The sun, with his attendant host of planets and satellites, may be likened to the ship. The planets may revolve around the sun just as the passengers may move about in the cabin, but as the passengers, by looking at objects on board, can never tell whither the ship is going, so we, by merely looking at the sun, or at the other planets or members of the solar system, can never tell if our system as a whole is in motion.

The conditions of a perfectly uniform movement along a perfectly calm sea are not often fulfilled on the waters with which we are acquainted, but the course of the sun and his system is untroubled by any disturbance, so that the majestic progress is conducted with absolute uniformity. We do not feel the motion; and as all the planets are travelling with us, we can get no information from them as to the common motion by which the whole system is animated.

The passengers are, however, at once apprised of the ship's motion when they go on deck, and when they look at the sea surrounding them. Let us suppose that their voyage is nearly accomplished, that the distant land appears in sight, and, as evening approaches, the harbour is discerned into which the ship is to enter. Let us suppose that the harbour has, as is often the case, a narrow entrance, and that its mouth is indicated by a lighthouse on each side. When the harbour is still a long way off, near the horizon, the two lights are seen close together, and now that the evening has closed in, and the night has become quite dark, these two lights are all that remain visible. While the ship is still some miles from its destination the two lights seem close together, but as the distance decreases the two lights seem to open out; gradually the ship gets nearer, while the lights are still opening, till finally, when the ship enters the harbour, instead of the two lights being directly in front, as at the commencement, one of the lights is passed by on the right hand, while the other is similarly found on the left. If, then, we are to discover the motion of the solar system, we must, like the passenger, look at objects unconnected with our system, and learn our own motion by their apparent movements. But are there any objects in the heavens unconnected with our system? If all the stars were like the earth, merely the appendages of our sun, then we never could discover whether we were at rest or whether we were in motion: our system might be in a condition of absolute rest, or it might be hurrying on with an inconceivably great velocity, for anything we could tell to the contrary. But the stars do not belong to the system of our sun; they are, rather, suns themselves, and do not recognise the sway of our sun, as this earth is obliged to do. The stars will, therefore, act as the external objects by which we can test whether our system is voyaging through space.

With the stars as our beacons, what ought we to expect if our system be really in motion? Remember that when the ship was approaching the harbour the lights gradually opened out to the right and left. But the astronomer has also lights by which he can observe the navigation of that vast craft, our solar system, and these lights will indicate the path along which he is borne. If our solar system be in motion, we should expect to find that the stars were gradually spreading away from that point in the heavens towards which our motion tends. This is precisely what we do find. The stars in the constellations are gradually spreading away from a central point near the constellation of Lyra, and hence we infer that it is towards Lyra that the motion of the solar system is directed.

There is one great difficulty in the discussion of this question. Have we not had occasion to observe that the stars themselves are in actual motion? It seems certain that every star, including the sun himself as a star, has each an individual motion of its own. The motions of the stars as we see them are partly apparent as well as partly real; they partly arise from the actual motion of each star and partly from the motion of the sun, in which we partake, and which produces an apparent motion of the star. How are these to be discriminated? Our telescopes and our observations can never effect this decomposition directly. To accomplish the analysis, Herschel resorted to certain geometrical methods. His materials at that time were but scanty, but in his hands they proved adequate, and he boldly announced his discovery of the movement of the solar system.

So astounding an announcement demanded the severest test which the most refined astronomical resources could suggest. There is a certain powerful and subtle method which astronomers use in the effort to interpret nature. Bishop Butler has said that probability is the guide of life. The proper motion of a star has to be decomposed into two parts, one real and the other apparent. When several stars are taken, we may conceive an infinite number of ways into which the movements of each star can be so decomposed. Each one of these conceivable divisions will have a certain element of probability in its favour. It is the business of the mathematician to determine the amount of that probability. The case, then, is as follows:—Among all the various systems one must be true. We cannot lay our finger for certain on the true one, but we can take that which has the highest degree of probability in its favour, and thus follow the precept of Butler to which we have already referred. A mathematician would describe his process by calling it the method of least squares. Since Herschel's discovery, one hundred years ago, many an astronomer using observations of hundreds of stars has attacked the same problem. Mathematicians have exhausted every refinement which the theory of probabilities can afford, but only to confirm the truth of that splendid theory which seems to have been one of the flashes of Herschel's genius.



CHAPTER XXII.

STAR CLUSTERS AND NEBULAE.

Interesting Sidereal Objects—Stars not Scattered uniformly—Star Clusters—Their Varieties—The Cluster in Perseus—The Globular Cluster in Hercules—The Milky Way—A Cluster of Minute Stars—The Magellanic Clouds—Nebulae distinct from Clouds—Number of known Nebulae—The Constellation of Orion—The Position of the Great Nebula—The Wonderful Star th Orionis—The Drawing of the Great Nebula in Lord Rosse's Telescope—Photographs of this Wonderful Object—The Great Nebula in Andromeda—The Annular Nebula in Lyra—Resemblance to Vortex Rings—Planetary Nebulae—Drawings of Several Remarkable Nebulae—Nature of Nebulae—Spectra of Nebulae—Their Distribution; the Milky Way.

We have already mentioned Saturn as one of the most glorious telescopic spectacles in the heavens. Setting aside the obvious claims of the sun and of the moon, there are, perhaps, two other objects visible from these latitudes which rival Saturn in the splendour and the interest of their telescopic picture. One of these objects is the star cluster in Hercules; the other is the great nebula in Orion. We take these objects as typical of the two great classes of bodies to be discussed in this chapter, under the head of Star Clusters and Nebulae.

The stars, which to the number of several millions bespangle the sky, are not scattered uniformly. We can see that while some regions are comparatively barren, others contain stars in profusion. Sometimes we have a small group, like the Pleiades; sometimes we have a stupendous region of the heavens strewn over with stars, as in the Milky Way. Such objects are called star clusters. We find every variety in the clusters; sometimes the stars are remarkable for their brilliancy, sometimes for their enormous numbers, and sometimes for the remarkable form in which they are grouped. Sometimes a star cluster is adorned with brilliantly-coloured stars; sometimes the luminous points are so close together that their separate rays cannot he disentangled; sometimes the stars are so minute or so distant that the cluster is barely distinguishable from a nebula.

Of the clusters remarkable at once both for richness and brilliancy of the individual stars, we may mention the cluster in the Sword-handle of Perseus. The position of this object is marked on Fig. 83, page 415. To the unaided eye a hazy spot is visible, which in the telescope expands into two clusters separated by a short distance. In each of them we have innumerable stars, crowded together so as to fill the field of view of the telescope. The splendour of this object may be appreciated when we reflect that each one of these stars is itself a brilliant sun, perhaps rivalling our own sun in lustre. There are, however, regions in the heavens near the Southern Cross, of course invisible from northern latitudes, in which parts of the Milky Way present a richer appearance even than the cluster in Perseus.

The most striking type of star cluster is well exhibited in the constellation of Hercules. In this case we have a group of minute stars apparently in a roughly globular form. Fig. 96 represents this object as seen in Lord Rosse's great telescope, and it shows three radiating streaks, in which the stars seem less numerous than elsewhere. It is estimated that this cluster must contain from 1,000 to 2,000 stars, all concentrated into an extremely small part of the heavens. Viewed in a very small telescope, this object resembles a nebula. The position of the cluster in Hercules is shown in a diagram previously given (Fig. 88, page 420). We have already referred to this glorious aggregation of stars as one of the three especially interesting objects in the heavens.



The Milky Way forms a girdle which, with more or less regularity, sweeps completely around the heavens; and when viewed with the telescope, is seen to consist of myriads of minute stars. In some places the stars are much more numerous than elsewhere. All these stars are incomparably more distant than the sun, which they surround, so it is evident that our sun and, of course, the system which attends him lie actually inside the Milky Way. It seems tempting to pursue the thought here suggested, and to reflect that the whole Milky Way may, after all, be merely a star cluster, comparable in size with some of the other star clusters which we see, and that, viewed from a remote point in space, the Milky Way would seem to be but one of the many clusters of stars containing our sun as an indistinguishable unit.



In the southern hemisphere there are two immense masses which are conspicuously visible to the naked eye, and resemble detached portions of the Milky Way. They cannot be seen by observers in our latitude, and are known as the Magellanic clouds or the two nubeculae. Their structure, as revealed to an observer using a powerful telescope, is of great complexity. Sir John Herschel, who made a special study of these remarkable objects, gives the following description of them: "The general ground of both consists of large tracts and patches of nebulosity in every stage of resolution, from light irresolvable, in a reflector of eighteen inches aperture, up to perfectly separated stars like the Milky Way, and clustering groups sufficiently insulated and condensed to come under the designation of irregular and in some cases pretty rich clusters. But besides these there are also nebulae in abundance and globular clusters in every state of condensation." It can hardly be doubted that the two nubeculae, which are, roughly speaking, round, or, rather, oval, are not formed accidentally by a vast number of very different objects being ranged at various distances along the same line of sight, but that they really represent two great systems of objects, widely different in constitution, which here are congregated in each other's neighbourhood, whereas they generally do not co-exist close to each other in the Milky Way, with which the mere naked-eye view would otherwise lead us to associate the Magellanic clouds.

