The universe around us

We have commented on the surprising emptiness of space: six specks of dust in Waterloo Station about represent the extent to which it is occupied by stars in its most crowded parts. The comment might well have taken another form. Six specks of dust contain, let us say, a thousand million million molecules. Our model of space is empty because this great number of molecules happens all to be aggregated into as few as six lumps. In real space the unit of aggregation is the star, and an average star contains about 10⁵⁶ molecules—a number so large that it is quite useless to try to imagine it. The emptiness of space does not originate from any paucity of molecules; it originates from the circumstance that, apart from those which form the tenuous clouds of gas stretching from star to star, the molecules are aggregated together in the huge colonies we call stars, with about 10⁵⁶ members to each. Why should the molecules in space herd together in this way, when the molecules in the rooms in which I am writing and you are reading do not?

Following a well-tried scientific method, we may attempt to discover why these aggregates have formed, by first examining what keeps them together now that they have formed. The earth’s atmosphere consists of about 10⁴¹ molecules. Why do they stay pressed down into an atmosphere instead of spreading out through space? The answer is of course provided by the earth’s gravitation. A bullet fired from the earth’s surface with a speed of 6·93 miles a second or more will fly off into space, because the earth’s gravitational pull is inadequate to hold it back when it moves with so high a speed. But a bullet fired with a speed of less than 6·93 miles a second does not leave the earth; its speed is inadequate to take it clear of the earth’s pull. Thus the molecule-bullets which form the earth’s atmosphere, flying with speeds less than a third of a mile a second, have no chance at all of getting away. The earth’s gravitation continually pulls them back to earth, so that the earth retains its covering of air.

At rare intervals a molecule may experience a succession of exceptionally lucky collisions with other molecules, and so attain a speed of more than 6·93 miles a second. A molecule which arrives at the outside of the earth’s atmosphere with such a speed will leave the earth altogether, and join the interstellar crowd of stray molecules. The earth is continually shedding its atmosphere in this way, but calculation shews that the loss, even in millions of millions of years, is quite insignificant, so that we may regard the earth’s atmosphere as permanent.

It is the same with the sun. The sun’s heat has broken up the molecules of its atmosphere into their constituent atoms, and these move with an average speed of about 2 miles a second. But an atom-bullet would have to move at about 380 miles a second to escape altogether from the sun, so that the solar atoms remain to form an atmosphere.

If all the molecules of air in an ordinary room were collected into a bunch at the centre of the room, the ball of air so formed would of course exert a gravitational pull on its outermost molecules, of the same kind as the earth and sun exert on the molecules of their atmospheres. But, because the weight of this ball of air is so small, the intensity of its gravitational pull would also be small; indeed it would be so feeble that a speed of about a yard a century would be enough to take the outermost molecules clear of it. As the molecules of ordinary air move at about 500 yards a second, such a ball of air would immediately scatter through the whole room. On the other hand, if the room were big enough to contain the sun, all its molecules could stay in a ball at the centre, just as they do in the sun. The outermost molecules would need a speed of at least 380 miles a second to escape, so that their actual speeds of 500 yards a second or so would be of no service to them.

PLANETARY ATMOSPHERES. In general the question of escape or no escape depends on the outcome of a battle between the molecular speeds of the outermost molecules, and the intensity of the gravitational hold which the remainder of the mass exerts on them. The solar system provides many examples of this. The moon has only a sixth as much gravitational hold over the molecules of an atmosphere as the earth has, with the result that any atmosphere the moon may ever have had, has escaped by now. Mercury has two-fifths of the earth’s gravitational hold, but, owing to its nearness to the sun, its sunward surface is very hot, with the consequence that its atmosphere also has escaped. The gravitational hold of Mars on its molecules is only a fifth of the earth’s, but its surface is cooler. Calculation shews that water-vapour and heavier molecules ought to remain, while the lighter molecules of helium and hydrogen ought to have escaped. This probably represents what has actually happened. The largest satellite of Saturn and the two largest satellites of Jupiter would exercise about the same gravitational hold as the moon, but as their surfaces must be enormously colder than that of the moon, they ought to be able to retain atmospheres. Some observers claim to have seen indications of atmospheres on all three satellites. All the four major planets exert stronger gravitational holds over their molecules than the earth, and so retain their atmospheres with ease, while Venus, with approximately the same gravitational hold as the earth, also retains an atmosphere.

