34 
The Light from the Stars [ch. ii 
There appears to be a slight excess of stars of absolute magnitudes between 
8 and 12, but our list is certainly deficient in stars fainter than twelfth mag 
nitude (cf. fig. 1, p. 8), and if all stars were included the excess would probably 
be in the faintest stars of all. Our sun is well up in the list, being fourth out 
of twenty-three. 
This distribution fails to represent that in the universe as a whole because 
the number of stars under discussion is so small as to contain no stars of very 
high luminosity. By counting the stars to far greater distances, Kapteyn and 
Seares have obtained results summarised in the following table: 
Table V. The Luminosity-Function ( Kapteyn-Seares). 
Abs. Mag. 
Luminosity 
No. of stars 
per magnitude 
-5 
10,000 
1 
-2-5 
1000 
90 
0 
100 
3,300 
2-5 
10 
42,000 
200,000 
5 
1 
7'5 
o-i 
350,000 
10 
0 01 
500,000 
12-5 
0 001 
600,000 
The last column gives the relative number of stars per unit absolute 
magnitude which have the absolute magnitude shewn in the first column, or 
the luminosity, in terms of the sun as unity, shewn in the second column. 
Between absolute magnitudes 4 and 12 the stars are again found to be fairly 
evenly distributed, although the excess of faint stars which we suspected in 
the smaller sample is now quite noticeable. But the table further shews the 
existence, in quite small numbers, of stars of very high luminosity, their 
numbers falling off steadily and very rapidly for absolute magnitudes less than 
about 5, i.e. for stars appreciably more luminous than the sun. 
The last column of Table IV gives the masses of the stars when these are 
known from direct observation. The mass of the sun is calculated from the 
circumstance that its gravitational attraction just suffices to keep the earth 
in its orbit. In the same way the masses of the two components of a binary 
system can be calculated from the fact that the gravitational attraction of 
each just retains the other in its orbit. There is no other means of calculating 
the masses of stars by direct observation, so that no masses are entered except 
for the components of binary systems. We shall, however, find later that 
purely physical considerations make it possible to calculate the masses of 
single stars with fair accuracy from their luminosities and the temperatures 
of their surfaces.