The discussion of the last chapter shewed that the orbits of binary stars, both spectroscopic and visual, are still far from conforming to the statistical laws which must finally prevail after the stars have interacted with one another for an unlimited length of time. The same is true of the components of the velocities of the stars in space. After a sufficiently long time of interaction between stars, these ought to conform to the well-known Maxwell law of distribution of velocities. The investigation of Seares already given has shewn that the resultant velocities conform well enough, at least to the extent of obeying the law of equipartition of energy, but the distribution of their directions is far from conforming to this law. After a sufficiently long time of interaction, stellar velocities must be distributed in all directions equally, their motion not favouring any one special direction. As Kapteyn shewed in 1904, the actual velocities of the stars shew a very marked favouritism for a definite direction in space, so that the law of distribution appropriate to the final state is far from being obeyed.

If the statistical laws which specify the final steady state had proved to be exactly obeyed, we could have concluded that the stars had been interacting with one another for a very long time, but we could not have estimated the length of this time except possibly in terms of a lower limit.

Now that the detailed discussion of particular problems is ended, we may perhaps attempt to summarise our results and tentative conclusions, sacrificing logical and chronological order in favour of the arrangement which offers the broadest and simplest view of the whole subject.

The easiest part of the problem of cosmogony is the interpretation of the observed shapes of astronomical bodies and formations. Here the effects of rotation have proved to be of primary importance. The earth and many of the planets have the shape of flattened oranges. The degree of flattening is such as would be produced by quite slow rotation about an axis, and there is no room for doubt that this is the actual cause of the observed flattening. It is possible to trace out theoretically the shapes assumed by astronomical bodies having all possible amounts of rotation. Mathematical investigation shews that the flattened-orange shape is assumed by all bodies in slow rotation, no matter what their internal constitution and arrangement may be, but that with more rapid rotation the shape depends on the internal arrangement of the body, being especially affected by the extent to which its mass is concentrated at or near its centre.

Two special and quite extreme types of arrangement have been considered in detail. In the first the body is supposed to consist of matter which cannot be compressed and is of uniform density throughout; to fix our ideas, we may think of a mass of water.

The moon, our nearest neighbour in the sky, is 240, 000 mites away from us; a distance which light, travelling at 186, 000 miles a second, traverses in a little over one second. The farthest astronomical objects whose distances are known are so remote that their light takes over one hundred million years to reach us. The ratio of these two periods of time–a hundred million years to a second–is the ratio of the greatest to the least distance with which the astronomer has to deal, and within this range of distances lie all the objects of his study.

As he wanders through this vast range with the aid of his telescope, he finds that the great majority of the objects he encounters fall into well-defined classes; they may almost be said to be “manufactured articles” in the sense in which Clerk Maxwell applied the phrase to atoms. Just as atoms of hydrogen or of oxygen are believed to be of similar structure and properties wherever they occur in nature, so the various astronomical objects–common stars, binary stars, variable stars, star-clusters, spiral nebulae, etc.–are believed to be, to a large extent at least, similar structures no matter whore they occur.

The similarity, it is true, is not so definite or precise as that between the atoms of chemistry, and perhaps a better comparison is provided by the different species of vegetation which inhabit a country.

GENERAL PRINCIPLES

The early spectroscopists believed that the spectrum of a star provided a sure indication of the star's age. Huggins and Lockyer had found, for instance, that the spectrum of Sirius exhibited hydrogen lines very strongly and calcium lines rather weakly; in the solar spectrum the relative strength of these two sets of lines was reversed, calcium being strong and hydrogen weak. They concluded that hydrogen was specially prominent in the constitution of Sirius and calcium in that of the sun. Believing that Sirius must one day develop into a star similar to our sun, they conjectured that its substance must gradually change from hydrogen into calcium and other more complex elements, thus finding support for the long-established hypothesis that the more complex elements were formed by gradual evolution out of the simplest. In this way they were led to regard a star's spectrum as an index to its age.

As we have seen, the true interpretation of these observations is merely that the surface of Sirius is at a temperature at which hydrogen is specially active in emitting and absorbing radiation, while the sun's surface is at a lower temperature at which hydrogen is comparatively inert, while calcium, iron, etc., have become active in its place.

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.