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of centrifugal force, are such that the liquid seeks to spread itself outwards from the axis of rotation. It is a singular fact that it is unnecessary to take any account of the size of the mass of liquid under consideration, because the shape assumed is exactly the same whether the mass be small or large, and this renders the statement of results much easier than would otherwise be the case.

A mass of liquid at rest will obviously assume the shape of a sphere, under the influence of gravitation, and it is a stable form, because any oscillation of the liquid which might be started would gradually die away under the influence of friction, however small. If now we impart to the whole mass of liquid a small speed of rotation about some axis, which may be called the polar axis, in such a way that there are no internal currents and so that it spins in the same way as if it were solid, the shape will become slightly flattened like an orange. Although the earth and the other planets are not homogeneous they behave in the same way, and are flattened at the poles and protuberant at the equator. This shape may therefore conveniently be described as planetary.

If the planetary body be slightly deformed the forces of restitution are slightly less than they were for the sphere; the shape is stable but somewhat less so than the sphere. We have then a planetary spheroid, rotating slowly, slightly flattened at the poles, with a high degree of stability, and possessing a certain amount of rotational momentum. Let us suppose this ideal liquid star to be somewhere in stellar space far removed from all other bodies; then it is subject to no external forces, and any change which ensues must come from inside. Now the amount of rotational momentum existing in a system in motion can neither be created nor destroyed by any internal causes, and therefore, whatever happens, the amount of rotational momentum possessed by the star must remain absolutely constant.

A real star radiates heat, and as it cools it shrinks. Let us suppose then that our ideal star also radiates and shrinks, but let the process proceed so slowly that any internal currents generated in the liquid by the cooling are annulled so quickly by fluid friction as to be insignificant; further let the liquid always remain at any instant incompressible and homogeneous. All that we are concerned with is that, as time passes, the liquid star shrinks, rotates in one piece as if it were solid, and remains incompressible and homogeneous. The condition is of course artificial, but it represents the actual processes of nature as well as may be, consistently with the postulated incompressibility and homogeneity. (Mathematicians are accustomed to regard the density as constant and the rotational momentum as increasing. But the way of looking at the matter, which I have adopted, is easier of comprehension, and it comes to the same in the end.)

The shrinkage of a constant mass of matter involves an increase of its density, and we have therefore to trace the changes which supervene as the star shrinks, and as the liquid of which it is composed increases in density. The shrinkage will, in ordinary parlance, bring the weights nearer to the axis of rotation. Hence in order to keep up the rotational momentum, which as we have seen must remain constant, the mass must rotate quicker. The greater speed of rotation augments the importance of centrifugal force compared with that of gravity, and as the flattening of the planetary spheroid was due to centrifugal force, that flattening is increased; in other words the ellipticity of the planetary spheroid increases.

As the shrinkage and corresponding increase of density proceed, the planetary spheroid becomes more and more elliptic, and the succession of forms constitutes a family classified according to the density of the liquid. The specific mark of this family is the flattening or ellipticity.

Now consider the stability of the system, we have seen that the spheroid with a slow rotation, which forms our starting-point, was slightly less stable than the sphere, and as we proceed through the family of ever flatter ellipsoids the stability continues to diminish. At length when it has assumed the shape shown in a figure titled “Planetary spheroid just becoming unstable” (Fig. 2.) where the equatorial and polar axes are proportional to the numbers 1000 and 583, the stability has just disappeared. According to the general principle explained above this is a form of bifurcation, and corresponds to the form denoted A. The specific difference a of this family must be regarded as the excess of the ellipticity of this figure above that of all the earlier ones, beginning with the slightly flattened planetary spheroid. Accordingly the specific difference a of the family has gradually diminished from the beginning and vanishes at this stage.

According to Poincare’s principle the vanishing of the stability serves us with notice that we have reached a figure of bifurcation, and it becomes necessary to inquire what is the nature of the specific difference of the new family of figures which must be coalescent with the old one at this stage. This difference is found to reside in the fact that the equator, which in the planetary family has hitherto been circular in section, tends to become elliptic. Hitherto the rotational momentum has been kept up to its constant value partly by greater speed of rotation and partly by a symmetrical bulging of the equator. But now while the speed of rotation still increases (The mathematician familiar with Jacobi’s ellipsoid will find that this is correct, although in the usual mode of exposition, alluded to above in a footnote, the speed diminishes.), the equator tends to bulge outwards at two diametrically opposite points and to be flattened midway between these protuberances. The specific difference in the new family, denoted in the general sketch by b, is this ellipticity of the equator. If we had traced the planetary figures with circular equators beyond this stage A, we should have found them to have become unstable, and the stability has been shunted off along the A + b family of forms with elliptic equators.

This new series of figures, generally named after the great mathematician Jacobi, is at first only just stable, but as the density increases the stability increases, reaches a maximum and then declines. As this goes on the equator of these Jacobian figures becomes more and more elliptic, so that the shape is considerably elongated in a direction at right angles to the axis of rotation.

At length when the longest axis of the three has become about three times as long as the shortest (The three axes of the ellipsoid are then proportional to 1000, 432, 343.), the stability of this family of figures vanishes, and we have reached a new form of bifurcation and must look for a new type of figure along which the stable development will presumably extend. Two sections of this critical Jacobian figure, which is a figure of bifurcation, are shown by the dotted lines in a figure titled “The ‘pear-shaped figure’ and the Jocobian figure from which it is derived” (Fig. 3.) comprising two figures, one above the other: the upper figure is the equatorial section at right angles to the axis of rotation, the lower figure is a section through the axis.

Now Poincare has proved that the new type of figure is to be derived from the figure of bifurcation by causing one of the ends to be prolonged into a snout and by bluntening the other end. The snout forms a sort of stalk, and between the stalk and the axis of rotation the surface is somewhat flattened. These are the characteristics of a pear, and the figure has therefore been called the “pear-shaped figure of equilibrium.” The firm line shows this new type of figure, whilst, as already explained, the dotted line shows the form of bifurcation from which it is derived. The specific mark of this new family is the protrusion of the stalk together with the other corresponding smaller differences. If we denote this difference by c, while A + b denotes the Jacobian figure of bifurcation from which it is derived, the new family may be called A + b + c, and c is zero initially. According to my calculations this series of figures is stable (M. Liapounoff contends that for constant density the new series of figures, which M. Poincare discovered, has less rotational momentum than that of the figure of bifurcation. If he is correct, the figure of bifurcation is a limit of stable figures, and none can exist with stability for greater rotational momentum. My own work seems to indicate that the opposite is true, and, notwithstanding M. Liapounoff’s deservedly great authority, I venture to state the conclusions in accordance with my own work.), but I do not know at what stage of its development it becomes unstable.

