small stars, not separately seen with his former
telescopes. "The glorious multitude of stars of all possible sizes
that presented themselves here to my view are truly astonishing; but
as the dazzling brightness of glittering stars may easily mislead
us so far as to estimate their number greater than it really is,
I endeavored to ascertain this point by counting many fields, and
computing from a mean of them, what a certain given portion of
the Milky Way might contain." By this means, applied not only to
the Milky Way but to all parts of the heavens, Herschel determined
the approximate number and distribution of all the stars within
reach of his instrument.

By comparing many hundred gauges or counts of stars visible in
a field of about one-quarter of the area of the moon, Herschel
found that the average number of stars increased toward the great
circle which most nearly conforms with the course of the Milky Way.
Ninety degrees from this plane, at the pole of the Milky Way, only
four stars, on the average, were seen in the field of the telescope.
In approaching the Milky Way this number increased slowly at first,
and then more and more rapidly, until it rose to an average of
122 stars per field.

[Illustration: Fig. 5. Erecting the polar axis of the 100-inch
telescope.]

These observations were made in the northern hemisphere, and
subsequently Sir John Herschel, using his father's telescope at
the Cape of Good Hope, found an almost exactly similar increase
of apparent star density for the southern hemisphere. According to
his estimates, the total number of stars in both hemispheres that
could be seen distinctly enough to be counted in this telescope
would probably be about five and one-half millions.

The Herschels concluded that "the stars of our firmament, instead
of being scattered in all directions indifferently through space,
form a stratum of which the thickness is small, in comparison with
its length and breadth; and in which the earth occupies a place
somewhere about the middle of its thickness, between the point
where it subdivides into two principal laminae inclined at a small
angle to each other." This view does not differ essentially from our
modern conception of the form of the Galaxy; but as the Herschels
were unable to see stars fainter than the fifteenth magnitude,
it is evident that their conclusions apply only to a restricted
region surrounding the solar system, in the midst of the enormously
e