even brighter. Yet, in all cases, the faintest stars listed are classed as of magnitude 9.5. Thus a ninth magnitude star in the galaxy, according to the Durchmusterung, is very different from one of this magnitude elsewhere.
DISTRIBUTION OF THE STARS HAVING A PROPER MOTION.
Having found that the stars of every magnitude show a tendency to crowd toward the region of the Milky Way, the question arises whether this is true of those stars which have a sensible proper motion. Kapteyn has examined this question in the case of the Bradley stars. His conclusion is that those having a considerable proper motion, say more than 10" per century, are nearly equally distributed over the sky, but that when we include those having a small proper motion, we see a continually increasing tendency to crowd toward the galactic plane.
But the irregularity in the distribution of the stars observed by Bradley seems to me to render this result quite unreliable. For every such star Auwers derived a proper motion. And, if these proper motions are considered, their distribution will be the same as that of the stars. To reach a more definite conclusion, we must base our work on lists of proper motions, which are as nearly complete within their limits as it is possible to make them. Such lists have been made by Auwers and Boss, their work being based on their observations of zones of stars for the catalogue of the Astronomische Gesellschaft. The zone observed by Auwers was that between 15° and 20° in N. Dec; while Boss's was between 1° and 5°. To speak more exactly, the limits were from 14° 50' to 20° 10' and 0° 50' to 5° 10', each zone of observation overlapping 10' on the adjoining one. Thus the actual breadths were 5° 20' and 4° 20'. Within these respective limits, Auwers, by a comparison with previous observations, found 1,300 stars having an appreciable proper motion, and Boss 295. But Boss's list is confined to stars having a motion of at least 10"; of such the list of Auwers contains 431. The number of square degrees in the two zones is 1,556 and 1,830, respectively. The corresponding number of stars with proper motions extending 10" is, for each 100 square degrees:
In Boss's zone, 18.9.
In Auwers's zone, 23.9.
The question whether the greater richness of nearly 25 per cent, in Auwers's zone is real is one on which it is not easy to give a conclusive answer. The probability, however, seems to be that it is mainly due to the greater richness of the material on which Auwers's proper motions are based. The question is not, however, essential in the present discussion.
We now examine the question of the respective richness of proper motion stars in this way:
