Since the light-curve is explicable by eclipses, it follows that the sizes of the two stars are determinable relatively to the distance between them. The period of their orbital motion is known, being identical with the complete period of the variability of their light, and an easy application of Kepler's law of periodic times enables us to compute the sum of the masses of the two stars divided by the cube of the distance between their centres. Now the sizes of the bodies being known, the mean density of the whole system may be calculated. In every case that density has been found to be much less than the sun's, and indeed the average of a number of mean densities which have been determined only amounts to one-eighth of that of the sun. In some cases the density is extremely small, and in no case is it quite so great as half the solar density.

It would be absurd to suppose that these stars can be uniform in density throughout, and from all that is known of celestial bodies it is probable that they are gaseous in their external parts with great condensation towards their centres. This conclusion is confirmed by arguments drawn from the theory of rotating masses of liquid. (See J.H. Jeans, "On the density of Algol variables", "Astrophysical Journ." Vol. XXII. (1905), page 97.)

Although, as already explained, a good deal is known about the shapes and the stability of figures consisting of homogeneous incompressible liquid in rotation, yet comparatively little has hitherto been discovered about the equilibrium of rotating gaseous stars. The figures calculated for homogeneous liquid can obviously only be taken to afford a general indication of the kind of figure which we might expect to find in the stellar universe. Thus the dotted curve in Fig. 5, which exhibits one of the figures which I calculated, has some interest when placed alongside the figures of the stars in RR Centauri, as computed from the observations, but it must not be accepted as the calculated form of such a system. I have moreover proved more recently that such a figure of homogeneous liquid is unstable. Notwithstanding this instability it does not necessarily follow that the analogous figure for compressible fluid is also unstable, as will be pointed out more fully hereafter.

Professor Jeans has discussed in a paper of great ability the difficult problems offered by the conditions of equilibrium and of stability of a spherical nebula. ("Phil. Trans. R.S." Vol. CXCIX. A (1902), page 1. See also A. Roberts, "S. African Assoc. Adv. Sci." Vol. I. (1903), page 6.) In a later paper ("Astrophysical Journ." Vol. XXII. (1905), page 97.), in contrasting the conditions which must govern the fission of a star into two parts when the star is gaseous and compressible with the corresponding conditions in the case of incompressible liquid, he points out that for a gaseous star (the agency which effects the separation will no longer be rotation alone; gravitation also will tend towards separation...From numerical results obtained in the various papers of my own,...I have been led to the conclusion that a gravitational instability of the kind described must be regarded as the primary agent at work in the actual evolution of the universe, Laplace's rotation playing only the secondary part of separating the primary and satellite after the birth of the satellite."

It is desirable to add a word in explanation of the expression "gravitational instability" in this passage. It means that when the concentration of a gaseous nebula (without rotation) has proceeded to a certain stage, the arrangement in spherical layers of equal density becomes unstable, and a form of bifurcation has been reached. For further concentration concentric spherical layers become unstable, and the new stable form involves a concentration about two centres. The first sign of this change is that the spherical layers cease to be quite concentric and then the layers of equal density begin to assume a somewhat pear-shaped form analogous to that which we found to occur under rotation for an incompressible liquid. Accordingly it appears that while a sphere of liquid is stable a sphere of gas may become unstable. Thus the conditions of stability are different in these two simple cases, and it is likely that while certain forms of rotating liquid are unstable the analogous forms for gas may be stable. This furnishes a reason why it is worth while to consider the unstable forms of rotating liquid.

There can I think be little doubt but that Jeans is right in looking to gravitational instability as the primary cause of fission, but when we consider that a binary system, with a mass larger than the sun's, is found to rotate in a few hours, there seems reason to look to rotation as a contributory cause scarcely less important than the primary one.

With the present extent of our knowledge it is only possible to reconstruct the processes of the evolution of stars by means of inferences drawn from several sources. We have first to rely on the general principles of stability, according to which we are to look for a series of families of forms, each terminating in an unstable form, which itself becomes the starting-point of the next family of stable forms. Secondly we have as a guide the analogy of the successive changes in the evolution of ideal liquid stars; and thirdly we already possess some slender knowledge as to the equilibrium of gaseous stars.

From these data it is possible to build up in outline the probable history of binary stars. Originally the star must have been single, it must have been widely diffused, and must have been endowed with a slow rotation. In this condition the strata of equal density must have been of the planetary form. As it cooled and contracted the symmetry round the axis of rotation must have become unstable, through the effects of gravitation, assisted perhaps by the increasing speed of rotation. (I learn from Professor Jeans that he now (December 1908) believes that he can prove that some small amount of rotation is necessary to induce instability in the symmetrical arrangement.) The strata of equal density must then become somewhat pear- shaped, and afterwards like an hour-glass, with the constriction more pronounced in the internal than in the external strata. The constrictions of the successive strata then begin to rupture from the inside progressively outwards, and when at length all are ruptured we have the twin stars portrayed by Roberts and by others.

