Man's Place in the Universe

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sec. This was discovered so long ago as 1675 by means of the eclipses of Jupiter's satellites. These satellites revolve round the planet in from 1

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to 16 days, and, owing to their moving very nearly in the plane of the ecliptic and the shadow of Jupiter being so large, the three which are nearest to the planet are eclipsed at every revolution. This rapid revolution of the satellites and frequency of the eclipses enabled their periods of recurrence to be determined with extreme accuracy, especially after many years of careful observation. It was then found that when Jupiter was at its farthest distance from the earth the eclipses of the satellites took place a little more than eight minutes later than the time calculated from the mean period of revolution, and when the planet was nearest to us the eclipses occurred the same amount earlier. And when further observation showed that there was no difference between calculation and observation when the planet was at its mean distance from us, and that the error arose and increased exactly in proportion to our varying distance from it, then it became clear that the only cause adequate to produce such an effect was, that light had not an infinite velocity but travelled at a certain fixed rate. This however, though a highly probable explanation, was not absolutely proved till nearly two centuries later, by means of two very difficult measurements—that of the actual distance of the sun from the earth, and that of the actual speed of light in miles per second; the latter corresponding almost exactly with the speed deduced from the eclipses of Jupiter's satellites and the sun's distance as measured by the transits of Venus.

(A) 5

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inches from it (accurately 5.72957795 inches)

But this problem of measuring the sun's distance, and through it the dimensions of the orbits of all the planets of our system, sinks into insignificance when compared with the enormous difficulties in the way of the determination of the distance of the stars. As a great many people, perhaps the majority of the readers of any popular scientific book, have little knowledge of mathematics and cannot realise what an angle of a minute or a second really means, a little explanation and illustration of these terms will not be out of place. An angle of one degree (1°) is the 360th part of a circle (viewed from its centre), the 90th part of a right angle, the 60th part of either of the angles of an equilateral triangle. To see exactly how much is an angle of one degree we draw a short line (B C) one-tenth of an inch long, and from a point we draw straight lines to B and C. Then the angle at A is one degree.

Now, in all astronomical work, one degree is considered to be quite a large angle. Even before the invention of the telescope the old observers fixed the position of the stars and planets to half or a quarter of a degree, while Mr. Proctor thinks that Tycho Brahé's positions of the stars and planets were correct to about one or two minutes of arc. But a minute of arc is obtained by dividing the line B C into sixty equal parts and seeing the distance between two of these with the naked eye from the point A. But as very long-sighted people can see very minute objects at 10 or 12 inches distance, we may double the distance A B, and then making the line B C one three-hundredth part of an inch long, we shall have the angle of one minute which Tycho Brahé was perhaps able to measure. How very large an amount a minute is to the modern astronomer is, however, well shown by the fact that the maximum difference between the calculated and observed positions of Uranus, which led Adams and Leverrier to search for and discover Neptune, was only 1

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minutes, a space so small as to be almost invisible to the average eye, so that if there had been two planets, one in the calculated, the other in the observed place, they would have appeared as one to unassisted vision.

In order now to realise what one second of arc really means, let us look at the circle here shown, which is as nearly as possible one-tenth of an inch in diameter—(one-O-tenth of an inch). If we remove this circle to a distance of 28 feet 8 inches it will subtend an angle of one minute, and we shall have to place it at a distance of nearly 1730 feet—almost one-third of a mile—to reduce the angle to one second. But the very nearest to us of the fixed stars, Alpha Centauri, has a parallax of only three-fourths of a second; that is, the distance of the earth from the sun—about 92

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millions of miles—would appear no wider, seen from the nearest star, than does three-fourths of the above small circle at one-third of a mile distance. To see this circle at all at that distance would require a very good telescope with a power of at least 100, while to see any small part of it and to measure the proportion of that part to the whole would need very brilliant illumination and a large and powerful astronomical telescope.

What is a Million?