These considerations amply explain why the molecules of the stars must necessarily remain aggregated now that the aggregates have once been formed, but the question of how and why these aggregates formed in the first instance is far more complex. What, for instance, determined that there should be about 10⁵⁶ molecules in each star rather than 10⁵⁴ or 10⁵⁸?

GRAVITATIONAL INSTABILITY

It is natural to enquire whether the forces which now keep a star together may not also have been responsible for its falling together in the first instance. This leads us to study the aggregating power of gravitation in some detail.

Five years after Newton had published his law of gravitation, Bentley, the Master of Trinity College, wrote him, raising the question of whether the newly discovered force of gravitation would not account for the aggregation of matter into stars, and we find Newton replying, in a letter of date December 10, 1692:

It seems to me, that if the matter of our sun and planets, and all the matter of the universe, were evenly scattered throughout all the heavens, and every particle had an innate gravity towards oil the rest, and the whole space throughout which this matter was scattered, was finite, the matter on the outside of this space would by its gravity tend towards all the matter on the inside, and by consequence fall down into the middle of the whole space, and there compose one great spherical mass. But if the matter were evenly disposed throughout an infinite space, it could never convene into one mass; but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered great distances from one to another throughout all that infinite space. And thus might the sun and fixed stars be formed, supposing the matter were of a lucid nature.

An exact mathematical investigation on which I embarked in 1901, not only confirms Newton’s conjecture in general terms, but also provides a method for calculating what size of aggregates would be formed under the action of gravitation.

THE FORMATION OF CONDENSATIONS. You stand in the middle of a room and clap your hands. In common language you are making a noise; the physicist, in his professional capacity, would say you are creating waves of sound. As they approach one another, your hands expel the intervening molecules of air. These stampede out, colliding with the molecules of outer layers of air, which are in turn driven away to collide with still more remote layers; the disturbance originally created by the motion of your hands is carried on in the form of a wave. Although the individual molecules have an average speed of 500 yards a second, the zig-zag quality of their motions reduces the speed of the disturbance, as we have already seen, to about 370 yards a second—the ordinary velocity of sound. As the disturbance reaches any point the number of molecules there becomes abnormally high, for the stampeding molecules add to the normal quota of molecules at the point. This of course produces an excess of pressure. It is this excess pressure acting on my ear-drum that transmits a sensation to my brain, so that I hear the noise of your clapping your hands.

This excess of pressure cannot of course persist for long, so that the excess of molecules which produces it must rapidly dissipate. It is thus that the wave passes on. Yet there is one factor which militates against its dissipation. Each molecule exerts a gravitational pull on all its neighbours, so that where there is an excess of molecules, there is also an excess of gravitational force. In an ordinary sound wave this is of absolutely inappreciable amount, yet such as it is, it provides a tiny force holding the molecules back, and preventing them scattering as freely as they otherwise would do. When the same phenomenon occurs on the astronomical scale, the corresponding forces may become of overwhelming importance.

Let us speak of the gas in any region of space where the number of molecules is above the average of the surrounding space, as a “condensation.” Then it can be proved that, if a condensation is of sufficient extent, the excess of gravitational force may be sufficient to inhibit scattering altogether. In such a case, the condensation may continually grow through attracting molecules into it from outside, whose molecular speeds are then inadequate to carry them away again.

Whether this happens or not will depend of course on the speed of molecular motion in the gas, as well as on the size of the condensation. But it will not depend at all on the extent to which the process of condensation has proceeded. By doubling the excess number of molecules in any condensation, we double the extent to which condensation has proceeded. In so doing, we double the gravitational pull tending to increase the condensation, but we also double the excess pressure which tends to dissipate it; we double the weights on each side of the balance, but the balance still swings in the same direction. If once conditions are favourable to its growth, a condensation goes on growing automatically until there are no further molecules left for it to absorb.

The greater the extent in space of a condensation, the more favourable conditions are to its continued growth. Other things being equal, a condensation two million miles in diameter will exert twice the gravitational force of a condensation one million miles in diameter, but the excess pressures are the same in the two cases. Thus, the larger a condensation is the more likely it is to go on growing, and by passing in imagination to larger and larger condensations we must in time come to condensations of such a size that they are bound to keep on growing. Nature’s law here is one of unrestricted competition. Nothing succeeds like success, and so we find that condensations which are big to start with have the capacity of increasing still further, while those which are small merely dissipate away.

