SIDE-LIGHTS ON ASTRONOMY
AND KINDRED FIELDS OF POPULAR SCIENCE
ESSAYS AND ADDRESSES
I. THE UNSOLVED PROBLEMS OF ASTRONOMY II. THE NEW PROBLEMS OF THE UNIVERSE III. THE STRUCTURE OF THE UNIVERSE IV. THE EXTENT OF THE UNIVERSE V. MAKING AND USING A TELESCOPE VI. WHAT THE ASTRONOMERS ARE DOING VII. LIFE IN THE UNIVERSE VIII. HOW THE PLANETS ARE WEIGHED IX. THE MARINER'S COMPASS X. THE FAIRYLAND OF GEOMETRY XI. THE ORGANIZATION OF SCIENTIFIC RESEARCH XII. CAN WE MAKE IT RAIN? XIII. THE ASTRONOMICAL EPHEMERIS AND NAUTICAL ALMANAC XIV. THE WORLD'S DEBT TO ASTRONOMY XV. AN ASTRONOMICAL FRIENDSHIP XVI. THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR XVII. THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE XVIII. ASPECTS OF AMERICAN ASTRONOMY XIX. THE UNIVERSE AS AN ORGANISM XX. THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS XXI. THE OUTLOOK FOR THE FLYING-MACHINE
PHOTOGRAPH OF THE CORONA OF THE SUN, TAKEN IN TRIPOLI DURING TOTAL ECLIPSE OF AUGUST 30, 1905.
A TYPICAL STAR CLUSTER-CENTAURI
THE GLASS DISK
THE OPTICIAN'S TOOL
THE OPTICIAN'S TOOL
GRINDING A LARGE LENS
IMAGE OF CANDLE-FLAME IN OBJECT-GLASS
TESTING ADJUSTMENT OF OBJECT-GLASS
A VERY PRIMITIVE MOUNTING FOR A TELESCOPE
THE HUYGHENIAN EYE-PIECE
SECTION OF THE PRIMITIVE MOUNTING
SPECTRAL IMAGES OF STARS, THE UPPER LINE SHOWING HOW THEY APPEAR WITH THE EYE-PIECE PUSHED IN, THE LOWER WITH THE EYE-PIECE DRAWN OUT
THE GREAT REFRACTOR OF THE NATIONAL OBSERVATORY AT WASHINGTON
THE "BROKEN-BACKED COMET-SEEKER"
NEBULA IN ORION
DIP OF THE MAGNETIC NEEDLE IN VARIOUS LATITUDES
PROFESSOR LANGLEY'S AIR-SHIP
In preparing and issuing this collection of essays and addresses, the author has yielded to what he could not but regard as the too flattering judgment of the publishers. Having done this, it became incumbent to do what he could to justify their good opinion by revising the material and bringing it up to date. Interest rather than unity of thought has determined the selection.
A prominent theme in the collection is that of the structure, extent, and duration of the universe. Here some repetition of ideas was found unavoidable, in a case where what is substantially a single theme has been treated in the various forms which it assumed in the light of constantly growing knowledge. If the critical reader finds this a defect, the author can plead in extenuation only the difficulty of avoiding it under the circumstances. Although mainly astronomical, a number of discussions relating to general scientific subjects have been included.
Acknowledgment is due to the proprietors of the various periodicals from the pages of which most of the essays have been taken. Besides Harper's Magazine and the North American Review, these include McClure's Magazine, from which were taken the articles "The Unsolved Problems of Astronomy" and "How the Planets are Weighed." "The Structure of the Universe" appeared in the International Monthly, now the International Quarterly; "The Outlook for the Flying-Machine" is mainly from The New York Independent, but in part from McClure's Magazine; "The World's Debt to Astronomy" is from The Chautauquan; and "An Astronomical Friendship" from the Atlantic Monthly.
SIMON NEWCOMB. WASHINGTON, JUNE, 1906.
THE UNSOLVED PROBLEMS OF ASTRONOMY
The reader already knows what the solar system is: an immense central body, the sun, with a number of planets revolving round it at various distances. On one of these planets we dwell. Vast, indeed, are the distances of the planets when measured by our terrestrial standards. A cannon-ball fired from the earth to celebrate the signing of the Declaration of Independence, and continuing its course ever since with a velocity of eighteen hundred feet per second, would not yet be half-way to the orbit of Neptune, the outer planet. And yet the thousands of stars which stud the heavens are at distances so much greater than that of Neptune that our solar system is like a little colony, separated from the rest of the universe by an ocean of void space almost immeasurable in extent. The orbit of the earth round the sun is of such size that a railway train running sixty miles an hour, with never a stop, would take about three hundred and fifty years to cross it. Represent this orbit by a lady's finger-ring. Then the nearest fixed star will be about a mile and a half away; the next more than two miles; a few more from three to twenty miles; the great body at scores or hundreds of miles. Imagine the stars thus scattered from the Atlantic to the Mississippi, and keep this little finger-ring in mind as the orbit of the earth, and one may have some idea of the extent of the universe.
One of the most beautiful stars in the heavens, and one that can be seen most of the year, is a Lyrae, or Alpha of the Lyre, known also as Vega. In a spring evening it may be seen in the northeast, in the later summer near the zenith, in the autumn in the northwest. On the scale we have laid down with the earth's orbit as a finger-ring, its distance would be some eight or ten miles. The small stars around it in the same constellation are probably ten, twenty, or fifty times as far.
Now, the greatest fact which modern science has brought to light is that our whole solar system, including the sun, with all its planets, is on a journey towards the constellation Lyra. During our whole lives, in all probability during the whole of human history, we have been flying unceasingly towards this beautiful constellation with a speed to which no motion on earth can compare. The speed has recently been determined with a fair degree of certainty, though not with entire exactness; it is about ten miles a second, and therefore not far from three hundred millions of miles a year. But whatever it may be, it is unceasing and unchanging; for us mortals eternal. We are nearer the constellation by five or six hundred miles every minute we live; we are nearer to it now than we were ten years ago by thousands of millions of miles, and every future generation of our race will be nearer than its predecessor by thousands of millions of miles.
When, where, and how, if ever, did this journey begin—when, where, and how, if ever, will it end? This is the greatest of the unsolved problems of astronomy. An astronomer who should watch the heavens for ten thousand years might gather some faint suggestion of an answer, or he might not. All we can do is to seek for some hints by study and comparison with other stars.
The stars are suns. To put it in another way, the sun is one of the stars, and rather a small one at that. If the sun is moving in the way I have described, may not the stars also be in motion, each on a journey of its own through the wilderness of space? To this question astronomy gives an affirmative answer. Most of the stars nearest to us are found to be in motion, some faster than the sun, some more slowly, and the same is doubtless true of all; only the century of accurate observations at our disposal does not show the motion of the distant ones. A given motion seems slower the more distant the moving body; we have to watch a steamship on the horizon some little time to see that she moves at all. Thus it is that the unsolved problem of the motion of our sun is only one branch of a yet more stupendous one: What mean the motions of the stars—how did they begin, and how, if ever, will they end? So far as we can yet see, each star is going straight ahead on its own journey, without regard to its neighbors, if other stars can be so called. Is each describing some vast orbit which, though looking like a straight line during the short period of our observation, will really be seen to curve after ten thousand or a hundred thousand years, or will it go straight on forever? If the laws of motion are true for all space and all time, as we are forced to believe, then each moving star will go on in an unbending line forever unless hindered by the attraction of other stars. If they go on thus, they must, after countless years, scatter in all directions, so that the inhabitants of each shall see only a black, starless sky.
Mathematical science can throw only a few glimmers of light on the questions thus suggested. From what little we know of the masses, distances, and numbers of the stars we see a possibility that the more slow-moving ones may, in long ages, be stopped in their onward courses or brought into orbits of some sort by the attraction of their millions of fellows. But it is hard to admit even this possibility in the case of the swift-moving ones. Attraction, varying as the inverse square of the distance, diminishes so rapidly as the distance increases that, at the distances which separate the stars, it is small indeed. We could not, with the most delicate balance that science has yet invented, even show the attraction of the greatest known star. So far as we know, the two swiftest-moving stars are, first, Arcturus, and, second, one known in astronomy as 1830 Groombridge, the latter so called because it was first observed by the astronomer Groombridge, and is numbered 1830 in his catalogue of stars. If our determinations of the distances of these bodies are to be relied on, the velocity of their motion cannot be much less than two hundred miles a second. They would make the circuit of the earth every two or three minutes. A body massive enough to control this motion would throw a large part of the universe into disorder. Thus the problem where these stars came from and where they are going is for us insoluble, and is all the more so from the fact that the swiftly moving stars are moving in different directions and seem to have no connection with each other or with any known star.
It must not be supposed that these enormous velocities seem so to us. Not one of them, even the greatest, would be visible to the naked eye until after years of watching. On our finger-ring scale, 1830 Groombridge would be some ten miles and Arcturus thirty or forty miles away. Either of them would be moving only two or three feet in a year. To the oldest Assyrian priests Lyra looked much as it does to us to-day. Among the bright and well-known stars Arcturus has the most rapid apparent motion, yet Job himself would not to-day see that its position had changed, unless he had noted it with more exactness than any astronomer of his time.
