THE MOVEMENTS OF THE STARS. 271 



which it actually happens to be, but the matter is quite 

 otherwise when proper motions are being measured by the 

 ordinary telescopic method. The displacement which the 

 telescope observes depends partly on the velocity with 

 which the body is moving and partly upon the distance at 

 which it is situated. If two stars had equal velocities per- 

 pendicular to the line of sight, but if one of those stars 

 was ten times as far as the other, then the apparent move - 

 ment of the more distant star, as measured by its dis- 

 placement on the heavens, would only seem to be one- tenth 

 part that of the nearer star. In the case of bodies which are 

 extremely distant from us, the circumstance that I have 

 just mentioned causes the determination of its movement 

 on the heavens to be impossible, owing to its minuteness. 

 A star might be so far off that even if it moved as quickly 

 as the most rapidly moving body that we know of, 

 still its apparent displacement on the heavens might be 

 quite inappreciable after the lapse of a year or many years, 

 and consequently we could hardly obtain any information 

 as to its movements across the face of the heavens. On the 

 other hand, the excessive distance of the star would be no 

 bar to the application of the spectroscopic method, so long 

 as the spectrum was bright enough to enable the lines to 

 be seen. The form, too, in which the spectroscope offers 

 to us its results is especially satisfactory ; it announces 

 definitely that the star is moving towards us or moving 

 from us, and it determines the velocity of that motion. 

 The telescopic method merely indicates that the star 

 traverses so many seconds of arc, or often mere fractions 

 of a second, in the course of a twelvemonth. We cannot 

 express the result in speed of miles per second unless we 



