| Mag. | Stars.
| |
| 9.5 | 33 | |
| 10.0 | 39 | |
| 10.5 | 64 | |
| 11.0 | 115 |
It is difficult to derive a precise value of the star ratio from this table, owing to the small number of stars of the brighter magnitudes which are insufficient to form the first term of the ratio. Assuming, however, that the ratio is otherwise satisfactorily determined up to the ninth magnitude, we find that there is but a slight increase from the ninth up to the tenth. The number of the eleventh magnitude is, however, nearly three times that of the tenth and nearly double that of 10.5.
Another way to consider the subject is to compare the total number of stars of the fainter magnitude with the number of lucid stars corresponding, which, in the general average, will be found in the same space. We may assume that near the poles of the galaxy there is about one lucid star to every ten square degrees. The five belts included in the above statement cover about thirteen square degrees. The region is, therefore, that which would contain about one star of the sixth magnitude. An increase of this number by somewhat more than 100 times in the five steps from the sixth magnitude to the eleventh, would indicate a ratio somewhat less than 3; about 2.5. But the comparison of the photographic and visual magnitudes renders this estimate somewhat doubtful. Besides this, it is questionable whether we should not reckon among stars of the eleventh magnitude those up to 11.5, which would greatly increase the number. It is a little uncertain whether we should regard the limit of magnitude on the Potsdam plates as 11.0 or 11 plus some fraction near to one-half.
Altogether, our general conclusion must be that up to the eleventh magnitude there is no marked falling off in the ratio of increase, even near the poles of the galaxy.
I have not made a corresponding count for the galactic region, but the great number of stars given on the plate show, as we might expect, that there is no diminution in the ratio of increase.
The question where the series begins to fall away is, therefore, still an undecided one, and must remain so until a very exact count is made of the photographs taken by the international photographic chart of the heavens, or of the Harvard photographs.
There is also a possibility of applying a photometric study of the sky to the question. From what has already been shown of the total amount of light received from stars of the smaller magnitudes, it would seem certain that a considerable fraction of the apparently smooth and uniform light of the nightly sky may come from these countless telescopic stars, even perhaps from those which are not found on the most
