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Transcriber's Note
The punctuation and spelling from the original text have been faithfully preserved. Only obvious typographical errors have been corrected. The advertisement from the beginning of the book has been joined with the other advertisements near the end of the book.
Greek words are spelled out and represented as [word]. Greek letters are represented as [a] "for alpha".
ASTRONOMY OF TO-DAY
ASTRONOMY OF TO-DAY
A POPULAR INTRODUCTION IN NON-TECHNICAL LANGUAGE
By
CECIL G. DOLMAGE, M.A., LL.D., D.C.L.
Fellow of the Royal Astronomical Society; Member of the British Astronomical Association; Member of the Astronomical Society of the Pacific; Membre de la Societe Astronomique de France; Membre de la Societe Belge d'Astronomie
With a Frontispiece in Colour and 45 Illustrations & Diagrams
THIRD EDITION
LONDON SEELEY AND CO. LIMITED 38 GREAT RUSSELL STREET 1910
PREFACE
The object of this book is to give an account of the science of Astronomy, as it is known at the present day, in a manner acceptable to the general reader.
It is too often supposed that it is impossible to acquire any useful knowledge of Astronomy without much laborious study, and without adventuring into quite a new world of thought. The reasoning applied to the study of the celestial orbs is, however, of no different order from that which is employed in the affairs of everyday life. The science of mathematics is perhaps responsible for the idea that some kind of difference does exist; but mathematical processes are, in effect, no more than ordinary logic in concentrated form, the shorthand of reasoning, so to speak. I have attempted in the following pages to take the main facts and theories of Astronomy out of those mathematical forms which repel the general reader, and to present them in the ordinary language of our workaday world.
The few diagrams introduced are altogether supplementary, and are not connected with the text by any wearying cross-references. Each diagram is complete in itself, being intended to serve as a pictorial aid, in case the wording of the text should not have perfectly conveyed the desired meaning. The full page illustrations are also described as adequately as possible at the foot of each.
As to the coloured frontispiece, this must be placed in a category by itself. It is the work of the artist as distinct from the scientist.
The book itself contains incidentally a good deal of matter concerned with the Astronomy of the past, the introduction of which has been found necessary in order to make clearer the Astronomy of our time.
It would be quite impossible for me to enumerate here the many sources from which information has been drawn. But I acknowledge my especial indebtedness to Professor F.R. Moulton's Introduction to Astronomy (Macmillan, 1906), to the works on Eclipses of the late Rev. S.J. Johnson and of Mr. W.T. Lynn, and to the excellent Journals of the British Astronomical Association. Further, for those grand questions concerned with the Stellar Universe at large, I owe a very deep debt to the writings of the famous American astronomer, Professor Simon Newcomb, and of our own countryman, Mr. John Ellard Gore; to the latter of whom I am under an additional obligation for much valuable information privately rendered.
In my search for suitable illustrations, I have been greatly aided by the kindly advice of Mr. W. H. Wesley, the Assistant Secretary of the Royal Astronomical Society. To those who have been so good as to permit me to reproduce pictures and photographs, I desire to record my best thanks as follows:—To the French Artist, Mdlle. Andree Moch; to the Astronomer Royal; to Sir David Gill, K.C.B., LL.D., F.R.S.; to the Council of the Royal Astronomical Society; to Professor E.B. Frost, Director of the Yerkes Observatory; to M.P. Puiseux, of the Paris Observatory; to Dr. Max Wolf, of Heidelberg; to Professor Percival Lowell; to the Rev. Theodore E.R. Phillips, M.A., F.R.A.S.; to Mr. W.H. Wesley; to the Warner and Swasey Co., of Cleveland, Ohio, U.S.A.; to the publishers of Knowledge, and to Messrs. Sampson, Low & Co. For permission to reproduce the beautiful photograph of the Spiral Nebula in Canes Venatici (Plate XXII.), I am indebted to the distinguished astronomer, the late Dr. W.E. Wilson, D.Sc., F.R.S., whose untimely death, I regret to state, occurred in the early part of this year.
Finally, my best thanks are due to Mr. John Ellard Gore, F.R.A.S., M.R.I.A., to Mr. W.H. Wesley, and to Mr. John Butler Burke, M.A., of Cambridge, for their kindness in reading the proof-sheets.
CECIL G. DOLMAGE.
LONDON, S.W., August 4, 1908.
PREFATORY NOTE TO THE SECOND EDITION
The author of this book lived only long enough to hear of the favour with which it had been received, and to make a few corrections in view of the second edition which it has so soon reached.
December 1908.
CONTENTS
CHAPTER I PAGE THE ANCIENT VIEW 17
CHAPTER II THE MODERN VIEW 20
CHAPTER III THE SOLAR SYSTEM 29
CHAPTER IV CELESTIAL MECHANISM 38
CHAPTER V CELESTIAL DISTANCES 46
CHAPTER VI CELESTIAL MEASUREMENT 55
CHAPTER VII ECLIPSES AND KINDRED PHENOMENA 61
CHAPTER VIII FAMOUS ECLIPSES OF THE SUN 83
CHAPTER IX FAMOUS ECLIPSES OF THE MOON 101
CHAPTER X THE GROWTH OF OBSERVATION 105
CHAPTER XI SPECTRUM ANALYSIS 121
CHAPTER XII THE SUN 127
CHAPTER XIII THE SUN—continued 134
CHAPTER XIV THE INFERIOR PLANETS 146
CHAPTER XV THE EARTH 158
CHAPTER XVI THE MOON 183
CHAPTER XVII THE SUPERIOR PLANETS 209
CHAPTER XVIII THE SUPERIOR PLANETS—continued 229
CHAPTER XIX COMETS 247
CHAPTER XX REMARKABLE COMETS 259
CHAPTER XXI METEORS OR SHOOTING STARS 266
CHAPTER XXII THE STARS 278
CHAPTER XXIII THE STARS—continued 287
CHAPTER XXIV SYSTEMS OF STARS 300
CHAPTER XXV THE STELLAR UNIVERSE 319
CHAPTER XXVI THE STELLAR UNIVERSE—continued 329
CHAPTER XXVII THE BEGINNING OF THINGS 333
CHAPTER XXVIII THE END OF THINGS 342
INDEX 351
LIST OF ILLUSTRATIONS
LIST OF PLATES
PLATE THE TOTAL ECLIPSE OF THE SUN OF AUGUST 30, 1905 Frontispiece
I. THE TOTAL ECLIPSE OF THE SUN OF MAY 17, 1882 To face page 96
II. GREAT TELESCOPE OF HEVELIUS " " 110
III. A TUBELESS, OR "AERIAL" TELESCOPE " " 112
IV. THE GREAT YERKES TELESCOPE " " 118
V. THE SUN, SHOWING SEVERAL GROUPS OF SPOTS " " 134
VI. PHOTOGRAPH OF A SUNSPOT " " 136
VII. FORMS OF THE SOLAR CORONA AT THE EPOCHS OF SUNSPOT MAXIMUM AND SUNSPOT MINIMUM RESPECTIVELY. (A) THE TOTAL ECLIPSE OF THE SUN OF DECEMBER 22, 1870. (B) THE TOTAL ECLIPSE OF THE SUN OF MAY 28, 1900 " " 142
VIII. THE MOON To face page 196
IX. MAP OF THE MOON, SHOWING THE PRINCIPAL "CRATERS," MOUNTAIN RANGES AND "SEAS" " " 198
X. ONE OF THE MOST INTERESTING REGIONS ON THE MOON " " 200
XI. THE MOON (SHOWING SYSTEMS OF "RAYS") " " 204
XII. A MAP OF THE PLANET MARS " " 216
XIII. MINOR PLANET TRAILS " " 226
XIV. THE PLANET JUPITER " " 230
XV. THE PLANET SATURN " " 236
XVI. EARLY REPRESENTATIONS OF SATURN " " 242
XVII. DONATI'S COMET " " 256
XVIII. DANIEL'S COMET OF 1907 " " 258
XIX. THE SKY AROUND THE NORTH POLE " " 292
XX. ORION AND HIS NEIGHBOURS " " 296
XXI. THE GREAT GLOBULAR CLUSTER IN THE SOUTHERN CONSTELLATION OF CENTAURUS " " 306
XXII. SPIRAL NEBULA IN THE CONSTELLATION OF CANES VENATICI " " 314
XXIII. THE GREAT NEBULA IN THE CONSTELLATION OF ANDROMEDA To face page 316
XXIV. THE GREAT NEBULA IN THE CONSTELLATION OF ORION " " 318
LIST OF DIAGRAMS
FIG. PAGE 1. THE PTOLEMAIC IDEA OF THE UNIVERSE 19
2. THE COPERNICAN THEORY OF THE SOLAR SYSTEM 21
3. TOTAL AND PARTIAL ECLIPSES OF THE MOON 64
4. TOTAL AND PARTIAL ECLIPSES OF THE SUN 67
5. "BAILY'S BEADS" 70
6. MAP OF THE WORLD ON MERCATOR'S PROJECTION, SHOWING A PORTION OF THE PROGRESS OF THE TOTAL SOLAR ECLIPSE OF AUGUST 30, 1905, ACROSS THE SURFACE OF THE EARTH 81
7. THE "RING WITH WINGS" 87
8. THE VARIOUS TYPES OF TELESCOPE 113
9. THE SOLAR SPECTRUM 123
10. A SECTION THROUGH THE SUN, SHOWING HOW THE PROMINENCES RISE FROM THE CHROMOSPHERE 131
11. ORBIT AND PHASES OF AN INFERIOR PLANET 148
12. THE "BLACK DROP" 153
13. SUMMER AND WINTER 176
14. ORBIT AND PHASES OF THE MOON 184
15. THE ROTATION OF THE MOON ON HER AXIS 187
16. LAPLACE'S "PERENNIAL FULL MOON" 191
17. ILLUSTRATING THE AUTHOR'S EXPLANATION OF THE APPARENT ENLARGEMENT OF CELESTIAL OBJECTS 195
18. SHOWING HOW THE TAIL OF A COMET IS DIRECTED AWAY FROM THE SUN 248
19. THE COMET OF 1066, AS REPRESENTED IN THE BAYEUX TAPESTRY 263
20. PASSAGE OF THE EARTH THROUGH THE THICKEST PORTION OF A METEOR SWARM 269
ASTRONOMY OF TO-DAY
CHAPTER I
THE ANCIENT VIEW
It is never safe, as we know, to judge by appearances, and this is perhaps more true of astronomy than of anything else.
