to our readers. I have, therefore, derived their general mean results for different parts of the sky with reference to the Milky Way and for stars of the various orders of magnitude. The following table shows the conclusions:
| Ratio of | Concluded | |||||||
| Zone. | increase. | result. | ||||||
| D. M. | S. D. | Diff. | ||||||
| I. | 2.99 | — | — | 3.24 | ||||
| II. | 3.00 | 3.49 | 0.49 | 3.25 | ||||
| III. | 3.07 | 3.72 | 0.65 | 3.37 | ||||
| IV. | 3.32 | 3.85 | 0.53 | 3.58 | ||||
| V. | 3.55 | 4.15 | 0.60 | 3.85 | ||||
| VI. | 3.28 | 3.68 | 0.40 | 3.48 | ||||
| VII. | 3.23 | 3.55 | 0.32 | 3.37 | ||||
| VIII. | 3.44 | 3.56 | 0.12 | 3.40 | ||||
| IX. | — | 3.49 | — | 3.24 |
In the first column we have the designation of the zone or region of the sky, as already given.
In the second and third columns we have the mean ratio of increase for whole magnitudes as derived from the Durchmusterung and the southern Durchmusterung, respectively. It will be recalled that region I., around the north galactic pole, is entirely wanting in the S. D., while the adjoining regions, II. and III., are only partially found, and that, in like manner, the D. M. includes none of region IX. around the south galactic pole, and but little of the adjoining region.
It will be seen that there is a very remarkable systematic difference between the two lists, the ratio of the number of faint to that of bright stars being much greater in the S. D. This difference is shown in the fourth column. I have assumed that the two systems are equally good, and there diminished all the ratios of the S. D. by 0.25, and increased those of the D. M. by the same amount. The mean of the two corrected results was then taken, giving the principal weight to the one or the other, according to the number of stars on which they depend.
It will be seen that the increase of the ratio from either galactic pole to the Milky Way itself is as well marked as in the case of the richness of the respective regions in stars. We may condense the results in this way:
| In the galactic zone, | ratio | = 3.85 |
| In zones IV. and VI., | " | = 3.53 |
| In polar zones I., II., VIII. and IX., | " | = 3.28 |
It will be recalled that zone V. is a central belt 20° broad, including the Milky Way in its limits. But the latter, as seen by the eye, especially its brightest portions, does not fill this zone. These portions, as we know, comprise the irregular collection of cloud-like masses described in the last chapter. Seeliger has investigated the ratio within