Professor Jeans has solved a problem which is of interest as throwing light on the future development of the pear-shaped figure, although it is of a still more ideal character than the one which has been discussed. He imagines an INFINITELY long circular cylinder of liquid to be in rotation about its central axis. The existence is virtually postulated of a demon who is always occupied in keeping the axis of the cylinder straight, so that Jeans has only to concern himself with the stability of the form of the section of the cylinder, which as I have said is a circle with the axis of rotation at the centre. He then supposes the liquid forming the cylinder to shrink in diameter, just as we have done, and finds that the speed of rotation must increase so as to keep up the constancy of the rotational momentum. The circularity of section is at first stable, but as the shrinkage proceeds the stability diminishes and at length vanishes. This stage in the process is a form of bifurcation, and the stability passes over to a new series consisting of cylinders which are elliptic in section. The circular cylinders are exactly analogous with our planetary spheroids, and the elliptic ones with the Jacobian ellipsoids.

With further shrinkage the elliptic cylinders become unstable, a new form of bifurcation is reached, and the stability passes over to a series of cylinders whose section is pear-shaped. Thus far the analogy is complete between our problem and Jeans’s, and in consequence of the greater simplicity of the conditions, he is able to carry his investigation further. He finds that the stalk end of the pear-like section continues to protrude more and more, and the flattening between it and the axis of rotation becomes a constriction. Finally the neck breaks and a satellite cylinder is born. Jeans’s figure for an advanced stage of development is shown in a figure titled “Section of a rotating cylinder of liquid” (Fig. 4.), but his calculations do not enable him actually to draw the state of affairs after the rupture of the neck.

There are certain difficulties in admitting the exact parallelism between this problem and ours, and thus the final development of our pear-shaped figure and the end of its stability in a form of bifurcation remain hidden from our view, but the successive changes as far as they have been definitely traced are very suggestive in the study of stellar evolution.

Attempts have been made to attack this problem from the other end. If we begin with a liquid satellite revolving about a liquid planet and proceed backwards in time, we must make the two masses expand so that their density will be diminished. Various figures have been drawn exhibiting the shapes of two masses until their surfaces approach close to one another and even until they just coalesce, but the discussion of their stability is not easy. At present it would seem to be impossible to reach coalescence by any series of stable transformations, and if this is so Professor Jeans’s investigation has ceased to be truly analogous to our problem at some undetermined stage. However this may be this line of research throws an instructive light on what we may expect to find in the evolution of real stellar systems.

In the second part of this paper I shall point out the bearing which this investigation of the evolution of an ideal liquid star may have on the genesis of double stars.

II.

There are in the heavens many stars which shine with a variable brilliancy. Amongst these there is a class which exhibits special peculiarities; the members of this class are generally known as Algol Variables, because the variability of the star Beta Persei or Algol was the first of such cases to attract the attention of astronomers, and because it is perhaps still the most remarkable of the whole class. But the circumstances which led to this discovery were so extraordinary that it seems worth while to pause a moment before entering on the subject.

John Goodricke, a deaf-mute, was born in 1764; he was grandson and heir of Sir John Goodricke of Ribston Hall, Yorkshire. In November 1782, he noted that the brilliancy of Algol waxed and waned (It is said that Georg Palitzch, a farmer of Prohlis near Dresden, had about 1758 already noted the variability of Algol with the naked eye. “Journ. Brit. Astron. Assoc.” Vol. XV. (1904-5), page 203.), and devoted himself to observing it on every fine night from the 28th December 1782 to the 12th May 1783. He communicated his observations to the Royal Society, and suggested that the variation in brilliancy was due to periodic eclipses by a dark companion star, a theory now universally accepted as correct. The Royal Society recognised the importance of the discovery by awarding to Goodricke, then only 19 years of age, their highest honour, the Copley medal. His later observations of Beta Lyrae and of Delta Cephei were almost as remarkable as those of Algol, but unfortunately a career of such extraordinary promise was cut short by death, only a fortnight after his election to the Royal Society. (“Dict. of National Biography”; article Goodricke (John). The article is by Miss Agnes Clerke. It is strange that she did not then seem to be aware that he was a deaf-mute, but she notes the fact in her “Problems of Astrophysics”, page 337, London, 1903.)

It was not until 1889 that Goodricke’s theory was verified, when it was proved by Vogel that the star was moving in an orbit, and in such a manner that it was only possible to explain the rise and fall in the luminosity by the partial eclipse of a bright star by a dark companion.

The whole mass of the system of Algol is found to be half as great again as that of our sun, yet the two bodies complete their orbit in the short period of 2d 20h 48m 55s. The light remains constant during each period, except for 9h 20m when it exhibits a considerable fall in brightness (Clerke, “Problems of Astrophysics” page 302 and chapter XVIII.); the curve which represents the variation in the light is shown in a figure titled “The light-curve and system of Beta Lyrae” (Fig. 7.).

The spectroscope has enabled astronomers to prove that many stars, although apparently single, really consist of two stars circling around one another (If a source of light is approaching with a great velocity the waves of light are crowded together, and conversely they are spaced out when the source is receding. Thus motion in the line of sight virtually produces an infinitesimal change of colour. The position of certain dark lines in the spectrum affords an exceedingly accurate measurement of colour. Thus displacements of these spectral lines enables us to measure the velocity of the source of light towards or away from the observer.); they are known as spectroscopic binaries. Campbell of the Lick Observatory believes that about one star in six is a binary (“Astrophysical Journ.” Vol. XIII. page 89, 1901. See also A. Roberts, “Nature”, Sept. 12, 1901, page 468.); thus there must be many thousand such stars within the reach of our spectroscopes.

The orientation of the planes of the orbits of binary stars appears to be quite arbitrary, and in general the star does not vary in brightness. Amongst all such orbits there must be some whose planes pass nearly through the sun, and in these cases the eclipse of one of the stars by the other becomes inevitable, and in each circuit there will occur two eclipses of unequal intensities.

It is easy to see that in the majority of such cases the two components must move very close to one another.

The coincidence between the spectroscopic and the photometric evidence permits us to feel complete confidence in the theory of eclipses. When then we find a star with a light-curve of perfect regularity and with a characteristics of that of Algol, we are justified in extending the theory of eclipses to it, although it may be too faint to permit of adequate spectroscopic examination. This extension of the theory secures a considerable multiplication of the examples available for observation, and some 30 have already been discovered.

Dr Alexander Roberts, of Lovedale in Cape Colony, truly remarks that the study of Algol variables “brings us to the very threshold of the question of stellar evolution.” (“Proc. Roy. Soc. Edinburgh”, XXIV. Part II. (1902), page 73.) It is on this account that I propose to explain in some detail the conclusion to which he and some other observers have been led.

Although these variable stars are mere points of light, it has been proved by means of the spectroscope that the law of gravitation holds good in the remotest regions of stellar space, and further it seems now to have become possible even to examine the shapes of stars by indirect methods, and thus to begin the study of their evolution. The chain of reasoning which I shall explain must of necessity be open to criticism, yet the explanation of the facts by the theory is so perfect that it is not easy to resist the conviction that we are travelling along the path of truth.

The brightness of a star is specified by what is called its “magnitude.” The average brightness of all the stars which can just be seen with the naked eye defines the sixth magnitude. A star which only gives two-fifths as much light is said to be of the seventh magnitude; while one which gives 2 1/2 times as much light is of the fifth magnitude, and successive multiplications or divisions by 2 1/2 define the lower or higher magnitudes. Negative magnitudes have clearly to be contemplated; thus Sirius is of magnitude minus 1.4, and the sun is of magnitude minus 26.

