410 ASTROMETRY 



that is, the hypothesis that the real proper motions do not favor any 

 particular direction, we must be able to find out the real arrange- 

 ment of the stars in the Milky Way and outside that stratum. 



Before discussing the difficulty here alluded to, I shall state another 

 difficulty, which, though it will not necessarily hinder us from un- 

 raveling the mystery of the structure of the Milky Way, may well 

 lead us to doubt the validity of our conclusions in regard to the 

 change of star-density with increasing distances from the sun. I am 

 speaking of the absorption of light in space. 



How fundamental the question of the absorption of light is for 

 the determination of the star-density appears from Fig. 2. The num- 

 ber of stars of any apparent magnitude present in any one shell is 

 known independently of any consideration of absorption of light. 

 Whether there is appreciable absorption or not, there are 771 stars 

 of the sixth apparent magnitude in shell VII. But if there is absorp- 

 tion to the amount of 1.8 magnitudes per unit of distance, as recently 

 proposed by Comstock, then, as the mean distance of shell VII is 2.13, 

 the light of the stars of this shell will be diminished by about 2.13 

 X 1.8=3.8 magnitudes. 



To appear to us as stars of the sixth magnitude these stars must 

 therefore have, not the absolute magnitude 4.4, which we had to 

 assume for them in a perfectly transparent space, but 3.8 magnitudes 

 brighter. We thus would find these stars to be of absolute magnitude 

 0.6 in the mean. 



For the several shells these new absolute magnitudes, correspond- 

 ing with apparent magnitude 6, have been inclosed in squares in 

 Fig. 2. 



Does it follow that in the same space in which in a transparent 

 universe we should have 771 stars of absolute magnitude 4.4, we 

 must now assume the presence of 771 stars of absolute magnitude 

 0.6? Not generally; for it must be evident that in the theory which 

 assumes absorption, the thickness of the spherical shells of Fig. 2 

 does no longer correspond with just one magnitude. It can be easily 

 proved, 1 however, that, if the proportion of the total number of 

 stars of two consecutive absolute magnitudes is a constant, and this 

 condition is approximately satisfied for the all-important magnitudes, 

 then we shall indeed have in shell VII just 771 stars of absolute 

 magnitude 0.6; in shell VI just 901 stars of absolute magnitude 3.0, 

 and so on. 



Now, whichever theory we adopt, the stars of absolute magnitude 

 4.4 will be found to be about 200 or 300 times more numerous than 

 the stars of absolute magnitude 0.6. 



For the density of intrinsically equally bright stars, therefore, 

 also for the total star-density in shell VII, we shall thus have to 

 1 See thb proof, Astronomical Journal, no. 566. 