When we direct a good telescope to the heavens, we shall occasionally meet with one of the remarkable celestial objects which are known as nebulae. They are faint cloudy spots, or stains of light on the black background of the sky. They are nearly all invisible to the naked eye. These celestial objects must not for a moment be confounded with clouds, in the ordinary meaning of the word. The latter exist only suspended in the atmosphere, while nebulae are immersed in the depths of space. Clouds shine by the light of the sun, which they reflect to us; nebulae shine with no borrowed light; they are self-luminous. Clouds change from hour to hour; nebulae do not change even from year to year. Clouds are far smaller than the earth; while the smallest nebula known to us is incomparably greater than the sun. Clouds are within a few miles of the earth; the nebulae are almost inconceivably remote.

Immediately after Herschel and his sister had settled at Slough he commenced his review of the northern heavens in a systematic manner. For observations of this kind it is essential that the sky be free from cloud, while even the light of the moon is sufficient to obliterate the fainter and more interesting objects. It was in the long and fine winter nights, when the stars were shining brilliantly and the pale path of the Milky Way extended across the heavens, that the labour was to be done. The telescope being directed to the heavens, the ordinary diurnal motion by which the sun and stars appear to rise and set carries the stars across the field of view in a majestic panorama. The stars enter slowly into the field of view, slowly move across it, and slowly leave it, to be again replaced by others. Thus the observer, by merely remaining passive at the eye-piece, sees one field after another pass before him, and is enabled to examine their contents. It follows, that even without moving the telescope a long narrow strip of the heavens is brought under review, and by moving the telescope slightly up and down the width of this strip can be suitably increased. On another night the telescope is brought into a different position, and another strip of the sky is examined; so that in the course of time the whole heavens can be carefully scrutinised.

Herschel stands at the eye-piece to watch the glorious procession of celestial objects. Close by, his sister Caroline sits at her desk, pen in hand, to take down the observations as they fall from her brother's lips. In front of her is a chronometer from which she can note the time, and a contrivance which indicates the altitude of the telescope, so that she can record the exact position of the object in connection with the description which her brother dictated. Such was the splendid scheme which this brother and sister had arranged to carry out as the object of their life-long devotion. The discoveries which Herschel was destined to make were to be reckoned not by tens or by hundreds, but by thousands. The records of these discoveries are to be found in the "Philosophical Transactions of the Royal Society," and they are among the richest treasures of those volumes. It was left to Sir John Herschel, the only son of Sir William, to complete his father's labour by repeating the survey of the northern heavens and extending it to the southern hemisphere. He undertook with this object a journey to the Cape of Good Hope, and sojourned there for the years necessary to complete the great work.



As the result of the gigantic labours thus inaugurated and continued by other observers, there are now about eight thousand nebulae known to us, and with every improvement of the telescope fresh additions are being made to the list. They differ from one another as eight thousand pebbles selected at random on a sea-beach might differ—namely, in form, size, colour, and material—but yet, like the pebbles, bear a certain generic resemblance to each other. To describe this class of bodies in any detail would altogether exceed the limits of this chapter; we shall merely select a few of the nebulae, choosing naturally those of the most remarkable character, and also those which are representatives of the different groups into which nebulae may be divided.



We have already stated that the great nebula in the constellation of Orion is one of the most interesting objects in the heavens. It is alike remarkable whether we consider its size or its brilliancy, the care with which it has been studied, or the success which has attended the efforts to learn something of its character. To find this object, we refer to Fig. 97 for the sketch of the chief stars in this constellation, where the letter A indicates the middle one of the three stars which form the sword-handle of Orion. Above the handle will be seen the three stars which form the well-known belt so conspicuous in the wintry sky. The star A, when viewed attentively with the unaided eye, presents a somewhat misty appearance. In the year 1618 Cysat directed a telescope to this star, and saw surrounding it a curious luminous haze, which proved to be the great nebula. Ever since his time this object has been diligently studied by many astronomers, so that very many observations have been made of the great nebula, and even whole volumes have been written which treat of nothing else. Any ordinary telescope will show the object to some extent, but the more powerful the telescope the more are the curious details revealed.



In the first place, the object which we have denoted by A (th Orionis, also called the trapezium of Orion) is in itself the most striking multiple star in the whole heavens. It consists really of six stars, represented in the next diagram (Fig. 98). These points are so close together that their commingled rays cannot be distinguished without a telescope. Four of them are, however, easily seen in quite small instruments, but the two smaller stars require telescopes of considerable power. And yet these stars are suns, comparable, it may be, with our sun in magnitude.

It is not a little remarkable that this unrivalled group of six suns should be surrounded by the renowned nebula; the nebula or the multiple star would, either of them alone, be of exceptional interest, and here we have a combination of the two. It seems impossible to resist drawing the conclusion that the multiple star really lies in the nebula, and not merely along the same line of vision. It would, indeed, seem to be at variance with all probability to suppose that the presentation of these two exceptional objects in the same field of view was merely accidental. If the multiple star be really in the nebula, then this object affords evidence that in one case at all events the distance of a nebula is a quantity of the same magnitude as the distance of a star. This is unhappily almost the entire extent of our knowledge of the distances of the nebulae from the earth.

The great nebula of Orion surrounds the multiple star, and extends out to a vast distance into the neighbouring space. The dotted circle drawn around the star marked A in Fig. 97 represents approximately the extent of the nebula, as seen in a moderately good telescope. The nebula is of a faint bluish colour, impossible to represent in a drawing. Its brightness is much greater in some places than in others; the central parts are, generally speaking, the most brilliant, and the luminosity gradually fades away as the edge of the nebula is approached. In fact, we can hardly say that the nebula has any definite boundary, for with each increase of telescopic power faint new branches can be seen. There seems to be an empty space in the nebula immediately surrounding the multiple star, but this is merely an illusion, produced by the contrast of the brilliant light of the stars, as the spectroscopic examination of the nebula shows that the nebulous matter is continuous between the stars.

The plate of the great nebula in Orion which is here shown (Plate XIV.) represents, in a reduced form, the elaborate drawing of this object, which has been made with the Earl of Rosse's great reflecting telescope at Parsonstown.[40] A telescopic view of the nebula shows two hundred stars or more, scattered over its surface. It is not necessary to suppose that these stars are immersed in the substance of the nebula as the multiple star appears to be; they may be either in front of it, or, less probably, behind it, so as to be projected on the same part of the sky.



A considerable number of drawings of this unique object have been made by other astronomers. Among these we must mention that executed by Professor Bond, in Cambridge, Mass., which possesses a faithfulness in detail that every student of this object is bound to acknowledge. Of late years also successful attempts have been made to photograph the great nebula. The late Professor Draper was fortunate enough to obtain some admirable photographs. In England Mr. Common was the first to take most excellent photographs of the nebula, and superb photographs of the same object have also been obtained by Dr. Roberts and Mr. W.E. Wilson, which show a vast extension of the nebula into regions which it was not previously known to occupy.

The great nebula in Andromeda, which is faintly visible to the unaided eye, is shown in Plate XV., which has been copied with permission from one of the astonishing photographs that Dr. Isaac Roberts has obtained. Two dark channels in the nebula cannot fail to be noticed, and the number of faint stars scattered over its surface is also a point to which attention may be drawn. To find this object we must look out for Cassiopeia and the Great Square of Pegasus, and then the nebula will be easily perceived in the position shown on p. 413. In the year 1885 a new star of the seventh magnitude suddenly appeared close to the brightest part of the nebula, and declined again to invisibility after the lapse of a few months.

The nebula in Lyra is the most conspicuous ring nebula in the heavens, but it is not to be supposed that it is the only member of this class. Altogether, there are about a dozen of these objects. It seems difficult to form any adequate conception of the nature of such a body. It is, however, impossible to view the annular nebulae without being, at all events, reminded of those elegant objects known as vortex rings. Who has not noticed a graceful ring of steam which occasionally escapes from the funnel of a locomotive, and ascends high into the air, only dissolving some time after the steam not so specialised has disappeared? Such vortex rings can be produced artificially by a cubical box, one open side of which is covered with canvas, while on the opposite side of the box is a circular hole. A tap on the canvas will cause a vortex ring to start from the hole; and if the box be filled with smoke, this ring will be visible for many feet of its path. It would certainly be far too much to assert that the annular nebulae have any real analogy to vortex rings; but there is, at all events, no other object known to us with which they can be compared.

The heavens contain a number of minute but brilliant objects known as the planetary nebulae. They can only be described as globes of glowing bluish-coloured gas, often small enough to be mistaken for a star when viewed through a telescope. One of the most remarkable of these objects lies in the constellation Draco, and can be found half-way between the Pole Star and the star g Draconis. Some of the more recently discovered planetary nebulae are extremely small, and they have indeed only been distinguished from small stars by the spectroscope. It is also to be noticed that such objects are a little out of the stellar focus in the refracting telescope in consequence of their blue colour. This remark does not apply to a reflecting telescope, as this instrument conducts all the rays to a common focus.

There are many other forms of nebulae: there are long nebulous rays; there are the wondrous spirals which have been disclosed in Lord Rosse's great reflector; there are the double nebulae. But all these various objects we must merely dismiss with this passing reference. There is a great difficulty in making pictorial representations of such nebulae. Most of them are very faint—so faint, indeed, that they can only be seen with close attention even in powerful instruments. In making drawings of these objects, therefore, it is impossible to avoid intensifying the fainter features if an intelligible picture is to be made. With this caution, however, we present Plate XVI., which exhibits several of the more remarkable nebulae as seen through Lord Rosse's great telescope.