Suppose now that an enormous mass of uniform gas extends through space for millions of millions of miles in every direction. Any disturbance which destroys its uniformity may be regarded as setting up condensations of every conceivable size.

This may not seem obvious at first; it may be thought that a disturbance which only affected a small area of gas would only produce a condensation of small extent. Such an argument overlooks the way in which the gravitational pull of a small body acts throughout the universe. The moon raises tides on the distant earth, and also tides, although incomparably less in amount, on the most distant of stars. Each time the child throws its toy out of its baby-carriage, it disturbs the motion of every star in the universe. So long as gravitation acts, no disturbance can be confined to any area less than the whole of space. The more violent the disturbance which creates them, the more intense the condensations will be to begin with, but even the smallest disturbance must set up condensations, although these may be of extremely feeble intensity. And we have seen that the fate of a condensation is not determined by its intensity but by its size. No matter how feeble their original intensity may have been, the big condensations go on growing, the small ones disappear. In time nothing is left but a collection of big condensations. The mathematical analysis already referred to shews that there is a definite minimum weight such that all condensations below this weight merely dissipate away into space. To a good enough approximation for our present purpose, this minimum weight is such that if a tenth of this weight of gas were isolated in space, and all the rest of the gas annihilated, the molecules would just and only just fail to escape from its surface[20].

We may say that the original uniformly distributed mass of gas was “unstable” because any disturbance, however slight, causes it to change its configuration entirely; it had the dynamical attributes of a stick balanced on its point, or of a soap-bubble which is just ready to burst.

PRIMAEVAL CHAOS. These general theoretical results may now be applied to any mass of gas we please. Let us begin by applying them to Newton’s hypothetical “matter evenly disposed throughout an infinite space.” We return in imagination to a time when all the substance of the present stars and nebulae was spread uniformly throughout space; in brief, we start from the primaeval chaos from which most scientific theories of cosmogony have started. Hubble has estimated that if the whole of the matter in those parts of the universe we know were redistributed evenly throughout space, the gas so formed would have only about 1·5 × 10⁻³¹ times the density of water. This estimate is almost certainly on the low side, even as representing present conditions, and in trying to reconstruct the primaeval gas we must add something to allow for the molecules and atoms which have melted away into radiation in the intervening period. On the whole, perhaps 10⁻³⁰ is not an unreasonable density to assign to the hypothetical primaeval nebula. It is almost inconceivably low. In ordinary air, at a density of one eight-hundredth that of water, the average distance between adjoining molecules is about an eight-millionth part of an inch; in the primaeval gas we are now considering, the corresponding distance is two or three yards. The contrast again leads back to the theme of the extreme emptiness of space.

What is the minimum weight of condensation that would persist in this primaeval gas?

Calculation shews that if ordinary air were attenuated to this extraordinary degree, no condensation could persist and continue to grow unless it had at least 62½ million times the weight of the sun; any smaller weight of gas would exert so slight a gravitational pull on its outermost molecules, that their normal molecular speeds of 500 yards a second would lead to the prompt dissipation of the whole condensation.

We can carry out similar calculations with reference to other assumed densities of gas, and other molecular velocities. The following table shews the weights of condensations which would be formed in primaeval masses of chaotic gas having the densities shewn in the first column, and the various molecular velocities mentioned at the heads of the remaining columns. In each case the weights of the condensations are given in terms of the weight of the sun:

All known stars have weights comparable with that of the sun. Thus if, as Newton conjectured, the stars first came into being as condensations of this kind, then the entries in this table ought to be comparable with unity. Newton’s conjecture, in the form in which we have just considered it, is clearly untenable, since all the calculated weights are many millions of times that of the sun. If there ever existed a primaeval chaos of the kind we are now considering, it would not condense into stars, but into enormously more massive condensations, each having the weight of millions of stars.

