Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/836

cross wires, and will be pointing not to the object, but to the centre of the wave it is receiving; its collimation axis coincides with a radius or wave-normal, not with a ray.

(2) A Doppler alteration of wave-length in every direction; as is obvious in the figure, from the distribution of drifted wave-fronts. It is positive on one side, and negative on the other side, of a certain direction, $\theta _{0}$, such that the radius vector is equal to the radius, or

$\cos \theta _{0}\ ={\frac {v}{2\mathrm {V} }}\ ={\tfrac {1}{2}}\alpha$ ;

the aberration angle for this particular case of no Doppler effect being twice the complement of $\theta _{0}$.

A spectator moving with the medium will perceive this change of wave-length as a change of pitch (or colour) of value

$\log {\tfrac {n}{n^{\prime }}}\ =\log {\tfrac {\lambda ^{\prime }}{\lambda }}\ =\log \left(\cos \epsilon +\alpha \cos \theta \right)\approx \alpha \cos \theta$.

An observer travelling with the medium will not observe any modification in interference or diffraction effects, nor will he experience any change of intensity due to motion; for the waves will be brought him at the customary time periods, and be subject to the ordinary flux of energy, as if everything were stationary.

Case of moving Source infixed Medium.

14. The same figure (fig. 4) serves to illustrate the common case of medium and observer stationary, and source alone moving.

But we must be careful to note that $\epsilon$ is only the aberration angle, and that whether it is to be called "aberration" or not depends on the meaning attached to that term. The source emits spherical waves in its successive positions, and leaves them to expand at their normal rate. The fixed telescope, pointing to centre of advancing wave, is therefore pointing to the source at the instant when it emitted that light; and, since it is thus seen in its true place at instant of emission, it is most natural to say that the aberration caused by moving source alone is nil; for that it may have moved by the time of vision, is obvious.

There is not much more to be said on this head, for the source after throwing off a wave may do what it likes, the light will convey information as to where and how it was at the time of emission. Phenomena depending on a succession of waves, e.g., changes of pitch, are of course produced, see fig. 4.

The question arises whether the waves thrown off from a moving source are really spherical shells: whether the motion of the source does not affect its vibration? It is not easy to answer this thoroughly and accurately, but practically there can be no doubt that the emission of light cannot be affected by any feasible terrestrial motion;