen, the motion (as regards the lateral limitation of a light bundle cut out by a diaphragm, the concentration through lenses, and the passage through other transparent bodies) will correspond to a motion in a stationary system, for which the oscillation period