SECT, xxxvu.] PBOPER MOTIONS OF THE STARS. 431 



nitude ; if we suppose the two to be really of the same size, 

 their distances from us must be in the ratio of 57'3 to 1, 

 because light diminishes as the square of the distance of 

 the luminous body increases. 



So many of the stars have proper motions altogether in- 

 dependent of the annual rotation of the earth in its orbit, 

 that it may be doubted whether there be such a thing as a 

 fixed star. Groombridge is the most rapid known, a Centauri 

 moves at the rate of 3"'58 annually, and 61 Cygni describes 

 a line in space of 5" - 12 in the same time. These motions 

 are probably in curves, but at the distance of the earth 

 they will appear to be rectilineal for ages to come. The 

 motion of little more than five seconds of space, which 

 61 Cygni describes annually, seems to us to be extremely 

 small ; but at the distance of that star an angle of one second 

 corresponds to twenty-four millions of millions of miles; 

 consequently the annual motion of 61 Cygni is 120 millions 

 of millions of miles, and yet, as M. Arago observes, we call 

 it a fixed star. From the same cause it is evident that the 

 crowding of the stars in the Milky Way may be apparent 

 only, and that the stars may be at vast distances from one 

 another. 



Were the solar system and the whole of the stars visible 

 to us carried forward in space by a motion common to all, 

 like ships drifting in a current, it would be impossible for 

 us, moving with the rest, to ascertain its direction. Sir 

 William Herschel perceived that a great part of the motions 

 of the stars are only apparent, arising from a real motion of 

 the sun in a contrary direction. Among many discrepancies 

 he found that the stars in the northern hemisphere have a 

 general tendency to move towards a point diametrically 

 opposite to X Herculis, which he attributed to a motion of 

 the solar system in a contrary direction. For it was evi- 

 dent to him, that the stars, from the effects of perspective 

 alone, would seem to diverge in the direction to which the 

 solar system was going, and would converge towards the space 



