the density will fall off towards the outside of the star, and the regions which we observe are entirely normal. The dense material is tucked away under high pressure in the interior.

Perhaps the most puzzling feature that remains is the extraordinary difference of development between Sirius and its Companion, which must both have originated at the same time. Owing to the radiation of mass the age of Sirius must be less than a billion years; an initial mass, however large, would radiate itself down to less than the present mass of Sirius within a billion years. But such a period is insignificant in the evolution of a small star which radiates more slowly, and it is difficult to see why the Companion should have already left the main series and gone on to this (presumably) later stage. This is akin to other difficulties in the problem of stellar evolution, and I feel convinced that there is something of fundamental importance that remains undiscovered.

Until recently I have felt that there was a serious (or, if you like, a comic) difficulty about the ultimate fate of the white dwarfs. Their high density is only possible because of the smashing of the atoms, which in turn depends on the high temperature . It does not seem permissible to suppose that the matter can remain in this compressed state if the temperature falls. We may look forward to a time when the supply of subatomic energy fails and there is nothing to maintain the high temperature; then on cooling down, the material will return to the normal density of terrestrial solids. The star must, therefore, expand, and in order to regain a density a thousandfold less the radius must expand tenfold. Energy will be required in order to force out the material against gravity. Where is this energy to come from? An ordinary star has not enough heat energy inside it to be able to expand against gravitation to this extent ; and the white dwarf can scarcely be supposed to have had sufficient foresight to make special provision for this remote demand. Thus the star may be in an awkward predicament -- it will be losing heat continually but will not have enough energy to cool down.

One suggestion for avoiding this dilemma is like the device of a novelist who brings his characters into such a mess that the only solution is to kill them off. We might assume that subatomic energy will never cease to be liberated until it has removed the whole mass -- or at least conducted the star out of the white dwarf condition. But this scarcely meets the difficulty; the theory ought in some way to guard automatically against an impossible predicament. and not to rely on disconnected properties of matter to protect the actual stars from trouble.

The whole difficulty seems, however, to have been removed in a recent investigation by R. H. Fowler. He concludes unexpectedly that the dense matter of the Companion of Sirius has an ample store of energy to provide for the expansion. The interesting point is that his solution invokes some of the most recent developments of the quantum theory -- the 'new statistics' of Einstein and Bose and the wave- theory of Schrodinger. It is a curious coincidence that about the time that this matter of transcendently high density was engaging the attention of astronomers, the physicists were developing a new theory of matter which specially concerns high density. According to this theory matter has certain wave properties which barely come into play at terrestrial densities; but they are of serious importance at densities such as that of the Companion of Sirius. It was in considering these properties that Fowler came upon the store of energy that solves our difficulty; the classical theory of matter gives no indication of it. The white dwarf appears to be a happy hunting ground for the most revolutionary developments of theoretical physics.

To gain some idea of the new theory of dense matter we can begin by referring to the photograph of the Balmer Series in Fig. 9. This shows the light radiated by a large number of hydrogen atoms in all possible states up to No. 30 in the proportions in which they occur naturally in the sun's chromosphere. The old-style elecro-magnetic theory predicted that electrons moving in curved paths would radiate continuous light; and the old-style statistical theory predicted the relative abundance of orbits of different sizes, so that the distribution of light along this continuous spectrum could be calculated. These predictions are wrong and do not give the distribution of light shown in the photograph; but they become less glaringly wrong as we draw near to the head of the series. The later lines of the series crowd together and presently become so close as to be practically indistinguishable from continuous light. Thus the classical prediction of continuous spectrum is becoming approximately true; simultaneously the classical prediction of its