THE BIRTH OF THE GREAT NEBULAE

Now it is significant that bodies are known in space having weights equal to those just calculated, namely the great extra-galactic nebulae. There are two nebulae whose weights can be determined with fair accuracy, namely the Great Nebula in Andromeda (Plate IV, p. 30) and the nebula N.G.C. 4594 in Virgo (Plate XV). Hubble estimates these to be as follows:

These estimates are again probably both on the low side, but their general order of magnitude is such as to suggest that the condensations which would first be formed out of the primaeval nebula must have been the great extra-galactic nebulae, and not mere stars. It is of course at best only a conjecture that the great nebulae were formed in this manner—if for no other reason because we can never know whether the hypothetical primaeval nebula even existed—but it seems the most reasonable hypothesis we can frame to explain the fact that the present nebulae exist. These nebulae are so generally similar to one another that it seems likely that they must all have been produced by the action of the same agency, and that which we have just considered provides a reasonable explanation which, apart from the postulated existence of the continuous primaeval nebula, is based on verae causae.

The great nebulae are of course not exactly similar, and our next inquiry must be as to the origin of their differences.

If the condensations in the primaeval gaseous nebula had formed and contracted in an absolutely regular fashion, the final product would be an array of perfectly equal and similar masses of gas spaced with perfect regularity. But nature is seldom as regular as this; and we need not be surprised that the observed nebular array is not evenly spaced, or that its members are neither equal in weight, nor symmetrically arranged. As the original condensations in the primaeval gas contracted, they must have produced currents, and these would hardly be likely to occur absolutely symmetrically. If the motion in each mass of condensing gas had been directly towards the centre of the condensation at every point, the final result would have been a spherical nebula devoid of all motion, but any less symmetrical system of currents would result in a spin being given to each contracting mass. This spin would no doubt be very slow at first, but the well-known principle of “conservation of angular momentum” requires that, as a spinning body contracts, its rate of spin must increase. Thus when the process of condensation was complete, the final product would be a series of nebulae rotating at different rates.

NEBULAR ROTATION. And this is exactly what is observed; so far as our evidence goes the nebulae are in rotation, and at different rates. The various parts of the surface of any rotating mass necessarily have different speeds in space. The sun for instance rotates about its axis in such a direction that the surface we see is moving always from east to west; as a result the eastern limb is always advancing towards the earth, while the western limb is receding from us. A spectroscope turned on to different parts of the sun’s surface in succession at once reveals these differences of speed; they not only assure us of the sun’s rotation, but enable us to measure its amount. The nebulae may be examined in the same way, and the examination shews that a large number of them are rotating with the perfectly regular motion of a solid body—a spinning-top, for instance. Measured by terrestrial standards their rates of rotation seem extraordinarily slow; for instance the Great Nebula M 31 in Andromeda requires about 19,000,000 years to make a complete rotation, but this apparent slowness is an inevitable result of the huge size of the nebula. Even to get round once in 19,000,000 years, the outer parts of the nebula have to move with speeds of hundreds of miles a second.

A few of the nebulae are quite irregular in shape, but the majority have regular shapes, and it is highly significant that these are precisely the shapes which, it can be calculated mathematically, would be exhibited by rotating masses of gas. Actually there is a far stronger case than this for supposing the nebulae to be rotating masses of gas. From the purely observational evidence of surface-brightness and other characteristics, Hubble found that nearly all of these nebulae could be arranged in a single linear sequence—they could be arranged in order like beads on a string. And this order proved to be practically identical with the sequence which had previously been calculated, by purely theoretical methods, for the configurations of masses of gas rotating at gradually increasing rates of speed.

Let us examine this sequence of theoretical configurations in their natural order.

A mass of gas which was not rotating at all would of course assume a spherical shape under its own gravitation. A number of perfectly spherical nebulae are known; a typical example is shewn in fig. 1 on Plate XVI.

With slight rotation the mass assumes the shape of a slightly flattened orange, like the earth or Jupiter. Nebulae of this shape are also known in abundance; an example is shewn in fig. 2 on the same plate.

With a higher degree of rotation the degree of flattening increases, but theoretical calculation shews that the orange shape is soon departed from. The equator first begins to shew a pronounced bulge, until finally, with sufficient rotation, this develops into a sharp edge, the rotating mass now being shaped like a double-convex lens. This prediction of theory is abundantly confirmed by observation, a large number of these lens-shaped nebulae being observed in the sky. An example is shewn in fig. 3 on Plate XVI.

The next step is somewhat sensational. Further rotation does not, as might be expected, result in still further flattening. Up to now, each increase in rotation has made the bulge on the equator sharper, but this is now as sharp as it can be. Theory shews that the flattening has also proceeded to the utmost possible limit, and that the next stage must consist in matter being ejected through the sharp edge of the equator and spread throughout the equatorial plane. Here again observation confirms theory; figs. 4 and 5 (Plate XVI) shew types of nebulae actually observed, the former being the nebula in Virgo which we have already had under discussion.

