Page:Ueber das Doppler'sche Princip.djvu/11

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The introduction of the substitutions (10), (12) or (13) always gives, if δ is given by the constraints along a given surface as an arbitrary function of time, the transition from the effect of a stationary source to the effect when it is in translational motion.

If, for example, we have \overline{\delta}=f(t) on a very small sphere of radius R, then the propagated dilation is given by:

\delta=\frac{R}{r}f\left(t-\frac{r-R}{\omega}\right).

The substitution (10) gives the influence of a translation of a "sounding" sphere parallel to the X-axis. The discussion of the result is equivalent to that employed under 3).