156-158] 
Gaseous Stars 
173 
Emission 
where 
f(M)=(4nr<r)l 
18-3 M(T e R)* 1* 
\c (\ c +1)_ 
(158-4). 
This would give the relation between a star’s mass, bolometric luminosity 
and effective temperature if the gas-laws were obeyed. 
We could of course exhibit the relation in a diagram of the type shewn 
in fig. 12, in which log# and log T e are taken as ordinate and abscissa re 
spectively. The lines of constant mass would have equations of the type 
E oo Tr, 
and so would be a series of straight parallel slant lines. 
Fig. 15. Effective temperature (or spectral type) as a function of mass and luminosity. 
It will, however, be more convenient to exhibit the relation in a different 
form. Equation (158-3) shews that a star of any given mass M and any given 
bolometric luminosity E can always find a value of T e such that it will be in 
equilibrium provided the gas-laws are obeyed throughout its mass. Thus we 
may think of a gaseous star’s effective temperature T e as being determined 
by its mass M and its bolometric luminosity, or total rate of generation of 
energy E, and we may exhibit the values of T e in a diagram in which E and M 
are taken as ordinate and abscissa, as in fig. 15.