Aberration of Light

ABERRATION OF LIGHT. This is an astronomical phe nomenon depending on the fact that light is not propagated instan taneously. Our observations of the heavenly bodies are taken from the earth, a planet whose speed of motion is not incomparably smaller than that of the light ; the result is that the apparent position of a star in the sky does not correspond to its true direc tion from the earth. We are accustomed to assume intuitively that a body is "where we see it to be"; or, since the distance can not always be judged, that at any rate it is in the direction in which we see it. But actually vision gives only an indirect ac quaintance with its position. That which affects our eyes is the light which has travelled to us from the object ; we have, there fore, to take into consideration the circumstances of propagation of the light. It is well known that a light-ray changes direction in passing from one transparent medium to another, e.g., water to air, and that its course is curved in a medium of varying density such as our atmosphere; an object seen by these dis located or curved rays is displaced from its correct position, and the corresponding correction for refraction by the earth's atmos phere is highly important in determining the positions of stars. The correction for aberration is also concerned with the propaga tion of light ; it arises from the fact that our actual judgment of the direction of a ray involves a combination of the earth's motion and the motion of the light.

The most elementary explanation can be given in terms of the old corpuscular theory of light—which was the theory accepted at the time aberration was discovered. If we think of the ray of light as a stream of missiles proceeding from the star with a speed of 186,000m. a second, it is clear that the apparent direction from which the missiles come will be affected by our own velocity if that is not too insignificant in comparison. A common illustra tion is that of a man walking through a rain-storm with the drops falling vertically ; the faster he walks, the more inclined is the position in which he must hold his umbrella to shield off the "missiles." The argument can be re-stated in terms of the wave theory of light without essential alteration ; but reference should be made to an account of that theory for an explanation of the signification of "rays of light." A rough way of alining the direction of a star is to point a long narrow tube so that we can see the star through it. The alinement is given by the two apertures at the ends of the tube, which must be such that the small pencil of rays admitted through one can make an exit through the other and thus reach the ob server's eye. The upper part of the diagram shows the rays of tight coming from a star ; the upper aperture E admits a narrow beam which continues in the original direction, so that F is the position in which the exit aperture has to be placed. Suppose that whilst the light travels the distance E F the earth moves through a distance G F ; then the required direction of our tube is G E. It will then admit the light at E, and, by the time the light has travelled down the tube, the lower aperture will have reached the position F and the light will pass out. It will be seen that the tube G E does not point in the true direction of the star F E. The same principle applies when the tube is furnished with lenses, as in a telescope.

The alinement is the same whether the tube is long or short, and we can conveniently appreciate the relative proportions if we take E F to be 186,00o miles. The light then takes 1 second to pass from E to F; and in 1 second the earth travels in its orbit represented by G F. Thus G F is of E F. The greatest possible angle between the observed direction and the true direction is 10,1000 of a radian, or more accurately 20.47"; this is called the constant of aberration. For comparison the ap parent radius of Jupiter is about 2o"; so that (when the aberra tion is a maximum) we see the centre of Jupiter when we are actually looking towards the edge of disc. As the direction of the earth's motion changes throughout the year so the direction of the aberration displacement of the star changes; the star is always displaced towards the "apex of the earth's way," i.e., the point of the sky towards which the earth's motion is directed. The star apparently moves in an ellipse around its true position as centre, making a circuit once a year. For a star at the pole of the ecliptic this ellipse is a circle of radius 20.47"; for other parts of the sky the path may be re garded as a parallel circle which is projected into an ellipse by foreshortening. The major axis of the ellipse is always 2o-47", but the minor axis depends on the latitude (i.e., distance from ecliptic) of the star.

Discovery of Aberration.

The discovery of the aberration of light in 1725, due to James Bradley (1693-1762) is one of the most important in the whole domain of astronomy; and in pure physics it has provoked a succession of investigations cul minating in the theory of relativity. It was entirely unexpected, and it was only by extraordinary perseverance and perspicuity that Bradley was able to explain it in 1729. The discovery arose in the course of an attempt to discover whether the stars had ap preciable parallaxes. We now know that stellar parallaxes are less than a second of arc, and the first authentic parallax was not measured until a century later. Many observers had, however, claimed to have discovered such parallaxes. In 168o Jean Picard in his Voyage d'Uraniborg stated, as the result of ten years' ob servations, that the Pole Star exhibited variations of position amounting to 4o" annually; some astronomers endeavoured to explain this by parallax, but the motion was at variance with that which parallax would occasion. J. Flamsteed, from measurements in 1689 and succeeding years with his mural quadrant, concluded that the declination of the Pole Star was 4o" less in July than September. R. Hooke in 1674 concluded from his observations that 7 Draconis was 23" more northerly in July than October.

