[[p. 2024]] My article on this subject in the issue of The Independent of February 26th having excited considerable interest, and several astronomers having done me the honor to criticise it, I gladly take the opportunity now offered me of making a brief reply to some of my critics, and also of defining my position somewhat more clearly.

    I may at once admit that my former article, owing to the limited time then at my disposal, was written somewhat hastily; and that I made several suggestions and admissions which were of little importance to my general subject, but which laid me open to adverse criticism. Such were a comparison of the stars of the Milky Way with the molecules of a gas, a comparison which I think I have seen made by some writer, but which was suggested to me by the repeated statements in all astronomical works that the proper motions of the stars are in all directions and at various velocities, which quite accords with those of gaseous molecules. I now see that there is probably no justification for this idea, and that the facts that suggested [[p. 2025]] it are apparent only. A similar unfounded notion (I now think) was that of a variation of gravity near the boundary of the universe, which, like the supposed loss of light in passing through the ether, had better be altogether left out of our calculations till some evidence has been adduced in support of them.

    One other point to which several of my critics have referred, and as to which I think they have somewhat misrepresented me, no doubt quite unintentionally, is my supposed statement that our sun is placed at the exact center of the universe. On looking over my article I find that I have in most places when referring to this question used qualifying words, such as "at or near the very central point"--that we are "nearly equally distant from every part of" the Milky Way--"that our sun is one of the central orbs of a globular star cluster," which cluster occupies "a nearly central position"--that it is "very near to, if not actually at, the center of the whole visible universe"--and then, for once, I omit the qualification and use the words, "in all probability, in the center of the whole material universe."

    But this one slip some of my critics appear to have had chiefly in mind. Professor Turner says that my argument is that life "is only possible at the exact center," and that, tho our sun is a mere unit of the solar cluster, I claim that it is "the central unit," whereas I say only "one of the central orbs." Professor Marcel Moye twice refers to me as saying that the sun is at "the very center" of the Galaxy and of the universe (Knowledge, June, p. 132). This, however, is a matter of detail hardly worth referring to. I will therefore pass at once to the more important criticisms, which are three in number: (1) That I have given no proof that the stars are not infinite; (2) that the sun's motion through space shows that our present central position can only be temporary, and (3) that there is no advantage whatever in a central position. Let us consider these points a little further.

    (1) Is the evidence at our command for or against the infinite extension of the stellar universe? This is the real question, the only question we are able to discuss rationally. As to proof or disproof, either is impossible as regards what exists or what does not exist in infinite space. And even as regards the probability of any particular form of existence being infinite we have and can have no evidence, and without evidence it is irrational to hold any definite opinion. What I urged in my article was that we do possess several distinct kinds of evidence, all pointing toward a limitation of our stellar universe; and I still think that this evidence is sufficient, because this universe being on the enormous scale we know it to be, it is the only kind of evidence we can possibly get. I also find that most students of general astronomy express themselves quite clearly on this point. Sir John Herschel says that in some parts of the Milky Way there are "spaces absolutely dark and completely void of any star, even of the smallest telescopic magnitude," and that, in other parts,

"extremely minute stars, tho 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, after stating that throughout by far the larger portion of the Milky Way the background of the sky is generally black, and that there is also an absence of excessive crowding of minute stars, he concludes that we have "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."¹

    These opinions of the man who had studied the whole sphere of the heavens most completely, and who had calmly and deliberately thought out most of the great problems of astronomy throughout a life devoted to the science, are certainly [[p. 2026]] worthy of our attention, and should outweigh the opinions or prejudices of those who ask for proofs of what cannot be proved.

    Among modern astronomers Dr. Isaac Roberts tells us that eleven years ago he took photographs of the Great Nebula in Andromeda, and has recently taken photographs of the same object with the same instrument (his 20-inch reflector) and with the same exposures, but with more sensitive plates than were obtainable at the earlier period. But altho in the more recent plates both the nebulosity and the star-images are denser, they show no greater number of stars than the earlier ones. Exactly similar facts are recorded in the case of the Orion Nebula and the Pleiades.

