and dwarf stars, replacing the old distinction of perfect and imperfect gas, is that the prolific and soon exhausted supplies of subatomic energy in the giant stage disappear and leave a much steadier supply in the dwarf stage.

When the sun has become a star of smaller mass it will need to resettle its internal conditions. Suppose that at first it tries to retain its present density. As explained on p. 12, we can calculate the internal temperature, and we find that the reduced mass coupled with constant density involves lower temperature. This will slightly turn off the tap of subatomic energy, because there can be little doubt that the release of subatomic energy is more rapid at higher temperature. The reduced supply will no longer be sufficient to balance the radiation; accordingly the star will contract just as it was supposed to do on the old contraction hypothesis which corresponds to the tap of subatomic energy being turned off altogether. The motive is loss of mass; the first consequence is an increase of density which is another characteristic of progress down the main series.

Tracing the consequences a little farther, the increasing density causes a rising temperature which in turn reopens the tap of subatomic energy. As soon as the tap is opened enough to balance the rate of radiation of the star, the contraction stops and the star remains settled in equilibrium at the smaller mass and higher density.

You will see that the laws of release of subatomic energy must be invoked if we are to explain quantitatively why a particular density corresponds to a particular mass in the progress down the main series. The contraction has to proceed so far as to bring the internal conditions to a state in which the release of energy is at the exact rate required to balance the radiation.

I am afraid this all sounds very complicated, but my purpose is to show that the adjustment of the star after an alteration of mass is automatic. After a change of mass the star has to re-solve the problem of the internal conditions necessary for its equilibrium. So far as mechanical conditions are concerned (supporting the weight of the upper layers) it can choose any one of a series of states of different density provided it has the internal temperature appropriate to that density. But such equilibrium is only temporary, and the star will not really settle down until the tap of subatomic energy is opened to the right extent to balance the rate of radiation which, as we have already seen, is practically fixed by the mass. The star fiddles about with the tap until it secures this balance.

One important conclusion has been pointed out by Professor Russell. When the star is adjusting the tap it does not do so intelligently; one trial must automatically lead to the next trial, and it is all-important that the next trial should automatically be nearer to and not farther from the right rate. The condition that it shall be nearer to the right rate is that the liberation of subatomic energy shall [Note... This increase was assumed in our detailed description of the automatic adjustment of the star, and it will be seen that it was essential to assume it. ...]increase with temperature or density. If it decreases, or even if it is unaltered, the trials will be successively farther and farther from the required rate, so that although a steady balance is possible the star will never be able to find it. It is therefore essential to admit as one of the laws of liberation of subatomic energy that the rate increases with temperature or with density or with both; otherwise subatomic energy will not fulfil the purpose for which it was introduced, viz. to keep the star steady for a very long time.

The strange thing is that the condition of balance is reached when the central temperature is near 40 million degrees -- the same whether the star is at the top, middle, or bottom of the main series. Stars at the top release from each gramme of material 700 ergs of energy per second; the sun releases 2 ergs per second; Krueger 60 releases 0.08 ergs per second. It seems extraordinary that stars requiring such different supplies should all have to ascend to the same temperature to procure them. It looks as though at temperatures below this standard not even 0.08 ergs per second is available, but on reaching the standard the supply is practically unlimited. We can scarcely believe that there is a kind of boiling- point (independent of pressure) at which matter boils off into energy. The whole phenomenon is most perplexing.