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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.

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.

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