For about half a century this nebular hypothesis was generally accepted, but during the last thirty years so many objections and difficulties have been suggested, that it has been felt impossible to retain it even as a working hypothesis. At the same time another hypothesis has been put forth which seems more in accordance with the facts of nature as we find them in our own solar system, and which is not open to any of the objections against the nebular theory, even if it introduces a few new ones.
A fundamental objection to Laplace's theory is, that in a gas of such extreme tenuity as the solar nebula must have been, even when it extended only to Saturn or Uranus, it could not possibly have had any cohesion, and therefore could not have given off whole rings at distant intervals, but only small fragments continuously as condensation went on, and these, rapidly cooling, would form solid particles, a kind of meteoric dust, which might aggregate into numerous small planets, or might persist for indefinite periods, like the rings of Saturn or the great ring of the Asteroids.
Another equally vital objection is, that, as the nebula when extending beyond the orbit of Neptune could have had a mean density of only about the two-hundred millionth of our air at sea level, it must have been many hundred times less dense than this at and near its outer surface, and would there be exposed to the cold of stellar space—a cold that would solidify hydrogen. It is thus evident that the gases of all the metallic and other solid elements could not possibly exist as such, but would rapidly, perhaps almost instantaneously, become first liquid and then solid, forming meteoric dust even before contraction had gone far enough to produce such increased rotation as would throw off any portion of the gaseous matter.
Here we have the foundations of the meteoritic hypothesis which is now steadily making its way. It is supported by the fact that we everywhere find proofs of such solid matter in the planetary spaces around us. It falls continually upon the earth. It can be collected on the Arctic and Alpine snows. It occurs everywhere in the deepest abysses of the ocean where there are not sufficient organic deposits to mask it. It constitutes, as has now been demonstrated, the rings of Saturn. Thousands of vast rings of solid particles circulate around the sun, and when our earth crosses any of these rings, and their particles enter our atmosphere with planetary velocity, the friction ignites them and we see falling stars. Comets' tails, the sun's corona, and the zodiacal light are three strange phenomena, which, though wholly insoluble on any theory of gaseous formation, receive their intelligible explanation by means of excessively minute solid particles—microscopic cosmic dust—driven outward by the tremendous electrical repulsions that emanate from the sun.
Having these and other proofs that solid matter, ranging in size, perhaps, from the majestic orbs of Jupiter and Saturn down to the inconceivably minute particles driven millions of miles into space to form a comet's tail, does actually exist everywhere around us, and by collisions between the particles or with planetary atmospheres can produce heat and light and gaseous emanations, we find a basis of fact and observation for the meteoritic hypothesis which Laplace's nebular, and essentially gaseous, theory does not possess.
During the latter half of the nineteenth century several writers suggested this idea of the possible formation of the Solar System, but so far as I am aware, the late R.A. Proctor was the first to discuss it in any detail, and to show that it explained many of the peculiarities in the size and arrangement of the planets and their satellites which the nebular hypothesis did not explain. This he does at some length in the chapter on meteors and comets in his Other Worlds than Ours, published in 1870. He assumed, instead of the fire-mist of Laplace, that the space now occupied by the solar system, and for an unknown distance around it, was occupied by vast quantities of solid particles of all the kinds of matter which we now find in the earth, sun, and stars. This matter was dispersed somewhat irregularly, as we see that all the matter of the universe is now distributed; and he further assumed that it was all in motion, as we now know that all the stars and other cosmical masses are, and must be, in motion towards or around some centre.
Under these conditions, wherever the matter was most aggregated, there would be a centre of attraction through gravitation, which would necessarily lead to further aggregation, and the continual impacts of such aggregating matter would produce heat. In course of time, if the supply of cosmic matter was ample (as the result shows that it must have been, whatever theory we adopt), our sun, thus formed, would approximate to its present mass and acquire sufficient heat by collision and gravitation to convert its whole body into the liquid or gaseous condition. While this was going on, subordinate centres of aggregation might form, which would capture a certain proportion of the matter flowing in under the attraction of the central mass, while, owing to the nearly uniform direction and velocity with which the whole system was revolving, each subordinate centre would revolve around the central mass, in somewhat different planes, but all in the same direction.
Mr. Proctor shows the probability that the largest outside aggregation would be at a great distance from the central mass, and this having once been formed, any centres farther away from the sun would be both smaller and very remote, while those inside the first would, as a rule, become smaller as they were nearer the centre. The heated condition of the earth's interior would thus be due, not to the primitive heat of matter in a gaseous state out of which it was formed—a condition physically impossible—but would be acquired in the process of aggregation by the collisions of meteoric masses falling on it, and by its own gravitative force producing continuous condensation and heat.
