The universe around us

The law governing all these phenomena is quite simple. It is that the earth’s gravitational pull causes all bodies to fall 16 feet earthward in a second. This is true of all bodies which are free to fall, no matter how they are moving; every body which is not in some way held up against gravitation is 16 feet lower at the end of any second than it would have been if gravitation had not acted through that second.

To illustrate what this means, let the big circular curve BʹAʹCʹ in fig. 2 represent the earth’s surface, and imagine that a shot is fired horizontally from A, the top of an elevation AAʹ. If the shot were not pulled earthwards by gravitation, it would travel indefinitely along the line AB out into space. If AB is the distance it would travel in a second under these imaginary conditions, the end of a second’s actual flight does not find it at B, but at a point 16 feet nearer the earth, gravitation having pulled it down this 16 feet during its flight. For instance, if BB′ in fig. 2 should happen to be 16 feet, the shot would strike the earth at Bʹ after a flight of precisely one second.

As another example, let us suppose that the 16-foot fall below B does not drag the shot down to earth but only to a point b, which is at precisely the same height above the earth’s surface as the point A at which the shot started. If gravitation were not acting, so that the shot travelled along the line AB, its height above the earth would continually increase. Actually in the case we are now considering, gravitation pulls the shot down at just such a rate as to neutralise the increase of height which would otherwise occur, so that the height of the shot neither increases nor decreases; it neither flies off into space nor drops to earth, but continues to describe circles round the earth indefinitely.

A simple geometrical calculation shews that for the distance Bb to be 16 feet, the distance AB travelled in one second must be 25,880 feet or 4·90 miles[2]. Thus if we could fire a shot horizontally with a speed of 4·90 miles a second, it would describe endless circles round the earth, the earth’s gravitational pull exactly neutralising the natural tendency of the shot to fly away along the straight line AB.

In 1665 Newton began to suspect that this same gravitational pull might be the cause of the moon describing a circular orbit around the earth instead of running away at a tangent into space. The moon’s distance from the earth’s centre is 238,857 miles, or 60·27 times the radius of the earth. As the moon describes a circle of this size every month (27 days, 4 hours, 43 minutes, 11·5 seconds), we can calculate that its speed in its orbit is 2287 miles an hour. After one second it will have travelled 3350 feet, and if it kept to a strictly rectilinear course this would carry it 0·0044 feet further away from the earth. Thus, to keep in an exact circular orbit around the earth, it must fall 0·0044 feet in a second. This is far less than a body falls in a second at the earth’s surface, but Newton conjectured that the force of gravity must weaken as we recede from the earth’s surface. Actually a body at the earth’s surface falls 3632 times as fast as the moon’s earthward fall in its orbit. Now 3632 is the square of 60·27 (or 3632 = 60·27 × 60·27), whence Newton saw that the moon’s fall would be of exactly the right amount if the force of gravity fell off as the inverse square of the distance—that is to say, if it decreased just as rapidly as the square of the distance increased. As we shall see later, astronomical observation confirms the truth of this law in innumerable ways. This led Newton to put forward his famous law of gravitation according to which the gravitational pull of any body, such as the earth, falls off inversely as the square of the distance from the body.

Professor C. V. Boys and others have measured the gravitational pull which a few tons of lead exert in the laboratory, and, with this knowledge, it is easy to calculate how many tons the earth must contain so as to exert its observed gravitational pull on bodies outside it. It is found that the earth’s weight must be just under six thousand million million million tons[3], or, as we shall write it, 6 × 10²¹ tons[4].

Just as the earth’s gravitational pull keeps the moon perpetually describing circles around it, so the sun’s gravitational pull keeps the earth and all the other planets describing circles around the sun. Knowing the distance of any planet from the sun, and also its speed in its orbit, we can calculate the distance this planet falls towards the sun in a second. This tells us the amount of the sun’s gravitational pull, and from this we can calculate that the sun’s weight must be about 332,000 times the weight of the earth, or almost exactly 2 × 10²⁷ tons. Whichever of the planets we use, we obtain exactly the same weight for the sun. This not only gives us confidence in our result, but incidentally it also provides striking confirmation of the truth of Newton’s law of gravitation, for if this law were inexact or untrue, the different planets would not all tell exactly the same story as to the sun’s weight. Einstein has recently shewn that the law is not absolutely exact, but the amount of inexactness is inappreciable except for the nearest planet, Mercury, and even here it is so exceedingly small that we need not trouble about it for our present purpose.

Just as we can weigh the sun and earth by studying the motion of a body gripped by their gravitational pull—or “in their gravitational fields,” as the mathematician would say—so we can weigh any other body which keeps a second small body moving round it by its gravitational attraction. The motions of Jupiter’s satellites make it possible to weigh Jupiter; its weight is found to be about 1·92 × 10²⁴ tons, which is 317 times that of the earth, although only ¹/₁₀₄₇ of that of the sun. Similarly the weight of Saturn is found to be 5·71 × 10²³ tons or about 94·9 times that of the earth.

WEIGHING THE STARS. And now we come to a striking application of the principles just explained—when we observe two stars in the sky describing orbits about one another, we can weigh the stars from a study of their orbits. Generally the problem is not quite so simple as those we have just discussed. For its adequate treatment, we must once again levy toll on the mathematical work of Newton.

We have seen that a projectile fired horizontally with a speed of 4·90 miles a second, would describe endless circles round the earth. What would happen if it were fired in some other direction and with some other speed?

The answer was provided by Newton. He shewed that when a small body is allowed to move freely under the gravitational pull of a big body, it will run away altogether if its speed exceeds a certain critical amount, in which case its orbit is the curve called a hyperbola. But if its speed is less than this critical amount, its orbit will always be an ellipse—a sort of pulled out circle or oval curve[5] (fig. 4, p. 47). Previous to this Kepler had found that the actual paths of the planets round the sun were not exact circles but ellipses, although for the most part ellipses which did not differ greatly from circles; they are what the mathematician calls “ellipses of small eccentricity.” This provides still further confirmation of Newton’s law of gravitation, for it can be proved that if the force of gravitation falls off in any way other than according to Newton’s law of the inverse square of the distance, the orbits of the planets will not be elliptical.

When the astronomer studies the motions of a binary star in the sky, he generally finds that the two components do not move in circles about one another but in ellipses[6]. Once again, Newton’s law is confirmed, and we are entitled to assume that the forces which keep binary stars together are the same gravitational forces as keep the moon from running away from the earth, or the planets from the sun. By a study of these ellipses it becomes possible to weigh the stars. If one of the component masses were enormously heavier than the other, the former would stand still while the lighter component described an ellipse around it, the motion being essentially similar to that of a planet around the sun. Such cases are not observed in actual binary stars because the two components are generally comparable in weight, and this brings new complications into the question. There is no need to enter into mathematical details here. Suffice it to say that neither star stands still; the two components describe ellipses of different sizes, and from a study of these two ellipses the weights of both the components can be determined.

The following table shews the result of weighing the four binary systems nearest the sun in this way, the sun’s weight being taken as unity:

Stellar Weights

Binary systems near the sun.

We see that the weights of these stars do not differ greatly from that of the sun, although naturally the whole of space provides a greater range than the four stars of our table which happen to be near the sun. But even in the whole of space, no star whose weight is known with any accuracy has a weight less than Kruger 60 B, although at the other end of the scale there are many stars with far greater weights than any in our table. Of stars whose weights are known with fair accuracy, the star H.D. 1337 (Pearce’s star) is the weightiest, its two components being respectively 36·3 and 33·8 times as heavy as the sun. Plaskett’s star B.D. 6° 1309 is certainly heavier still, its components weighing at least 75 and 63 times as much as the sun, and probably more; the exact weights are not known (see p. 55 below). The system 27 Canis Majoris consists of four stars, whose combined weight, according to the evidence at present available, appears to be at least 940 times that of the sun, but we may properly exercise a certain amount of caution before accepting a figure so far outside the usual run of stellar weights.

The average constituent star in the above very short table has 0·94 times the weight of the sun, so that our sun appears to be of rather more than average weight, and this is confirmed by a more extensive study of stellar weights.

We might have expected a priori that the stars would prove to have all sorts of weights, for there is no obvious reason why stars should not exist with weights millions of times that of the sun, or again with weights only equal to that of the earth or less. Actually we find that the weights of the stars are mostly fairly equal, very few stars having weights greatly dissimilar from that of the sun. This seems to indicate that a star is a definite species of astronomical product, not a mere random chunk of luminous matter.

