1914] on The Stars around the North Pole 127 



15. Having found the law of distribution of the distances of 

 these stars, it is not difficult to determine something about their 

 absolute luminosities— i.e. how they would compare with the sun in 

 brightness if placed at an equal distance from us. 



If the sun were at a distance of one parsec, it would appear as a 

 bright star brighter than the first magnitude, actually of magnitude 

 0*5. If at a distance of 100 parsecs, its magnitude would be 

 10*5. Now all the stars in Carrington's catalogue may be taken as 

 brighter than 10"" '5. Thus at least 95 per cent of the 3700 stars of 

 this catalogue are intrinsically brighter than the sun, and at least 



80 per cent are 4 times as bright 

 40 „ 16 



8 „ 50 



We may conclude that the great majority of the stars brighter 

 than 10™ -5 are intrinsically brighter than the sun, and a considerable 

 proportion very much brighter. 



16. The distribution of bright and faint stars in a given volume 

 of space is quite different, and contains a much larger proportion of 

 faint stars. If we make the assumptions that the density of the 

 stars and the proportions of bright and faint ones are the same at the 

 different distances from the sun within which these Carrington stars 

 are situated, it is possible to find the actual number of stars of 

 different luminosities in a given volume of space. In a sphere with 

 radius 100 parsecs, or 20 million times the distance of the earth from 

 the sun, there are at least — 



24 which are 100 times as luminous as the sun 



340 „ 50 „ 



1530 „ 25 „ 



4840 „ 10 „ 



23,200 „ 1 „ 



93,300 „ 3-V „ 



The data only admit of a rough determination of the number of 

 very faint stars, and the number of very bright ones. The figures 

 give a general indication of the density of the stars in space and of 

 their intrinsic brightness, and serve to draw attention to the fact that 

 there are many stars much less luminous than the sun, and a certain 

 proportion very much more luminous. 



17. Our conclusions, up to this point, have been based entirely 

 on a consideration of the proper motions of the stars, irrespective of 

 whether they are bright or faint, provided only that they are suffi- 

 ciently bright to have been observed by Carrington. But as the 

 apparent magnitude of a star depends on its distance as well as on 

 its intrinsic brightness, we naturally expect some assistance, in assign- 

 ing the distances of these stars, from their magnitudes. The brightest 

 star in this small area round the pole is Polaris — the pole star — whose 



