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:
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[AU 2]
- ↑ W. Voigt, Crelles Journ. Vol. 89, 298.
- ↑ This will be made more precise, so that the radius should be small compared to the wave-length. Yet the formulas (16) and (17) don't require this assumption:
- ↑ There one also finds the laws for the emission of a linearly oscillating sphere, which allows the same way of use.