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[1] 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. | |||||
| " | " | |||||||
| 0 | to | 5 | 786 | 474 | ||||
| 6 | to | 9 | 203 | 194 | ||||
| 10 | to | 19 | 159 | 223 | ||||
| 20 | to | 29 | 25 | 86 | ||||
| 30 | to | 49 | 13 | 71 | ||||
| 50 | and more | 3 | 58 | |||||
| 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. Between 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.