The comparatively thin layer of gas which now lies in the equatorial plane is similar in one respect at least to Newton’s matter “evenly disposed throughout an infinite space.” Disturbances can be set up in it in a variety of ways, and any disturbance, no matter how slight, must result in the creation of a series of condensations. As before, those below a certain limit of size disappear of themselves, while those above this limit continually increase in intensity until they have absorbed all the gas in the equatorial plane. Again, as with the hypothetical primaeval chaos, we can calculate the minimum size of condensation which can be expected to have a permanent existence, and once again the result proves to be highly significant.

Hubble’s estimates of the total weights of two conspicuous nebulae have already been given. As the distances, and therefore also the sizes, of both these nebulae are known, it is an easy matter to calculate the average density of the gas throughout the whole nebula. The average density in M 31 is found to be about 5 × 10⁻²² of that of water; the corresponding number for N.G.C. 4594 is 2 × 10⁻²¹. These figures give us some idea of the density of matter in the outer regions of the nebulae. Although these densities are about a thousand million times as great as the estimated density of the original primaeval nebula of space, they are still almost inconceivably low. There is still only about one molecule to the cubic inch, and a single breath from the lungs of a fly could fill a large cathedral with air of this density.

On proceeding to calculate the weights of the smallest condensations which could form and persist in a gas of this low density, we obtain the results shewn in the following table. The molecular velocities are taken rather low, so as to allow for the cooling which must occur when the gas is spread out in the equatorial plane of the nebula.

Again the weights of the condensations are given in terms of the weight of the sun. And the significant fact emerges that most of the entries in the table represent weights comparable with that of the sun. We are dealing with stellar weights at last; the condensations which must form in the outer regions of the great nebulae will have weights comparable with those of the stars.

THE BIRTH OF STARS

And indeed there can be but little doubt that the process we have just been considering is that of the birth of stars. Even a casual glance at photographs of nebulae suffices to shew that the matter which has been ejected into the equatorial plane of a nebula does not lie uniformly spread out in that plane; it is seen to have fallen into bunches, knots or condensations. These are apparent enough in many of the nebular photographs already shewn, but they can be seen still more clearly in nebulae which are viewed nearly full-on, such as for instance the two striking nebulae shewn in Plates XVII and XVIII.

These bunches are invariably too large to be interpreted as single stars; they are more probably groups of stars. In the largest telescopes they break up into great numbers of points of light in the way already exhibited in Plate XI (p. 70). We have already mentioned the reasons which compel us to regard these points of light as actual stars, the principal being that some of them shew the characteristic light-fluctuations of the Cepheid variables. It is not altogether clear whether the stars are formed directly as condensations in the equatorial plane of the nebula, or whether larger condensations form first, namely the bunches observable in nebular photographs, which subsequently form smaller condensations, the stars. On the whole it seems likely that there are two processes involved—first the break-up of the nebular matter into big condensations, and then the break-up of these big condensations into stars. Such a succession of processes might well accompany a gradual cooling of the matter, and it is of course possible that there are even more than two processes involved. There is no need to form a final opinion on this at present, as it is in no way essential to the progress of the main argument.

A collection of nebular photographs enables us to follow nebular evolution from the earliest stages shewn in Plate XVI (p. 207), through the first appearance of granular bunches, such as are shewn in Plate XVII, and the first distinct appearance of stars shewn in Plate XVIII, down to the later stages, such as are shewn in Plates XIX and XX, in which the nebula appears to be but little more than a cloud of stars. Hubble has found it possible to follow the sequence still further, and can trace a continuous transition from the nebulae of this last type to pure star-clouds such as the Greater and Lesser Magellanic Clouds shewn in Plate XXI.

Thus the stars appear to have been born in much the same way as we have conjectured that their parents, the great nebulae, had been born before them, namely, through the agency of what is generally known as “Gravitational Instability.” This causes any mass of chaotic gas to break up into detached condensations, and, the more tenuous the original gas, the greater the weights of the condensations formed out of it. The original primaeval nebula was of such low density that the condensations which formed in it weighed thousands of millions of times as much as the sun. These increased their density so much in contracting that when their rotation caused them to eject gaseous matter, this condensed into masses of stellar weight which we believe actually to be stars.

