J 
21 
329 
294-296] Mass-ratio in Binary Systems 
where C is a constant; thus the luminosity-function changes by a factor of 
464 for each change of 2-5 magnitudes. 
This theoretical relation is comparatively insensitive to the exact relation 
which is assumed to hold between L and M. If this is taken to be L = M 3 < 
instead of L = M Z (cf. § 118) the factor 4 64 is replaced by 5 08. 
The luminosity-function which expresses the observed distribution of 
luminosities in the galactic system has already been given in Table V (p. 34). 
The entries for intervals of 2*5 magnitudes are repeated in the table below, 
together with values calculated from the theoretical law (295 - 2). In calculating 
these values the constant has been selected so as to make the theoretical and 
observed numbers agree for stars of the luminosity of the sun (m = 5). 
A.bs. Mag. 
Observed no. of 
stars per mag. 
Calculated no. in 
steady state 
-5 
1 
430 
-2-5 
90 
2,000 
0 
3,300 
9,290 
2-5 
42,000 
43,000 
6 
200,000 
200,000 
7-5 
350,000 
929,000 
10 
500.000 
4,300,000 
125 
600,000 
20,000,000 
By comparison with the theoretical steady-state distribution, observation 
reveals a great deficiency of both very bright and very faint stars, which we 
may, for the moment, identify with very old and very young stars. This 
indicates that the galactic system is not the outcome of a continuous 
steady creation of stars. The process must have started long enough back 
for the faintest stars in the system to have attained their present small 
masses, but seems to have reached a very marked maximum of intensity at 
the time of birth of the stars which are now of absolute magnitudes from 2 
to 5, subsequently declining so as to become almost negligible. If this 
maximum rate of creation had been maintained there would be 430 times as 
many very young stars of absolute magnitude — 5 as actually exist. 
Recapitulation. 
296. Let us attempt to sum up the results obtained in this and the 
preceding chapter. 
We have examined the various agencies which can produce changes in the 
periods and eccentricities of binary systems, and have found that only one, 
namely encounters with other stars, is capable of producing effects compar 
able with those put in evidence by the observed periods and eccentricities. 
It is possible to calculate the rate at which the periods and eccentricities 
of binary systems are being changed by encounters, and hence we can