LUMINOSITY. The last column of the table on p. 48 gives the “luminosities” of the stars, which means their candle-power as lights, that of the sun being taken as unity. For instance the entry of 26·3 for Sirius means that Sirius, regarded as a lighthouse in space, has 26·3 times the candle-power of the sun. The luminosities of the stars shew an enormously greater range than their weights. In a general way the heaviest stars are found to be the most luminous, as we should naturally expect, but their luminosity is out of all proportion to their weight. The heavier component of Sirius has only 2·9 times the weight of the lighter component, but 10,000 times its luminosity. Again, in the system of Procyon the heavier component has 3·2 times the weight, but 180,000 times the luminosity, of the lighter component. It appears to be an almost universal law that the candle-power per ton is far greater in heavy stars than in light. This is one of the central and, at first sight, one of the most perplexing facts of physical astronomy: it is so fundamental and so pervading that no view of stellar mechanism can be accepted which fails to explain it.

SPECTROSCOPIC VELOCITIES. When a star’s distance is known, its motion across the sky tells us its speed in a direction at right angles to the line along which we look at it—i.e. across the line of sight—but provides no means of discovering its speed along this line. We cannot see the motion of a body which is coming straight towards us, and a star moving at a million miles a second in a direction exactly along the line of sight would yet appear to be standing still in the sky. To evaluate velocities along the line of sight, the astronomer calls in the aid of the spectroscope.

All light is a blend of lights of different colours, and just as Newton, with his famous prism, analysed sunlight into all the colours of the rainbow, so the spectroscope analyses the light from a star, or indeed from any source whatever, into its various constituent colours. The instrument spreads out the analysed light into a strip of light of continuously graduated colour, which is described as a “spectrum.” In this the colours are the same, and are found to be arranged in the same order, as in the rainbow, running from violet through green and orange to red. There is a physical reason for this. We shall see later (p. 114) that light consists of trains of waves—like the ripples which the wind blows up on a pond—and that the different colours of light result from waves of different lengths, red light being produced by the longest waves, and violet light by the shortest. The colours in the spectrum occur in the order of their wave-lengths, from the longest (red) to the shortest (violet). In the typical stellar spectrum certain short ranges of colour or wave-length are generally missing, for reasons we shall discuss later (p. 126), so that the spectrum appears to be crossed by a number of dark lines or bands, thus forming a pattern rather than a continuous gradation of colours. Examples of stellar spectra are shewn in Plate VIII.

It is frequently convenient to classify stars by the type of spectra they emit. It is now known that a star’s spectrum depends primarily upon the temperature of its surface. As a consequence, stellar spectra can, in the main, be arranged in a single continuous sequence, and their usual classification is by a sequence of letters, O, B, A, F, G, K, M with decimal subdivisions, the temperature falling as we pass along the sequence, so that O-type stars have the highest surface-temperatures and M-type stars the lowest. Spectral types are indicated on the left in Plate VIII.

When the light received from a star is analysed in a spectroscope, the pattern of lines or bands may be found to be shifted bodily in one direction or the other. If the shift is towards the red end of the spectrum, the light emitted by the star is reaching us in a redder state than that in which it ought normally to be, and as red light has the longest wave-length, this means that every wave of light is longer—more drawn out—than normal. We conclude that the star is receding from us. In the same way, if the spectral pattern is shifted toward the violet end of the spectrum, we know that the star must be approaching us. The shift of a spectrum resulting from the motion of the body which emits it is generally described as the “Doppler Effect.” From its amount we can calculate a star’s actual speed along the line of sight, and the calculation is surprisingly simple. If each line or band in a spectrum is found to represent a wave-length a hundredth of one per cent. longer than that usually associated with it, then the star’s speed of recession is a hundredth of one per cent. of the velocity of light, or 18·6 miles a second—and similarly for all other displacements.

SPECTROSCOPIC BINARIES. As the two components of a binary system are generally moving with different speeds, the normal spectrum of a binary system consists of two distinct superposed spectra, the two spectra shewing different shifts which correspond to the speeds of the two components. From the observed orbits of the two components of a binary system, an astronomer might proceed to calculate with what speeds these components would move in the direction of the line of sight, and could then predict to what extent the two spectra ought to be displaced if the light from the system were analysed in a spectroscope; the spectroscope would of course confirm his prediction.

