INADEQUACY OF TERRESTRIALLY-KNOWN SOURCES.

We have Been that each square centimetre of the sun's surface emits sufficient energy to drive an eight-horse-power engine continuously; the output from each square centimetre of an O or B type star, such as Plaskett's star or V Puppis, which is at least 200 times as great, is sufficient to drive an express locomotive at full speed year after year and century after century for millions of years. Since the full implications of the doctrine of conservation of energy have been understood, efforts have been made to discover the origin of the energy which is poured out with such terrific profusion by the sun and stars.

A priori there are two general possibilities open. Either the stream of energy liberated from a star's surface may be continually fed to the star from outside, or it may be generated in the star's interior, and driven out through its surface, as the only means of preventing an intolerable heating of the interior. An illustration of the former mode of liberation of energy is provided by a meteorite falling through the earth's atmosphere, the energy of its radiation being provided by the impact of molecules of air on its surface ; an illustration of the latter is provided by an ordinary coal fire.

The only serious effort to explain the sun's energy as being supplied from outside was that of Robert Mayer, who conceived solar energy as arising from a continuous fall of meteors into the solar atmosphere.

Over 2000 stars are known to be variable, and of these about 1000 are definitely periodic. These periodic variables fall into the two main classes of Cepheid and long-period variables.

It is still uncertain whether Cepheid and long-period variables are essentially different objects or varieties of essentially similar objects. If the latter, the varieties are quite distinct. Long-period variables have periods ranging from about 60 to 500 days, whereas no Cepheid is known whose period exceeds 38.7 days (U Carinae), and most have periods substantially shorter than this. Apart from their different ranges of period, the two classes of variables have many features in common. The light curve of Cepheid variables does not shew a regular symmetrical rise and fall, but rather a fairly rapid rise to maximum brightness followed by a slow decline to minimum, and many long-period variables shew the same features, although generally to a less degree. The Cepheid variables shew a very marked correlation between period and spectral type, shorter periods accompanying the earlier spectral types. Adams and Joy* find a similar correlation in the long-period variables, and this proves to be a direct extension of that already established for Cepheids. In a diagram in which spectral type and period are taken as co-ordinates, they find that a single smooth curve runs through the positions occupied by the long-period variables, the normal Cepheid variables and the cluster variables which form a special short-period group of Cepheids.

STELLAR MAGNITUDES AND LUMINOSITIES.

The ancients thought of the stars as luminous points immovably attached to a spherical shell which covered in the flat earth much as a telescope-dome covers in the telescope, so that when one star differed from another in glory, it was not because the two stars were at different distances from us, but because one was intrinsically more luminous than the other.

Hipparchus introduced the conception of “magnitude” as measuring the brightnesses of the stars, and Ptolemy, in his Almagest, divided the stars into six groups of six different magnitudes. The 20 brightest stars formed the first magnitude stars, while stars which were only just visible to the eye were the sixth magnitude stars. Thus Ptolemy regarded the differences of visible glory as being represented by five steps, each step down being represented as an increase of one magnitude.

According to the well-known physiological law of Fechner, the effect which any cause produces on our senses is proportional to the logarithm of the cause. If we can just, and only just, appreciate the difference between 10 and 11, we shall not notice any difference at all between 20 and 21, but shall just be able to detect the difference between 20 and 22, or between 5 and 5½. Our senses do not supply us with a direct estimate of the intensity of the phenomenon which is affecting them, but of its logarithm.

368. The original aim of cosmogony was to discover the origin of the solar system, but the whole history of cosmogony illustrates how nothing fails so surely in science as the direct frontal attack. The plan of action in the present book has been to study the various transformations which astronomical matter must undergo through the action of physical forces, identifying the formations predicted by theory with those observed in the sky when possible. In this way it has proved possible to trace out the origin and evolution of many astronomical objects, including elliptical and spiral nebulae, star clusters of various forms, binary and multiple stars and (conjecturally at least) Cepheid and long-period variables. But nowhere have we come upon anything bearing the least resemblance to the solar system.

If the sun had been unattended by planets, its origin and evolution would have presented no difficulty. It would have been a quite ordinary star, born out of a nebula in the ordinary way, but endowed with insufficient rotation to carry it on to the later stages of fission into a binary or multiple system; it could in fact be supposed to have had precisely the same evolutionary career as half of the stars in the sky. In support of the conjecture that the sun had stopped short of fission on its evolutionary career we should only have had to note the slowness of its present rotation.