markedly in several instances, is one which cannot reasonably be ascribed to mere coincidence. Let it be noted, moreover, that whatever significance we attach to it, when considering the stars of the first five orders of magnitude, must be enhanced if, as we proceed, we recognise a similar feature (on a different scale, however) among stars of lower orders of magnitude. Throughout this paper, I am not presenting a series of considerations so related one with the other that the failure of one destroys the validity of my reasoning; I am dealing with arguments which are independent of each other, though severally adding to each other's strength. If some of them fail, my case is only pro tanto weakened; it is not by any means destroyed.

Before leaving Fig. 1, however, I would invite special attention to the manner in which the two star streams are conjoined. We see these streams converging upon a single star brighter than those which form the streams themselves; and we may also trace, not indistinctly, a certain general equality of distribution among the stars of the two streams. The former feature is, however, the only one I care at present to dwell upon; and it is to this particular arrangement of streams-two or more (but usually two) proceeding from a single star-or of branches proceeding, as it were, from a single stem, that I have given the title of star sprays. In searching among the star-depths revealed by telescopes of considerable power, many cases may be noticed in which such star sprays exhibit a singular uniformity of structure. The stars of the leading magnitudes are too few in number to afford many well-marked instances. I may note, however, the arrangement of the stars in Coma Berenices as one illustration of this sort; the stars y, 14 and 13, forming the stalk of the spray. Another illustration may be recognised in the stars forming the poop of Argo and the hind-quarters of Canis Major, or (to use a more satisfactory way of indicating the orbs I refer to) the streams of stars converging on & and p Argûs, from Canis Major and from Argûs. At & Canis Major there is another subdivision; one stream of stars passing to Columbæ, the other over u and x Puppis to Argûs. The streams from the water-can of Aquarius form a more extensive, but perhaps less satisfactory, illustration of the same peculiarity.

I need give the less attention to those cases of stream-formation which may be recognised among the stars of the first six orders inclusive, because I have already discussed the relations among the stars, in the second edition of my " Other Worlds." Of the peculiarities of distribution recognisable among the stars there dealt with, I may say with confidence that it is wholly impossible to regard them as accidental; they indicate

beyond all possibility of question the existence of some real cause which has led to a drifting of the stars towards certain regions. As regards such peculiarities of arrangement as would fall more particularly under the head of my present subject, I think it is almost equally impossible to feel any doubt. If some of the streams and reticulations which can be recognised in the isographic chart added to the second edition, be due to chance distribution, the coincidence is very much more remarkable than the theory of star streams which I am at present advocating. It is truer to say, however, that the laws of probability as at present understood will not permit us to regard such singular configurations as accidental.

It would be desirable that we should have equal-surface charts of the heavens to include stars down to the seventh, eighth, and ninth magnitude severally; because it is only by thus considering the separate stages of space-penetration that we can obtain complete recognition of the laws of stellar distribution throughout space. We owe, I think, to the elder Struve the first recognition of the importance of such graduated advances within the star-depths; though he dwelt rather on the importance of star-gauging (and that, also, according to averages) than on the value of star-charts capable of revealing to the eye the statistics of stellar distribution. It will not be difficult to construct charts including stars down to the seventh, and eighth, and ninth orders of magnitude; because as soon as the complete survey of the heavens has been effected after the plan already extended by Argelander to the northern hemisphere, the charts forming the survey, if carefully drawn,* will enable us to construct charts of complete hemispheres including stars down to the seventh, eighth, and ninth magnitudes severally inclusive.

At present, however, for want of such intermediate charts (so to speak) I pass from my equal-surface projection of all the stars down to the sixth magnitude inclusive, to an equal-surface projection which I have just completed, in which all stars in Argelander's series of forty northern maps have been marked in with careful reference as well to their arrangement as to their magnitude. In these forty charts, as many of my readers

It is important that the size of the discs used to indicate the several magnitudes should remain unchanged during the whole process of engraving, and also that the several charts forming the series should be printed with exactly the same degree of fulness. In Argelander's splendid series of forty charts, in which all the northern stars down to the magnitude intermediate between the ninth and tenth are included, slight changes have taken place during the progress of the work, which creates some degree of doubt as to the orders to which the stars belong in some of the charts.