    Another modern astronomer, Mr. J. E. Gore, speaks very strongly on this question. 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 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. Altho the number of stars visible in the Pleiades rapidly increases at first with increase in the size of the telescope used, and altho 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 2,000 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."

And, referring to the fact that, near the North Pole of the Galaxy, Celoria, with a quite small telescope he was able to see almost exactly the same number of stars as Sir William Herschel, with his very powerful instruments, 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."²

    These extracts are sufficient to show that astronomers of repute, and with a combination of practical and theoretical knowledge which I make no claim to possess, have arrived at the conclusion that the stellar universe is limited in extent; and I might have quoted Professor Newcomb, Miss Clerke and many others in a similar sense. But directly I, an outsider, venture to set forth the same view, and found it upon three distinct kinds of evidence, of which this is one, I am accused of "starting a myth," and it is asserted that my "attempted demonstration of the finite nature of the universe breaks down entirely." This statement is founded upon the possible and probable existence of dark stars and other cosmic matter to such an enormous amount that they would shut out the light from all stars beyond a certain distance. Of course, there probably are great numbers of dark stars, but what proportion they bear to the bright stars no one can tell at present. It is a point which cannot be determined from any general principles, because it must depend upon the whole series of causes which produce so many luminous stars. We must know what is the average life of a luminous star, and also what is the average dormant period of a dark star before it becomes luminous again, if it ever does so. Of these two groups of facts we know absolutely nothing, except that there has been very little change in the brighter stars during the historical period, and that our sun has certainly been giving out both light and heat to nearly its present amount for many millions of years. We may fairly suppose that the dark stars are at least equal in number to the bright ones, or, perhaps, that they are ten times or a hundred times as numerous; few probably would believe, without any evidence whatever, that they are a thousand times as numerous. But even if they were so abundant as this they would not materially diminish the light of the stars, as has been well shown by one of my less adverse critics, Mr. W. H. S. Monck, who on this point is on my side. In Knowledge (May, 1903), he shows that the [[p. 2027]] difference between the light the stars actually give and what they would give if they extended to an infinite distance, and were distributed in anything approaching a similar density, is so enormous that, even if the dark stars were 150,000 times as numerous as the bright ones and both extended to infinity, every part of the heavens should be as bright as the face of the moon. Few persons, I presume, will claim that they are more numerous than this high proportion, while even if they are so numerous some one or more occultations of bright stars (not due to a dark companion) would almost certainly have been observed, since we must assume that all these dark stars have on the average an equal size and as great proper motions as the bright ones. A dark star with a diameter of a million miles and a velocity of ten miles a second would occult a star of the same size and double the distance for about fourteen hours, but with only a few minutes of total obscurity. If the dark star were larger and the bright one less distant from it the period of obscuration would be greater. As such occultations of lucid stars would be visible to the naked eye, and from what we know of the proper motions of the stars and their great diversity of size, might last for periods of from a few hours to a few days, and not recur, and as such a phenomenon has never been observed, we must conclude that the proportion of dark bodies is not so excessive as in the case supposed by Mr. Monck, and therefore that the stars as a whole--bright and dark--are not infinite in number.

    My critics who put forward the hypothesis of dark stars partially obscuring the bright ones, and ultimately totally obscuring those beyond a certain distance, do not attempt to show what that hypothesis implies, or consider if it would explain the observed facts. They ignore the essential point in the evidence, which is, that the ratio of increase in the number of stars from magnitude to magnitude, as determined by the lucid stars, continues to be fairly accurate down to the ninth or tenth magnitude, and then, almost suddenly, ceases to be accurate, so that all minute stars down to the seventeenth magnitude are much less numerous than they ought to be. If we assume dark stars to exist in any large proportion we have no right to assume that they are distributed very differently, on the average, from the bright ones. Consequently, the lucid stars and the telescopic stars down to the tenth magnitude ought to have their light diminished in the same proportion as the remainder down to the seventeenth magnitude. We must remember that there is no proof whatever of these very minute stars being on the average further off than the rest. If they are most abundant in the Milky Way, so are stars of the first magnitude. Professor Newcomb says:

    "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."

