Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/833

self-propelled, at its own definite velocity. No aberrational effect can be produced by any cause which does not act on a wave-front for a finite time.

Fig. 2.

Diagram of disturbances or waves emitted without momentum from a moving source; leaving target or telescope, at $\mathrm {Y}$ if stationary, at $\mathrm {Z}$ if moving. The line $\mathrm {ABCD}$ is the locus of successive disturbances, but is not the ray or real path. The diagram may also be taken to represent the effect of a cross stream of medium, with source stationary.

Hence waves emitted by a revolving source advance just as they would if it were stationary; any peculiarity on the surface, say a Sun spot, is depicted in a precisely radial direction, and there will be no displacement of the Sun's centre. So also with light from a flying star: the star will be seen in its position at time of emission, just as it is seen in the physical state corresponding to that instant, not to the instant of vision.

Fig. 3.

Diagram of parallel beams emitted from a revolving lighthouse. $\mathrm {ABCD}$ is the apparent beam, but $\mathrm {AS}$, $\mathrm {BS}$, &c., are the lines of vision or true rays.

As to a beam from a revolving lighthouse, it is not the path of a labelled disturbance, or true ray, which displays itself by illuminating dust particles, but it is the locus of successive disturbances sent out from a given moving point; so if the source has revolved through an angle $\theta$ while the light travels a distance $r$, $\theta =\left(\omega /\mathrm {V} \right)r$, and their shape is a spiral of Archimedes as suspected above; though the direction of vision is not tangential to them, but is truly radial as already stated.

The analogy between rays of light and lines of force is fairly close, and just as it is convenient to say that a rotating source revolves its rays, so it is convenient to say that a rotating magnet revolves its lines of force. The induction phenomena obtained from a magnet spinning on its own axis are a sufficient justification of this statement.^[1]

In an old note-book of date 1876, I find a suggestion for measuring the speed of magnetic propagation, by rotating a long bar magnet on its axis and observing its action on a distant magnetic needle;

1. See also Mr. Tolver Preston, ' Phil, Mag.,' February and March, 1885