422 POPULAR SCIENCE MONTHLY. 



He divides the regions studied into six degrees of brightness. For 

 our present purpose it is only necessary to consider three regions, the 

 brightest, the faintest and those intermediate between the two. Besides 

 the count from the Durchmusterung he made a count of the same sort 

 from Dr. Wolf's photographs and from Herschel's gauges of the 

 heavens. In the following table I have reduced all his results, so as to 

 express the number of stars in a square degree in the three separate 

 regions. At the top of each column is given the authority, whether 

 Argelander, Wolf or Herschel. Wolf had two sets of photographs, one 

 supposed to include all the stars to the eleventh, the other to the twelfth 

 magnitude. The magnitudes included are given in the second line. 

 That Herschel's count extends to the fifteenth magnitude is by no 

 means certain; but we can judge from the great number of his stars that 

 it goes considerably beyond Wolf's in the faintness of the stars included. 

 Below this we give, in the regions A, B and C, which are, respectively, 

 those of least, of medium and of greatest brightness, the number of 

 stars per square degree according to each of the authorities: 



Authority Arg. Wolf (A). Wolf (B). Hersch. 



Magnitude 1—9 1—11 1—12 1—15 (?) 



Region A 23 72 224 405 



Region B 33 134 764 4114 



Region C 48 217 1,266 6,920 



0— A 25 145 1,042 6,425 



RatioC:A 2.1 3.0 5-7 14.0 



The vastly greater number of individual stars per square degree in 

 the brighter regions is what we should expect from the studies we 

 have made of the lucid stars. But what is of most interest in the table 

 is the continual increase in the proportion of faint stars in the separate 

 regions. We notice that, when we consider only the stars of the ninth 

 magnitude, there are twice as many in the brightest as in the darkest 

 portions. When we go to the eleventh magnitude, as shown by Wolf's 

 photograph A, we find the number of stars in the brighter regions to 

 be threefold. When the twelfth magnitude is included we find that 

 there are between five and six times as many stars in the bright regions 

 as in the dark ones. Finally, when we come to stars from Herschel's 

 gauges there are fourteen times as many stars per square degree in the 

 brighter regions as in the dark. 



At first sight this result seems to show a great difference between 

 the clusters of stars described in the last chapter, and the collections 

 of the Milky Way, in that the former include few or no faint stars, while 

 the latter include a greater and greater number as we ascend in the 

 scale of magnitude. This difference is important as showing a vastly 

 greater range of actual brightness among the galactic stars than among 

 those which form the scattered clusters. Allowing for this difference, 



