view of afterward drawing such conclusions as we can in regard to their distance.
APPARENT DISTRIBUTION OF THE STARS IN THE SKY.
Distribution of the Lucid Stars: Our question now is how are the stars, as we see them, distributed over the sky? We know in a general way that there are vastly more stars round the belt of the Milky Way than in the remainder of the heavens. But we wish to know in detail what the law of increase is from the poles of the galaxy to the belt itself.
In considering any question of the number of stars in a particular region of the heavens, we are met by a fundamental difficulty. We can set no limit to the minuteness of stars, and the number will depend upon the magnitude of those which we include in our account. As already remarked, there are, at least up to a certain limit, three or four times as many stars of each magnitude as of the magnitude next brighter. Now, the smallest stars that can be seen, or that may be included in any count, vary greatly with the power of the instrument used in making the count. If we had any one catalogue, extending over the whole celestial sphere, and made on an absolutely uniform plan, so that we knew it included all the stars down to some given magnitude, and no others, it would answer our immediate purpose. If, however, one catalogue should extend only to the ninth magnitude, while another should extend to the tenth, we should be led quite astray in assuming that the number of stars in the two catalogues expressed the star density in the regions which they covered. The one would show three or four times as many stars as the other, even though the actual density in the two cases were the same.
If we could be certain, in any one case, just what the limit of magnitude was for any catalogue, or if the magnitudes in different catalogues always corresponded to absolutely the same brightness of the star, this difficulty would be obviated. But this is the case only with that limited number of stars whose brightness has been photometrically measured. In all other cases our count must be more or less uncertain. One illustration of this will suffice:
I have already remarked that in making the photographic census of the southern heavens, Gill and Kapteyn did not assume that stars of which the images were equally intense on different plates were actually of the same magnitude. Each plate was assumed to have a scale of its own, which was fixed by comparing the intensity of the photographic impressions of those stars whose magnitudes had been previously determined with these determinations, and thus forming as it were a separate scale for each plate. But, in forming the catalogue from the international photographic chart of the heavens, it is assumed that the photographs taken with telescopes of the same aperture, in which