The definition of magnitude is also extended to fractions; for example, the lights given by two candles which are placed at 100 feet and 100 feet 6 inches from the observer differ in brightness by one-hundredth of a magnitude.

A great deal of thought has been devoted to the measurement of the brightness of stars, but I will only describe one of the methods used, that of the great astronomer Argelander. In the neighbourhood of the star under observation some half dozen standard stars are selected of known invariable magnitudes, some being brighter and some fainter than the star to be measured; so that these stars afford a visible scale of brightness. Suppose we number them in order of increasing brightness from 1 to 6; then the observer estimates that on a given night his star falls between stars 2 and 3, on the next night, say between 3 and 4, and then again perhaps it may return to between 2 and 3, and so forth. With practice he learns to evaluate the brightness down to small fractions of a magnitude, even a hundredth part of a magnitude is not quite negligible.

For example, in observing the star RR Centauri five stars were in general used for comparison by Dr Roberts, and in course of three months he secured thereby 300 complete observations. When the period of the cycle had been ascertained exactly, these 300 values were reduced to mean values which appertained to certain mean places in the cycle, and a mean light-curve was obtained in this way. Figures titled “Light curve of RR Centauri” (Fig. 5) and “The light-curve and system of Beta Lyrae” (Fig. 7) show examples of light curves.

I shall now follow out the results of the observation of RR Centauri not only because it affords the easiest way of explaining these investigations, but also because it is one of the stars which furnishes the most striking results in connection with the object of this essay. (See “Monthly notices R.A.S.” Vol. 63, 1903, page 527.) This star has a mean magnitude of about 7 1/2, and it is therefore invisible to the naked eye. Its period of variability is 14h 32m 10s.76, the last refinement of precision being of course only attained in the final stages of reduction. Twenty-nine mean values of the magnitude were determined, and they were nearly equally spaced over the whole cycle of changes. The black dots in Fig. 5 exhibit the mean values determined by Dr Roberts. The last three dots on the extreme right are merely the same as the first three on the extreme left, and are repeated to show how the next cycle would begin. The smooth dotted curve will be explained hereafter, but, by reference to the scale of magnitudes on the margins of the figure, it may be used to note that the dots might be brought into a perfectly smooth curve by shifting some few of the dots by about a hundredth of a magnitude.

This light-curve presents those characteristics which are due to successive eclipses, but the exact form of the curve must depend on the nature of the two mutually eclipsing stars. If we are to interpret the curve with all possible completeness, it is necessary to make certain assumptions as to the stars. It is assumed then that the stars are equally bright all over their disks, and secondly that they are not surrounded by an extensive absorptive atmosphere. This last appears to me to be the most dangerous assumption involved in the whole theory.

Making these assumptions, however, it is found that if each of the eclipsing stars were spherical it would not be possible to generate such a curve with the closest accuracy. The two stars are certainly close together, and it is obvious that in such a case the tidal forces exercised by each on the other must be such as to elongate the figure of each towards the other. Accordingly it is reasonable to adopt the hypothesis that the system consists of a pair of elongated ellipsoids, with their longest axes pointed towards one another. No supposition is adopted a priori as to the ratio of the two masses, or as to their relative size or brightness, and the orbit may have any degree of eccentricity. These last are all to be determined from the nature of the light-curve.

In the case of RR Centauri, however, Dr Roberts finds the conditions are best satisfied by supposing the orbit to be circular, and the sizes and masses of the components to be equal, while their luminosities are to one another in the ratio of 4 to 3. As to their shapes he finds them to be so much elongated that they overlap, as exhibited in his figure titled “The shape of the star RR Centauri” (Fig. 6.). The dotted curve shows a form of equilibrium of rotating liquid as computed by me some years before, and it was added for the sake of comparison.

On turning back to Fig. 5 the reader will see in the smooth dotted curve the light variation which would be exhibited by such a binary system as this. The curve is the result of computation and it is impossible not to be struck by the closeness of the coincidence with the series of black dots which denote the observations.

It is virtually certain that RR Centauri is a case of an eclipsing binary system, and that the two stars are close together. It is not of course proved that the figures of the stars are ellipsoids, but gravitation must deform them into a pair of elongated bodies, and, on the assumptions that they are not enveloped in an absorptive atmosphere and that they are ellipsoidal, their shapes must be as shown in the figure.

This light-curve gives an excellent illustration of what we have reason to believe to be a stage in the evolution of stars, when a single star is proceeding to separate into a binary one.

As the star is faint, there is as yet no direct spectroscopic evidence of orbital motion. Let us turn therefore to the case of another star, namely V Puppis, in which such evidence does already exist. I give an account of it, because it presents a peculiarly interesting confirmation of the correctness of the theory.

In 1895 Pickering announced in the “Harvard Circular” No. 14 that the spectroscopic observations at Arequipa proved V Puppis to be a double star with a period of 3d 2h 46m. Now when Roberts discussed its light-curve he found that the period was 1d 10h 54m 27s, and on account of this serious discrepancy he effected the reduction only on the simple assumption that the two stars were spherical, and thus obtained a fairly good representation of the light-curve. It appeared that the orbit was circular and that the two spheres were not quite in contact. Obviously if the stars had been assumed to be ellipsoids they would have been found to overlap, as was the case for RR Centauri. (“Astrophysical Journ.” Vol. XIII. (1901), page 177.) The matter rested thus for some months until the spectroscopic evidence was re-examined by Miss Cannon on behalf of Professor Pickering, and we find in the notes on page 177 of Vol. XXVIII. of the “Annals of the Harvard Observatory” the following: “A.G.C. 10534. This star, which is the Algol variable V Puppis, has been found to be a spectroscopic binary. The period 1d.454 (i.e. 1d 10h 54m) satisfies the observations of the changes in light, and of the varying separation of the lines of the spectrum. The spectrum has been examined on 61 plates, on 23 of which the lines are double.” Thus we have valuable evidence in confirmation of the correctness of the conclusions drawn from the light-curve. In the circumstances, however, I have not thought it worth while to reproduce Dr Roberts’s provisional figure.

I now turn to the conclusions drawn a few years previously by another observer, where we shall find the component stars not quite in contact. This is the star Beta Lyrae which was observed by Goodricke, Argelander, Belopolsky, Schur, Markwick and by many others. The spectroscopic method has been successfully applied in this case, and the component stars are proved to move in an orbit about one another. In 1897, Mr. G.W. Myers applied the theory of eclipses to the light-curve, on the hypothesis that the stars are elongated ellipsoids, and he obtained the interesting results exhibited in Fig. 7. (“Astrophysical Journ.” Vol. VII. (1898), page 1.)

The period of Beta Lyrae is relatively long, being 12d 21h 47m, the orbit is sensibly eccentric, and the two spheroids are not so much elongated as was the case with RR Centauri. The mass of the system is enormous, one of the two stars being 10 times and the other 21 times as heavy as our sun.

Further illustrations of this subject might be given, but enough has been said to explain the nature of the conclusions which have been drawn from this class of observation.

