A discussion of the difficulties of Russell’s theory led me to undertake a mathematical investigation of the stability of stars in general, and this was found to provide a simple and somewhat unexpected explanation of the otherwise incomprehensible distribution of stars in the Russell diagram; it is in brief that the unoccupied regions of the diagram represent stars in an unstable condition. I do not know what proportion of astronomers accept this explanation; some, whose opinion I value, do not. I do not think that much so far written in this book would be seriously challenged by competent critics, but it is only fair to say that at this point we are entering controversial ground. THE HYPOTHESIS OF LIQUID STARS Let us begin by imagining an enormous number of stars built on all possible plans, out of all kinds of substances. Mathematical investigation shews that some of these stars may be unable to shine with a steady light for either or both of two reasons—they may explode, like a heated keg of gunpowder, or they may have an inherent tendency to contract or expand without limit. Whether a star escapes the first pitfall or not depends mainly upon the properties of the substance of which it is built; whether it escapes the second depends mainly upon the way it is built. The two pitfalls are not altogether distinct, and when we consider the stability of wholly gaseous stars of enormously great weight, we find that the pits on the two sides of the path merge into one, or at most only a narrow strip of safe ground is left between them. Nevertheless stars of enormously great weight are known to exist, and continue shining steadily. If then, these stars are wholly gaseous, they must occupy the one safe spot of ground between the two pits, and this informs us both as to the way they are built and as to the properties of the substance of which they are built. We find that such stars only escape both pitfalls if their substance possesses properties which appear very improbable, and contrary to anything of which we have any experience or knowledge in physics; in brief, for such a star to remain stable, the annihilation of its matter must proceed at a rate which depends on the temperature. Such a property seems in every way contrary to the physical principles explained in Chapter II, as it is to all our expectations of atomic behaviour. The annihilation of matter is a far more violent change, and involves quanta of far higher energy, than mere radio-active disintegration, and as the latter process is not affected by temperature changes, it hardly seems possible that the process of annihilation should be, at any rate until we reach temperatures of the order of the 2,200,000,000,000 degrees tabulated on p. 144[26]. [26] This provides a further objection to Russell’s hypothesis, which, to avoid confusion, was not mentioned on p. 295.