at the distances two, three, four, etc., Herschel called of the second, third, and fourth magnitudes.
By a series of experiments, the details of which cannot be given here, Herschel determined the space-penetrating power of each of his telescopes. The twenty-foot would penetrate into space seventy-five times farther than the naked eye; the twenty-five foot, ninety-six times; and the forty-foot, one hundred and ninety-two times. If the seventh-magnitude stars are those just visible to the naked eye, and if we still suppose all stars to be of equal intrinsic brightness, such seventh-magnitude stars would remain visible in the forty-foot, even if removed to 1,344 times the distance of Sirius (1,344 = 7 x 192). If, further, we suppose that the visibility of a star is strictly proportional to the total intensity of the light from it which strikes the eye, then a condensed cluster of 25,000 stars of the 1,344th magnitude could still be seen in the forty-foot at a distance where each star would have become 25,000 times fainter, that is, at about 158 times the distance of Sirius
