THE SOURCE OF STELLAR ENERGY 
311 
larger mass seems too strong to be overthrown. If the evidence of the 
Taurus cluster and similar coeval groups compels us to give up the theory 
of radiation of mass, we must presumably find some other method by 
which a star can change its mass. Some attention is given to this alterna 
tive in Chapter xm, §§ 266-7; but it does not seem likely to provide an 
escape from our difficulty. 
218. It has been pointed out by H. Vogt* that if the components of a 
double star radiate away their masses the mass ratio must tend to approach 
unity as the system grows older. In proportion to its mass the heavier 
star loses more than the light star. Data for 93 stars collected by Vogt 
tend to confirm this effect, the average mass ratio progressing towards 
unity for the systems considered to be furthest advanced in evolution. 
Allowance must be made for selection effects especially when it is remem 
bered that the earlier systems are generally spectroscopic and the later 
systems visual binaries; but we see no reason why dwarf systems of types 
K and M with large mass ratio should escape observation and we think 
that Vogt has made out a fair case. 
By a discussion of 342 double stars (the mass ratio being inferred from 
the differences of luminosity) G. Shajnf has shown very conclusively that 
in giant systems the component with higher effective temperature has, 
in general, the smaller mass, whilst in dwarf systems it has the larger mass, 
the difference of mass increasing with the difference of spectrum. The 
two cases are combined in the statement that the less massive component 
is further advanced in the Russell-Hertzsprung scheme of evolutionJ. A 
similar phenomenon is shown in globular clusters where the most luminous 
Table 42. 
Mass Ratio and Difference of Type. 
Giants 
Dwarfs 
Diff. of 
Spectrum 
Mass ratio 
No. of 
Systems 
Dili, of 
Spectrum 
Mass ratio 
No. of 
Systems 
0-0-0-4 
0-88 
78 
0-0-0-4 
0-88 
65 
0-5-0-9 
•72 
12 
0-5-0-9 
•85 
16 
1-0-1-4 
•66 
33 
10-1-4 
•70 
15 
1-5-1-9 
•62 
20 
1-5-1-9 
•63 
12 
2-0-2-4 
•45 
18 
2-0-4-5 
•35 
4 
2-Ö-2-9 
•56 
9 
3-0-4-5 
•37 
9 
* Zeits. fur Physik, 26, p. 139. f Monthly Notices, 85, p. 245. 
f As stated in § 207 the close eclipsing binaries almost without exception follow 
the opposite rule. These may be recently formed systems which have not yet reached 
a balance of L and E. 
/