Then we have the remarkable fact that the 31 bright stars, above 3.5 magnitude, whose parallax has been measured are twice as far from us on the average as the 41 stars from 3.5 down to 9.5, these being the whole of the stars whose distances Professor Newcomb considers to be fairly well determined. Mr. Thomas Lewis, of the Royal Observatory, Greenwich, announced the same fact in 1895, but dividing the stars somewhat differently. He found that stars from 2.70 down to about 8.40 magnitude had, on the average, double the parallaxes of the brighter stars above 2.70, and were therefore only half the distance from us. We thus see that there is no fixed relation between the apparent size and the nearness of the stars, and it follows that the rapid diminution in the number of stars below a certain magnitude cannot be explained by any amount of dark bodies unless we suppose also an exceedingly unequal distribution of those bodies. Hypothetically numerous dark stars, hypothetically distributed, do not form a very strong argument for rejecting direct inferences from the distribution of the stars. I therefore venture to think that the three converging lines of evidence which I have adduced, leading to the conclusion that the stellar universe is limited in extent, have not even been weakened by the arguments hitherto brought against them.

    (2) The next point urged by my critics, and that on which they lay most [[p. 2028]] stress, is, that even if our sun is in a central position now, its known motion through space shows that the position is only temporary and can have no real significance. Professor Turner assures us that, without the tremendous inference I draw from it,

"the fact itself, if fact it be, can only invite our polite attention as a curious coincidence. Even as a coincidence it does not take high rank; for it can, in any case, only be temporary. If there is a center to the visible universe and if we occupy it to-day, we certainly did not do so yesterday, and shall not do so to-morrow. The solar system is known to be moving among the stars with a velocity which would carry us to Sirius in 100,000 years if we happened to be traveling in his direction, as we are not. In the 50 or 100 million years during which, according to geologists, this earth has been a habitable globe, we must have passed by thousands of stars on the right hand and on the left."

And he concludes that

"so far from our having tranquilly enjoyed a central position 'in unbroken continuity for scores or perhaps hundreds of millions of years,' we should in that time have traversed the Universe from boundary to boundary."³

    Taking Professor Newcomb's estimate of the dimensions of the whole stellar universe, he finds that we should pass across it from boundary to boundary in forty-five million years. Thus lightly and confidently does Professor Turner dispose of the fact that we are, broadly speaking, in a central position with regard to the Milky Way.

    Mr. E. Walter Maunder (in Knowledge, April, 1903) supports this view. He says, speaking of our sun's motion through space:

    "If this pace has been maintained in a straight line, five million years ago we were deep in the actual stream of the Milky Way; five million years hence we shall have completely crossed the gulf which it encircles and again be a member of one of its constituent groups on the opposite side."

This statement begins with an "if," but it concludes so positively that no reader would imagine there was any reasonable doubt as to the conclusion arrived at.

    Another astronomical critic, Prof. Marcel Moye, of Montpellier University, adopts the same view (in Knowledge, of June, 1903). He says:

    "Further, if, by hypothesis, at a given instant, the sun were at the center of the universe, it would lose its position soon, and never return to it again. We must not forget the proper motion of our luminary, a motion of ten miles per second, at least."

    The views here stated by three official astronomers have greatly surprised me, because they assume that the sun, and presumably most of the other stars, are alike moving in straight lines at various speeds and in various directions, and that these motions have been in the same straight lines for many millions of years past, and will be so for many million years to come, carrying us and them in various directions into or beyond the Milky Way. As regards our sun this view is put forth as a proof that its present nearly central position cannot have existed in the past and will not exist in the future; and, therefore, as a complete refutation of my view, that its present central position is a fact of great significance.

