3U STAR division between them, so that we may sup- pose them to be clustering toward two differ- ent regions. By a computation founded on observations which ascertain the number of stars in different fields of view, it appears that our space [i. e., our selected region] in Cyg- nus, taking an average breadth of about five degrees of it, contains more than 331,000 stars; and admitting them to be clustering two different ways, we have 165,000 stars for each clustering collection. Now the above mentioned milky appearances deserve the name of clustering collections, as they are certainly much brighter about the middle, and fainter near their undefined borders. . . . We may indeed partly ascribe the increase both of brightness and of apparent compression to a greater depth of the space which contains the stars, but this will equally tend to show their clustering condition ; for since the increase of brightness is gradual, the space containing the clustering stars must tend to a spherical form if the gradual increase of brightness is to be explained by the situation of the stars." That is to say, whether we consider the greater richness in the centre to be due to the cluster- ing of stars toward the middle of these aggre- gations, or to the shape of the groups them- selves, or partly take both causes of central richness into account, we are alike led to the conclusion that the groups are roughly spherical in shape. This conclusion, it need hardly be said, is utterly opposed to Herschel's old belief in a star system generally uniform throughout its whole extent ; for here, and in all similar cases, we see rounded clouds of stars as dis- tinct from the stars scattered around us as rounded clouds in the sky are distinct from a thin low-lying fog through which their shapes are seen. Accordingly, before long Sir W. Herschel saw the necessity of devising a new method of star gauging, based, not on the numerical richness of star fields, but on the telescopic power necessary to effect the reso- lution of the milky light of clustering aggre- gations into discrete stars. By this process lie hoped to determine the relative distances of star groups. Supposing that a particular aggregation began to be resolved into discrete stars with a certain telescopic power, and was entirely resolved when a certain higher power was employed, there would be prima facie evidence as to the distance of the aggregation, if the stars forming different aggregations are similarly distributed. For, given a group of stars of certain sizes and set at certain dis- tances from each other, it is clear that the further away the group is placed, the higher will be the telescopic powers, required (1) to begin and (2) to complete the resolution of that group into separate stars. How perfectly unlike this method was, at once in principle and in practical details, to the former, will be seen from a comparison of the earlier method, above, with the following summary of the qualities of the later method. In the new method, the same part of the heavens was to be examined successively with different tele- scopes ; the observer was not to count stars, but to note the extent to which resolution was effected ; it was assumed that the stars within the clustering aggregations were distributed far more richly than elsewhere ; and the tele- scope was required to effect resolution within a particular region of space, not to merely ex- tend vision to particular distances. It is mani- fest that the new method and the assumptions on which it is based are open to exception. Herschel had found that the stars are not spread uniformly through the star system, as he had before surmised ; and one would have supposed that having thus been misled by one assump- tion, he could not adopt others differing from it in degree only, not in kind. Yet his second method of star gauging could only give him, as he hoped, the means of " ascertaining a scale whereby the extent of the universe, so far as it is possible for us to penetrate into space, may be fathomed," if, first, the stars were spread uniformly within each clustering aggre- gation, and secondly, if different clustering aggregations were similarly constituted. For clearly, if one and the same aggregation in- cluded several orders of stars, each order dis- tributed with a degree of richness peculiar to itself, and still more if there were not even any law of distribution for the several orders, then no reliance could be placed on the method ; for a telescope might effect resolution with respect to some particular order of stars within the aggregation which would leave orders of smaller or more closely set stars within it quite unresolved. Nor again could any comparison be instituted between the distances of two ag- gregations resolved by particular telescopes, even though there were reason to believe that within each there was a general uniformity of distribution, unless we were certain that they were alike in constitution. If the more remote of two aggregations consisted of large stars sparsely strewn, and the nearer consisted of small stars closely set, the two aggregations might require exactly the same power for their resolution, notwithstanding the difference of distance. On the latter point Herschel's ob- servations by the new method could throw little light, since there is no telescopic means of discriminating really large from really small stars. But on the former point he obtained evi- dence which should have been decisive against the new method of gauging, or rather against the assumptions on which it was based. For he observed several clusters which began to be resolved with very low telescopic powers, but were not entirely resolved even with the larg- est telescopes and highest powers Herschel em- ployed. As these clusters were of small extent and round in figure, it followed that if the stars were spread uniformly within them, the extension of these clusters in the direction of the line of sight must enormously exceed their thwart diameter; in other words, that they