But when we have to deal with millions, and even with hundreds and thousands of millions, there is another difficulty—that few people can form any clear conception of what a million is. It has been suggested that in every large school the walls of one room or hall should be devoted to showing a million at one view. For this purpose it would be necessary to have a hundred large sheets of paper each about 4 feet 6 inches square, ruled in quarter inch squares. In each alternate square a round black wafer or circle should be placed a little over-lapping the square, thus leaving an equal amount of white space between the black spots. At each tenth spot a double width should be left so as to separate each hundred spots (10 × 10). Each sheet would then hold ten thousand spots, which would all be distinctly visible from the middle of a room 20 feet wide, each horizontal or vertical row containing a thousand. One hundred such sheets would contain a million spots, and they would occupy a space 450 feet long in one row, or 90 feet long in five rows, so that they would entirely cover the walls of a room, about 30 feet square and 25 feet high, from floor to ceiling, allowing space for doors but not for windows, the hall or gallery being lighted from above. Such a hall would be in the highest degree educational in a country where millions are spoken of so glibly and wasted so recklessly; while no one can really appreciate modern science, dealing as it does with the unimaginably great and little, unless he is enabled to realise by actual vision, and summing up, what a vast number is comprised in one of those millions, which, in modern astronomy and physics, he has to deal with not singly only, but by hundreds and thousands or even by millions. In every considerable town, at all events, a hall or gallery should have a million thus shown upon its walls. It would in no way interfere with the walls being covered when required with maps, or ornamental hangings, or pictures; but when these were removed, the visible and countable million would remain as a permanent lesson to all visitors; and I believe that it would have widespread beneficial effects in almost every department of human thought and action. On a small scale any one can do this for himself by getting a hundred sheets of engineer's paper ruled in small squares, and making the spots very small; and even this would be impressive, but not so much so as on the larger scale.

In order to enable every reader of this volume at once to form some conception of the number of units in a million, I have made an estimate of the number of letters contained in it, and I find them to amount to about 420,000—considerably less than half a million. Try and realise, when reading it, that if every letter were a pound sterling, we waste as many pounds as there are letters in two such volumes whenever we build a battleship.

Having thus obtained some real conception of the immensity of a million, we can better realise what it must be to have every one of the dots above described, or every one of the letters in two such volumes as this lengthened out so as to be each a mile long, and even then we should have reached little more than a hundredth part of the distance from our earth to the sun. When, by careful consideration of these figures, we have even partially realised this enormous distance, we may take the next step, which is, to compare this distance with that of the nearest fixed star. We have seen that the parallax of that star is three-fourths of a second, an amount which implies that the star is 271,400 times as far from us as our sun is. If after seeing what a million is, and knowing that the sun is 92

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times this distance from us in miles—a distance which itself is almost inconceivable to us—we find that we have to multiply this almost inconceivable distance 271,400 times—more than a quarter of a million times—to reach the nearest of the fixed stars, we shall begin to realise, however imperfectly, how vast is the system of suns around us, and on what a scale of immensity the material universe, which we see so gloriously displayed in the starry heavens and the mysterious galaxy, is constructed.

This somewhat lengthy preliminary discussion is thought necessary in order that my readers may form some idea of the enormous difficulty of obtaining any measurement whatever of such distances. I now propose to point out what the special difficulties are, and how they have been overcome; and thus I hope to be able to satisfy them that the figures astronomers give us of the distances of the stars are in no way mere guesses or probabilities, but are real measurements which, within certain not very wide limits of error, may be trusted as giving us correct ideas of the magnitude of the visible universe.