Another unsolved problem among the greatest which present themselves to the astronomer is that of the size of the universe of stars. We know that several thousand of these bodies are visible to the naked eye; moderate telescopes show us millions; our giant telescopes of the present time, when used as cameras to photograph the heavens, show a number past count, perhaps one hundred millions. Are all these stars only those few which happen to be near us in a universe extending out without end, or do they form a collection of stars outside of which is empty infinite space? In other words, has the universe a boundary? Taken in its widest scope this question must always remain unanswered by us mortals because, even if we should discover a boundary within which all the stars and clusters we ever can know are contained, and outside of which is empty space, still we could never prove that this space is empty out to an infinite distance. Far outside of what we call the universe might still exist other universes which we can never see.
It is a great encouragement to the astronomer that, although he cannot yet set any exact boundary to this universe of ours, he is gathering faint indications that it has a boundary, which his successors not many generations hence may locate so that the astronomer shall include creation itself within his mental grasp. It can be shown mathematically that an infinitely extended system of stars would fill the heavens with a blaze of light like that of the noonday sun. As no such effect is produced, it may be concluded that the universe has a boundary. But this does not enable us to locate the boundary, nor to say how many stars may lie outside the farthest stretches of telescopic vision. Yet by patient research we are slowly throwing light on these points and reaching inferences which, not many years ago, would have seemed forever beyond our powers.
Every one now knows that the Milky Way, that girdle of light which spans the evening sky, is formed of clouds of stars too minute to be seen by the unaided vision. It seems to form the base on which the universe is built and to bind all the stars into a system. It comprises by far the larger number of stars that the telescope has shown to exist. Those we see with the naked eye are almost equally scattered over the sky. But the number which the telescope shows us become more and more condensed in the Milky Way as telescope power is increased. The number of new stars brought out with our greatest power is vastly greater in the Milky Way than in the rest of the sky, so that the former contains a great majority of the stars. What is yet more curious, spectroscopic research has shown that a particular kind of stars, those formed of heated gas, are yet more condensed in the central circle of this band; if they were visible to the naked eye, we should see them encircling the heavens as a narrow girdle forming perhaps the base of our whole system of stars. This arrangement of the gaseous or vaporous stars is one of the most singular facts that modern research has brought to light. It seems to show that these particular stars form a system of their own; but how such a thing can be we are still unable to see.
The question of the form and extent of the Milky Way thus becomes the central one of stellar astronomy. Sir William Herschel began by trying to sound its depths; at one time he thought he had succeeded; but before he died he saw that they were unfathomable with his most powerful telescopes. Even today he would be a bold astronomer who would profess to say with certainty whether the smallest stars we can photograph are at the boundary of the system. Before we decide this point we must have some idea of the form and distance of the cloudlike masses of stars which form our great celestial girdle. A most curious fact is that our solar system seems to be in the centre of this galactic universe, because the Milky Way divides the heavens into two equal parts, and seems equally broad at all points. Were we looking at such a girdle as this from one side or the other, this appearance would not be presented. But let us not be too bold. Perhaps we are the victims of some fallacy, as Ptolemy was when he proved, by what looked like sound reasoning, based on undeniable facts, that this earth of ours stood at rest in the centre of the heavens!
A related problem, and one which may be of supreme importance to the future of our race, is, What is the source of the heat radiated by the sun and stars? We know that life on the earth is dependent on the heat which the sun sends it. If we were deprived of this heat we should in a few days be enveloped in a frost which would destroy nearly all vegetation, and in a few months neither man nor animal would be alive, unless crouching over fires soon to expire for want of fuel. We also know that, at a time which is geologically recent, the whole of New England was covered with a sheet of ice, hundreds or even thousands of feet thick, above which no mountain but Washington raised its head. It is quite possible that a small diminution in the supply of heat sent us by the sun would gradually reproduce the great glacier, and once more make the Eastern States like the pole. But the fact is that observations of temperature in various countries for the last two or three hundred years do not show any change in climate which can be attributed to a variation in the amount of heat received from the sun.
The acceptance of this theory of the heat of those heavenly bodies which shine by their own light—sun, stars, and nebulae—still leaves open a problem that looks insoluble with our present knowledge. What becomes of the great flood of heat and light which the sun and stars radiate into empty space with a velocity of one hundred and eighty thousand miles a second? Only a very small fraction of it can be received by the planets or by other stars, because these are mere points compared with their distance from us. Taking the teaching of our science just as it stands, we should say that all this heat continues to move on through infinite space forever. In a few thousand years it reaches the probable confines of our great universe. But we know of no reason why it should stop here. During the hundreds of millions of years since all our stars began to shine, has the first ray of light and heat kept on through space at the rate of one hundred and eighty thousand miles a second, and will it continue to go on for ages to come? If so, think of its distance now, and think of its still going on, to be forever wasted! Rather say that the problem, What becomes of it? is as yet unsolved.
Thus far I have described the greatest of problems; those which we may suppose to concern the inhabitants of millions of worlds revolving round the stars as much as they concern us. Let us now come down from the starry heights to this little colony where we live, the solar system. Here we have the great advantage of being better able to see what is going on, owing to the comparative nearness of the planets. When we learn that these bodies are like our earth in form, size, and motions, the first question we ask is, Could we fly from planet to planet and light on the surface of each, what sort of scenery would meet our eyes? Mountain, forest, and field, a dreary waste, or a seething caldron larger than our earth? If solid land there is, would we find on it the homes of intelligent beings, the lairs of wild beasts, or no living thing at all? Could we breathe the air, would we choke for breath or be poisoned by the fumes of some noxious gas?
To most of these questions science cannot as yet give a positive answer, except in the case of the moon. Our satellite is so near us that we can see it has no atmosphere and no water, and therefore cannot be the abode of life like ours. The contrast of its eternal deadness with the active life around us is great indeed. Here we have weather of so many kinds that we never tire of talking about it. But on the moon there is no weather at all. On our globe so many things are constantly happening that our thousands of daily journals cannot begin to record them. But on the dreary, rocky wastes of the moon nothing ever happens. So far as we can determine, every stone that lies loose on its surface has lain there through untold ages, unchanged and unmoved.
We cannot speak so confidently of the planets. The most powerful telescopes yet made, the most powerful we can ever hope to make, would scarcely shows us mountains, or lakes, rivers, or fields at a distance of fifty millions of miles. Much less would they show us any works of man. Pointed at the two nearest planets, Venus and Mars, they whet our curiosity more than they gratify it. Especially is this the case with Venus. Ever since the telescope was invented observers have tried to find the time of rotation of this planet on its axis. Some have reached one conclusion, some another, while the wisest have only doubted. The great Herschel claimed that the planet was so enveloped in vapor or clouds that no permanent features could be seen on its surface. The best equipped recent observers think they see faint, shadowy patches, which remain the same from day to day, and which show that the planet always presents the same face to the sun, as the moon does to the earth. Others do not accept this conclusion as proved, believing that these patches may be nothing more than variations of light, shade, and color caused by the reflection of the sun's light at various angles from different parts of the planet.
There is also some mystery about the atmosphere of this planet. When Venus passes nearly between us and the sun, her dark hemisphere is turned towards us, her bright one being always towards the sun. But she is not exactly on a line with the sun except on the very rare occasions of a transit across the sun's disk. Hence, on ordinary occasions, when she seems very near on a line with the sun, we see a very small part of the illuminated hemisphere, which now presents the form of a very thin crescent like the new moon. And this crescent is supposed to be a little broader than it would be if only half the planet were illuminated, and to encircle rather more than half the planet. Now, this is just the effect that would be produced by an atmosphere refracting the sun's light around the edge of the illuminated hemisphere.
The difficulty of observations of this kind is such that the conclusion may be open to doubt. What is seen during transits of Venus over the sun's disk leads to more certain, but yet very puzzling, conclusions. The writer will describe what he saw at the Cape of Good Hope during the transit of December 5, 1882. As the dark planet impinged on the bright sun, it of course cut out a round notch from the edge of the sun. At first, when this notch was small, nothing could be seen of the outline of that part of the planet which was outside the sun. But when half the planet was on the sun, the outline of the part still off the sun was marked by a slender arc of light. A curious fact was that this arc did not at first span the whole outline of the planet, but only showed at one or two points. In a few moments another part of the outline appeared, and then another, until, at last, the arc of light extended around the complete outline. All this seems to show that while the planet has an atmosphere, it is not transparent like ours, but is so filled with mist and clouds that the sun is seen through it only as if shining in a fog.
