426 POPULAR SCIENCE MONTHLY. 



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 equa- 

 tor near 6" of E. A., ratio = 4.02. 



In that portion from Cassiopeia in the opposite direction to near 19" 

 of E. 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 gen- 

 erally, though not always, the higher ratio. The highest of all is in a 

 patch south of Gemini, between 6" and 7 h 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 in- 

 ternational chart of the heavens, which extend to magnitude 11. 

 These are published only for a few special regions. Five of the pub- 

 lished 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 frac- 

 tions of a magnitude could not be precisely determined from the photo- 

 graphed images. The results are practically given to fourths of a mag- 

 nitude, although expressed in tenths. But it is found that the num- 

 bers corresponding to round magnitudes and their halves are dispropor- 

 tionately 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 