Measurement of Stellar Distances

The fundamental difficulty of this measurement is, of course, that the distances are so vast that the longest available base-line, the diameter of the earth's orbit, only subtends an angle of little more than a second from the nearest star, while for all the rest it is less than one second and often only a small fraction of it. But this difficulty, great as it is, is rendered far greater by the fact that there is no fixed point in the heavens from which to measure, since many of the stars are known to be in motion, and all are believed to be so in varying degrees, while the sun itself is now known to be moving among the stars at a rate which is not yet accurately determined, but in a direction which is fairly well known. As the various motions of the earth while passing round the sun, though extremely complex, are very accurately known, it was first attempted to determine the changed position of stars by observations, many times repeated at six months' intervals, of the moment of their passage over the meridian and their distance from the zenith; and then by allowing for all the known motions of the earth, such as precession of the equinoxes and nutation of the earth's axis, as well as for refraction and for the aberration of light, to determine what residual effect was due to the difference of position from which the star was viewed; and a result was thus obtained in several cases, though almost always a larger one than has been found by later observations and by better methods. These earlier observations, however perfect the instruments and however skilful the observer, are liable to errors which it seems impossible to avoid. The instruments themselves are subject in all their parts to expansion and contraction by changes of temperature; and when these changes are sudden, one part of the instrument may be affected more than another, and this will often lead to minute errors which may seriously affect the amount to be measured when that is so small. Another source of error is due to atmospheric refraction, which is subject to changes both from hour to hour and at different seasons. But perhaps most important of all are minute changes in level of the foundations of the instruments even when they are carried down to solid rock. Both changes of temperature and changes of moisture of the soil produce minute alterations of level; while earth-tremors and slow movements of elevation or depression are now known to be very frequent. Owing to all these causes, actual measurements of differences of position at different times of the year, amounting to small fractions of a second, are found to be too uncertain for the determination of such minute angles with the required accuracy.

But there is another method which avoids almost all these sources of error, and this is now generally preferred and adopted for these measurements. It is, that of measuring the distance between two stars situated apparently very near each other, one of which has large proper motion, while the other has none which is measurable. The proper motions of the stars was first suspected by Halley in 1717, from finding that several stars, whose places had been given by Hipparchus, 130 B.C., were not in the positions where they now ought to be; and other observations by the old astronomers, especially those of occultations of stars by the moon, led to the same result. Since the time of Halley very accurate observations of the stars have been made, and in many cases it is found that they move perceptibly from year to year, while others move so slowly that it is only after forty or fifty years that the motion can be detected. The greatest proper motions yet determined amount to between 7" and 8" in a year, while other stars require twenty, or even fifty or a hundred years to show an equal amount of displacement. At first it was thought that the brightest stars would have the largest proper motion, because it was supposed they were nearest to us, but it was soon found that many small and quite inconspicuous stars moved as rapidly as the most brilliant, while in many very bright stars no proper motion at all can be detected. That which moves most rapidly is a small star of less than the sixth magnitude.

It is a matter of common observation that the motion of things at a distance cannot be perceived so well as when near, even though the speed may be the same. If a man is seen on the top of a hill several miles off, we have to observe him closely for some time before we can be sure whether he is walking or standing still. But objects so enormously distant as we now know that the stars are, may be moving at the rate of many miles in a second and yet require years of observation to detect any movement at all.

The proper motions of nearly a hundred stars have now been ascertained to be more than one second of arc annually, while a large number have less than this, and the majority have no perceptible motion, presumably due to their enormous distance from us. It is therefore not difficult in most cases to find one or two motionless stars sufficiently close to a star having a large proper motion (anything more than one-tenth of a second is so called) to serve as fixed points of measurement. All that is then required is, to measure with extreme accuracy the angular distance of the moving from the fixed stars at intervals of six months. The measurements can be made, however, on every fine night, each one being compared with one at nearly an interval of six months from it. In this way a hundred or more measurements of the same star may be made in a year, and the mean of the whole, allowance being made for proper motion in the interval, will give a much more accurate result than any single measurement. This kind of measurement can be made with extreme accuracy when the two stars can be seen together in the field of the telescope; either by the use of a micrometer, or by means of an instrument called a heliometer, now often constructed for the purpose. This is an astronomical telescope of rather large size, the object glass of which is cut in two straight across the centre, and the two halves made to slide upon each other by means of an exceedingly fine and accurate screw-motion, so adjusted and tested as to measure the angular distance of two objects with extreme accuracy. This is done by the number of turns of the screw required to bring the two stars into contact with each other, the image of each one being formed by one of the halves of the object glass.