We have less certain knowledge of the former process than of the latter. Our only reason for thinking that the former process ever occurred is that the extra-galactic nebulae now exist. There is no evidence that the primaeval chaotic nebula ever existed, beyond the fact that the hypothesis of its previous existence leads to a very satisfactory explanation of the present nebulae existing as they now do. On the other hand, we not only know that the stars exist: we also know that the masses of gas exist out of which theory shews that stars must necessarily be born. They are the tenuous equatorial fringes of the great nebulae. Our telescopes shew us both the nebular fringes and the stars, and we can almost study the actual process of birth.

THE GALACTIC SYSTEM OF STARS. If this is the true account of the birth of the stars, then our sun and its companions in space must have been born out of a rotating nebula. Observation gives strong support to this conclusion. Since the time of the Herschels, it has been a matter of frequent comment that the galactic system has the general shape of the extra-galactic nebulae, the galactic plane of course representing the equatorial plane of the original nebula. On purely observational grounds, present-day astronomical thought is moving rapidly towards regarding the whole galactic system either as a rotating nebula or the remains of one. It is even possible that this may still retain a central region which is as yet uncondensed into stars. In the direction of the constellations Scorpio and Ophiuchus are dark clouds which may either veil the centre of the system or may conceivably be the centre itself.

In 1904, Kapteyn found that the directions of motion of the stars in the vicinity of the sun were not distributed at random. The stars appeared to prefer to move to and fro along a certain direction in the galactic plane rather than in other directions—“star-streaming,” he called it. This peculiarity in the motion of the stars may be expected to throw some light on their origin.

Each star moves in a complicated orbit under the gravitational attraction of all the other stars of the galactic system. It is not possible to calculate this orbit in detail. The orbit of a planet round the sun is easily calculated because only two bodies are involved, the planet and the sun. But even when there are only three bodies involved, it is impossible to calculate the orbits that each describes under the attractions of the other two jointly: this is the famous problem of three bodies, which has never been solved. When, as in the galactic system, thousands of millions of stars are involved, it is naturally useless to try to calculate the orbit of each star—it would be as futile as trying to calculate the path of each molecule in a gas.

Yet the same statistical methods which give us useful information as to the properties of a gas may be applied to studying the motions of the stars. There are so many stars that we do not trouble about individuals at all, we just treat them all together as a crowd. To treat them as individuals would be as though the railway company tried to forecast the Bank Holiday traffic from London to Brighton by considering the finances, habits and psychology of each individual Londoner.

Without going into individual details, we can see that each star must describe an orbit which, after touring round a large part of the galaxy, comes back to somewhere near its starting point. Calculation shews that each such circuit must take hundreds of millions of years to complete. Even so, the stars will mostly have performed several complete circuits while the earth has been in existence, and if we are right in supposing the ages of the stars to be millions of millions of years, each star must have toured round the galaxy several thousands of times. We should accordingly expect the galaxy to have assumed a definite permanent shape by now; the distribution of stars in its different parts ought to have become something like steady, and the stars ought to have settled down to a state approximating to one of steady motion.

Statistical methods of investigation shew that there is not a great number of possible arrangements for a system of stars which has lived long enough to attain a steady state. If the system as a whole has no rotation at all, there is only one arrangement; the stars form a globular mass with perfect symmetry in all directions. The observed globular clusters (Plate IX, p. 63) provide good approximations to this type of formation, although Shapley has found that the majority are not absolutely spherical in shape. If the system as a whole is endowed with rotation, the possible configurations are all of a flattened symmetrical shape, like a coin, a watch or a round biscuit—in other words a system of stars in rotation must be shaped pretty much as we believe the galaxy to be shaped. Furthermore the motions of these stars must shew “star-streaming” of precisely the kind discovered by Kapteyn.

Thus both the shape of the galaxy and the peculiarities of motion of its stars indicate that the galactic system as a whole must be in a state of rotation. And, as we have seen (p. 67), recent observational researches by Oort, Plaskett and others make it fairly certain that the rotation required by theory is an actual fact. The motions of the stars indicate that the whole galactic system is rotating at a rate which varies from one region to another, being about one revolution every 230 million years in the vicinity of the sun. And the hub of this gigantic wheel is found to coincide very closely with the spot which Shapley had previously fixed as the geometrical centre of the galactic system from his researches on the distribution of the globular clusters.