When James Bradley and Samuel Molyneux entered this sphere of astronomical research in 1725 there was much uncertainty as to whether genuine stellar parallaxes had been detected or not; and it was with the intention of answering this question definitely that they erected a large telescope in the house of the latter at Kew. They determined to re-investigate y Draconis, a star selected because it passed almost through the zenith in the lati tude of London; its position would therefore not be affected by troublesome and uncertain corrections for refraction. The tele scope constructed by George Graham (1675-1751), a celebrated instrument-maker, was affixed to a vertical chimney-stack; the eye-piece could be moved a little laterally so as to measure deviation from the vertical by means of a screw, the vertical being fixed by a plumb-line. The first observations were made on the 3rd, 5th, 11th, 12th Dec., 1725. On the 17th Bradley found the star to be moving southwards, and confirmed this on the loth. (The change of position by aberration at this time of the year is rapid, and amounts to about 3.2" in ten days.) The star was found to continue its southerly course until March when it was about 20" south of the December position. By the middle of April it was apparent that it was returning north again. In September it reached its northerly limit, the extreme range between March and September being 4o".

Although the observers were seeking an apparent shift of the star, they 'immediately realized that what they had found could not be attributed to parallax. The maximum range of parallactic shift for 7 Draconis should be between June and December. Aberration and parallax are easily distinguished by this three months' difference of phase ; the displacement of a star due to aberration is always at right angles to that due to parallax. Bradley and Molyneux discussed several hypotheses in the hope of arriving at an explanation. One hypothesis was that the direc tion of the earth's axis and therefore of the plumb-line varied, causing an apparent displacement of the star when its position was measured with respect to the plumb-line. Observations were therefore made of another star on the opposite side of the pole; from a comparison of the displacements with those of y Draconis it was found that they could not be explained by a shift of the earth's axis. The precaution, however, was fruitful ; for by long continued observation Bradley ultimately established that shifts due to a change of the earth's axis actually occurred ; and he was led to his second famous discovery—nutation. Bradley realized that observations of many more stars were required in order to determine the laws governing this mysterious effect. For this purpose he set up a more convenient telescope at the Rectory, Wanstead, the residence of the widow of his uncle, James Pound, who had guided him in his early astronomical work. This tele scope, erected in Aug. 1727 had a range of 61° on each side of the zenith and thus covered a much larger area of the sky than the Kew instrument. Fifty stars were kept under close ob servation. Bradley disentangled from these observations the conclusion that a star had its extreme declinations at the times of the year when it passed through the zenith at 6 o'clock morn ing or evening.

The true theory of the phenomenon was discovered by an acci dent reminding us of the more apochryphal story of Newton and the apple-tree. Sailing on the Thames, Bradley noticed the shif t ing of the vane on the mast, as the boat altered her course; the shift was not due to unsteadiness of the wind, but to the com bining of the changing motion of the boat with the steady velocity of the wind. This suggested that the changing direction of the ray from the star was the result of combining the changing motion of the earth with the steady velocity of the starlight. The finite velocity of light had been discovered by Roemer 6o years earlier. Astronomical Effects.—In modern astronomy the aberration due to the earth's orbital motion is included along with pre cession and nutation as part of the "star correction" applied to reduce from Apparent to Mean Place. A small correction for diurnal aberration is also applied, arising from the motion of the observer caused by the diurnal rotation of the earth. For planets and comets a different procedure is adopted. It must be remem bered that, even after allowing for the aberration, we see the body not where it is now but where it was when the light left it. Thus the corrected direction F E joins the position of the earth at the instant of observation to the position of the planet some minutes or hours before. Using the previous diagram but with a new connotation, let E be the planet when the light left it, and let F be the position of the earth when the light arrives. Whilst the light travels from E to F the earth travels from G to, F, so that the apparent direction of the planet G E is the actual direction joining the positions of the earth and planet at the time when the light left the planet. Accordingly we do not trouble about the hybrid direction F E. We accept G E uncorrected ; but we apply a correction to the time of observation, antedating it by the light-time. This simple procedure is inapplicable to the stars whose light-time is many years, because it assumes that the earth's velocity has been constant throughout the interval. But it answers a question often raised—whether we ought not to apply a cor rection on account of the aberration due to the motion of the whole solar system through space towards a point in Hercules. This motion, being uniform, admits of the above treatment; and the answer is that no correction is required provided that it is understood that the observation relates to the state of things when the light left the star; the aberration rather helpfully "puts back the sun" to the earlier date which must in any case pertain to the star.

Since the velocity of light is known with great accuracy the observed value of the constant of aberration determines the earth's orbital velocity. This can_ also be calculated when we know the radius of the earth's orbit from observations of the solar parallax. There has long been a rivalry between the con stant of aberration and the solar parallax as to which shall pro vide the more accurate determination ; at present the degree of accuracy seems to be about equal, and the two methods are in satisfactory accord.

Aberration and Aether.

