Let us now direct our attention to the planets, and examine the circumstances in which volcanoes located thereon could eject a meteorite which should ultimately tumble on the earth. We cannot see the planets well enough to tell whether they have or ever had any volcanoes; but the almost universal presence of heat in the large celestial masses seems to leave us in little doubt that some form of volcanic action might be found in the planets. We may at once dismiss the giant planets, such as Jupiter or Saturn: their appearance is very unlike a volcanic surface; while their great mass would render it necessary to suppose that the meteorites were expelled with terrific velocity if they should succeed in escaping from the gravitation of the planet. Applying the rule already given, a volcano on Jupiter would have to be five or six times as powerful as the volcano on the earth. To avoid this difficulty, we naturally turn to the smaller planets of the system; take, for instance, one of that innumerable host of minor planets, and let us enquire how far this body is likely to have ejected a missile which should fall upon the earth. Some of these globes are only a few miles in diameter. There are bodies in the solar system so small that a very moderate velocity would be sufficient to project a missile away from them altogether. We have, indeed, already illustrated this point in discussing the minor planets. It has been suggested that a volcano placed on one of the minor planets might be quite powerful enough to start the meteorites on a long ramble through space until the chapter of accidents brought them into collision with the earth. There is but little difficulty in granting that there might be such volcanoes, and that they might be sufficiently powerful to drive bodies from the surface of the planet; but we must remember that the missiles are to fall on the earth, and dynamical considerations are involved which merit our close attention. To concentrate our ideas, we shall consider one of the minor planets, and for this purpose let us take Ceres. If a meteorite is to fall upon the earth, it must pass through the narrow ring, some 8,000 miles wide, which marks the earth's path; it will not suffice for the missile to pass through the ecliptic on the inside or on the outside of the ring, it must be actually through this narrow strip, and then if the earth happens to be there at the same moment the meteorite will fall. The first condition to be secured is, therefore, that the path of the meteorite shall traverse this narrow ring. This is to be effected by projection from some point in the orbit of Ceres. But it can be shown on purely dynamical grounds that although the volcanic energy sufficient to remove the projectile from Ceres may be of no great account, yet if that projectile is to cross the earth's track, the dynamical requirements of the case demand a volcano on Ceres at the very least of three-mile power. We have thus gained but little by the suggestion of a minor planet, for we have not found that a moderate volcanic power would be adequate. But there is another difficulty in the case of Ceres, inasmuch as the ring on the ecliptic is very narrow in comparison with the other dimensions of the problem. Ceres is a long way off, and it would require very great accuracy in volcanic practice on Ceres to project a missile so that it should just traverse this ring and fall neither inside nor outside, neither above nor below. There must be a great many misses for every hit. We have attempted to make the calculation by the aid of the theory of probabilities, and we find that the chances against this occurrence are about 50,000 to 1, so that out of every 50,000 projectiles hurled from a point in the orbit of Ceres only a single one can be expected to satisfy even the first of the conditions necessary if it is ever to tumble on our globe. It is thus evident that there are two objections to Ceres (and the same may be said of the other minor planets) as a possible source of the meteorites. Firstly, that notwithstanding the small mass of the planet a very powerful volcano would still be required; and secondly, that we are obliged to assume that for every one which ever reached the earth at least 50,000 must have been ejected. It is thus plain that if the meteorites have really been driven from some planet of the solar system, large or small, the volcano must, from one cause or another, have been a very powerful one. We are thus led to enquire which planet possesses on other grounds the greatest probability in its favour.

We admit of course that at the present time the volcanoes on the earth are utterly devoid of the necessary power; but were the terrestrial volcanoes always so feeble as they are in these later days? Grounds are not wanting for the belief that in the very early days of geological time the volcanic energy on the earth was much greater than at present. We admit fully the difficulties of the view that the meteorites have really come from the earth; but they must have some origin, and it is reasonable to indicate the source which seems to have most probability in its favour. Grant for a moment that in the primaeval days of volcanic activity there were some mighty throes which hurled forth missiles with the adequate velocity: these missiles would ascend, they would pass from the gravitation of the earth, they would be seized by the gravitation of the sun, and they would be compelled to revolve around the sun for ever after. No doubt the resistance of the air would be a very great difficulty, but this resistance would be greatly lessened were the crater at a very high elevation above the sea level, while, if a vast volume of ejected gases or vapours accompanied the more solid material, the effect of the resistance of the air would be still further reduced. Some of these objects might perhaps revolve in hyperbolic orbits, and retreat never to return; while others would be driven into elliptic paths. Round the sun these objects would revolve for ages, but at each revolution—and here is the important point—they would traverse the point from which they were originally launched. In other words, every object so projected from the earth would at each revolution cross the track of the earth. We have in this fact an enormous probability in favour of the earth as contrasted with Ceres. Only one Ceres-ejected meteorite out of every 50,000 would probably cross the earth's track, while every earth-projected meteorite would necessarily do so.

If this view be true, then there must be hosts of meteorites traversing space in elliptic orbits around the sun. These orbits have one feature in common: they all intersect the track of the earth. It will sometimes happen that the earth is found at this point at the moment the meteorite is crossing; when this is the case the long travels of the little body are at an end, and it tumbles back on the earth from which it parted so many ages ago.

It is well to emphasise the contrast between the lunar theory of meteorites (which we think improbable) and the terrestrial theory (which appears to be probable). For the lunar theory it would, as we have seen, be necessary that some of the lunar volcanoes should be still active. In the terrestrial theory it is only necessary to suppose that the volcanoes on the earth once possessed sufficient explosive power. No one supposes that the volcanoes at present on the earth eject now the fragments which are to form future meteorites; but it seems possible that the earth may be now slowly gathering back, in these quiet times, the fragments she ejected in an early stage of her history. Assuming, therefore, with Tschermak, that many meteorites have had a volcanic origin on some considerable celestial body, we are led to agree with those who think that most probably that body is the earth.

It is interesting to notice a few circumstances which seem to corroborate the view that many meteorites are of ancient terrestrial origin. The most characteristic constituent of these bodies is the alloy of iron and nickel, which is almost universally present. Sometimes, as in the Rowton siderite, the whole object consists of little else; sometimes this alloy is in grains distributed through the mass. When Nordenskjoeld discovered in Greenland a mass of native iron containing nickel, this was at once regarded as a celestial visitor. It was called the Ovifak meteorite, and large pieces of the iron were conveyed to our museums. There is, for instance, in the national collection a most interesting exhibit of the Ovifak substance. Close examination shows that this so-called meteorite lies in a bed of basalt which has been vomited from the interior of the earth. Those who believe in the meteoric origin of the Ovifak iron are constrained to admit that shortly after the eruption of the basalt, and while it was still soft, this stupendous iron meteorite of gigantic mass and bulk happened to fall into this particular soft bed. The view is, however, steadily gaining ground that this great iron mass was no celestial visitor at all, but that it simply came forth from the interior of the earth with the basalt itself. The beautiful specimens in the British Museum show how the iron graduates into the basalt in such a way as to make it highly probable that the source of the iron is really to be sought in the earth and not external thereto. Should further research establish this, as now seems probable, a most important step will have been taken in proving the terrestrial origin of meteorites. If the Ovifak iron be really associated with the basalt, we have a proof that the iron-nickel alloy is indeed a terrestrial substance, found deep in the interior of the earth, and associated with volcanic phenomena. This being so, it will be no longer difficult to account for the iron in undoubted meteorites. When the vast volcanoes were in activity they ejected masses of this iron-alloy, which, having circulated round the sun for ages, have at last come back again. As if to confirm this view, Professor Andrews discovered particles of native iron in the basalt of the Giant's Causeway, while the probability that large masses of iron are there associated with the basaltic formation was proved by the researches on magnetism of the late Provost Lloyd.

Besides the more solid meteorites there can be no doubt that the debris of the ordinary shooting stars must rain down upon the earth in gentle showers of celestial dust. The snow in the Arctic regions has often been found stained with traces of dust which contains particles of iron. Similar particles have been found on the towers of cathedrals and in many other situations where it could only have been deposited from the air. There can be hardly a doubt that some of the motes in the sunbeam, and many of the particles which good housekeepers abhor as dust, have indeed a cosmical origin. In the famous cruise of the Challenger the dredges brought up from the depths of the Atlantic no "wedges of gold, great anchors, heaps of pearl," but among the mud which they raised are to be found numerous magnetic particles which there is every reason to believe fell from the sky, and thence subsided to the depths of the ocean. Sand from the deserts of Africa, when examined under the microscope, yield traces of minute iron particles which bear the marks of having experienced a high temperature.

The earth draws in this cosmic dust continuously, but the earth now never parts with a particle of its mass. The consequence is inevitable; the mass of the earth must be growing, and though the change may be a small one, yet to those who have studied Darwin's treatise on "Earth-worms," or to those who are acquainted with the modern theory of evolution, it will be manifest that stupendous results can be achieved by slight causes which tend in one direction. It is quite probable that an appreciable part of the solid substance of our globe may have been derived from meteoric matter which descends in perennial showers upon its surface.



CHAPTER XVIII.