Not many years ago the planet Mars, which is the next one outside of us, was supposed to have a surface like that of our earth. Some parts were of a dark greenish gray hue; these were supposed to be seas and oceans. Other parts had a bright, warm tint; these were supposed to be the continents. During the last twenty years much has been learned as to how this planet looks, and the details of its surface have been mapped by several observers, using the best telescopes under the most favorable conditions of air and climate. And yet it must be confessed that the result of this labor is not altogether satisfactory. It seems certain that the so-called seas are really land and not water. When it comes to comparing Mars with the earth, we cannot be certain of more than a single point of resemblance. This is that during the Martian winter a white cap, as of snow, is formed over the pole, which partially melts away during the summer. The conclusion that there are oceans whose evaporation forms clouds which give rise to this snow seems plausible. But the telescope shows no clouds, and nothing to make it certain that there is an atmosphere to sustain them. There is no certainty that the white deposit is what we call snow; perhaps it is not formed of water at all. The most careful studies of the surface of this planet, under the best conditions, are those made at the Lowell Observatory at Flagstaff, Arizona. Especially wonderful is the system of so-called canals, first seen by Schiaparelli, but mapped in great detail at Flagstaff. But the nature and meaning of these mysterious lines are still to be discovered. The result is that the question of the real nature of the surface of Mars and of what we should see around us could we land upon it and travel over it are still among the unsolved problems of astronomy.
If this is the case with the nearest planets that we can study, how is it with more distant ones? Jupiter is the only one of these of the condition of whose surface we can claim to have definite knowledge. But even this knowledge is meagre. The substance of what we know is that its surface is surrounded by layers of what look like dense clouds, through which nothing can certainly be seen.
I have already spoken of the heat of the sun and its probable origin. But the question of its heat, though the most important, is not the only one that the sun offers us. What is the sun? When we say that it is a very hot globe, more than a million times as large as the earth, and hotter than any furnace that man can make, so that literally "the elements melt with fervent heat" even at its surface, while inside they are all vaporized, we have told the most that we know as to what the sun really is. Of course we know a great deal about the spots, the rotation of the sun on its axis, the materials of which it is composed, and how its surroundings look during a total eclipse. But all this does not answer our question. There are several mysteries which ingenious men have tried to explain, but they cannot prove their explanations to be correct. One is the cause and nature of the spots. Another is that the shining surface of the sun, the "photosphere," as it is technically called, seems so calm and quiet while forces are acting within it of a magnitude quite beyond our conception. Flames in which our earth and everything on it would be engulfed like a boy's marble in a blacksmith's forge are continually shooting up to a height of tens of thousands of miles. One would suppose that internal forces capable of doing this would break the surface up into billows of fire a thousand miles high; but we see nothing of the kind. The surface of the sun seems almost as placid as a lake.
Yet another mystery is the corona of the sun. This is something we should never have known to exist if the sun were not sometimes totally eclipsed by the dark body of the moon. On these rare occasions the sun is seen to be surrounded by a halo of soft, white light, sending out rays in various directions to great distances. This halo is called the corona, and has been most industriously studied and photographed during nearly every total eclipse for thirty years. Thus we have learned much about how it looks and what its shape is. It has a fibrous, woolly structure, a little like the loose end of a much-worn hempen rope. A certain resemblance has been seen between the form of these seeming fibres and that of the lines in which iron filings arrange themselves when sprinkled on paper over a magnet. It has hence been inferred that the sun has magnetic properties, a conclusion which, in a general way, is supported by many other facts. Yet the corona itself remains no less an unexplained phenomenon.
A phenomenon almost as mysterious as the solar corona is the "zodiacal light," which any one can see rising from the western horizon just after the end of twilight on a clear winter or spring evening. The most plausible explanation is that it is due to a cloud of small meteoric bodies revolving round the sun. We should hardly doubt this explanation were it not that this light has a yet more mysterious appendage, commonly called the Gegenschein, or counter-glow. This is a patch of light in the sky in a direction exactly opposite that of the sun. It is so faint that it can be seen only by a practised eye under the most favorable conditions. But it is always there. The latest suggestion is that it is a tail of the earth, of the same kind as the tail of a comet!
We know that the motions of the heavenly bodies are predicted with extraordinary exactness by the theory of gravitation. When one finds that the exact path of the moon's shadow on the earth during a total eclipse of the sun can be mapped out many years in advance, and that the planets follow the predictions of the astronomer so closely that, if you could see the predicted planet as a separate object, it would look, even in a good telescope, as if it exactly fitted over the real planet, one thinks that here at least is a branch of astronomy which is simply perfect. And yet the worlds themselves show slight deviations in their movements which the astronomer cannot always explain, and which may be due to some hidden cause that, when brought to light, shall lead to conclusions of the greatest importance to our race.
One of these deviations is in the rotation of the earth. Sometimes, for several years at a time, it seems to revolve a little faster, and then again a little slower. The changes are very slight; they can be detected only by the most laborious and refined methods; yet they must have a cause, and we should like to know what that cause is.
The moon shows a similar irregularity of motion. For half a century, perhaps through a whole century, she will go around the earth a little ahead of her regular rate, and then for another half-century or more she will fall behind. The changes are very small; they would never have been seen with the unaided eye, yet they exist. What is their cause? Mathematicians have vainly spent years of study in trying to answer this question.
The orbit of Mercury is found by observations to have a slight motion which mathematicians have vainly tried to explain. For some time it was supposed to be caused by the attraction of an unknown planet between Mercury and the sun, and some were so sure of the existence of this planet that they gave it a name, calling it Vulcan. But of late years it has become reasonably certain that no planet large enough to produce the effect observed can be there. So thoroughly has every possible explanation been sifted out and found wanting, that some astronomers are now inquiring whether the law of gravitation itself may not be a little different from what has always been supposed. A very slight deviation, indeed, would account for the facts, but cautious astronomers want other proofs before regarding the deviation of gravitation as an established fact.
Intelligent men have sometimes inquired how, after devoting so much work to the study of the heavens, anything can remain for astronomers to find out. It is a curious fact that, although they were never learning so fast as at the present day, yet there seems to be more to learn now than there ever was before. Great and numerous as are the unsolved problems of our science, knowledge is now advancing into regions which, a few years ago, seemed inaccessible. Where it will stop none can say.
THE NEW PROBLEMS OF THE UNIVERSE
The achievements of the nineteenth century are still a theme of congratulation on the part of all who compare the present state of the world with that of one hundred years ago. And yet, if we should fancy the most sagacious prophet, endowed with a brilliant imagination, to have set forth in the year 1806 the problems that the century might solve and the things which it might do, we should be surprised to see how few of his predictions had come to pass. He might have fancied aerial navigation and a number of other triumphs of the same class, but he would hardly have had either steam navigation or the telegraph in his picture. In 1856 an article appeared in Harper's Magazine depicting some anticipated features of life in A.D. 3000. We have since made great advances, but they bear little resemblance to what the writer imagined. He did not dream of the telephone, but did describe much that has not yet come to pass and probably never will.
The fact is that, much as the nineteenth century has done, its last work was to amuse itself by setting forth more problems for this century to solve than it has ever itself succeeded in mastering. We should not be far wrong in saying that to-day there are more riddles in the universe than there were before men knew that it contained anything more than the objects they could see.
So far as mere material progress is concerned, it may be doubtful whether anything so epoch-making as the steam-engine or the telegraph is held in store for us by the future. But in the field of purely scientific discovery we are finding a crowd of things of which our philosophy did not dream even ten years ago.
The greatest riddles which the nineteenth century has bequeathed to us relate to subjects so widely separated as the structure of the universe and the structure of atoms of matter. We see more and more of these structures, and we see more and more of unity everywhere, and yet new facts difficult of explanation are being added more rapidly than old facts are being explained.
We all know that the nineteenth century was marked by a separation of the sciences into a vast number of specialties, to the subdivisions of which one could see no end. But the great work of the twentieth century will be to combine many of these specialties. The physical philosopher of the present time is directing his thought to the demonstration of the unity of creation. Astronomical and physical researches are now being united in a way which is bringing the infinitely great and the infinitely small into one field of knowledge. Ten years ago the atoms of matter, of which it takes millions of millions to make a drop of water, were the minutest objects with which science could imagine itself to be concerned, Now a body of experimentalists, prominent among whom stand Professors J. J. Thompson, Becquerel, and Roentgen, have demonstrated the existence of objects so minute that they find their way among and between the atoms of matter as rain-drops do among the buildings of a city. More wonderful yet, it seems likely, although it has not been demonstrated, that these little things, called "corpuscles," play an important part in what is going on among the stars. Whether this be true or not, it is certain that there do exist in the universe emanations of some sort, producing visible effects, the investigation of which the nineteenth century has had to bequeath to the twentieth.
For the purpose of the navigator, the direction of the magnetic needle is invariable in any one place, for months and even years; but when exact scientific observations on it are made, it is found subject to numerous slight changes. The most regular of these consists in a daily change of its direction. It moves one way from morning until noon, and then, late in the afternoon and during the night, turns back again to its original pointing. The laws of this change have been carefully studied from observations, which show that it is least at the equator and larger as we go north into middle latitudes; but no explanation of it resting on an indisputable basis has ever been offered.
