The attractive feature of the giant and dwarf theory was the simple explanation given for the up-and- down progress of the temperature. The passing over from the giant to the dwarf series was supposed to occur when the density had reached such a value (about one-quarter the density of water) that the deviation of the material from a perfect gas began to be serious. It was shown by Lane fifty years ago that a globe of perfect gas must rise in temperature as it contracts, his method of finding the internal temperature being that considered on p. 12; thus the rising temperature in the giant stage is predicted. But the rise depends essentially on the easy compressibility of the gas; and when the compressibility is lost at high density the rising temperature may be expected to give place to falling temperature so that the star cools as a solid or liquid would do. That was believed to account for the dwarf stage.

I have been trying to recall ideas of twenty and ten years ago, and you must not suppose that from the standpoint of present-day knowledge I can endorse everything here stated. I have intentionally been vague as to whether by the hotness of a star I mean the internal or the surface temperature since ideas were formerly very loose on this point; I have made no reference to white dwarfs, which are now thought to be the densest and presumably the oldest stars of all. But it is the last paragraph especially which conflicts with our latest conclusions, for we no longer admit that stellar material will cease to behave as a perfect gas at one-quarter the density of water. Our result that the material in the dense dwarf stars is still perfect gas (p. 38) strikes a fatal blow at this part of the giant and dwarf theory.

It would be difficult to say what is the accepted theory of stellar evolution to-day. The theory is in the melting pot and we are still waiting for something satisfactory to emerge. The whole subject is in doubt and we are prepared to reconsider almost anything. Provisionally, however, I shall assume that the former theory was right in assuming that the sequence of evolution is from the most diffuse to the densest stars. Although I make this assumption I do not feel sure that it is allowable. The former theory had strong reasons for making it which no longer apply. So long as contraction was supposed to be the source of a star's heat, contraction and increasing density were essential throughout its whole career; with the acceptance of subatomic energy contraction ceases to play this fundamental role.

I propose to confine attention to the dwarf stars [Note... The term 'dwarf stars' is not meant to include white dwarfs....] because it is among them that the upset has occurred. They form a well-defined series stretching from high surface-temperature to low surface-temperature, high luminosity to low luminosity, and the density increases steadily along the series. We now call this the Main Series. It comprises the great majority of the stars. To fix ideas let us take three typical stars along the series Algol near the top, the Sun near the middle, and Krueger 60 near the bottom. The relevant information about them is summarized below :

Star Algol Sun Krueger 60
Mass (Sun=1) 4.3 1 0.27
Mean density (Water=1) 0.15 1.4 9.1
Central temperature
(million deg) 40 40 35
Surface temp. (deg.) 12,000 6,000 3,000
Colour white yellow red
Luminosity
(Sun=1) 150 1 0.01

The idea of evolution is that these represent the stages passed through in the life-history [Note... We can scarcely suppose that all stars after reaching the main series pass through precisely the same stages. For example, Algol, when it has become reduced to the mass of the Sun, may have slightly different density and temperature. But the observational evidence indicates that these individual differences are small. The main series is nearly a linear sequence; it must have some 'breadth' as well as 'length', but at present the scatter of the individual stars away from the central line of the sequence seems to be due chiefly to the probable errors of the observational data and the true breadth has not been determined....] of an individual star. The increasing density in the third column should be noticed; according to our accepted criterion it indicates that the order of development is Algol->Sun->Krueger 60.

A confusion between internal temperature and surface temperature is responsible for some of the mistakes of the older theories. To outward view the star cools from 12,000 degrees to 3,000 degrees in passing down the series, but there is no such change in its internal heat. The central temperature remains surprisingly steady. (No special reliance can be placed on the slight falling off apparently shown by Krueger 60.) It