THE STARRY HEAVENS.

The Constellations—The Great Bear and the Pointers—The Pole Star—Cassiopeia—Andromeda, Pegasus, and Perseus—The Pleiades: Auriga, Capella, Aldebaran—Taurus, Orion, Sirius; Castor and Pollux—The Lion—Booetes, Corona, and Hercules—Virgo and Spica—Vega and Lyra—The Swan.

The student of astronomy should make himself acquainted with the principal constellations in the heavens. This is a pleasing acquirement, and might well form a part of the education of every child in the kingdom. We shall commence our discussion of the sidereal system with a brief account of the principal constellations visible in the northern hemisphere, and we accompany our description with such outline maps of the stars as will enable the beginner to identify the chief features of the starry heavens.

In an earlier chapter we directed the attention of the student to the remarkable constellation of stars which is known to astronomers as Ursa Major, or the Great Bear. It forms the most conspicuous group in the northern skies, and in northern latitudes it never sets. At eleven p.m. in the month of April the Great Bear is directly overhead (for an observer in the United Kingdom); at the same hour in September it is low down in the north; at the same hour July it is in the west; by Christmas it is at the east. From the remotest antiquity this group of stars has attracted attention. The stars in the Great Bear were comprised in a great catalogue of stars, made two thousand years ago, which has been handed down to us. From the positions of the stars given in this catalogue it is possible to reconstruct the Great Bear as it appeared in those early days. This has been done, and it appears that the seven principal stars have not changed in this lapse of time to any large extent, so that the configuration of the Great Bear remains practically the same now as it was then. The beginner must first obtain an acquaintance with this group of seven stars, and then his further progress in this branch of astronomy will be greatly facilitated. The Great Bear is, indeed, a splendid constellation, and its only rival is to be found in Orion, which contains more brilliant stars, though it does not occupy so large a region in the heavens.



In the first place, we observe how the Great Bear enables the Pole Star, which is the most important object in the northern heavens, to be readily found. The Pole Star is very conveniently indicated by the direction of the two stars, b and a, of the Great Bear, which are, accordingly, generally known as the "pointers." This use of the Great Bear is shown on the diagram in Fig. 80, in which the line b a, produced onwards and slightly curved, will conduct to the Pole Star. There is no likelihood of making any mistake in this star, as it is the only bright one in the neighbourhood. Once it has been seen it will be readily identified on future occasions, and the observer will not fail to notice how constant is the position which it preserves in the heavens. The other stars either rise or set, or, like the Great Bear, they dip down low in the north without actually setting, but the Pole Star exhibits no considerable changes. In summer or winter, by night or by day, the Pole Star is ever found in the same place—at least, so far as ordinary observation is concerned. No doubt, when we use the accurate instruments of the observatory the notion of the fixity of the Pole Star is abandoned; we then see that it has a slow motion, and that it describes a small circle every twenty-four hours around the true pole of the heavens, which is not coincident with the Pole Star, though closely adjacent thereto. The distance is at present a little more than a degree, and it is gradually lessening, until, in the year A.D. 2095, the distance will be under half a degree.

The Pole Star itself belongs to another inconsiderable group of stars known as the Little Bear. The two principal members of this group, next in brightness to the Pole Star, are sometimes called the "Guards." The Great Bear and the Little Bear, with the Pole Star, form a group in the northern sky not paralleled by any similarly situated constellation in the southern heavens. At the South Pole there is no conspicuous star to indicate its position approximately—a circumstance disadvantageous to astronomers and navigators in the southern hemisphere.

It will now be easy to add a third constellation to the two already acquired. On the opposite side of the Pole Star to the Great Bear, and at about the same distance, lies a very pleasing group of five bright stars, forming a W. These are the more conspicuous members of the constellation Cassiopeia, which contains altogether about sixty stars visible to the naked eye. When the Great Bear is low down in the north, then Cassiopeia is high overhead. When the Great Bear is high overhead, then Cassiopeia is to be looked for low down in the north. The configuration of the leading stars is so striking that once the eye has recognised them future identification will be very easy—the more so when it is borne in mind that the Pole Star lies midway between Cassiopeia and the Great Bear (Fig. 81). These important constellations will serve as guides to the rest. We shall accordingly show how the learner may distinguish the various other groups visible from the British Islands or similar northern latitudes.

The next constellation to be recognised is the imposing group which contains the Great Square of Pegasus. This is not, like Ursa Major, or like Cassiopeia, said to be "circumpolar." The Great Square of Pegasus sets and rises daily. It cannot be seen conveniently during the spring and the summer, but in autumn and in winter the four stars which mark the corners of the square can be easily recognised. There are certain small stars within the region so limited; perhaps about thirty can be counted by an unaided eye of ordinary power in these latitudes. In the south of Europe, with its pure and bright skies, the number of visible stars appears to be greatly increased. An acute observer at Athens has counted 102 in the same region.



The Great Square of Pegasus can be reached by a line from the Pole Star over the end of Cassiopeia. If it be produced about as far again it will conduct the eye to the centre of the Great Square of Pegasus (Fig. 82).

The line through b and a in Pegasus continued 45 deg. to the south points out the important star Fomalhaut in the mouth of the Southern Fish. To the right of this line, nearly half-way down, is the rather vague constellation of Aquarius, where a small equilateral triangle with a star in the centre may be noticed.

The square of Pegasus is not a felicitous illustration of the way in which the boundaries of the constellations should be defined. There can be no more naturally associated group than the four stars of this square, and they ought surely to be included in the same constellation. Three of the stars—marked a, b, g—do belong to Pegasus; but that at the fourth corner—also marked a—is placed in a different figure, known as Andromeda, whereof it is, indeed, the brightest member. The remaining bright stars of Andromeda are marked b and g, and they are readily identified by producing one side of the Square of Pegasus in a curved direction. We have thus a remarkable array of seven stars, which it is both easy to identify and easy to remember, notwithstanding that they are contributed to by three different constellations. They are respectively a, b, and g of Pegasus; a, b, and g of Andromeda; and a of Perseus. The three form a sort of handle, as it were, extending from one side of the square, and are a group both striking in appearance, and useful in the further identification of celestial objects. b Andromedae, with two smaller stars, form the girdle of the unfortunate heroine.

a Persei lies between two other stars (g and d) of the same constellation. If we draw a curve through these three and prolong it in a bold sweep, we are conducted to one of the gems of the northern heavens—the beautiful star Capella, in Auriga (Fig. 83). Close to Capella are three small stars forming an isosceles triangle—these are the Hoedi or Kids. Capella and Vega are, with the exception of Arcturus, the two most brilliant stars in the northern heavens; and though Vega is probably the more lustrous of the two, yet the opposite opinion has been entertained. Different eyes will frequently form various estimates of the relative brilliancy of stars which approach each other in brightness. The difficulty of making a satisfactory comparison between Vega and Capella is greatly increased by the wide distance in the heavens at which they are separated, as well as by a slight difference in colour, for Vega is distinctly whiter than Capella. This contrast between the colour of stars is often a source of uncertainty in the attempt to compare their relative brilliancy; so that when actual measurements have to be effected by instrumental means, it is necessary to compare the two stars alternately with some object of intermediate hue.



On the opposite side of the pole to Capella, but not quite so far away, will be found four small stars in a quadrilateral. They form the head of the Dragon, the rest of whose form coils right round the pole.

If we continue the curve formed by the three stars g, a, and d in Perseus, and if we bend round this curve gracefully into one of an opposite flexion, in the manner shown in Fig. 83, we are first conducted to two other principal stars in Perseus, marked e and z. The region of Perseus is one of the richest in the heavens. We have here a most splendid portion of the Milky Way, and the field of the telescope is crowded with stars beyond number. Even a small telescope or an opera-glass directed to this teeming constellation cannot fail to delight the observer, and convey to him a profound impression of the extent of the sidereal heavens. We shall give in a subsequent paragraph a brief enumeration of some of the remarkable telescopic objects in Perseus. Pursuing in the same figure the line e and z, we are conducted to the remarkable little group known as the Pleiades.



The Pleiades form a group so universally known and so easily identified that it hardly seems necessary to give any further specific instructions for their discovery. It may, however, be observed that in these latitudes they cannot be seen before midnight during the summer. Let us suppose that the search is made at about 11 p.m. at night: on the 1st of January the Pleiades will be found high up in the sky in the south-west; on the 1st of March, at the same hour, they will be seen to be setting in the west. On the 1st of May they are not visible; on the 1st of July they are not visible; on the 1st of September they will be seen low down in the east. On the 1st of November they will be high in the heavens in the south-east. On the ensuing 1st of January the Pleiades will be in the same position as they were on the same date in the previous year, and so on from year to year. It need, perhaps, hardly be explained here that these changes are not really due to movements of the constellations; they are due, of course, to the apparent annual motion of the sun among the stars.



The Pleiades are shown in the figure (Fig. 84), where a group of ten stars is represented, this being about the number visible with the unaided eye to those who are gifted with very acute vision. The lowest telescopic power will increase the number of stars to thirty or forty (Galileo saw more than forty with his first telescope), while with telescopes of greater power the number is largely increased; indeed, no fewer than 625 have been counted with the aid of a powerful telescope. The group is, however, rather too widely scattered to make an effective telescopic object, except with a large field and low power. Viewed through an opera-glass it forms a very pleasing spectacle.



