Page:Elektrische und Optische Erscheinungen (Lorentz) 096.jpg

to Mascart for an investigation^[1] on the interference fringes that appear at calcite plates in polarized light.

The entrainment of light waves by ponderable matter.

§ 68. In a stationary, isotropic or anisotropic body a bundle of plane light waves propagate, as to which the components of ${\mathfrak {D}}$ and ${\mathfrak {H}}$ can be expressed by expressions of the form

$A\ \cos {\frac {2\pi }{T}}\left(t-{\frac {b_{x}x+b_{y}y+b_{z}z}{W}}+B\right)$

(79)

thus W is the velocity of propagation. This magnitude can depend on $b_{x},b_{y},b_{z}$, and T. After we have given to the body the velocity ${\mathfrak {p}}$, a state of motion can occur in it, for which expressions like

$A\ \cos {\frac {2\pi }{T}}\left(t'-{\frac {b_{x}x+b_{y}y+b_{z}z}{W}}+B\right)$

or

$A\ \cos {\frac {2\pi }{T}}\left\{t-{\frac {{\mathfrak {p}}_{x}x+{\mathfrak {p}}_{y}y+{\mathfrak {p}}_{z}z}{V^{2}}}-{\frac {b_{x}x+b_{y}y+b_{z}z}{W}}+B\right\}$

(80)

apply. The direction constants $b'_{x},b'_{y},b'_{z}$ of the wave normal are now proportional to the magnitudes

${\frac {b_{x}}{W}}+{\frac {{\mathfrak {p}}_{x}}{V^{2}}},\ {\frac {b_{y}}{W}}+{\frac {{\mathfrak {p}}_{y}}{V^{2}}},\ {\frac {b_{z}}{W}}+{\frac {{\mathfrak {p}}_{z}}{V^{2}}}$

If we consequently put

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

(81)

then (80) becomes

$A\ \cos {\frac {2\pi }{T}}\left\{t-{\frac {b'_{x}x+b'_{y}y+b'_{z}z}{W'}}+B\right\}$

for which we can see, that $W'$ is the velocity by which the waves of relative oscillation period T are propagating

1. Mascart. Ann. de l'école normale, 2e sér., T. 1, pp. 191—196, 1873