The rate of increase in the number of stars from one magnitude to the next, as shown in § 187, is proof of another kind of irregularity in their distribution. It is not difficult to show, mathematically, that if in distant regions of space the stars were on the average as numerous and as bright as they are in the regions nearer to the sun, then the stars of any particular magnitude ought to be four times as numerous as those of the next brighter magnitude--e. g., four times as many sixth-magnitude stars as there are fifth-magnitude ones. But, as we have already seen in § 187, by actual count there are only three times as many, and from the discrepancy between these numbers, an actual threefold increase instead of a fourfold one, we must conclude that on the whole the stars near the sun are either bigger or brighter or more numerous than in the remoter depths of space. 221. THE STELLAR SYSTEM.--But the arrangement of the stars is not altogether lawless and chaotic; there are traces of order and system, and among these the Milky Way is the dominant feature. Telescope and photographic plate alike show that it is made up of stars which, although quite irregularly scattered along its course, are on the average some twenty times as numerous in the galaxy as at its poles, and which thin out as we recede from it on either side, at first rapidly and then more slowly. This tendency to cluster along the Milky Way is much more pronounced among the very faint telescopic stars than among the brighter ones, for the lucid stars and the telescopic ones down to the tenth or eleventh magnitude, while very plainly showing the clustering tendency, are not more than three times as numerous in the galaxy as in the constellations most remote from it. It is remarkable as showing the condensation of the brightest stars that one half of all the stars in the sky which are brighter than the second magnitude are included within a belt extending 12° on either side of the center line of the galaxy. In addition to this general condensation of stars toward the Milky Way, there are peculiarities in the distribution of certain classes of stars which are worth attention. Planetary nebulæ and new stars are seldom, if ever, found far from the Milky Way, and stars with bright lines in their spectra especially affect this region of the sky. Stars with spectra of the first type--Sirian stars--are much more strongly condensed toward the Milky Way than are stars of the solar type, and in consequence of this the Milky Way is peculiarly rich in light of short wave lengths. Resolvable star clusters are so much more numerous in the galaxy than elsewhere, that its course across the sky would be plainly indicated by their grouping upon a map showing nothing but clusters of this kind.