The actual nature of the nebulae offers a problem of the greatest interest, which naturally occupied the mind of the first assiduous observer of nebulae, William Herschel, for many years. At first he assumed all nebulae to be nothing but dense aggregations of stars—a very natural conclusion for one who had so greatly advanced the optical power of telescopes, and was accustomed to see many objects which in a small telescope looked nebulous become "resolved" into stars when scrutinised with a telescope of large aperture. But in 1864, when Sir William Huggins first directed a telescope armed with a spectroscope to one of the planetary nebulae, it became evident that at least some nebulae were really clouds of fiery mist and not star clusters.

We shall in our next chapter deal with the spectra of the fixed stars, but we may here in anticipation remark that these spectra are continuous, generally showing the whole length of spectrum, from red to violet, as in the sun's spectrum, though with many and important differences as to the presence of dark and bright lines. A star cluster must, of course, give a similar spectrum, resulting from the superposition of the spectra of the single stars in the cluster. Many nebulae give a spectrum of this kind; for instance, the great nebula in Andromeda. But it does not by any means follow from this that these objects are only clusters of ordinary stars, as a continuous spectrum may be produced not only by matter in the liquid or solid state, or by gases at high pressure, but also by gases at lower pressure but high temperature under certain conditions. A continuous spectrum in the case of a nebula, therefore, need not indicate that the nebula is a cluster of bodies comparable in size and general constitution with our sun. But if a spectrum of bright lines is given by a nebula, we can be certain that gases at low pressure are present in the object under examination. And this was precisely what Sir William Huggins discovered to be the case in many nebulae. When he first decided to study the spectra of nebulae, he selected for observation those objects known as planetary nebulae—small, round, or slightly oval discs, generally without central condensation, and looking like ill-defined planets. The colour of their light, which often is blue tinted with green, is remarkable, since this is a colour very rare among single stars. The spectrum was found to be totally different to that of any star, consisting merely of three or four bright lines. The brightest one is situated in the bluish-green part of the spectrum, and was at first thought to be identical with a line of the spectrum of nitrogen, but subsequent more accurate measures have shown that neither this nor the second nebular line correspond to any dark line in the solar spectrum, nor can they be produced experimentally in the laboratory, and we are therefore unable to ascribe them to any known element. The third and fourth lines were at once seen to be identical with the two hydrogen lines which in the solar spectrum are named F and g.



Spectrum analysis has here, as on so many other occasions, rendered services which no telescope could ever have done. The spectra of nebulae have, after Huggins, been studied, both visually and photographically, by Vogel, Copeland, Campbell, Keeler, and others, and a great many very faint lines have been detected in addition to those four which an instrument of moderate dimensions shows. It is remarkable that the red C-line of hydrogen, ordinarily so bright, is either absent or excessively faint in the spectra of nebulae, but experiments by Frankland and Lockyer have shown that under certain conditions of temperature and pressure the complicated spectrum of hydrogen is reduced to one green line, the F-line. It is, therefore, not surprising that the spectra of gaseous nebulae are comparatively simple, as the probably low density of the gases in them and the faintness of these bodies would tend to reduce the spectra to a small number of lines. Some gaseous nebulae also show faint continuous spectra, the place of maximum brightness of which is not in the yellow (as in the solar spectrum), but about the green. It is probable that these continuous spectra are really an aggregate of very faint luminous lines.

A list of all the nebulae known to have a gaseous spectrum would now contain about eighty members. In addition to the planetary nebulae, many large and more diffused nebulae belong to this class, and this is also the case with the annular nebula in Lyra and the great nebula of Orion. It is needless to say that it is of special interest to find this grand object enrolled among the nebulae of a gaseous nature. In this nebula Copeland detected the wonderful D3 line of helium at a time when "helium" was a mere name, a hypothetical something, but which we now know to be an element very widely distributed through the universe. It has since been found in several other nebulae. The ease with which the characteristic gaseous spectrum is recognised has suggested the idea of sweeping the sky with a spectroscope in order to pick up new planetary nebulae, and a number of objects have actually been discovered by Pickering and Copeland in this manner, as also more recently by Pickering by examining spectrum photographs of various regions of the sky. Most of these new objects when seen through a telescope look like ordinary stars, and their real nature could never have been detected without the spectroscope.

When we look up at the starry sky on a clear night, the stars seem at first sight to be very irregularly distributed over the heavens. Here and there a few bright stars form characteristic groups, like Orion or the Great Bear, while other equally large tracts are almost devoid of bright stars and only contain a few insignificant ones. If we take a binocular, or other small telescope, and sweep the sky with it, the result seems to be the same—now we come across spaces rich in stars; now we meet with comparatively empty places. But when we approach the zone of the Milky Way, we are struck with the rapid increase of the number of stars which fill the field of the telescope; and when we reach the Milky Way itself, the eye is almost unable to separate the single points of light, which are packed so closely together that they produce the appearance to the naked eye of a broad, but very irregular, band of dim light, which even a powerful telescope in some places can hardly resolve into stars. How are we to account for this remarkable arrangement of the stars? What is the reason of our seeing so few at the parts of the heavens farthest from the Milky Way, and so very many in or near that wonderful belt? The first attempt to give an answer to these questions was made by Thomas Wright, an instrument maker in London, in a book published in 1750. He supposed the stars of our sidereal system to be distributed in a vast stratum of inconsiderable thickness compared with its length and breadth. If we had a big grindstone made of glass, in which had become uniformly imbedded a vast quantity of grains of sand or similar minute particles, and if we were able to place our eye somewhere near the centre of this grindstone, it is easy to see that we should see very few particles near the direction of the axle of the grindstone, but a great many if we looked towards any point of the circumference. This was Wright's idea of the structure of the Milky Way, and he supposed the sun to be situated not very far from the centre of this stellar stratum.



If the Milky Way itself did not exist—and we had simply the fact to build on that the stars appeared to increase rapidly in number towards a certain circle (almost a great circle) spanning the heavens—then the disc theory might have a good deal in its favour. But the telescopic study of the Milky Way, and even more the marvellous photographs of its complicated structure produced by Professor Barnard, have given the death blow to the old theory, and have made it most reasonable to conclude that the Milky Way is really, and not only apparently, a mighty stream of stars encircling the heavens. We shall shortly mention a few facts which point in this direction. A mere glance is sufficient to show that the Milky Way is not a single belt of light; near the constellation Aquila it separates into two branches with a fairly broad interval between them, and these branches do not meet again until they have proceeded far into the southern hemisphere. The disc theory had, in order to explain this, to assume that the stellar stratum was cleft in two nearly to the centre. But even if we grant this, how can we account for the numerous more or less dark holes in the Milky Way, the largest and most remarkable of which is the so-called "coal sack" in the southern hemisphere? Obviously we should have to assume the existence of a number of tunnels, drilled through the disc-like stratum, and by some strange sympathy all directed towards the spot where our solar system is situated. And the many small arms which stretch out from the Milky Way would have to be either planes seen edgeways or the convexities of curved surfaces viewed tangentially. The improbability of these various assumptions is very great. But evidence is not wanting that the relatively bright stars are crowded together along the same zone where the excessively faint ones are so closely packed. The late Mr. Proctor plotted all the stars which occur in Argelander's great atlas of the northern hemisphere, 324,198 in number, on a single chart, and though these stars are all above the tenth magnitude, and thus superior in brightness to that innumerable host of stars of which the individual members are more or less lost in the galactic zone, and on the hypothesis of uniform distribution ought to be relatively near to us, the chart shows distinctly the whole course of the Milky Way by the clustering of these stars. This disposes sufficiently of the idea that the Milky Way is nothing but a disc-like stratum seen projected on the heavenly sphere; after this it is hardly necessary to examine Professor Barnard's photographs and see how fairly bright and very faint regions alternate without any attempt at regularity, in order to become convinced that the Milky Way is more probably a stream of stars clustered together, a stream or ring of incredibly enormous dimensions, inside which our solar system happens to be situated. But it must be admitted that it is premature to attempt to find the actual figure of this stream or to determine the relative distance of the various portions of it.



CHAPTER XXIII.

THE PHYSICAL NATURE OF THE STARS.

Star Spectroscopes—Classification of Stellar Spectra—Type I., with very Few Absorption Lines—Type II., like the Sun—Type III., with Strongly Marked Dark Bands—Distribution of these Classes over the Heavens—Motion in the Line of Sight—Orbital Motion Discovered with the Spectroscope: New Class of Binaries—Spectra of Temporary Stars—Nature of these Bodies.

We have frequently in the previous chapters had occasion to refer to the revelations of the spectroscope, which form an important chapter in the history of modern science. By its aid a mighty stride has been taken in our attempt to comprehend the physical constitution of the sun. In the present chapter we propose to give an account of what the spectroscope tells us about the physical constitution of the fixed stars.

Quite a new phase of astronomy is here opened up. Every improvement in telescopes revealed fainter and fainter objects, but all the telescopes in the world could not answer the question as to whether iron and other elements are to be found in the stars. The ordinary star is a mighty glowing globe, hotter than a Bessemer converter or a Siemens furnace; if iron is in the star, it must be not only white-hot and molten, but actually converted into vapour. But the vapour of iron is not visible in the telescope. How would you recognise it? How would you know if it commingled with the vapour of many other metals or other substances? It is, in truth, a delicate piece of analysis to discriminate iron in the glowing atmosphere of a star. But the spectroscope is adequate to the task, and it renders its analysis with an amount of evidence that is absolutely convincing.

