Alexander W. Roberts of Lovedale, South Africa, gives some of the main results of this branch of inquiry. Of course all the variable stars are to be found among the spectroscopic binaries. They consist of that portion of the cla.s.s in which the plane of the orbit is directed towards us, so that during their revolution one of the pair either wholly or partially eclipses the other. In some of these cases there are irregularities, such as double maxima and minima of unequal lengths, which may be due to triple systems or to other causes not yet explained, but as they all have short periods and always appear as one star in the most powerful telescopes, they form a special division of the spectroscopic binary systems.

There are known at present twenty-two variables of the Algol type, that is, stars having each a dark companion very close to it which obscures it either wholly or partially during every revolution. In these cases the density of the systems can be approximately determined, and they are found to be, on the average, only one-fifth that of water, or one-eighth that of our sun. But as many of them are as large as our sun, or even considerably larger, it is evident that they must be wholly gaseous, and, even if very hot, of a less complex const.i.tution than our luminary. Mr. A.W. Roberts tells us that five out of these twenty-two variables revolve _in absolute contact_ forming systems of the shape of a dumb-bell. The periods vary from twelve days to less than nine hours; and, starting from these, we now have a continuous series of lengthening periods up to the twin stars of Castor which require more than a thousand years to complete their revolution.

During his observations of the above five stars, Mr. Roberts states that one, X Carinae, was found to have parted company, so that instead of being actually united to its companion the two are now at a distance apart equal to one-tenth of their diameters, and he may thus be said to have been almost a witness of the birth of a stellar system.

A year later we find the record (in _Knowledge_, October 1902) of Professor Campbell's researches at the Lick Observatory. He states that, out of 350 stars observed spectroscopically, one in eight is a spectroscopic binary; and so impressed is he with their abundance that, as accuracy of measurement increases, he believes that _the star that is not a spectroscopic binary will prove to be the rare exception_! Professor G.

Darwin had already shown that the 'dumb-bell' was a figure of equilibrium in a rotating ma.s.s of fluid; and we now find proofs that such figures exist, and that they form the starting-point for the enormous and ever-increasing quant.i.ties of spectroscopic binary star-systems that are now known. The origin of these binary stars is also of especial interest as giving support to Professor Darwin's well-known explanation of the origin of the moon by disruption from the earth, owing to the very rapid rotation of the parent planet. It now appears that suns often subdivide in the same manner, but, owing perhaps to their intensely heated gaseous state they seem usually to form nearly equal globes. The evolution of this special form of star-system is therefore now an observed fact; though it by no means follows that all double stars have had the same mode of origin.

Cl.u.s.tERS OF STARS AND VARIABLES

The cl.u.s.ters of stars, which are tolerably abundant in the heavens and offer so many strange and beautiful forms to the telescopist, are yet among the most puzzling phenomena the philosophic astronomer has to deal with.

Many of these cl.u.s.ters which are not very crowded and of irregular forms, strongly suggest an origin from the equally irregular and fantastic forms of nebulae by a process of aggregation like that which Dr. Roberts describes as developing within the spiral nebulae. But the dense globular cl.u.s.ters which form such beautiful telescopic objects, and in some of which more than six thousand stars have been counted besides considerable numbers so crowded in the centre as to be uncountable, are more difficult to explain.

One of the problems suggested by these cl.u.s.ters is as to their stability.

Professor Simon Newcomb remarks on this point as follows: 'Where thousands of stars are condensed into a s.p.a.ce so small, what prevents them from all falling together into one confused ma.s.s? Are they really doing so, and will they ultimately form a single body? These are questions which can be satisfactorily answered only by centuries of observation; they must therefore be left to the astronomers of the future.'

There are, however, some remarkable features in these cl.u.s.ters which afford possible indications of their origin and essential const.i.tution. When closely examined most of them are seen to be less regular than they at first appear. Vacant s.p.a.ces can be noted in them; even rifts of definite forms. In some there is a radiated structure; in others there are curved appendages; while some have fainter centres. These features are so exactly like what are found, in a more p.r.o.nounced form, in the larger nebulae, that we can hardly help thinking that in these cl.u.s.ters we have the result of the condensation of very large nebulae, which have first aggregated towards numerous centres, while these agglomerations have been slowly drawn towards the common centre of gravity of the whole ma.s.s. It is suggestive of this origin that while the smaller telescopic nebulae are far removed from the Milky Way, the larger ones are most abundant near its borders; while the star-cl.u.s.ters are excessively abundant on and near the Milky Way, but very scarce elsewhere, except in or near vast nebulae like the Magellanic Clouds.