Besides these regular changes, there are others of a very irregular character. Every now and then the changes in the direction of the magnet are wider and more rapid than those which occur regularly every day. The needle may move back and forth in a way so fitful as to show the action of some unusual exciting cause. Such movements of the needle are commonly seen when there is a brilliant aurora. This connection shows that a magnetic storm and an aurora must be due to the same or some connected causes.
Those of us who are acquainted with astronomical matters know that the number of spots on the sun goes through a regular cycle of change, having a period of eleven years and one or two months. Now, the curious fact is, when the number and violence of magnetic storms are recorded and compared, it is found that they correspond to the spots on the sun, and go through the same period of eleven years. The conclusion seems almost inevitable: magnetic storms are due to some emanation sent out by the sun, which arises from the same cause that produces the spots. This emanation does not go on incessantly, but only in an occasional way, as storms follow each other on the earth. What is it? Every attempt to detect it has been in vain. Professor Hale, at the Yerkes Observatory, has had in operation from time to time, for several years, his ingenious spectroheliograph, which photographs the sun by a single ray of the spectrum. This instrument shows that violent actions are going on in the sun, which ordinary observation would never lead us to suspect. But it has failed to show with certainty any peculiar emanation at the time of a magnetic storm or anything connected with such a storm.
A mystery which seems yet more impenetrable is associated with the so-called new stars which blaze forth from time to time. These offer to our sight the most astounding phenomena ever presented to the physical philosopher. One hundred years ago such objects offered no mystery. There was no reason to suppose that the Creator of the universe had ceased His functions; and, continuing them, it was perfectly natural that He should be making continual additions to the universe of stars. But the idea that these objects are really new creations, made out of nothing, is contrary to all our modern ideas and not in accord with the observed facts. Granting the possibility of a really new star—if such an object were created, it would be destined to take its place among the other stars as a permanent member of the universe. Instead of this, such objects invariably fade away after a few months, and are changed into something very like an ordinary nebula. A question of transcendent interest is that of the cause of these outbursts. It cannot be said that science has, up to the present time, been able to offer any suggestion not open to question. The most definite one is the collision theory, according to which the outburst is due to the clashing together of two stars, one or both of which might previously have been dark, like a planet. The stars which may be actually photographed probably exceed one hundred millions in number, and those which give too little light to affect the photographic plate may be vastly more numerous than those which do. Dark stars revolve around bright ones in an infinite variety of ways, and complex systems of bodies, the members of which powerfully attract each other, are the rule throughout the universe. Moreover, we can set no limit to the possible number of dark or invisible stars that may be flying through the celestial spaces. While, therefore, we cannot regard the theory of collision as established, it seems to be the only one yet put forth which can lay any claim to a scientific basis. What gives most color to it is the extreme suddenness with which the new stars, so far as has yet been observed, invariably blaze forth. In almost every case it has been only two or three days from the time that the existence of such an object became known until it had attained nearly its full brightness. In fact, it would seem that in the case of the star in Perseus, as in most other cases, the greater part of the outburst took place within the space of twenty-four hours. This suddenness and rapidity is exactly what would be the result of a collision.
The most inexplicable feature of all is the rapid formation of a nebula around this star. In the first photographs of the latter, the appearance presented is simply that of an ordinary star. But, in the course of three or four months, the delicate photographs taken at the Lick Observatory showed that a nebulous light surrounded the star, and was continually growing larger and larger. At first sight, there would seem to be nothing extraordinary in this fact. Great masses of intensely hot vapor, shining by their own light, would naturally be thrown out from the star. Or, if the star had originally been surrounded by a very rare nebulous fog or vapor, the latter would be seen by the brilliant light emitted by the star. On this was based an explanation offered by Kapteyn, which at first seemed very plausible. It was that the sudden wave of light thrown out by the star when it burst forth caused the illumination of the surrounding vapor, which, though really at rest, would seem to expand with the velocity of light, as the illumination reached more and more distant regions of the nebula. This result may be made the subject of exact calculation. The velocity of light is such as would make a circuit of the earth more than seven times in a second. It would, therefore, go out from the star at the rate of a million of miles in between five and six seconds. In the lapse of one of our days, the light would have filled a sphere around the star having a diameter more than one hundred and fifty times the distance of the sun from the earth, and more than five times the dimensions of the whole solar system. Continuing its course and enlarging its sphere day after day, the sight presented to us would have been that of a gradually expanding nebulous mass—a globe of faint light continually increasing in size with the velocity of light.
The first sentiment the reader will feel on this subject is doubtless one of surprise that the distance of the star should be so great as this explanation would imply. Six months after the explosion, the globe of light, as actually photographed, was of a size which would have been visible to the naked eye only as a very minute object in the sky. Is it possible that this minute object could have been thousands of times the dimensions of our solar system?
To see how the question stands from this point of view, we must have some idea of the possible distance of the new star. To gain this idea, we must find some way of estimating distances in the universe. For a reason which will soon be apparent, we begin with the greatest structure which nature offers to the view of man. We all know that the Milky Way is formed of countless stars, too minute to be individually visible to the naked eye. The more powerful the telescope through which we sweep the heavens, the greater the number of the stars that can be seen in it. With the powerful instruments which are now in use for photographing the sky, the number of stars brought to light must rise into the hundreds of millions, and the greater part of these belong to the Milky Way. The smaller the stars we count, the greater their comparative number in the region of the Milky Way. Of the stars visible through the telescope, more than one-half are found in the Milky Way, which may be regarded as a girdle spanning the entire visible universe.
Of the diameter of this girdle we can say, almost with certainty, that it must be more than a thousand times as great as the distance of the nearest fixed star from us, and is probably two or three times greater. According to the best judgment we can form, our solar system is situate near the central region of the girdle, so that the latter must be distant from us by half its diameter. It follows that if we can imagine a gigantic pair of compasses, of which the points extend from us to Alpha Centauri, the nearest star, we should have to measure out at least five hundred spaces with the compass, and perhaps even one thousand or more, to reach the region of the Milky Way.
With this we have to connect another curious fact. Of eighteen new stars which have been observed to blaze forth during the last four hundred years, all are in the region of the Milky Way. This seems to show that, as a rule, they belong to the Milky Way. Accepting this very plausible conclusion, the new star in Perseus must have been more than five hundred times as far as the nearest fixed star. We know that it takes light four years to reach us from Alpha Centauri. It follows that the new star was at a distance through which light would require more than two thousand years to travel, and quite likely a time two or three times this. It requires only the most elementary ideas of geometry to see that if we suppose a ray of light to shoot from a star at such a distance in a direction perpendicular to the line of sight from us to the star, we can compute how fast the ray would seem to us to travel. Granting the distance to be only two thousand light years, the apparent size of the sphere around the star which the light would fill at the end of one year after the explosion would be that of a coin seen at a distance of two thousand times its radius, or one thousand times its diameter—say, a five-cent piece at the distance of sixty feet. But, as a matter of fact, the nebulous illumination expanded with a velocity from ten to twenty times as great as this.
The idea that the nebulosity around the new star was formed by the illumination caused by the light of the explosion spreading out on all sides therefore fails to satisfy us, not because the expansion of the nebula seemed to be so slow, but because it was many times as swift as the speed of light. Another reason for believing that it was not a mere wave of light is offered by the fact that it did not take place regularly in every direction from the star, but seemed to shoot off at various angles.
Up to the present time, the speed of light has been to science, as well as to the intelligence of our race, almost a symbol of the greatest of possible speeds. The more carefully we reflect on the case, the more clearly we shall see the difficulty in supposing any agency to travel at the rate of the seeming emanations from the new star in Perseus.
As the emanation is seen spreading day after day, the reader may inquire whether this is not an appearance due to some other cause than the mere motion of light. May not an explosion taking place in the centre of a star produce an effect which shall travel yet faster than light? We can only reply that no such agency is known to science.
But is there really anything intrinsically improbable in an agency travelling with a speed many times that of light? In considering that there is, we may fall into an error very much like that into which our predecessors fell in thinking it entirely out of the range of reasonable probability that the stars should be placed at such distances as we now know them to be.
Accepting it as a fact that agencies do exist which travel from sun to planet and from star to star with a speed which beggars all our previous ideas, the first question that arises is that of their nature and mode of action. This question is, up to the present time, one which we do not see any way of completely answering. The first difficulty is that we have no evidence of these agents except that afforded by their action. We see that the sun goes through a regular course of pulsations, each requiring eleven years for completion; and we see that, simultaneously with these, the earth's magnetism goes through a similar course of pulsations. The connection of the two, therefore, seems absolutely proven. But when we ask by what agency it is possible for the sun to affect the magnetism of the earth, and when we trace the passage of some agent between the two bodies, we find nothing to explain the action. To all appearance, the space between the earth and the sun is a perfect void. That electricity cannot of itself pass through a vacuum seems to be a well-established law of physics. It is true that electromagnetic waves, which are supposed to be of the same nature with those of light, and which are used in wireless telegraphy, do pass through a vacuum and may pass from the sun to the earth. But there is no way of explaining how such waves would either produce or affect the magnetism of the earth.