But the greatest advantage of this method of determining parallax is, as Sir John Herschell points out, that it gets rid of all the sources of error which render the older methods so uncertain and inaccurate. No corrections are required for precession, nutation, or aberration, since these affect both stars alike, as is the case also with refraction; while alterations of level of the instrument have no prejudicial effect, since the measures of angular distance taken by this method are quite independent of such movements. A test of the accuracy of the determination of parallax by this instrument is the very close agreement of different observers, and also their agreement with the new and perhaps even superior method by photography. This method was first adopted by Professor Pritchard of the Oxford Observatory, with a fine reflector of thirteen inches aperture. Its great advantage is, that all the small stars in the vicinity of the star whose parallax is sought are shown in their exact positions upon the plate, and the distances of all of them from it can be very accurately measured, and by comparing plates taken at six months' intervals, each of these stars gives a determination of parallax, so that the mean of the whole will lead to a very accurate result. Should, however, the result from any one of these stars differ considerably from that derived from the rest, it will be due in all probability to that star having a proper motion of its own, and it may therefore be rejected. To illustrate the amount of labour bestowed by astronomers on this difficult problem, it may be mentioned that for the photographic measurement of the star 61 Cygni, 330 separate plates were taken in 1886-7, and on these 30,000 measurements of distances of the pairs of star-images were made. The result agreed closely with the best previous determination by Sir Robert Ball, using the micrometer, and the method was at once admitted by astronomers as being of the greatest value.

Although, as a rule, stars having large proper motions are found to be comparatively near us, there is no regular proportion between these quantities, indicating that the rapidity of the motion of the stars varies greatly. Among fifty stars whose distances have been fairly well determined, the rate of actual motion varies from one or two up to more than a hundred miles per second. Among six stars with less than a tenth of a second of annual proper motion there is one with a parallax of nearly half a second, and another of one-ninth of a second, so that they are nearer to us than many stars which move several seconds a year. This may be due to actual slowness of motion, but is almost certainly caused in part by their motion being either towards us or away from us, and therefore only measurable by the spectroscope; and this had not been done when the lists of parallaxes and proper motions from which these facts are taken were published. It is evident that the actual direction and rate of motion of a star cannot be known till this radial movement, as it is termed—that is, towards or away from us—has been measured; but as this element always tends to increase the visually observed rate of motion, we cannot, through its absence, exaggerate the actual motions of the stars.

The Sun's Movement Through Space

But there is yet another important factor which affects the apparent motions of all the stars—the movement of our sun, which, being a star itself, has a proper motion of its own. This motion was suspected and sought for by Sir William Herschel a century ago, and he actually determined the direction of its motion towards a point in the constellation Hercules, not very far removed from that fixed upon as the average of the best observations since made. The method of determining this motion is very simple, but at the same time very difficult. When we are travelling in a railway carriage near objects pass rapidly out of sight behind us, while those farther from us remain longer in view, and very distant objects appear almost stationary for a considerable time. For the same reason, if our sun is moving in any direction through space, the nearer stars will appear to travel in an opposite direction to our movement, while the more distant will remain quite stationary. This movement of the nearest stars is detected by an examination and comparison of their proper motions, by which it is found that in one part of the heavens there is a preponderance of the proper motions in one direction and a deficiency in the opposite direction, while in the directions at right angles to these the proper motions are not on the average greater in one direction than in the opposite. But the proper motions of the stars being themselves so minute, and also so irregular, it is only by a most elaborate mathematical investigation of the motions of hundreds or even of thousands of stars, that the direction of the solar motion can be determined. Till quite recently astronomers were agreed that the motion was towards a point in Hercules near the outstretched arm in the figure of that constellation. But the latest inquiries into this problem, involving the comparison of the motions of several thousand stars in all parts of the heavens, have led to the conclusion that the most probable direction of the 'solar apex' (as the point towards which the sun is moving is termed), is in the adjacent constellation Lyra, and not far from the brilliant star Vega. This is the position which Professor Newcomb of Washington thinks most probable, though there is still room for further investigation. To determine the rate of the motion is very much more difficult than to fix its direction, because the distances of so few stars have been determined, and very few indeed of these lie in the directions best adapted to give accurate results. The best measurements down to 1890 led to a motion of about 15 miles a second. But more recently the American astronomer, Campbell, has determined by the spectroscope the motion in the line of sight of a considerable number of stars towards and away from the solar apex, and by comparing the average of these motions, he derives a motion for the sun of about 12

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miles a second, and this is probably as near as we can yet reach towards the true amount.