We thus see that the two phenomena may be complementary to each other, the condensation of nebulae having gone on most rapidly where material was most abundant, resulting in numerous star-cl.u.s.ters where there are now few nebulae.

There is one striking feature of the globular cl.u.s.ters which calls for notice; the presence in some of them of enormous quant.i.ties of variable stars, while in others few or none can be found. The Harvard Observatory has for several years devoted much time to this cla.s.s of observations, and the results are given in Professor Newcomb's recent volume on 'The Stars.'

It appears that twenty-three cl.u.s.ters have been observed spectroscopically, the number of stars examined in each cl.u.s.ter varying from 145 up to 3000, the total number of stars thus minutely tested being 19,050. Out of this total number 509 were found to be variable; but the curious fact is, the extreme divergence in the proportion of variables to the whole number examined in the several cl.u.s.ters. In two cl.u.s.ters, though 1279 stars were examined, not a single variable was found. In three others the proportion was from one in 1050 to one in 500. Five more ranged up to one in 100, and the remainder showed from that proportion up to one in seven, 900 stars being examined in the last mentioned cl.u.s.ter of which 132 were variable!

When we consider that variable stars form only a portion, and necessarily a very small proportion, of binary systems of stars, it follows that in all the cl.u.s.ters which show a large proportion of variables, a very much larger proportion--in some cases perhaps all, must be double or multiple stars revolving round each other. With this remarkable evidence, in addition to that adduced for the prevalence of double stars and variables among the stars in general, we can understand Professor Newcomb adding his testimony to that of Professor Campbell already quoted, that 'it is probable that among the stars in general, single stars are the exception rather than the rule. If such be the case, the rule should hold yet more strongly among the stars of a condensed cl.u.s.ter.'

THE EVOLUTION OF THE STARS

So long as astronomers were limited to the use of the telescope only, or even the still greater powers of the photographic plate, nothing could be learnt of the actual const.i.tution of the stars or of the process of their evolution. Their apparent magnitudes, their movements, and even the distances of a few could be determined; while the diversity of their colours offered the only clue (a very imperfect one) even to their temperature. But the discovery of spectrum a.n.a.lysis has furnished the means of obtaining some definite knowledge of the physics and chemistry of the stars, and has thus established a new branch ofscience--Astrophysics--which has already attained large proportions, and which furnishes the materials for a periodical and some important volumes. This branch of the subject is very complex, and as it is not directly connected with our present inquiry, it is only referred to again in order to introduce such of its results as bear upon the question of the cla.s.sification and evolution of the stars.

By a long series of laboratory experiments it has been shown that numerous changes occur in the spectra of the elements when subjected to different temperatures, ranging upwards to the highest attainable by means of a battery producing an electric spark several feet long. These changes are not in the relative position of the bands or dark lines, but in their number, breadth, and intensity. Other changes are due to the density of the medium in which the elements are heated, and to their chemical condition as to purity; and from these various modifications and their comparison with the solar spectrum and those of its appendages, it has become possible to determine, from the spectrum of a star, not only its temperature as compared with that of the electric spark and of the sun, but also its place in a developmental series.

The first general result obtained by this research is, that the bluish white or pure white stars, having a spectrum extending far towards the violet end, and which exhibits the coloured bands of gases only, usually hydrogen and helium, are the hottest. Next come those with a shorter spectrum not extending so far towards the violet end, and whose light is therefore more yellow in tint. To this group our sun belongs; and they are all characterised like it by dark lines due to absorption, and by the presence of metals, especially iron, in a gaseous state. The third group have the shortest spectra and are of a red colour, while their spectra contain lines denoting the presence of carbon. These three groups are often spoken of as 'gaseous stars,' 'metallic stars,' and 'carbon stars.' Other astronomers call the first group 'Sirian stars,' because Sirius, though not the hottest, is a characteristic type; the second being termed 'solar stars'; others again speak of them as stars of Cla.s.s I., Cla.s.s II., etc., according to the system of cla.s.sification they have adopted. It was soon perceived, however, that neither the colour nor the temperature of stars gave much information as to their nature and state of development, because, unless we supposed the stars to begin their lives already intensely hot (and all the evidence is against this), there must be a period during which heat increases, then one of maximum heat, followed by one of cooling and final loss of light altogether. The meteoritic theory of the origin of all luminous bodies in the heavens, now very widely adopted, has been used, as we have seen, to explain the development of stars from nebulae, and its chief exponent in this country, Sir Norman Lockyer, has propounded a complete scheme of stellar evolution and decay which may be here briefly outlined:

Beginning with nebulae, we pa.s.s on to stars having banded or fluted spectra, indicating comparatively low temperatures and showing bands or lines of iron, manganese, calcium, and other metals. They are more or less red in colour, Antares in the Scorpion being one of the most brilliant red stars known. These stars are supposed to be in the process of aggregation, to be continually increasing in size and heat, and thus to be subject to great disturbances. Alpha Cygni has a similar spectrum but with more hydrogen, and is much hotter. The increase of heat goes on through Rigel and Beta Crucis, in which we find mainly hydrogen, helium, oxygen, nitrogen, and also carbon, but only faint traces of metals. Reaching the hottest of all--Epsilon Orionis and two stars in Argo--hydrogen is predominant, with traces of a few metals and carbon. The cooling series is indicated by thicker lines of hydrogen and thinner lines of the metallic elements, through Sirius, to Arcturus and our sun, thence to 19 Piscium, which shows chiefly flutings of carbon, with a few faint metallic lines.

The process of further cooling brings us to the dark stars.

We have here a complete scheme of evolution, carrying us from those ill-defined but enormously diffused ma.s.ses of gas and cosmic dust we know as nebulae, through planetary nebulae, nebulous stars, variable and double-stars, to red and white stars and on to those exhibiting the most intense blue-white l.u.s.tre. We must remember, however, that the most brilliant of these stars, showing a gaseous spectrum and forming the culminating point of the ascending series, are not necessarily hotter than, or even so hot as, some of those far down on the descending scale; since it is one of the apparent paradoxes of physics that a body may become hotter during the very process of contraction through loss of heat. The reason is that by cooling it contracts and thus becomes denser, that a portion of its ma.s.s falls towards its centre, and in doing so produces an amount of heat which, though absolutely less than the heat lost in cooling, will under certain conditions cause the reduced surface to become hotter.

The essential point is, that the body in question must be wholly gaseous, allowing of free circulation from surface to centre. The law, as given by Professor S. Newcomb, is as follows:--

'_When a spherical ma.s.s of incandescent gas contracts through the loss of its heat by radiation into s.p.a.ce, its temperature continually becomes higher as long as the gaseous condition is retained._'

To put it in another way: if the compression was caused by external force and no heat was lost, the globe would get hotter by a calculable amount for each unit of contraction. But the heat lost in causing a similar amount of contraction is so little more than the increase of heat produced by contraction, that the slightly diminished total heat in a smaller bulk causes the temperature of the ma.s.s to increase.

But if, as there is reason to believe, the various types of stars differ also in chemical const.i.tution, some consisting mainly of the more permanent gases, while in others the various metallic and non-metallic elements are present in very different proportions, there should really be a cla.s.sification by const.i.tution as well as by temperature, and the course of evolution of the differently const.i.tuted groups may be to some extent dissimilar.

With this limitation the process of evolution and decay of sun through a cycle of increasing and decreasing temperature, as suggested by Sir Norman Lockyer, is clear and suggestive. During the ascending series the star is growing both in ma.s.s and heat, by the continual accretion of meteoritic matter either drawn to it by gravitation or falling towards it through the proper motions of independent ma.s.ses. This goes on till all the matter for some distance around the star has been utilised, and a maximum of size, heat, and brilliancy attained. Then the loss of heat by radiation is no longer compensated by the influx of fresh matter, and a slow contraction occurs accompanied by a slightly increased temperature. But owing to the more stable conditions continuous envelopes of metals in the gaseous state are formed, which check the loss of heat and reduce the brilliancy of colour; whence it follows that bodies like our sun may be really hotter than the most brilliant white stars, though not giving out quite so much heat. The loss of heat is therefore reduced; and this may serve to account for the undoubted fact that during the enormous epochs of geological time there has been very little diminution in the amount of heat we have received from the sun.