On this view Jupiter would probably be formed first, and after him at very great distances, Saturn, Uranus, and Neptune; while the inner aggregations would be smaller, as the much greater attractive power of the sun would give them comparatively little opportunity of capturing the meteoric matter that was continuously flowing towards him.
The Meteoritic Nature of the Nebulæ
Having thus reached the conclusion that wherever apparently nebulous matter exists within the limits of the solar system it is not gaseous but consists of solid particles, or, if heated gases are associated with the solid matter they can be accounted for by the heat due to collisions either with other solid particles or with accumulations of gases at a low temperature, as when meteorites enter our atmosphere, it was an easy step to consider whether the cosmic nebulæ and stars may not have had a similar origin.
From this point of view the nebulæ are supposed to be vast aggregations of meteorites or cosmic dust, or of the more persistent gases, revolving with circular or spiral motions, or in irregular streams, and so sparsely scattered that the separate particles of dust may be miles—perhaps hundreds of miles—apart; yet even those nebulæ, only visible by the telescope, may contain as much matter as the whole solar system. From this simple origin, by steps which can be observed in the skies, almost all the forms of suns and systems can be traced by means of the known laws of motion, of heat-production, and of chemical action. The chief English advocate of this view at the present time is Sir Norman Lockyer, who, in numerous papers, and in his works on The Meteoritic Hypothesis and Inorganic Evolution, has developed it in detail, as the result of many years' continuous research, aided by the contributory work of continental and American astronomers. These views are gradually spreading among astronomers and mathematicians, as will be seen by the very brief outline which will now be given of the explanations they afford of the main groups of phenomena presented by the stellar universe.
Dr. Roberts on Spiral Nebulæ
Dr. Isaac Roberts, who possesses one of the finest telescopes constructed for photographing stars and nebulæ, has given his views on stellar evolution, in Knowledge of February 1897, illustrated by four beautiful photographs of spiral nebulæ. These curious forms were at first thought to be rare, but are now found to be really very numerous when details are brought out by the camera. Many of the very large and apparently quite irregular nebulæ, like the Magellanic Clouds, are found to have faint indications of spiral structure. As more than ten thousand nebulæ are now known, and new ones are continually being discovered, it will be a long time before these can all be carefully studied and photographed, but present indications seem to show that a considerable proportion of them will exhibit spiral forms.
Dr. Roberts tells us that all the spiral nebulæ he has photographed are characterised by having a nucleus surrounded by dense nebulosity, most of them being also studded with stars. These stars are always arranged more or less symmetrically, following the curves of the spiral, while outside the visible nebula are other stars arranged in curves strongly suggesting a former greater extension of the nebulous matter. This is so marked a feature that it at once leads to a possible explanation of the numerous slightly curved lines of stars found in every part of the heavens, as being the result of their origin from spiral nebulæ whose material substance has been absorbed by them.
Dr. Roberts proposes several problems in relation to these bodies: Of what materials are spiral nebulæ composed? Whence comes the vortical motion which has produced their forms? The material he finds in those faint clouds of nebulous matter, often of vast extent, that exist in many parts of the sky, and these are so numerous that Sir William Herschel alone recorded the positions of fifty-two such regions, many of which have been confirmed by recent photographs. Dr. Roberts considers these to be either gaseous or with discrete solid particles intermixed. He also enumerates smaller nebulous masses undergoing condensation and segregation into more regular forms; spiral nebulæ in various stages of condensation and of aggregation; elliptic nebulæ; and globular nebulæ. In the last three classes there is clear evidence, on every photograph that has been taken, that condensation into stars or star like forms is now going on.
He adopts Sir Norman Lockyer's view that collisions of meteorites within each swarm or cloud would produce luminous nebulosity; so also would collisions between separate swarms of meteorites produce the conditions required to account for the vortical motions and the peculiar distribution of the nebulosity in the spiral nebulæ. Almost any collision between unequal masses of diffused matter would, in the absence of any massive central body round which they would be forced to revolve, lead to spiral motions. It is to be noted that, although the stars formed in the spiral convolutions of the nebulæ follow those curves, and retain them after the nebulous matter has been all absorbed by them, yet, whenever such a nebula is seen by us edgewise, the convolutions with their enclosed stars will appear as straight lines; and thus not only numbers of star groups arranged in curves, but also those which form almost perfect straight lines, may possibly be traced back to an origin from spiral nebulæ.
