Mag. 1 Total Light = 1 " 2 " = 1.4 " 3 " = 2.0 " 4 " = 2.8 " 5 " = 4.0 " 6 " = 5.7 " 7 " = 8.0 " 8 " = 11.3 " 9 " = 16.0 " 10 " = 22.6 -------- Total light to Mag. 10 = 74.8 -------- Thus the total amount of the light given by all stars down to the tenth magnitude is seventy-four times as great as that from the few first magnitude stars. We also see that the light given by the stars of any magnitude is twice as much as that of the stars two magnitudes higher in the scale, so that we can easily calculate what additional light we ought to receive from each additional magnitude if they continue to increase in numbers below the tenth as they do above that magnitude. Now it has been calculated as the result of careful observations, that the total light given by stars down to nine and a half magnitude is one-eightieth of full moonlight, though some make it much more. But if we continue the table of light-ratios from this low starting-point down to magnitude seventeen and a half, we shall find, if the numbers of the stars go on increasing at the same rate as before, that the light of all combined should be at least seven times as great as moonlight; whereas the photometric measurements make it actually about one-twentieth. And as the calculation from light-ratios only includes stars just visible in the largest telescopes, and does not include all those proved to exist by photography, we have in this case a demonstration that the numbers of the stars below the tenth and down to the seventeenth magnitude diminish rapidly. We must remember that the minuter telescopic stars preponderate enormously in and near the Milky Way. At a distance from it they diminish rapidly, till near its poles they are almost entirely absent. This is shown by the fact (already referred to at p. 146) that Professor Celoria of Milan, with a telescope of less than three inches aperture, counted almost as many stars in that region as did Herschel with his eighteen-inch reflector. But if the stellar universe extends without limit we can hardly suppose it to do so in one plane only; hence the absence of the minuter stars and of diffused milky light over the larger part of the heavens is now held to prove that the myriads of very minute stars in the Milky Way really belong to it, and not to the depths of space far beyond. It seems to me that here we have a fairly direct proof that the stars of our universe are really limited in number. There are thus four distinct lines of argument all pointing with more or less force to the conclusion that the stellar universe we see around us, so far from being infinite, is strictly limited in extent and of a definite form and constitution. They may be briefly summarised as follows:--