For instance, the idea which one would most naturally form of the earth and heaven is that the solid earth on which we live and move extends to a great distance in every direction, and that the heaven is an immense dome upon the inner surface of which the stars are fixed. Such must needs have been the idea of the universe held by men in the earliest times. In their view the earth was of paramount importance. The sun and moon were mere lamps for the day and for the night; and these, if not gods themselves, were at any rate under the charge of special deities, whose task it was to guide their motions across the vaulted sky.
Little by little, however, this simple estimate of nature began to be overturned. Difficult problems agitated the human mind. On what, for instance, did the solid earth rest, and what prevented the vaulted heaven from falling in upon men and crushing them out of existence? Fantastic myths sprang from the vain attempts to solve these riddles. The Hindoos, for example, imagined the earth as supported by four elephants which stood upon the back of a gigantic tortoise, which, in its turn, floated on the surface of an elemental ocean. The early Western civilisations conceived the fable of the Titan Atlas, who, as a punishment for revolt against the Olympian gods, was condemned to hold up the expanse of sky for ever and ever.
Later on glimmerings of the true light began to break in upon men. The Greek philosophers, who busied themselves much with such matters, gradually became convinced that the earth was spherical in shape, that is to say, round like a ball. In this opinion we now know that they were right; but in their other important belief, viz. that the earth was placed at the centre of all things, they were indeed very far from the truth.
By the second century of the Christian era, the ideas of the early philosophers had become hardened into a definite theory, which, though it appears very incorrect to us to-day, nevertheless demands exceptional notice from the fact that it was everywhere accepted as the true explanation until so late as some four centuries ago. This theory of the universe is known by the name of the Ptolemaic System, because it was first set forth in definite terms by one of the most famous of the astronomers of antiquity, Claudius Ptolemaeus Pelusinensis (100-170 A.D.), better known as Ptolemy of Alexandria.
In his system the Earth occupied the centre; while around it circled in order outwards the Moon, the planets Mercury and Venus, the Sun, and then the planets Mars, Jupiter, and Saturn. Beyond these again revolved the background of the heaven, upon which it was believed that the stars were fixed—
"Stellis ardentibus aptum,"
as Virgil puts it (see Fig. 1).
The Ptolemaic system persisted unshaken for about fourteen hundred years after the death of its author. Clearly men were flattered by the notion that their earth was the most important body in nature, that it stood still at the centre of the universe, and was the pivot upon which all things revolved.
CHAPTER II
THE MODERN VIEW
It is still well under four hundred years since the modern, or Copernican, theory of the universe supplanted the Ptolemaic, which had held sway during so many centuries. In this new theory, propounded towards the middle of the sixteenth century by Nicholas Copernicus (1473-1543), a Prussian astronomer, the earth was dethroned from its central position and considered merely as one of a number of planetary bodies which revolve around the sun. As it is not a part of our purpose to follow in detail the history of the science, it seems advisable to begin by stating in a broad fashion the conception of the universe as accepted and believed in to-day.
The Sun, the most important of the celestial bodies so far as we are concerned, occupies the central position; not, however, in the whole universe, but only in that limited portion which is known as the Solar System. Around it, in the following order outwards, circle the planets Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune (see Fig. 2, p. 21). At an immense distance beyond the solar system, and scattered irregularly through the depth of space, lie the stars. The two first-mentioned members of the solar system, Mercury and Venus, are known as the Inferior Planets; and in their courses about the sun, they always keep well inside the path along which our earth moves. The remaining members (exclusive of the earth) are called Superior Planets, and their paths lie all outside that of the earth.
The five planets, Mercury, Venus, Mars, Jupiter, and Saturn, have been known from all antiquity. Nothing then can bring home to us more strongly the immense advance which has taken place in astronomy during modern times than the fact that it is only 127 years since observation of the skies first added a planet to that time-honoured number. It was indeed on the 13th of March 1781, while engaged in observing the constellation of the Twins, that the justly famous Sir William Herschel caught sight of an object which he did not recognise as having met with before. He at first took it for a comet, but observations of its movements during a few days showed it to be a planet. This body, which the power of the telescope alone had thus shown to belong to the solar family, has since become known to science under the name of Uranus. By its discovery the hitherto accepted limits of the solar system were at once pushed out to twice their former extent, and the hope naturally arose that other planets would quickly reveal themselves in the immensities beyond.
For a number of years prior to Herschel's great discovery, it had been noticed that the distances at which the then known planets circulated appeared to be arranged in a somewhat orderly progression outwards from the sun. This seeming plan, known to astronomers by the name of Bode's Law, was closely confirmed by the distance of the new planet Uranus. There still lay, however, a broad gap between the planets Mars and Jupiter. Had another planet indeed circuited there, the solar system would have presented an appearance of almost perfect order. But the void between Mars and Jupiter was unfilled; the space in which one would reasonably expect to find another planet circling was unaccountably empty.
On the first day of the nineteenth century the mystery was however explained, a body being discovered[1] which revolved in the space that had hitherto been considered planetless. But it was a tiny globe hardly worthy of the name of planet. In the following year a second body was discovered revolving in the same space; but it was even smaller in size than the first. During the ensuing five years two more of these little planets were discovered. Then came a pause, no more such bodies being added to the system until half-way through the century, when suddenly the discovery of these so-called "minor planets" began anew. Since then additions to this portion of our system have rained thick and fast. The small bodies have received the name of Asteroids or Planetoids; and up to the present time some six hundred of them are known to exist, all revolving in the previously unfilled space between Mars and Jupiter.
In the year 1846 the outer boundary of the solar system was again extended by the discovery that a great planet circulated beyond Uranus. The new body, which received the name of Neptune, was brought to light as the result of calculations made at the same time, though quite independently, by the Cambridge mathematician Adams, and the French astronomer Le Verrier. The discovery of Neptune differed, however, from that of Uranus in the following respect. Uranus was found merely in the course of ordinary telescopic survey of the heavens. The position of Neptune, on the other hand, was predicted as the result of rigorous mathematical investigations undertaken with the object of fixing the position of an unseen and still more distant body, the attraction of which, in passing by, was disturbing the position of Uranus in its revolution around the sun. Adams actually completed his investigation first; but a delay at Cambridge in examining that portion of the sky, where he announced that the body ought just then to be, allowed France to snatch the honour of discovery, and the new planet was found by the observer Galle at Berlin, very near the place in the heavens which Le Verrier had mathematically predicted for it.
Nearly fifty years later, that is to say, in our own time, another important planetary discovery was made. One of the recent additions to the numerous and constantly increasing family of the asteroids, a tiny body brought to light in 1898, turned out after all not to be circulating in the customary space between Mars and Jupiter, but actually in that between our earth and Mars. This body is very small, not more than about twenty miles across. It has received the name of Eros (the Greek equivalent for Cupid), in allusion to its insignificant size as compared with the other leading members of the system.
This completes the list of the planets which, so far, have revealed themselves to us. Whether others exist time alone will show. Two or three have been suspected to revolve beyond the path of Neptune; and it has even been asserted, on more than one occasion, that a planet circulates nearer to the sun than Mercury. This supposed body, to which the name of "Vulcan" was provisionally given, is said to have been "discovered" in 1859 by a French doctor named Lescarbault, of Orgeres near Orleans; but up to the present there has been no sufficient evidence of its existence. The reason why such uncertainty should exist upon this point is easy enough to understand, when we consider the overpowering glare which fills our atmosphere all around the sun's place in the sky. Mercury, the nearest known planet to the sun, is for this reason always very difficult to see; and even when, in its course, it gets sufficiently far from the sun to be left for a short time above the horizon after sunset, it is by no means an easy object to observe on account of the mists which usually hang about low down near the earth. One opportunity, however, offers itself from time to time to solve the riddle of an "intra-Mercurial" planet, that is to say, of a planet which circulates within the path followed by Mercury. The opportunity in question is furnished by a total eclipse of the sun; for when, during an eclipse of that kind, the body of the moon for a few minutes entirely hides the sun's face, and the dazzling glare is thus completely cut off, astronomers are enabled to give an unimpeded, though all too hurried, search to the region close around. A goodly number of total eclipses of the sun have, however, come and gone since the days of Lescarbault, and no planet, so far, has revealed itself in the intra-Mercurial space. It seems, therefore, quite safe to affirm that no globe of sufficient size to be seen by means of our modern telescopes circulates nearer to the sun than the planet Mercury.