Motion being a necessary result of gravitation, we know that every star, planet, comet, or nebula must be in motion through space, and these motions—except in systems physically connected or which have had a common origin—are, apparently, in all directions. How these motions originated and are now regulated we do not know; but there they are, and they furnish the motive power of the collisions, which, when affecting large bodies or masses of diffused matter, lead to the formation of the various kinds of permanent stars; while when smaller masses of matter are concerned those temporary stars are formed which have interested astronomers in all ages. It must be noted that although the motions of the single stars appear to be in straight lines, yet the spaces through which they have been observed to move are so small that they may really be moving in curved orbits around some central body, or the centre of gravity of some aggregation of stars bright and dark, which may itself be comparatively at rest. There may be thousands of such centres around us, and this may sufficiently explain the apparent motions of stars in all directions.
A Suggestion As To the Formation Of
Spiral Nebulæ
In a remarkable paper in the Astrophysical Journal (July 1901), Mr. T.C. Chamberlin suggests an origin for the spiral nebulæ, as well as of swarms of meteorites and comets, which seems likely to be a true, although perhaps not the only one.
There is a well-known principle which shows that when two bodies in space, of stellar size, pass within a certain distance of each other, the smaller one will be liable to be torn into fragments by the differential attraction of the larger and denser body. This was originally proved in the case of gaseous and liquid bodies, and the distance within which the smaller one will be disrupted (termed the Roche limit) is calculated on the supposition that the disrupted body is a liquid mass. Mr. Chamberlin shows, however, that a solid body will also be disrupted at a lesser distance dependent on its size and cohesive strength; but, as the size of the two bodies increases, the distance at which disruption will occur increases also, till with very large bodies, such as suns, it becomes almost as large as in the case of liquids or gases.
The disruption occurs from the well-known law of differential gravitation on the two sides of a body leading to tidal deformation in a liquid, and to unequal strain in a solid. When the changes of gravitative force take place slowly, and are also small in amount, the tides in liquids or strains in solids are very small, as in the case of our earth when acted on by the sun and moon, the result is a small tide in the ocean and atmosphere, and no doubt also in the molten interior, to which the comparatively thin crust may partially adjust itself. But if we suppose two dark or luminous suns whose proper motions are in such a direction as to bring them near each other, then, as they approach, each will be deflected towards the other, and will pass round their common centre of gravity with immense velocity, perhaps hundreds of miles in a second. At a considerable distance they will begin to produce tidal elongation towards and away from each other, but when the disruptive limit is nearly reached, the gravitative forces will be increasing so rapidly that even a liquid mass could not adjust its shape with sufficient quickness and the tremendous internal strains would produce the effects of an explosion, tearing the whole mass (of the smaller of the two) into fragments and dust.
But it is also shown that, during the entire process, the two elongated portions of the originally spherical mass would be so acted upon by gravity as to produce increasing rotation, which as the crisis approached would extend the elongation, and aid in the explosive result. This rapid rotation of the elongated mass would, when the disruption occurred, necessarily give to the fragments a whirling or spiral motion, and thus initiate a spiral nebula of a size and character dependent on the size and constitution of the two masses, and on the amount of the explosive forces set up by their approach.
There is one very suggestive phenomenon which seems to prove that this is one of the modes of formation of spiral nebulæ. When the explosive disruption occurs the two protuberances or elongations of the body will fly apart, and having also a rapid rotatory movement, the resulting spiral will necessarily be a double one. Now, it is the fact that almost all the well-developed spiral nebulæ have two such arms opposite to each other, as beautifully shown in M. 100 Comæ, M. 51 Canum, and others photographed by Dr. I. Roberts. It does not seem likely that any other origin of these nebulæ should give rise to a double rather than to a single spiral.
The Evolution of Double Stars
The advance in knowledge of double and multiple stars has been wonderfully rapid, numerous observers having devoted themselves to this special branch. Many thousands were discovered during the first half of the nineteenth century, and as telescopic power increased new ones continued to flow in by hundreds and thousands, and there has been recently published by the Yerkes Observatory a catalogue of 1290 such stars, discovered between 1871 and 1899 by one observer, Mr. S.W. Burnham. All these have been found by the use of the telescope, but during the last quarter of a century the spectroscope has opened up a new world of double stars of enormous extent and the highest interest.