The mysterious emanations from various substances, under certain conditions, may have an intimate relation with yet another of the mysteries of the universe. It is a fundamental law of the universe that when a body emits light or heat, or anything capable of being transformed into light or heat, it can do so only by the expenditure of force, limited in supply. The sun and stars are continually sending out a flood of heat. They are exhausting the internal supply of something which must be limited in extent. Whence comes the supply? How is the heat of the sun kept up? If it were a hot body cooling off, a very few years would suffice for it to cool off so far that its surface would become solid and very soon cold. In recent years, the theory universally accepted has been that the supply of heat is kept up by the continual contraction of the sun, by mutual gravitation of its parts as it cools off. This theory has the advantage of enabling us to calculate, with some approximation to exactness, at what rate the sun must be contracting in order to keep up the supply of heat which it radiates. On this theory, it must, ten millions of years ago, have had twice its present diameter, while less than twenty millions of years ago it could not have existed except as an immense nebula filling the whole solar system. We must bear in mind that this theory is the only one which accounts for the supply of heat, even through human history. If it be true, then the sun, earth, and solar system must be less than twenty million years old.
Here the geologists step in and tell us that this conclusion is wholly inadmissible. The study of the strata of the earth and of many other geological phenomena, they assure us, makes it certain that the earth must have existed much in its present condition for hundreds of millions of years. During all that time there can have been no great diminution in the supply of heat radiated by the sun.
The astronomer, in considering this argument, has to admit that he finds a similar difficulty in connection with the stars and nebulas. It is an impossibility to regard these objects as new; they must be as old as the universe itself. They radiate heat and light year after year. In all probability, they must have been doing so for millions of years. Whence comes the supply? The geologist may well claim that until the astronomer explains this mystery in his own domain, he cannot declare the conclusions of geology as to the age of the earth to be wholly inadmissible.
Now, the scientific experiments of the last two years have brought this mystery of the celestial spaces right down into our earthly laboratories. M. and Madame Curie have discovered the singular metal radium, which seems to send out light, heat, and other rays incessantly, without, so far as has yet been determined, drawing the required energy from any outward source. As we have already pointed out, such an emanation must come from some storehouse of energy. Is the storehouse, then, in the medium itself, or does the latter draw it from surrounding objects? If it does, it must abstract heat from these objects. This question has been settled by Professor Dewar, at the Royal Institution, London, by placing the radium in a medium next to the coldest that art has yet produced—liquid air. The latter is surrounded by the only yet colder medium, liquid hydrogen, so that no heat can reach it. Under these circumstances, the radium still gives out heat, boiling away the liquid air until the latter has entirely disappeared. Instead of the radiation diminishing with time, it rather seems to increase.
Called on to explain all this, science can only say that a molecular change must be going on in the radium, to correspond to the heat it gives out. What that change may be is still a complete mystery. It is a mystery which we find alike in those minute specimens of the rarest of substances under our microscopes, in the sun, and in the vast nebulous masses in the midst of which our whole solar system would be but a speck. The unravelling of this mystery must be the great work of science of the twentieth century. What results shall follow for mankind one cannot say, any more than he could have said two hundred years ago what modern science would bring forth. Perhaps, before future developments, all the boasted achievements of the nineteenth century may take the modest place which we now assign to the science of the eighteenth century—that of the infant which is to grow into a man.
THE STRUCTURE OF THE UNIVERSE
The questions of the extent of the universe in space and of its duration in time, especially of its possible infinity in either space or time, are of the highest interest both in philosophy and science. The traditional philosophy had no means of attacking these questions except considerations suggested by pure reason, analogy, and that general fitness of things which was supposed to mark the order of nature. With modern science the questions belong to the realm of fact, and can be decided only by the results of observation and a study of the laws to which these results may lead.
From the philosophic stand-point, a discussion of this subject which is of such weight that in the history of thought it must be assigned a place above all others, is that of Kant in his "Kritik." Here we find two opposing propositions—the thesis that the universe occupies only a finite space and is of finite duration; the antithesis that it is infinite both as regards extent in space and duration in time. Both of these opposing propositions are shown to admit of demonstration with equal force, not directly, but by the methods of reductio ad absurdum. The difficulty, discussed by Kant, was more tersely expressed by Hamilton in pointing out that we could neither conceive of infinite space nor of space as bounded. The methods and conclusions of modern astronomy are, however, in no way at variance with Kant's reasoning, so far as it extends. The fact is that the problem with which the philosopher of Konigsberg vainly grappled is one which our science cannot solve any more than could his logic. We may hope to gain complete information as to everything which lies within the range of the telescope, and to trace to its beginning every process which we can now see going on in space. But before questions of the absolute beginning of things, or of the boundary beyond which nothing exists, our means of inquiry are quite powerless.
Another example of the ancient method is found in the great work of Copernicus. It is remarkable how completely the first expounder of the system of the world was dominated by the philosophy of his time, which he had inherited from his predecessors. This is seen not only in the general course of thought through the opening chapters of his work, but among his introductory propositions. The first of these is that the universe—mundus—as well as the earth, is spherical in form. His arguments for the sphericity of the earth, as derived from observation, are little more than a repetition of those of Ptolemy, and therefore not of special interest. His proposition that the universe is spherical is, however, not based on observation, but on considerations of the perfection of the spherical form, the general tendency of bodies—a drop of water, for example—to assume this form, and the sphericity of the sun and moon. The idea retained its place in his mind, although the fundamental conception of his system did away with the idea of the universe having any well-defined form.
The question as attacked by modern astronomy is this: we see scattered through space in every direction many millions of stars of various orders of brightness and at distances so great as to defy exact measurement, except in the case of a few of the nearest. Has this collection of stars any well-defined boundary, or is what we see merely that part of an infinite mass which chances to lie within the range of our telescopes? If we were transported to the most distant star of which we have knowledge, should we there find ourselves still surrounded by stars on all sides, or would the space beyond be void? Granting that, in any or every direction, there is a limit to the universe, and that the space beyond is therefore void, what is the form of the whole system and the distance of its boundaries? Preliminary in some sort to these questions are the more approachable ones: Of what sort of matter is the universe formed? and into what sort of bodies is this matter collected?
To the ancients the celestial sphere was a reality, instead of a mere effect of perspective, as we regard it. The stars were set on its surface, or at least at no great distance within its crystalline mass. Outside of it imagination placed the empyrean. When and how these conceptions vanished from the mind of man, it would be as hard to say as when and how Santa Claus gets transformed in the mind of the child. They are not treated as realities by any astronomical writer from Ptolemy down; yet, the impressions and forms of thought to which they gave rise are well marked in Copernicus and faintly evident in Kepler. The latter was perhaps the first to suggest that the sun might be one of the stars; yet, from defective knowledge of the relative brightness of the latter, he was led to the conclusion that their distances from each other were less than the distance which separated them from the sun. The latter he supposed to stand in the centre of a vast vacant region within the system of stars.
For us the great collection of millions of stars which are made known to us by the telescope, together with all the invisible bodies which may be contained within the limits of the system, form the universe. Here the term "universe" is perhaps objectionable because there may be other systems than the one with which we are acquainted. The term stellar system is, therefore, a better one by which to designate the collection of stars in question.
It is remarkable that the first known propounder of that theory of the form and arrangement of the system which has been most generally accepted seems to have been a writer otherwise unknown in science—Thomas Wright, of Durham, England. He is said to have published a book on the theory of the universe, about 1750. It does not appear that this work was of a very scientific character, and it was, perhaps, too much in the nature of a speculation to excite notice in scientific circles. One of the curious features of the history is that it was Kant who first cited Wright's theory, pointed out its accordance with the appearance of the Milky Way, and showed its general reasonableness. But, at the time in question, the work of the philosopher of Konigsberg seems to have excited no more notice among his scientific contemporaries than that of Wright.
Kant's fame as a speculative philosopher has so eclipsed his scientific work that the latter has but recently been appraised at its true value. He was the originator of views which, though defective in detail, embodied a remarkable number of the results of recent research on the structure and form of the universe, and the changes taking place in it. The most curious illustration of the way in which he arrived at a correct conclusion by defective reasoning is found in his anticipation of the modern theory of a constant retardation of the velocity with which the earth revolves on its axis. He conceived that this effect must result from the force exerted by the tidal wave, as moving towards the west it strikes the eastern coasts of Asia and America. An opposite conclusion was reached by Laplace, who showed that the effect of this force was neutralized by forces producing the wave and acting in the opposite direction. And yet, nearly a century later, it was shown that while Laplace was quite correct as regards the general principles involved, the friction of the moving water must prevent the complete neutralization of the two opposing forces, and leave a small residual force acting towards the west and retarding the rotation. Kant's conclusion was established, but by an action different from that which he supposed.