That the spectra of the moon and planets are practically nothing but faint reproductions of the spectrum of the sun was discovered by the great German optician Fraunhofer about the year 1816. By placing a prism in front of the object glass of a small theodolite (an instrument used for geodetic measurements) he was able to ascertain that Venus and Mars showed the same spectrum as the sun, while Sirius gave a very different one. This important observation encouraged him to procure better instrumental means with which to continue the work, and he succeeded in distinguishing the chief characteristics of the various types of stellar spectra. The form of instrument which Fraunhofer adopted for this work, in which the prism was placed outside the object glass of the telescope, has not been much used until within the last few years, owing to the difficulty of obtaining prisms of large dimensions (for it is obvious that the prism ought to be as large as the object glass if the full power of the latter is to be made use of), but this is the simplest form of spectroscope for observing spectra of objects of no sensible angular diameter, like the fixed stars. The parallel rays from the stars are dispersed by the prism into a spectrum, and this is viewed by means of the telescope. But as the image of the star in the telescope is nothing but a luminous point, its spectrum will be merely a line in which it would not be possible to distinguish any lines crossing it laterally such as those we see in the spectrum of the sun. A cylindrical lens is, therefore, placed before the eye-piece of the telescope, and as this has the effect of turning a point into a line and a line into a band, the narrow spectrum of the star is thereby broadened out into a luminous band in which we can distinguish any details that exist. In other forms of stellar spectroscope we require a slit which must be placed in the focus of the object glass, and the general arrangement is similar to that which we have described in the chapter on the sun, except that a cylindrical lens is required.

The study of the spectra of the fixed stars made hardly any progress until the principles of spectrum analysis had been established by Kirchhoff in 1859. When the dark lines in the solar spectrum had been properly interpreted, it was at once evident that science had opened wide the gates of a new territory for human exploration, of the very existence of which hardly anyone had been aware up to that time. We have seen to what splendid triumphs the study of the sun has led the investigators in this field, and we have seen how very valuable results have been obtained by the new method when applied to observations of comets and nebulae. We shall now give some account of what has been learned with regard to the constitution of the fixed stars by the researches which were inaugurated by Sir William Huggins and continued and developed by him, as well as by Secchi, Vogel, Pickering, Lockyer, Duner, Scheiner and others. Here, as in the other modern branches of astronomy, photography has played a most important part, not only because photographed spectra of stars extend much farther at the violet end than the observer can follow them with his eye, but also because the positions of the lines can be very accurately measured on the photographs.

The first observer who reduced the apparently chaotic diversity of stellar spectra to order was Secchi, who showed that they might all be grouped according to four types. Within the last thirty years, however, so many modifications of the various types have been found that it has become necessary to subdivide Secchi's types, and most observers now make use of Vogel's classification, which we shall also for convenience adopt in this chapter.

Type I.—In the spectra of stars of this class the metallic lines, which are so very numerous and conspicuous in the sun's violet spectrum, are very faint and thin, or quite invisible, and the blue and white parts are very intensely bright. Vogel subdivides the class into three groups. In the first (I.a) the hydrogen lines are present, and are remarkably broad and intense; Sirius, Vega, and Regulus are examples of this group. The great breadth of the lines probably indicates that these stars are surrounded by hydrogen atmospheres of great dimensions. It is generally acknowledged that stars of this group must be the hottest of all, and support is lent to this view by the appearance in their spectra of a certain magnesium line, which, as Sir Norman Lockyer showed many years ago, by laboratory experiments, does not appear in the ordinary spectrum of magnesium, but is indicative of the presence of the substance at a very high temperature. In the spectra of stars of Group I.b the hydrogen lines and the few metallic lines are of equal breadth, and the magnesium line just mentioned is the strongest of all. Rigel and several other bright stars in Orion belong to this group, and it is remarkable that helium is present at least in some of these stars, so that (as Professor Keeler remarks) the spectrum of Rigel may almost be regarded as the nebular spectrum reversed (lines dark instead of bright), except that the two chief nebular lines are not reversed in the star. This fact will doubtless eventually be of great importance to our understanding the successive development of a star from a nebula; and a star like Rigel is no doubt also of very high temperature. This is probably not the case with stars of the third subdivision of Type I. (I.c), the spectra of which are distinguished by the presence of bright hydrogen lines and the bright helium line D3. Among the stars having this very remarkable kind of spectrum is a very interesting variable star in the constellation Lyra (b) and the star known as g Cassiopeiae, both of which have been assiduously observed, their spectra possessing numerous peculiarities which render an explanation of the physical constitution of the stars of this subdivision a very difficult matter.

Passing to Type II., we find spectra in which the metallic lines are strong. The more refrangible end of the spectrum is fainter than in the previous Class, and absorption bands are sometimes found towards the red end. In its first subdivision (II.a) are contained spectra with a large number of strong and well-defined lines due to metals, the hydrogen lines being also well seen, though they are not specially conspicuous. Among the very numerous stars of this group are Capella, Aldebaran, Arcturus, Pollux, etc. The spectra of these stars are in fact practically identical with the spectrum of our own sun, as shown, for instance, by Dr. Scheiner, of the Potsdam Astrophysical Observatory, who has measured several hundred lines on photographs of the spectrum of Capella, and found a very close agreement between these lines and corresponding ones in the solar spectrum. We can hardly doubt that the physical constitution of these stars is very similar to that of our sun. This cannot be the case with the stars of the second subdivision (II.b), the spectra of which are very complex, each consisting of a continuous spectrum crossed by numerous dark lines, on which is superposed a second spectrum of bright lines. Upwards of seventy stars are known to possess this extraordinary spectrum, the only bright one among them being a star of the third magnitude in the southern constellation Argus. Here again we have hydrogen and helium represented by bright lines, while the origin of the remaining bright lines is doubtful. With regard to the physical constitution of the stars of this group it is very difficult to come to a definite conclusion, but it would seem not unlikely that we have here to do with stars which are not only surrounded by an atmosphere of lower temperature, causing the dark lines, but which, outside of that, have an enormous envelope of hydrogen and other gases. In one star at least of this group Professor Campbell, of the Lick Observatory, has seen the F line as a long line extending a very appreciable distance on each side of the continuous spectrum, and with an open slit it was seen as a large circular disc about six seconds in diameter; two other principal hydrogen lines showed the same appearance. As far as this observation goes, the existence of an extensive gaseous envelope surrounding the star seems to be indicated.

Type III. contains comparatively few stars, and the spectra are characterised by numerous dark bands in addition to dark lines, while the more refrangible parts are very faint, for which reason the stars are more or less red in colour. This class has two strongly marked subdivisions. In the first (III.a) the principal absorption lines coincide with similar ones in the solar spectrum, but with great differences as to intensity, many lines being much stronger in these stars than in the sun, while many new lines also appear. These dissimilarities are, however, of less importance than the peculiar absorption bands in the red, yellow, and green parts of the spectrum, overlying the metallic lines, and being sharply defined on the side towards the violet and shading off gradually towards the red end of the spectrum. Bands of this kind belong to chemical combinations, and this appears to show that somewhere in the atmospheres of these distant suns the temperature is low enough to allow stable chemical combinations to be formed. The most important star of this kind is Betelgeuze or a Orionis, the red star of the first magnitude in the shoulder of Orion; but it is of special importance to note that many variable stars of long period have spectra of Type III.a. Sir Norman Lockyer predicted in 1887 that bright lines, probably of hydrogen, would eventually be found to appear at the maximum of brightness, when the smaller swarm is supposed to pass through the larger one, and this was soon afterwards confirmed by the announcement that Professor Pickering had found a number of hydrogen lines bright on photographs, obtained at Harvard College Observatory, of the spectrum of the remarkable variable, Mira Ceti, at the time of maximum. Professor Pickering has since then reported that bright lines have been found on the plates of forty-one previously known variables of this class, and that more than twenty other stars have been detected as variables by this peculiarity of their spectrum; that is, bright lines being seen in them suggested that the stars were variable, and further photometric investigations corroborated the fact.

The second subdivision (III.b) contains only comparatively faint stars, of which none exceed the fifth magnitude, and is limited to a small number of red stars. The strongly marked bands in their spectra are sharply defined and dark on the red side, while they fade away gradually towards the violet, exactly the reverse of what we see in the spectra of III.a. These bands appear to arise from the absorption due to hydrocarbon vapours present in the atmospheres of these stars; but there are also some lines visible which indicate the presence of metallic vapours, sodium being certainly among these. There can be little doubt that these stars represent the last stage in the life of a sun, when it has cooled down considerably and is not very far from actual extinction, owing to the increasing absorption of its remaining light in the atmosphere surrounding it.

