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

 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).