142 PLEASANT WA YS IN SCIENCE. 



For example, we have in this process the means of 

 settling the question whether the apparent brightness of a 

 star is indeed a test of relative nearness. According to 

 accepted theories the sixth-magnitude stars are ten or twelve 

 times as far off as those of the first magnitude. Hence theii 

 motions should, on the average, be correspondingly small. 

 Now, to make assurance doubly sure, I divided the stars into 

 two sets, the first including the stars of the ist, 2nd, and 3rd, 

 the second including those of the 4th,5th, and 6th magnitude. 

 According to accepted views, the average proper motion for 

 the first set should be about five times as great as that for 

 the second. I was prepared to find it about three times as 

 great ; that is, not so much greater as the accepted theories 

 require, but still considerably greater. To my surprise, I 

 found that the average proper motion of the brighter orders 

 of stars is barely equal to that of the three lower orders. 



This proves beyond all possibility of question that by far 

 the greater number of the fainter orders of stars (I refer here 

 throughout to lucid stars) owe their faintness not to vastness 

 of distance, but to real relative minuteness. 



To pass over a number of other modes of research, the 

 actual mapping of the stellar motions, and the discovery of 

 the peculiarity to which I have given the name of star-drift, 

 remain to be considered. 



In catalogues it is not easy to recognize any instances of 

 community of motion which may exist among the stars, 

 owing to the method in which the stars are arranged. What 

 is wanted in this case (as in many others which yet remain to 

 be dealt with) is the adoption of a plan by which such 

 relations may be rendered obvious to the eye. The plan I 

 adopted was to attach to each star in my maps a small arrow, 

 indicating the amount and direction of that star's apparent 

 motion in 36,000 years (the time-interval being purposely 

 lengthened, as otherwise most of the arrows would have 

 been too small to be recognized). \Vhen this was done, 

 several well-marked instances of community of motion could 

 immediately be recognized. 