It is more instructive to imagine the reverse process. Suppose that on analysing the light from a star, the astronomer obtains a composite spectrum in which two distinct spectra shift rhythmically backwards and forwards about their normal position. The fact that there are two spectra tells him that he is dealing with a binary system; if the rhythmic shift repeats itself every two years, he knows that its orbit takes two years to complete. He studies the star by direct vision and finds it is a binary system in which the constituents revolve about one another every two years.

He examines another spectrum, and finds that it shifts rhythmically every two days. On looking directly at this star he can only see a single point of light. There must, of course, be two stars, but the mere fact that they get around one another in so short a time as two days proves that they must be very close to one another, and he need feel no surprise that his telescope has failed to separate the image into two distinct points of light. Systems of this kind, which the spectroscope shews to be binary, but the telescope usually shews as a single point of light, are called “spectroscopic binaries.” Over a thousand such systems are known.

If the astronomer tries to construct the orbit of such a system from the spectroscopic observations alone, he finds himself in difficulties. His observations only tell him the velocities along the line of sight, and these depend both on the actual speed and on the degree of foreshortening; the same velocity may arise either from a big orbit in a plane nearly at right angles to the line of sight, or from a much foreshortened little orbit. It is impossible to calculate the actual orbit or the weights of the stars from spectroscopic observation alone.

ECLIPSING BINARIES. There is one exception. Suppose that a star’s light is seen to diminish in amount at regular intervals and subsequently to return to its original strength. The obvious interpretation of the diminution of light is that one component of the system is eclipsing the other, and this can only happen if the orbit is so completely foreshortened that its plane passes through, or at least very close to, the earth. In such a case it is possible to reconstruct the whole orbit, and thence to calculate the weights of the two components. Not only so, but the length of time during which the eclipses last tells us the actual sizes of the two components, so that it is possible to draw a complete picture of the system. Diagrams of the dimensions and orbits of two typical eclipsing binaries are shewn in fig. 6; these are drawn to the same scale, this being indicated by the small circle representing the sun.

When no eclipse occurs in a spectroscopic binary, we do not know how much foreshortening to allow for, but we can obtain a general idea of the weights of the components by assuming an average degree of foreshortening. If we assume different degrees of foreshortening in turn, we shall find that the computed weights come out least when the plane of the orbit is assumed to pass through the earth—i.e. when the orbits are computed as though the system were an eclipsing one. Thus although we cannot discover the actual weights of the components of a non-eclipsing binary, we can always state limits above which they must lie, namely the weights computed as though the system were an eclipsing one. In this way, we know that the two components of Plaskett’s star must have more than 75 and 63 times the weight of the sun.

VARIABLE STARS

The majority of stars shine with a perfectly steady light, so that we can say that a star is of so many candle-power. The sun, for instance, emits a light of 3·23 × 10²⁷ candle-power.

Yet there are classes of exceptional stars in which the light flickers up and down. In some, as in the eclipsing binaries just described, the light-fluctuations are quite regular, repeating themselves with such precision that the stars might well be used as time-keepers. In others the fluctuations, though not perfectly regular, are nearly so, while still others exist in which the fluctuations appear at present to be completely irregular, although no doubt the changes in these will be reduced to law and order in due course. For our present discussion, the various types of irregular variables are not of great importance.

CEPHEID VARIABLES. The really interesting stars are those of a certain class of regular variable, generally called “Cepheid variables,” after their prototype δ Cephei. The physical nature of these stars and the mechanism of their light-fluctuation is still far from being understood; competing theories are in the field which we need not discuss at this stage (see p. 223 below).

Whatever their mechanism may be, observation shews that these stars possess a certain definite property, which proves to be of the utmost value. This being so, we may accept it gratefully without troubling as to its why and wherefore. The perfectly regular light-fluctuations of the eclipsing binaries would make them suitable for time-keepers even though we did not understand the mechanism behind these fluctuations. In the same way the fluctuations of Cepheid variables have a quality which makes them valuable as measuring-rods with which to survey the distant parts of the universe. In brief, this property is that we can deduce the intrinsic brightness of these stars, and so their distances, from their observed light-fluctuations.