Next in importance to the planets, as permanent members of the solar system, come the relatively small and secondary bodies known by the name of Satellites. The name satellite is derived from a Latin word signifying an attendant; for the bodies so-called move along always in close proximity to their respective "primaries," as the planets which they accompany are technically termed.
The satellites cannot be considered as allotted with any particular regularity among the various members of the system; several of the planets, for instance, having a goodly number of these bodies accompanying them, while others have but one or two, and some again have none at all. Taking the planets in their order of distance outward from the Sun, we find that neither Mercury nor Venus are provided with satellites; the Earth has only one, viz. our neighbour the Moon; while Mars has but two tiny ones, so small indeed that one might imagine them to be merely asteroids, which had wandered out of their proper region and attached themselves to that planet. For the rest, so far as we at present know, Jupiter possesses seven,[2] Saturn ten, Uranus four, and Neptune one. It is indeed possible, nay more, it is extremely probable, that the two last-named planets have a greater number of these secondary bodies revolving around them; but, unfortunately, the Uranian and Neptunian systems are at such immense distances from us, that even the magnificent telescopes of to-day can extract very little information concerning them.
From the distribution of the satellites, the reader will notice that the planets relatively near to the sun are provided with few or none, while the more distant planets are richly endowed. The conclusion, therefore, seems to be that nearness to the sun is in some way unfavourable either to the production, or to the continued existence, of satellites.
A planet and its satellites form a repetition of the solar system on a tiny scale. Just as the planets revolve around the sun, so do these secondary bodies revolve around their primaries. When Galileo, in 1610, turned his newly invented telescope upon Jupiter, he quickly recognised in the four circling moons which met his gaze, a miniature edition of the solar system.
Besides the planets and their satellites, there are two other classes of bodies which claim membership of the solar system. These are Comets and Meteors. Comets differ from the bodies which we have just been describing in that they appear filmy and transparent, whereas the others are solid and opaque. Again, the paths of the planets around the sun and of the satellites around their primaries are not actually circles; they are ovals, but their ovalness is not of a marked degree. The paths of comets on the other hand are usually very oval; so that in their courses many of them pass out as far as the known limits of the solar system, and even far beyond. It should be mentioned that nowadays the tendency is to consider comets as permanent members of the system, though this was formerly not by any means an article of faith with astronomers.
Meteors are very small bodies, as a rule perhaps no larger than pebbles, which move about unseen in space, and of which we do not become aware until they arrive very close to the earth. They are then made visible to us for a moment or two in consequence of being heated to a white heat by the friction of rushing through the atmosphere, and are thus usually turned into ashes and vapour long before they reach the surface of our globe. Though occasionally a meteoric body survives the fiery ordeal, and reaches the earth more or less in a solid state to bury itself deep in the soil, the majority of these celestial visitants constitute no source of danger whatever for us. Any one who will take the trouble to gaze at the sky for a short time on a clear night, is fairly certain to be rewarded with the view of a meteor. The impression received is as if one of the stars had suddenly left its accustomed place, and dashed across the heavens, leaving in its course a trail of light. It is for this reason that meteors are popularly known under the name of "shooting stars."
[1] By the Italian astronomer, Piazzi, at Palermo.
[2] Probably eight. (See note, page 232.)
CHAPTER III
THE SOLAR SYSTEM
We have seen, in the course of the last chapter, that the solar system is composed as follows:—there is a central body, the sun, around which revolve along stated paths a number of important bodies known as planets. Certain of these planets, in their courses, carry along in company still smaller bodies called satellites, which revolve around them. With regard, however, to the remaining members of the system, viz. the comets and the meteors, it is not advisable at this stage to add more to what has been said in the preceding chapter. For the time being, therefore, we will devote our attention merely to the sun, the planets, and the satellites.
Of what shape then are these bodies? Of one shape, and that one alone which appears to characterise all solid objects in the celestial spaces: they are spherical, which means round like a ball.
Each of these spherical bodies rotates; that is to say, turns round and round, as a top does when it is spinning. This rotation is said to take place "upon an axis," a statement which may be explained as follows:—Imagine a ball with a knitting-needle run right through its centre. Then imagine this needle held pointing in one fixed direction while the ball is turned round and round. Well, it is the same thing with the earth. As it journeys about the sun, it keeps turning round and round continually as if pivoted upon a mighty knitting needle transfixing it from North Pole to South Pole. In reality, however, there is no such material axis to regulate the constant direction of the rotation, just as there are no actual supports to uphold the earth itself in space. The causes which keep the celestial spheres poised, and which control their motions, are far more wonderful than any mechanical device.
At this juncture it will be well to emphasise the sharp distinction between the terms rotation and revolution. The term "rotation" is invariably used by astronomers to signify the motion which a celestial body has upon an axis; the term "revolution," on the other hand, is used for the movement of one celestial body around another. Speaking of the earth, for instance, we say, that it rotates on its axis, and that it revolves around the sun.
So far, nothing has been said about the sizes of the members of our system. Is there any stock size, any pattern according to which they may be judged? None whatever! They vary enormously. Very much the largest of all is the Sun, which is several hundred times larger than all the planets and satellites of the system rolled together. Next comes Jupiter and afterwards the other planets in the following order of size:—Saturn, Uranus, Neptune, the Earth, Venus, Mars, and Mercury. Very much smaller than any of these are the asteroids, of which Ceres, the largest, is less than 500 miles in diameter. It is, by the way, a strange fact that the zone of asteroids should mark the separation of the small planets from the giant ones. The following table, giving roughly the various diameters of the sun and the principal planets in miles, will clearly illustrate the great discrepancy in size which prevails in the system.
Sun 866,540 miles Mercury 2,765 " Venus 7,826 " Earth 7,918 " Mars 4,332 "
ZONE OF ASTEROIDS
Jupiter 87,380 " Saturn 73,125 " Uranus[3] 34,900 " Neptune[3] 32,900 "
It does not seem possible to arrive at any generalisation from the above data, except it be to state that there is a continuous increase in size from Mercury to the earth, and a similar decrease in size from Jupiter outwards. Were Mars greater than the earth, the planets could then with truth be said to increase in size up to Jupiter, and then to decrease. But the zone of asteroids, and the relative smallness of Mars, negative any attempt to regard the dimensions of the planets as an orderly sequence.
Next with respect to relative distance from the sun, Venus circulates nearly twice as far from it as Mercury, the earth nearly three times as far, and Mars nearly four times. After this, just as we found a sudden increase in size, so do we meet with a sudden increase in distance. Jupiter, for instance, is about thirteen times as far as Mercury, Saturn about twenty-five times, Uranus about forty-nine times, and Neptune about seventy-seven. (See Fig. 2, p. 21.)
It will thus be seen how enormously the solar system was enlarged in extent by the discovery of the outermost planets. The finding of Uranus plainly doubled its breadth; the finding of Neptune made it more than half as broad again. Nothing indeed can better show the import of these great discoveries than to take a pair of compasses and roughly set out the above relative paths in a series of concentric circles upon a large sheet of paper, and then to consider that the path of Saturn was the supposed boundary of our solar system prior to the year 1781.
We have seen that the usual shape of celestial bodies themselves is spherical. Of what form then are their paths, or orbits, as these are called? One might be inclined at a venture to answer "circular," but this is not the case. The orbits of the planets cannot be regarded as true circles. They are ovals, or, to speak in technical language, "ellipses." Their ovalness or "ellipticity" is, however, in each case not by any means of the same degree. Some orbits—for instance, that of the earth—differ only slightly from circles; while others—those of Mars or Mercury, for example—are markedly elliptic. The orbit of the tiny planet Eros is, however, far and away the most elliptic of all, as we shall see when we come to deal with that little planet in detail.
It has been stated that the sun and planets are always rotating. The various rates at which they do so will, however, be best appreciated by a comparison with the rate at which the earth itself rotates.
But first of all, let us see what ground we have, if any, for asserting that the earth rotates at all?
If we carefully watch the heavens we notice that the background of the sky, with all the brilliant objects which sparkle in it, appears to turn once round us in about twenty-four hours; and that the pivot upon which this movement takes place is situated somewhere near what is known to us as the Pole Star. This was one of the earliest facts noted with regard to the sky; and to the men of old it therefore seems as if the heavens and all therein were always revolving around the earth. It was natural enough for them to take this view, for they had not the slightest idea of the immense distance of the celestial bodies, and in the absence of any knowledge of the kind they were inclined to imagine them comparatively near. It was indeed only after the lapse of many centuries, when men had at last realised the enormous gulf which separated them from even the nearest object in the sky, that a more reasonable opinion began to prevail. It was then seen that this revolution of the heavens about the earth could be more easily and more satisfactorily explained by supposing a mere rotation of the solid earth about a fixed axis, pointed in the direction of the polar star. The probability of such a rotation on the part of the earth itself was further strengthened by the observations made with the telescope. When the surfaces of the sun and planets were carefully studied these bodies were seen to be rotating. This being the case, there could not surely be much hesitation in granting that the earth rotated also; particularly when it so simply explained the daily movement of the sky, and saved men from the almost inconceivable notion that the whole stupendous vaulted heaven was turning about them once in every twenty-four hours.
