CHAPTER XXV.

THE ABERRATION OF LIGHT.

The Real and Apparent Movements of the Stars-How they can be Discriminated— Aberration produces Effects dependent on the Position of the Stars-The Pole of the Ecliptic-Aberration make Stars seems to Move in a Circle-An Ellipse or a Straight Line according to Position-All the Ellipses have Equal Major Axes How is this Movement to be Explained?-How to be Distinguished from Annual Parallax-The Apex of the Earth's Way-How this is to be Explained by the Velocity of Light-How the Scale of the Solar System can be Measured by the Aberration of Light.

We have in this chapter to narrate a discovery of a recondite character, which illustrates in a very forcible manner some of the great fundamental truths of Astronomy. Our discussion of it will naturally be divided into two parts. In the first part we must describe the nature of the phenomenon, and then we must give the extremely elegant explanation afforded by the properties of light. The telescopic discovery of aberration, as well as its explanation, are both due to the illustrious Bradley.

The

The expression fixed star, so often used in astronomy, is to be received in a very qualified sense. The stars are, no doubt, well fixed in their places, so far as coarse observation is concerned. lineaments of the constellations remain unchanged for centuries, and in contrast with the ceaseless movements of the planets, the stars are not inappropriately called fixed. We have, however, had more than one occasion to show throughout the course of this work that the expression "fixed star" is not an accurate one when minute quantities are held in estimation. With the exact measures of modern instruments, many of these quantities are so perceptible, that they have to be always reckoned with in astronomical inquiry. We can divide the movements of the stars into two great classes: the real movements and the apparent movements. The proper motion of the stars and the movements of revolution of the binary stars con

stitute the real movements of these bodies.

These movements are

special to each star, so that two stars, although close together in the heavens, may differ in the widest degree as to the real movements which they possess. It may, indeed, sometimes happen, as Mr. Proctor has pointed out, that stars in a certain region are animated with a common movement. In this phenomenon, which has been called star-drift by its discoverer, we have traces of a real movement shared in by a number of stars in a certain group. With this exception, however, the real movements of the stars are governed by no systematic law, and the rapidly rotating binary stars and the other rapidly moving stars are scattered here and there indiscriminately over the heavens.

The apparent movements of the stars have a different character, inasmuch as we find the movement of each star determined by the place which it occupies in the heavens and not by the individual features of the particular object. It is by this means that we can readily discriminate the real movements of the star from its apparent movements, and examine the character of both.

In the present chapter we are concerned with the apparent movements only, and of these there are three, due respectively to precession, to nutation, and to aberration. Each of these apparent movements obeys laws peculiar to itself, and thus it becomes possible to analyse the total apparent motion, and to discriminate the proportions in which the precession, the nutation, and the aberration have severally contributed. We are thus enabled to isolate the effect of aberration as completely as if it were the sole agent of apparent displacement, so that, by an alliance between mathematical calculation and astronomical observation, we can study the effects of aberration as clearly as if the stars were affected by no other motions.

Concentrating our attention solely on the phenomena of aberration, we shall describe its particular effect upon stars in different regions of the sky, and thus ascertain the laws according to which the effects of aberration are exhibited. When this step has been taken, we shall be in a position to give the beautiful explanation of those laws, dependent upon the velocity of light.

At one particular region of the heavens the effect of aberration has a degree of simplicity which is not manifested anywhere else. This region lies in the constellation Draco, at the pole of the ecliptic. At this pole, or in its immediate neighbourhood, each star, in virtue of aberration, describes a circle in the heavens. This circle is very minute: it would take something like 2,000 of these circles together to form an area equal to the area of the moon. Expressed in the usual astronomical language, we would say that the diameter of this small circle is about 40.9 seconds of arc. This is a quantity which, though small to the unaided observation, is really of great relative magnitude in the present state of telescopic research. It is not only large enough to be perceived, but it can be measured with an accuracy which actually does not admit of a doubt, to the hundredth part of the whole. It is also observed that each star describes its little circle in precisely the same period of time; and that period is one year, or, in other words, the time of the revolution of the earth around the sun. It is found that for all stars in this region, be they large stars or small, single or double, white or coloured, the circles appropriate to each have all the same size, and are all described in the same time. Even from this alone it would be manifest that the cause of the phenomenon cannot lie in the star itself. This unanimity in stars of every magnitude and distance requires some simpler explanation.