The light-fluctuations are so distinctive as to make the stars easy of detection. There is a rapid increase of light, followed by a slow gradual decline; then again the same rapid increase and slow decline as before. It is as though someone were throwing armfuls of fuel on to a bonfire at perfectly regular intervals.

One other class of variable stars, generally known as “long-period variables,” shews somewhat similar light-fluctuations, but the two classes are easily distinguished by their very different periods of light-fluctuation. The Cepheid variable completes its cycle in a time which may be a few hours, or may be days or weeks, but is never more than about a month, whereas the long-period variable generally requires about a year.

Fig. 7 shews the light curves of typical variable stars of the different classes. In each diagram the progress of time is represented by motion across the page from left to right; the higher the fluctuating curve is above the horizontal line at any instant, the brighter the star at that instant.

Out near the boundary of the galactic system is a cluster of stars known as the Lesser Magellanic Cloud (Plate XXI, p. 214), in which Cepheid variables occur in great profusion. In 1912, Miss Leavitt of Harvard found that the light of the brighter Cepheids in this cloud fluctuated more slowly than the light of the fainter ones. Whatever was responsible for turning the stellar lights up and down, acted more rapidly for feeble than for brilliant lights. The apparent brightnesses of a number of Cepheids at varying distances would of course depend only in part on their intrinsic brightness or candle-power, but the stars in the Magellanic Cloud are all, nearly enough, at the same distance from the earth. Thus differences in the apparent brightnesses of stars in this cloud must represent real differences of intrinsic brightness, and Miss Leavitt’s discovery could be stated in the form that the period of light-fluctuation of a Cepheid depended on its candle-power. Although this was only proved for the Cepheids in the Magellanic Cloud, it must be true for all Cepheids wherever they are, for it is inconceivable that we could make a star’s light fluctuate more slowly or more rapidly merely by altering its distance from us—by ourselves receding from it, in fact.

Professor Hertzsprung of Leiden and Dr Shapley, then of Mount Wilson Observatory, were quick to seize upon the implications of this discovery. If two Cepheids A, B in different parts of the sky are found to fluctuate with equal rapidities, then their intrinsic candle-powers must be equal. Thus any difference in their apparent brightness must be traceable to a difference in their distances from us. If A looks a hundred times as bright as B, then B must be at ten times the distance of A. In the same way, a third Cepheid C may prove to be at ten times the distance of B. We now know that C is a hundred times as remote as A. And if D can be found ten times as distant as C, we know that D is a thousand times as remote as A. So we can go on constructing and ever extending our measuring-rod; there is no limit until we reach distances so great that even Cepheid variables, which are exceptionally bright stars, fade into invisibility.

So far we have only considered the comparative distances of Cepheids. The absolute distances of many of the nearer Cepheids have, however, been determined by the parallactic method already explained—i.e. by measuring their apparent motion in the sky, resulting from the earth’s motion round the sun. Taking any one of these stars as our original Cepheid A, we can step continually from one Cepheid to another, and so calculate the absolute distances of all the Cepheid variables in the sky.

In this way the observed relation between the period of fluctuation and the brightness of Cepheid variables—commonly known as the “period-luminosity law”—can be made to provide a scale on which the absolute luminosity, or candle-power, of a Cepheid can be read off directly from the observed period of its light-fluctuations. The Cepheid variables may be regarded as lighthouses set up in distant parts of the universe. We can recognise them, just as a sailor recognises lighthouses, by the quality of their light. We can read off their candle-power from the period of their observed light-fluctuations as easily as the sailor could read off the candle-power of a lighthouse from an Admiralty chart. The apparent brightness of the Cepheid informs us as to its distance from us[7].

It would be difficult to over-estimate the importance of all this to modern astronomical science. It means that a method has been found for surveying, if not the whole of the universe, at least those parts of it in which Cepheid variables are visible. Actually this last reservation is unimportant, for Cepheid variables are very freely scattered in space. Naturally the method is of most value for the exploration of the most distant parts of the universe; here it achieves triumphant success where other methods fail completely. The parallactic method begins to fail when we try to sound distances of more than about a hundred light-years. The apparent path in the sky, which a star at this distance describes, in consequence of the earth’s motion round the sun, is of the size of a pin-head two miles away. With all their refinements, modern instruments find it difficult enough to detect so small a motion as this, and it is practically impossible to measure it with accuracy. The “period-luminosity” law measures the distances of objects up to a million light-years away, with a smaller percentage of error than is to be expected in the parallactic measures of stars only a hundred light-years away.