The telescopic binaries which have been observed for a sufficient time to determine their orbits, range from periods of about eleven years as a minimum up to hundreds and even more than a thousand years. But the spectroscope reveals the fact that the many thousands of telescopic binaries form only a very small part of the binary systems in existence. The overwhelming importance of this discovery is, that it carries the times of revolution from the minimum of the telescopic doubles downward in unbroken series through periods of a few years, to those reckoned by months, by days, and even by hours. And with this reduction of period there necessarily follows a corresponding reduction of distance, so that sometimes the two stars must be in contact, and thus the actual birth or origin of a double star has been observed to occur, even though not actually seen. This mode of origin was indeed anticipated by Dr. Lee of Chicago in 1892, and it has been confirmed by observation in the short space of ten years.
In a remarkable communication to Nature (September 12th, 1901) Mr. 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 class 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 constitution 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 Carinæ, 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 mass of fluid; and we now find proofs that such figures exist, and that they form the starting-point for the enormous and ever-increasing quantities 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.
Clusters of Stars and Variables
The clusters 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 clusters which are not very crowded and of irregular forms, strongly suggest an origin from the equally irregular and fantastic forms of nebulæ by a process of aggregation like that which Dr. Roberts describes as developing within the spiral nebulæ. But the dense globular clusters 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 clusters is as to their stability. Professor Simon Newcomb remarks on this point as follows: 'Where thousands of stars are condensed into a space so small, what prevents them from all falling together into one confused mass? 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 clusters which afford possible indications of their origin and essential constitution. When closely examined most of them are seen to be less regular than they at first appear. Vacant spaces 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 pronounced form, in the larger nebulæ, that we can hardly help thinking that in these clusters we have the result of the condensation of very large nebulæ, which have first aggregated towards numerous centres, while these agglomerations have been slowly drawn towards the common centre of gravity of the whole mass. It is suggestive of this origin that while the smaller telescopic nebulæ are far removed from the Milky Way, the larger ones are most abundant near its borders; while the star-clusters are excessively abundant on and near the Milky Way, but very scarce elsewhere, except in or near vast nebulæ like the Magellanic Clouds. We thus see that the two phenomena may be complementary to each other, the condensation of nebulæ having gone on most rapidly where material was most abundant, resulting in numerous star-clusters where there are now few nebulæ.
There is one striking feature of the globular clusters which calls for notice; the presence in some of them of enormous quantities of variable stars, while in others few or none can be found. The Harvard Observatory has for several years devoted much time to this class of observations, and the results are given in Professor Newcomb's recent volume on 'The Stars.' It appears that twenty-three clusters have been observed spectroscopically, the number of stars examined in each cluster 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 clusters. In two clusters, 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 cluster 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 clusters 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 cluster.'
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 constitution 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 analysis has furnished the means of obtaining some definite knowledge of the physics and chemistry of the stars, and has thus established a new branch of science—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 classification 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 Class I., Class II., etc., according to the system of classification 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 nebulæ, 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 nebulæ, we pass 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 masses of gas and cosmic dust we know as nebulæ, through planetary nebulæ, nebulous stars, variable and double-stars, to red and white stars and on to those exhibiting the most intense blue-white lustre. 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 mass 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 mass of incandescent gas contracts through the loss of its heat by radiation into space, 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 mass to increase.
But if, as there is reason to believe, the various types of stars differ also in chemical constitution, 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 classification by constitution as well as by temperature, and the course of evolution of the differently constituted 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 mass 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 masses. 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 assumed by most astronomers that they must sometimes occur—then meteoric particles of all sizes would be produced which might exhibit any complexity of mineral constitution. 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.
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 space to be utterly valueless. I have limited my inquiries strictly to the evidence accumulated 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 space, 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 space, 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 space 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 space.... But there is not a particle of evidence that any such toll is exacted; contrary indications are strong; and the assertion that its payment is inevitable depends upon analogies which may be wholly visionary. We are then, for the present, entitled 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 space so that every great portion of space 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 shells, each of the same thickness. The volume of each of these shells 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 shells 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 passing 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 passing 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 passing through space; 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 nebulæ) 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 nebulæ: 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 masses or of clouds of cosmic dust, so far from being incomparably greater than the whole of the visible stars and nebulæ, 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 constituting 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 quantity 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 assumed 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 cluster, 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 'spaces 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 multitudes 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 multitude and excessive crowding of the smallest visible magnitudes, and of glare produced by the aggregate light of multitudes 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 space-penetrating power of our telescopes suffices fairly to pierce through and beyond it.'[2]
This expression of opinion by the astronomer who, probably beyond any now living, was the most competent authority on this question, to which he devoted a long life of observation and study extending over the whole heavens, cannot be lightly set aside by the opinions or conjectures of those who seem to assume that we must believe in an infinity of stars if the contrary cannot be absolutely proved. But as not a particle of evidence can be adduced to prove infinity, and as all the facts and indications point, as here shown, in a directly opposite direction, we must, if we are to trust to evidence at all in this matter, arrive at the conclusion that the universe of stars is limited in extent.