In the explanation of aberration we pictured the light as travelling in a straight line from the star uninfluenced by the motion of the earth carrying the observer. On the wave theory this would not be true if the aether in our neighbourhood were carried along with the earth ; for when the light reaches this moving region of the aether its course will be disturbed, the motion of the aether (if the phrase has any literal meaning) being superposed on the ordinary velocity of the light traversing it. According to the modern idea of the atom, intro duced by Rutherford in 1911, the electrons and atomic nuclei are so minute that the aether can slip through the void interior of the atom as easily as through the solar system, and there is no longer any reason to anticipate a convection; but in the last century it seemed almost contrary to reason to imagine solid matter pushing its way through the aetherial medium without serious disturbance. Apart from this prejudice, experimental evi dence in the last century suggested that the aether in the lower part of our atmosphere was travelling with the earth, and further that moving matter such as a stream of water partially dragged the aether with it. Thus in 1818 Arago pointed out that the refraction by a prism (depending on the ratio of the velocities of light in air and glass) ought to be altered by the motion of the prism through the aether; since no such alteration was ob served he concluded that the surrounding aether shared the motion of the prism. Fresnel explained this effect by a "drag ging co-efficient," his hypothesis being that the "condensed" aether carrying the light inside the prism did not have the full motion of the prism but was only partially dragged in the same direction. This was apparently verified by Fizeau in 1851, who sent light in opposite directions round a circulating stream of water and thus studied its velocity with and against the current. In 1871 Airy performed his water-telescope experiment (originally sug gested by Boscovitch) in which he measured the constant of ab erration with a telescope that had its tube filled with water. Rea soning crudely, the aberration should have been increased, since the velocity of light in water is less than in air; but the normal value was obtained. Fresnel had already predicted that there would be a compensation when account was taken of the altera tion of refraction at the surface of the moving liquid.

In the light of Fresnel's theory, it seemed to emerge from these results that the aether-drag was limited to the interior of the moving bodies, and that its effects were compensated by changes of refraction at the surface of the bodies, except when (as in Fizeau's experiment) differential motions were concerned. Thus the aether just outside the solid earth would be stagnant as the theory of aberration requires. But in 1887 Michelson and Morley made a much more delicate attempt to detect the difference of velocity of the earth and surrounding aether (see RELATIVITY) this seemed to decide that the aether was carried with the earth. Thus the conflict between stagnant and convected aether was brought to a head, the former being demanded by astronomical aberration and the latter by the Michelson-Morley experiment and certain later experiments involving similar principles. The astronomical observations prove that the ray as it reaches the telescope is travelling in the same direction as when it started from the star; this., however, does not entirely rule out possible motions of the aether near the earth. It was shown by Sir George Stokes (1845) that the necessary and sufficient condition was that the motion should be of the kind known as "irrotational" in hydrodynamics. This would allow the kind of disturbance which might be anticipated from the earth's pushing its way through a fluid aether, since there is a well-known irrotational solution of the problem of a sphere moving through a liquid; but it does little to help the present difficulty since it involves a sliding of the aether over the surface of the sphere, which is precisely the point denied by the Michelson-Morley experiment. If the aether is allowed to be compressible (the density having, however, no effect on the velocity of light) an irrotational solution can be found which does not involve any slip of the aether at the earth's surface. This was pointed out by Planck, but the condensation required is so extreme, that the loop-hole cannot be considered very seriously. The reconciliation was ultimately effected by the theoretical investigations of Lorentz and Larmor. Their work showed that the electrical structure of matter involves an altera tion of length of all material objects in the direction of their velocity through the aether, which would compensate the effect looked for in the Michelson-Morley experiment—confirming a suggestion originally made by FitzGerald. When allowance is made for this contraction, none of the numerous experiments are capable of testing the relative motion of the earth and aether. The position about 1900-05 can be summed up as follows:— The earth moves through the stagnant aether without disturbing it, as the original explanation of astronomical aberration demands. The objection that bodies carried on the earth show no effects of this relative motion falls to the ground because it turns out that in all the experiments the effects are precisely compensated. For the further developments originating from these ideas refer ence should be made to the article RELATIVITY.

Astronomical aberration provides no means of determining a uniform motion through the aether; this will be apparent from what we have said as to the aberration from the motion of the solar system through space. But it provides a means of determin ing differences of velocity, such as the differences in the earth's orbital motion at different times of the year. Equally it can test any possible difference of aether-drift at different levels, e.g., at the top and bottom of a mountain. Prof. D. C. Miller's recent attempt to test this by performing the Michelson-Morley experi ment at the top of a mountain appears to us to have been mis conceived; for even if (contrary to current theory) the experi ment can reveal aether-drift, it is by no means comparable in accuracy with the test by astronomical observations, which assure us that the light of the stars is not deflected by any change of the aether current between a mountain observatory and the sea-level. All observable effects of aberration are due to relative velocity or change of velocity. On absolute velocity it is silent ; and there is reason to believe that all other experiments are silent also—a conclusion which has led to the principle of relativity.

BIBLIOGRAPHY.-For Bradley's work see S. Rigaud, Memoirs of Bibliography.-For Bradley's work see S. Rigaud, Memoirs of Bradley (1832) or H. H. Turner, Astronomical Discovery (1904)• The practical application in astronomy is treated in all text-books on spherical astronomy. For the long controversy regarding stagnant and convected aether see J. Larmor, Aether and Matter (1900) and E. T. Whittaker, A History of the Theory of Aether and Electricity (two). (A. S. E.)