The theory of Wright and Kant, which was still further developed by Herschel, was that our stellar system has somewhat the form of a flattened cylinder, or perhaps that which the earth would assume if, in consequence of more rapid rotation, the bulging out at its equator and the flattening at its poles were carried to an extreme limit. This form has been correctly though satirically compared to that of a grindstone. It rests to a certain extent, but not entirely, on the idea that the stars are scattered through space with equal thickness in every direction, and that the appearance of the Milky Way is due to the fact that we, situated in the centre of this flattened system, see more stars in the direction of the circumference of the system than in that of its poles. The argument on which the view in question rests may be made clear in the following way.
Let us chose for our observations that hour of the night at which the Milky Way skirts our horizon. This is nearly the case in the evenings of May and June, though the coincidence with the horizon can never be exact except to observers stationed near the tropics. Using the figure of the grindstone, we at its centre will then have its circumference around our horizon, while the axis will be nearly vertical. The points in which the latter intersects the celestial sphere are called the galactic poles. There will be two of these poles, the one at the hour in question near the zenith, the other in our nadir, and therefore invisible to us, though seen by our antipodes. Our horizon corresponds, as it were, to the central circle of the Milky Way, which now surrounds us on all sides in a horizontal direction, while the galactic poles are 90 degrees distant from every part of it, as every point of the horizon is 90 degrees from the zenith.
Let us next count the number of stars visible in a powerful telescope in the region of the heavens around the galactic pole, now our zenith, and find the average number per square degree. This will be the richness of the region in stars. Then we take regions nearer the horizontal Milky Way—say that contained between 10 degrees and 20 degrees from the zenith—and, by a similar count, find its richness in stars. We do the same for other regions, nearer and nearer to the horizon, till we reach the galaxy itself. The result of all the counts will be that the richness of the sky in stars is least around the galactic pole, and increases in every direction towards the Milky Way.
Without such counts of the stars we might imagine our stellar system to be a globular collection of stars around which the object in question passed as a girdle; and we might take a globe with a chain passing around it as representative of the possible figure of the stellar system. But the actual increase in star-thickness which we have pointed out shows us that this view is incorrect. The nature and validity of the conclusions to be drawn can be best appreciated by a statement of some features of this tendency of the stars to crowd towards the galactic circle.
Most remarkable is the fact that the tendency is seen even among the brighter stars. Without either telescope or technical knowledge, the careful observer of the stars will notice that the most brilliant constellations show this tendency. The glorious Orion, Canis Major containing the brightest star in the heavens, Cassiopeia, Perseus, Cygnus, and Lyra with its bright-blue Vega, not to mention such constellations as the Southern Cross, all lie in or near the Milky Way. Schiaparelli has extended the investigation to all the stars visible to the naked eye. He laid down on planispheres the number of such stars in each region of the heavens of 5 degrees square. Each region was then shaded with a tint that was darker as the region was richer in stars. The very existence of the Milky Way was ignored in this work, though his most darkly shaded regions lie along the course of this belt. By drawing a band around the sky so as to follow or cover his darkest regions, we shall rediscover the course of the Milky Way without any reference to the actual object. It is hardly necessary to add that this result would be reached with yet greater precision if we included the telescopic stars to any degree of magnitude—plotting them on a chart and shading the chart in the same way. What we learn from this is that the stellar system is not an irregular chaos; and that notwithstanding all its minor irregularities, it may be considered as built up with special reference to the Milky Way as a foundation.
Another feature of the tendency in question is that it is more and more marked as we include fainter stars in our count. The galactic region is perhaps twice as rich in stars visible to the naked eye as the rest of the heavens. In telescopic stars to the ninth magnitude it is three or four times as rich. In the stars found on the photographs of the sky made at the Harvard and other observatories, and in the stargauges of the Herschels, it is from five to ten times as rich.
Another feature showing the unity of the system is the symmetry of the heavens on the two sides of the galactic belt Let us return to our supposition of such a position of the celestial sphere, with respect to the horizon, that the latter coincides with the central line of this belt, one galactic pole being near our zenith. The celestial hemisphere which, being above our horizon, is visible to us, is the one to which we have hitherto directed our attention in describing the distribution of the stars. But below our horizon is another hemisphere, that of our antipodes, which is the counterpart of ours. The stars which it contains are in a different part of the universe from those which we see, and, without unity of plan, would not be subject to the same law. But the most accurate counts of stars that have been made fail to show any difference in their general arrangement in the two hemispheres. They are just as thick around the south galactic poles as around the north one. They show the same tendency to crowd towards the Milky Way in the hemisphere invisible to us as in the hemisphere which we see. Slight differences and irregularities, are, indeed, found in the enumeration, but they are no greater than must necessarily arise from the difficulty of stopping our count at a perfectly fixed magnitude. The aim of star-counts is not to estimate the total number of stars, for this is beyond our power, but the number visible with a given telescope. In such work different observers have explored different parts of the sky, and in a count of the same region by two observers we shall find that, although they attempt to stop at the same magnitude, each will include a great number of stars which the other omits. There is, therefore, room for considerable difference in the numbers of stars recorded, without there being any actual inequality between the two hemispheres.
A corresponding similarity is found in the physical constitution of the stars as brought out by the spectroscope. The Milky Way is extremely rich in bluish stars, which make up a considerable majority of the cloudlike masses there seen. But when we recede from the galaxy on one side, we find the blue stars becoming thinner, while those having a yellow tinge become relatively more numerous. This difference of color also is the same on the two sides of the galactic plane. Nor can any systematic difference be detected between the proper motions of the stars in these two hemispheres. If the largest known proper motion is found in the one, the second largest is in the other. Counting all the known stars that have proper motions exceeding a given limit, we find about as many in one hemisphere as in the other. In this respect, also, the universe appears to be alike through its whole extent. It is the uniformity thus prevailing through the visible universe, as far as we can see, in two opposite directions, which inspires us with confidence in the possibility of ultimately reaching some well-founded conclusion as to the extent and structure of the system.
All these facts concur in supporting the view of Wright, Kant, and Herschel as to the form of the universe. The farther out the stars extend in any direction, the more stars we may see in that direction. In the direction of the axis of the cylinder, the distances of the boundary are least, so that we see fewer stars. The farther we direct our attention towards the equatorial regions of the system, the greater the distance from us to the boundary, and hence the more stars we see. The fact that the increase in the number of stars seen towards the equatorial region of the system is greater, the smaller the stars, is the natural consequence of the fact that distant stars come within our view in greater numbers towards the equatorial than towards the polar regions.
Objections have been raised to the Herschelian view on the ground that it assumes an approximately uniform distribution of the stars in space. It has been claimed that the fact of our seeing more stars in one direction than in another may not arise merely from our looking through a deeper stratum, as Herschel supposed, but may as well be due to the stars being more thinly scattered in the direction of the axis of the system than in that of its equatorial region. The great inequalities in the richness of neighboring regions in the Milky Way show that the hypothesis of uniform distribution does not apply to the equatorial region. The claim has therefore been made that there is no proof of the system extending out any farther in the equatorial than in the polar direction.
The consideration of this objection requires a closer inquiry as to what we are to understand by the form of our system. We have already pointed out the impossibility of assigning any boundary beyond which we can say that nothing exists. And even as regards a boundary of our stellar system, it is impossible for us to assign any exact limit beyond which no star is visible to us. The analogy of collections of stars seen in various parts of the heavens leads us to suppose that there may be no well-defined form to our system, but that, as we go out farther and farther, we shall see occasional scattered stars to, possibly, an indefinite distance. The truth probably is that, as in ascending a mountain, we find the trees, which may be very dense at its base, thin out gradually as we approach the summit, where there may be few or none, so we might find the stars to thin out could we fly to the distant regions of space. The practical question is whether, in such a flight, we should find this sooner by going in the direction of the axis of our system than by directing our course towards the Milky Way. If a point is at length reached beyond which there are but few scattered stars, such a point would, for us, mark the boundary of our system. From this point of view the answer does not seem to admit of doubt. If, going in every direction, we mark the point, if any, at which the great mass of the stars are seen behind us, the totality of all these points will lie on a surface of the general form that Herschel supposed.
There is still another direct indication of the finitude of our stellar system upon which we have not touched. If this system extended out without limit in any direction whatever, it is shown by a geometric process which it is not necessary to explain in the present connection, but which is of the character of mathematical demonstration, that the heavens would, in every direction where this was true, blaze with the light of the noonday sun. This would be very different from the blue-black sky which we actually see on a clear night, and which, with a reservation that we shall consider hereafter, shows that, how far so-ever our stellar system may extend, it is not infinite. Beyond this negative conclusion the fact does not teach us much. Vast, indeed, is the distance to which the system might extend without the sky appearing much brighter than it is, and we must have recourse to other considerations in seeking for indications of a boundary, or even of a well-marked thinning out, of stars.