In my account of these remarkable systems the consideration of one very important conclusion has been purposely deferred. 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.

The question of the nature and physical meaning of a corpuscle or electron remains for consideration. On the hypothesis of a universal luminiferous aether, Larmor has suggested a centre of aethereal strain “a place where the continuity of the medium has been broken and cemented together again (to use a crude but effective image) without accurately fitting the parts, so that there is a residual strain all round the place.” (Larmor, loc. cit.) Thus he explains in quasi-mechanical terms the properties of an electron. But whether we remain content for the time with our identification of matter and electricity, or attempt to express both of them in terms of hypothetical aether, we have made a great step in advance on the view that matter is made up of chemical atoms fundamentally distinct and eternally isolated.

Such was the position when the phenomena of radio-activity threw a new light on the problem, and, for the first time in the history of science, gave definite experimental evidence of the transmutation of matter from one chemical element to another.

In 1896 H. Becquerel discovered that compounds of the metal uranium continually emitted rays capable of penetrating opaque screens and affecting photographic plates. Like cathode and Rontgen rays, the rays from uranium make the air through which they pass a conductor of electricity, and this property gives the most convenient method of detecting the rays and of measuring their intensity. An electroscope may be made of a strip of gold-leaf attached to an insulated brass plate and confined in a brass vessel with glass windows. When the gold-leaf is electrified, it is repelled from the similarly electrified brass plate, and the angle at which it stands out measures the electrification. Such a system, if well insulated, holds its charge for hours, the leakage of electricity through the air being very slow. But, if radio-active radiation reach the air within, the gold-leaf falls, and the rate of its fall, as watched through a microscope with a scale in the eye-piece, measures the intensity of the radiation. With some form of this simple instrument, or with the more complicated quadrant electrometer, most radio- active measurements have been made.

It was soon discovered that the activity of uranium compounds was proportional to the amount of uranium present in them. Thus radio-activity is an atomic property dependent on the amount of an element and independent of its state of chemical combination.

In a search for radio-activity in different minerals, M. and Mme Curie found a greater effect in pitch-blende than its contents of uranium warranted, and, led by the radio-active property alone, they succeeded, by a long series of chemical separations, in isolating compounds of a new and intensely radio-active substance which they named radium.

Radium resembles barium in its chemical properties, and is precipitated with barium in the ordinary course of chemical analysis. It is separated by a prolonged course of successive crystallisation, the chloride of radium being less soluble than that of barium, and therefore sooner separated from an evaporating solution. When isolated, radium chloride has a composition, which, on the assumption that one atom of metal combines with two of chlorine as in barium chloride, indicates that the relative weight of the atom of radium is about 225. As thus prepared, radium is a well-marked chemical element, forming a series of compounds analogous to those of barium and showing a characteristic line spectrum. But, unlike most other chemical elements, it is intensely radio-active, and produces effects some two million times greater than those of uranium.

In 1899 E. Rutherford, then of Montreal, discovered that the radiation from uranium, thorium and radium was complex. (Rutherford, “Radio-activity” (2nd edition), Cambridge, 1905.) Three types of rays were soon distinguished. The first, named by Rutherford alpha-rays, are absorbed by thin metal foil or a few centimetres of air. When examined by measurements of the deflections caused by magnetic and electric fields, the alpha-rays are found to behave as would positively electrified particles of the magnitude of helium atoms possessing a double ionic charge and travelling with a velocity about one-tenth that of light. The second or beta type of radiation is much more penetrating. It will pass through a considerable thickness of metallic foil, or many centimetres of air, and still affect photographic plates or discharge electroscopes. Magnetic and electric forces deflect beta-rays much more than alpha-rays, indicating that, although the speed is greater, approaching in some cases within five per cent. that of light, the mass is very much less. The beta-rays must be streams of particles, identical with those of cathode rays, possessing the minute mass of J.J. Thomson’s corpuscle, some eight-hundredth part of that of a hydrogen atom. A third or gamma type of radiation was also detected. More penetrating even than beta-rays, the gamma-rays have never been deflected by any magnetic or electric force yet applied. Like Rontgen rays, it is probable that gamma-rays are wave-pulses in the luminiferous aether, though the possibility of explaining them as flights of non- electrified particles is before the minds of some physicists.

Still another kind of radiation has been discovered more recently by Thomson, who has found that in high vacua, rays become apparent which are absorbed at once by air at any ordinary pressure.

The emission of all these different types of radiation involves a continual drain of energy from the radio-active body. When M. and Mme Curie had prepared as much as a gramme of radium chloride, the energy of the radiation became apparent as an evolution of heat. The radium salt itself, and the case containing it, absorbed the major part of the radiation, and were thus maintained at a temperature measurably higher than that of the surroundings. The rate of thermal evolution was such that it appeared that one gramme of pure radium must emit about 100 gramme-calories of heat in an hour. This observation, naturally as it follows from the phenomena previously discovered, first called attention to the question of the source of the energy which maintains indefinitely and without apparent diminution the wonderful stream of radiation proceeding from a radio-active substance. In the solution of this problem lies the point of the present essay.

In order to appreciate the evidence which bears on the question we must now describe two other series of phenomena.

It is a remarkable fact that the intensity of the radiation from a radio- active body is independent of the external conditions of temperature, pressure, etc. which modify so profoundly almost all other physical and chemical processes. Exposure to the extreme cold of liquid air, or to the great heat of a furnace, leaves the radio-activity of a substance unchanged, apparent exceptions to this statement having been traced to secondary causes.

Then, it is found that radio-activity is always accompanied by some chemical change; a new substance always appears as the parent substance emits these radiations. Thus by chemical reactions it is possible to separate from uranium and thorium minute quantities of radio-active materials to which the names of uranium-X and thorium-X have been given. These bodies behave differently from their parents uranium and thorium, and show all the signs of distinct chemical individuality. They are strongly radio-active, while, after the separation, the parents uranium and thorium are found to have lost some of their radio-activity. If the X-substances be kept, their radio-activity decays, while that of the uranium or thorium from which they were obtained gradually rises to the initial value it had before the separation. At any moment, the sum of the radio-activity is constant, the activity lost by the product being equal to that gained by the parent substance. These phenomena are explained if we suppose that the X-product is slowly produced in the substance of the parent, and decays at a constant rate. Uranium, as usually seen, contains a certain amount of uranium-X, and its radio-activity consists of two parts–that of the uranium itself, and that of the X product. When the latter is separated by means of its chemical reactions, its radio-activity is separated also, and the rates of decay and recovery may be examined.

Radium and thorium, but not uranium, give rise to radio-active gases which have been called emanations. Rutherford has shown that their radio- activity, like that of the X products, suffers decay, while the walls of the vessel in which the emanation is confined, become themselves radio- active. If washed with certain acids, however, the walls lose their activity, which is transferred to the acid, and can be deposited by evaporation from it on to a solid surface. Here again it is clear that the emanation gives rise to a radio-active substance which clings to the walls of the vessel, and is soluble in certain liquids, but not in others.