If we draw a ray from the Pole Star to Capella, and produce it sufficiently far, as shown in Fig. 85, we come to the great constellation of our winter sky, the splendid group of Orion. The brilliancy of the stars in Orion, the conspicuous belt, and the telescopic objects which it contains, alike render this group remarkable, and place it perhaps at the head of the constellations. The leading star in Orion is known either as a Orionis, or as Betelgeuze, by which name it is here designated. It lies above the three stars, d, e, z, which form the belt. Betelgeuze is a star of the first magnitude, and so also is Rigel, on the opposite side of the belt. Orion thus enjoys the distinction of containing two stars of the first magnitude in its group, while the five other stars shown in Fig. 85 are of the second magnitude.

The neighbourhood of Orion contains some important stars. If we carry on the line of the belt upwards to the right, we are conducted to another star of the first magnitude, Aldebaran, which strongly resembles Betelgeuze in its ruddy colour. Aldebaran is the brightest star in the constellation of Taurus. It is this constellation which contains the Pleiades already referred to, and another more scattered group known as the Hyades, which can be discovered near Aldebaran.



The line of the belt of Orion continued downwards to the left conducts the eye to the gem of the sky, the splendid Sirius, which is the most brilliant star in the heavens. It has, indeed, been necessary to create a special order of magnitude for the reception of Sirius alone; all the other first magnitude stars, such as Vega and Capella, Betelgeuze and Aldebaran, coming a long way behind. Sirius, with a few other stars of much less lustre, form the constellation of Canis Major.

It is useful for the learner to note the large configuration, of an irregular lozenge shape, of which the four corners are the first magnitude stars, Aldebaran, Betelgeuze, Sirius, and Rigel (Fig. 85). The belt of Orion is placed symmetrically in the centre of the group, and the whole figure is so striking that once perceived it is not likely to be forgotten.

About half way from the Square of Pegasus to Aldebaran is the chief star in the Ram—a bright orb of the second magnitude; with two others it forms a curve, at the other end of which will be found g of the same constellation, which was the first double star ever noticed.

We can again invoke the aid of the Great Bear to point out the stars in the constellation of Gemini (Fig. 86). If the diagonal joining the stars d and b of the body of the Bear be produced in the direction opposite to the tail, it will lead to Castor and Pollux, two remarkable stars of the second magnitude. This same line carried a little further on passes near the star Procyon, of the first magnitude, which is the only conspicuous object in the constellation of the Little Dog.



The pointers in the Great Bear marked a b will also serve to indicate the constellation of the Lion. If we produce the line joining them in the direction opposite from that used in finding the Pole, we are brought into the body of the Lion. This group will be recognised by the star of the first magnitude called Regulus. It is one of a series of stars forming an object somewhat resembling a sickle: three of the group are of the second magnitude. The Sickle has a special claim on our notice because it contains the radiant point from which the periodic shooting star shower known as the Leonids diverges. Regulus lies alongside the sun's highway through the stars, at a point which he passes on the 21st of August every year.

Between Gemini and Leo the inconspicuous constellation of the Crab may be found; the most striking object it contains is the misty patch called Praesepe or the Bee-Hive, which the smallest opera-glass will resolve into its component stars.



The tail of the Great Bear, when prolonged with a continuation of the curve which it possesses, leads to a brilliant star of the first magnitude known as Arcturus, the principal star in the constellation of Booetes (Fig. 88). A few other stars, marked b, g, d, and e in the same constellation, are also shown in the figure. Among the stars visible in these latitudes Arcturus is to be placed next to Sirius in point of brightness. Two stars in the southern hemisphere, invisible in these latitudes, termed a Centauri and Canopus, are nearly as bright as Vega and Capella, but not quite as bright as Arcturus.

In the immediate neighbourhood of Booetes is a striking semicircular group known as the Crown or Corona Borealis. It will be readily found from its position as indicated in the figure, or it may be identified by following the curved line indicated by b, d, e, and z in the Great Bear.



The constellation of Virgo is principally characterised by the first magnitude star called Spica, or a Virginis. This may be found from the Great Bear; for if the line joining the two stars a and g in that constellation be prolonged with a slight curve, it will conduct the eye to Spica. We may here notice another of those large configurations which are of great assistance in the study of the stars. There is a fine equilateral triangle, whereof Arcturus and Spica form two of the corners, while the third is indicated by Denebola, the bright star near the tail of the Lion (Fig. 89).

In the summer evenings when the Crown is overhead, a line from the Pole Star through its fainter edge, continued nearly to the southern horizon, encounters the brilliant red star Cor Scorpionis, or the Scorpion's Heart (Antares), which was the first star mentioned as having been seen with the telescope in the daytime.

The first magnitude star, Vega, in the constellation of the Lyre, can be readily found at the corner of a bold triangle, of which the Pole Star and Arcturus form the base (Fig. 90). The brilliant whiteness of Vega will arrest the attention, while the small group of neighbouring stars which form the Lyre produces one of the best defined constellations.

Near Vega is another important constellation, known as the Swan or Cygnus. The brightest star will be identified as the vertex of a right-angled triangle, of which the line from Vega to the Pole Star is the base, as shown in Fig. 91. There are in Cygnus five principal stars, which form a constellation of rather remarkable form.

The last constellation which we shall here describe is that of Aquila or the Eagle, which contains a star of the first magnitude, known as Altair; this group can be readily found by a line from Vega over b Cygni, which passes near the line of three stars, forming the characteristic part of the Eagle.

We have taken the opportunity to indicate in these sketches of the constellations the positions of some other remarkable telescopic objects, the description of which we must postpone to the following chapters.



CHAPTER XIX.

THE DISTANT SUNS.

Sirius Contrasted with the Sun—Stars can be Weighed, but not in general Measured—The Companion of Sirius—Determination of the Weights of Sirius and his Companion—Dark Stars—Variable and Temporary Stars—Enormous Number of Stars.

The splendid pre-eminence of Sirius has caused it to be observed with minute care from the earliest times in the history of astronomy. Each generation of astronomers devoted time and labour to determine the exact places of the brightest stars in the heavens. A vast mass of observations as to the place of Sirius among the stars had thus been accumulated, and it was found that, like many other stars, Sirius had what astronomers call proper motion. Comparing the place of Sirius with regard to the other stars now with the place which it occupied one hundred years ago, there is a difference of two minutes (127") in its situation. This is a small quantity: it is so small that the unaided eye could not see it. Could we now see the sky as it appeared one century ago, we should still see this star in its well-known place to the left of Orion. Careful alignment by the eye would hardly detect that Sirius was moving in two, or even in three or in four centuries. But the accuracy of the meridian circle renders these minute quantities evident, and gives to them their true significance. To the eye of the astronomer, Sirius, instead of creeping along with a movement which centuries will not show, is pursuing its majestic course with a velocity appropriate to its dimensions.

Though the velocity of Sirius is about 1,000 miles a minute, yet it is sometimes a little more and sometimes a little less than its mean value. To the astronomer this fact is pregnant with information. Were Sirius an isolated star, attended only by planets of comparative insignificance, there could be no irregularity in its motion. If it were once started with a velocity of 1,000 miles a minute, then it must preserve that velocity. Neither the lapse of centuries nor the mighty length of the journey could alter it. The path of Sirius would be inflexible in its direction; and it would be traversed with unalterable velocity.



The fact that Sirius had not been moving uniformly was of such interest that it arrested the attention of Bessel when he discovered the irregularities in 1844. Believing, as Bessel did, that there must be some adequate cause for these disturbances, it was hardly possible to doubt what the cause must be. When motion is disturbed there must be force in action, and the only force that we recognise in such cases is that known as gravitation. But gravity can only act from one body to another body; so that when we seek for the derangement of Sirius by gravitation, we are obliged to suppose that there must be some mighty and massive body near Sirius. The question was taken up again by Peters and by Auwers, who were able to discover, from the irregularities of Sirius, the nature of the path of the disturbing body. They were able to show that it must revolve around Sirius in a period of about fifty years, and although they could not tell its distance from Sirius, yet they were able to point out the direction in which it must lie. Fig. 92 shows the orbit of Sirius as given by Mr. Burnham, of Yerkes Observatory.

