# Page:StokesAberration1848.djvu/4

does not tend, as $\mu$ vanishes, to become one for which $udx+\dots$ is an exact differential, and therefore the motion which would be obtained by supposing $udx+\dots$ an exact differential, and applying to the æther the common equations of hydrodynamics, would be unstable. The proof supposes the motion in question to be steady; but such it may be proved to be, if the velocity of the earth be regarded as uniform, and an equal and opposite velocity be conceived impressed both on the earth and on the æther. Hence the stars would appear to be displaced in a manner different from that expressed by the well-known law of aberration.
When, however, we take account of a tangential force in the æther, depending, not on relative velocities, or at least not on relative velocities only, but on relative displacements, it then becomes possible, as I have shown (Phil. Mag., vol. xxix. p. 6), to explain not only the perfect regularity of the motion, but also the circumstance that $udx+\dots$ is an exact differential, at least for the æther which occupies free space; for as regards the motion of the æther which penetrates the air, whether about the limits of the atmosphere or elsewhere, I do not think it prudent, in the present state of our knowledge, to enter into speculation; I prefer resting in the supposition that $udx+\dots$ is an exact differential. According to this explanation, any nascent irregularity of motion, any nascent deviation from the motion for which $udx+\dots$ is an exact differential, is carried off into space, with the velocity of light, by transversal vibrations, which as such are identical in their physical nature with light, but which do not necessarily produce the sensation of light, either because they are too feeble, as they probably would be, or because their lengths of wave, if the vibrations take place in regular series, fall beyond the limits of the visible spectrum, or because they are discontinuous, and the sensation of light may require the succession of a number of similar vibrations. It is certainly curious that the astronomical phænomenon of the aberration of light should afford an argument in support of the theory of transversal vibrations. 