We shall return to this point, and trace farther the history of the radio- active matter. At present we wish to emphasise the fact that, as in other cases, the radio-activity of the emanation is accompanied by the appearance of a new kind of substance with distinct chemical properties.

We are now in a position to consider as a whole the evidence on the question of the source of radio-active energy.

(1) Radio-activity is accompanied by the appearance of new chemical substances. The energy liberated is therefore probably due to the associated chemical change. (2) The activity of a series of compounds is found to accompany the presence of a radio-active element, the activity of each compound depends only on the contents of the element, and is independent of the nature of its combination. Thus radio-activity is a property of the element, and is not affected by its state of isolation or chemical combination. (3) The radio-activity of a simple transient product decays in a geometrical progression, the loss per second being proportional to the mass of substance still left at the moment, and independent of its state of concentration or dilution. This type of reaction is well known in chemistry to mark a mono-molecular change, where each molecule is dissociated or altered in structure independently. If two or more molecules were concerned simultaneously, the rate of reaction would depend on the nearness of the molecules to each other, that is, to the concentration of the material. (4) The amount of energy liberated by the change of a given mass of material far transcends the amount set free by any known ordinary chemical action. The activity of radium decays so slowly that it would not sink to half its initial value in less than some two thousand years, and yet one gramme of radium emits about 100 calories of heat during each hour of its existence.

The energy of radio-activity is due to chemical change, but clearly to no chemical change hitherto familiar to science. It is an atomic property, characteristic of a given element, and the atoms undergo the change individually, not by means of interaction among each other. The conclusion is irresistible that we are dealing with a fundamental change in the structure of the individual atoms, which, one by one, are dissociating into simpler parts. We are watching the disintegration of the “atoms” of the chemist, hitherto believed indestructible and eternal, and measuring the liberation of some of the long-suspected store of internal atomic energy. We have stumbled on the transmutation dreamed by the alchemist, and discovered the process of a veritable evolution of matter.

The transmutation theory of radio-activity was formulated by Rutherford (Rutherford, “Radio-activity” (2nd edition), Cambridge, 1905, page 307.) and Soddy in 1903. By its light, all recent work on the subject has been guided; it has stood the supreme test of a hypothesis, and shown power to suggest new investigations and to co-ordinate and explain them, when carried out. We have summarised the evidence which led to the conception of the theory; we have now to consider the progress which has been made in tracing the successive disintegration of radio-active atoms.

Soon after the statement of the transmutation theory, a striking verification of one of its consequences appeared. The measurement of the magnetic and electric deflection of the alpha-rays suggested to Rutherford the idea that the stream of projectiles of which they consisted was a flight of helium atoms. Ramsay and Soddy, confining a minute bubble of radium emanation in a fine glass tube, were able to watch the development of the helium spectrum as, day by day, the emanation decayed. By isolating a very narrow pencil of alpha-rays, and watching through a microscope their impact on a fluorescent screen, Rutherford has lately counted the individual alpha-projectiles, and confirmed his original conclusion that their mass corresponded to that of helium atoms and their charge to double that on a univalent atom. (“Proc. Roy. Soc.” A, page 141, 1908.) Still more recently, he has collected the alpha-particles shot through an extremely thin wall of glass, and demonstrated by direct spectroscopic evidence the presence of helium. (“Phil. Mag.” February 1909.)

But the most thorough investigation of a radio-active pedigree is found in Rutherford’s classical researches on the successive disintegration products of radium, in order to follow the evidence on which his results are founded, we must describe more fully the process of decay of the activity of a simple radio-active substance. The decay of activity of the body known as uranium-X is shown in a falling curve (Fig. 1.). It will be seen that, in each successive 22 days, the activity falls to half the value it possessed at the beginning.

This change in a geometrical progression is characteristic of simple radio- active processes, and can be expressed mathematically by a simple exponential formula.

As we have said above, solid bodies exposed to the emanations of radium or thorium become coated with a radio-active deposit. The rate of decay of this activity depends on the time of exposure to the emanation, and does not always show the usual simple type of curve. Thus the activity of a rod exposed to radium emanation for 1 minute decays in accordance with a curve (Fig. 2) which represents the activity as measured by the alpha-rays. If the electroscope be screened from the alpha-rays, it is found that the activity of the rod in beta- an gamma-rays increases for some 35 minutes and then diminishes (Fig. 3.).

These complicated relations have been explained satisfactorily and completely by Rutherford on the hypothesis of successive changes of the radio-active matter into one new body after another. (Rutherford, “Radio- activity” (2nd edition), Cambridge, 1905, page 379.) The experimental curve represents the resultant activity of all the matter present at a given moment, and the process of disentangling the component effects consists in finding a number of curves, which express the rise and fall of activity of each kind of matter as it is produced and decays, and, fitted together, give the curve of the experiments.

Other methods of investigation also are open. They have enabled Rutherford to complete the life-history of radium and its products, and to clear up doubtful points left by the analysis of the curves. By the removal of the emanation, the activity of radium itself has been shown to consist solely of alpha-rays. This removal can be effected by passing air through the solution of a radium salt. The emanation comes away, and the activity of the deposit which it leaves behind decays rapidly to a small fraction of its initial value. Again, some of the active deposits of the emanation are more volatile than others, and can be separated from them by the agency of heat.

From such evidence Rutherford has traced a long series of disintegration products of radium, all but the first of which exist in much too minute quantities to be detected otherwise than by their radio-activities. Moreover, two of these products are not themselves appreciably radio- active, though they are born from radio-active parents, and give rise to a series of radio-active descendants. Their presence is inferred from such evidence as the rise of beta and gamma radio-activity in the solid newly deposited by the emanation; this rise measuring the growth of the first radio-active offspring of one of the non-active bodies. Some of the radium products give out alpha-rays only, one beta- and gamma-rays, while one yields all three types of radiation. The pedigree of the radium family may be expressed in the following table, the time noted in the second column being the time required for a given quantity to be half transformed into its next derivative.

Time of half Radio- Properties decay activity

Radium About 2600 years alpha rays Element chemically analogous to barium.
>
Emanation 3.8 days alpha rays Chemically inert gas; condenses at -150 deg C. >
Radium-A 3 minutes alpha rays Behaves as a solid deposited on surfaces; concentrated on a negative electrode. >
Radium-B 21 minutes no rays Soluble in strong acids; volatile at a white heat; more volatile than A or C. >
Radium-C 28 minutes alpha, beta, Soluble in strong acids; less gamma rays volatile than B. >
Radium-D about 40 years no rays Soluble in strong acids; volatile below 1000 deg C.
>
Radium-E 6 days beta, gamma Non-volatile at 1000 deg C. rays
>
Radium-F 143 days alpha rays Volatile at 1000 deg C. Deposited from solution on a bismuth plate.

Of these products, A, B, and C constitute that part of the active deposit of the emanation which suffers rapid decay and nearly disappears in a few hours. Radium-D, continually producing its short-lived descendants E and F, remains for years on surfaces once exposed to the emanation, and makes delicate radio-active researches impossible in laboratories which have been contaminated by an escape of radium emanation.

