in this region the stars are no thicker than elsewhere. In the region from 18h. to 21h. there is an excess of 45 stars having proper motions. Whether this excess is real may well be doubted. It is scarcely, if at all, greater than might be the result of accidental inequalities of distribution. Were the proper motion stars proportional to the whole number, there ought to be 240 within the strip. The actual number is 38 less than this.
It is to be remembered that Auwers's proper motions are not limited to a definite magnitude, as were Boss's, but that he looked for all stars having a sensible proper motion. The question, what proper motion would be sensible, is a somewhat indefinite one, depending very largely on the data. It may, therefore, well be that the small excess of 45 found within this strip is due to the fact that more stars were observed and investigated, and, therefore, more proper motions found. Besides this, some uncertainty may exist as to the reality of the minuter proper motions.
The conclusion is interesting and important. If we should blot out from the sky all the stars having no proper motion large enough to be detected, we should find remaining stars of all magnitudes; but they would be scattered almost uniformly over the sky, and show no tendency toward the galaxy.
From this again it follows that the stars belonging to the galaxy lie farther away than those whose proper motions can be detected.