There are in all, in the sky, 20 stars having an apparent magnitude brighter than 1m.5. The brightest of them is Sirius, which, owing to its brilliancy and position, is visible to the whole civilized world. It has a spectrum of the type A0 and hence a colour-index nearly equal to 0.0 (observations in Harvard give c = +0.06). Its apparent magnitude is -1m.6, nearly the same as that of Mars in his opposition. Its absolute magnitude is -0m.3, i.e., fainter than the apparent magnitude, from which we may conclude that it has a distance from us smaller than one siriometer. We find, indeed, from the eighth column that r = 0.5 sir. The proper motion of Sirius is 1″.32 per year, which is rather large but still not among the largest proper motions as will be seen below. From the 11th column we find that Sirius is moving towards us with a velocity of 1.6 sir./st. (= 7.6 km./sec.), a rather small velocity. The third column shows that its right ascension is 6h 40m and its declination -16°. It lies in the square GD7 and its galactic coordinates are seen in the 5th and 6th columns.
The next brightest star is Canopus or α Carinæ at the south sky. If we might place absolute confidence in the value of M (= -8.2) in the 12th column this star would be, in reality, a much more imposing apparition than Sirius itself. Remembering that the apparent magnitude of the moon, according to [§6], amounts to -11.6, we should find that Canopus, if placed at a distance from us equal to that of Sirius (r = 0.5 sir.), would shine with a lustre equal to no less than a quarter of that of the moon. It is not altogether astonishing that a fanciful astronomer should have thought Canopus to be actually the central star in the whole stellar system. We find, however, from column 8 that its supposed distance is not less that 30 sir. We have already pointed out that distances greater than 4 sir., when computed from annual parallaxes, must generally be considered as rather uncertain. As the value of M is intimately dependent on that of r we must consider speculations based on this value to be very vague. Another reason for a doubt about a great value for the real luminosity of this star is found from its type of spectrum which, according to the last column, is F0, a type which, as will be seen, is seldom found among giant stars. A better support for a large distance could on the other hand be found from the small proper motion of this star. Sirius and Canopus are the only stars in the sky having a negative value of the apparent visual magnitude.
Space will not permit us to go through this list star for star. We may be satisfied with some general remarks.
In the fourth column is the galactic square. We call to mind that all these squares have the same area, and that there is therefore the same probability a priori of finding a star in one of the squares as in another. The squares GC and GD lie along the galactic equator (the Milky Way). We find now from column 4 that of the 20 stars here considered there are no less than 15 in the galactic equator squares and only 5 outside, instead of 10 in the galactic squares and 10 outside, as would have been expected. The number of objects is, indeed, too small to allow us to draw any cosmological conclusions from this distribution, but we shall find in the following many similar instances regarding objects that are principally accumulated along the Milky Way and are scanty at the galactic poles. We shall find that in these cases we may generally conclude from such a partition that we then have to do with objects situated far from the sun, while objects that are uniformly distributed on the sky lie relatively near us. It is easy to understand that this conclusion is a consequence of the supposition, confirmed by all star counts, that the stellar system extends much farther into space along the Milky Way than in the direction of its poles.
If we could permit ourselves to draw conclusions from the small material here under consideration, we should hence have reason to believe that the bright stars lie relatively far from us. In other words we should conclude that the bright stars seem to be bright to us not because of their proximity but because of their large intrinsic luminosity. Column 8 really tends in this direction. Certainly the distances are not in this case colossal, but they are nevertheless sufficient to show, in some degree, this uneven partition of the bright stars on the sky. The mean distance of these stars is as large as 7.5 sir. Only α Centauri, Sirius, Procyon and Altair lie at a distance smaller than one siriometer. Of the other stars there are two that lie as far as 30 siriometers from our system. These are the two giants Canopus and Rigel. Even if, as has already been said, the distances of these stars may be considered as rather uncertain, we must regard them as being rather large.
As column 8 shows that these stars are rather far from us, so we find from column 12, that their absolute luminosity is rather large. The mean absolute magnitude is, indeed, -2m.1. We shall find that only the greatest and most luminous stars in the stellar system have a negative value of the absolute magnitude.
The mean value of the proper motions of the bright stars amounts to 0″.56 per year and may be considered as rather great. We shall, indeed, find that the mean proper motion of the stars down to the 6th magnitude scarcely amounts to a tenth part of this value. On the other hand we find from the table that the high value of this mean is chiefly due to the influence of four of the stars which have a large proper motion, namely Sirius, Arcturus, α Centauri and Procyon. The other stars have a proper motion smaller than 1″ per year and for half the number of stars the proper motion amounts to approximately 0″.05, indicating their relatively great distance.
That the absolute velocity of these stars is, indeed, rather small may be found from column 10, giving their radial velocity, which in the mean amounts to only three siriometers per stellar year. From the discussion below of the radial velocities of the stars we shall find that this is a rather small figure. This fact is intimately bound up with the general law in statistical mechanics, to which we return later, that stars with large masses generally have a small velocity. We thus find in the radial velocities fresh evidence, independent of the distance, that these bright stars are giants among the stars in our stellar system.
We find all the principal spectral types represented among the bright stars. To the helium stars (B) belong Rigel, Achernar, β Centauri, Spica, Regulus and β Crucis. To the Sirius type (A) belong Sirius, Vega, Altair, Fomalhaut and Deneb. To the Calcium type (F) Canopus and Procyon. To the sun type (G) Capella and α Centauri. To the K-type belong Arcturus, Aldebaran and Pollux and to the M-type the two red stars Betelgeuze and Antares. Using the spectral indices as an expression for the spectral types we find that the mean spectral index of these stars is +1.1 corresponding to the spectral type F1.