A somewhat similar pedigree has been made out in the case of thorium. Here thorium-X is interposed between thorium and its short-lived emanation, which decays to half its initial quantity in 54 seconds. Two active deposits, thorium A and B, arise successively from the emanation. In uranium, we have the one obvious derivative uranium-X, and the question remains whether this one descent can be connected with any other individual or family. Uranium is long-lived, and emits only alpha-rays. Uranium-X decays to half value in 22 days, giving out beta- and gamma-rays. Since our evidence goes to show that radio-activity is generally accompanied by the production of new elements, it is natural to search for the substance of uranium-X in other forms, and perhaps under other names, rather than to surrender immediately our belief in the conservation of matter.

With this idea in mind we see at once the significance of the constitution of uranium minerals. Formed in the remote antiquity of past geological ages, these minerals must become store-houses of all the products of uranium except those which may have escaped as gases or possibly liquids. Even gases may be expected to some extent to be retained by occlusion. Among the contents of uranium minerals, then, we may look for the descendants of the parent uranium. If the descendants are permanent or more long-lived than uranium, they will accumulate continually. If they are short-lived, they will accumulate at a steady rate till enough is formed for the quantity disintegrating to be equal to the quantity developed. A state of mobile equilibrium will then be reached, and the amount of the product will remain constant. This constant amount of substance will depend only on the amount of uranium which is its source, and, for different minerals, if all the product is retained, the quantity of the product will be proportional to the quantity of uranium. In a series of analyses of uranium minerals, therefore, we ought to be able to pick out its more short-lived descendants by seeking for instances of such proportionality.

Now radium itself is a constituent of uranium minerals, and two series of experiments by R.J. Strutt and B.B. Boltwood have shown that the content of radium, as measured by the radio-activity of the emanation, is directly proportional to the content of uranium. (Strutt, “Proc. Roy. Soc.” A, February 1905; Boltwood, “Phil. Mag.” April, 1905.) In Boltwood’s investigation, some twenty minerals, with amounts of uranium varying from that in a specimen of uraninite with 74.65 per cent., to that in a monazite with 0.30 per cent., gave a ratio of uranium to radium, constant within about one part in ten.

The conclusion is irresistible that radium is a descendant of uranium, though whether uranium is its parent or a more remote ancestor requires further investigation by the radio-active genealogist. On the hypothesis of direct parentage, it is easy to calculate that the amount of radium produced in a month by a kilogramme of a uranium salt would be enough to be detected easily by the radio-activity of its emanation. The investigation has been attempted by several observers, and the results, especially those of a careful experiment of Boltwood, show that from purified uranium salts the growth of radium, if appreciable at all, is much less than would be found if the radium was the first product of change of the uranium. It is necessary, therefore, to look for one or more intermediate substances.

While working in 1899 with the uranium residues used by M. and Mme Curie for the preparation of radium, Debierne discovered and partially separated another radio-active element which he called actinium. It gives rise to an intermediate product actinium-X, which yields an emanation with the short half-life of 3.9 seconds. The emanation deposits two successive disintegration products actinium-A and actinium-B.

Evidence gradually accumulated that the amounts of actinium in radio-active minerals were, roughly at any rate, proportional to the amounts of uranium. This result pointed to a lineal connection between them, and led Boltwood to undertake a direct attack on the problem. Separating a quantity of actinium from a kilogramme of ore, Boltwood observed a growth of 8.5 x (10 to the power -9) gramme of radium in 193 days, agreeing with that indicated by theory within the limits of experimental error. (“American Journal of Science”, December, 1906.) We may therefore insert provisionally actinium and its series of derivatives between uranium and radium in the radio- active pedigree.

Turning to the other end of the radium series we are led to ask what becomes of radium-F when in turn it disintegrates? What is the final non- active product of the series of changes we have traced from uranium through actinium and radium?

One such product has been indicated above. The alpha-ray particles appear to possess the mass of helium atoms, and the growth of helium has been detected by its spectrum in a tube of radium emanation. Moreover, helium is found occluded in most if not all radio-active minerals in amount which approaches, but never exceeds, the quantity suggested by theory. We may safely regard such helium as formed by the accumulation of alpha-ray particles given out by successive radio-active changes.

In considering the nature of the residue left after the expulsion of the five alpha-particles, and the consequent passage of radium to radium-F we are faced by the fact that lead is a general constituent of uranium minerals. Five alpha-particles, each of atomic weight 4, taken from the atomic weight (about 225) of radium gives 205–a number agreeing fairly well with the 207 of lead. Since lead is more permanent than uranium, it must steadily accumulate, no radio-active equilibrium will be reached, and the amount of lead will depend on the age of the mineral as well as on the quantity of uranium present in it. In primary minerals from the same locality, Boltwood has shown that the contents of lead are proportional to the amounts of uranium, while, accepting this theory, the age of minerals with a given content of uranium may be calculated from the amount of lead they contain. The results vary from 400 to 2000 million years. (“American Journal of Science”, October, 1905, and February, 1907.)

We can now exhibit in tabular form the amazing pedigree of radio-active change shown by this one family of elements. An immediate descent is indicated by >, while one which may either be immediate or involve an intermediate step is shown by …. No place is found in this pedigree for thorium and its derivatives. They seem to form a separate and independent radio-active family.

Atomic Weight Time of half Radio-Activity decay

Uranium 238.5 alpha >
Uranium-X ? 22 days beta, gamma …
Actinium ? ? no rays >
Actinium-X ? 10.2 days alpha (beta, gamma) >
Actinium Emanation ? 3.9 seconds alpha >
Actinium-A ? 35.7 minutes no rays >
Actinium-B ? 2.15 minutes alpha, beta, gamma …
Radium 225 about 2600 years alpha >
Radium Emanation ? 3.8 days alpha >
Radium-A ? 3 minutes alpha >
Radium-B ? 21 minutes no rays >
Radium-C ? 28 minutes alpha, beta, gamma >
Radium-D ? about 40 years no rays >
Radium-E ? 6 days beta (gamma) >
Radium-F ? 143 days alpha …
Lead 207 ? no rays

As soon as the transmutation theory of radio-activity was accepted, it became natural to speculate about the intimate structure of the radio- active atoms, and the mode in which they broke up with the liberation of some of their store of internal energy. How could we imagine an atomic structure which would persist unchanged for long periods of time, and yet eventually spontaneously explode, as here an atom and there an atom reached a condition of instability?

The atomic theory of corpuscles or electrons fortunately was ready to be applied to this new problem. Of the resulting speculations the most detailed and suggestive is that of J.J. Thomson. (“Phil. Mag.” March, 1904.) Thomson regards the atom as composed of a number of mutually repelling negative corpuscles or electrons held together by some central attractive force which he represents by supposing them immersed in a uniform sphere of positive electricity. Under the action of the two forces, the electrons space themselves in symmetrical patterns, which depend on the number of electrons. Three place themselves at the corner of an equilateral triangle, four at those of a square, and five form a pentagon. With six, however, the single ring becomes unstable, one corpuscle moves to the middle and five lie round it. But if we imagine the system rapidly to rotate, the centrifugal force would enable the six corpuscles to remain in a single ring. Thus internal kinetic energy would maintain a configuration which would become unstable as the energy drained away. Now in a system of electrons, electromagnetic radiation would result in a loss of energy, and at one point of instability we might well have a sudden spontaneous redistribution of the constituents, taking place with an explosive violence, and accompanied by the ejection of a corpuscle as a beta-ray, or of a large fragment of the atom as an alpha-ray.