If, as was formerly supposed, the stars did not greatly differ in the amount of light emitted by each, and if their diversity of apparent magnitude were due principally to the greater distance of the fainter stars, then the brightness of a star would enable us to form a more or less approximate idea of its distance. But the accumulated researches of the past seventy years show that the stars differ so enormously in their actual luminosity that the apparent brightness of a star affords us only a very imperfect indication of its distance. While, in the general average, the brighter stars must be nearer to us than the fainter ones, it by no means follows that a very bright star, even of the first magnitude, is among the nearer to our system. Two stars are worthy of especial mention in this connection, Canopus and Rigel. The first is, with the single exception of Sirius, the brightest star in the heavens. The other is a star of the first magnitude in the southwest corner of Orion. The most long-continued and complete measures of parallax yet made are those carried on by Gill, at the Cape of Good Hope, on these two and some other bright stars. The results, published in 1901, show that neither of these bodies has any parallax that can be measured by the most refined instrumental means known to astronomy. In other words, the distance of these stars is immeasurably great. The actual amount of light emitted by each is certainly thousands and probably tens of thousands of times that of the sun.
Notwithstanding the difficulties that surround the subject, we can at least say something of the distance of a considerable number of the stars. Two methods are available for our estimate—measures of parallax and determination of proper motions.
The problem of stellar parallax, simple though it is in its conception, is the most delicate and difficult of all which the practical astronomer has to encounter. An idea of it may be gained by supposing a minute object on a mountain-top, we know not how many miles away, to be visible through a telescope. The observer is allowed to change the position of his instrument by two inches, but no more. He is required to determine the change in the direction of the object produced by this minute displacement with accuracy enough to determine the distance of the mountain. This is quite analogous to the determination of the change in the direction in which we see a star as the earth, moving through its vast circuit, passes from one extremity of its orbit to the other. Representing this motion on such a scale that the distance of our planet from the sun shall be one inch, we find that the nearest star, on the same scale, will be more than four miles away, and scarcely one out of a million will be at a less distance than ten miles. It is only by the most wonderful perfection both in the heliometer, the instrument principally used for these measures, and in methods of observation, that any displacement at all can be seen even among the nearest stars. The parallaxes of perhaps a hundred stars have been determined, with greater or less precision, and a few hundred more may be near enough for measurement. All the others are immeasurably distant; and it is only by statistical methods based on their proper motions and their probable near approach to equality in distribution that any idea can be gained of their distances.
To form a conception of the stellar system, we must have a unit of measure not only exceeding any terrestrial standard, but even any distance in the solar system. For purely astronomical purposes the most convenient unit is the distance corresponding to a parallax of 1", which is a little more than 200,000 times the sun's distance. But for the purposes of all but the professional astronomer the most convenient unit will be the light-year—that is, the distance through which light would travel in one year. This is equal to the product of 186,000 miles, the distance travelled in one second, by 31,558,000, the number of seconds in a year. The reader who chooses to do so may perform the multiplication for himself. The product will amount to about 63,000 times the distance of the sun.
The nearest star whose distance we know, Alpha Centauri, is distant from us more than four light-years. In all likelihood this is really the nearest star, and it is not at all probable that any other star lies within six light-years. Moreover, if we were transported to this star the probability seems to be that the sun would now be the nearest star to us. Flying to any other of the stars whose parallax has been measured, we should probably find that the average of the six or eight nearest stars around us ranges somewhere between five and seven light-years. We may, in a certain sense, call eight light-years a star-distance, meaning by this term the average of the nearest distances from one star to the surrounding ones.
To put the result of measures of parallax into another form, let us suppose, described around our sun as a centre, a system of concentric spheres each of whose surfaces is at the distance of six light-years outside the sphere next within it. The inner is at the distance of six light-years around the sun. The surface of the second sphere will be twelve light-years away, that of the third eighteen, etc. The volumes of space within each of these spheres will be as the cubes of the diameters. The most likely conclusion we can draw from measures of parallax is that the first sphere will contain, beside the sun at its centre, only Alpha Centauri. The second, twelve light-years away, will probably contain, besides these two, six other stars, making eight in all. The third may contain twenty-one more, making twenty-seven stars within the third sphere, which is the cube of three. Within the fourth would probably be found sixty-four stars, this being the cube of four, and so on.
Beyond this no measures of parallax yet made will give us much assistance. We can only infer that probably the same law holds for a large number of spheres, though it is quite certain that it does not hold indefinitely. For more light on the subject we must have recourse to the proper motions. The latest words of astronomy on this subject may be briefly summarized. As a rule, no star is at rest. Each is moving through space with a speed which differs greatly with different stars, but is nearly always swift, indeed, when measured by any standard to which we are accustomed. Slow and halting, indeed, is that star which does not make more than a mile a second. With two or three exceptions, where the attraction of a companion comes in, the motion of every star, so far as yet determined, takes place in a straight line. In its outward motion the flying body deviates neither to the right nor left. It is safe to say that, if any deviation is to take place, thousands of years will be required for our terrestrial observers to recognize it.
Rapid as the course of these objects is, the distances which we have described are such that, in the great majority of cases, all the observations yet made on the positions of the stars fail to show any well-established motion. It is only in the case of the nearer of these objects that we can expect any motion to be perceptible during the period, in no case exceeding one hundred and fifty years, through which accurate observations extend. The efforts of all the observatories which engage in such work are, up to the present time, unequal to the task of grappling with the motions of all the stars that can be seen with the instruments, and reaching a decision as to the proper motion in each particular case. As the question now stands, the aim of the astronomer is to determine what stars have proper motions large enough to be well established. To make our statement on this subject clear, it must be understood that by this term the astronomer does not mean the speed of a star in space, but its angular motion as he observes it on the celestial sphere. A star moving forward with a given speed will have a greater proper motion according as it is nearer to us. To avoid all ambiguity, we shall use the term "speed" to express the velocity in miles per second with which such a body moves through space, and the term "proper motion" to express the apparent angular motion which the astronomer measures upon the celestial sphere.
Up to the present time, two stars have been found whose proper motions are so large that, if continued, the bodies would make a complete circuit of the heavens in less than 200,000 years. One of these would require about 160,000; the other about 180,000 years for the circuit. Of other stars having a rapid motion only about one hundred would complete their course in less than a million of years.
Quite recently a system of observations upon stars to the ninth magnitude has been nearly carried through by an international combination of observatories. The most important conclusion from these observations relates to the distribution of the stars with reference to the Milky Way, which we have already described. We have shown that stars of every magnitude, bright and faint, show a tendency to crowd towards this belt. It is, therefore, remarkable that no such tendency is seen in the case of those stars which have proper motions large enough to be accurately determined. So far as yet appears, such stars are equally scattered over the heavens, without reference to the course of the Milky Way. The conclusion is obvious. These stars are all inside the girdle of the Milky Way, and within the sphere which contains them the distribution in space is approximately uniform. At least there is no well-marked condensation in the direction of the galaxy nor any marked thinning out towards its poles. What can we say as to the extent of this sphere?
To answer this question, we have to consider whether there is any average or ordinary speed that a star has in space. A great number of motions in the line of sight—that is to say, in the direction of the line from us to the star—have been measured with great precision by Campbell at the Lick Observatory, and by other astronomers. The statistical investigations of Kaptoyn also throw much light on the subject. The results of these investigators agree well in showing an average speed in space—a straight-ahead motion we may call it—of twenty-one miles per second. Some stars may move more slowly than this to any extent; others more rapidly. In two or three cases the speed exceeds one hundred miles per second, but these are quite exceptional. By taking several thousand stars having a given proper motion, we may form a general idea of their average distance, though a great number of them will exceed this average to a considerable extent. The conclusion drawn in this way would be that the stars having an apparent proper motion of 10" per century or more are mostly contained within, or lie not far outside of a sphere whose surface is at a distance from us of 200 light-years. Granting the volume of space which we have shown that nature seems to allow to each star, this sphere should contain 27,000 stars in all. There are about 10,000 stars known to have so large a proper motion as 10". But there is no actual discordance between these results, because not only are there, in all probability, great numbers of stars of which the proper motion is not yet recognized, but there are within the sphere a great number of stars whose motion is less than the average. On the other hand, it is probable that a considerable number of the 10,000 stars lie at a distance at least one-half greater than that of the radius of the sphere.
On the whole, it seems likely that, out to a distance of 300 or even 400 light-years, there is no marked inequality in star distribution. If we should explore the heavens to this distance, we should neither find the beginning of the Milky Way in one direction nor a very marked thinning out in the other. This conclusion is quite accordant with the probabilities of the case. If all the stars which form the groundwork of the Milky Way should be blotted out, we should probably find 100,000,000, perhaps even more, remaining. Assigning to each star the space already shown to be its quota, we should require a sphere of about 3000 light-years radius to contain such a number of stars. At some such distance as this, we might find a thinning out of the stars in the direction of the galactic poles, or the commencement of the Milky Way in the direction of this stream.