If the sun be regularly observed through a telescope, it will gradually be gathered from the slow displacement of sunspots across its face, their disappearance at one edge and their reappearance again at the other edge, that it is rotating on an axis in a period of about twenty-six days. The movement, too, of various well-known markings on the surfaces of the planets Mars, Jupiter, and Saturn proves to us that these bodies are rotating in periods, which are about twenty-four hours for the first, and about ten hours for each of the other two. With regard, however, to Uranus and Neptune there is much more uncertainty, as these planets are at such great distances that even our best telescopes give but a confused view of the markings which they display; still a period of rotation of from ten to twelve hours appears to be accepted for them. On the other hand the constant blaze of sunlight in the neighbourhood of Mercury and Venus equally hampers astronomers in this quest. The older telescopic observers considered that the rotation periods of these two planets were about the same as that of the earth; but of recent years the opinion has been gaining ground that they turn round on their axes in exactly the same time as they revolve about the sun. This question is, however, a very doubtful one, and will be again referred to later on; but, putting it on one side, it will be seen from what we have said above, that the rotation periods of the other planets of our system are usually about twenty-four hours, or under. The fact that the rotation period of the sun should run into days need not seem extraordinary when one considers its enormous size.
The periods taken by the various planets to revolve around the sun is the next point which has to be considered. Here, too, it is well to start with the earth's period of revolution as the standard, and to see how the periods taken by the other planets compare with it.
The earth takes about 365-1/4 days to revolve around the sun. This period of time is known to us as a "year." The following table shows in days and years the periods taken by each of the other planets to make a complete revolution round the sun:—
Mercury about 88 days. Venus " 226 " Mars " 1 year and 321 days. Jupiter " 11 years and 313 days. Saturn " 29 years and 167 days. Uranus " 84 years and 7 days. Neptune " 164 years and 284 days.
From these periods we gather an important fact, namely, that the nearer a planet is to the sun the faster it revolves.
Compared with one of our years what a long time does an Uranian, or Neptunian, "year" seem? For instance, if a "year" had commenced in Neptune about the middle of the reign of George II., that "year" would be only just coming to a close; for the planet is but now arriving back to the position, with regard to the sun, which it then occupied. Uranus, too, has only completed a little more than 1-1/2 of its "years" since Herschel discovered it.
Having accepted the fact that the planets are revolving around the sun, the next point to be inquired into is:—What are the positions of their orbits, or paths, relatively to each other?
Suppose, for instance, the various planetary orbits to be represented by a set of hoops of different sizes, placed one within the other, and the sun by a small ball in the middle of the whole; in what positions will these hoops have to be arranged so as to imitate exactly the true condition of things?
First of all let us suppose the entire arrangement, ball and hoops, to be on one level, so to speak. This may be easily compassed by imagining the hoops as floating, one surrounding the other, with the ball in the middle of all, upon the surface of still water. Such a set of objects would be described in astronomical parlance as being in the same plane. Suppose, on the other hand, that some of these floating hoops are tilted with regard to the others, so that one half of a hoop rises out of the water and the other half consequently sinks beneath the surface. This indeed is the actual case with regard to the planetary orbits. They do not by any means lie all exactly in the same plane. Each one of them is tilted, or inclined, a little with respect to the plane of the earth's orbit, which astronomers, for convenience, regard as the level of the solar system. This tilting, or "inclination," is, in the larger planets, greatest for the orbit of Mercury, least for that of Uranus. Mercury's orbit is inclined to that of the earth at an angle of about 7 deg., that of Venus at a little over 3 deg., that of Saturn 2-1/2 deg.; while in those of Mars, Neptune, and Jupiter the inclination is less than 2 deg. But greater than any of these is the inclination of the orbit of the tiny planet Eros, viz. nearly 11 deg.
The systems of satellites revolving around their respective planets being, as we have already pointed out, mere miniature editions of the solar system, the considerations so far detailed, which regulate the behaviour of the planets in their relations to the sun, will of necessity apply to the satellites very closely. In one respect, however, a system of satellites differs materially from a system of planets. The central body around which planets are in motion is self-luminous, whereas the planetary body around which a satellite revolves is not. True, planets shine, and shine very brightly too; as, for instance, Venus and Jupiter. But they do not give forth any light of their own, as the sun does; they merely reflect the sunlight which they receive from him. Putting this one fact aside, the analogy between the planetary system and a satellite system is remarkable. The satellites are spherical in form, and differ markedly in size; they rotate, so far as we know, upon their axes in varying times; they revolve around their governing planets in orbits, not circular, but elliptic; and these orbits, furthermore, do not of necessity lie in the same plane. Last of all the satellites revolve around their primaries at rates which are directly comparable with those at which the planets revolve around the sun, the rule in fact holding good that the nearer a satellite is to its primary the faster it revolves.
[3] As there seems to be much difference of opinion concerning the diameters of Uranus and Neptune, it should here be mentioned that the above figures are taken from Professor F.R. Moulton's Introduction to Astronomy (1906). They are there stated to be given on the authority of "Barnard's many measures at the Lick Observatory."
CHAPTER IV
CELESTIAL MECHANISM
As soon as we begin to inquire closely into the actual condition of the various members of the solar system we are struck with a certain distinction. We find that there are two quite different points of view from which these bodies can be regarded. For instance, we may make our estimates of them either as regards volume—that is to say, the mere room which they take up; or as regards mass—that is to say, the amount of matter which they contain.
Let us imagine two globes of equal volume; in other words, which take up an equal amount of space. One of these globes, however, may be composed of material much more tightly put together than in the other; or of greater density, as the term goes. That globe is said to be the greater of the two in mass. Were such a pair of globes to be weighed in scales, one globe in each pan, we should see at once, by its weighing down the other, which of the two was composed of the more tightly packed materials; and we should, in astronomical parlance, say of this one that it had the greater mass.
Volume being merely another word for size, the order of the members of the solar system, with regard to their volumes, will be as follows, beginning with the greatest:—the Sun, Jupiter, Saturn, Uranus, Neptune, the Earth, Venus, Mars, and Mercury.
With regard to mass the same order strangely enough holds good. The actual densities of the bodies in question are, however, very different. The densest or closest packed body of all is the Earth, which is about five and a half times as dense as if it were composed entirely of water. Venus follows next, then Mars, and then Mercury. The remaining bodies, on the other hand, are relatively loose in structure. Saturn is the least dense of all, less so than water. The density of the Sun is a little greater than that of water.
This method of estimating is, however, subject to a qualification. It must be remembered that in speaking of the Sun, for instance, as being only a little denser than water, we are merely treating the question from the point of view of an average. Certain parts of it in fact will be ever so much denser than water: those are the parts in the centre. Other portions, for instance, the outside portions, will be very much less dense. It will easily be understood that in all such bodies the densest or most compressed portions are to be found towards the centre; while the portions towards the exterior being less pressed upon, will be less dense.
We now reach a very important point, the question of Gravitation. Gravitation, or gravity, as it is often called, is the attractive force which, for instance, causes objects to fall to the earth. Now it seems rather strange that one should say that it is owing to a certain force that things fall towards the earth. All things seem to us to fall so of their own accord, as if it were quite natural, or rather most unnatural if they did not. Why then require a "force" to make them fall?
The story goes that the great Sir Isaac Newton was set a-thinking on this subject by seeing an apple fall from a tree to the earth. He then carried the train of thought further; and, by studying the movements of the moon, he reached the conclusion that a body even so far off as our satellite would be drawn towards the earth in the same manner. This being the case, one will naturally ask why the moon herself does not fall in upon the earth. The answer is indeed found to be that the moon is travelling round and round the earth at a certain rapid pace, and it is this very same rapid pace which keeps her from falling in upon us. Any one can test this simple fact for himself. If we tie a stone to the end of a string, and keep whirling it round and round fast enough, there will be a strong pull from the stone in an outward direction, and the string will remain tight all the time that the stone is being whirled. If, however, we gradually slacken the speed at which we are making the stone whirl, a moment will come at length when the string will become limp, and the stone will fall back towards our hand.
It seems, therefore, that there are two causes which maintain the stone at a regular distance all the time it is being steadily whirled. One of these is the continual pull inward towards our hand by means of the string. The other is the continual pull away from us caused by the rate at which the stone is travelling. When the rate of whirling is so regulated that these pulls exactly balance each other, the stone travels comfortably round and round, and shows no tendency either to fall back upon our hand or to break the string and fly away into the air. It is indeed precisely similar with regard to the moon. The continual pull of the earth's gravitation takes the place of the string. If the moon were to go round and round slower than it does, it would tend to fall in towards the earth; if, on the other hand, it were to go faster, it would tend to rush away into space.
The same kind of pull which the earth exerts upon the objects at its surface, or upon its satellite, the moon, exists through space so far as we know. Every particle of matter in the universe is found in fact to attract every other particle. The moon, for instance, attracts the earth also, but the controlling force is on the side of the much greater mass of the earth. This force of gravity or attraction of gravitation, as it is also called, is perfectly regular in its action. Its power depends first of all exactly upon the mass of the body which exerts it. The gravitational pull of the sun, for instance, reaches out to an enormous distance, controlling perhaps, in their courses, unseen planets circling far beyond the orbit of Neptune. Again, the strength with which the force of gravity acts depends upon distance in a regularly diminishing proportion. Thus, the nearer an object is to the earth, for instance, the stronger is the gravitational pull which it gets from it; the farther off it is, the weaker is this pull. If then the moon were to be brought nearer to the earth, the gravitational pull of the latter would become so much stronger that the moon's rate of motion would have also to increase in due proportion to prevent her from being drawn into the earth. Last of all, the point in a body from which the attraction of gravitation acts, is not necessarily the centre of the body, but rather what is known as its centre of gravity, that is to say, the balancing point of all the matter which the body contains.
It should here be noted that the moon does not actually revolve around the centre of gravity of the earth. What really happens is that both orbs revolve around their common centre of gravity, which is a point within the body of the earth, and situated about three thousand miles from its centre. In the same manner the planets and the sun revolve around the centre of gravity of the solar system, which is a point within the body of the sun.