SOUNDING SPACE

This by no means exhausts the list of modern methods of surveying space. Any standard type of astronomical object, which is easily recognisable and emits the same amount of light no matter where it occurs, provides an obvious means of measuring astronomical distances, for when once the intrinsic luminosity of such an object has been determined, the distance of every example of it can be estimated from its apparent brightness.

Cepheid variables of assigned periods provide the most striking instance of such standard objects, but three others are available, although they are not so generally useful as Cepheids. First comes another type of variable star, the “long-period variables” already mentioned, which are generally similar to Cepheids except that their light fluctuates much more slowly. These stars are intrinsically far more luminous even than Cepheids, many of them being 10,000 times as luminous as the sun. They are accordingly visible at enormous distances, and may ultimately be found to provide a means of sounding depths of space at which even Cepheids are lost to sight.

Next come “novae” or new stars. Every now and then an ordinary star in the sky suddenly bursts out in a phenomenal blaze of light, shining with perhaps a thousand times its original brilliance. The cause of these violent outbursts is still a matter for debate, and no thoroughly convincing explanation has as yet been given. A study of comparatively near novae has, however, provided information as to the luminosity of the average nova when at its brightest, and as novae appear in various parts of the sky, and particularly in the extra-galactic nebulae, they provide a rough means of measuring stellar and nebular distances.

Blue stars provide yet another method. These are exceedingly luminous, and they vary but little in intrinsic luminosity. Moreover, the luminosity of any particular star can generally be estimated fairly closely from the quality of the light it emits, by methods which will be explained later. This makes it possible to determine the distances of blue stars, and so of course of the astronomical objects in which they occur.

Still two other methods of a different kind may be briefly mentioned. Dr W. S. Adams, Director of Mount Wilson Observatory, and others have found that certain definite peculiarities in the spectra of certain classes of stars convey information as to the intrinsic brightness of the star emitting them; with this information it is easy to estimate the star’s distance from its apparent brightness. This is commonly described as the method of Spectroscopic Parallaxes.

Finally the diffuse cloud of nebular matter which is spread through interstellar space (p. 30) is found to affect the quality of light travelling through it, so that a star’s spectrum gives an indication of the amount of cloud through which the light of the star has travelled, and this again provides a rough means of estimating distances inside the galactic system.

GLOBULAR CLUSTERS. The law of Cepheid luminosity was first used by Hertzsprung to estimate the distance of the Lesser Magellanic Cloud, the study of which had been responsible for the original discovery of the law. Shapley subsequently used it to determine the distances of the rather mysterious groups of stars known as “Globular Clusters.” A typical example of these is shewn in Plate IX. About 100 of these clusters are known and they all look pretty much alike, except for differences in apparent size. Even these latter can be traced mainly to differences of distance, so that the globular clusters are probably almost identical objects, and Plate IX might almost be regarded as a picture of any one of them. Cepheid variables abound in them all.

Shapley found the nearest globular cluster, ω Centauri, to lie at a distance of about 22,000 light-years, the furthest, N.G.C. 7006, being about ten times as remote, at a distance of 220,000 light-years. At such distances the parallactic method of measuring distances would of course fail hopelessly. The parallactic orbit of a star at 220,000 light-years’ distance is about the size of a pin-head held at a distance of 4000 miles; no telescope on earth could detect, still less measure, such an orbit.

The mere figure of 220,000 light-years can convey but little conception of the distance of this remotest of star-clusters from us. We may apprehend it better if we reflect that the light by which we see the cluster started on its long journey from it to us somewhere about the time when primaeval man first appeared on earth. Through the childhood, youth and age of countless generations of men, through the long prehistoric ages, through the slow dawn of civilisation and through the whole span of time which history records, through the rise and fall of dynasties and empires, this light has travelled steadily on its course, covering 186,000 miles every second, and is only just reaching us now. And yet this enormous stretch of space does not carry us to the confines of the universe; we shall now see that in all probability it has barely carried us to the confines of the galactic system.