Thus, since rotation cannot be generated out of nothing, all the phenomena agree in shewing that the galactic system must have been born out of a rotating body. We are acquainted with only one type of astronomical body which is of sufficient size to turn into a galactic system, namely the great nebulae, and as the majority of these are believed, and some are known with certainty, to be in rotation, it seems reasonable to conclude that the galactic system must have been born out of a nebula, unless indeed its structure is still such that we should even now describe it as a nebula if we saw it from the great distance from which we view the other great nebulae. The observed period of rotation of the galactic system, of the order of 230 million years, is substantially longer than the period, either known or suspected, of any of the nebulae, but the dimensions of the galactic system are also greater than those of any known nebula, and the two facts hang together. Again, the number of stars in the galactic system is probably substantially higher than in any nebula, as also is the total weight of these stars[21]. All this makes it clear that if the galaxy is, or ever has been, one of the great nebulae, it must have been one of unusual size and weight.

We have seen how the sun and all the stars are continually losing weight as the result of their emission of radiation. It follows that the total weight of the galactic system is for ever decreasing, and as a consequence its gravitational hold on its constituent stars is continually weakening. If this gravitational hold were suddenly to vanish altogether, each star would replace its present curved path by a perfectly straight line, along which it would travel at its present speed, undeflected by any gravitational forces from other stars, so that the stars which now constitute the galactic system would soon be scattered through the whole of space. In brief, if the gravitational pull of the stars were suddenly abolished, the galaxy would begin to expand at a great rate.

Although this is not likely to happen, the gradual abolition of the gravitational pull of the stars, as they turn their weight into radiation, must cause the galaxy to expand all the time at a slow rate: calculation suggests that its present rate of expansion would double its size in about 30 million million years. The expansion must have been far more rapid in the past, when the stars were full of youthful vigour and squandered their substance more lavishly than now, so that it seems probable that the galactic system was substantially smaller and more compact in the past than now, and the original nebula probably smaller still.

We have seen how the stars in the great nebulae appear to be congregated in bunches or clusters. The globular clusters in the galactic system may possibly be bunches of stars of the same general type, which have remained undisturbed by other groups of stars and so have assumed the globular form under their own attraction—just as a mass of gas would do. Shapley finds that these clusters lie somewhat outside the galactic plane; it looks as though they were broken up or disorganised in travelling through this plane, where they would encounter other stars.

By contrast groups of stars of the type generally described as moving clusters—the Pleiades, the Hyades, the stars of the Great Bear and a crowd of others voyaging in company with them through space—are generally found to move in the galactic plane. These may quite possibly represent the final vestiges of globular clusters which have been broken up by interaction with other stars, all except the most massive members having been knocked out of formation. Mathematical analysis shews that the interaction between the stars of such moving clusters and other stars in the galactic plane would cause each cluster to assume the shape of a flat biscuit or watch, of diameter equal to 2½ times its thickness. It is significant that the majority of the moving clusters shew a flattening of this kind, its amount agreeing tolerably well with the calculated value. It is even conceivable that the “local cluster” surrounding the sun (p. 65) may be the remains of such a bunch of stars.

The motions of these clusters may also induce a further flattening, in a direction perpendicular to their motion. Some clusters shew this further flattening, the Ursa Major cluster being a striking example.

THE BIRTH OF BINARY SYSTEMS

In discussing the way in which nebulae might be born out of chaos, we noticed that the existence of currents in the primordial medium would endow the resulting nebulae with varying amounts of rotation. For the same reason the children of the nebulae, the stars, must also be endowed with rotation at their birth. There is a further reason for such rotation. The general principle of the “conservation of angular momentum” requires that rotation, like energy, cannot entirely disappear. Its total amount is conserved, so that when a nebula breaks up into stars, the original rotation of the nebula must be conserved in the rotations of the stars. Thus the stars, as soon as they come into being, are endowed with rotations transmitted to them by their parent nebula, in addition to the rotations resulting from the currents set up in the process of condensation.

Their continual loss of weight causes the physical conditions of the stars to change, and we shall find in the next chapter that this change generally involves a shrinkage of the star’s diameter. The same principle of “conservation of angular momentum” now requires that, as a star shrinks, its speed of rotation shall increase. In brief, as a star ages, it spins faster and faster.