On the general question of the meteoritic hypothesis one of our first mathematicians, Professor George Darwin, has thus expressed his views: 'The conception of the growth of the planetary bodies by the aggregation of meteorites is a good one, and perhaps seems more probable than the hypothesis that the whole solar system was gaseous.' I may add, that one of the chief objections made to it, that meteorites are too complex to be supposed to be the primitive matter out of which suns and worlds have been made, does not seem to me valid. The primitive matter, whatever it was, may have been used up again and again, and if collisions of large solid globes ever occur--and it is a.s.sumed by most astronomers that they must sometimes occur--then meteoric particles of all sizes would be produced which might exhibit any complexity of mineral const.i.tution. The material universe has probably been in existence long enough for all the primitive elements to have been again and again combined into the minerals found upon the earth and many others. It cannot be too often repeated that no explanation--no theory--can ever take us to the beginning of things, but only one or two steps at a time into the dim past, which may enable us to comprehend, however imperfectly, the processes by which the world, or the universe, as it is, has been developed out of some earlier and simpler condition.

CHAPTER VII

ARE THE STARS INFINITE IN NUMBER?

Most of the critics of my first short discussion of this subject laid great stress upon the impossibility of proving that the universe, a part of which we see, is not infinite; and a well-known astronomer declared that unless it can be demonstrated that our universe is finite the entire argument founded upon our position within it fall to the ground. I had laid myself open to this objection by rather incautiously admitting that if the preponderance of evidence pointed in this direction any inquiry as to our place in the universe would be useless, because as regards infinity there can be no difference of position. But this statement is by no means exact, and even in an infinite universe of matter containing an infinite number of stars, such as those we see, there might well be such infinite diversities of distribution and arrangement as would give to certain positions all the advantages which I submit we actually possess. Supposing, for example, that beyond the vast ring of the Milky Way the stars rapidly decrease in number in all directions for a distance of a hundred or a thousand times the diameter of that ring, and that then for an equal distance they slowly increase again and become aggregated into systems or universes totally distinct from ours in form and structure, and so remote that they can influence us in no way whatever. Then, I maintain, our position within our own stellar universe might have exactly the same importance, and be equally suggestive, as if ours were the only material universe in existence--as if the apparent diminution in the number of stars (which is an observed fact) indicated a continuous diminution, leading at some unknown distance to entire absence of luminous--that is, of active, energy-emitting aggregations of matter.[1] As to whether there are such other material universes or not I offer no opinion, and have no belief one way or the other. I consider all speculations as to what may or may not exist in infinite s.p.a.ce to be utterly valueless. I have limited my inquiries strictly to the evidence acc.u.mulated by modern astronomers, and to direct inferences and logical deductions from that evidence. Yet, to my great surprise, my chief critic declares that 'Dr. Wallace's underlying error is, indeed, that he has reasoned from the area which we can embrace with our limited perceptions to the infinite beyond our mental or intellectual grasp.' I have distinctly _not_ done this, but many astronomers have done so. The late Richard Proctor not only continually discussed the question of infinite matter as well as infinite s.p.a.ce, but also argued, from the supposed attributes of the Deity, for the necessity of holding this material universe to be infinite, and the last chapter of his _Other Worlds than Ours_ is mainly devoted to such speculations. In a later work, _Our Place among Infinities_, he says that 'the teachings of science bring us into the presence of the unquestionable infinities of time and of s.p.a.ce, and the presumable infinities of matter and of operation--hence therefore into the presence of infinity of energy. But science teaches us nothing about these infinities as such. They remain none the less inconceivable, however clearly we may be taught to recognise their reality.' All this is very reasonable, and the last sentence is particularly important.

Nevertheless, many writers allow their reasonings from facts to be influenced by these ideas of infinity. In Proctor's posthumous work, _Old and New Astronomy_, the late Mr. Ranyard, who edited it, writes: 'If we reject as abhorrent to our minds the supposition that the universe is not infinite, we are thrown back on one of two alternatives--either the ether which transmits the light of the stars to us is not perfectly elastic, or a large proportion of the light of the stars is obliterated by dark bodies.'

Here we have a well-informed astronomer allowing his abhorrence of the idea of a finite universe to affect his reasoning on the actual phenomena we can observe--doing in fact exactly what my critic erroneously accuses me of doing. But setting aside all ideas and prepossessions of the kind here indicated, let us see what are the actual facts revealed by the best instruments of modern astronomy, and what are the natural and logical inferences from those facts.

ARE THE STARS INFINITE IN NUMBER?