Dr. Isaac Roberts gives similar evidence as regards the use of photographic plates. He writes:—'Eleven years ago photographs of the Great Nebula in Andromeda were taken with the 20-inch reflector, and exposures of the plates during intervals up to four hours; and upon some of them were depicted stars to the faintness of 17th to 18th magnitude, and nebulosity to an equal degree of faintness. The films of the plates obtainable in those days were less sensitive than those which have been available during the past five years, and during this period photographs of the nebula with exposures up to four hours have been taken with the 20-inch reflector. No extensions of the nebulosity, however, nor increase in the number of the stars can be seen on the later rapid plates than were depicted upon the earlier slower ones, though the star-images and the nebulosity have greater density on the later plates.'
Exactly similar facts are recorded in the cases of the Great Nebula in Orion, and the group of the Pleiades. In the case of the Milky Way in Cygnus photographs have been taken with the same instrument, but with exposures varying from one hour to two hours and a half, but no fainter stars could be found on one than on the other; and this fact has been confirmed by similar photographs of other areas in the sky.
The Law of Diminishing Numbers of Stars
We will now consider another kind of evidence equally weighty with the two already adduced. This is what may be termed the law of diminishing numbers beyond a certain magnitude, as observed by larger and larger telescopes.
For some years past star-magnitudes have been determined very accurately by means of careful photometric comparisons. Down to the sixth magnitude stars are visible to the naked eye, and are hence termed lucid stars. All fainter stars are telescopic, and continuing the magnitudes in a series in which the difference in luminosity between each successive magnitude is equal, the seventeenth magnitude is reached and indicates the range of visibility in the largest telescopes now in existence. By the scale now used a star of any magnitude gives nearly two and a half times as much light as one of the next lower magnitude, and for accurate comparison the apparent brightness of each star is given to the tenth of a magnitude which can easily be observed. Of course, owing to differences in the colour of stars, these determinations cannot be made with perfect accuracy, but no important error is due to this cause. According to this scale a sixth magnitude star gives about one-hundredth part of the light of an average first magnitude star. Sirius is so exceptionally bright that it gives nine times as much light as a standard or average first magnitude star.
Now it is found that from the first to the sixth magnitude the stars increase in number at the rate of about three and a half times those of the preceding magnitudes. The total number of stars down to the sixth magnitude is given by Professor Newcomb as 7647. For higher magnitudes the numbers are so great that precision and uniformity are more difficult of attainment; yet there is a wonderful continuance of the same law of increase down to the tenth magnitude, which is estimated to include 2,311,000 stars, thus conforming very nearly with the ratio of 3.5 as determined by the lucid stars.
But when we pass beyond the tenth magnitude to those vast numbers of faint stars only to be seen in the best or the largest telescopes, there appears to be a sudden change in the ratio of increased numbers per magnitude. The numbers of these stars are so great that it is impossible to count the whole as with the higher magnitude stars, but numerous counts have been made by many astronomers in small measured areas in different parts of the heavens, so that a fair average has been obtained, and it is possible to make a near approximation to the total number visible down to the seventeenth magnitude. The estimate of these by astronomers who have made a special study of this subject is, that the total number of visible stars does not exceed one hundred millions.[3]
But if we take the number of stars down to the ninth magnitude, which are known with considerable accuracy, and find the numbers in each succeeding magnitude down to the seventeenth, according to the same ratio of increase which has been found to correspond very nearly in the case of the higher magnitudes, Mr. J.E. Gore finds that the total number should be about 1400 millions. Of course neither of these estimates makes any pretence to exact accuracy, but they are founded on all the facts at present available, and are generally accepted by astronomers as being the nearest approach that can be made to the true numbers. The discrepancy is, however, so enormous that probably no careful observer of the heavens with very large telescopes doubts that there is a very real and very rapid diminution in the numbers of the fainter as compared with the brighter stars.
There is, however, yet one more indication of the decreasing numbers of the faint telescopic stars, which is almost conclusive on this question, and, so far as I am aware, has not yet been used in this relation. I will therefore briefly state it.
The Light Ratio as Indicating the Number
of Faint Stars
Professor Newcomb points out a remarkable result depending on the fact that, while the average light of successively lower magnitudes diminishes in a ratio of 2.5, their numbers increase at nearly a ratio of 3.5. From this it follows that, so long as this law of increase continues, the total of starlight goes on increasing by about forty per cent. for each successive magnitude, and he gives the following table to illustrate it:—