Some Numerical Results of the Above

Measurements

The measurements of distances and proper motions of a considerable number of the stars, of the motion of our sun in space (its proper motion), together with accurate determinations of the comparative brilliancy of the brightest stars as compared with our sun and with each other, have led to some very remarkable numerical results which serve as indications of the scale of magnitude of the stellar universe.

The parallaxes of about fifty stars have now been repeatedly measured with such consistent results that Professor Newcomb considers them to be fairly trustworthy, and these vary from one-hundredth to three-quarters of a second. Three more, all stars of the first magnitude—Rigel, Canopus, and Alpha Cygni—have no measurable parallax, notwithstanding the long-continued efforts of many astronomers, affording a striking example of the fact that brilliancy alone is no test of proximity. Six more stars have a parallax of only one-fiftieth of a second, and five of these are either of the first or second magnitudes. Of these nine stars having very small parallax or none, six are situated in or near to the Milky Way, another indication of exceeding remoteness, which is further shown by the fact that they all have a very small proper motion or none at all. These facts support the conclusion, which had been already reached by astronomers from a careful study of the distribution of the stars, that the larger portion of the stars of all magnitudes scattered throughout the Milky Way or along its borders really belong to the same great system, and may be said to form a part of it. This is a conclusion of extreme importance because it teaches us that the grandest of the suns, such as Rigel and Betelgeuse in the constellation Orion, Antares in the Scorpion, Deneb in the Swan (Alpha Cygni), and Canopus (Alpha Argus), are in all probability as far removed from us as are the innumerable minute stars which give the nebulous or milky appearance to the Galaxy.

It is well to consider for a moment what these facts mean. Professor S. Newcomb, one of the highest authorities on these problems, tells us that the long series of measurements to discover the parallax of Canopus, the brightest star in the southern hemisphere, would have shown a parallax of one-hundredth of a second, had such existed. Yet the results always seemed to converge to a mean of 0".000! Suppose, then, we assume the parallax of this star to be somewhat less than the hundredth of a second—let us say

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of a second. At the distance this gives, light would take almost exactly 400 years to reach us, so that if we suppose this very brilliant star to be situated a little on this side of the Galaxy, we must give to that great luminous circle of stars a distance of about 500 light years. We shall now perceive the advantage of being able to realise what a million really is. A person who had once seen a wall-space more than 100 feet long and 20 feet high completely covered with quarter-inch spots a quarter of an inch apart; and then tried to imagine every spot to be a mile long and to be placed end to end in one row, would form a very different conception of a million miles than those who almost daily read of millions, but are quite unable to visualise even one of them. Having really seen one million, we can partially realise the velocity of light, which travels over this million miles in a little less than 5

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seconds; and yet light takes more than 4

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years at this inconceivable speed to come to us from the very nearest of the stars. To realise this still more impressively, let us take the distance of this nearest star, which is 26 millions of millions of miles. Let us look in imagination at this large and lofty hall covered from floor to ceiling with quarter-inch spots—only one million. Let all these be imagined as miles. Then repeat this number of miles in a straight line, one after the other, as many times as there are spots in this hall; and even then you have reached only one twenty-sixth part of the distance to the nearest fixed star! This million times a million miles has to be repeated twenty-six times to reach the nearest fixed star; and it seems probable that this gives us a good indication of the distance from each other of at least all the stars down to the sixth magnitude, perhaps even of a large number of the telescopic stars. But as we have found that the bright stars of the Milky Way must be at least one hundred times farther from us than these nearest stars, we have found what may be termed a minimum distance for that vast star-ring. It may be immensely farther, but it is hardly possible that it should be anything less.

