these masses, and compared it with, the stellar density, or the number of stars per square degree. The mean results are:
In that portion of the galaxy extending from Cassiopeia to the equator near 6" of R. A., ratio = 4.02.
In that portion from Cassiopeia in the opposite direction to near 19" of R. A. in Aquila, ratio = 3.70.
These remarkable results are derived from the D. M., and will be yet more striking if corrected by half the difference between it and the S. D., as we have done for the sky generally. They will then be 4.27 and 3.95, respectively.
As might be expected, the regions of greater star density have generally, though not always, the higher ratio. The highest of all is in a patch south of Gemini, between 6h and 7h of E. A., and about 5° of declination. Here it amounts to 5.94, showing that there are eighty-six stars of magnitude 9.0 to every one of magnitude 6.5.
The D. M. does not stop at magnitude 9, as the above numbers do, but extends to 9.5, while the S. D. extends to magnitude 10. For these magnitudes Seeliger finds a yet higher ratio. This is, however, to be attributed to the personal equation of the observers, and need not be further considered.
The only available material for finding the ratio of increase above the ninth magnitude is found in the Potsdam photographs for the international chart of the heavens, which extend to magnitude 11. These are published only for a few special regions. Five of the published plates fall in regions not far from the galactic pole. I have made a count by magnitudes of the 312 stars contained in these plates. An adjustment is, however, necessary from the fact that the minuter fractions of a magnitude could not be precisely determined from the photographed images. The results are practically given to fourths of a magnitude, although expressed in tenths. But it is found that the numbers corresponding to round magnitudes and their halves are disproportionately more frequent than those corresponding to the intermediate fourths. For example, there are only nineteen stars of magnitude 10.7 and 10.8 taken together; while there are forty-nine of 10.5. Under these circumstances I have made an adjustment to half magnitudes by taking the stars of quarter magnitudes, and dividing them between half magnitudes next higher and next lower. The result is as follows:
| Mag. | Stars. | |
| 6.5 | 2 | |
| 7.0 | 2 | |
| 7.5 | 4 | |
| 8.0 | 11 | |
| 8.5 | 15 | |
| 9.0 | 29 |