As we have seen, the study of the forms of equilibrium of rotating liquid is almost complete, and Jeans has made a good beginning in the investigation of the equilibrium of gaseous stars, but much more remains to be discovered. The field for the mathematician is a wide one, and in proportion as the very arduous exploration of that field is attained so will our knowledge of the processes of cosmical evolution increase.

From the point of view of observation, improved methods in the use of the spectroscope and increase of accuracy in photometry will certainly lead to a great increase in our knowledge within the next few years. Probably the observational advance will be more rapid than that of theory, for we know how extraordinary has been the success attained within the last few years, and the theory is one of extreme difficulty; but the two ought to proceed together hand in hand. Human life is too short to permit us to watch the leisurely procedure of cosmical evolution, but the celestial museum contains so many exhibits that it may become possible, by the aid of theory, to piece together bit by bit the processes through which stars pass in the course of their evolution.

In the sketch which I have endeavoured to give of this fascinating subject, I have led my reader to the very confines of our present knowledge. It is not much more than a quarter of a century since this class of observation has claimed the close attention of astronomers; something considerable has been discovered already and there seems scarcely a discernible limit to what will be known in this field a century from now. Some of the results which I have set forth may then be shown to be false, but it seems profoundly improbable that we are being led astray by a Will-of-the-Wisp.

XXIX. THE EVOLUTION OF MATTER.

By W.C.D. WHETHAM, M.A., F.R.S. Trinity College, Cambridge.

The idea of evolution in the organic world, made intelligible by the work of Charles Darwin, has little in common with the recent conception of change in certain types of matter. The discovery that a process of disintegration may take place in some at least of the chemical atoms, previously believed to be indestructible and unalterable, has modified our view of the physical universe, even as Darwin's scheme of the mode of evolution changed the trend of thought concerning the organic world. Both conceptions have in common the idea of change throughout extended realms of space and time, and, therefore, it is perhaps not unfitting that some account of the most recent physical discoveries should be included in the present volume.

The earliest conception of the evolution of matter is found in the speculation of the Greeks. Leucippus and Democritus imagined unchanging eternal atoms, Heracleitus held that all things were in a continual state of flux--Panta rei.

But no one in the Ancient World--no one till quite modern times--could appreciate the strength of the position which the theory of the evolution of matter must carry before it wins the day. Vague speculation, even by the acute minds of philosophers, is of little use in physical science before experimental facts are available. The true problems at issue cannot even be formulated, much less solved, till the humble task of the observer and experimenter has given us a knowledge of the phenomena to be explained.

It was only through the atomic theory, at first apparently diametrically opposed to it, that the conception of evolution in the physical world was to gain an established place. For a century the atomic theory, when put into a modern form by Dalton, led farther and farther away from the idea of change in matter. The chemical elements seemed quite unalterable, and the atoms, of which each element in modern view is composed, bore to Clerk Maxwell, writing about 1870, "the stamp of manufactured articles" exactly similar in kind, unchanging, eternal.

Nevertheless throughout these years, on the whole so unfavourable to its existence, there persisted the idea of a common origin of the distinct kinds of matter known to chemists. Indeed, this idea of unity in substance in nature seems to accord with some innate desire or intimate structure of the human mind. As Mr Arthur Balfour well puts it, "There is no a priori reason that I know of for expecting that the material world should be a modification of a single medium, rather than a composite structure built out of sixty or seventy elementary substances, eternal and eternally different. Why then should we feel content with the first hypothesis and not with the second? Yet so it is. Men of science have always been restive under the multiplication of entities. They have eagerly watched for any sign that the different chemical elements own a common origin, and are all compounded out of some primordial substance. Nor, for my part, do I think that such instincts should be ignored...that they exist is certain; that they modify the indifferent impartiality of pure empiricism can hardly be denied." ("Report of the 74th Meeting of the British Association" (Presidential Address, Cambridge 1904), page 9, London, 1905.)

When Dalton's atomic theory had been in existence some half century, it was noted that certain numerical relations held good between the atomic weights of elements chemically similar to one another. Thus the weight (88) of an atom of strontium compared with that of hydrogen as unity, is about the mean of those of calcium (40) and barium (137). Such relations, in this and other chemical groups, were illustrated by Beguyer de Chancourtois in 1862 by the construction of a spiral diagram in which the atomic weights are placed in order round a cylinder and elements chemically similar are found to fall on vertical lines.

Newlands seems to have been the first to see the significance of such a diagram. In his "law of octaves," formulated in 1864, he advanced the hypothesis that, if arranged in order of rising atomic weight, the elements fell into groups, so that each eighth element was chemically similar. Stated thus, the law was too definite; no room was left for newly- discovered elements, and some dissimilar elements were perforce grouped together.

