tars, and so on with
the successive spheres. For instance, the sphere of radius 7 has room
for 343 stars, but of this space 125 parts belong to the spheres inside
of it; there is, therefore, room for 218 stars between the spheres of
radii 5 and 7.

HERSCHEL designates the several distances of these layers of stars as
orders; the stars between spheres 1 and 3 are of the first order of
distance, those between 3 and 5 of the second order, and so on.
Comparing the room for stars between the several spheres with the number
of stars of the several magnitudes which actually exists in the sky, he
found the result to be as follows:

--------------------------------------------------------
Order of | Number of | | Number of
Distance. | Stars there | Magnitude. | Stars of that
| is Room for. | | Magnitude.
--------------------------------------------------------
1........ | 26 | 1 | 17
2........ | 98 | 2 | 57
3........ | 218 | 3 | 206
4........ | 386 | 4 | 454
5........ | 602 | 5 | 1,161
6........ | 866 | 6 | 6,103
7........ | 1,178 | 7 | 6,146
8........ | 1,538 | |
---------------------------------------------------------

The result of this comparison is, that if the order of magnitudes could
indicate the distance of the stars, it would denote at first a gradual
and afterward a very abrupt condensation of them, at and beyond the
region of the sixth-magnitude stars.

If we assume the brightness of any star to be inversely proportional to
the square of its distance, it leads to a scale of distance different
from that adopted by HERSCHEL, so that a sixth-magnitude star on the
common scale would be about of the eighth order of distance according to
this scheme--that is, we must remove a star of the first magnitude to
eight times its actual distance to make it shine like a star of the
sixth magnitude.

On the scheme here laid down, HERSCHEL subsequently assigned the _order_
of distance of various objects, mostly star-clusters, and his estimates
of these distances are still quoted. They rest on the fundamental
hypothesis which has been explained, and the error in the assumption of
equal intrinsic brilliancy for all stars affects these estimates. It is
perhaps pro