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future than to that of our day. How are men to determine the figure and dimensions of the sidereal system, to understand its structure and complexities, to trace out the motions taking place within its limits, when as yet they seem to have scarce any means of even attempting to solve these problems? Yet here, unless I mistake, is a work from which future astronomers will not shrink, a problem whose solution (for it will be solved) cannot but reveal results altogether surpassing in interest any which astronomers have yet obtained. It is true that if we consider the means we have for attacking this noble problem, they seem ineffective indeed; if we look at the results of past research we find little to encourage present confidence. Yet it is only necessary to consider the amazing interest of the problem to set doubt and irresolution on one side, and at least patiently to test the means we have at our disposal.

I have elsewhere* pointed out reasons for regarding the views hitherto accepted respecting the sidereal system as unsatisfactory. The results obtained by Sir William Herschel, and apparently confirmed by the labours of Sir John Herschel, the elder Struve, and others, seem, according to the evidence I have adduced, to be self-contradictory and not accordant with other equally reliable researches. I confess I can no longer entertain any doubt that there is an error in the

* In Other Worlds than Ours, and more especially the second edition, where additional, and, I think, conclusive arguments are brought forward.

hypothesis which underlies Sir William Herschel's reasoning. It is absolutely essential, if we would form any adequate conceptions at all respecting the nature of the scheme to which the Sun belongs, that that hypothesis and its results should be re-considered. I must avoid here, however, all reference to arguments already enforced, and indeed I propose but to sum up here the results I have exhibited elsewhere, and then to pass on to consider one special circumstance connected with the Sun's relation to his fellow suns-the proper motion by which he speeds through interstellar space.

Sir William Herschel, fired with the noble thought of gauging the celestial depths, took as the fundamental hypothesis on which his gaugings were to rest, the conception that the stars are spread with a certain general uniformity within a definite region of space.* If this one hypothesis be admitted, it becomes possible, by means of a telescope powerful enough to reach the most distant and the smallest stars of the system, to gauge the extent of the system. All that is necessary is to count the number of stars seen in the telescopic field of view when the instrument is directed towards different parts of the heavens. Where many stars are seen, there the system must necessarily have its greatest

It is sometimes added that Sir William Herschel supposed a certain general uniformity of size and brilliancy to exist among the stars. This, however, is a mistake. The only general hypothesis made by Sir William Herschel was the one stated above; he added, as necessary to the admission of his own star-gaugings, the theory that his telescope reached-at least in most directions-the limits of the sidereal system.

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extension; where there are few stars, there the limits of the system must be nearest to us.

It is well known that by this process of star-gauging Sir William Herschel was led to the conclusion that the sidereal system has the form of a cloven disc. The extension of this disc is towards the region of the heavens occupied by the Milky Way, the parts of the heavens where no milky light is seen corresponding to the flattened sides of the disc. According to the essential principle of this method of star-gauging, applied to the observed numerical relations, it follows inevitably that the stars visible to the naked eye lie far within the limits of the cloven disc. The same conclusion follows, also, from Sir John Herschel's gauges of the southern heavens; though his view of the sidereal system differed in this respect from his father's, that he considered the stars visible to the naked eye, and others down to about the tenth magnitude, to be less richly spread through space than those whose united lustre produces the milky light of the galaxy. But whether the richer parts of the sidereal system form, as Sir William Herschel thought, a cloven disc in space, or, as Sir J. Herschel supposes, a cloven ring, surrounding the lucid stars in either case, accepting only Sir William Herschel's fundamental hypothesis, we are bound to admit that the lucid stars lie far within the limits of the sidereal system.* In

* For convenience, astronomers speak of the stars visible to the naked eye as the lucid stars. The title has no reference, it will be understood, to the intrinsic brilliancy of the light of the visible stars.

whatever direction we turn our eyes to look upon the lucid stars, we may be quite certain, if only this hypothesis be true, that the bounds of the star-system lie far beyond the constellations we are regarding.

Now it is at this point that my study of the stars has led to the recognition of evidence which opposes itself in the most striking manner to the views usually accepted. I find among the lucid stars the most convincing signs of aggregation along certain definite regions, and of segregation from others. I have applied to these signs the strictest principles of mathematical calculation, in order to determine whether they can by any possibility be due to chance distribution, and I find that it is wholly impossible so to interpret them. But in this result, regarded by itself, there is in truth nothing opposed to the accepted theories. It is indeed an interesting circumstance that such traces of aggregation and segregation should be recognisable, and perhaps it may seem to many a perplexing circumstance that these signs should so long have escaped recognition. But, apart from the interest thus attaching as I think to the discovery, there is nothing which may not be conceived to accord very well with the views of the Herschels. For such peculiarities of structure, if one may so speak, within the sphere of

This may be ascribed wholly to the strange nature of the staratlases hitherto constructed, in which the authors seem to have studied how they might best (by distorting the celestial spaces and by covering them over with monstrous figures of men and animals) conceal altogether from view any laws of association which may really exist among the stars.

the lucid stars might extend throughout the whole of the 'cloven-disc star-system' conceived by Sir William Herschel, and yet the averages on which he based his conclusions might not be disturbed. It is when another and most unexpected relation is mentioned that the accepted theories are found to fail. The aggregation of stars distinctly recognised in some regions and very marked in others is most marked of all along the Milky Way. Not only are lucid stars so richly strewn on the Milky Way that for the whole heavens to be as richly spread 6,000 new lucid stars would be wanted, but the gaps and lacunæ in the Milky Way are so bare and vacant that were the whole heavens no richer 4,600 stars now visible would have to be blotted from our view. Such, briefly stated, is the statistical evidence on this point. There can be no question that it is of the most convincing character. The probabilities against such a result if chance distribution were alone in question—that is, if no real relation existed between the lucid stars seen amid the milky light of the galaxy and the clustering groups of telescopic stars which produce that light-may be readily shown to be so overwhelming that no illustration can be devised to convey an adequate idea of their immensity. The chance that the Sun will rise to-morrcw is ridiculously small (at least as Quêtelet calculates it) by comparison. So that as long as the laws of probability are to be our guide in such matters (and in every scientific conclusion ever yet adopted we have had no other evidence) it must be regarded as certain that the lucid stars seen

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