The detection of the attendant of Sirius, and the measures which have been made thereon, enable us to determine the weight of this famous star. Let us attempt to illustrate this subject. It must, no doubt, be admitted that the numerical estimates we employ have to be received with a certain degree of caution. The companion of Sirius is a difficult object to observe, and previous to 1896 it had only been followed through an arc of 90 deg.. We are, therefore, hardly as yet in a position to speak with absolute accuracy as to the periodic time in which the companion completes its revolution. We may, however, take this time to be fifty-two years. We also know the distance from Sirius to his companion, and we may take it to be about twenty-one times the distance from the earth to the sun. It is useful, in the first place, to compare the revolution of the companion around Sirius with the revolution of the planet Uranus around the sun. Taking the earth's distance as unity, the radius of the orbit of Uranus is about nineteen, and Uranus takes eighty-four years to accomplish a complete revolution. We have no planet in the solar system at a distance of twenty-one; but from Kepler's third law it may be shown that, if there were such a planet, its periodic time would be about ninety-nine years. We have now the necessary materials for making the comparison between the mass of Sirius and the mass of the sun. A body revolving around Sirius at a certain distance completes its journey in fifty-two years. To revolve around the sun at the same distance a body should complete its journey in ninety-nine years. The quicker the body is moving the greater must be the centrifugal force, and the greater must be the attractive power of the central body. It can be shown from the principles of dynamics that the attractive power is inversely proportional to the square of the periodic time. Hence, then, the attractive power of Sirius must bear to the attractive power of the sun the proportion which the square of ninety-nine has to the square of fifty-two. As the distances are in each case supposed to be equal, the attractive powers will be proportional to the masses, and hence we conclude that the mass of Sirius, together with that of his companion, is to the mass of the sun, together with that of his planet, in the ratio of three and a half to one. We had already learned that Sirius was much brighter than the sun; now we have learned that it is also much more massive.

Before we leave the consideration of Sirius, there is one additional point of very great interest which it is necessary to consider. There is a remarkable contrast between the brilliancy of Sirius and his companion. Sirius is a star far transcending all other stars of the first magnitude, while his companion is extremely faint. Even if it were completely withdrawn from the dazzling proximity of Sirius, the companion would be only a small star of the eighth or ninth magnitude, far below the limits of visibility to the unaided eye. To put the matter in numerical language, Sirius is 5,000 times as bright as its companion, but only about twice as heavy! Here is a very great contrast; and this point will appear even more forcible if we contrast the companion of Sirius with our sun. The companion is slightly heavier than our sun; but in spite of its slightly inferior bulk, our sun is much more powerful as a light-giver. One hundred of the companions of Sirius would not give as much light as our sun! This is a result of very considerable significance. It teaches us that besides the great bodies in the universe which attract attention by their brilliancy, there are also other bodies of stupendous mass which have but little brilliancy—probably some of them possess none at all. This suggests a greatly enhanced conception of the majestic scale of the universe. It also invites us to the belief that the universe which we behold bears but a small ratio to the far larger part which is invisible in the sombre shades of night. In the wide extent of the material universe we have here or there a star or a mass of gaseous matter sufficiently heated to be luminous, and thus to become visible from the earth; but our observation of these luminous points can tell us little of the remaining contents of the universe.

The most celebrated of all the variable stars is that known as Algol, whose position in the constellation of Perseus is shown in Fig. 83. This star is conveniently placed for observation, being visible every night in our latitude, and its interesting changes can be observed without any telescopic aid. Everyone who desires to become acquainted with the great truths of astronomy should be able to recognise this star, and should have also followed it during one of its periods of change. Algol is usually a star of the second magnitude; but in a period between two and three days, or, more accurately, in an interval of 2 days 20 hours 48 minutes and 55 seconds, its brilliancy goes through a most remarkable cycle of variations. The series commences with a gradual decline of the star's brightness, which in the course of four and a half hours falls from the second magnitude down to the fourth. At this lowest stage of brightness Algol remains for about twenty minutes, and then begins to increase, until in three and a half hours it regains the second magnitude, at which it continues for about 2 days 12 hours, when the same series commences anew. It seems that the period required by Algol to go through its changes is itself subject to a slow but certain variation. We shall see in a following chapter how it has been proved that the variability of Algol is due to the occasional interposition of a dark companion which cuts off a part of the lustre of the star. All the circumstances can thus be accounted for, and even the weight and the size of Algol and its dark companion be determined.

There are, however, other classes of variable stars, the fluctuation of whose light can hardly be due to occasional obscuration by dark bodies. This is particularly the case with those variables which are generally faint, but now and then flare up for a short time, after which temporary exaltation they again sink down to their original condition. The periods of such changes are usually from six months to two years. The best known example of a star of this class was discovered more than three hundred years ago. It is situated in the constellation Cetus, a little south of the equator. This object was the earliest known case of a variable star, except the so-called temporary stars, to which we shall presently refer. The variable in Cetus received the name of Mira, or the wonderful. The period of the fluctuations of Mira Ceti is about eleven months, during the greater part of which time the star is of the ninth magnitude, and consequently invisible to the naked eye. When the proper time has arrived, its brightness begins to increase rather suddenly. It soon becomes a conspicuous object of the second or third magnitude. In this condition it remains for eight or ten days, and then declines more slowly than it rose until it is reduced to its original faintness, about three hundred days after the rise commenced.

More striking to the general observer than the ordinary variable stars are the temporary stars which on rare occasions suddenly make their appearance in the heavens. The most famous object of this kind was that which blazed out in the beginning of November, 1572, and which when first seen was as bright as Venus at its maximum brightness. It could, indeed, be seen in full daylight by sharp-sighted people. As far as history can tell us, no other temporary star has ever been as bright as this one. It is specially associated with the name of Tycho Brahe, for although he was not the discoverer, he made the best observations of the object, and he proved that it was at a distance comparable with that of the ordinary fixed stars. Tycho described carefully the gradual decline of the wonderful star until it disappeared from his view about the end of March, 1574, for the telescope, by which it could doubtless have been followed further, had not yet been invented. During the decline the colour of the object gradually changed; at first it was white, and by degrees became yellow, and in the spring of 1573 reddish, like Aldebaran. About May, 1573, we are told somewhat enigmatically that it "became like lead, or somewhat like Saturn," and so it remained as long as it was visible. What a fund of information our modern spectroscopes and other instruments would supply us with if so magnificent a star were to burst out in these modern days!

But though we have not in our own times been favoured with a view of a temporary star as splendid as the one seen by Tycho Brahe and his contemporaries, it has been our privilege to witness several minor outbursts of this kind. It seems likely that we should possess more records of temporary stars from former times if a better watch had been kept for them. That is at any rate the impression we get when we see how several of the modern stars of this kind have nearly escaped us altogether, notwithstanding the great number of telescopes which are now pointed to the sky on every clear night.

In 1866 a star of the second magnitude suddenly appeared in the constellation of the crown (Corona Borealis). It was first seen on the 12th May, and a few days afterwards it began to fade away. Argelander's maps of the northern heavens had been published some years previously, and when the position of the new star had been accurately determined, it was found that it was identical with an insignificant looking star marked on one of the maps as of the 9-1/2 magnitude. The star exists in the same spot to this day, and it is of the same magnitude as it was prior to its spasmodic outburst in 1866. This was the first new star which was spectroscopically examined. We shall give in Chapter XXIII. a short account of the features of its spectrum.

The next of these temporary bright stars, Nova Cygni, was first seen by Julius Schmidt at Athens on the 24th November, 1876, when it was between the third and fourth magnitudes, and he maintains that it cannot have been conspicuous four days earlier, when he was looking at the same constellation. By some inadvertence the news of the discovery was not properly circulated, and the star was not observed elsewhere for about ten days, when it had already become considerably fainter. The decrease of brightness went on very slowly; in October, 1877, the star was only of the tenth magnitude, and it continued getting fainter until it reached the fifteenth magnitude; in other words, it became a minute telescopic star, and it is so still in the very same spot. As this star did not reach the first or second magnitude it would probably have escaped notice altogether if Schmidt had not happened to look at the Swan on that particular evening.

We are not so likely to miss seeing a new star since astronomers have pressed the photographic camera into their service. This became evident in 1892, when the last conspicuous temporary star appeared in Auriga. On the 24th January, Dr. Anderson, an astronomer in Edinburgh, noticed a yellowish star of the fifth magnitude in the constellation Auriga, and a week later, when he had compared a star-map with the heavens and made sure that the object was really a new star, he made his discovery public. In the case of this star we are able to fix fairly closely the moment when it first blazed out. In the course of the regular photographic survey of the heavens undertaken at the Harvard College Observatory (Cambridge, Massachusetts) the region of the sky where the new star appeared had been photographed on thirteen nights from October 21st to December 1st, 1891, and on twelve nights from December 10th to January 20th, 1892. On the first series of plates there was no trace of the Nova, while it was visible on the very first plate of the second series as a star of the fifth magnitude. Fortunately it turned out that Professor Max Wolf of Heidelberg, a most successful celestial photographer, had photographed the same region on the 8th December, and this photograph does not show the star, so that it cannot on that night have been as bright as the ninth magnitude. Nova Auriga must therefore have flared up suddenly between the 8th and the 10th of December. According to the Harvard photographs, the first maximum of brightness occurred about the 20th of December, when the magnitude was 4-1/2. The decrease of the brightness was very irregular; the star fluctuated for the five weeks following the first of February between the fourth and the sixth magnitude, but after the beginning of March, 1892, the brightness declined very rapidly, and at the end of April the star was seen as an exceedingly faint one (sixteenth magnitude) with the great Lick Refractor. When this mighty instrument was again pointed to the Nova in the following August, it had risen nearly to the tenth magnitude, after which it gradually became extremely faint again, and is so still.

