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 a.s.sume 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 DIMINIs.h.i.+NG 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 diminis.h.i.+ng 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 pa.s.s 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 ill.u.s.trate it:--

Mag. 1 Total Light = 1 " 2 " = 1.4 " 3 " = 2.0 " 4 " = 2.8 " 5 " = 4.0 " 6 " = 5.7 " 7 " = 8.0 " 8 " = 11.3 " 9 " = 16.0 " 10 " = 22.6 -------- Total light to Mag. 10 = 74.8 --------

Thus the total amount of the light given by all stars down to the tenth magnitude is seventy-four times as great as that from the few first magnitude stars. We also see that the light given by the stars of any magnitude is twice as much as that of the stars two magnitudes higher in the scale, so that we can easily calculate what additional light we ought to receive from each additional magnitude if they continue to increase in numbers below the tenth as they do above that magnitude. Now it has been calculated as the result of careful observations, that the total light given by stars down to nine and a half magnitude is one-eightieth of full moonlight, though some make it much more. But if we continue the table of light-ratios from this low starting-point down to magnitude seventeen and a half, we shall find, if the numbers of the stars go on increasing at the same rate as before, that the light of all combined should be at least seven times as great as moonlight; whereas the photometric measurements make it actually about one-twentieth. And as the calculation from light-ratios only includes stars just visible in the largest telescopes, and does not include all those proved to exist by photography, we have in this case a demonstration that the numbers of the stars below the tenth and down to the seventeenth magnitude diminish rapidly.

We must remember that the minuter telescopic stars preponderate enormously in and near the Milky Way. At a distance from it they diminish rapidly, till near its poles they are almost entirely absent. This is shown by the fact (already referred to at p. 146) that Professor Celoria of Milan, with a telescope of less than three inches aperture, counted almost as many stars in that region as did Herschel with his eighteen-inch reflector. But if the stellar universe extends without limit we can hardly suppose it to do so in one plane only; hence the absence of the minuter stars and of diffused milky light over the larger part of the heavens is now held to prove that the myriads of very minute stars in the Milky Way really belong to it, and not to the depths of s.p.a.ce far beyond.

It seems to me that here we have a fairly direct proof that the stars of our universe are really limited in number.

There are thus four distinct lines of argument all pointing with more or less force to the conclusion that the stellar universe we see around us, so far from being infinite, is strictly limited in extent and of a definite form and const.i.tution. They may be briefly summarised as follows:--

(1) Professor Newcomb shows that, if the stars were infinite in number, and if those we see were approximately a fair sample of the whole, and further, if there were not sufficient dark bodies to shut out almost the whole of their light, then we should receive from them an amount of light theoretically greater than that of sunlight. I have shown, at some length, that neither of these causes of loss of light will account for the enormous disproportion between the theoretical and the actual light received from the stars; and therefore Professor Newcomb's argument must be held to be a valid one against the infinite extent of our universe. Of course, this does not imply that there may not be any number of other universes in s.p.a.ce, but as we know absolutely nothing of them--even whether they are material or non-material--all speculation as to their existence is worse than useless.

(2) The next argument depends on the fact that all over the heavens, even in the Milky Way itself, there are areas of considerable extent, besides rifts, lanes, and circular patches, where stars are either quite absent or very faint and few in number. In many of these areas the largest telescopes show no more stars than those of moderate size, while the few stars seen are projected on an intensely dark background. Sir William Herschel, Humboldt, Sir John Herschel, R.A. Proctor, and many living astronomers hold that, in these dark areas, rifts, and patches, we see completely through our stellar universe into the starless depths of s.p.a.ce beyond.

(3) Then we have the remarkable fact that the steady increase in the number of stars, down to the ninth or tenth magnitudes, following one constant ratio either gradually or suddenly changes, so that the total number from the tenth down to the seventeenth magnitudes is only about one-tenth of what it would have been had the same ratio of increase continued. The conclusion to be drawn from this fact clearly is, that these faint stars are becoming more and more thinly scattered in s.p.a.ce, while the dark background on which they are usually seen shows that, except in the region of the Milky Way, there are _not_ mult.i.tudes of still smaller invisible stars beyond them.

(4) The last indication of a limited stellar universe--the estimate of numbers by the light-ratio of each successive magnitude--powerfully supports the three preceding arguments.