Further examination of stars in different regions sheds new light on the subject. As we proceed from the pole of the ecliptic, we still find that each star exhibits an annual movement of the same character as the stars just considered. In one respect, however, there is a difference. The apparent path of the star is no longer a circle; it has become an ellipse. It is, however, soon perceived that the shape and the position of this ellipse is governed by the simple law, that the further the star is from the pole of the ecliptic the greater is the eccentricity of the ellipse. The stars at the same distance from the pole have equal eccentricity, and of the axes of the ellipse, the shorter is always directed to the pole, the longer being of course perpendicular thereto. It is, however, found that no matter how great the eccentricity may become, the major axis

always retains its original length. It is always equal to about 40.9 seconds, that is, to the diameter of the circle of aberration at the pole itself. As we proceed further and further from the pole of the ecliptic, we find that each star describes a path more and more eccentric, until at length, when we examine a star on the ecliptic, the ellipse has become so attenuated that it has flattened into a line. Each star which happens to lie on the ecliptic oscillates to and fro along the ecliptic through an amplitude of 409 seconds. Half-a-year accomplishes the journey one way, and the other half of the year restores the star to its original position. When we come to stars on the other side of the ecliptic, we see the same series of changes proceed in an inverse order. The ellipse, from being actually linear, gradually grows in width, though still preserving the same length of major axis, until at length the stars near the southern pole of the ecliptic are each found to describe a circle equal to the paths pursued by the stars at the north pole of the ecliptic.

:

The circumstance that the major axes of all these ellipses are of equal length suggests a still further simplification. Let us suppose that every star, either at the role of the ecliptic or elsewhere, pursues an absolutely circular path, and that all these circles agree, not only in magnitude, but also in being all parallel to the plane of the ecliptic it is easy to see that this simple supposition will account for the observed facts. The stars at the pole of the ecliptic will, of course, show their circles turned fairly towards us, and we shall see that they pursue circular paths. The circular paths of the stars remote from the pole of the ecliptic will, however, be only seen edgewise, and thus the apparent paths will be elliptical, as we actually find them. We can even calculate the degree of ellipticity which this surmise would require, and we find that it coincides with the observed ellipticity. Finally, when we observe stars actually moving in the ecliptic, the circles they follow would be seen edgewise, and thus the stars would have merely the linear movement which they are seen to possess. All the observed phenomena are thus found to be completely consistent with the supposition that every star of all the millions in the heavens describes

once each year a circular path; and that, whether the star be far or near, this circle has always the same apparent diameter, and lies in a plane always parallel to the plane of the ecliptic.

We have now wrought the facts of observation into a form which enables us to examine into the cause of a movement so systematic. Why is it that each star should seem to describe a small circular path? Why should that path be parallel to the ecliptic? Why should it be completed exactly in a twelvemonth? We are at once referred to the motion of the earth around the sun. That movement takes place in the ecliptic. It is completed in a year. The coincidences are so obvious that we feel almost necessarily compelled to connect in some way this apparent movement of the stars with the annual movement of the earth around the sun. If there were no such connection, it would be in the highest degree improbable that the planes of the circles should be all parallel to the ecliptic, or that the time of revolution of each star in its circle should equal that of the revolution of the earth around the sun. As both these conditions are fulfilled, the probability of the connection rises to a value almost infinite.

The important question has then arisen as to why the movement of the earth around the sun should be associated in so remarkable a manner with this universal star movement. There is here one obvious point to be noticed and to be dismissed. We have in a previous chapter discussed the important question of the annual parallax of stars, and we have shown how, in virtue of annual parallax, each star describes an ellipse. It can further be demonstrated that these ellipses are really circles parallel to the ecliptic; so that here we might hastily assume that annual parallax was the cause of the phenomenon discovered by Bradley. A single circumstance will dispose of this suggestion. The circle described by a star in virtue of annual parallax has a magnitude dependent on the distance of the star, so that the circles described by various stars are all of various dimensions, corresponding to the varied distances of different stars. The phenomena of aberration, however, distinctly assert that the circular path of each star is of the same size, quite independently of what its distance may be, and