The views of those astronomers who have paid attention to this subject are, on the whole, in favour of the view that the stellar universe is limited in extent and the stars therefore limited in number. A few quotations will best exhibit their opinions on this question, with some of the facts and observations on which they are founded.

Miss A.M. Clerke, in her admirable volume, _The System of the Stars_, says: 'The sidereal world presents us, to all appearance, with a finite system.... The probability amounts almost to certainty that star-strewn s.p.a.ce is of measurable dimensions. For from innumerable stars a limitless sum-total of radiations should be derived, by which darkness would be banished from our skies; and the "intense inane," glowing with the mingled beams of suns individually indistinguishable, would bewilder our feeble senses with its monotonous splendour.... Unless, that is to say, light suffer some degree of enfeeblement in s.p.a.ce.... But there is not a particle of evidence that any such toll is exacted; contrary indications are strong; and the a.s.sertion that its payment is inevitable depends upon a.n.a.logies which may be wholly visionary. We are then, for the present, ent.i.tled to disregard the problematical effect of a more than dubious cause.'

Professor Simon Newcomb, one of the first of American mathematicians and astronomers, arrives at a similar conclusion in his most recent volume, _The Stars_ (1902). He says, in his conclusions at the end of the work: 'That collection of stars which we call the universe is limited in extent.

The smallest stars that we see with the most powerful telescopes are not, for the most part, more distant than those a grade brighter, but are mostly stars of less luminosity situate in the same regions' (p. 319). And on page 229 of the same work he gives reasons for this conclusion, as follows: 'There is a law of optics which throws some light on the question. Suppose the stars to be scattered through infinite s.p.a.ce so that every great portion of s.p.a.ce is, in the general average, equally rich in stars. Then at some great distance we describe a sphere having its centre in our sun.

Outside this sphere describe another one of a greater radius, and beyond this other spheres at equal distances apart indefinitely. Thus we shall have an endless succession of spherical sh.e.l.ls, each of the same thickness.

The volume of each of these sh.e.l.ls will be nearly proportional to the squares of the diameters of the spheres which bound it. Hence each of the regions will contain a number of stars increasing as the square of the radius of the region. Since the amount of light we receive from each star is as the inverse square of its distance, it follows that the sum total of the light received from each of these spherical sh.e.l.ls will be equal. Thus as we add sphere after sphere we add equal amounts of light without limit.

The result would be that if the system of stars extended out indefinitely the whole heavens would be filled with a blaze of light as bright as the sun.'

But the whole light given us by the stars is variously estimated at from one-fortieth to one-twentieth or, as an extreme limit, to one-tenth of moonlight, while the sun gives as much light as 300,000 full moons, so that starlight is only equivalent at a fair estimate to the six-millionth part of sunlight. Keeping this in mind, the possible causes of the extinction of almost the whole of the light of the stars (if they are infinite in number and distributed, on the average, as thickly beyond the Milky Way as they are up to its outer boundary) are absurdly inadequate.

These causes are (1) the loss of light in pa.s.sing through the ether, and (2) the stoppage of light by dark stars or diffused meteoritic dust. As to the first, it is generally admitted that there is not a particle of evidence of its existence. There is, however, some distinct evidence that, if it exists, it is so very small in amount that it would not produce a perceptible effect for any distances less remote than hundreds or perhaps thousands of times as far as the farthest limits of the Milky Way are from us. This is indicated by the fact that the brightest stars are _not_ always, or even generally, the nearest to us, as is shown both by their small proper motions and the absence of measurable parallax. Mr. Gore states that out of twenty-five stars, with proper motions of more than two seconds annually, only two are above the third magnitude. Many first magnitude stars, including Canopus, the second brightest star in the heavens, are so remote that no parallax can be found, notwithstanding repeated efforts. They must therefore be much farther off than many small and telescopic stars, and perhaps as far as the Milky Way, in which so many brilliant stars are found; whereas if any considerable amount of light were lost in pa.s.sing that distance we should find but few stars of the first two or three magnitudes that were very remote from us. Of the twenty-three stars of the first magnitude, only ten have been found to have parallaxes of more than one-twentieth of a second, while five range from that small amount down to one or two hundredths of a second, and there are two with no ascertainable parallax. Again, there are 309 stars brighter than magnitude 3.5, yet only thirty-one of these have proper motions of more than 100" a century, and of these only eighteen have parallaxes of more than one-twentieth of a second. These figures are from tables given in Professor Newcomb's book, and they have very great significance, since they indicate that the brightest stars are _not_ the nearest to us. More than this, they show that out of the seventy-two stars whose distance has been measured with some approach to certainty, only twenty-three (having a parallax of more than one-fiftieth of a second) are of greater magnitudes than 3.5, while no less than forty-nine are smaller stars down to the eighth or ninth magnitude, and these are on the average much nearer to us than the brighter stars!