But in 1869 Mendeleeff developed Newland's hypothesis in a form that attracted at once general attention. Placing the elements in order of rising atomic weight, but leaving a gap where necessary to bring similar elements into vertical columns, he obtained a periodic table with natural vacancies to be filled as new elements were discovered, and with a certain amount of flexibility at the ends of the horizontal lines. From the position of the vacancies, the general chemical and physical properties of undiscovered elements could be predicted, and the success of such predictions gave a striking proof of the usefulness of Mendeleeff's generalisation.

When the chemical and physical properties of the elements were known to be periodic functions of their atomic weights, the idea of a common origin and common substance became much more credible. Differences in atomic weight and differences in properties alike might reasonably be explained by the differences in the amount of the primordial substance present in the various atoms; an atom of oxygen being supposed to be composed of sixteen times as much stuff as the atom of hydrogen, but to be made of the same ultimate material. Speculations about the mode of origin of the elements now began to appear, and put on a certain air of reality. Of these speculations perhaps the most detailed was that of Crookes, who imagined an initial chaos of a primordial medium he named protyle, and a process of periodic change in which the chemical elements successively were precipitated.

From another side too, suggestions were put forward by Sir Norman Lockyer and others that the differences in spectra observed in different classes of stars, and produced by different conditions in the laboratory, were to be explained by changes in the structure of the vibrating atoms.

The next step in advance gave a theoretical basis for the idea of a common structure of matter, and was taken in an unexpected direction. Clerk Maxwell's electromagnetic theory of light, accepted in England, was driven home to continental minds by the confirmatory experiments of Hertz, who in 1888 detected and measured the electromagnetic waves that Maxwell had described twenty years earlier. But, if light be an electromagnetic phenomenon, the light waves radiated by hot bodies must take their origin in the vibrations of electric systems. Hence within the atoms must exist electric charges capable of vibration. On these lines Lorentz and Larmor have developed an electronic theory of matter, which is imagined in its essence to be a conglomerate of electric charges, with electro-magnetic inertia to explain mechanical inertia. (Larmor, "Aether and Matter", Cambridge, 1900.) The movement of electric charges would be affected by a magnetic field, and hence the discovery by Zeeman that the spectral lines of sodium were doubled by a strong magnetic force gave confirmatory evidence to the theory of electrons.

Then came J.J. Thomson's great discovery of minute particles, much smaller than any chemical atom, forming a common constituent of many different kinds of matter. (Thomson, "Conduction of Electricity through Gases" (2nd edition), Cambridge, 1906.) If an electric discharge be passed between metallic terminals through a glass vessel containing air at very low pressure, it is found that rectilinear rays, known as cathode rays, proceed from the surface of the cathode or negative terminal. Where these rays strike solid objects, they give rise to the Rontgen rays now so well known; but it is with the cathode rays themselves that we are concerned. When they strike an insulated conductor, they impart to it a negative charge, and Thomson found that they were deflected from their path both by magnetic and electric forces in the direction in which negatively electrified particles would be deflected. Cathode rays then were accepted as flights of negatively charged particles, moving with high velocities. The electric and magnetic deflections give two independent measurements which may be made on a cathode ray, and both the deflections involve theoretically three unknown quantities, the mass of the particles, their electric charge and their velocity. There is strong cumulative evidence that all such particles possess the same charge, which is identical with that associated with a univalent atom in electrolytic liquids. The number of unknown quantities was thus reduced to two--the mass and the velocity. The measurement of the magnetic and electric deflections gave two independent relations between the unknowns, which could therefore be determined. The velocities of the cathode ray particles were found to vary round a value about one-tenth that of light, but the mass was found always to be the same within the limits of error, whatever the nature of the terminals, of the residual gas in the vessel, and of the conditions of the experiment. The mass of a cathode ray particle, or corpuscle, as Thomson, adopting Newton's name, called it, is about the eight-hundredth part of the mass of a hydrogen atom.

These corpuscles, found in so many different kinds of substance, are inevitably regarded as a common constituent of matter. They are associated each with a unit of negative electricity. Now electricity in motion possesses electromagnetic energy, and produces effects like those of mechanical inertia. In other words, an electric charge possesses mass, and there is evidence to show that the effective mass of a corpuscle increases as its velocity approaches that of light in the way it would do if all its mass were electromagnetic. We are led therefore to regard the corpuscle from one aspect as a disembodied charge of electricity, and to identify it with the electron of Lorentz and Larmor.

Thus, on this theory, matter and electricity are identified; and a great simplification of our conception of the physical structure of Nature is reached. Moreover, from our present point of view, a common basis for matter suggests or implies a common origin, and a process of development possibly intelligible to our minds. The idea of the evolution of matter becomes much more probable.