THE SOURCE OF STELLAR ENERGY 
299 
to the density; if so, the falling off of intrinsic potency of the material is 
1 : 1 , 000 , 000 . 
It would be difficult to account for this decline as the result of a single 
process gradually exhausting itself. If the process is a single one the amount 
of the source remaining will decrease exponentially with the time or 
perhaps with an acceleration due to the increasing density. Thus the time 
between V Puppis (680 ergs per gm.) and the sun (2 ergs per gm.) will be 
much greater than the time between the sun and Krueger 60 (0-08 ergs 
per gm.). It appears then that the duration of the stage dwarf G to M 
is much shorter than the preceding stages; but it has always been held 
that the great abundance of these late dwarf stars shows that this stage 
occupies the main part of the star’s life-history. We do not necessarily 
suppose that the dwarf stars have all passed through the stage of V Puppis; 
the point of introducing V Puppis is to show that the source is capable of 
producing 680 ergs per gm. at solar temperature and therefore that less 
than •g-jjQ- of it remains in the sun. Thus in any case the solar stage has a 
much longer history behind than in front of it. 
The difficulty can, of course, be met by postulating a number of 
different sources, so that the exhaustion does not follow the single ex 
ponential law. But that concession gives up the hope of interpreting the 
main series as a simple phenomenon. 
An alternative view of the main series was suggested in § 122. There 
the source is considered practically inexhaustible but it is only tapped 
at a critical temperature of about 40 million degrees. The idea is that in 
the giant stage the star uses up various sources of subatomic energy, which 
(although prolific while they last) are soon exhausted. It then continues 
to contract until its central temperature reaches 40 million degrees when 
the main supply of energy is suddenly released; this is perhaps the cancel 
lation of protons and electrons, and the greater part of the star’s mass may 
burn itself away in this stage. A star on the main series must keep just 
enough of its material above the critical temperature to furnish the supply 
required; a comparatively small expansion will suffice to decrease the 
supply to any extent required as the star (by diminishing mass) progresses 
along the main series. On this view the energy is liberated near the centre 
of the star and the stellar model approximates to that treated in § 91. 
The principal astronomical objection is that such a method of liberation 
of heat gives the star over-stability. A slight compression of Krueger 60 
would make it liberate as much heat as V Puppis. Clearly there would 
be a great rebound from compression, and oscillations of the star would 
be maintained and increased. According to § 136 over-stability occurs 
whenever e increases faster than T 2 so that a discontinuous increase at 
a critical temperature is fatal. This difficulty of over-stability occurs in 
most of our attempts at a theory, because the margin between stability 
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