io 4 



A Short History of Astronomy 



[Cri. IV. 



judging the direction of an object ta'Ken oy itself; it can 

 only judge the difference between the direction of the 

 object and some other direction, whether that of another 

 object or a direction fixed in some way by the body 

 of the observer. Thus when after looking at a star twice 

 at an interval of time we decide that it has moved, this 

 means that its direction has changed relatively to, say, some 

 tree or house which we had noticed nearly in its direction, 

 or that its direction has changed relatively to the direction 

 in which we are directing our eyes or holding our bodies. 

 Such a change can evidently be interpreted as a change of 



direction, either of the star 

 or of the line from the eye 

 to the tree which we used 

 as a line of reference. To 

 apply this to the case of the 

 celestial sphere, let us sup- 

 pose that s represents a star 

 on the celestial sphere, which 

 (for simplicity) is overhead 

 to an observer on the earth 

 at A, this being determined 

 by comparison with a line 

 A B drawn upright on the 

 earth. Next, earth and ce- 

 lestial sphere being supposed 

 to have a common centre 

 at o, let us suppose firstly 



that the celestial sphere turns round (in the direction of 

 the hands of a clock) till s comes to s', and that the 

 observer now sees the star on his horizon or in a direction 

 at right angles to the original direction A B, the angle 

 turned through by the celestial sphere being s o s' ; and 

 secondly that, the celestial sphere being unchanged, the 

 earth turns round in the opposite direction, till A B comes 

 to A' B', and the star is again seen by the observer on his 

 horizon. Whichever of these motions has taken place, 

 the observer sees exactly the same apparent motion in the 

 sky ; and the figure shews at once that the angle s o s' 

 through which the celestial sphere was supposed to turn 

 in the first case is equal to the angle A o A' through which 



FL-. 39. The daily rotation of 

 the earth. 



