NEWS FROM THE STARS ABBOT. 163 



revolving about their common center of gravity. Spectroscopic de- 

 terminations of radial motion for such telescopic double stars give 

 sufficient additional information to yield us their distances. 



Secondly, there are a number of large groups of stars, each of 

 which have been found to have their peculiar motions all toward a 

 single converging point. If the reader will stand at one end of a 

 long corridor and look down the four corners of it as they stretch 

 away from him, or, still better, will look from the back of a train 

 at a long, straight stretch of railway, he will see at once that this 

 convergence really means for these stars that their motions are all 

 parallel. This could only happen if the stars were all of a single 

 flock, moved by some common cause in the same direction. Finally, 

 as these stars have been moving since a time imnieasurahly long ago, 

 they would not now have been seen in the same part of the sky if 

 their speeds Avere unequal. Such a group, therefore, consists of stars 

 moving at equal speeds in parallel paths. 



Yet their proper motions are unequal. This is because their dis- 

 tances are unequal. If now the distance of a single one of these stars 

 can be determined in some way, the distance of every one of them 

 whose proper motion is known follows at once. 



But the great extension of knowledge as to star distances comes 

 when stars are classified according to proper motion. Consider a 

 large number of stars of equal proper motion. It is to be supposed 

 that generally (apart from special groups like those just mentioned) 

 their real motions will be at random in space, and though some will 

 be moving squarely across the line of sight and showing all of their 

 real motion, others moving nearly along the line of sight showing 

 but little of it, the average of all proper motions will be approxi- 

 mately two-thirds of the average real motion. The same is of course 

 true for large groups at two, four, or any number of times smaller 

 average proper motion than the group first considered. Their aver- 

 age real motions will also be approximately 3/2 their average proper 

 motions. 



It is further to be supposed that the average of all the real mo- 

 tions in each of these large groups of stars is the same, whatever 

 their distance from us. We may at least adopt this hypothesis for 

 lack of knowledge to the contrary. If so, it follows at once that a 

 large group of stars whose mean proper motion is one second is twice 

 as far away on the whole as a large group of stars whose mean 

 proper motion is two seconds. 



Prof. Kapteyn has carefully compared all the known distances of 

 individual stars with their proper motions, and has considered also 

 in this comparison certain other data, especially brightness. In this 

 way he has worked out a formula by which one can determine the 

 average distances of stars of different mean proper motions, and thus 