The temporary and the variable stars form but a very small section of the vast number of stars with which the vault of the heavens is studded. That the sun is no more than a star, and the stars are no less than suns, is a cardinal doctrine of astronomy. The imposing magnificence of this truth is only realised when we attempt to estimate the countless myriads of stars. This is a problem on which our calculations are necessarily vain. Let us, therefore, invoke the aid of the poet to attempt to express the innumerable, and conclude this chapter with the following lines of Mr. Allingham:—

"But number every grain of sand, Wherever salt wave touches land; Number in single drops the sea; Number the leaves on every tree, Number earth's living creatures, all That run, that fly, that swim, that crawl; Of sands, drops, leaves, and lives, the count Add up into one vast amount, And then for every separate one Of all those, let a flaming SUN Whirl in the boundless skies, with each Its massy planets, to outreach All sight, all thought: for all we see Encircled with infinity, Is but an island."



CHAPTER XX.

DOUBLE STARS.

Interesting Stellar Objects—Stars Optically Double—The Great Discovery of the Binary Stars made by Herschel—The Binary Stars describe Elliptic Paths—Why is this so important?—The Law of Gravitation—Special Double Stars—Castor—Mizar—The Coloured Double Stars—b Cygni.

The sidereal heavens contain few more interesting objects for the telescope than can be found in the numerous class of double stars. They are to be counted in thousands; indeed, many thousands can be found in the catalogues devoted to this special branch of astronomy. Many of these objects are, no doubt, small and comparatively uninteresting, but some of them are among the most conspicuous stars in the heavens, such as Sirius, whose system we have already described. We shall in this brief account select for special discussion and illustration a few of the more remarkable double stars. We shall particularly notice some of those that can be readily observed with a small telescope, and we have indicated on the sketches of the constellations in a previous chapter how the positions of these objects in the heavens can be ascertained.

It had been shown by Cassini in 1678 that certain stars, which appeared to the unaided eye as single points of light, really consisted of two or more stars, so close together that the telescope was required for their separation.[36] The number of these objects was gradually increased by fresh discoveries, until in 1781 (the same year in which Herschel discovered Uranus) a list containing eighty double stars was published by the astronomer Bode. These interesting objects claimed the attention of Herschel during his memorable researches. The list of known doubles rapidly swelled. Herschel's discoveries are to be enumerated by hundreds, while he also commenced systematic measurements of the distance by which the stars were separated, and the direction in which the line joining them pointed. It was these measurements which ultimately led to one of the most important and instructive of all Herschel's discoveries. When, in the course of years, his observations were repeated, Herschel found that in some cases the relative position of the stars had changed. He was thus led to the discovery that in many of the double stars the components are so related that they revolve around each other. Mark the importance of this result. We must remember that the stars are suns, comparable, it may be, with our sun in magnitude; so that here we have the astonishing spectacle of pairs of suns in mutual revolution. There is nothing very surprising in the fact that movements should be observed, for in all probability every body in the universe is in motion. It is the particular character of the movement which is specially interesting and instructive.

It had been imagined that the proximity of the two stars forming a double must be only accidental. It was thought that amid the vast host of stars in the heavens it not unfrequently happened that one star was so nearly behind another (as seen from the earth) that when the two were viewed in the telescope they produced the effect of a double star. No doubt many of the so-called double stars are produced in this way. Herschel's discovery shows that this explanation will not always answer, but that in many cases we really have two stars close together, and in motion round their common centre of gravity.

When the measurements of the distances and the positions of double stars had been accumulated during many years, they were taken over by the mathematicians to be treated by their methods. There is one peculiarity about double star observations: they have not—they cannot have—the accuracy which the computer of an orbit demands. If the distance between the pair of stars forming a binary be four seconds, the orbit we have to scrutinise is only as large as the apparent size of a penny-piece at the distance of one mile. It would require very careful measurement to make out the form of a penny a mile off, even with good telescopes. If the penny were tilted a little, it would appear, not circular, but oval; and it would be possible, by measuring this oval, to determine how much the penny was tilted. All this requires skilful work: the errors, viewed intrinsically, may not be great, but viewed with reference to the whole size of the quantities under consideration, they are very appreciable. We therefore find the errors of observation far more prominent in observations of this class than is generally the case when the mathematician assumes the task of discussing the labours of the observer.

The interpretation of Herschel's discovery was not accomplished by himself; the light of mathematics was turned on his observations of the binary stars by Savary, and afterwards by other mathematicians. Under their searching enquiries the errors of the measurements were disclosed, and the observations were purified from the grosser part of their inaccuracy. Mathematicians could then apply to their corrected materials the methods of enquiry with which they were familiar; they could deduce with fair precision the actual shape of the orbit of the binary stars, and the position of the plane in which that orbit is contained. The result is not a little remarkable. It has been proved that the motion of each of the stars is performed in an ellipse which contains the centre of gravity of the two stars in its focus. This has been actually shown to be true in many binary stars; it is believed to be true in all. But why is this so important? Is not motion in an ellipse common enough? Does not the earth revolve in an ellipse round the sun? And do not the planets also revolve in ellipses?

It is this very fact that elliptic motion is so common in the planets of the solar system which renders its discovery in binary stars of such importance. From what does the elliptic motion in the solar system arise? Is it not due to the law of attraction, discovered by Newton, which states that every mass attracts every other mass with a force which varies inversely as the square of the distance? That law of attraction had been found to pervade the whole solar system, and it explained the movements of the bodies of our system with marvellous fidelity. But the solar system, consisting of the sun, and the planets, with their satellites, the comets, and a host of smaller bodies, formed merely a little island group in the universe. In the economy of this tiny cosmical island the law of gravitation reigns supreme; before Herschel's discovery we never could have known whether that law was not merely a piece of local legislation, specially contrived for the exigencies of our particular system. This discovery gave us the knowledge which we could have gained from no other source. From the binary stars came a whisper across the vast abyss of space. That whisper told us that the law of gravitation was not peculiar to the solar system. It told us the law extended to the distant shores of the abyss in which our island is situated. It gives us grounds for believing that the law of gravitation is obeyed throughout the length, breadth, and depth of the entire visible universe.

One of the finest binary stars is that known as Castor, the brighter of the two principal stars in the constellation of Gemini. The position of Castor on the heavens is indicated in Fig. 86, page 418. Viewed by the unaided eye, Castor resembles a single star; but with a moderately good telescope it is found that what seems to be one star is really two separate stars, one of which is of the third magnitude, while the other is somewhat less. The angular distance of these two stars in the heavens is not so great as the angle subtended by a line an inch long viewed at a distance of half a mile. Castor is one of the double stars in which the components have been observed to possess a motion of revolution. The movement is, however, extremely slow, and the lapse of centuries will be required before a revolution is completely effected.

A beautiful double star can be readily identified in the constellation of Ursa Major (see Fig. 80, page 410). It is known as Mizar, and is the middle star (z) of the three which form the tail. In the close neighbourhood of Mizar is the small star Alcor, which can be readily seen with the unaided eye; but when we speak of Mizar as a double star, it is not to be understood that Alcor is one of the components of the double. Under the magnifying power of the telescope Alcor is seen to be transferred a long way from Mizar, while Mizar itself is split up into two suns close together. These components are of the second and the fourth magnitudes respectively, and as the apparent distance is nearly three times as great as in Castor, they are observed with facility even in a small telescope. This is, indeed, the best double star in the heavens for the beginner to commence his observations upon. We cannot, however, assert that Mizar is a binary, inasmuch as observations have not yet established the existence of a motion of revolution. Still less are we able to say whether Alcor is also a member of the same group, or whether it may not merely be a star which happens to fall nearly in the line of vision. Recent spectroscopic observations have shown that the larger component of Mizar is itself a double, consisting of a pair of suns so close together that there is not the slightest possibility of their ever being seen separately by the most powerful telescope in the world.

A pleasing class of double stars is that in which we have the remarkable phenomenon of colours, differing in a striking degree from the colours of ordinary stars. Among the latter we find, in the great majority of cases, no very characteristic hue; some are, however, more or less tinged with red, some are decidedly ruddy, and some are intensely red. Stars of a bluish or greenish colour are much more rare,[37] and when a star of this character does occur, it is almost invariably as one of a pair which form a double. The other star of the double is sometimes of the same hue, but more usually it is yellow or ruddy.

One of the loveliest of these objects, which lies within reach of telescopes of very moderate pretensions, is that found in the constellation of the Swan, and known as b Cygni (Fig. 91). This exquisite object is composed of two stars. The larger, about the third magnitude, is of a golden-yellow, or topaz, colour; the smaller, of the sixth magnitude, is of a light blue. These colours are nearly complementary, but still there can be no doubt that the effect is not merely one of contrast. That these two stars are both tinged with the hues we have stated can be shown by hiding each in succession behind a bar placed in the field of view. It has also been confirmed in a very striking manner by spectroscopic investigation; for we see that the blue star has experienced a special absorption of the red rays, while the more ruddy light of the other star has arisen from the absorption of the blue rays. The contrast of the colours in this object can often be very effectively seen by putting the eye-piece out of focus. The discs thus produced show the contrast of colours better than when the telescope exhibits merely two stellar points.