are doubtless aware, Argelander has included all stars down to magnitude nine and a-half, within ninety-two degrees of north polar distance the two degrees south of the equator being added in order to facilitate the comparison of the northern atlas with charts forming the southern survey, one day to be completed (it may be hoped) at southern stations. In all there are 324,198 stars. All these I have carefully copied in, upon a circular chart two feet in diameter, isographically divided (in pencil) by radial lines and circles, into spaces extending one degree in declination and one degree in right ascension for sixty degrees to the north of the equator, the nominal extension in R.A. being correspondingly increased with proximity to the pole. In fact, all the spaces in Argelander's series of charts (some 26,400 in all) were represented in pencil in my projection, before a single star was charted in. Then the stars were carefully copied in, space by space, from Argelander's atle; at such a rate (on the average), that the whole work of charting occupied me about 400 hours.* I do not think that the labour was thrown away, when it is remembered that, as a result, the statistical distribution of all the stars down to the 94th magnitude was presented to the eye. The gauges

of the Herschels had included in all about 160,000 stars, and Struve, in the elaborate series of inquiries on which he founded the theories propounded in his Études d'Astronomie stellaire,' dealt with about 32,000 stars; but the labours of Argelander enabled me not merely to count, but to delineate, 324,198 stars --not merely to draw inferences from statistical enumeration as to the real laws of stellar distribution, but to exhibit those laws of distribution to the eye.

Now the first and most important conclusion deduced from this process of charting relates to the Milky Way; and it will be well to defer the consideration of that conclusion until I come to speak of the Milky Way as itself a vast conglomeration of star streams and star sprays.

But another conclusion, not obviously deducible from the chart itself, or its photographic reductions, was forced upon me in a very marked manner as the work of charting proceeded. Again and again I had occasion to notice the tendency of the

Argelander and his assistants were engaged no less than seven years and one month in completing their magnificent contribution to uranography. The rate at which I copied in the stars was such as to enable me to copy carefully within each space on my projection the stars shown in the corresponding space in the large atlas. It is worthy of notice that a single second of extra time (on the average) per star would have caused an addition of ninety hours', or say ten days', work. The time actually employed on the average was slightly less than four and a half seconds per star.

stars to associate themselves into streams and sprays, the star sprays being ordinarily of the form illustrated in Fig. 1. It would be quite impossible for me to convey by means of pictures any adequate idea of the persistence with which these peculiarities of structure were renewed, especially in certain parts of the chart. Indeed, it would be absolutely necessary to include a much larger portion of the heavens than could here be conveniently pictured, to show the most significant feature of all, the manner namely in which the sprays are divided and sub-divided.

Now the point to be chiefly noticed here is, that so far as à priori considerations are concerned, one would be led to expect that no very marked signs of stream-formation would be shown among stars down nearly to the tenth order of magnitude. For the further we increase our range of vision, the more likely must we be, it would seem, to obtain a view in which the actual relations of the stars are confused by seeming combinations, due to the accidental agreement, in general direction, of star-groups at very different orders of distance. For either there is or there is not a general uniformity of star-magnitude (within certain limits). If there is such uniformity, so that the fainter stars are in reality as large (on the average) as others, but more distant, then it is certain that amongst the stars dealt with in Argelander's charts there are in all directions stars at very different distances; stars therefore not in reality associated, but which yet, being seen in nearly the same direction, are brought into seeming juxtaposition. If, on the other hand, there is not among the stars, even in a general sense, any approach to uniformity of magnitude, then we may be even more completely deceived; for certain near stars which are really very small (relatively) may be brought, not merely into seeming juxtaposition with more distant stars, but even to a seeming equality of magnitude.

This being remembered, it was to be expected that the distribution of the stars included in Argelander's charts would correspond much more closely to a real chance distribution of so many points over a hemisphere, than where we considered only a comparatively small number of stars belonging to the leading orders of magnitude. Moreover, even assuming the point which I am now endeavouring to prove, viz., that the stars are in many cases arranged into the form of streams and sprays, it would yet seem highly probable that all signs of these streams and sprays would be obliterated, simply because streams and sprays of stars would probably lie at very different distances in all directions, and the configuration of the nearer streams would be blended with and confuse the configuration of the more distant.

Figs. 2 and 3 will serve to illustrate my meaning. It is not difficult to recognise in both these figures the existence of star

A portion of one of Argelander's charts, the centre of the space here shown being nearly in 32° N. Dec., and 10h. 28m. R.A.

streams and star sprays too well marked to be regarded as due to accident; but yet we are led to suspect that the streams