THE MASS-LUMINOSITY RELATION 
177 
i 
122. The motion (if any) of a star along QR must be due to changing 
mass and not to any lack of balance of supply and demand of energy. 
It is important to remember this because it has usually been supposed that 
the impulse for a star to move on to a new condition comes from a failure 
of energy supply. But here a failure of supply would cause the star to 
move away from QR along a line parallel to SS '; it cannot reach any other 
point on QR without changing its mass. 
It appears then that along QR there is a semipermanent balance of 
supply of sub-atomic energy and loss by radiation, the radiation being 
determined by Table 14. For different masses the corresponding point on 
this line gives the right internal conditions for a liberation of sub-atomic 
energy at a rate which balances the fixed rate of radiation. This will be 
true for the greater part of the star’s life, but the composition of the 
material is gradually being transformed and the time ultimately arrives, 
when the star must leave the line. 
It is therefore of interest to study the internal conditions of stars on 
the line of the main series. I do not think we should expect to find any 
common characteristic, because, for example, V Puppis has to liberate 
8500 times as much energy per gram as Krueger 60 in order to keep the 
balance. But whether by accident or by some significant law of physics 
there is a common characteristic; the stars on the main series possess nearly 
the same internal temperature distribution. 
Attention has been called to this curious result by H. N. Bussell*. 
Examples of it were given in § 106. Perhaps the best way of discovering 
how closely the stars conform to it is to assume a common central tempera 
ture of 40 million degrees for all stars of the main series, and calculate the 
resulting relation between absolute magnitude (or mass) and effective 
temperature (or type). 
In Table 23 the first two columns are taken directly from Table 14. 
Then by (99-3) the radius R of the star is given by 
R = 0-856^1^ (122-1). 
I 
Hence R corresponding to the assumed central temperature can be found. 
If m is the absolute bolometric magnitude, and m 0 the magnitude taken 
directly from Table 14, 
m Q — 2 log (T e /5 200) = m = — § log L + const. 
= — 5 log R — 10 log T e + const. 
so that 8 log T e = - m 0 - 5 log R + const (122-2). 
Thus T e is found and is given in the fifth column of the Table. We can 
now determine m (= m 0 — 2 log (TJ 5200)) and reduce it to visual mag 
nitude. 
* Nature, 116, p. 209 (1925). 
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