The neatly poised movements of the planets around the sun, and of the satellites around their respective planets, will therefore be readily understood to result from a nice balance between gravitation and speed of motion.
The mass of the earth is ascertained to be about eighty times that of the moon. Our knowledge of the mass of a planet is learned from comparing the revolutions of its satellite or satellites around it, with those of the moon around the earth. We are thus enabled to deduce what the mass of such a planet would be compared to the earth's mass; that is to say, a study, for instance, of Jupiter's satellite system shows that Jupiter must have a mass nearly three hundred and eighteen times that of our earth. In the same manner we can argue out the mass of the sun from the movements of the planets and other bodies of the system around it. With regard, however, to Venus and Mercury, the problem is by no means such an easy one, as these bodies have no satellites. For information in this latter case we have to rely upon such uncertain evidence as, for instance, the slight disturbances caused in the motion of the earth by the attraction of these planets when they pass closest to us, or their observed effect upon the motions of such comets as may happen to pass near to them.
Mass and weight, though often spoken of as one and the same thing, are by no means so. Mass, as we have seen, merely means the amount of matter which a body contains. The weight of a body, on the other hand, depends entirely upon the gravitational pull which it receives. The force of gravity at the surface of the earth is, for instance, about six times as great as that at the surface of the moon. All bodies, therefore, weigh about six times as much on the earth as they would upon the moon; or, rather, a body transferred to the moon's surface would weigh only about one-sixth of what it did on the terrestrial surface. It will therefore be seen that if a body of given mass were to be placed upon planet after planet in turn, its weight would regularly alter according to the force of gravity at each planet's surface.
Gravitation is indeed one of the greatest mysteries of nature. What it is, the means by which it acts, or why such a force should exist at all, are questions to which so far we have not had even the merest hint of an answer. Its action across space appears to be instantaneous.
The intensity of gravitation is said in mathematical parlance "to vary inversely with the square of the distance." This means that at twice the distance the pull will become only one-quarter as strong, and not one-half as otherwise might be expected. At four times the distance, therefore, it will be one-sixteenth as strong. At the earth's surface a body is pulled by the earth's gravitation, or "falls," as we ordinarily term it, through 16 feet in one second of time; whereas at the distance of the moon the attraction of the earth is so very much weakened that a body would take as long as one minute to fall through the same space.
Newton's investigations showed that if a body were to be placed at rest in space entirely away from the attraction of any other body it would remain always in a motionless condition, because there would plainly be no reason why it should move in any one direction rather than in another. And, similarly, if a body were to be projected in a certain direction and at a certain speed, it would move always in the same direction and at the same speed so long as it did not come within the gravitational attraction of any other body.
The possibility of an interaction between the celestial orbs had occurred to astronomers before the time of Newton; for instance, in the ninth century to the Arabian Musa-ben-Shakir, to Camillus Agrippa in 1553, and to Kepler, who suspected its existence from observation of the tides. Horrox also, writing in 1635, spoke of the moon as moved by an emanation from the earth. But no one prior to Newton attempted to examine the question from a mathematical standpoint.
Notwithstanding the acknowledged truth and far-reaching scope of the law of gravitation—for we find its effects exemplified in every portion of the universe—there are yet some minor movements which it does not account for. For instance, there are small irregularities in the movement of Mercury which cannot be explained by the influence of possible intra-Mercurial planets, and similarly there are slight unaccountable deviations in the motions of our neighbour the Moon.
CHAPTER V
CELESTIAL DISTANCES
Up to this we have merely taken a general view of the solar system—a bird's-eye view, so to speak, from space.
In the course of our inquiry we noted in a rough way the relative distances at which the various planets move around the sun. But we have not yet stated what these distances actually are, and it were therefore well now to turn our attention to this important matter.
Each of us has a fair idea of what a mile is. It is a quarter of an hour's sharp walk, for instance; or yonder village or building, we know, lies such and such a number of miles away.
The measurements which have already been given of the diameters of the various bodies of the solar system appear very great to us, who find that a walk of a few miles at a time taxes our strength; but they are a mere nothing when we consider the distances from the sun at which the various planets revolve in their orbits.
The following table gives these distances in round numbers. As here stated they are what are called "mean" distances; for, as the orbits are oval, the planets vary in their distances from the sun, and we are therefore obliged to strike a kind of average for each case:—
Mercury about 36,000,000 miles. Venus " 67,200,000 " Earth " 92,900,000 " Mars " 141,500,000 " Jupiter " 483,300,000 " Saturn " 886,000,000 " Uranus " 1,781,900,000 " Neptune " 2,791,600,000 "
From the above it will be seen at a glance that we have entered upon a still greater scale of distance than in dealing with the diameters of the various bodies of the system. In that case the distances were limited to thousands of miles; in this, however, we have to deal with millions. A million being ten hundred thousand, it will be noticed that even the diameter of the huge sun is well under a million miles.
How indeed are we to get a grasp of such distances, when those to which we are ordinarily accustomed—the few miles' walk, the little stretch of sea or land which we gaze upon around us—are so utterly minute in comparison? The fact is, that though men may think that they can picture in their minds such immense distances, they actually can not. In matters like these we unconsciously employ a kind of convention, and we estimate a thing as being two or three or more times the size of another. More than this we are unable to do. For instance, our ordinary experience of a mile enables us to judge, in a way, of a stretch of several miles, such as one can take in with a glance; but in our estimation of a thousand miles, or even of one hundred, we are driven back upon a mental trick, so to speak.
In our attempts to realise such immense distances as those in the solar system we are obliged to have recourse to analogies; to comparisons with other and simpler facts, though this is at the best a mere self-cheating device. The analogy which seems most suited to our purpose here, and one which has often been employed by writers, is borrowed from the rate at which an express train travels.
Let us imagine, for instance, that we possess an express train which is capable of running anywhere, never stops, never requires fuel, and always goes along at sixty miles an hour. Suppose we commence by employing it to gauge the size of our own planet, the earth. Let us send it on a trip around the equator, the span of which is about 24,000 miles. At its sixty-miles-an-hour rate of going, this journey will take nearly 17 days. Next let us send it from the earth to the moon. This distance, 240,000 miles, being ten times as great as the last, will of course take ten times as long to cover, namely, 170 days; that is to say, nearly half a year. Again, let us send it still further afield, to the sun, for example. Here, however, it enters upon a journey which is not to be measured in thousands of miles, as the others were, but in millions. The distance from the earth to the sun, as we have seen in the foregoing table, is about 93 millions of miles. Our express train would take about 178 years to traverse this.
Having arrived at the sun, let us suppose that our train makes a tour right round it. This will take more than five years.
Supposing, finally, that our train were started from the sun, and made to run straight out to the known boundaries of the solar system, that is to say, as far as the orbit of Neptune, it would take over 5000 years to traverse the distance.
That sixty miles an hour is a very great speed any one, I think, will admit who has stood upon the platform of a country station while one of the great mail trains has dashed past. But are not the immensities of space appalling to contemplate, when one realises that a body moving incessantly at such a rate would take so long as 10,000 years to traverse merely the breadth of our solar system? Ten thousand years! Just try to conceive it. Why, it is only a little more than half that time since the Pyramids were built, and they mark for us the Dawn of History. And since then half-a-dozen mighty empires have come and gone!
Having thus concluded our general survey of the appearance and dimensions of the solar system, let us next inquire into its position and size in relation to what we call the Universe.
A mere glance at the night sky, when it is free from clouds, shows us that in every direction there are stars; and this holds good, no matter what portion of the globe we visit. The same is really true of the sky by day, though in that case we cannot actually see the stars, for their light is quite overpowered by the dazzling light of the sun.
We thus reach the conclusion that our earth, that our solar system in fact, lies plunged within the midst of a great tangle of stars. What position, by the way, do we occupy in this mighty maze? Are we at the centre, or anywhere near the centre, or where?
It has been indeed amply proved by astronomical research that the stars are bodies giving off a light of their own, just as our sun does; that they are in fact suns, and that our sun is merely one, perhaps indeed a very unimportant member, of this great universe of stars. Each of these stars, or suns, besides, may be the centre of a system similar to what we call our solar system, comprising planets and satellites, comets and meteors;—or perchance indeed some further variety of attendant bodies of which we have no example in our tiny corner of space. But as to whether one is right in a conjecture of this kind, there is up to the present no proof whatever. No telescope has yet shown a planet in attendance upon one of these distant suns; for such bodies, even if they do exist, are entirely out of the range of our mightiest instruments. On what then can we ground such an assumption? Merely upon analogy; upon the common-sense deduction that as the stars have characteristics similar to our particular star, the sun, it would seem unlikely that ours should be the only such body in the whole of space which is attended by a planetary system.
"The Stars," using that expression in its most general sense, do not lie at one fixed distance from us, set here and there upon a background of sky. There is in fact no background at all. The brilliant orbs are all around us in space, at different distances from us and from each other; and we can gaze between them out into the blackness of the void which, perhaps, continues to extend unceasingly long after the very outposts of the stellar universe has been left behind. Shall we then start our imaginary express train once more, and send it out towards the nearest of the stars? This would, however, be a useless experiment. Our express-train method of gauging space would fail miserably in the attempt to bring home to us the mighty gulf by which we are now faced. Let us therefore halt for a moment and look back upon the orders of distance with which we have been dealing. First of all we dealt with thousands of miles. Next we saw how they shrank into insignificance when we embarked upon millions. We found, indeed, that our sixty-mile-an-hour train, rushing along without ceasing, would consume nearly the whole of historical time in a journey from the sun to Neptune.