The Probable Size of the Stars

Having thus obtained an inferior limit for the distance of several stars of the first magnitude, and their actual brilliancy or light-emission as compared with our sun having been carefully measured, we have afforded us some indication of size though perhaps an uncertain one. By these means it has been found that Rigel gives out about ten thousand times as much light as our sun, so that if its surface is of the same brightness, it must be a hundred times the diameter of the sun. But as it is one of the white or Sirian type of stars it is probably very much more luminous, but even if it were twenty times brighter it would still have to be twenty-two and a half times the diameter of the sun; and as the stars of this type are probably wholly gaseous and much less dense than our sun, this enormous size may not be far from the truth. It is believed that the Sirian stars generally have a greater surface brilliancy than our sun. Beta Aurigæ, a star of the second magnitude but of the Sirian type, is one of the double stars whose distance has been measured, and this has enabled Mr. Gore to find the mass of the binary system to be five times that of the sun, and their light one hundred and seventeen times greater. Even if the density is much less than the sun's, the intrinsic brilliancy of the surface will be considerably greater. Another double star, Gamma Leonis, has been found to be three hundred times more brilliant than the sun if of the same density, but it would require to be seven times rarer than air to have the extent of surface needed to give the same amount of light if its surface emitted no more light than our sun from equal areas.

It is clear, therefore, that many of the stars are much larger than our sun as well as more luminous; but there are also large numbers of small stars whose large proper motions, as well as the actual measurement of some, prove them to be comparatively near to us which yet are only about one-fiftieth part as bright as the sun. These must, therefore, be either comparatively small, or if large must be but slightly luminous. In the case of some double stars it has been proved that the latter is the case; but it seems probable that others are very much smaller than the average. Up to the present time no means of determining the size of a star by actual measurement has been discovered, since their distances are so enormous that the most powerful telescopes show only a point of light. But now that we have really measured the distance of a good many stars we are able to determine an upper limit for their actual dimensions. As the nearest fixed star, Alpha Centauri, has a parallax of 0".75, this means that if this star has a diameter as great as our distance from the sun (which is not much more than a hundred times the sun's diameter) it would be seen to have a distinct disc about as large as that of Jupiter's first satellite. If it were even one-tenth of the size supposed it would probably be seen as a disc in our best modern telescopes. The late Mr. Ranyard remarks that if the Nebular Hypothesis is true, and our sun once extended as far as the orbit of Neptune, then, among the millions of visible suns there ought to be some now to be found in every stage of development. But any sun having a diameter at all approaching this size, and situated as far off as a hundred times the distance of Alpha Centauri, would be seen by the Lick telescope to have a disc half a second in diameter. Hence the fact that there are no stars with visible discs proves that there are no suns of the required size, and adds another argument, though not perhaps a strong one, against the acceptance of the Nebular Hypothesis.

CHAPTER VI

THE UNITY AND EVOLUTION OF THE STAR SYSTEM

The very condensed sketch now given of such of the discoveries of recent Astronomy as relate to the subject we are discussing will, it is hoped, give some idea both of the work already done and of the number of interesting problems yet remaining to be solved. The most eminent astronomers in every part of the world look forward to the solution of these problems not, perhaps, as of any great value in themselves, but as steps towards a more complete knowledge of our universe as a whole. Their aim is to do for the star-system what Darwin did for the organic world, to discover the processes of change that are at work in the heavens, and to learn how the mysterious nebulæ, the various types of stars, and the clusters and systems of stars are related to each other. As Darwin solved the problem of the origin of organic species from other species, and thus enabled us to understand how the whole of the existing forms of life have been developed out of pre-existing forms,One so astronomers hope to be able to solve the problem of the evolution of suns from some earlier stellar types, so as to be able, ultimately, to form some intelligible conception of how the whole stellar universe has come to be what it is. Volumes have already been written on this subject, and many ingenious suggestions and hypotheses have been advanced. But the difficulties are very great; the facts to be co-ordinated are excessively numerous, and they are necessarily only a fragment of an unknown whole. Yet certain definite conclusions have been reached; and the agreement of many independent observers and thinkers on the fundamental principles of stellar evolution seems to assure us that we are progressing, if slowly yet with some established basis of truth, towards the solution of this, the most stupendous scientific problem with which the human intellect has ever attempted to grapple.

The Unity of the Stellar Universe