CHAPTERS ON THE STARS. 453 



of the different stars and the separate study of the proper motions 

 peculiar to each type. The next point is the reference of the motions 

 to the solar apex. The third is the study of the relations of the stars 

 to the galactic plane. 



A remarkable relation existing between the spectral type of stars and 

 their proper motions* was brought out by these investigations. The 

 stars of Type I. have, in the general mean, smaller proper motions 

 than those of Type II. The following table is made up from Kapteyn's 

 work. First we give the limits of proper motion; then on the same 

 line the number of stars of the respective Types I. and II. having proper 

 motions within these limits: 



Centennial Number of Stars. 



Prop, motions. Type I. Type II. 



Total 1,189 1,106 



It will be seen that in the case of stars having proper motions of 

 less than 5" per century a large majority are of Type I. In the case of 

 proper motions between 6" and 9" the number is nearly equal. Be- 

 tween 10" and 20" there is a large majority of Type II. Between 30" 

 and 49" the number of Type II. is nearly five times that of Type I. 

 Finally, only three stars of Type I. have proper motions exceeding 50", 

 while 58 stars of Type II. have a proper motion exceeding this limit. 



We may make two hypotheses on this subject: one, that the stars 

 of Type II. really move more rapidly than those of Type I.; the other, 

 that their actual motion is the same, but that the stars of Type I. are 

 more distant stars. The last conclusion seems much more probable, 

 and is strengthened by the much greater condensation of stars of Type 

 I. toward the Milky Way. 



Let us now consider the principles by which we may study a great 

 collection of proper motions statistically. There are scattered around 

 us in the stellar spaces, in every direction from us, a large number 

 of stars, each moving onward in a straight line and in a direction which, 

 with rare exceptions, has nothing in common with the motion of any 

 other star. The velocities of the motion vary from one star to another 

 in a way that can not be determined, some moving slowly and some 

 rapidly. Is it possible from such a maze of motions to determine any- 



*The author believes that Monck, of England, independently pointed out this 

 relation, possibly in advance of Kapteyn. 