In the spaces beyond the solar system we are faced, however, by a new order of distance. From sun to planets is measured in millions of miles, but from sun to sun is measured in billions. But does the mere stating of this fact convey anything? I fear not. For the word "billion" runs as glibly off the tongue as "million," and both are so wholly unrealisable by us that the actual difference between them might easily pass unnoticed.
Let us, however, make a careful comparison. What is a million? It is a thousand thousands. But what is a billion? It is a million millions. Consider for a moment! A million of millions. That means a million, each unit of which is again a million. In fact every separate "1" in this million is itself a million. Here is a way of trying to realise this gigantic number. A million seconds make only eleven and a half days and nights. But a billion seconds will make actually more than thirty thousand years!
Having accepted this, let us try and probe with our express train even a little of the new gulf which now lies before us. At our old rate of going it took almost two years to cover a million miles. To cover a billion miles—that is to say, a million times this distance—would thus take of course nearly two million years. Alpha Centauri, the nearest star to our earth, is some twenty-five billions of miles away. Our express train would thus take about fifty millions of years to reach it!
This shows how useless our illustration, appropriate though it seemed for interplanetary space, becomes when applied to the interstellar spaces. It merely gives us millions in return for billions; and so the mind, driven in upon itself, whirls round and round like a squirrel in its revolving cage. There is, however, a useful illustration still left us, and it is the one which astronomers usually employ in dealing with the distances of the stars. The illustration in question is taken from the velocity of light.
Light travels at the tremendous speed of about 186,000 miles a second. It therefore takes only about a second and a quarter to come to us from the moon. It traverses the 93,000,000 of miles which separate us from the sun in about eight minutes. It travels from the sun out to Neptune in about four hours, which means that it would cross the solar system from end to end in eight. To pass, however, across the distance which separates us from Alpha Centauri it would take so long as about four and a quarter years!
Astronomers, therefore, agree in estimating the distances of the stars from the point of view of the time which light would take to pass from them to our earth. They speak of that distance which light takes a year to traverse as a "light year." According to this notation, Alpha Centauri is spoken of as being about four and a quarter light years distant from us.
Now as the rays of light coming from Alpha Centauri to us are chasing one another incessantly across the gulf of space, and as each ray left that star some four years before it reaches us, our view of the star itself must therefore be always some four years old. Were then this star to be suddenly removed from the universe at any moment, we should continue to see it still in its place in the sky for some four years more, after which it would suddenly disappear. The rays which had already started upon their journey towards our earth must indeed continue travelling, and reaching us in their turn until the last one had arrived; after which no more would come.
We have drawn attention to Alpha Centauri as the nearest of the stars. The majority of the others indeed are ever so much farther. We can only hazard a guess at the time it takes for the rays from many of them to reach our globe. Suppose, for instance, we see a sudden change in the light of any of these remote stars, we are inclined to ask ourselves when that change did actually occur. Was it in the days of Queen Elizabeth, or at the time of the Norman Conquest; or was it when Rome was at the height of her glory, or perhaps ages before that when the Pyramids of Egypt were being built? Even the last of these suppositions cannot be treated lightly. We have indeed no real knowledge of the distance from us of those stars which our giant telescopes have brought into view out of the depths of the celestial spaces.
CHAPTER VI
CELESTIAL MEASUREMENT
Had the telescope never been invented our knowledge of astronomy would be trifling indeed.
Prior to the year 1610, when Galileo first turned the new instrument upon the sky, all that men knew of the starry realms was gathered from observation with their own eyes unaided by any artificial means. In such researches they had been very much at a disadvantage. The sun and moon, in their opinion, were no doubt the largest bodies in the heavens, for the mere reason that they looked so! The mighty solar disturbances, which are now such common-places to us, were then quite undreamed of. The moon displayed a patchy surface, and that was all; her craters and ring-mountains were surprises as yet in store for men. Nothing of course was known about the surfaces of the planets. These objects had indeed no particular characteristics to distinguish them from the great host of the stars, except that they continually changed their positions in the sky while the rest did not. The stars themselves were considered as fixed inalterably upon the vault of heaven. The sun, moon, and planets apparently moved about in the intermediate space, supported in their courses by strange and fanciful devices. The idea of satellites was as yet unknown. Comets were regarded as celestial portents, and meteors as small conflagrations taking place in the upper air.
In the entire absence of any knowledge with regard to the actual sizes and distances of the various celestial bodies, men naturally considered them as small; and, concluding that they were comparatively near, assigned to them in consequence a permanent connection with terrestrial affairs. Thus arose the quaint and erroneous beliefs of astrology, according to which the events which took place upon our earth were considered to depend upon the various positions in which the planets, for instance, found themselves from time to time.
It must, however, be acknowledged that the study of astrology, fallacious though its conclusions were, indirectly performed a great service to astronomy by reason of the accurate observations and diligent study of the stars which it entailed.
We will now inquire into the means by which the distances and sizes of the celestial orbs have been ascertained, and see how it was that the ancients were so entirely in the dark in this matter.
There are two distinct methods of finding out the distance at which any object happens to be situated from us.
One method is by actual measurement.
The other is by moving oneself a little to the right or left, and observing whether the distant object appears in any degree altered in position by our own change of place.
One of the best illustrations of this relative change of position which objects undergo as a result of our own change of place, is to observe the landscape from the window of a moving railway carriage. As we are borne rapidly along we notice that the telegraph posts which are set close to the line appear to fly past us in the contrary direction; the trees, houses, and other things beyond go by too, but not so fast; objects a good way off displace slowly; while some spire, or tall landmark, in the far distance appears to remain unmoved during a comparatively long time.
Actual change of position on our own part is found indeed to be invariably accompanied by an apparent displacement of the objects about us, such apparent displacement as a result of our own change of position being known as "parallax." The dependence between the two is so mathematically exact, that if we know the amount of our own change of place, and if we observe the amount of the consequent displacement of any object, we are enabled to calculate its precise distance from us. Thus it comes to pass that distances can be measured without the necessity of moving over them; and the breadth of a river, for instance, or the distance from us of a ship at sea, can be found merely by such means.
It is by the application of this principle to the wider field of the sky that we are able to ascertain the distance of celestial bodies. We have noted that it requires a goodly change of place on our own part to shift the position in which some object in the far distance is seen by us. To two persons separated by, say, a few hundred yards, a ship upon the horizon will appear pretty much in the same direction. They would require, in fact, to be much farther apart in order to displace it sufficiently for the purpose of estimating their distance from it. It is the same with regard to the moon. Two observers, standing upon our earth, will require to be some thousands of miles apart in order to see the position of our satellite sufficiently altered with regard to the starry background, to give the necessary data upon which to ground their calculations.
The change of position thus offered by one side of the earth's surface at a time is, however, not sufficient to displace any but the nearest celestial bodies. When we have occasion to go farther afield we have to seek a greater change of place. This we can get as a consequence of the earth's movement around the sun. Observations, taken several days apart, will show the effect of the earth's change of place during the interval upon the positions of the other bodies of our system. But when we desire to sound the depths of space beyond, and to reach out to measure the distance of the nearest star, we find ourselves at once thrown upon the greatest change of place which we can possibly hope for; and this we get during the long journey of many millions of miles which our earth performs around the sun during the course of each year. But even this last change of place, great as it seems in comparison with terrestrial measurements, is insufficient to show anything more than the tiniest displacements in a paltry forty-three out of the entire host of the stars.
We can thus realise at what a disadvantage the ancients were. The measuring instruments at their command were utterly inadequate to detect such small displacements. It was reserved for the telescope to reveal them; and even then it required the great telescopes of recent times to show the slight changes in the position of the nearer stars, which were caused by the earth's being at one time at one end of its orbit, and some six months later at the other end—stations separated from each other by a gulf of about one hundred and eighty-six millions of miles.
The actual distances of certain celestial bodies being thus ascertainable, it becomes a matter of no great difficulty to determine the actual sizes of the measurable ones. It is a matter of everyday experience that the size which any object appears to have, depends exactly upon the distance it is from us. The farther off it is the smaller it looks; the nearer it is the bigger. If, then, an object which lies at a known distance from us looks such and such a size, we can of course ascertain its real dimensions. Take the moon, for instance. As we have already shown, we are able to ascertain its distance. We observe also that it looks a certain size. It is therefore only a matter of calculation to find what its actual dimensions should be, in order that it may look that size at that distance away. Similarly we can ascertain the real dimensions of the sun. The planets, appearing to us as points of light, seem at first to offer a difficulty; but, by means of the telescope, we can bring them, as it were, so much nearer to us, that their broad expanses may be seen. We fail, however, signally with regard to the stars; for they are so very distant, and therefore such tiny points of light, that our mightiest telescopes cannot magnify them sufficiently to show any breadth of surface.
Instead of saying that an object looks a certain breadth across, such as a yard or a foot, a statement which would really mean nothing, astronomers speak of it as measuring a certain angle. Such angles are estimated in what are called "degrees of arc"; each degree being divided into sixty minutes, and each minute again into sixty seconds. Popularly considered the moon and sun look about the same size, or, as an astronomer would put it, they measure about the same angle. This is an angle, roughly, of thirty-two minutes of arc; that is to say, slightly more than half a degree. The broad expanse of surface which a celestial body shows to us, whether to the naked eye, as in the case of the sun and moon, or in the telescope, as in the case of other members of our system, is technically known as its "disc."
