observer stationed upon a planet at the center of the cluster, would shine eleven hundred times as bright as Sirius appears to us. The number of the stars in each shell would increase as they receded from the center in proportion to the squares of the radii of the successive shells, while their luminosity, as seen from the center, would vary inversely as those squares. Still, the outermost stars--the total number being limited to fourteen or fifteen thousand--would appear to our observer at the center of the system about five times as brilliant as Sirius. It is clear, then, that he would be dwelling in a sort of perpetual daylight. His planet might receive from the particular sun around which it revolved as brilliant a daylight as our sun gives to us, but let us see what would be the illumination of its night side. Adopting Zoellner's estimate of the light of the sun as 618,000 times as great as that of the full moon, and choosing among the various estimates of the light of Sirius as compared with the sun 1/4000000000 as probably the nearest the truth, we find that the moon sends us about sixty-five hundred times as much light as Sirius does. Now, since the dozen stars nearest the center of the cluster would each appear to our observer eleven hundred times as bright as Sirius, all of them together would give a little more than twice as much light as the full moon sheds upon the earth. But as only half the stars in the cluster would be above the horizon at once we must diminish this estimate by one half, in order to obtain the amount of light that our supposititious planet would receive on its night side from the nearest stars in the cluster. And since the number of these stars increases with their distance from the center in the same ratio as their light diminishes, it follows that the total light received from the cluster would exceed that received from the dozen nearest stars as many times as there were spherical shells in the cluster. This would be about fifteen times, and accordingly all the stars together would shed, at the center, some thirty times as much light as that of the moon. Dividing this again by two, because only half of the stars could be seen at once, we find that the night side of our observer's planet would be illuminated with fifteen times as much light as the full moon sheds upon the earth.