Bradley’s explanation shews that the apparent position of a star is determined by the motion of the star’s light _relative_ to the earth, so that the star appears slightly nearer to the point on the celestial sphere towards which the earth is moving than would otherwise be the case. A familiar illustration of a precisely analogous effect may perhaps be of service. Any one walking on a rainy but windless day protects himself most effectually by holding his umbrella, not immediately over his head, but a little in front, exactly as he would do if he were at rest and there were a slight wind blowing in his face. In fact, if he were to ignore his own motion and pay attention only to the direction in which he found it advisable to point his umbrella, he would believe that there was a slight head-wind blowing the rain towards him. [Illustration: FIG. 75.—The aberration of light.] 209. The passage quoted from Bradley’s paper deals only with the simple case in which the star is at right angles to the direction of the earth’s motion. He shews elsewhere that if the star is in any other direction the effect is of the same kind but less in amount. In Bradley’s figure (fig. 74) the amount of the star’s displacement from its true position is represented by the angle B C A, which depends on the proportion between the lines A C and A B; but if (as in fig. 75) the earth is moving (without change of speed) in the direction A B′ instead of A B, so that the direction of the star is oblique to it, it is evident from the figure that the star’s displacement, represented by the angle A C B′, is less than before; and the amount varies according to a simple mathematical law[118] with the angle between the two directions. It follows therefore that the displacement in question is different for different stars, as Bradley’s observations had already shewn, and is, moreover, different for the same star in the course of the year, so that a star appears to describe a curve which is very nearly an ellipse (fig. 76), the centre (S) corresponding to the position which the star would occupy if aberration did not exist. It is not difficult to see that, wherever a star is situated, the earth’s motion is twice a year, at intervals of six months, at right angles to the direction of the star, and that at these times the star receives the greatest possible displacement from its mean position, and is consequently at the ends of the greatest axis of the ellipse which it describes, as at A and A′, whereas at intermediate times it undergoes its least displacement, as at B and B′. The greatest displacement S A, or half of A A′, which is the same for all stars, is known as the =constant of aberration=, and was fixed by Bradley at between 20″ and 20-1∕2″, the value at present accepted being 20″·47. The least displacement, on the other hand, S B, or half of B B′, was shewn to depend in a simple way upon the star’s distance from the ecliptic,