Even if this were not found at the distance which we have supposed, it is quite certain that, at some greater distance, we should at least find that the region of the Milky Way is richer in stars than the region near the galactic poles. There is strong reason, based on the appearance of the stars of the Milky Way, their physical constitution, and their magnitudes as seen in the telescope, to believe that, were we placed on one of these stars, we should find the stars around us to be more thickly strewn than they are around our system. In other words, the quota of space filled by each star is probably less in the region of the Milky Way than it is near the centre where we seem to be situated.
We are, therefore, presented with what seems to be the most extraordinary spectacle that the universe can offer, a ring of stars spanning it, and including within its limits by far the great majority of the stars within our system. We have in this spectacle another example of the unity which seems to pervade the system. We might imagine the latter so arranged as to show diversity to any extent. We might have agglomerations of stars like those of the Milky Way situated in some corner of the system, or at its centre, or scattered through it here and there in every direction. But such is not the case. There are, indeed, a few star-clusters scattered here and there through the system; but they are essentially different from the clusters of the Milky Way, and cannot be regarded as forming an important part of the general plan. In the case of the galaxy we have no such scattering, but find the stars built, as it were, into this enormous ring, having similar characteristics throughout nearly its whole extent, and having within it a nearly uniform scattering of stars, with here and there some collected into clusters. Such, to our limited vision, now appears the universe as a whole.
We have already alluded to the conclusion that an absolutely infinite system of stars would cause the entire heavens to be filled with a blaze of light as bright as the sun. It is also true that the attractive force within such a universe would be infinitely great in some direction or another. But neither of these considerations enables us to set a limit to the extent of our system. In two remarkable papers by Lord Kelvin which have recently appeared, the one being an address before the British Association at its Glasgow meeting, in 1901, are given the results of some numerical computations pertaining to this subject. Granting that the stars are scattered promiscuously through space with some approach to uniformity in thickness, and are of a known degree of brilliancy, it is easy to compute how far out the system must extend in order that, looking up at the sky, we shall see a certain amount of light coming from the invisible stars. Granting that, in the general average, each star is as bright as the sun, and that their thickness is such that within a sphere of 3300 light-years there are 1,000,000,000 stars, if we inquire how far out such a system must be continued in order that the sky shall shine with even four per cent of the light of the sun, we shall find the distance of its boundary so great that millions of millions of years would be required for the light of the outer stars to reach the centre of the system. In view of the fact that this duration in time far exceeds what seems to be the possible life duration of a star, so far as our knowledge of it can extend, the mere fact that the sky does not glow with any such brightness proves little or nothing as to the extent of the system.
We may, however, replace these purely negative considerations by inquiring how much light we actually get from the invisible stars of our system. Here we can make a definite statement. Mark out a small circle in the sky 1 degree in diameter. The quantity of light which we receive on a cloudless and moonless night from the sky within this circle admits of actual determination. From the measures so far available it would seem that, in the general average, this quantity of light is not very different from that of a star of the fifth magnitude. This is something very different from a blaze of light. A star of the fifth magnitude is scarcely more than plainly visible to ordinary vision. The area of the whole sky is, in round numbers, about 50,000 times that of the circle we have described. It follows that the total quantity of light which we receive from all the stars is about equal to that of 50,000 stars of the fifth magnitude—somewhat more than 1000 of the first magnitude. This whole amount of light would have to be multiplied by 90,000,000 to make a light equal to that of the sun. It is, therefore, not at all necessary to consider how far the system must extend in order that the heavens should blaze like the sun. Adopting Lord Kelvin's hypothesis, we shall find that, in order that we may receive from the stars the amount of light we have designated, this system need not extend beyond some 5000 light-years. But this hypothesis probably overestimates the thickness of the stars in space. It does not seem probable that there are as many as 1,000,000,000 stars within the sphere of 3300 light-years. Nor is it at all certain that the light of the average star is equal to that of the sun. It is impossible, in the present state of our knowledge, to assign any definite value to this average. To do so is a problem similar to that of assigning an average weight to each component of the animal creation, from the microscopic insects which destroy our plants up to the elephant. What we can say with a fair approximation to confidence is that, if we could fly out in any direction to a distance of 20,000, perhaps even of 10,000, light-years, we should find that we had left a large fraction of our system behind us. We should see its boundary in the direction in which we had travelled much more certainly than we see it from our stand-point.
We should not dismiss this branch of the subject without saying that considerations are frequently adduced by eminent authorities which tend to impair our confidence in almost any conclusion as to the limits of the stellar system. The main argument is based on the possibility that light is extinguished in its passage through space; that beyond a certain distance we cannot see a star, however bright, because its light is entirely lost before reaching us. That there could be any loss of light in passing through an absolute vacuum of any extent cannot be admitted by the physicist of to-day without impairing what he considers the fundamental principles of the vibration of light. But the possibility that the celestial spaces are pervaded by matter which might obstruct the passage of light is to be considered. We know that minute meteoric particles are flying through our system in such numbers that the earth encounters several millions of them every day, which appear to us in the familiar phenomena of shooting-stars. If such particles are scattered through all space, they must ultimately obstruct the passage of light. We know little of the size of these bodies, but, from the amount of energy contained in their light as they are consumed in the passage through our atmosphere, it does not seem at all likely that they are larger than grains of sand or, perhaps, minute pebbles. They are probably vastly more numerous in the vicinity of the sun than in the interstellar spaces, since they would naturally tend to be collected by the sun's attraction. In fact there are some reasons for believing that most of these bodies are the debris of comets; and the latter are now known to belong to the solar system, and not to the universe at large.
But whatever view we take of these possibilities, they cannot invalidate our conclusion as to the general structure of the stellar system as we know it. Were meteors so numerous as to cut off a large fraction of the light from the more distant stars, we should see no Milky Way, but the apparent thickness of the stars in every direction would be nearly the same. The fact that so many more of these objects are seen around the galactic belt than in the direction of its poles shows that, whatever extinction light may suffer in going through the greatest distances, we see nearly all that comes from stars not more distant than the Milky Way itself.
Intimately connected with the subject we have discussed is the question of the age of our system, if age it can be said to have. In considering this question, the simplest hypothesis to suggest itself is that the universe has existed forever in some such form as we now see it; that it is a self-sustaining system, able to go on forever with only such cycles of transformation as may repeat themselves indefinitely, and may, therefore, have repeated themselves indefinitely in the past. Ordinary observation does not make anything known to us which would seem to invalidate this hypothesis. In looking upon the operations of the universe, we may liken ourselves to a visitor to the earth from another sphere who has to draw conclusions about the life of an individual man from observations extending through a few days. During that time, he would see no reason why the life of the man should have either a beginning or an end. He sees a daily round of change, activity and rest, nutrition and waste; but, at the end of the round, the individual is seemingly restored to his state of the day before. Why may not this round have been going on forever, and continue in the future without end? It would take a profounder course of observation and a longer time to show that, notwithstanding this seeming restoration, an imperceptible residual of vital energy, necessary to the continuance of life, has not been restored, and that the loss of this residuum day by day must finally result in death.
The case is much the same with the great bodies of the universe. Although, to superficial observation, it might seem that they could radiate their light forever, the modern generalizations of physics show that such cannot be the case. The radiation of light necessarily involves a corresponding loss of heat and with it the expenditure of some form of energy. The amount of energy within any body is necessarily limited. The supply must be exhausted unless the energy of the light sent out into infinite space is, in some way, restored to the body which expended it. The possibility of such a restoration completely transcends our science. How can the little vibration which strikes our eye from some distant star, and which has been perhaps thousands of years in reaching us, find its way back to its origin? The light emitted by the sun 10,000 years ago is to-day pursuing its way in a sphere whose surface is 10,000 light-years distant on all sides. Science has nothing even to suggest the possibility of its restoration, and the most delicate observations fail to show any return from the unfathomable abyss.
Up to the time when radium was discovered, the most careful investigations of all conceivable sources of supply had shown only one which could possibly be of long duration. This is the contraction which is produced in the great incandescent bodies of the universe by the loss of the heat which they radiate. As remarked in the preceding essay, the energy generated by the sun's contraction could not have kept up its present supply of heat for much more than twenty or thirty millions of years, while the study of earth and ocean shows evidence of the action of a series of causes which must have been going on for hundreds of millions of years.
The antagonism between the two conclusions is even more marked than would appear from this statement. The period of the sun's heat set by the astronomical physicist is that during which our luminary could possibly have existed in its present form. The period set by the geologist is not merely that of the sun's existence, but that during which the causes effecting geological changes have not undergone any complete revolution. If, at any time, the sun radiated much less than its present amount of heat, no water could have existed on the earth's surface except in the form of ice; there would have been scarcely any evaporation, and the geological changes due to erosion could not have taken place. Moreover, the commencement of the geological operations of which we speak is by no means the commencement of the earth's existence. The theories of both parties agree that, for untold aeons before the geological changes now visible commenced, our planet was a molten mass, perhaps even an incandescent globe like the sun. During all those aeons the sun must have been in existence as a vast nebulous mass, first reaching as far as the earth's orbit, and slowly contracting its dimensions. And these aeons are to be included in any estimate of the age of the sun.