Shapley has mapped out the complete system of the globular clusters, and finds that they occupy an oblong region, lying on both sides of the plane of the Milky Way, its greatest diameter of about 250,000 light-years lying in this plane, and its two transverse diameters being considerably shorter. The sun is nearer to the edge of this oblong region than to its centre, which explains why all the globular clusters appear in one half of the sky, as Hinks first noted in 1911. The general arrangement is shewn in fig. 8. The page of the book represents the plane of the Milky Way, the various dots representing the points in this plane which are nearest to the different clusters, so that the diagram exhibits the system of globular clusters as they would appear to an observer out in space who viewed the galactic plane “full-on.” All the globular clusters except N.G.C. 7006 lie within a circle of about 125,000 light-years’ radius, having its centre at about 50,000 light-years from the sun.

THE ARRANGEMENT OF THE GALACTIC SYSTEM. Although the matter has long been one of vigorous controversy, it is now becoming clear that the region of space mapped out by these globular clusters approximately coincides with that occupied by the galactic system itself. Herschel and Kapteyn appear to have been in error in supposing the centre of the galactic system to be in the neighbourhood of the sun; a considerable accumulation of evidence indicates that it lies in a massive star-cloud in the constellations of Ophiuchus and Scorpio. Dr Shapley and Miss Swope, at Harvard Observatory, have recently determined the distance of this star-cloud from the sun as 47,000 light-years, which places it almost exactly at the centre of the system of globular clusters, as shewn in fig. 8. There is what Shapley describes as a “local system” of fairly bright stars surrounding the sun, and the error of identifying this with the main galactic system has apparently been responsible for a large part of the confusion which has hitherto beset the problem of the architecture of the galaxy. This local system has the same flattened shape as the main system, but it does not lie exactly in the plane of the Milky Way, being inclined at an angle of about 12 degrees to it. The sun appears to lie very near to the plane of the central plane of the system; recent determinations place it about 100 light-years to the north of this plane. Fig. 9 shews a cross-section of the system, as it is now imagined to lie.

We have already compared the shape of the galactic system to that of a wheel. It obviously could not retain this shape if the stars which formed it were standing still in space. For the gravitational pull of the inner stars would cause the outermost stars—the rim of the wheel—to fall inwards, and the system would end as a confused jumble of stars somewhere in the vicinity of the hub of the wheel. In 1913, Henri Poincaré, Professor of Mathematics at the Sorbonne, suggested that the galactic “wheel” might escape this fate if it were in a state of rotation. Just as the earth’s motion saves it from falling into the sun, and the moon’s motion saves it from falling on to the earth, so, Poincaré suggested, the stars which form the rim of the wheel might be saved from falling into the hub, by a motion of rotation of the whole wheel. A rough calculation suggested that it would be necessary for the wheel to rotate at the rate of a complete revolution about every 500 million years.

Naturally it is no simple matter to detect so slow a rotation. It was first suspected to occur in the following way. We know that when a spinning-top or gyroscope is set in rapid rotation, a considerable force is needed to twist the top or gyroscope about in space. This is the principle of the gyroscopic compass such as is used to steer ships. A gyroscope, a sort of big steel spinning-top, is started spinning with its two ends pivoted in a swinging frame. No matter how the ship turns, the motion of the gyroscope keeps the frame pointing away in the same direction, and by the help of this fixed direction the ship is kept on its course. Now the solar system has many of the properties of a huge spinning-top, the revolutions of the planets corresponding to the spin of the top. As there is no twist impressed on this “spinning-top” from outside, its axis of rotation must always point in the same direction, thus providing a sort of “gyroscopic compass” to give us our bearings in space.

In 1913 Charlier believed he had found that this “gyroscopic compass” was turning round against the distant background of the Milky Way, at the rate of a complete rotation every 370 million years, a period which subsequent measurements increased to 530 million years. Eddington then suggested that it might be the background rather than the gyroscopic compass that was turning, the Milky Way actually rotating in the way imagined by Poincaré, and at just about the rate which Poincaré had calculated.

Recent investigations by Oort, Plaskett, Lindblad and others prove beyond doubt that such a rotation really occurs, although it is not of the simple “cart-wheel type” we have so far discussed. In the solar system the innermost planets move more rapidly than the outermost: they must necessarily do so if the motion of each planet is to counteract the sun’s attraction. In the same way, if the rotational motion of the galaxy is to counteract the gravitational attraction of its innermost stars, its inner parts must rotate more rapidly than its outermost. Thus the sun ought to be overtaking those stars which lie outside it on the galactic wheel, while being itself overtaken by those which lie inside it. Such an overtaking motion is fairly easy to detect. A careful analysis of observed stellar motions has disclosed such a motion, shewing that the galaxy as a whole is in rotation in precisely the way just described, the inner parts rotating most rapidly.

