Page:Elektrische und Optische Erscheinungen (Lorentz) 138.jpg

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

(128)

and those will follow the incident oscillations in all points of the marginal surface, when the coefficient of z is the same as in formula (126).

Therefore we have

$\sin \beta =\left(W-{\mathfrak {p}}_{z}\sin \beta {\frac {W^{2}}{V^{2}}}\right)\left({\frac {\sin \alpha }{V}}+{\frac {{\mathfrak {p}}_{z}}{V^{2}}}\right)$,

or we denote the refraction angle in the stationary plate by $\beta _{0}$, so that

$\sin \beta _{0}={\frac {W}{V}}\sin \alpha$

$\sin \beta =\sin \beta _{0}+{\frac {W{\mathfrak {p}}_{z}}{V^{2}}}\cos ^{2}\beta _{0}$.

From that it follows

$\cos \beta =\cos \beta _{0}-{\frac {W{\mathfrak {p}}_{z}}{V^{2}}}\sin \beta _{0}\cos \beta _{0}$

(129)

However, for the factor which we above have called $m_{2}$, the value is given by (128)

$-{\frac {\cos \beta }{W'}}$,

and this one, in consequence of (127) and (129), actually is independent of the translation.