    Now what surprises me is that all these gentlemen should have either forgotten or have purposely ignored the existence of gravitation. For within a system of hundreds of millions of suns, irregularly distributed, and supposed to be on the average much larger than ours, motion in a straight line, not only for millions of years, but for any one year, is impossible. This view of even approximately straight line motion of our sun--"traversing the universe from boundary to boundary"--implies that such motion was not acquired by gravitation within the universe, but was given to it by some outer force; and, therefore, if all the proper motions of the stars were acquired in the same way--that they were driven into the universe from without--then indeed the whole system would be more analogous to the molecules of a gas than to a universe in which gravitation was the chief or the only ruling force.

    Still more surprising is the circumstance that my critics have ignored the fact that this determination of the sun's motion at a certain rate and in a certain direction is founded upon an assumption, which assumption is known to be partially and may be wholly erroneous. The assumption is that the proper motions of the stars are not systematic, have no [[p. 2029]] relation to each other, but are wholly random motions. Now, in the first place, hardly any mathematical astronomers believe this to be really the case, and many are searching in every direction for systematic motions in some part or the whole of the heavens. And, in the second place, some such systematic motions do actually exist. By carefully charting all the proper motions known at the time, the late Mr. R. A. Proctor showed that in various parts of the heavens groups of stars were moving together in the same direction and at exactly or nearly the same speed. Five stars in the Great Bear, three in Cassiopeia, and almost all in the Pleiades thus move together. He termed these motions "star drift," and till such motions are carefully searched for and compared with each other we cannot say that the apparent motions of any stars are not systematic. M. Rancken and Mr. Maxwell Hall have both discovered what they believe to be very extensive systematic motions.

    As to the effect of these facts and indications upon the determination of the direction and rate of motion of our sun, I will give the opinion of three astronomical writers of repute. Mr. W. H. S. Monck, of Dublin, says:

    "The proof of this motion rests on the assumption that if we take a sufficient number of stars their real motions in all directions will be equal, and that, therefore, the apparent preponderances which we observe in particular directions result from the real motion of the sun. But there is no impossibility in a systematic motion of the majority of the stars used in these researches which might reconcile the observed facts with a motionless sun. And, in the second place, if the sun is not in the exact center of gravity of the universe, we might expect him to be moving in an orbit around this center of gravity, and our observations on his actual motion are not sufficiently numerous or accurate to enable us to affirm that he is moving in a right line rather than in such an orbit."

Again, Miss A. M. Clerke, the historian of modern astronomy, in her "System of the Stars," speaks still more strongly on the same question, as follows:

    "For the assumption that the absolute movements of the stars have no preference for one direction over another forms the basis of all investigations hitherto conducted into the translatory advance of the solar system. The little fabric of laboriously acquired knowledge regarding it at once crumbles if that basis has to be removed."

And quite recently Mr. W. W. Campbell, of the Lick Observatory, writes as follows:

    "The motion of the Solar System is a purely relative quantity. It refers to specified groups of stars. The results for various groups may differ widely, and all be correct. It would be easy to select a group of stars with reference to which the solar motion would be reversed 180 degrees from the value assigned above."⁴

    It appears, then, that whether we consider the effects of gravitation, which almost always lead to motions either in elliptical orbits or in some other allied curves, or whether we take into account the extreme uncertainty, if not total invalidity, of the data on which all determinations of the sun's motion through space depend, my chief astronomical critics have misled their readers by setting before them the supposed motion of the sun as if it were certainly in a straight line and not in some orbit around a center, and also as if both its direction and velocity were determined by methods of observation as secure as those by which the distances of the sun and of the nearest stars have been measured. So far, then, as the objections to my views depending upon the sun's motion through space are concerned, I submit that I have shown them to be wholly worthless.

