with this special telescope, which makes it one hundred
times more brilliant in appearance. If we could move the star bodily
away from us to a distance ten times its present distance, we could thus
reduce its brightness, as seen with the telescope, to what it was at
first, as seen with the eye 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 must be so lost was evident, but no data
existed for determining the loss. HERSCHEL was thus led to a long series
of photometric experiments on the reflecting powers of the metals used
in his mirrors, and on the amount of light transmitted by lenses.
Applying the corrections thus deduced experimentally, he found that the
space-penetrating power of his twenty-foot telescope, with which he made
his star-gauges, was sixty-one times that of the unassisted eye, while
the space-penetrating power of his great forty-foot telescope was one
hundred and ninety-two times that of the eye. In support of his
important conclusions HERSCHEL had an almost unlimited amount of
experimental data in the records of his observations, of which he made
effective use.

By far the most important of HERSCHEL'S work in the domain of pure
physics was published in the same year (1800), and related to radiant
heat. The investigation of the space-penetrating powers of telescopes
was undertaken for the sole purpose of aiding him in measuring the
dimensions of the stellar universe, and there was no temptation for him
to pur