The method employed for the spectroscopic determination of the motion of a star in the line of sight is the same as the method we have described in the chapter on the sun. The position of a certain line in the spectrum of a star is compared with the position of the corresponding bright line of an element in an artificially produced spectrum, and in this manner a displacement of the stellar line either towards the violet (indicating that the star is approaching us) or towards the red (indicating that it is receding) may be detected. The earliest attempt of this sort was made in 1867 by Sir William Huggins, who compared the F line in the spectrum of Sirius with the same line of the spectrum of hydrogen contained in a vacuum tube reflected into the field of his astronomical spectroscope, so that the two spectra appeared side by side. The work thus commenced and continued by him was afterwards taken up at the Greenwich Observatory; but the results obtained by these direct observations were never satisfactory, as remarkable discrepancies appeared between the values obtained by different observers, and even by the same observer on different nights. This is not to be wondered at when we bear in mind that the velocity of light is so enormous compared with any velocity with which a heavenly body may travel, that the change of wave length resulting from the latter motion can only be a very minute one, difficult to perceive, and still more difficult to measure. But since photography was first made use of for these investigations by Dr. Vogel, of Potsdam, much more accordant and reliable results have been obtained, though even now extreme care is required to avoid systematic errors. To give some idea of the results obtainable, we present in the following table the values of the velocity per second of a number of stars observed in 1896 and 1897 by Mr. H.F. Newall with the Bruce spectrograph attached to the great 25-inch Newall refractor of the Cambridge Observatory, and we have added the values found at Potsdam by Vogel and Scheiner. The results are expressed in kilometres (1 km. = 0.62 English mile). The sign + means that the star is receding from us,-that it is approaching.

Newall. Vogel. Scheiner. Aldebaran + 49.2 + 47.6 + 49.4 Betelgeuze + 10.6 + 15.6 + 18.8 Procyon - 4.2 - 7.2 - 10.5 Pollux - 0.7 + 1.9 + 0.4 g Leonis - 39.9 - 36.5 - 40.5 Arcturus - 6.4 - 7.0 - 8.3

These results have been corrected for the earth's orbital motion round the sun, but not for the sun's motion through space, as the amount of the latter is practically unknown, or at least very uncertain; so that the above figures really represent the velocity per second of the various stars relative to the sun. We may add that the direction and velocity of the sun's motion may eventually be ascertained from spectroscopic measures of a great number of stars, and it seems likely that the sun's velocity will be much more accurately found in this way than by the older method of combining proper motions of stars with speculations as to the average distances of the various classes of stars. This has already been attempted by Dr. Kempf, who from the Potsdam spectrographic observations found the sun's velocity to be 18.6 kilometres, or 11.5 miles per second, a result which is probably not far from the truth.

But the spectra of the fixed stars can also tell us something about orbital motion in these extremely distant systems. If one star revolved round another in a plane passing through the sun, it must on one side of the orbit move straight towards us and on the other side move straight away from us, while it will not alter its distance from us while it is passing in front of, or behind, the central body. If we therefore find from the spectroscopic observations that a star is alternately moving towards and away from the earth in a certain period, there can be no doubt that this star is travelling round some unseen body (or, rather, round the centre of gravity of both) in the period indicated by the shifting of the spectral lines. In Chapter XIX. we mentioned the variable star Algol in the constellation Perseus, which is one of a class of variable stars distinguished by the fact that for the greater part of the period they remain of unaltered brightness, while for a very short time they become considerably fainter. That this was caused by some sort of an eclipse—or, in other words, by the periodic passage of a dark body in front of the star, hiding more or less of the latter from us—was the simplest possible hypothesis, and it had already years ago been generally accepted. But it was not possible to prove that this was the true explanation of the periodicity of stars like Algol until Professor Vogel, from the spectroscopic observations made at Potsdam, found that before every minimum Algol is receding from the sun, while it is approaching us after the minimum. Assuming the orbit to be circular, the velocity of Algol was found to be twenty-six miles per second. From this and the length of the period (2d. 22h. 48m. 55s.) and the time of obscuration it was easy to compute the size of the orbit and the actual dimensions of the two bodies. It was even possible to go a step further and to calculate from the orbital velocities the masses of the two bodies,[41] assuming them to be of equal density—an assumption which is no doubt very uncertain. The following are the approximate elements of the Algol system found by Vogel:—

Diameter of Algol 1,054,000 miles. Diameter of companion 825,000 miles. Distance between their centres 3,220,000 miles. Orbital velocity of Algol 26 miles per sec. Orbital velocity of companion 55 miles per sec. Mass of Algol 4/9 of sun's mass. Mass of companion 2/9 of sun's mass.

The period of Algol has been gradually decreasing during the last century (by six or seven seconds), but whether this is caused by the motion of the pair round a third and very much more distant body, as suggested by Mr. Chandler, has still to be found out.

We have already mentioned that in order to produce eclipses, and thereby variations of light, it is necessary that the line of sight should lie nearly in the plane of the orbit. It is also essential that there should be a considerable difference of brightness between the two bodies. These conditions must be fulfilled in the fifteen variable stars of the Algol class now known; but according to the theory of probability, there must be many more binary systems like that of Algol where these conditions are not fulfilled, and in those cases no variations will occur in the stars' brightness. Of course, we know many cases of a luminous star travelling round another, but there must also be cases of a large companion travelling round another at so small a distance that our telescopes are unable to "divide" the double star. This has actually been discovered by means of the spectroscope. If we suppose an extremely close double star to be examined with the spectroscope, the spectra of the two components will be superposed, and we shall not be aware that we really see two different spectra. But during the revolution of the two bodies round their common centre of gravity there must periodically come a time when one body is moving towards us and the other moving from us, and consequently the lines in the spectrum of the former will be subject to a minute, relative shift towards the violet end of the spectrum, and those of the other to a minute shift towards the red. Those lines which are common to the two spectra will therefore periodically become double. A discovery of this sort was first made in 1889 by Professor Pickering from photographs of the spectrum of Mizar, or z Ursa Majoris, the larger component of the well-known double star in the tail of the Great Bear. Certain of the lines were found to be double at intervals of fifty-two days. The maximum separation of the two components of each line corresponds to a relative velocity of one star as compared with the other of about a hundred miles per second, but subsequent observations have shown the case to be very complicated, either with a very eccentric elliptic orbit or possibly owing to the presence of a third body. The Harvard College photographs also showed periodic duplicity of lines in the star b Aurigae, the period being remarkably short, only three days and twenty-three hours and thirty-seven minutes. In 1891 Vogel found, from photographs of the spectrum of Spica, the first magnitude star in Virgo, that this star alternately recedes from and approaches to the solar system, the period being four days. Certain other "spectroscopic binaries" have since then been found, notably one component of Castor, with a period of three days, found by M. Belopolsky, and a star in the constellation Scorpio, with a period of only thirty-four hours, detected on the Harvard spectrograms.

Quite recently Mr. H.F. Newall, at Cambridge, and Mr. Campbell, of the Lick Observatory, have shown that a Aurigae, or Capella, consists of a sun-like star and a Procyon-like star, revolving in 104 days.

At first sight there is something very startling in the idea of two suns circling round each other, separated by an interval which, in comparison with their diameters, is only a very small one. In the Algol system, for instance, we have two bodies, one the size of our own sun and the other slightly larger, moving round their common centre of gravity in less than three days, and at a distance between their surfaces equal to only twice the diameter of the larger one. Again, in the system of Spica we have two great suns swinging round each other in only four days, at a distance equal to that between Saturn and his sixth satellite. But although we have at present nothing analogous to this in our solar system, it can be proved mathematically that it is perfectly possible for a system of this kind to preserve its stability, if not for ever, at any rate for ages, and we shall see in our last chapter that there was in all probability a time when the earth and the moon formed a peculiar system of two bodies revolving rapidly at a very small distance compared to the diameters of the bodies.

It is possible that we have a more complicated system in the star known as b Lyrae. This is a variable star of great interest, having a period of twelve days and twenty-two hours, in which time it rises from magnitude 4-1/2 to a little above 3-1/2, sinks nearly to the fourth magnitude, rises again to fully 3-1/2, and finally falls to magnitude 4-1/2. In 1891 Professor Pickering discovered that the bright lines in the spectrum of this star changed their position from time to time, appearing now on one side, now on the other side of corresponding dark lines. Obviously these bright lines change their wave length, the light-giving source alternately receding from and approaching to the earth, and the former appeared to be the case during one-half of the period of variation of the star's light, the latter during the other half. The spectrum of this star has been further examined by Belopolsky and others, who have found that the lines are apparently double, but that one of the components either disappears or becomes very narrow from time to time. On the assumption that these lines were really single (the apparent duplicity resulting from the superposition of a dark line), Belopolsky determined the amount of their displacement by measuring the distances from the two edges of a line of hydrogen (F) to the artificial hydrogen line produced by gas glowing in a tube and photographed along with the star-spectrum. Assuming the alternate approach and recession to be caused by orbital revolution, Belopolsky found that the body emitting the light of the bright lines moved with an orbital velocity of forty-one miles. He succeeded in 1897 in observing the displacement of a dark line due to magnesium, and found that the body emitting it was also moving in an orbit, but while the velocities given by the bright F line are positive after the principal minimum of the star's light, those given by the dark line are negative. Therefore, during the principal minimum it is a star giving the dark line which is eclipsed, and during the secondary minimum another star giving the bright line is eclipsed. This wonderful variable will, however, require more observatioens before the problem of its constitution is finally solved, and the same may be said of several variable stars, e.g. e Aquilae and d Cephei, in which a want of harmony has been found between the changes of velocity and the fluctuations of the light.

There are some striking analogies between the complicated spectrum of b Lyrae and the spectra of temporary stars. The first "new star" which could be spectroscopically examined was that which appeared in Corona Borealis in 1866, and which was studied by Sir W. Huggins. It showed a continuous spectrum with dark absorption lines, and also the bright lines of hydrogen; practically the same spectrum as the stars of Type II.b. This was also the case with Schmidt's star of 1876, which showed the helium line (D3) and the principal nebula line in addition to the lines of hydrogen; but in the autumn of 1877, when the star had fallen to the tenth magnitude, Dr. Copeland was surprised to find that only one line was visible, the principal nebula line, in which almost the whole light of the star was concentrated, the continuous spectrum being hardly traceable. It seemed, in fact, that the star had been transformed into a planetary nebula, but later the spectrum seems to have lost this peculiar monochromatic character, the nebula line having disappeared and a faint continuous spectrum alone being visible, which is also the case with the star of 1866 since it sank down to the tenth magnitude. A continuous spectrum was all that could be seen of the new star which broke out in the nebula of Andromeda in 1885, much the same as the spectrum of the nebula itself.