Such are a few of these double and multiple stars. Their numbers are being annually augmented; indeed, one observer—Mr. Burnham, formerly on the staff of the Lick Observatory, and now an observer in the Yerkes Observatory—has added by his own researches more than 1,000 new doubles to the list of those previously known.

The interest in this class of objects must necessarily be increased when we reflect that, small as the stars appear to be in our telescopes, they are in reality suns of great size and splendour, in many cases rivalling our own sun, or, perhaps, even surpassing him. Whether these suns have planets attending upon them we cannot tell; the light reflected from the planet would be utterly inadequate to the penetration of the vast extent of space which separates us from the stars. If there be planets surrounding these objects, then, instead of a single sun, such planets will be illuminated by two, or, perhaps, even more suns. What wondrous effects of light and shade must be the result! Sometimes both suns will be above the horizon together, sometimes only one sun, and sometimes both will be absent. Especially remarkable would be the condition of a planet whose suns were of the coloured type. To-day we have a red sun illuminating the heavens, to-morrow it would be a blue sun, and, perhaps, the day after both the red sun and the blue sun will be in the firmament together. What endless variety of scenery such a thought suggests! There are, however, grave dynamical reasons for doubting whether the conditions under which such a planet would exist could be made compatible with life in any degree resembling the life with which we are familiar. The problem of the movement of a planet under the influence of two suns is one of the most difficult that has ever been proposed to mathematicians, and it is, indeed, impossible in the present state of analysis to solve with accuracy all the questions which it implies. It seems not at all unlikely that the disturbances of the planet's orbit would be so great that it would be exposed to vicissitudes of light and of temperature far transcending those experienced by a planet moving, like the earth, under the supreme control of a single sun.



CHAPTER XXI.

THE DISTANCES OF THE STARS.

Sounding-line for Space—The Labours of Bessel—Meaning of Annual Parallax—Minuteness of the Parallactic Ellipse Illustrated—The Case of 61 Cygni—Different Comparison Stars used—The Proper Motion of the Star—Struve's Investigations—Can they be Reconciled?—Researches at Dunsink—Conclusion obtained—Accuracy which such Observations admit Examined—The Proper Motion of 61 Cygni—The Permanence of the Sidereal Heavens—The New Star in Cygnus—Its History—No Appreciable Parallax—A Mighty Outburst of Light—The Movement of the Solar System through Space—Herschel's Discovery—Journey towards Lyra—Probabilities.

We have long known the dimensions of the solar system with more or less accuracy. Our knowledge includes the distances of the planets and the comets from the sun, as well as their movements. We have also considerable knowledge of the diameters and the masses of many of the different bodies which belong to the solar system. We have long known, in fact, many details of the isolated group nestled together under the protection of the sun. The problem for consideration in the present chapter involves a still grander survey than is required for measures of our solar system. We propose to carry the sounding-line across the vast abyss which separates the group of bodies closely associated about our sun from the other stars which are scattered through the realms of space. For centuries the great problem of star distance has engaged the attention of those who have studied the heavens. It would be impossible to attempt here even an outline of the various researches which have been made on the subject. In the limited survey which we can make, we must glance first at the remarkable speculative efforts which have been directed to the problem, and then we shall refer to those labours which have introduced the problem into the region of accurate astronomy.

No attempt to solve the problem of the absolute distances of the stars was successful until many years after Herschel's labours were closed. Fresh generations of astronomers, armed with fresh appliances, have for many years pursued the subject with unremitting diligence, but for a long time the effort seemed hopeless. The distances of the stars were so great that they could not be ascertained until the utmost refinements of mechanical skill and the most elaborate methods of mathematical calculation were brought to converge on the difficulty. At last it was found that the problem was beginning to yield. A few stars have been induced to disclose the secret of their distance. We are able to give some answer to the question—How far are the stars? though it must be confessed that our reply up to the present moment is both hesitating and imperfect. Even the little knowledge which has been gained possesses interest and importance. As often happens in similar cases, the discovery of the distance of a star was made independently about the same time by two or three astronomers. The name of Bessel stands out conspicuously in this memorable chapter of astronomy. Bessel proved (1840) that the distance of the star known as 61 Cygni was a measurable quantity. His demonstration possessed such unanswerable logic that universal assent could not be withheld. Almost simultaneously with the classical labours of Bessel we have Struve's measurement of the distance of Vega, and Henderson's determination of the distance of the southern star a Centauri. Great interest was excited in the astronomical world by these discoveries, and the Royal Astronomical Society awarded its gold medal to Bessel. It appropriately devolved on Sir John Herschel to deliver the address on the occasion of the presentation of the medal: that address is a most eloquent tribute to the labours of the three astronomers. We cannot resist quoting the few lines in which Sir John said:—

"Gentlemen of the Royal Astronomical Society,—I congratulate you and myself that we have lived to see the great and hitherto impassable barrier to our excursion into the sidereal universe, that barrier against which we have chafed so long and so vainly—aestuantes angusto limite mundi—almost simultaneously overleaped at three different points. It is the greatest and most glorious triumph which practical astronomy has ever witnessed. Perhaps I ought not to speak so strongly; perhaps I should hold some reserve in favour of the bare possibility that it may be all an illusion, and that future researches, as they have repeatedly before, so may now fail to substantiate this noble result. But I confess myself unequal to such prudence under such excitement. Let us rather accept the joyful omens of the time, and trust that, as the barrier has begun to yield, it will speedily be effectually prostrated."

Before proceeding further, it will be convenient to explain briefly how the distance of a star can be measured. The problem is one of a wholly different character from that of the sun's distance, which we have already discussed in these pages. The observations for the determination of stellar parallax are founded on the familiar truth that the earth revolves around the sun. We may for our present purpose assume that the earth revolves in a circular path. The centre of that path is at the centre of the sun, and the radius of the path is 92,900,000 miles. Owing to our position on the earth, we observe the stars from a point of view which is constantly changing. In summer the earth is 185,800,000 miles distant from the position which it occupied in winter. It follows that the apparent positions of the stars, as projected on the background of the sky, must present corresponding changes. We do not now mean that the actual positions of the stars are really displaced. The changes are only apparent, and while oblivious of our own motion, which produces the displacements, we attribute the changes to the stars.

On the diagram in Fig. 93 is an ellipse with certain months—viz., January, April, July, October—marked upon its circumference. This ellipse may be regarded as a miniature picture of the earth's orbit around the sun. In January the earth is at the spot so marked; in April it has moved a quarter of the whole journey; and so on round the whole circle, returning to its original position in the course of one year. When we look from the position of the earth in January, we see the star A projected against the point of the sky marked 1. Three months later the observer with his telescope is carried round to April; but he now sees the star projected to the position marked 2. Thus, as the observer moves around the whole orbit in the annual revolution of the earth, so the star appears to move round in an ellipse on the background of the sky. In the technical language of astronomers, we speak of this as the parallactic ellipse, and it is by measuring the major axis of this ellipse that we determine the distance of the star from the sun. Half of this major axis, or, what comes to the same thing, the angle which the radius of the earth's orbit subtends as seen from the star, is called the star's "annual parallax."



The figure shows another star, B, more distant from the earth and the solar system generally than the star previously considered. This star also describes an elliptic path. We cannot, however, fail to notice that the parallactic ellipse belonging to B is much smaller than that of A. The difference in the sizes of the ellipses arises from the different distances of the stars from the earth. The nearer the star is to the earth the greater is the ellipse, so that the nearest star in the heavens will describe the largest ellipse, while the most distant star will describe the smallest ellipse. We thus see that the distance of the star is inversely proportional to the size of the ellipse, and if we measure the angular value of the major axis of the ellipse, then, by an exceedingly simple mathematical manipulation, the distance of the star can be expressed as a multiple of a radius of the earth's orbit. Assuming that radius to be 92,900,000 miles, the distance of the star is obtained by simple arithmetic. The difficulty in the process arises from the fact that these ellipses are so small that our micrometers often fail to detect them.

How shall we adequately describe the extreme minuteness of the parallactic ellipses in the case of even the nearest stars? In the technical language of astronomers, we may state that the longest diameter of the ellipse never subtends an angle of more than one and a half seconds. In a somewhat more popular manner, we would say that one thousand times the major axis of the very largest parallactic ellipse would not be as great as the diameter of the full moon. For a still more simple illustration, let us endeavour to think of a penny-piece placed at a distance of two miles. If looked at edgeways it will be linear, if tilted a little it would be elliptic; but the ellipse would, even at that distance, be greater than the greatest parallactic ellipse of any star in the sky. Suppose a sphere described around an observer, with a radius of two miles. If a penny-piece were placed on this sphere, in front of each of the stars, every parallactic ellipse would be totally concealed.

