Page:Elektrische und Optische Erscheinungen (Lorentz) 098.jpg

As regards this result, two things shall be remarked. First, the given derivation applies to every value of T, thus for every kind of light, and second, this has to be understood, that the substitution of the values of N and W, which belong in the stationary body to a particular T, gives the value of $W''$ for the relative oscillation period T.^[1]

§ 70. If the considered body is birefringent, than it may not be forgotten, that W and W' in equation (82) are related to different directions of the wave normal, namely W to direction ($b_{x},b_{y},b_{z}$), and W to direction ($b'_{x},b'_{y},b'_{z}$). Concerning the question, as to how the velocities in stationary and in moving bodies are mutually different for a given direction of the waves, the equation doesn't directly give an answer. To a simple theorem, however, leads the introduction of light rays.

In a stationary birefringent body, to any direction of the wave normal (as soon as one of the two possible oscillation directions is chosen) belongs a particular direction for the light-rays, i.e., for the describing lines of a cylindric limiting-surface of a light bundle. For the points of such a line, it is now, when $c_{x},c_{y},c_{z}$ are the direction constants, and s means the distance of a fixed point ($x_{0},y_{0},z_{0}$) of the line,

$x=x_{0}+c_{x}s,\ y=y_{0}+c_{y}s,\ z=z_{0}+c_{z}s$.

(85)

By that, when we put

${\frac {W}{b_{x}c_{x}+b_{y}c_{y}+b_{z}c_{z}}}=U$

and understand by $B'$ a new constant, the expression (79) is transformed into

$A\ \cos {\frac {2\pi }{T}}\left(t-{\frac {s}{U}}+B'\right)$.

1. A derivation of equation (84) from the electromagnetic light theory was published by R. Reiff Wied. Arm., Bd. 50, p. 861, 1893). Long before me, also J. J. Thomson has dealt with this subject (Phil. Mag., 5th. Ser., Vol. 9, p. 284, 1880; Recent Researches in Electricity and Magnetism, p. 543), however, without obtaining Fresnel's coefficient.