Taking the whole of the stars whose parallaxes are given by Professor Newcomb, we find that the average parallax of the thirty-one bright stars (from 3.5 magnitude up to Sirius) is 0.11 seconds; while that of the forty-one stars below 3.5 magnitude down to about 9.5, is 0.21 seconds, showing that they are, on the average, only half as far from us as the brighter stars. The same conclusion was reached by Mr. Thomas Lewis of the Greenwich Observatory in 1895, namely, that the stars from 2.70 magnitude down to about 8.40 magnitude have, on the average, double the parallaxes of the brighter stars. This very curious and unexpected fact, however it may be accounted for, is directly opposed to the idea of there being any loss of light by the more distant as compared with the nearer stars; for if there should be such a loss it would render the above phenomenon still more difficult of explanation, because it would tend to exaggerate it. The bright stars being on the whole farther away from us than the less bright down to the eighth and ninth magnitudes, it follows, if there is any loss of light, that the bright stars are really brighter than they appear to us, because, owing to their enormous distance some of their light has been lost before it reached us. Of course it may be said that this does not _demonstrate_ that no light is lost in pa.s.sing through s.p.a.ce; but, on the other hand, it is exactly the opposite of what we should expect if the more distant stars were perceptibly dimmed by this cause, and it may be considered to prove that if there is any loss it is exceedingly small, and will not affect the question of the limits of our stellar system, which is all that we are dealing with.

This remarkable fact of the enormous remoteness of the majority of the brighter stars is equally effective as an argument against the loss of light by dark stars or cosmic dust, because, if the light is not appreciably diminished for stars which have less than the fiftieth of a second of parallax, it cannot greatly interfere with our estimates of the limits of our universe.

Both Mr. E.W. Maunder of the Greenwich Observatory and Professor W.W.

Turner of Oxford lay great stress on these dark bodies, and the former quotes Sir Robert Ball as saying, 'the dark stars are incomparably more numerous than those that we can see ... and to attempt to number the stars of our universe by those whose transitory brightness we can perceive would be like estimating the number of horseshoes in England by those which are red-hot.' But the proportion of dark stars (or nebulae) to bright ones cannot be determined _a priori_, since it must depend upon the causes that heat the stars, and how frequently those causes come into action as compared with the life of a bright star. We do know, both from the stability of the light of the stars during the historic period and much more precisely by the enormous epochs during which our sun has supported life upon this earth--yet which must have been 'incomparably' less than its whole existence as a light-giver--that the life of most stars must be counted by hundreds or perhaps by thousands of millions of years. But we have no knowledge whatever of the rate at which true stars are born. The so-called 'new stars' which occasionally appear evidently belong to a different category. They blaze out suddenly and almost as suddenly fade away into obscurity or total invisibility. But the true stars probably go through their stages of origin, growth, maturity, and decay, with extreme slowness, so that it is not as yet possible for us to determine by observation when they are born or when they die. In this respect they correspond to species in the organic world. They would probably first be known to us as stars or minute nebulae: at the extreme limit of telescopic vision or of photographic sensitiveness, and the growth of their luminosity might be so gradual as to require hundreds, perhaps thousands of years to be distinctly recognisable. Hence the argument derived from the fact that we have never witnessed the birth of a true permanent star, and that, therefore, such occurrences are very rare, is valueless. New stars may arise every year or every day without our recognising them; and if this is the case, the reservoir of dark bodies, whether in the form of large ma.s.ses or of clouds of cosmic dust, so far from being incomparably greater than the whole of the visible stars and nebulae, may quite possibly be only equal to it, or at most a few times greater; and in that case, considering the enormous distances that separate the stars (or star-systems) from each other, they would have no appreciable effect in shutting out from our view any considerable proportion of the luminous bodies const.i.tuting our stellar universe. It follows, that Professor Newcomb's argument as to the very small total light given by the stars has not been even weakened by any of the facts or arguments adduced against it.

