$ 78] Relative Motion 103 



at the corresponding times, the sun remaining at rest at s, 

 exactly the same effect is produced on the eye, provided 

 that the lines as, ^s, rs, */s are, as in the figure, equal in 

 length and parallel in direction to E A, E B, E c, E D re- 

 spectively. The same being true of intermediate points, 

 exactly the same apparent effect is produced whether the 

 sun describe the circle A B c D, or the earth describe at 

 the same rate the equal circle abed. It will be noticed 

 further that, although the corresponding motions in the 

 two cases are at the same times in opposite directions (as 

 at A and #), yet each circle as a whole is described, 



6 

 FIG. 38. The relative motion of the sun and moon. 



as indicated by the arrow-heads, in the same direction 

 (contrary to that of the motion of the hands of a clock, 

 in the figures given). It follows in the same sort of way 

 that an apparent motion (as of a planet) may be explained 

 as due partially to the motion of the object, partially to 

 that of the observer. 



Coppernicus gives the familiar illustration of the 

 passenger in a boat who sees the land apparently moving 

 away from him, by quoting and explaining Virgil's line : 



" Provehimur portu, terraeque urbesque recedunt." 



78. The application of the same ideas to an apparent 

 rotation round the observer, as in the case of the apparent 

 daily motion of the celestial sphere, is a little more difficult. 

 It must be remembered that the eye has no means of 