The star in the Swan known as 61 Cygni is not remarkable either for its size or for its brightness. It is barely visible to the unaided eye, and there are some thousands of stars which are apparently larger and brighter. It is, however, a very interesting example of that remarkable class of objects known as double stars. It consists of two nearly equal stars close together, and evidently connected by a bond of mutual attraction. The attention of astronomers is also specially directed towards the star by its large proper motion. In virtue of that proper motion, the two components are carried together over the sky at the rate of five seconds annually. A proper motion of this magnitude is extremely rare, yet we do not say it is unparalleled, for there are some few stars which have a proper motion even more rapid; but the remarkable duplex character of 61 Cygni, combined with the large proper motion, render it an unique object, at all events, in the northern hemisphere.

When Bessel proposed to undertake the great research with which his name will be for ever connected, he determined to devote one, or two, or three years to the continuous observations of one star, with the view of measuring carefully its parallactic ellipse. How was he to select the object on which so much labour was to be expended? It was all-important to choose a star which should prove sufficiently near to reward his efforts by exhibiting a measurable parallax. Yet he could have but little more than surmise and analogy as a guide. It occurred to him that the exceptional features of 61 Cygni afforded the necessary presumption, and he determined to apply the process of observation to this star. He devoted the greater part of three years to the work, and succeeded in discovering its distance from the earth.

Since the date of Sir John Herschel's address, 61 Cygni has received the devoted and scarcely remitted attention of astronomers. In fact, we might say that each succeeding generation undertakes a new discussion of the distance of this star, with the view of confirming or of criticising the original discovery of Bessel. The diagram here given (Fig. 94) is intended to illustrate the recent history of 61 Cygni.

When Bessel engaged in his labours, the pair of stars forming the double were at the point indicated on the diagram by the date 1838. The next epoch occurred fifteen years later, when Otto Struve undertook his researches, and the pair of stars had by that time moved to the position marked 1853. Finally, when the same object was more recently observed at Dunsink Observatory, the pair had made still another advance, to the position indicated by the date 1878. Thus, in forty years this double star had moved over an arc of the heavens upwards of three minutes in length. The actual path is, indeed, more complicated than a simple rectilinear movement. The two stars which form the double have a certain relative velocity, in consequence of their mutual attraction. It will not, however, be necessary to take this into account, as the displacement thus arising in the lapse of a single year is far too minute to produce any inconvenient effect on the parallactic ellipse.



The case of 61 Cygni is, however, exceptional. It is one of our nearest neighbours in the heavens. We can never find its distance accurately to one or two billions of miles; but still we have a consciousness that an uncertainty amounting to twenty billions is too large a percentage of the whole. We shall presently show that we believe Struve was right, yet it does not necessarily follow that Bessel was wrong. The apparent paradox can be easily explained. It would not be easily explained if Struve had used the same comparison star as Bessel had done; but Struve's comparison star was different from either of Bessel's, and this is probably the cause of the discrepancy. It will be recollected that the essence of the process consists of the comparison of the small ellipse made by the distant star with the larger ellipse made by the nearer star. If the two stars were at the same distance, the process would be wholly inapplicable. In such a case, no matter how near the stars were to the earth, no parallax could be detected. For the method to be completely successful, the comparison star should be at least eight times as far as the principal star. Bearing this in mind, it is quite possible to reconcile the measures of Bessel with those of Struve. We need only assume that Bessel's comparison stars are about three times as far as 61 Cygni, while Struve's comparison star is at least eight or ten times as far. We may add that, as the comparison stars used by Bessel are brighter than that of Struve, there really is a presumption that the latter is the most distant of the three.

We have here a characteristic feature of this method of determining parallax. Even if all the observations and the reductions of a parallax series were mathematically correct, we could not with strict propriety describe the final result as the parallax of one star. It is only the difference between the parallax of the star and that of the comparison star. We can therefore only assert that the parallax sought cannot be less than the quantity determined. Viewed in this manner, the discrepancy between Struve and Bessel vanishes. Bessel asserted that the distance of 61 Cygni could not be more than sixty billions of miles. Struve did not contradict this—nay, he certainly confirmed it—when he showed that the distance could not be more than forty billions.

Nearly half a century has elapsed since Struve made his observations. Those observations have certainly been challenged; but they are, on the whole, confirmed by other investigations. In a critical review of the subject Auwers showed that Struve's determination is worthy of considerable confidence. Yet, notwithstanding this authoritative announcement, the study of 61 Cygni has been repeatedly resumed. Dr. Bruennow, when Astronomer Royal of Ireland, commenced a series of observations on the parallax of 61 Cygni, which were continued and completed by the present writer, his successor. Bruennow chose a fourth comparison star (marked on the diagram), different from any of those which had been used by the earlier observers. The method of observing which Bruennow employed was quite different from that of Struve, though the filar micrometer was used in both cases. Bruennow sought to determine the parallactic ellipse by measuring the difference in declination between 61 Cygni and the comparison star.[38] In the course of a year it is found that the difference in declination undergoes a periodic change, and from that change the parallactic ellipse can be computed. In the first series of observations I measured the difference of declination between the preceding star of 61 Cygni and the comparison star; in the second series I took the other component of 61 Cygni and the same comparison star. We had thus two completely independent determinations of the parallax resulting from two years' work. The first of these makes the distance forty billions of miles, and the second makes it almost exactly the same. There can be no doubt that this work supports Struve's determination in correction of Bessel's, and therefore we may perhaps sum up the present state of our knowledge of this question by saying that the distance of 61 Cygni is much nearer to the forty billions of miles which Struve found than to the sixty billions which Bessel found.[39]

It is desirable to give the reader the means of forming his own opinion as to the quality of the evidence which is available in such researches. The diagram in Fig. 95 here shown has been constructed with this object. It is intended to illustrate the second series of observations of difference of declination which I made at Dunsink. Each of the dots represents one night's observations. The height of the dot is the observed difference of declination between 61 (B) Cygni and the comparison star. The distance along the horizontal line—or the abscissa, as a mathematician would call it—represents the date. These observations are grouped more or less regularly in the vicinity of a certain curve. That curve expresses where the observations should have been, had they been absolutely perfect. The distances between the dots and the curve may be regarded as the errors which have been committed in making the observations.



Perhaps it will be thought that in many cases these errors appear to have attained very undesirable dimensions. Let us, therefore, hasten to say that it was precisely for the purpose of setting forth these errors that this diagram has been shown; we have to exhibit the weakness of the case no less than its strength. The errors of the observations are not, however, intrinsically so great as might at first sight be imagined. To perceive this, it is only necessary to interpret the scale on which this diagram has been drawn by comparison with familiar standards. The distance from the very top of the curve to the horizontal line denotes an angle of only four-tenths of a second. This is about the apparent diameter of a penny-piece at a distance of ten miles! We can now appraise the true magnitude of the errors which have been made. It will be noticed that no one of the dots is distant from the curve by much more than half of the height of the curve. It thus appears that the greatest error in the whole series of observations amounts to but two or three tenths of a second. This is equivalent to our having pointed the telescope to the upper edge of a penny-piece fifteen or twenty miles off, instead of to the lower edge. This is not a great blunder. A rifle team whose errors in pointing were more than a hundred times as great might still easily win every prize at Bisley.

We have entered into the history of 61 Cygni with some detail, because it is the star whose distance has been most studied. We do not say that 61 Cygni is the nearest of all the stars; it would, indeed, be very rash to assert that any particular star was the nearest of all the countless millions in the heavenly host. We certainly know one star which seems nearer than 61 Cygni; it lies in one of the southern constellations, and its name is a Centauri. This star is, indeed, of memorable interest in the history of the subject. Its parallax was first determined at the Cape of Good Hope by Henderson; subsequent researches have confirmed his observations, and the elaborate investigations of Dr. Gill have proved that the parallax of this star is about three-quarters of a second, so that it is only two-thirds of the distance of 61 Cygni.

61 Cygni arrested our attention, in the first instance, by the circumstance that it had the large proper motion of five seconds annually. We have also ascertained that the annual parallax is about half a second. The combination of these two statements leads to a result of considerable interest. It teaches us that 61 Cygni must each year traverse a distance of not less than ten times the radius of the earth's orbit. Translating this into ordinary figures, we learn that this star must travel nine hundred and twenty million miles per annum. It must move between two and three million miles each day, but this can only be accomplished by maintaining the prodigious velocity of thirty miles per second. There seems to be no escape from this conclusion. The facts which we have described, and which are now sufficiently well established, are inconsistent with the supposition that the velocity of 61 Cygni is less than thirty miles per second; the velocity may be greater, but less it cannot be.

For the last hundred and fifty years we know that 61 Cygni has been moving in the same direction and with the same velocity. Prior to the existence of the telescope we have no observation to guide us; we cannot, therefore, be absolutely certain as to the earlier history of this star, yet it is only reasonable to suppose that 61 Cygni has been moving from remote antiquity with a velocity comparable with that it has at present. If disturbing influences were entirely absent, there could be no trace of doubt about the matter. Some disturbing influence, however, there must be; the only question is whether that disturbing influence is sufficient to modify seriously the assumption we have made. A powerful disturbing influence might greatly alter the velocity of the star; it might deflect the star from its rectilinear course; it might even force the star to move around a closed orbit. We do not, however, believe that any disturbing influence of this magnitude need be contemplated, and there can be no reasonable doubt that 61 Cygni moves at present in a path very nearly straight, and with a velocity very nearly uniform.