Mr. W.H.S. Monck, in a letter to _Knowledge_ (May 1903), puts the case very strongly so as to support my view. He says:--'The highest estimate that I have seen of the total light of the full moon is 1/300000 of that of the sun. Suppose that the dark bodies were a hundred and fifty thousand times as numerous as the bright ones. Then the whole sky ought to be as bright as the illuminated portion of the moon. Every one knows that this is not so. But it is said that the stars, though infinite, may only extend to infinity in particular directions, _e.g._ in that of the Galaxy. Be it so.

Where, in the very brightest portion of the Galaxy, will we find a part equal in angular magnitude to the moon which affords us the same quant.i.ty of light? In the very brightest spot, the light probably does not amount to one hundredth part that of the full moon.' It follows that, even if dark stars were fifteen million times as numerous as the bright ones, Professor Newcomb's argument would still apply against an infinite universe of stars of the same average density as the portion we see.

TELESCOPIC EVIDENCE AS TO THE LIMITS OF THE STAR SYSTEM

Throughout the earlier portion of the nineteenth century every increase of power and of light-giving qualities of telescopes added so greatly to the number of the stars which became visible, that it was generally a.s.sumed that this increase would go on indefinitely, and that the stars were really infinite in number and could not be exhausted. But of late years it has been found that the increase in the number of stars visible in the larger telescopes was not so great as might be expected, while in many parts of the heavens a longer exposure of the photographic plate adds comparatively little to the number of stars obtained by a shorter exposure with the same instrument.

Mr. J.E. Gore's testimony on this point is very clear. He says:--'Those who do not give the subject sufficient consideration, seem to think that the number of the stars is practically infinite, or at least, that the number is so great that it cannot be estimated. But this idea is totally incorrect, and due to complete ignorance of telescopic revelations. It is certainly true that, to a certain extent, the larger the telescope used in the examination of the heavens, the more the number of the stars seems to increase; but we now know that there is a limit to this increase of telescopic vision. And the evidence clearly shows that we are rapidly approaching this limit. Although the number of stars visible in the Pleiades rapidly increases at first with increase in the size of the telescope used, and although photography has still further increased the number of stars in this remarkable cl.u.s.ter, it has recently been found that an increased length of exposure--beyond three hours--adds very few stars to the number visible on the photograph taken at the Paris Observatory in 1885, on which over two thousand stars can be counted. Even with this great number on so small an area of the heavens, comparatively large vacant places are visible between the stars, and a glance at the original photograph is sufficient to show that there would be ample room for many times the number actually visible. I find that if the whole heavens were as rich in stars as the Pleiades, there would be only thirty-three millions in both hemispheres.'

Again, referring to the fact that Celoria, with a telescope showing stars down to the eleventh magnitude, could see almost exactly the same number of stars near the north pole of the Galaxy as Sir William Herschel found with his much larger and more powerful telescope, he remarks: 'Their absence, therefore, seems certain proof that very faint stars do _not_ exist in that direction, and that here, at least, the sidereal universe is limited in extent.'

Sir John Herschel notes the same phenomena, stating that even in the Milky Way there are found 's.p.a.ces absolutely dark _and completely void of any star_, even of the smallest telescopic magnitude'; while in other parts 'extremely minute stars, though never altogether wanting, occur in numbers so moderate as to lead us irresistibly to the conclusion that in these regions we see _fairly through_ the starry stratum, since it is impossible otherwise (supposing their light not intercepted) that the numbers of the smaller magnitudes should not go on continually increasing ad infinitum. In such cases, moreover, the ground of the heavens, as seen between the stars, is for the most part perfectly dark, which again would not be the case if innumerable mult.i.tudes of stars, too minute to be individually discernible, existed beyond.' And again he sums up as follows:--'Throughout by far the larger portion of the extent of the Milky Way in both hemispheres, the general blackness of the ground of the heavens on which its stars are projected, and the absence of that innumerable mult.i.tude and excessive crowding of the smallest visible magnitudes, and of glare produced by the aggregate light of mult.i.tudes too small to affect the eye singly, which the contrary supposition would appear to necessitate, must, we think, be considered unequivocal indications that its dimensions _in directions where these conditions obtain_, are not only not infinite, but that the s.p.a.ce-penetrating power of our telescopes suffices fairly to pierce through and beyond it.'[2]