The discovery of the new property of radio-activity in a small number of chemical elements led physicists to ask whether the property might not be found in other elements, though in a much less striking form. Are ordinary materials slightly radio-active? Does the feeble electric conductivity always observed in the air contained within the walls of an electroscope depend on ionizing radiations from the material of the walls themselves? The question is very difficult, owing to the wide distribution of slight traces of radium. Contact with radium emanation results in a deposit of the fatal radium-D, which in 40 years is but half removed. Is the “natural” leak of a brass electroscope due to an intrinsic radio-activity of brass, or to traces of a radio-active impurity on its surface? Long and laborious researches have succeeded in establishing the existence of slight intrinsic radio-activity in a few metals such as potassium, and have left the wider problem still unsolved.

It should be noted, however, that, even if ordinary elements are not radio- active, they may still be undergoing spontaneous disintegration. The detection of ray-less changes by Rutherford, when those changes are interposed between two radio-active transformations which can be followed, show that spontaneous transmutation is possible without measureable radio- activity. And, indeed, any theory of disintegration, such as Thomson’s corpuscular hypothesis, would suggest that atomic rearrangements are of much more general occurrence than would be apparent to one who could observe them only by the effect of the projectiles, which, in special cases, owing to some peculiarity of atomic configuration, happened to be shot out with the enormous velocity needed to ionize the surrounding gas. No evidence for such ray-less changes in ordinary elements is yet known, perhaps none may ever be obtained; but the possibility should not be forgotten.

In the strict sense of the word, the process of atomic disintegration revealed to us by the new science of radio-activity can hardly be called evolution. In each case radio-active change involves the breaking up of a heavier, more complex atom into lighter and simpler fragments. Are we to regard this process as characteristic of the tendencies in accord with which the universe has reached its present state, and is passing to its unknown future? Or have we chanced upon an eddy in a backwater, opposed to the main stream of advance? In the chaos from which the present universe developed, was matter composed of large highly complex atoms, which have formed the simpler elements by radio-active or ray-less disintegration? Or did the primaeval substance consist of isolated electrons, which have slowly come together to form the elements, and yet have left here and there an anomaly such as that illustrated by the unstable family of uranium and radium, or by some such course are returning to their state of primaeval simplicity?

INDEX.

Abraxas grossulariata.

Acquired characters, transmission of.

Acraea johnstoni.

Adaptation.

Adloff.

Adlumia cirrhosa.

Agassiz, A.

Agassiz, L.

Alexander.

Allen, C.A.

Alternation of generations.

Ameghino.

Ammon, O., Works of.

Ammonites, Descent of.

Amphidesmus analis.

Anaea divina.

Andrews, C.W.

Angiosperms, evolution of.

Anglicus, Bartholomaeus.

Ankyroderma.

Anomma.

Antedon rosacea.

Antennularia antennina.

Anthropops.

Ants, modifications of.

Arber, E.A.N.,
–and J. Parkin, on the origin of Angiosperms.

Archaeopteryx.

Arctic regions, velocity of development of life in.

Ardigo.

Argelander.

Argyll, Huxley and the Duke of.

Aristotle.

Arrhenius.

Asterias, Loeb on hybridisation of.

Autogamy.

Avena fatua.

Avenarius.

Bacon, on mutability of species.

Baehr, von, on Cytology.

Baer, law of von.

Bain.

Baldwin, J.M.

Balfour, A.J.

Ball, J.

Barber, Mrs M.E., on Papilio nireus.

Barclay, W.

Barratt.

Bary, de.

Bates, H.W., on Mimicry.
–Letters from Darwin to.
–elsewhere.

Bateson, A.

BATESON, W., on “Heredity and Variation in Modern lights”. –on discontinuous evolution.
–on hybridisation.

Bateson, W. and R.P. Gregory.

Bathmism.

Beche, de la.

Beck, P.

Becquerel, H.

Beebe, C.W., on the plumage of birds. –on sexual selection.

Beguyer de Chancourtois.

Bell’s (Sir Charles) “Anatomy of Expression”.

Belopolsky.

Belt, T., on Mimicry.

Beneden, E. van.

Benson, M.

Bentham, G., on Darwin’s species-theory. –on geographical distribution.

Bentham, Jeremy.

Bergson, H.

Berkeley.

Berthelot.

Betham, Sir W.

Bickford, E., experiments on degeneration by.

Bignonia capreolata.

Biophores.

Birds, geological history of.

Blanford, W.T.

Blaringhem, on wounding.

Blumenbach.

Bodin.

Boltwood, B.B.

Bonald, on war.

Bonnet.

Bonney, T.G.

Bonnier, G.

Bopp, F., on language.

BOUGLE C., on “Darwinism and Sociology”.

Bourdeau.

Bourget, P.

Boutroux.

Boveri, T.

Brachiopods, history of.

Brassica, hybrids of.

Brassica Napus.

Broca.

Brock, on Kant.

Brown, Robert.

Brugmann and Osthoff.

Brugmann.

Brunetiere.

Bruno, on Evolution.

Buch, von.

Bucher, K.

Buckland.

Buckle.

Buffon.

Burchell, W.J.

Burck, W.

Burdon-Sanderson, J., letter from.

BURY, J.B., on “Darwinism and History”.

Butler, A.G.

Butler, Samuel.

Butschli, O.

Butterflies, mimicry in.
–sexual characters in.

Cabanis.

Campbell.

Camels, geological history of.

Camerarius, R.J.

Candolle, A. de.

Cannon and Davenport, experiments on Daphniae by.

Capsella bursapastoris.

Carneri.

Castnia linus.

Catasetum barbatum.

Catasetum tridentatum.

Caterpillars, variation in.

Celosia, variability of.

Cereals, variability in.

Cesnola, experiments on Mantis by.

Chaerocampa, colouring of.

Chambers, R., “The Vestiges of Creation” by.

Chromosomes and Chromomeres.

Chun.

Cieslar, experiments by.

Circumnutation, Darwin on.

Claus.

Cleistogamy.

Clerke, Miss A.

Clodd, E.

Cluer.

Clytus arietis.

Coadaptation.

Codrington.

Cohen and Peter.

Collingwood.

Colobopsis truncata.

Colour, E.B. Poulton on The Value in the Struggle for life of. –influence and temperature on changes in. –in relation to Sexual Selection.

Colours, incidental.
–warning.

Comte, A.

Condorcet.

Cope.

Coral reefs, Darwin’s work on.

Correlation of organisms, Darwin’s idea of the.

Correlation of parts.

Corydalis claviculata.

Cournot.

Couteur, Col. Le.

Crooks, Sir William.

Cruger, on Orchids.

Cunningham and Marchand, on the brain.

Curie, M. and Mme.

Cuvier.

Cycadeoidea dacotensis.