When the new star in Auriga was announced, in February, 1892, astronomers were better prepared to observe it spectroscopically, as it was now possible by means of photography to study the ultra-violet part of the spectrum which to the eye is invisible. The visible spectrum was very like that of Nova Cygni of 1876, but when the wave-lengths of all the bright lines seen and photographed at the Lick Observatory and at Potsdam were measured, a strong resemblance to the bright line spectrum of the chromosphere of the sun became very evident. The hydrogen lines were very conspicuous, while the iron lines were very numerous, and calcium and magnesium were also represented. The most remarkable revelation made by the photographs was, however, that the bright lines were in many cases accompanied, on the side next the violet, by broad dark bands, while both bright and dark lines were of a composite character. Many of the dark lines had a thin bright line superposed in the middle, while on the other hand many of the bright lines had two or three points maxima of brightness. The results of the measures of motion in the line of sight were of special importance. They showed that the source of light, whence came the thin bright lines within the dark ones, was travelling towards the sun at the enormous rate of 400 miles per second, and if the bright lines were actual "reversals" of the dark ones, then the source of the absorption spectrum must have been endowed with much the same velocity. On the other hand, if the two or three maxima of brightness in the bright lines really represent two or three separate bodies giving bright lines, the measures indicate that the principal one was almost at rest as regards the sun, while the others were receding from us at the extraordinary rates of 300 and 600 miles per second. And as if this were not sufficiently puzzling, the star on its revival in August, 1892, as a tenth magnitude star had a totally different spectrum, showing nothing but a number of the bright lines belonging to planetary nebulae! It is possible that the principal ones of these were really present in the spectrum from the first, but that their wave lengths had been different owing to change of the motion in the line of sight, so that the nebula lines seen in the autumn were identical with others seen in the spring at slightly different places. Subsequent observations of these nebula lines seemed to point to a motion of the Nova towards the solar system (of about 150 miles per second) which gradually diminished.

But although we are obliged to confess our inability to say for certain why a temporary star blazes up so suddenly, we have every cause to think that these strange bodies will by degrees tell us a great deal about the constitution of the fixed stars. The great variety of spectra which we see in the starry universe, nebula spectra with bright lines, stellar spectra of the same general character, others with broad absorption bands, or numerous dark lines like our sun, or a few absorption lines only—all this shows us the universe as teeming with bodies in various stages of evolution. We shall have a few more words to say on this matter when we come to consider the astronomical significance of heat; but we have reached a point where man's intellect can hardly keep pace with the development of our instrumental resources, and where our imagination stands bewildered when we endeavour to systematise the knowledge we have gained. That great caution will have to be exercised in the interpretation of the observed phenomena is evident from the recent experience of Professor Rowland, of Baltimore, from which we learn that spectral lines are not only widened by increased pressure of the light-giving vapour, but that they may be bodily shifted thereby. Dr. Zeeman's discovery, that a line from a source placed in a strong magnetic field may be both widened, broadened, and doubled, will also increase our difficulties in the interpretation of these obscure phenomena.



CHAPTER XXIV.

THE PRECESSION AND NUTATION OF THE EARTH'S AXIS.

The Pole is not a Fixed Point—Its Effect on the Apparent Places of the Stars—The Illustration of the Peg-Top—The Disturbing Force which acts on the Earth—Attraction of the Sun on a Globe—The Protuberance at the Equator—The Attraction of the Protuberance by the Sun and by the Moon produces Precession—The Efficiency of the Precessional Agent varies inversely as the Cube of the Distance—The Relative Efficiency of the Sun and the Moon—How the Pole of the Earth's Axis revolves round the Pole of the Ecliptic—Variation of Latitude.

The position of the pole of the heavens is most conveniently indicated by the bright star known as the Pole Star, which lies in its immediate vicinity. Around this pole the whole heavens appear to rotate once in a sidereal day; and we have hitherto always referred to the pole as though it were a fixed point in the heavens. This language is sufficiently correct when we embrace only a moderate period of time in our review. It is no doubt true that the pole lies near the Pole Star at the present time. It did so during the lives of the last generation, and it will do so during the lives of the next generation. All this time, however, the pole is steadily moving in the heavens, so that the time will at length come when the pole will have departed a long way from the present Pole Star. This movement is incessant. It can be easily detected and measured by the instruments in our observatories, and astronomers are familiar with the fact that in all their calculations it is necessary to hold special account of this movement of the pole. It produces an apparent change in the position of a star, which is known by the term "precession."



The movement of the pole is very clearly shown in the accompanying figure (Fig. 100), for which I am indebted to the kindness of the late Professor C. Piazzi Smyth. The circle shows the track along which the pole moves among the stars.

The centre of the circle in the constellation of Draco is the pole of the ecliptic. A complete journey of the pole occupies the considerable period of about 25,867 years. The drawing shows the position of the pole at the several dates from 4000 B.C. to 2000 A.D. A glance at this map brings prominently before us how casual is the proximity of the pole to the Pole Star. At present, indeed, the distance of the two is actually lessening, but afterwards the distance will increase until, when half of the revolution has been accomplished, the pole will be at a distance of twice the radius of the circle from the Pole Star. It will then happen that the pole will be near the bright star Vega or a Lyrae, so that our successors some 12,000 years hence may make use of Vega for many of the purposes for which the Pole Star is at present employed! Looking back into past ages, we see that some 2,000 or 3,000 years B.C. the star a Draconis was suitably placed to serve as the Pole Star, when b and d of the Great Bear served as pointers. It need hardly be added, that since the birth of accurate astronomy the course of the pole has only been observed over a very small part of the mighty circle. We are not, however, entitled to doubt that the motion of the pole will continue to pursue the same path. This will be made abundantly clear when we proceed to render an explanation of this very interesting phenomenon.

The north pole of the heavens is the point of the celestial sphere towards which the northern end of the axis about which the earth rotates is directed. It therefore follows that this axis must be constantly changing its position. The character of the movement of the earth, so far as its rotation is concerned, may be illustrated by a very common toy with which every boy is familiar. When a peg-top is set spinning, it has, of course, a very rapid rotation around its axis; but besides this rotation there is usually another motion, whereby the axis of the peg-top does not remain in a constant direction, but moves in a conical path around the vertical line. The adjoining figure (Fig. 101) gives a view of the peg-top. It is, of course, rotating with great rapidity around its axis, while the axis itself revolves around the vertical line with a very deliberate motion. If we could imagine a vast peg-top which rotated on its axis once a day, and if that axis were inclined at an angle of twenty-three and a half degrees to the vertical, and if the slow conical motion of the axis were such that the revolution of the axis were completed in about 26,000 years, then the movements would resemble those actually made by the earth. The illustration of the peg-top comes, indeed, very close to the actual phenomenon of precession. In each case the rotation about the axis is far more rapid than that of the revolution of the axis itself; in each case also the slow movement is due to an external interference. Looking at the figure of the peg-top (Fig. 101) we may ask the question, Why does it not fall down? The obvious effect of gravity would seem to say that it is impossible for the peg-top to be in the position shown in the figure. Yet everybody knows that this is possible so long as the top is spinning. If the top were not spinning, it would, of course, fall. It therefore follows that the effect of the rapid rotation of the top so modifies the effect of gravitation that the latter, instead of producing its apparently obvious consequence, causes the slow conical motion of the axis of rotation. This is, no doubt, a dynamical question of some difficulty, but it is easy to verify experimentally that it is the case. If a top be constructed so that the point about which it is spinning shall coincide with the centre of gravity, then there is no effect of gravitation on the top, and there is no conical motion perceived.



If the earth were subject to no external interference, then the direction of the axis about which it rotates must remain for ever constant; but as the direction of the axis does not remain constant, it is necessary to seek for a disturbing force adequate to the production of the phenomena which are observed. We have invariably found that the dynamical phenomena of astronomy can be accounted for by the law of universal gravitation. It is therefore natural to enquire how far gravitation will render an account of the phenomenon of precession; and to put the matter in its simplest form, let us consider the effect which a distant attracting body can have upon the rotation of the earth.

To answer this question, it becomes necessary to define precisely what we mean by the earth; and as for most purposes of astronomy we regard the earth as a spherical globe, we shall commence with this assumption. It seems also certain that the interior of the earth is, on the whole, heavier than the outer portions. It is therefore reasonable to assume that the density increases as we descend; nor is there any sufficient ground for thinking that the earth is much heavier in one part than at any other part equally remote from the centre. It is therefore usual in such calculations to assume that the earth is formed of concentric spherical shells, each one of which is of uniform density; while the density decreases from each shell to the one exterior thereto.

