Closely connected with the work of cataloguing the stars is that of
enumerating them. In view of what may possibly be associated with
any one star--planets with intellectual beings inhabiting them--the
question how many stars there are in the heavens is one of perennial
interest. But beyond the general statement we have already made, this
question does not admit of even an approximate answer. The question
which we should be able to answer is this: How many stars are there
of each easily visible magnitude? How many of the first magnitude, of
the second, of the third, and so on to the smallest that have been
measured? Even in this form we cannot answer the question in a way
which is at the same time precise and satisfactory. One magnitude
merges into another by insensible gradations, so that no two observers
will agree as to where the line should be drawn between them. The
difficulty is enhanced by the modern system--very necessary, it is
true--of regarding magnitude as a continuously varying quantity and
estimating it with all possible precision. In adjusting the new system
to the old one, it may be assumed that an average star of any given
magnitude on the old system would be designated by the corresponding
number on the new system. For example, an average star of the fourth
magnitude would be called 4.0; one of the fifth, 5.0, etc. Then the
brightest stars, which formerly were called of the fourth magnitude,
would now be, if the estimate were carried to hundredths, 3.50, while
the faintest would be 4.50. What were formerly called stars of the
fifth magnitude would range from 4.50 to 5.50, and so on. But we have
meet with a difficulty when we come to the sixth magnitude. On the
modern system, magnitude 6.0 represents the faintest star visible to
the naked eye; but the stars formerly included in this class would,
on the average, be somewhat brighter than this, because none could be
catalogued except those so visible.
The most complete enumeration of the lucid stars by magnitudes has been
made by Pickering (‘Annals of the Harvard Observatory,’ Vol. XIV). The
stars were classified by half magnitudes, calling
M. M.
Mag. 2.0 all from 1.75 to 2.25
2.5 all from 2.25 to 2.75
etc., etc.
For the northern stars Pickering used the Harvard Photometry; for the
southern, Gould’s ‘Uranometria Argentina.’ A zone from the equator to
30° south declination is common to both; for this zone I use Gould.
The number of each class in the entire sky, north and south of the
celestial equator, is as follows:
Northern Southern
Hemisphere. Hemisphere.
Pickering. Gould. Total.
1± 9 14 23
2.0 17 15 32
2.5 17 24 41
3.0 37 41 78
3.5 61 74 135
4.0 114 126 240
4.5 228 234 462
5.0 450 426 876
5.5 787 681 1,468
6.0 789 1,189 1,978
----- ----- -----
Sum. 2,509 2,824 5,333
It would seem from this that the number of lucid stars in the southern
celestial hemisphere is 315 greater than in the northern. But this
arises wholly from a seemingly greater number of stars of magnitude 6.
In the zone 0° to 30° S., Pickering has 214 stars of this class fewer
than Gould. Hence it is not likely that there is any really greater
richness of the southern sky.
The total number of lucid stars is thus found to be 5,333. But it is
not likely that stars of magnitudes 6.1 and 6.2 should be included in
this class, though this is done in the above table. From a careful
study and comparison of the same data from Pickering and Gould,
Schiaparelli enumerated the stars to magnitude 6.0. He found:
North pole to 30° S. 3,113 stars.
30° S. to south pole 1,190 stars.
-----
Total lucid stars 4,303
For most purposes a classification by entire magnitudes is more
instructive than one by half magnitudes. From the third magnitude
downward we may assume that 40 per cent. of the stars of each half
magnitude belong to the magnitude next above, and 60 per cent. to that
next below. We thus find that of
Total.
Mag. 0 and 1 there are 21 stars 21
Mag. 2 there are 52 stars 73
Mag. 3 there are 157 stars 230
Mag. 4 there are 506 stars 736
Mag. 5 there are 1,740 stars 2,476
Mag. 6 there are 5,171 stars 7,647
Here it is to be remarked that under magnitude 6 are included many
other than the lucid stars, namely, all down to magnitude 6.4. The last
column gives the entire number of stars down to each order of magnitude.
It will be remarked that the number of stars of each order is rather
more than three times that of the order next higher. How far does this
law extend? Argelander’s ‘Durchmusterung,’ which is supposed to include
all stars to magnitude 9.5, gives 315,039 stars for the northern
hemisphere, from which it would be inferred that the whole sky contains
630,000 stars to the ninth magnitude. Comparing this with the number
7,647 of stars to the magnitude 6.5, we see that it is forty-fold, so
that it would require a ratio of about 3.5 from each magnitude to the
next lower. But it is now found that Argelander’s list contains, in the
greater part of the heavens, all the stars to the tenth magnitude.
On the other hand, Thome’s Cordoba ‘Durchmusterung’ gives 340,380 stars
between the parallels -22° and -42°. This is 0.14725 of the whole sky,
so that, on Thome’s scale of magnitude, there are about 2,311,000 stars
to the tenth magnitude in the sky. This is more than three times the
Argelander number to the ninth magnitude.
It would, therefore, seem that the ratio of number for each magnitude
must exceed 3, even up to the tenth. If a ratio of only 3 extends four
steps farther, the whole number of stars in the sky down to magnitude
14.5 inclusive must approach 200 millions. Until the international
photographic chart of the sky is subjected to a detailed examination,
it is impossible to make an estimation with any approach to certainty.