Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/834

738 the idea being that with a finite speed of propagation the lines of force would lag, and thereby acquire a curvature out of the magnet's meridian; so that a distant needle instead of pointing straight at the magnet would be tangential to these lines, and would therefore be slightly deflected during the spin.

We now see, however, that no such aberrational effect is to be expected, except on a corpuscular view of magnetic propagation.

Concerning the effect of motion of other kinds, certain things are experimentally known; e.g., motion of the receiver is known to cause aberration, however the fact be precisely accounted for; and motion of the medium alone is known not to cause aberration of any perceptible magnitude, else would terrestrial surveying operations be inaccurate. But no experimental data as yet obtained are evidence concerning small quantities of the second order, and it will be well to examine critically and geometrically the whole subject of wave motion from a moving point to a moving telescope through a uniformly moving medium, all the velocities being possibly different in magnitude and direction. So far as steady and uniform motion is concerned this may be considered the most general case.

Convenience of attributing Relative Motion to Medium.

12. Before considering separately the phenomena mentioned in § 9, it may be convenient to consider what it is which must be in motion in order to produce one or other of them. And, first, which of them a motion of the medium alone causes.

Nothing can be more certain than that relative motion is all we are concerned with, so that whether a source travels through a medium, or the medium drifts past the source, comes to precisely the same thing. Sometimes one mode of expression is convenient, sometimes the other. It may be most natural to contemplate the medium as stationary, and to throw all motion on source and receiver, but I find that it is often very simple and helpful to invert this order, and to think of the ether of space as drifting past the earth, or other body, supposed stationary.

We shall not invariably use this device, but whenever a number of things—source, mirrors, telescope, and observer—have to be thought of as moving all precisely alike through the ether, it is simpler to think of the ether as streaming past them.

Case of Fixed Source in Moving Medium.

13. Consider now a fixed point-source in a uniformly moving medium.

Spherical wave-fronts are thrown off and immediately begin to drift, so that their centres get displaced a distance, $$vt$$, while their radii enlarge by an amount, $$\mathrm{V}t$$; and the distance through space which a disturbance has by that time travelled in the direction $$\theta$$ will be compounded of these two distances, and will be inclined to the radius, or direction of travel if all were stationary, by an angle $$\epsilon$$, which may be