A globe of this constitution being submitted to the attraction of some external body, let us examine the effects which that external body can produce. Suppose, for instance, the sun attracts a globe of this character, what movements will be the result? The first and most obvious result is that which we have already so frequently discussed, and which is expressed by Kepler's laws: the attraction will compel the earth to revolve around the sun in an elliptic path, of which the sun is in the focus. With this movement we are, however, not at this moment concerned. We must enquire how far the sun's attraction can modify the earth's rotation around its axis. It can be demonstrated that the attraction of the sun would be powerless to derange the rotation of the earth so constituted. This is a result which can be formally proved by mathematical calculation. It is, however, sufficiently obvious that the force of attraction of any distant point on a symmetrical globe must pass through the centre of that globe: and as the sun is only an enormous aggregate of attracting points, it can only produce a corresponding multitude of attractive forces; each of these forces passes through the centre of the earth, and consequently the resultant force which expresses the joint result of all the individual forces must also be directed through the centre of the earth. A force of this character, whatever other potent influence it may have, will be powerless to affect the rotation of the earth. If the earth be rotating on an axis, the direction of that axis would be invariably preserved; so that as the earth revolves around the sun, it would still continue to rotate around an axis which always remained parallel to itself. Nor would the attraction of the earth by any other body prove more efficacious than that of the sun. If the earth really were the symmetrical globe we have supposed, then the attraction of the sun and moon, and even the influence of all the planets as well, would never be competent to make the earth's axis of rotation swerve for a single second from its original direction.

We have thus narrowed very closely the search for the cause of the "precession." If the earth were a perfect sphere, precession would be inexplicable. We are therefore forced to seek for an explanation of precession in the fact that the earth is not a perfect sphere. This we have already demonstrated to be the case. We have shown that the equatorial axis of the earth is longer than the polar axis, so that there is a protuberant zone girdling the equator. The attraction of external bodies is able to grasp this protuberance, and thereby force the earth's axis of rotation to change its direction.

There are only two bodies in the universe which sensibly contribute to the precessional movement of the earth's axis: these bodies are the sun and the moon. The shares in which the labour is borne by the sun and the moon are not what might have been expected from a hasty view of the subject. This is a point on which it will be desirable to dwell, as it illustrates a point in the theory of gravitation which is of very considerable importance.

The law of gravitation asserts that the intensity of the attraction which a body can exercise is directly proportional to the mass of that body, and inversely proportional to the square of its distance from the attracted point. We can thus compare the attraction exerted upon the earth by the sun and by the moon. The mass of the sun exceeds the mass of the moon in the proportion of about 26,000,000 to 1. On the other hand, the moon is at a distance which, on an average, is about one-386th part of that of the sun. It is thus an easy calculation to show that the efficiency of the sun's attraction on the earth is about 175 times as great as the attraction of the moon. Hence it is, of course, that the earth obeys the supremely important attraction of the sun, and pursues an elliptic path around the sun, bearing the moon as an appendage.

But when we come to that particular effect of attraction which is competent to produce precession, we find that the law by which the efficiency of the attracting body is computed assumes a different form. The measure of efficiency is, in this case, to be found by taking the mass of the body and dividing it by the cube of the distance. The complete demonstration of this statement must be sought in the formulae of mathematics, and cannot be introduced into these pages; we may, however, adduce one consideration which will enable the reader in some degree to understand the principle, though without pretending to be a demonstration of its accuracy. It will be obvious that the nearer the disturbing body approaches to the earth the greater is the leverage (if we may use the expression) which is afforded by the protuberance at the equator. The efficiency of a given force will, therefore, on this account alone, increase in the inverse proportion of the distance. The actual intensity of the force itself augments in the inverse square of the distance, and hence the capacity of the attracting body for producing precession will, for a double reason, increase when the distance decreases. Suppose, for example, that the disturbing body is brought to half its original distance from the disturbed body, the leverage is by this means doubled, while the actual intensity of the force is at the same time quadrupled according to the law of gravitation. It will follow that the effect produced in the latter case must be eight times as great as in the former case. And this is merely equivalent to the statement that the precession-producing capacity of a body varies inversely as the cube of the distance.

It is this consideration which gives to the moon an importance as a precession-producing agent to which its mere attractive capacity would not have entitled it. Even though the mass of the sun be 26,000,000 times as great as the mass of the moon, yet when this number is divided by the cube of the relative value of the distances of the bodies (386), it is seen that the efficiency of the moon is more than twice as great as that of the sun. In other words, we may say that one-third of the movement of precession is due to the sun, and two-thirds to the moon.

For the study of the joint precessional effect due to the sun and the moon acting simultaneously, it will be advantageous to consider the effect produced by the two bodies separately; and as the case of the sun is the simpler of the two, we shall take it first. As the earth travels in its annual path around the sun, the axis of the earth is directed to a point in the heavens which is 23-1/2 deg. from the pole of the ecliptic. The precessional effect of the sun is to cause this point—the pole of the earth—to revolve, always preserving the same angular distance from the pole of the ecliptic; and thus we have a motion of the type represented in the diagram. As the ecliptic occupies a position which for our present purpose we may regard as fixed in space, it follows that the pole of the ecliptic is a fixed point on the surface of the heavens; so that the path of the pole of the earth must be a small circle in the heavens, fixed in its position relatively to the surrounding stars. In this we find a motion strictly analogous to that of the peg-top. It is the gravitation of the earth acting upon the peg-top which forces it into the conical motion. The immediate effect of the gravitation is so modified by the rapid rotation of the top, that, in obedience to a profound dynamical principle, the axis of the top revolves in a cone rather than fall down, as it would do were the top not spinning. In a similar manner the immediate effect of the sun's attraction on the protuberance at the equator would be to bring the pole of the earth's axis towards the pole of the ecliptic, but the rapid rotation of the earth modifies this into the conical movement of precession.

The circumstances with regard to the moon are much more complicated. The moon describes a certain orbit around the earth; that orbit lies in a certain plane, and that plane has, of course, a certain pole on the celestial sphere. The precessional effect of the moon would accordingly tend to make the pole of the earth's axis describe a circle around that point in the heavens which is the pole of the moon's orbit. This point is about 5 deg. from the pole of the ecliptic. The pole of the earth is therefore solicited by two different movements—one a revolution around the pole of the ecliptic, the other a revolution about another point 5 deg. distant, which is the pole of the moon's orbit. It would thus seem that the earth's pole should make a certain composite movement due to the two separate movements. This is really the case, but there is a point to be very carefully attended to, which at first seems almost paradoxical. We have shown how the potency of the moon as a precessional agent exceeds that of the sun, and therefore it might be thought that the composite movement of the earth's pole would conform more nearly to a rotation around the pole of the plane of the moon's orbit than to a rotation around the pole of the ecliptic; but this is not the case. The precessional movement is represented by a revolution around the pole of the ecliptic, as is shown in the figure. Here lies the germ of one of those exquisite astronomical discoveries which delight us by illustrating some of the most subtle phenomena of nature.

The plane in which the moon revolves does not occupy a constant position. We are not here specially concerned with the causes of this change in the plane of the moon's orbit, but the character of the movement must be enunciated. The inclination of this plane to the ecliptic is about 5 deg., and this inclination does not vary (except within very narrow limits); but the line of intersection of the two planes does vary, and, in fact, varies so quickly that it completes a revolution in about 18-2/3 years. This movement of the plane of the moon's orbit necessitates a corresponding change in the position of its pole. We thus see that the pole of the moon's orbit must be actually revolving around the pole of the ecliptic, always remaining at the same distance of 5 deg., and completing its revolution in 18-2/3 years. It will, therefore, be obvious that there is a profound difference between the precessional effect of the sun and of the moon in their action on the earth. The sun invites the earth's pole to describe a circle around a fixed centre; the moon invites the earth's pole to describe a circle around a centre which is itself in constant motion. It fortunately happens that the circumstances of the case are such as to reduce considerably the complexity of the problem. The movement of the moon's plane, only occupying about 18-2/3 years, is a very rapid motion compared with the whole precessional movement, which occupies about 26,000 years. It follows that by the time the earth's axis has completed one circuit of its majestic cone, the pole of the moon's plane will have gone round about 1,400 times. Now, as this pole really only describes a comparatively small cone of 5 deg. in radius, we may for a first approximation take the average position which it occupies; but this average position is, of course, the centre of the circle which it describes—that is, the pole of the ecliptic.

We thus see that the average precessional effect of the moon simply conspires with that of the sun to produce a revolution around the pole of the ecliptic. The grosser phenomena of the movements of the earth's axis are to be explained by the uniform revolution of the pole in a circular path; but if we make a minute examination of the track of the earth's axis, we shall find that though it, on the whole, conforms with the circle, yet that it really traces out a sinuous line, sometimes on the inside and sometimes on the outside of the circle. This delicate movement arises from the continuous change in the place of the pole of the moon's orbit. The period of these undulations is 18-2/3 years, agreeing exactly with the period of the revolution of the moon's nodes. The amount by which the pole departs from the circle on either side is only about 9.2 seconds—a quantity rather less than the twenty-thousandth part of the radius of the sphere. This phenomenon, known as "nutation," was discovered by the beautiful telescopic researches of Bradley, in 1747. Whether we look at the theoretical interest of the subject or at the refinement of the observations involved, this achievement of the "Vir incomparabilis," as Bradley has been called by Bessel, is one of the masterpieces of astronomical genius.