The hub of this gigantic wheel lies almost exactly in the direction which Shapley assigned to the centre of the galaxy from his study of the globular clusters. Its distance from the sun, which cannot yet be determined with any great accuracy, is probably somewhere about 37,000 light-years. To within the limits of accuracy which are at present attainable, this places the centre of the galactic wheel at the centre of the system of globular clusters (see fig. 8, p. 64). In the vicinity of the sun, the galactic wheel performs a complete revolution in a period of about 230 million years, and this endows the stars near the sun with a motion through space at a speed of nearly 200 miles a second, arising from the rotation of the galaxy alone.

With these data, it is possible to weigh the stars of the galactic system en masse. Individual stars far away from the centre of the galactic system must be describing orbits under the gravitational pull of the system as a whole, the pull which prevents the stars from scattering away into space, and so keeps the galactic system in being. The aggregate of these orbital motions produces the general rotation of the galaxy which we have just discussed. And from the figures just mentioned, it can be calculated that the total weight of matter inside the sun’s orbit must be about that of 240,000 million suns. Part of this may of course arise from interstellar dust or gas. Nevertheless, as the average star weighs considerably less than the sun, the total number of stars in the galactic system may well be of the order of 400,000 million. This estimate of course includes all stars, dark as well as luminous, but there are reasons for believing that the number of dark stars is comparatively small (see p. 269 below).

Other estimates of the number of stars in the galaxy have been made, generally lower than the foregoing. Two estimates by Lindblad, for instance, give the total weight of the galaxy as 110,000 and 180,000 million suns respectively.

Again we are confronted with the difficulty of visualising such large numbers. With perfect eyesight on a clear moonless night we can see about 3000 stars. Imagine each of these 3000 stars to spread out into a complete sky-full of 3000 new stars, and we are contemplating 9 million stars, which is still only the number visible in a telescope of 5 inches aperture. We probably cannot ask our imagination to play the same trick for us a second time, but if it can be persuaded to do so, and if we can think of each of these 9 million stars as again generating a whole sky-full of stars, we still have only 27,000 million stars within our purview—a number which is still far below any permissible estimate of the total number of stars in the galactic system. Or again, let us notice that the number of stars photographically visible in the 100-inch telescope, namely 1500 million, is about equal to the number of men, women and children in the world. Each inhabitant of the earth—each man, woman and child living in the five continents or travelling on the seven seas—can be allowed to choose his own particular star, and can then repeat the process tens, and more probably hundreds, of times without going outside the galactic system.

After this we can still go exploring outside the galactic system and find more and ever more stars. The galactic system, with its hundreds of millions of stars, no more contains all the stars in space than one house contains all the inhabitants of Great Britain. There are millions of other houses and millions of other families of stars.

THE EXTRA-GALACTIC NEBULAE. We have already spoken of the faint nebulous objects which Herschel described, somewhat conjecturally, as “island universes.” These are the other houses in which other families of stars are to be found. The most powerful of modern telescopes shew that they consist, in part at least, of huge clouds of stars. Just as a powerful microscope shews that a puff of cigarette smoke, in spite of its appearance of continuity, consists of a cloud of minute but quite distinct particles, so a powerful modern telescope breaks up the light from the outer regions of these nebulae into distinct spots of light; the nebula is resolved into a cloud of shining particles, just as the Milky Way was in Galileo’s tiny telescope of three centuries ago. Plate XI shews an example; it represents a magnification of a small area in the top left-hand corner of the Great Nebula M 31 in Andromeda already shewn in Plate IV (p. 30), and the resolution into distinct spots of light is unmistakable. We know that some at least of these spots of light are stars, because we recognise them as Cepheid variables, their light shewing the unmistakable characteristic fluctuations of the familiar Cepheid variables nearer home. The other shining particles are of comparable brightness and shew about the range of brightness above and below that of the Cepheids which is needed to justify us in supposing that they are ordinary stars.