As the distance of 61 Cygni from the sun is forty billions of miles, and its velocity is thirty miles a second, it is easy to find how long the star would take to accomplish a journey equal to its distance from the sun. The time required will be about 40,000 years. In the last 400,000 years 61 Cygni will have moved over a distance ten times as great as its present distance from the sun, whatever be the direction of motion. This star must therefore have been about ten times as far from the earth 400,000 years ago as it is at present. Though this epoch is incredibly more remote than any historical record, it is perhaps not incomparable with the duration of the human race; while compared with the vast lapse of geological time, such periods seem trivial and insignificant. Geologists have long ago repudiated mere thousands of years; they now claim millions, and many millions of years, for the performance of geological phenomena. If the earth has existed for the millions of years which geologists assert, it becomes reasonable for astronomers to speculate on the phenomena which have transpired in the heavens in the lapse of similar ages. By the aid of our knowledge of star distances, combined with an assumed velocity of thirty miles per second, we can make the attempt to peer back into the remote past, and show how great are the changes which our universe seems to have undergone.

In a million years 61 Cygni will apparently have moved through a distance which is twenty-five times as great as its present distance from the sun. Whatever be the direction in which 61 Cygni is moving—whether it be towards the earth or from the earth, to the right or to the left, it must have been about twenty-five times as far off a million years ago as it is at present; but even at its present distance 61 Cygni is a small star; were it ten times as far it could only be seen with a good telescope; were it twenty-five times as far it would barely be a visible point in our greatest telescopes.

The conclusions arrived at with regard to 61 Cygni may be applied with varying degrees of emphasis to other stars. We are thus led to the conclusion that many of the stars with which the heavens are strewn are apparently in slow motion. But this motion though apparently slow may really be very rapid. When standing on the sea-shore, and looking at a steamer on the distant horizon, we can hardly notice that the steamer is moving. It is true that by looking again in a few minutes we can detect a change in its place; but the motion of the steamer seems slow. Yet if we were near the steamer we would find that it was rushing along at the rate of many miles an hour. It is the distance which causes the illusion. So it is with the stars: they seem to move slowly because they are very distant, but were we near them, we could see that in the majority of cases their motions are a thousand times as fast as the quickest steamer that ever ploughed the ocean.

It thus appears that the permanence of the sidereal heavens, and the fixity of the constellations in their relative positions, are only ephemeral. When we rise to the contemplation of such vast periods of time as the researches of geology disclose, the durability of the constellations vanishes! In the lapse of those stupendous ages stars and constellations gradually dissolve from view, to be replaced by others of no greater permanence.

It not unfrequently happens that a parallax research proves abortive. The labour has been finished, the observations are reduced and discussed, and yet no value of the parallax can be obtained. The distance of the star is so vast that our base-line, although it is nearly two hundred millions of miles long, is too short to bear any appreciable ratio to the distance of the star. Even from such failures, however, information may often be drawn.

Let me illustrate this by an account derived from my own experience at Dunsink. We have already mentioned that on the 24th November, 1876, a well-known astronomer—Dr. Schmidt, of Athens—noticed a new bright star of the third magnitude in the constellation Cygnus. On the 20th of November Nova Cygni was invisible. Whether it first burst forth on the 21st, 22nd, or 23rd no one can tell; but on the 24th it was discovered. Its brilliancy even then seemed to be waning; so, presumably, it was brightest at some moment between the 20th and 24th of November. The outbreak must thus have been comparatively sudden, and we know of no cause which would account for such a phenomenon more simply than a gigantic collision. The decline in the brilliancy was much more tardy than its growth, and more than a fortnight passed before the star relapsed into insignificance—two or three days (or less) for the rise, two or three weeks for the fall. Yet even two or three weeks was a short time in which to extinguish so mighty a conflagration. It is comparatively easy to suggest an explanation of the sudden outbreak; it is not equally easy to understand how it can have been subdued in a few weeks. A good-sized iron casting in one of our foundries takes nearly as much time to cool as sufficed to abate the celestial fires in Nova Cygni!

On this ground it seemed not unreasonable to suppose that perhaps Nova Cygni was not really a very extensive conflagration. But, if such were the case, the star must have been comparatively near to the earth, since it presented so brilliant a spectacle and attracted so much attention. It therefore appeared a plausible object for a parallax research; and consequently a series of observations were made some years ago at Dunsink. I was at the time too much engaged with other work to devote very much labour to a research which might, after all, only prove illusory. I simply made a sufficient number of micrometric measurements to test whether a large parallax existed. It has been already pointed out how each star appears to describe a minute parallactic ellipse, in consequence of the annual motion of the earth, and by measurement of this ellipse the parallax—and therefore the distance—of the star can be determined. In ordinary circumstances, when the parallax of a star is being investigated, it is necessary to measure the position of the star in its ellipse on many different occasions, distributed over a period of at least an entire year. The method we adopted was much less laborious. It was sufficiently accurate to test whether or not Nova Cygni had a large parallax, though it might not have been delicate enough to disclose a small parallax. At a certain date, which can be readily computed, the star is at one end of the parallactic ellipse, and six months later the star is at the other end. By choosing suitable times in the year for our observations, we can measure the star in those two positions when it is most deranged by parallax. It was by observations of this kind that I sought to detect the parallax of Nova Cygni. Its distance from a neighbouring star was carefully measured by the micrometer at the two seasons when, if parallax existed, those distances should show their greatest discrepancy; but no certain difference between these distances could be detected. The observations, therefore, failed to reveal the existence of a parallactic ellipse—or, in other words, the distance of Nova Cygni was too great to be measured by observations of this kind.

It is certain that if Nova Cygni had been one of the nearest stars these observations would not have been abortive. We are therefore entitled to believe that Nova Cygni must be at least 20,000,000,000,000 miles from the solar system; and the suggestion that the brilliant outburst was of small dimensions must, it seems, be abandoned. The intrinsic brightness of Nova Cygni, when at its best, cannot have been greatly if at all inferior to the brilliancy of our sun himself. If the sun were withdrawn from us to the distance of Nova Cygni, it would seemingly have dwindled down to an object not more brilliant than the variable star. How the lustre of such a stupendous object declined so rapidly remains, therefore, a mystery not easy to explain. Have we not said that the outbreak of brilliancy in this star occurred between the 20th and the 24th of November, 1876? It would be more correct to say that the tidings of that outbreak reached our system at the time referred to. The real outbreak must have taken place at least three years previously. Indeed, at the time that the star excited such commotion in the astronomical world here, it had already relapsed again into insignificance.

In connection with the subject of the present chapter we have to consider a great problem which was proposed by Sir William Herschel. He saw that the stars were animated by proper motion; he saw also that the sun is a star, one of the countless host of heaven, and he was therefore led to propound the stupendous question as to whether the sun, like the other stars which are its peers, was also in motion. Consider all that this great question involves. The sun has around it a retinue of planets and their attendant satellites, the comets, and a host of smaller bodies. The question is, whether all this superb system is revolving around the sun at rest in the middle, or whether the whole system—sun, planets, and all—is not moving on bodily through space.

Herschel was the first to solve this noble problem; he discovered that our sun and the splendid retinue by which it is attended are moving in space. He not only discovered this, but he ascertained the direction in which the system was moving, as well as the approximate velocity with which that movement was probably performed. It has been shown that the sun and his system is now hastening towards a point of the heavens near the constellation Lyra. The velocity with which the motion is performed corresponds to the magnitude of the system; quicker than the swiftest rifle-bullet that was ever fired, the sun, bearing with it the earth and all the other planets, is now sweeping onwards. We on the earth participate in that motion. Every half hour we are something like ten thousand miles nearer to the constellation of Lyra than we should have been if the solar system were not animated by this motion. As we are proceeding at this stupendous rate towards Lyra, it might at first be supposed that we ought soon to get there; but the distances of the stars in that neighbourhood seem not less than those of the stars elsewhere, and we may be certain that the sun and his system must travel at the present rate for far more than a million years before we have crossed the abyss between our present position and the frontiers of Lyra. It must, however, be acknowledged that our estimate of the actual speed with which our solar system is travelling is exceedingly uncertain, but this does not in the least affect the fact that we are moving in the direction first approximately indicated by Herschel (see Chapter XXIII.).

It remains to explain the method of reasoning which Herschel adopted, by which he was able to make this great discovery. It may sound strange to hear that the detection of the motion of the sun was not made by looking at the sun; all the observations of the luminary itself with all the telescopes in the world would never tell us of that motion, for the simple reason that the earth, whence our observations must be made, participates in it. A passenger in the cabin of a ship usually becomes aware that the ship is moving by the roughness of the sea; but if the sea be perfectly calm, then, though the tables and chairs in the cabin are moving as rapidly as the ship, yet we do not see them moving, because we are also travelling with the ship. If we could not go out of the cabin, nor look through the windows, we would never know whether the ship was moving or at rest; nor could we have any idea as to the direction in which the ship was going, or as to the velocity with which that motion was performed.