alone, i.e., to bare visibility. Moving the star to ten times its present distance would increase the surface of the sphere which it illuminates a hundred-fold. We cannot move any special star, but we can examine stars of all brightnesses, and thus (presumably) of all distances.
Herschel's argument was, then, as follows: Since with such a telescope one can see a star ten times as far off as is possible to the naked eye, this telescope has the power of penetrating into space ten times farther than the eye alone. But this number ten, also, expresses the ratio of the diameter of the objective to that of the pupil of the eye, consequently the general law is that the space-penetrating power of a telescope is found by dividing the diameter of the mirror in inches by two-fifths. The diameter of the pupil of the eye (two-fifths of an inch) Herschel determined by many measures.
This simple ratio would only hold good, however, provided no more light were lost by the repeated reflections and refractions in the telescope than in the eye. That light
