CHAPTERS ON THE STARS. 427 



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, how- 

 ever, 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 cor- 

 responding, 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 mag- 

 nitude. An increase of this number by somewhat more than 100 times 

 in the five steps from the sixth magnitude to the eleventh, would indi- 

 cate a ratio somewhat less than 3; about 2.5. But the comparison of 

 the photographic and visual magnitudes renders this estimate some- 

 what 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 tele- 

 scopic stars, even perhaps from those which are not found on the most 