Cycads, geological history of.

Cystidea, an ancient group.

Cytology and heredity.

Cytolysis and fertilisation.

Czapek.

Dalton’s atomic theory.

Dana, J.D., on marine faunas.

Danaida chrysippus.

Danaida genutia.

Danaida plexippus.

Dante.

Dantec, Le,

Darwin, Charles, as an Anthropologist. –on ants.
–and the “Beagle” Voyage.
–on the Biology of Flowers.
–as a Botanist.
–his influence on Botany.
–and S. Butler.
–at Cambridge.
–on Cirripedia.
–on climbing plants.
–on colour.
–on coral reefs.
–on the Descent of Man.
–his work on Drosera.
–at Edinburgh.
–his influence on Animal Embryology. –on Geographical Distribution.
–his work on Earthworms.
–evolutionist authors referred to in the “Origin” by. –and E. Forbes.
–on the geological record.
–and Geology.
–his early love for geology.
–his connection with the Geological Society of London. –and Haeckel.
–and Henslow.
–and History.
–and Hooker.
–and Huxley.
–on ice-action.
–on igneous rocks.
–on Lamarck.
–on Language.
–his Scientific Library.
–and the Linnean Society.
–and Lyell.
–and Malthus.
–on Patrick Matthew.
–on mental evolution.
–on Mimicry.
–a “Monistic Philosopher.”
–on the movements of plants.
–on Natural Selection.
–a “Naturalist for Naturalists.”
–on Paley.

Darwin, Charles, his Pangenesis hypothesis. –on the permanence of continents.
–his personality.
–his influence on Philosophy.
–predecessors of.
–his views on religion, etc.
–his influence on religious thought. –his influence on the study of religions. –his methods of research.
–and Sedgwick.
–on Sexual Selection.
–the first germ of his species theory. –on H. Spencer.
–causes of his success.
–on Variation.
–on the “Vestiges of Creation”.
–on volcanic islands.
–and Wallace.
–letter to Wallace from.
–letter to E.B. Wilson from.

Darwin, E., on the colour of animals. –Charles Darwin’s reference to.
–on evolution.

DARWIN, F., on “Darwin’s work on the Movements of Plants”. –on Darwin as a botanist.
–observations on Earthworms by.
–on Lamarckism.
–on Memory.
–on Prichard’s “Anticipations”.
–various.

DARWIN, SIR G., on “The Genesis of Double Stars”. –on the earth’s mass.

Darwin, H.

Darwin, W.

Darwinism, Sociology, Evolution and.

Davenport and Cannon, experiments on Daphniae by.

David, T.E., his work on Funafuti.

Death, cause of natural.

Debey, on Cretaceous plants.

Debierne.

Degeneration.

Delage, experiments on parthenogenesis by.

Delbruck.

Democritus.

Deniker.

Descartes.

Descent, history of doctrine of.

“Descent of Man”, G. Schwalbe on “The”. –Darwin on Sexual Selection in “The”.
–rejection in Germany of “The”.

Desmatippus.

Desmoulins, A., on Geographical Distribution.

Detto.

Development, effect of environment on.

Dianthus caryophyllus.

Diderot.

Digitalis purpurea.

Dimorphism, seasonal.

Dismorphia astynome.

Dismorphia orise.

Distribution, H. Gadow on Geographical. –Sir W. Thiselton-Dyer on.

Dittrick, O.

Dixey, F.A., on the scent of Butterflies.

Dolichonyx oryzivorus.

Dorfmeister.

Down, Darwin at.

Draba verna.

Dragomirov.

Driesch, experiments by.
–elsewhere.

Drosera, Darwin’s work on.

Dryopithecus.

Dubois, E., on Pithecanthropus.

Duhring.

Duhamel.

Duncan, J.S.

Duncan, P.B.

Duns Scotus.

Duret, C.

Durkheim, on division of labour.

Dutrochet.

Echinoderms, ancestry of.

Ecology.

Eimer.

Ekstam.

Elephants, geological history of.

Elymnias phegea.

E. undularis.

Embleton, A.L.

Embryology, A. Sedgwick on the influence of Darwin on.

Embryology, as a clue to Phylogeny.
–the Origin of Species and.

Empedocles.

Engles.

Environment, action of.
–Klebs on the influence on plants of. –Loeb on experimental study in relation to.

Eohippus.

Epicurus, a poet of Evolution.

Eristalis.

Ernst.

Ernst, A., on the Flora of Krakatau.

Eschscholzia californica.

Espinas.

Eudendrium racemosum.

Evolution, in relation to Astronomy.
–and creation.
–conception of.
–discontinuous.
–experimental.
–factors of.
–fossil plants as evidence of.
–and language.
–of matter, W.C.D. Whetham on.
–mental.
–Lloyd Morgan on mental factors in. –Darwinism and Social.
–Saltatory.
–Herbert Spencer on.
–Uniformitarian.
–Philosophers and modern methods of studying.

Expression of the Emotions.

Fabricius, J.C., on geographical distribution.

Farmer, J.B.

Farrer, Lord.

Fearnsides, W.G.

Felton, S., on protective resemblance.

Ferri.

Ferrier, his work on the brain.

Fertilisation, experimental work on animal-.

Fertilisation of Flowers.

Fichte.

Field, Admiral A.M.

Fischer, experiments on Butterflies by.

Fitting.

Flemming, W.

Flourens.

Flowering plants, ancestry of.

Flowers, K. Goebel on the Biology of.

Flowers and Insects.

Flowers, relation of external influences to the production of.

Fol, H.

Forbes, E.
–and C. Darwin.

Ford, S.O. and A.C. Seward, on the Araucarieae.

Fossil Animals, W.B. Scott on their bearing on evolution.

Fossil Plants, D.H. Scott on their bearing on evolution.

Fouillee.

Fraipont, on skulls from Spy.

FRAZER, J.G., on “Some Primitive Theories of the Origin of Man”. –various.

Fruwirth.

Fumaria officinalis.

Funafuti, coral atoll of.

Fundulus.

F. heteroclitus.

GADOW, H., on “Geographical Distribution of Animals”. –elsewhere.

Gartner, K.F.

Gallus bankiva.

Galton, F.

Gamble, F.W. and F.W. Keeble.

Gasca, La.

Geddes, P.

Geddes, P. and A.W. Thomson.

Gegenbauer.

Geikie, Sir A.

Geitonogamy.

Genetics.

Geographical Distribution of Animals. –of Plants.
–influence of “The Origin of Species” on. –Wallace’s contribution to.

Geography of former periods, reconstruction of.

Geology, Darwin and.

Geranium spinosum.

Germ-plasm, continuity of.
–Weismann on.

Germinal Selection.

Gibbon.

Gilbert.

GILES, P., on “Evolution and the Science of Language”.

Giuffrida-Ruggeri.

Giotto.

Gizycki.

Glossopteris Flora.

Gmelin.

Godlewski, on hybridisation.

GOEBEL, K., on “The Biology of Flowers”. –his work on Morphology.

Goethe and Evolution.
–on the relation between Man and Mammals. –elsewhere.

Goldfarb.

Gondwana Land.