    (3) The third most confidently stated criticism of my article was that, even if we were in a central position in the stellar universe, and if that position were a permanent one, it would not be of the least use to us as an inhabited world. Professor H. H. Turner says:

    "We have no reason for supposing that if the stars were blotted out of existence our sun would become dead and cold sensibly sooner than under present conditions. The accepted belief is that his slow contraction is sufficient to account for the energy radiated, and other observed phenomena; and it has never, so far as I am aware, been suggested that we are kept alive by the attractive powers of our neighbors, the fixed stars, or by their influence in any other form. We might wander into outer space without losing anything more [[p. 2030]] serious than we lose when the night is cloudy and we cannot see the stars."⁵

    Now this way of looking at the question is a very one-sided and imperfect one. We are situated in a vast universe and are products of it. We cannot detach ourselves from it and say, "we do not want the rest of the universe; the stars are no good to us; so long as we have our sun all the rest may go." The universe is a mighty organism; its whole aspect and structure assure us of the fact. We are a portion of it, and owe our position, our surroundings, our very existence to it. Looking at it as an evolutionist, I believe that it is only by tracing it back to some necessary earlier state that we shall be able to form some rational conception of how it has evolved, how it has come to be what it is, how we have come to be where we are. Then, and then only, shall we be able to give any probable answer to the question, What advantages have we derived from our nearly central position?

    On all these points I could find hardly any suggestions of enlightenment in astronomical literature, but, rather, what seem to me now to be unnecessary difficulties thrown in the way of the inquirer; and at the time I wrote my article I had no clear ideas on the subject myself. Hence my vague and weak suggestion of stellar radiations affecting us. But, having undertaken to write a book upon the same subject as my article, I have for some three or four months been almost daily more or less occupied with it, and have quite recently reached what is, to myself at all events, a satisfactory explanation.

    Light first came to me through reading (so far as a nonmathematician can read such a work) Lord Kelvin's remarkable article in the Philosophical Magazine of January, 1902, "On the Clustering of Gravitational Matter in Any Part of the Universe." In the first place, this removed the difficulty, which almost all writers upon the stellar universe had dwelt upon, as to the proper motions of the stars being often so large that they could not have been produced by gravitation within the universe. By different, but yet quite probable assumptions as to the primitive extent of the universe and the mass of matter within it, Lord Kelvin shows that the average proper motions are such as could be produced by gravitation. But he does not, as I had hoped he would have done, go on to explain how his preliminary assumptions would or might lead to a universe constituted like that which we see around us.

    Having arrived at the last chapter of my book I was for some weeks puzzling myself over this problem, some solution of which I felt to be essential to the completion of my work; and at last--as I usually find to be the case--the sought-for solution came to me, and brought with it, as I had expected it would bring, a very clear explanation of the extreme importance of our central position as the only one which could afford the conditions which are absolutely essential for the long processes of life development. This enabled me to complete my work, which is now ready for the press, and I hope will be published shortly after the appearance of this article.

    The careful study of the whole subject during the preparation of this work has greatly strengthened the position I took in my first article. In the portion devoted to the biology and physics of the earth and solar system especially, I have found that such delicate adjustments and such numerous combinations of physical and chemical conditions are required for the development and maintenance of life as to render it in the highest degree improbable that they should all be again found combined in any planet; while within the solar system this improbability approaches very near indeed to a certainty. This part of my work contains so much novel and suggestive matter as to throw quite a new light on a subject which, so far as I know, has never before been so fully discussed.

    In the astronomical portion of the volume also I have shown that a large body of facts due to recent researches have a direct bearing upon the question of there being other inhabited planets revolving around other suns. On this question of course there can be no direct evidence; but the facts that I adduce will, I think, satisfy those who come to [[p. 2031]] the subject without prepossessions on one side or the other that the combination of probabilities against such an occurrence are so great as to lead to the provisional conclusion that our earth is the only inhabited planet in the whole stellar universe.

Notes Appearing in the Original Work

1. "Outlines of Astronomy," last edition, pp. 578-579. [[on p. 2025]]

2. "Concise Science Astronomy," pp. 538-540. [[on p. 2026]]

3. The Fortnightly Review, April, 1903, p. 600. [[on p. 2028]]

4. The Astrophysical Journal, Vol. XIII, p. 87, 1901. [[on p. 2029]]

5. The Fortnightly Review, April, 1903, p. 600. [[on p. 2030]]