The four distinct cla.s.ses of evidence now adduced must be held to const.i.tute, as nearly as the circ.u.mstances permit, a satisfactory proof that the stellar universe, of which our solar system forms a part, has definite limits; and that a full knowledge of its form, structure, and extent, is not beyond the possibility of attainment by the astronomers of the future.

FOOTNOTES:

[1] In a letter to _Knowledge_, June 1903, Mr. W.H.T. Monck puts the same point in a mathematical form.

[2] _Outlines of Astronomy_, pp. 578-9. In the pa.s.sages quoted the italics are Sor John Herschel's.

[3] Mr. J.E. Gore in _Concise Knowledge Astronomy_, pp. 541-2.

CHAPTER VIII

OUR RELATION TO THE MILKY WAY

We now approach what may be termed the very heart of the subject of our inquiry, the determination of how we are actually situated within this vast but finite universe, and how that position is likely to affect our globe as being the theatre of the development of life up to its highest forms.

We begin with our relation to the Milky Way (which we have fully described in our fourth chapter), because it is by far the most important feature in the whole heavens. Sir John Herschel termed it 'the ground-plane of the sidereal system'; and the more it is studied the more we become convinced that the whole of the stellar universe--stars, cl.u.s.ters of stars, and nebulae--are in some way connected with it, and are probably dependent on it or controlled by it. Not only does it contain a greater number of stars of the higher magnitudes than any other part of the heavens of equal extent, but it also comprises a great preponderance of star-cl.u.s.ters, and a great extent of diffused nebulous matter, besides the innumerable myriads of minute stars which produce its characteristic cloud-like appearance. It is also the region of those strange outbursts forming new stars; while gaseous stars of enormous bulk--some probably a thousand or even ten thousand times that of our sun, and of intense heat and brilliancy--are more abundant there than in any other part of the heavens. It is now almost certain that these enormous stars and the myriads of minute stars just visible with the largest telescopes, are actually intermingled, and together const.i.tute its essential features; in which case the fainter stars are really small and cannot be far apart, forming, as it were, the first aggregations of the nebulous substratum, and perhaps supplying the fuel which keeps up the intense brilliancy of the giant suns. If this is so, then the Galaxy must be the theatre of operation of vast forces, and of continuous combinations of matter, which escape our notice owing to its enormous distance from us. Among its millions of minute telescopic stars, hundreds or thousands may appear or disappear yearly without being perceived by us, till the photographic charts are completed and can be minutely scrutinised at short intervals. As undoubted changes have occurred in many of the larger nebulae during the last fifty years, we may antic.i.p.ate that a.n.a.logous changes will soon be noted in the stars and the nebulous ma.s.ses of the Milky Way. Dr. Isaac Roberts has even observed changes in nebulae after such a short interval as eight years.

THE MILKY WAY A GREAT CIRCLE

Notwithstanding all its irregularities, its divisions, and its diverging branches, astronomers are generally agreed that the Milky Way forms a great circle in the heavens. Sir John Herschel, whose knowledge of it was unrivalled, stated that its course 'conforms, as nearly as the indefiniteness of its boundary will allow it to be fixed, to that of a great circle'; and he gives the Right Ascension and Declination of the points where it crosses the equinoctial, in figures which define those points as being exactly opposite each other. He also defines its northern and southern poles by other figures, so as to show that they are the poles of a great circle. And after referring to Struve's view that it was _not_ a great circle, he says, 'I retain my own opinion.' Professor Newcomb says that its position 'is nearly always near a great circle of the sphere'; and again he says: 'that we are in the galactic plane itself seems to be shown in two ways: (1) the equality in the counts of stars on the two sides of this plane all the way to its poles; and (2) the fact that the central line of the Galaxy is a great circle, which it would not be if we viewed it from one side of its central plane' (_The Stars_, p. 317). Miss Clerke, in her _History of Astronomy_, speaks of 'our situation _in_ the galactic plane'

as one of the undisputed facts of astronomy; while Sir Norman Lockyer, in a lecture delivered in 1899, said, 'the middle line of the Milky Way is really not distinguishable from a great circle,' and again in the same lecture--'but the recent work, chiefly of Gould in Argentina, has shown that it practically is a great circle.'[4]

About this fact, then, there can be no dispute. A great circle is a circle dividing the celestial sphere into two equal portions, as seen from the earth, and therefore the plane of this circle must pa.s.s through the earth.

