I have tested this matter, and the conclusion to which I have been led-this namely, that although among 1,500 or 2,000 points distributed at random over a surface of any kind, certain groups resembling streams might be recognised, such streams would not be nearly so well marked as the streams actually observed among the stars down to the fifth magnitude. But, on the other hand, it is not to be expected that the star streams actually recognised should be so exceedingly well marked and regular, or should be traceable over such great distances, that the reality of the stream-formation would be obvious at once. Had this been the case, indeed, the reasoning by which I have endeavoured to establish the reality of the phenomenon would not have been required. The first astronomers would have recognised the phenomenon as clearly as we can do. Therefore I do not consider the arguments which have been chiefly urged against these streams of lucid stars, regarded as having a real existence, as needing refutation. It has been urged that the streams can only be traced over such and such distances; that they can be carried this way or that, according to fancy, and so on. This, however, was to be expected; if it were otherwise, the reality of the streams would long since have been recognised and apart from this, remembering that we are looking into the depths of space, and that, supposing star streams really to exist, we must see them foreshortened-in many instances projected on a background of stars less systematically distributed, and in other cases mixed up seemingly with other streams, either nearer or farther offthe wonder rather is that any well-marked portion of any stream should be recognisable, than that no stream should be traceable over very large areas on the heavens, and still less from its beginning to its end. That the reader may form his own opinion as to the reality of the streams traceable

among stars down to the fifth magnitude, I give the case of a star-group which is certainly not the most remarkable for streaminess, but chances to be more convenient for the purposes of illustration than most others. Fig. 3 presents the stars forming the connecting band of Pisces. The bright star in the lower left-hand corner is the knot of the band, one part of the band being formed by the curved stream of stars passing to the lower right-hand corner, the other by

In

the curved stream passing, with an inflection near the double star in the figure, towards the upper right-hand corner. this figure the fact that certain sets of stars lie on certain curved lines is of slight significance, for assuredly in any chance distribution of stars the like would be found; the fact which is really significant is the paucity of stars on either side of the curved streams. We have certain lines along which the stars are plentifully strewn, while the adjacent

spaces are relatively vacant. This feature, recognisable not only in this case, but in others, and even more 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. 3, 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 Majoris and from π Argûs. At & Canis Majoris there is another subdivision; one stream of stars passing to κ 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 lucid stars, in the preceding essay and in '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 charts forming Plates I., II. and VI. 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 magnitudes 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 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)

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 create some degree of doubt as to the orders to which the stars belong in some of the charts.