209] 



Aberration 



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 wpuld 

 believe that there was a slight head-wind blowing the rain 

 towards hirr. 



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 displace- 

 ment from its true position is represented by 

 the angle B c A, which depends on the pro- 

 portion 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 u, 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* 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, dif- 

 ferent 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) 

 * It is k sin CAB, where k is the constant of aberration. 



IB' 



A B 



FIG. 75. The 

 aberration of 

 light. 