Of course the whole thing is on such a vast scale, the Milky Way varying from ten to thirty degrees wide, that the plane of its circular course cannot be determined with minute accuracy. But this is of little importance. When carefully laid down on a chart, as in that of Mr. Sidney Waters (see end of volume), we can see that its central line does follow a very even circular course, conforming 'as nearly as may be' to a great circle. We are therefore certainly well within the s.p.a.ce that would be enclosed if its northern and southern margins were connected together across the vast intervening abyss, and in all probability not far from the central plane of that enclosed s.p.a.ce.

THE FORM OF THE MILKY WAY AND OUR POSITION ON ITS PLANE

Although the Galaxy forms a great circle in the heavens from our point of view, it by no means follows that it is circular in plan. Being unequal in width and irregular in outline, it might be elliptic or even angular in shape without being at all obviously so to us. If we were standing in an open plain or field two or three miles in diameter, and bounded in every direction by woods of very irregular height and density and great diversity of tint, we should find it difficult to judge of the shape of the field, which might be either a true circle, an oval, a hexagon, or quite irregular in outline, without our being able to detect the exact shape unless some parts were very much nearer to us than others. Again, just as the woods bounding the field might be either a narrow belt of nearly uniform width, or might in some places be only a few yards wide and in others stretch out for miles, so there have been many opinions as to the width of the Milky Way in the direction of its plane, that is, in the direction in which we look towards it. Lately, however, as the result of long-continued observation and study, astronomers are fairly well agreed as to its general form and extent, as will be seen by the following statements of fact and reasoning.

Miss Clerke, after giving the various views of many astronomers--and as the historian of modern astronomy her opinion has much weight--considers that the most probable view of it is, that it is really very much what it seems to us--an immense ring with streaming appendages extending from the main body in all directions, producing the very complex effect we see. The belief seems to be now spreading that the whole universe of stars is spherical or spheroidal, the Milky Way being its equator, and therefore in all probability circular or nearly so in plan; and it is also held that it must be rotating--perhaps very slowly--as nothing else can be supposed to have led to the formation of such a vast ring, or can preserve it when formed.

Professor Newcomb considers, from the numbers of the stars in all directions towards the Milky Way being approximately equal, that there cannot be much difference in our distance from it in various directions. It would follow that its plan is approximately circular or broadly elliptic.

The existence of ring-nebulae may be held to render such a form probable.

Sir Norman Lockyer gives facts which tend in the same direction. In an article in _Nature_ of November 8th, 1900, he says: 'We find that the gaseous stars are not only confined to the Milky Way, but they are the most remote in every direction, in every galactic longitude; all of them have the smallest proper motion.' And again, referring to the hottest stars being equally remote on all sides of us, he says: 'It is because we are in the centre, because the solar system is in the centre, that the observed effect arises.' He also considers that the ring-nebula in Lyra nearly represents the form of our whole system; and he adds: 'We practically know that in our system the centre is the region of least disturbance, and therefore cooler conditions.'

These various facts and conclusions of some of the most eminent astronomers all point to one definite inference, that our position, or that of the solar system, is not very far from the centre of the vast ring of stars const.i.tuting the Milky Way, while the same facts imply a nearly circular form to this ring. Here, more than as regards our position in the plane of the Galaxy, there is no possibility of precise determination; but it is quite certain that if we were situated very far away from the centre, say, for instance, one-fourth of its diameter from one side of it and three-fourths from the other, the appearances would not be what they are, and we should easily detect the excentricity of our position. Even if we were one-third the diameter from one side and two-thirds from the other, it will, I think, be admitted that this also would have been ascertained by the various methods of research now available. We must, therefore, be somewhere between the actual centre and a circle whose radius is one-third of the distance to the Milky Way. But if we are about midway between these two positions, we shall only be one-sixth of the radius or one-twelfth of the diameter of the Milky Way from its exact centre; and if we form part of a cl.u.s.ter or group of stars slowly revolving around that centre, we should probably obtain all the advantages, if any, that may arise from a nearly central position in the entire star-system.

