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If we substitute according to (10), it is, if is set:

This gives for *x = ϰt*, if we write , :

thus we have an oscillating and at the same time propagating plane; however, the propagated displacement reads:

15) |

where we now have .

We notice that different laws as the Doppler principle are given, even if we limit ourselves to the first approximation, and ϰ²ω² is neglected compared to 1.

3) If the illuminating surface is a very small^{[AU 1]} sphere of radius *R*, which oscillates according to the law for the rotation angle

around the *X*-axis, then, at the distance from the center of the sphere, the propagated rotations ψ are given by^{[1]}^{[AU 2]}

16) |

where

- ↑
*W. Voigt*, Crelles Journ. Vol. 89, 298.