CHAPTER VII
ECLIPSES AND KINDRED PHENOMENA
Since some members of the solar system are nearer to us than others, and all are again much nearer than any of the stars, it must often happen that one celestial body will pass between us and another, and thus intercept its light for a while. The moon, being the nearest object in the universe, will, of course, during its motion across the sky, temporarily blot out every one of the others which happen to lie in its path. When it passes in this manner across the face of the sun, it is said to eclipse it. When it thus hides a planet or star, it is said to occult it. The reason why a separate term is used for what is merely a case of obscuring light in exactly the same way, will be plain when one considers that the disc of the sun is almost of the same apparent size as that of the moon, and so the complete hiding of the sun can last but a few minutes at the most; whereas a planet or a star looks so very small in comparison, that it is always entirely swallowed up for some time when it passes behind the body of our satellite.
The sun, of course, occults planets and stars in exactly the same manner as the moon does, but we cannot see these occultations on account of the blaze of sunlight.
By reason of the small size which the planets look when viewed with the naked eye, we are not able to note them in the act of passing over stars and so blotting them out; but such occurrences may be seen in the telescope, for the planetary bodies then display broad discs.
There is yet another occurrence of the same class which is known as a transit. This takes place when an apparently small body passes across the face of an apparently large one, the phenomenon being in fact the exact reverse of an occultation. As there is no appreciable body nearer to us than the moon, we can never see anything in transit across her disc. But since the planets Venus and Mercury are both nearer to us than the sun, they will occasionally be seen to pass across his face, and thus we get the well-known phenomena called Transits of Venus and Transits of Mercury.
As the satellites of Jupiter are continually revolving around him, they will often pass behind or across his disc. Such occultations and transits of satellites can be well observed in the telescope.
There is, however, a way in which the light of a celestial body may be obscured without the necessity of its being hidden from us by one nearer. It will no doubt be granted that any opaque object casts a shadow when a strong light falls directly upon it. Thus the earth, under the powerful light which is directed upon it from the sun, casts an extensive shadow, though we are not aware of the existence of this shadow until it falls upon something. The shadow which the earth casts is indeed not noticeable to us until some celestial body passes into it. As the sun is very large, and the earth in comparison very small, the shadow thrown by the earth is comparatively short, and reaches out in space for only about a million miles. There is no visible object except the moon, which circulates within that distance from our globe, and therefore she is the only body which can pass into this shadow. Whenever such a thing happens, her surface at once becomes dark, for the reason that she never emits any light of her own, but merely reflects that of the sun. As the moon is continually revolving around the earth, one would be inclined to imagine that once in every month, namely at what is called full moon, when she is on the other side of the earth with respect to the sun, she ought to pass through the shadow in question. But this does not occur every time, because the moon's orbit is not quite upon the same plane with the earth's. It thus happens that time after time the moon passes clear of the earth's shadow, sometimes above it, and sometimes below it. It is indeed only at intervals of about six months that the moon can be thus obscured. This darkening of her light is known as an eclipse of the moon. It seems a great pity that custom should oblige us to employ the one term "eclipse" for this and also for the quite different occurrence, an eclipse of the sun; in which the sun's face is hidden as a consequence of the moon's body coming directly between it and our eyes.
The popular mind seems always to have found it more difficult to grasp the causes of an eclipse of the moon than an eclipse of the sun. As Mr. J.E. Gore[4] puts it: "The darkening of the sun's light by the interposition of the moon's body seems more obvious than the passing of the moon through the earth's shadow."
Eclipses of the moon furnish striking spectacles, but really add little to our knowledge. They exhibit, however, one of the most remarkable evidences of the globular shape of our earth; for the outline of its shadow when seen creeping over the moon's surface is always circular.
Eclipses of the Moon, or Lunar Eclipses, as they are also called, are of two kinds—Total, and Partial. In a total lunar eclipse the moon passes entirely into the earth's shadow, and the whole of her surface is consequently darkened. This darkening lasts for about two hours. In a partial lunar eclipse, a portion only of the moon passes through the shadow, and so only part of her surface is darkened (see Fig. 3). A very striking phenomenon during a total eclipse of the moon, is that the darkening of the lunar surface is usually by no means so intense as one would expect, when one considers that the sunlight at that time should be wholly cut off from it. The occasions indeed upon which the moon has completely disappeared from view during the progress of a total lunar eclipse are very rare. On the majority of these occasions she has appeared of a coppery-red colour, while sometimes she has assumed an ashen hue. The explanations of these variations of colour is to be found in the then state of the atmosphere which surrounds our earth. When those portions of our earth's atmosphere through which the sun's rays have to filter on their way towards the moon are free from watery vapour, the lunar surface will be tinged with a reddish light, such as we ordinarily experience at sunset when our air is dry. The ashen colour is the result of our atmosphere being laden with watery vapour, and is similar to what we see at sunset when rain is about. Lastly, when the air around the earth is thickly charged with cloud, no light at all can pass; and on such occasions the moon disappears altogether for the time being from the night sky.
Eclipses of the Sun, otherwise known as Solar Eclipses, are divided into Total, Partial, and Annular. A total eclipse of the sun takes place when the moon comes between the sun and the earth, in such a manner that it cuts off the sunlight entirely for the time being from a portion of the earth's surface. A person situated in the region in question will, therefore, at that moment find the sun temporarily blotted out from his view by the body of the moon. Since the moon is a very much smaller body than the sun, and also very much the nearer to us of the two, it will readily be understood that the portion of the earth from which the sun is seen thus totally eclipsed will be of small extent. In places not very distant from this region, the moon will appear so much shifted in the sky that the sun will be seen only partially eclipsed. The moon being in constant movement round the earth, the portion of the earth's surface from which an eclipse is seen as total will be always a comparatively narrow band lying roughly from west to east. This band, known as the track of totality, can, at the utmost, never be more than about 165 miles in width, and as a rule is very much less. For about 2000 miles on either side of it the sun is seen partially eclipsed. Outside these limits no eclipse of any kind is visible, as from such regions the moon is not seen to come in the way of the sun (see Fig. 4 (i.), p. 67).
It may occur to the reader that eclipses can also take place in the course of which the positions, where the eclipse would ordinarily be seen as total, will lie outside the surface of the earth. Such an eclipse is thus not dignified with the name of total eclipse, but is called a partial eclipse, because from the earth's surface the sun is only seen partly eclipsed at the utmost (see Fig. 4 (ii.), p. 67).
An Annular eclipse is an eclipse which just fails to become total for yet another reason. We have pointed out that the orbits of the various members of the solar system are not circular, but oval. Such oval figures, it will be remembered, are technically known as ellipses. In an elliptic orbit the controlling body is situated not in the middle of the figure, but rather towards one of the ends; the actual point which it occupies being known as the focus. The sun being at the focus of the earth's orbit, it follows that the earth is, at times, a little nearer to him than at others. The sun will therefore appear to us to vary a little in size, looking sometimes slightly larger than at other times. It is so, too, with the moon, at the focus of whose orbit the earth is situated. She therefore also appears to us at times to vary slightly in size. The result is that when the sun is eclipsed by the moon, and the moon at the time appears the larger of the two, she is able to blot out the sun completely, and so we can get a total eclipse. But when, on the other hand, the sun appears the larger, the eclipse will not be quite total, for a portion of the sun's disc will be seen protruding all around the moon like a ring of light. This is what is known as an annular eclipse, from the Latin word annulus, which means a ring. The term is consecrated by long usage, but it seems an unfortunate one on account of its similarity to the word "annual." The Germans speak of this kind of eclipse as "ring-formed," which is certainly much more to the point.
There can never be a year without an eclipse of the sun. Indeed there must be always two such eclipses at least during that period, though there need be no eclipse of the moon at all. On the other hand, the greatest number of eclipses which can ever take place during a year are seven; that is to say, either five solar eclipses and two lunar, or four solar and three lunar. This general statement refers merely to eclipses in their broadest significance, and informs us in no way whether they will be total or partial.
Of all the phenomena which arise from the hiding of any celestial body by one nearer coming in the way, a total eclipse of the sun is far the most important. It is, indeed, interesting to consider how much poorer modern astronomy would be but for the extraordinary coincidence which makes a total solar eclipse just possible. The sun is about 400 times farther off from us than the moon, and enormously greater than her in bulk. Yet the two are relatively so distanced from us as to look about the same size. The result of this is that the moon, as has been seen, can often blot out the sun entirely from our view for a short time. When this takes place the great blaze of sunlight which ordinarily dazzles our eyes is completely cut off, and we are thus enabled, unimpeded, to note what is going on in the immediate vicinity of the sun itself.
In a total solar eclipse, the time which elapses from the moment when the moon's disc first begins to impinge upon that of the sun at his western edge until the eclipse becomes total, lasts about an hour. During all this time the black lunar disc may be watched making its way steadily across the solar face. Notwithstanding the gradual obscuration of the sun, one does not notice much diminution of light until about three-quarters of his disc are covered. Then a wan, unearthly appearance begins to pervade all things, the temperature falls noticeably, and nature seems to halt in expectation of the coming of something unusual. The decreasing portion of sun becomes more and more narrow, until at length it is reduced to a crescent-shaped strip of exceeding fineness. Strange, ill-defined, flickering shadows (known as "Shadow Bands") may at this moment be seen chasing each other across any white expanse such as a wall, a building, or a sheet stretched upon the ground. The western side of the sky has now assumed an appearance dark and lowering, as if a rainstorm of great violence were approaching. This is caused by the mighty mass of the lunar shadow sweeping rapidly along. It flies onward at the terrific velocity of about half a mile a second.
