axis is fixed with respect to the earth, i.e. the north and south poles occupy permanent geographical positions, yet the axis is not directed towards a fixed point in the heavens; variation of latitude, however, is associated with the shifting of the axis within the earth, i.e. the geographical position of the north pole varies.
Nutation of the axis would determine a similar apparent motion for all stars: thus, all stars having the same polar distance as γ Draconis should exhibit the same apparent motion after or before this star by a constant interval. Many stars satisfy the condition of equality of polar distance with that of γ Draconis, but few were bright enough to be observed in Molyneux’s telescope. One such star, however, with a right ascension nearly equal to that of γ Draconis, but in the opposite sense, was selected and kept under observation. This star was seen to possess an apparent motion similar to that which would be a consequence of the nutation of the earth’s axis; but since its declination varied only one half as much as in the case of γ Draconis, it was obvious that nutation did not supply the requisite solution. The question as to whether the motion was due to an irregular distribution of the earth’s atmosphere, thus involving abnormal variations in the refractive index, was also investigated; here, again, negative results were obtained.
Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the maximum positions was nearly proportional to the sun’s distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted. For this purpose he repaired to the Rectory, Wanstead, then the residence of Mrs Pound, the widow of his uncle James Pound, with whom he had made many observations of the heavenly bodies. Here he had set up, on the 19th of August 1727, a more convenient telescope than that at Kew, its range extending over 614° on each side of the zenith, thus covering a far larger area of the sky. Two hundred stars in the British Catalogue of Flamsteed traversed its field of view; and, of these, about fifty were kept under close observation. His conclusions may be thus summarized: (1) only stars near the solstitial colure had their maximum north and south positions when the sun was near the equinoxes, (2) each star was at its maximum positions when it passed the zenith at six o’clock morning and evening (this he afterwards showed to be inaccurate, and found the greatest change in declination to be proportional to the latitude of the star), (3) the apparent motions of all stars at about the same time was in the same direction.
 Fig. 2. |
A re-examination of his previously considered hypotheses as to the cause of these phenomena was fruitless; the true theory was ultimately discovered by a pure accident, comparable in simplicity and importance with the association of a falling apple with the discovery of the principle of universal gravitation. Sailing on the river Thames, Bradley repeatedly observed the shifting of a vane on the mast as the boat altered its course; and, having been assured that the motion of the vane meant that the boat, and not the wind, had altered its direction, he realized that the position taken up by the vane was determined by the motion of the boat and the direction of the wind. The application of this observation to the phenomenon which had so long perplexed him was not difficult, and, in 1727, he published his theory of the aberration of light—a corner-stone of the edifice of astronomical science.
Let S (fig. 2) be a star and the observer be carried along the line AB; let SB be perpendicular to AB. If the observer be stationary at B, the star will appear in the direction BS; if, however, he traverses the distance BA in the same time as light passes from the star to his eye, the star will appear in the direction AS. Since, however, the observer is not conscious of his own translatory motion with the earth in its orbit, the star appears to have a displacement which is at all times parallel to the motion of the observer. To generalize this, let S (fig. 3) be the sun, ABCD the earth’s orbit, and s the true position of a star. When the earth is at A, in consequence of aberration, the star is displaced to a point a, its displacement sa being parallel to the earth’s motion at A; when the earth is at B, the star appears at b; and so on throughout an orbital revolution of the earth. Every star, therefore, describes an apparent orbit, which, if the line joining the sun and the star be perpendicular to the plane ABCD, will be exactly similar to that of the earth, i.e. almost a circle. As the star decreases in latitude, this circle will be viewed more and more obliquely, becoming a flatter and flatter ellipse until, with zero latitude, it degenerates into a straight line (fig. 4).
 Fig. 3. |
 Fig. 4. |
The major axis of any such aberrational ellipse is always parallel to AC, i.e. the ecliptic, and since it is equal to the ratio of the velocity of light to the velocity of the earth, it is necessarily constant. This constant length subtends an angle of about 40″ at the earth; the “constant of aberration” is half this angle. The generally accepted value is 20·445″, due to Struve; the last two figures are uncertain, and all that can be definitely affirmed is that the value lies between 20·43″ and 20·48″. The minor axis, on the other hand, is not constant, but, as we have already seen, depends on the latitude, being the product of the major axis into the sine of the latitude.
Assured that his explanation was true, Bradley corrected his observations for aberration, but he found that there still remained a residuum which was evidently not a parallax, for it did not exhibit an annual cycle. He reverted to his early idea of a nutation of the earth’s axis, and was rewarded by the discovery that the earth did possess such an oscillation (see Astronomy). Bradley recognized the fact that the experimental determination of the aberration constant gave the ratio of the velocities of light and of the earth; hence, if the velocity of the earth be known, the velocity of light is determined. In recent years much attention has been given to the nature of the propagation of light from the heavenly bodies to the earth, the argument generally being centred about the relative effect of the motion of the aether on the velocity of light. This subject is discussed in the articles Aether and Light.
References.—A detailed account of Bradley’s work is given in S. Rigaud, Memoirs of Bradley (1832), and in Charles Hutton, Mathematical and Philosophical Dictionary (1795); a particularly clear and lucid account is given in H. H. Turner, Astronomical Discovery (1904). The subject receives treatment in all astronomical works.
II. Aberration in Optical Systems
Aberration in optical systems, i.e. in lenses or mirrors or a series of them, may be defined as the non-concurrence of rays from the points of an object after transmission through the system; it happens generally that an image formed by such a system is irregular, and consequently the correction of optical systems for aberration is of fundamental importance to the instrument-maker. Reference should he made to the articles Reflexion, Refraction and Caustic for the general characters of reflected and refracted rays (the article Lens considers in detail the properties of this instrument, and should also be consulted); in this article will be discussed the nature, varieties and modes of aberrations mainly from the practical point of view, i.e. that of the optical-instrument maker.
Aberrations may be divided in two classes: chromatic (Gr. χρῶμα, colour) aberrations, caused by the composite nature of