The phenomena of precession and nutation depend on movements of the earth itself, and not on movements of the axis of rotation within the earth. Therefore the distance of any particular spot on the earth from the north or south pole is not disturbed by either of these phenomena. The latitude of a place is the distance of the place from the earth's equator, and this quantity remains unaltered in the course of the long precession cycle of 26,000 years. But it has been discovered within the last few years that latitudes are subject to a small periodic change of a few tenths of a second of arc. This was first pointed out about 1880 by Dr. Kuestner, of Berlin, and by a masterly analysis of all available observations, made in the course of many years past at various observatories, Dr. Chandler, of Boston, has shown that the latitude of every point on the earth is subject to a double oscillation, the period of one being 427 days and the other about a year, the mean amplitude of each being O".14. In other words, the spot in the arctic regions, directly in the prolongation of the earth's axis of rotation, is not absolutely fixed; the end of the imaginary axis moves about in a complicated manner, but always keeping within a few yards of its average position. This remarkable discovery is not only of value as introducing a new refinement in many astronomical researches depending on an accurate knowledge of the latitude, but theoretical investigations show that the periods of this variation are incompatible with the assumption that the earth is an absolutely rigid body. Though this assumption has in other ways been found to be untenable, the confirmation of this view by the discovery of Dr. Chandler is of great importance.



CHAPTER XXV.

THE ABERRATION OF LIGHT.

The Real and Apparent Movements of the Stars—How they can be Discriminated—Aberration produces Effects dependent on the Position of the Stars—The Pole of the Ecliptic—Aberration makes Stars seem to Move in a Circle, an Ellipse, or a Straight Line according to Position—All the Ellipses have Equal Major Axes—How is this Movement to be Explained?—How to be Distinguished from Annual Parallax—The Apex of the Earth's Way—How this is to be Explained by the Velocity of Light—How the Scale of the Solar System can be Measured by the Aberration of Light.

We have in this chapter to narrate a discovery of a recondite character, which illustrates in a forcible manner some of the fundamental truths of Astronomy. Our discussion of it will naturally be divided into two parts. In the first part we must describe the nature of the phenomenon, and then we must give the extremely elegant explanation afforded by the properties of light. The telescopic discovery of aberration, as well as its explanation, are both due to the illustrious Bradley.

The expression fixed star, so often used in astronomy, is to be received in a very qualified sense. The stars are, no doubt, well fixed in their places, so far as coarse observation is concerned. The lineaments of the constellations remain unchanged for centuries, and, in contrast with the ceaseless movements of the planets, the stars are not inappropriately called fixed. We have, however, had more than one occasion to show throughout the course of this work that the expression "fixed star" is not an accurate one when minute quantities are held in estimation. With the exact measures of modern instruments, many of these quantities are so perceptible that they have to be always reckoned with in astronomical enquiry. We can divide the movements of the stars into two great classes: the real movements and the apparent movements. The proper motion of the stars and the movements of revolution of the binary stars constitute the real movements of these bodies. These movements are special to each star, so that two stars, although close together in the heavens, may differ in the widest degree as to the real movements which they possess. It may, indeed, sometimes happen that stars in a certain region are animated with a common movement. In this phenomenon we have traces of a real movement shared by a number of stars in a certain group. With this exception, however, the real movements of the stars seem to be governed by no systematic law, and the rapidly moving stars are scattered here and there indiscriminately over the heavens.

The apparent movements of the stars have a different character, inasmuch as we find the movement of each star determined by the place which it occupies in the heavens. It is by this means that we discriminate the real movements of the star from its apparent movements, and examine the character of both.

In the present chapter we are concerned with the apparent movements only, and of these there are three, due respectively to precession, to nutation, and to aberration. Each of these apparent movements obeys laws peculiar to itself, and thus it becomes possible to analyse the total apparent motion, and to discriminate the proportions in which the precession, the nutation, and the aberration have severally contributed. We are thus enabled to isolate the effect of aberration as completely as if it were the sole agent of apparent displacement, so that, by an alliance between mathematical calculation and astronomical observation, we can study the effects of aberration as clearly as if the stars were affected by no other motions.

Concentrating our attention solely on the phenomena of aberration we shall describe its particular effect upon stars in different regions of the sky, and thus ascertain the laws according to which the effects of aberration are exhibited. When this step has been taken, we shall be in a position to give the beautiful explanation of those laws dependent upon the velocity of light.

At one particular region of the heavens the effect of aberration has a degree of simplicity which is not manifested anywhere else. This region lies in the constellation Draco, at the pole of the ecliptic. At this pole, or in its immediate neighbourhood, each star, in virtue of aberration, describes a circle in the heavens. This circle is very minute; it would take something like 2,000 of these circles together to form an area equal to the area of the moon. Expressed in the usual astronomical language, we should say that the diameter of this small circle is about 40.9 seconds of arc. This is a quantity which, though small to the unaided eye, is really of great relative magnitude in the present state of telescopic research. It is not only large enough to be perceived, but it can be measured, with an accuracy which actually does not admit of a doubt, to the hundredth part of the whole. It is also observed that each star describes its little circle in precisely the same period of time; and that period is one year, or, in other words, the time of the revolution of the earth around the sun. It is found that for all stars in this region, be they large stars or small, single or double, white or coloured, the circles appropriate to each have all the same size, and are all described in the same time. Even from this alone it would be manifest that the cause of the phenomenon cannot lie in the star itself. This unanimity in stars of every magnitude and distance requires some simpler explanation.

Further examination of stars in different regions sheds new light on the subject. As we proceed from the pole of the ecliptic, we still find that each star exhibits an annual movement of the same character as the stars just considered. In one respect, however, there is a difference. The apparent path of the star is no longer a circle; it has become an ellipse. It is, however, soon perceived that the shape and the position of this ellipse are governed by the simple law that the further the star is from the pole of the ecliptic the greater is the eccentricity of the ellipse. The apparent path of the stars at the same distance from the pole have equal eccentricity, and of the axes of the ellipse the shorter is always directed to the pole, the longer being, of course, perpendicular to it. It is, however, found that no matter how great the eccentricity may become, the major axis always retains its original length. It is always equal to about 40.9 seconds—that is, to the diameter of the circle of aberration at the pole itself. As we proceed further and further from the pole of the ecliptic, we find that each star describes a path more and more eccentric, until at length, when we examine a star on the ecliptic, the ellipse has become so attenuated that it has flattened into a line. Each star which happens to lie on the ecliptic oscillates to and fro along the ecliptic through an amplitude of 40.9 seconds. Half a year accomplishes the journey one way, and the other half of the year restores the star to its original position. When we pass to stars on the southern side of the ecliptic, we see the same series of changes proceed in an inverse order. The ellipse, from being actually linear, gradually grows in width, though still preserving the same length of major axis, until at length the stars near the southern pole of the ecliptic are each found to describe a circle equal to the paths pursued by the stars at the north pole of the ecliptic.

The circumstance that the major axes of all those ellipses are of equal length suggests a still further simplification. Let us suppose that every star, either at the pole of the ecliptic or elsewhere, pursues an absolutely circular path, and that all these circles agree not only in magnitude, but also in being all parallel to the plane of the ecliptic: it is easy to see that this simple supposition will account for the observed facts. The stars at the pole of the ecliptic will, of course, show their circles turned fairly towards us, and we shall see that they pursue circular paths. The circular paths of the stars remote from the pole of the ecliptic will, however, be only seen somewhat edgewise, and thus the apparent paths will be elliptical, as we actually find them. We can even calculate the degree of ellipticity which this surmise would require, and we find that it coincides with the observed ellipticity. Finally, when we observe stars actually moving in the ecliptic, the circles they follow would be seen edgewise, and thus the stars would have merely the linear movement which they are seen to possess. All the observed phenomena are thus found to be completely consistent with the supposition that every star of all the millions in the heavens describes once each year a circular path; and that, whether the star be far or near, this circle has always the same apparent diameter, and lies in a plane always parallel to the plane of the ecliptic.

We have now wrought the facts of observation into a form which enables us to examine into the cause of a movement so systematic. Why is it that each star should seem to describe a small circular path? Why should that path be parallel to the ecliptic? Why should it be completed exactly in a twelvemonth? We are at once referred to the motion of the earth around the sun. That movement takes place in the ecliptic. It is completed in a year. The coincidences are so obvious that we feel almost necessarily compelled to connect in some way this apparent movement of the stars with the annual movement of the earth around the sun. If there were no such connection, it would be in the highest degree improbable that the planes of the circles should be all parallel to the ecliptic, or that the time of revolution of each star in its circle should equal that of the revolution of the earth around the sun. As both these conditions are fulfilled, the probability of the connection rises to a value almost infinite.

The important question has then arisen as to why the movement of the earth around the sun should be associated in so remarkable a manner with this universal star movement. There is here one obvious point to be noticed and to be dismissed. We have in a previous chapter discussed the important question of the annual parallax of stars, and we have shown how, in virtue of annual parallax, each star describes an ellipse. It can further be demonstrated that these ellipses are really circles parallel to the ecliptic; so that we might hastily assume that annual parallax was the cause of the phenomenon discovered by Bradley. A single circumstance will, however, dispose of this suggestion. The circle described by a star in virtue of annual parallax has a magnitude dependent on the distance of the star, so that the circles described by various stars are of various dimensions, corresponding to the varied distances of different stars. The phenomena of aberration, however, distinctly assert that the circular path of each star is of the same size, quite independently of what its distance may be, and hence annual parallax will not afford an adequate explanation. It should also be noticed that the movements of a star produced by annual parallax are much smaller than those due to aberration. There is not any known star whose circular path due to annual parallax has a diameter one-twentieth part of that of the circle due to aberration; indeed, in the great majority of cases the parallax of the star is an absolutely insensible quantity.