This question of our situation within the great circle of the Milky Way is of considerable importance from the point of view I am here suggesting, so that every fact bearing upon it should be noted; and there is one which has not, I think, been given the full weight due to it. It is generally admitted that the greater brilliancy of some parts of the Milky Way is no indication of nearness, because surfaces possess equal brilliancy from whatever distance they are seen. Thus each planet has its special brilliancy or reflective power, technically termed its 'albedo,' and this remains the same at all distances if the other conditions are similar. But notwithstanding this well-known fact, Sir John Herschel's remark that the greater brightness of the southern Milky Way 'conveys strongly the impression of greater proximity,' and therefore, that we are excentrically placed in its plane, has been adopted by many writers as if it were the statement of a fact, or at least a clearly expressed opinion, instead of being a mere 'impression,' and really a misleading one. I therefore wish to adduce a phenomenon which has a real bearing on the question. It is evident that, if the Milky Way were actually of uniform width throughout, then differences of apparent width would indicate differences of distance. In the parts nearer to us it would appear wider, where more remote, narrower; but in these opposite directions there would not necessarily be any differences in brightness. We should, however, expect that in the parts nearer to us the lucid stars, as well as those within any definite limits of magnitude, would be either more numerous or more wide apart on the average. No such difference as this, however, has been recorded; but there _is_ a peculiar correspondence in the opposite portions of the Galaxy which is very suggestive. In the beautiful charts of the Nebulae and Star Cl.u.s.ters by the late Mr. Sidney Waters, published by the Royal Astronomical Society and here reproduced by their permission (see end of volume), the Milky Way is delineated in its whole extent with great detail and from the best authorities. These charts show us that, in both hemispheres, it reaches its maximum extension on the right and left margins of the charts, where it is almost equal in extent; while in the centre of each chart, that is at its nearest points to the north and south poles respectively, it is at its narrowest portion; and, although this part in the southern hemisphere is brightest and most strongly defined, yet the actual extent, including the fainter portions, is, again, not very unequal in the opposite segments.

Here we have a remarkable and significant symmetry in the proportions of the Milky Way, which, taken in connection with the nearly symmetrical scattering of the stars in all parts of the vast ring, is strongly suggestive of a nearly circular form and of our nearly central position within its plane. There is one other feature in this delineation of the Milky Way which is worthy of notice. It has been the universal practice to speak of it as being double through a considerable portion of its extent, and all the usual star-maps show the division greatly exaggerated, especially in the northern hemisphere; and this division was considered so important as to lead to the cloven-disc theory of its form, or that it consisted of two separate irregular rings, the nearer one partly hiding the more distant; while various spiral combinations were held by others to be the best way of explaining its complex appearance. But this newer map, reduced from a large one by Lord Rosse's astronomer, Dr. Boedd.i.c.ker, who devoted five years to its delineation, shows us that there is no actual division in any portion of it in the northern hemisphere, but that everywhere, throughout its whole width, it consists of numerous intermingled streams and branches, varying greatly in luminosity, and with many faint or barely distinguishable extensions along its margins, yet forming one unmistakable nebulous belt; and the same general character applies to it in the southern hemisphere as delineated by Dr. Gould.

Another feature, which is well shown to the eye by these more accurate maps, is the regular curvature of the central line of the Milky Way. We can judge of this almost sufficiently by the eye; but if, with a pair of compa.s.ses, we find the proper radius and centre of curvature, we shall see that the true circular curve is always in the very centre of the nebulous ma.s.s, and the same radius applied in the same manner to the opposite hemisphere gives a similar result. It will be noted that as the Milky Way is obliquely situated on these charts, the centre of the curve will be about in R.A. 0h. 40m. in the map of the southern hemisphere, and in R.A.

12h. 40m. in that of the northern hemisphere; while the radius of curvature will be about the length of the chord of eight hours of R.A. as measured on the margin of the maps. This great regularity of curve of the central line of the Galaxy strongly suggests rotation as the only means by which it could have originated and be maintained.

THE SOLAR Cl.u.s.tER

Astronomers are now generally agreed that there is a cl.u.s.ter of stars of which our sun forms a part, though its exact dimensions, form, and limits are still under discussion. Sir William Herschel long ago arrived at the conclusion that the Milky Way 'consists of stars very differently scattered from those immediately around us.' Dr. Gould believed that there were about five hundred bright stars much nearer to us than the Milky Way, which he termed the solar cl.u.s.ter. And Miss Clerke observes that the actual existence of such a cl.u.s.ter is indicated by the fact that 'an enumeration of the stars in photometric order discloses a systematic excess of stars brighter than the 4th magnitude, making it certain that there is an actual condensation in the neighbourhood of the sun--that the average allowance of cubical s.p.a.ce per star is smaller within a sphere enclosing him with a radius, say, of 140 light-years, than further away.'[5]