e 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_ (158 x 158 = 24,964). The light from the
nearest star requires some three years to reach the earth. From a star
1,344 times farther it would require about 4,000 years, and for such a
cluster as we have imagined no less than 600,000 years are needed. That
is, the light by which we see such a group has not just now left it.
On the contrary, it has been travelling through space for centuries and
centuries since it first darted forth. It is the ancient history of such
groups that we are studying now, and it was thus that HERSCHEL declared
that telescopes penetrated into time as well as into space.

Other more exact researches on the relative light of stars were made by
HERSCHEL. These were only one more attempt to obtain a scale of
celestial distances, according to which some notion of the limits and of
the interior dimensions of the universe could be gained. Two telescopes,
_exactly equal_ in every respect, were chosen and placed side by side.
Pairs of stars which were _exactly equal_, were selected by means of
them. By diminishing the aperture of one telescope directed to a bright
star, and keeping the other telescope unchanged and directed to a
fainter star, the two stars could be equalized in light, and, from the
relative size of the apertures, the relative light of this pair of stars
could be accurately computed, and so on for other pairs. This was the
first use of the method of _limiting apertures_. His general results
were that the stars of the first magnitude would still remain visible to
the naked eye, even if they were at a distance from us _twelve_ times
their actual distance.

This method received a still further development at his hands. He did
not leave it until he had gained all the information it was capable of
giving. He prepared a set of telescopes collecting 4, 9, 16, etc.
(2 x 2, 3 x 3, 4 x 4, etc.), times as much light as the naked eye.
These were to extend the determinations of distance to the telescopic
stars. For example, a certain portion of the heavens which he examined
contained no star visible to the naked eye, but many telescopic stars.
We cannot say that no one of these is as bright in itself as some of our
first-magnitude stars. Th