Now rotation was the essential factor in the birth of the stars out of the parent nebula. A nebula perfectly devoid of rotation would not, so far as we can see, break up into stars at all, and this prediction of theory appears to be confirmed by observation, since nebulae of the perfectly spherical type shewn in fig. 1 of Plate XVI can never be resolved into stars in the telescope. On the other hand we saw how nebulae which were initially endowed with rotation would continually increase their speed of rotation under shrinkage, until finally their rotation broke them up and produced a family of stars out of each. The question now obviously arises whether, as the speed of rotation of the stars increases, these are likely to break up in their turn, and produce yet a third generation of astronomical bodies. Again we might expect that mathematical analysis would apply to large and small bodies equally, irrespective of scale. And a detailed examination of the problem shews that in actual fact the process we have had under consideration would repeat itself, and again bring a further generation of smaller bodies into being, provided the physical conditions were suitable.

The physical conditions, however, prove not to be suitable; they certainly fail in one respect at least. Although a rotating star may eject gaseous matter in its equatorial plane, the whole process will be on a much smaller scale than in the nebulae. We might expect the ejected matter to form condensations as before, but calculation shews that, unless the molecular velocity is extraordinarily low, no condensation can survive unless it has a weight greater than the whole weight of the star! This means that with any reasonable molecular velocity, the ejected gas would not form condensations at all. It would merely scatter into the surrounding space, forming an atmosphere without any distinct condensations.

Such is the course of events if the stars, like the nebulae before them, are treated as pure masses of gas. Another alternative must, however, be considered.

THE FISSION OF LIQUID STARS. We have seen how a gaseous nebula devoid of rotation would assume a strictly spherical shape under its own gravitational attraction, while slight rotation would cause it to flatten into an orange shape, like the earth. The earth also has assumed this shape on account of its rotation, although its internal structure is very different from that of a gaseous nebula.

Strict mathematical investigation shews that this flattened-orange shape must be common to all slowly rotating bodies, regardless of their internal composition; gases, liquids, and plastic bodies assume it equally. But the shape of a rapidly rotating body must depend very greatly on its internal arrangement and constitution, being especially affected by the extent to which the weight of the body is concentrated near its centre.

As a consequence of the high compressibility of gases, this central concentration of weight reaches its extreme limit in a purely gaseous mass. The opposite extreme is reached in a mass of uniform incompressible liquid such as water, in which there can be no central concentration at all. As a mass of this latter type increases its speed of rotation, the slightly flattened-orange shape merely gives place to the shape of a more flattened orange. The tendency of a gaseous mass to form a sharp edge round the equator is entirely absent, and the cross-section of its figure remains elliptical throughout. At a still higher speed of rotation, the equator loses its circular shape and it too becomes elliptical. The figure has now three unequal diameters, but every cross-section is strictly elliptical; the figure is an “ellipsoid.” After this, its longest diameter begins to elongate until the mass, still ellipsoidal in shape, has formed a cigar-shaped figure with a length nearly three times its shortest diameter.

A new series of events now begins. The mass of liquid gradually concentrates about two distinct points on its longest diameter, a waist or furrow forming across its middle. This furrow gets deeper and deeper until it has cut the body into two distinct detached masses, which now rotate in orbital motion about one another and form a binary star. The sequence of events is shewn in fig. 11; diagrams of the final stage as represented by actual binary stars have already been given on p. 54.

For comparison the sequence of shapes assumed by a rotating mass of gas is shewn in fig. 12, this being identical with the sequence of observed nebular shapes which is actually observed, and is illustrated photographically in Plate XVI (p. 207).

The two chains of configurations shewn in figs. 11 and 12 represent, it will be remembered, the two extreme cases of a rotating body whose substance is distributed with complete uniformity, and of a rotating body whose substance is very highly condensed towards its centre. As the constitutions of actual astronomical bodies must lie somewhere between these two extremes, we might naturally expect such a body to follow a series of configurations intermediate between the two shewn in figs. 11 and 12. Theory shews that as a matter of fact it does not. All bodies having less than a certain critical degree of central condensation follow the sequence shewn in fig. 11, or a sequence differing only immaterially from this; all bodies having more than this critical amount of central condensation follow the sequence shewn in fig. 12. Thus when this critical degree of central condensation is reached there is a sudden swing over from fig. 11 to fig. 12. In brief, every rotating body conducts itself either as if it were purely liquid, or as if it were purely gaseous; there are no intermediate possibilities.