If the gradually diminishing crescent of sun be now watched through a telescope, the observer will notice that it does not eventually vanish all at once, as he might have expected. Rather, it breaks up first of all along its length into a series of brilliant dots, known as "Baily's Beads." The reason of this phenomenon is perhaps not entirely agreed upon, but the majority of astronomers incline to the opinion that the so-called "beads" are merely the last remnants of sunlight peeping between those lunar mountain peaks which happen at the moment to fringe the advancing edge of the moon. The beads are no sooner formed than they rapidly disappear one after the other, after which no portion of the solar surface is left to view, and the eclipse is now total (see Fig. 5).
But with the disappearance of the sun there springs into view a new and strange appearance, ordinarily unseen because of the blaze of sunlight. It is a kind of aureole, or halo, pearly white in colour, which is seen to surround the black disc of the moon. This white radiance is none other than the celebrated phenomenon widely known as the Solar Corona. It was once upon a time thought to belong to the moon, and to be perhaps a lunar atmosphere illuminated by the sunlight shining through it from behind. But the suddenness with which the moon always blots out stars when occulting them, has amply proved that she possesses no atmosphere worth speaking about. It is now, however, satisfactorily determined that the corona belongs to the sun, for during the short time that it remains in view the black body of the moon can be seen creeping across it.
All the time that the total phase (as it is called) lasts, the corona glows with its pale unearthly light, shedding upon the earth's surface an illumination somewhat akin to full moonlight. Usually the planet Venus and a few stars shine out the while in the darkened heaven. Meantime around the observer animal and plant life behave as at nightfall. Birds go to roost, bats fly out, worms come to the surface of the ground, flowers close up. In the Norwegian eclipse of 1896 fish were seen rising to the surface of the water. When the total phase at length is over, and the moon in her progress across the sky has allowed the brilliant disc of the sun to spring into view once more at the other side, the corona disappears.
There is another famous accompaniment of the sun which partly reveals itself during total solar eclipses. This is a layer of red flame which closely envelops the body of the sun and lies between it and the corona. This layer is known by the name of the Chromosphere. Just as at ordinary times we cannot see the corona on account of the blaze of sunlight, so are we likewise unable to see the chromosphere because of the dazzling white light which shines through from the body of the sun underneath and completely overpowers it. When, however, during a solar eclipse, the lunar disc has entirely hidden the brilliant face of the sun, we are still able for a few moments to see an edgewise portion of the chromosphere in the form of a narrow red strip, fringing the advancing border of the moon. Later on, just before the moon begins to uncover the face of the sun from the other side, we may again get a view of a strip of chromosphere.
The outer surface of the chromosphere is not by any means even. It is rough and billowy, like the surface of a storm-tossed sea. Portions of it, indeed, rise at times to such heights that they may be seen standing out like blood-red points around the black disc of the moon, and remain thus during a good part of the total phase. These projections are known as the Solar Prominences. In the same way as the corona, the chromosphere and prominences were for a time supposed to belong to the moon. This, however, was soon found not to be the case, for the lunar disc was noticed to creep slowly across them also.
The total phase, or "totality," as it is also called, lasts for different lengths of time in different eclipses. It is usually of about two or three minutes' duration, and at the utmost it can never last longer than about eight minutes.
When totality is over and the corona has faded away, the moon's disc creeps little by little from the face of the sun, light and heat returns once more to the earth, and nature recovers gradually from the gloom in which she has been plunged. About an hour after totality, the last remnant of moon draws away from the solar disc, and the eclipse is entirely at an end.
The corona, the chromosphere, and the prominences are the most important of these accompaniments of the sun which a total eclipse reveals to us. Our further consideration of them must, however, be reserved for a subsequent chapter, in which the sun will be treated of at length.
Every one who has had the good fortune to see a total eclipse of the sun will, the writer feels sure, agree with the verdict of Sir Norman Lockyer that it is at once one of the "grandest and most awe-inspiring sights" which man can witness. Needless to say, such an occurrence used to cause great consternation in less civilised ages; and that it has not in modern times quite parted with its terrors for some persons, is shown by the fact that in Iowa, in the United States, a woman died from fright during the eclipse of 1869.
To the serious observer of a total solar eclipse every instant is extremely precious. Many distinct observations have to be crowded into a time all too limited, and this in an eclipse-party necessitates constant rehearsals in order that not a moment may be wasted when the longed-for totality arrives. Such preparation is very necessary; for the rarity and uncommon nature of a total eclipse of the sun, coupled with its exceeding short duration, tends to flurry the mind, and to render it slow to seize upon salient points of detail. And, even after every precaution has been taken, weather possibilities remain to be reckoned with, so that success is rather a lottery.
Above all things, therefore, a total solar eclipse is an occurrence for the proper utilisation of which personal experience is of absolute necessity. It was manifestly out of the question that such experience could be gained by any individual in early times, as the imperfection of astronomical theory and geographical knowledge rendered the predicting of the exact position of the track of totality well-nigh impossible. Thus chance alone would have enabled one in those days to witness a total phase, and the probabilities, of course, were much against a second such experience in the span of a life-time. And even in more modern times, when the celestial motions had come to be better understood, the difficulties of foreign travel still were in the way; for it is, indeed, a notable fact that during many years following the invention of the telescope the tracks were placed for the most part in far-off regions of the earth, and Europe was visited by singularly few total solar eclipses. Thus it came to pass that the building up of a body of organised knowledge upon this subject was greatly delayed.
Nothing perhaps better shows the soundness of modern astronomical theory than the almost exact agreement of the time predicted for an eclipse with its actual occurrence. Similarly, by calculating backwards, astronomers have discovered the times and seasons at which many ancient eclipses took place, and valuable opportunities have thus arisen for checking certain disputed dates in history.
It should not be omitted here that the ancients were actually able, in a rough way, to predict eclipses. The Chaldean astronomers had indeed noticed very early a curious circumstance, i.e. that eclipses tend to repeat themselves after a lapse of slightly more than eighteen years.
In this connection it must, however, be pointed out, in the first instance, that the eclipses which occur in any particular year are in no way associated with those which occurred in the previous year. In other words, the mere fact that an eclipse takes place upon a certain day this year will not bring about a repetition of it at the same time next year. However, the nicely balanced behaviour of the solar system, an equilibrium resulting from aeons of orbital ebb and flow, naturally tends to make the members which compose that family repeat their ancient combinations again and again; so that after definite lapses of time the same order of things will almost exactly recur. Thus, as a consequence of their beautifully poised motions, the sun, the moon, and the earth tend, after a period of 18 years and 10-1/3 days,[5] to occupy very nearly the same positions with regard to each other. The result of this is that, during each recurring period, the eclipses comprised within it will be repeated in their order.
To give examples:—
The total solar eclipse of August 30, 1905, was a repetition of that of August 19, 1887.
The partial solar eclipse of February 23, 1906, corresponded to that which took place on February 11, 1888.
The annular eclipse of July 10, 1907, was a recurrence of that of June 28, 1889.
In this way we can go on until the eighteen year cycle has run out, and we come upon a total solar eclipse predicted for September 10, 1923, which will repeat the above-mentioned ones of 1905 and 1887; and so on too with the others.
From mere observation alone, extending no doubt over many ages, those time-honoured watchers of the sky, the early Chaldeans, had arrived at this remarkable generalisation; and they used it for the rough prediction of eclipses. To the period of recurrence they give the name of "Saros."
And here we find ourselves led into one of the most interesting and fascinating by-paths in astronomy, to which writers, as a rule, pay all too little heed.
In order not to complicate matters unduly, the recurrence of solar eclipses alone will first be dealt with. This limitation will, however, not affect the arguments in the slightest, and it will be all the more easy in consequence to show their application to the case of eclipses of the moon.
The reader will perhaps have noticed that, with regard to the repetition of an eclipse, it has been stated that the conditions which bring it on at each recurrence are reproduced almost exactly. Here, then, lies the crux of the situation. For it is quite evident that were the conditions exactly reproduced, the recurrences of each eclipse would go on for an indefinite period. For instance, if the lapse of a saros period found the sun, moon, and earth again in the precise relative situations which they had previously occupied, the recurrences of a solar eclipse would tend to duplicate its forerunner with regard to the position of the shadow upon the terrestrial surface. But the conditions not being exactly reproduced, the shadow-track does not pass across the earth in quite the same regions. It is shifted a little, so to speak; and each time the eclipse comes round it is found to be shifted a little farther. Every solar eclipse has therefore a definite "life" of its own upon the earth, lasting about 1150 years, or 64 saros returns, and working its way little by little across our globe from north to south, or from south to north, as the case may be. Let us take an imaginary example. A partial eclipse occurs, say, somewhere near the North Pole, the edge of the "partial" shadow just grazing the earth, and the "track of totality" being as yet cast into space. Here we have the beginning of a series. At each saros recurrence the partial shadow encroaches upon a greater extent of earth-surface. At length, in its turn, the track of totality begins to impinge upon the earth. This track streaks across our globe at each return of the eclipse, repeating itself every time in a slightly more southerly latitude. South and south it moves, passing in turn the Tropic of Cancer, the Equator, the Tropic of Capricorn, until it reaches the South Pole; after which it touches the earth no longer, but is cast into space. The rear portion of the partial shadow, in its turn, grows less and less in extent; and it too in time finally passes off. Our imaginary eclipse series is now no more—its "life" has ended. |
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