examination of the line-of-sight velocities of stars from the same
point of view, this physical interpretation must be received with some
degree of caution; but there can be no doubt of the reality of the
anomalies in the statistical distribution of proper motions of the
stars, and of these it offers a simple and adequate explanation.
Having determined the motions of the two drifts, and knowing also that the; stars are nearly equally divided between them, it is evidently possible to determine the mean motion of the drifts combined. This is of course that relative motion of the sun and stars which we have previously called the solar motion. The position of the solar apex calculated in this way agrees satisfactorily with that found by the usual methods. It is naturally fairly close to the apex of the faster drift, but is displaced from it in the direction of the apex of the other drift. In this connexion it may be noticed that, when the smaller and larger proper motions are discussed separately, the latter category will include an unduly great proportion of stars belonging to the fast-moving drift, and the resulting determination will lead to a solar apex too near the apex of that drift, i.e. with too low a declination. This appears to be the explanation of Stumpe’s and Porter’s results; they both divided their proper motions into groups according to theif numerical amount, and found that the declination of the solar apex progressively increased as the size of the motions used diminished. Another anomalous determination of the apex, due to H. A. Kobold (Astro. Nach., 3163, 3451, and 3491) is also explained when the two drifts are recognized. Kobold, using a peculiar and ingenious method, found for it a declination -3°, which disagrees very badly with all other determinations; but it is a peculiarity of Kobold’s method that it gives the line of symmetry of motion, which joins the apex and antapex, without indicating which end is the apex. Now the position of this line, as found by Kobpld, actually is a (properly weighted) mean between the corresponding lines of symmetry of the two drifts, but naturally it lies in the acute angle between them, whereas the line of the solar motion is also a weighted mean between the two lines of drift, but lies in the obtuse angle between them.
The Structure of the Universe.—We now arrive at the greatest of all the problems of sidereal astronomy, the structure and nature of the universe as a whole. It can by no means be taken for granted that the universe has anything that may properly be called a structure. If it is merely the aggregate of the stars, eac.h star or small group of stars may be a practically independent unit, its birth and development taking place without any relation to the evolution of the whole. But it is becoming more and more generally recognized that the stars are not unrelated; they are parts of a greater system, and we have to deal with, not merely the history of a number of independent units, but with a far vaster conception, the evolution and development of an ordered universe.
Our first inquiry is whether the universe extends indefinitely
in all directions, or whether there are limits beyond which the stars
are not distributed. It is not difficult to obtain at least
a partial answer to this question; anything approaching
a uniform distribution of the stars cannot extend
Limits of the
Universe.
indefinitely. It can be shown that, if the density of distribution
of the stars through infinite space is nowhere less than a certain
limit (which may be as small as we please), the total amount of light
received from them (assuming that there is no absorption of light in
space) would be infinitely great, so that the background of the sky
would shine with a. dazzling brilliancy. We therefore conclude that
beyond a certain distance there is a thinning out in the distribution
of the stars; the stars visible in our telescopes form a universe having
a more or less defined boundary; and, if there are other systems
of stars unknown to us in the space beyond, they are, as it were,
isolated from the universe in which we are. It is necessary however
to emphasize that the foregoing argument assumes that there is no
appreciable absorption of light in interstellar space. Recently,
however, the trend of astronomical opinion has been rather in
favour of the belief that diffused matter may exist through space
in sufficient quantity to cause appreciable absorption; so that the
argument has no longer the weight formerly attached to it.
Another line of reasoning indicates that the boundary of the universe
is not immeasurably distant, and that the thinning out of the stars
is quite perceptible with our telescopes. This depends on the law
of progression in the number of stars as the brightness diminishes.
If the stars were all of the same intrinsic brightness it is
evident that the comparison of the number of stars of successive
magnitudes would show directly where the decreased density of
distributibn began. Actually we know that the intrinsic brightness
varies very greatly, so that each increase of telescopic power not
only enables us to see stars more remote than before, but also reveals
very many smaller stars within the limits previously penetrated.
But notwithstanding the great variety of intrinsic brightness of the
stars, the ratio of the number of stars of one magnitude to the
number of the magnitude next lower (the “star-ratio”) is a guide
to the uniformity of their distribution. If the uniform distribution
extends indefinitely, or as far as the telescope can penetrate, the
star-ratio should have the theoretical value 3·98,[1] any decrease in
density or limit to the distribution of the stars will be indicated
by a continual falling off in the star-ratio for the higher magnitudes.
H. H. Seeliger, who investigated this ratio for the stars of the
Bonn Durchmusterung and Southern Durchmusterung, came to the
Conclusion (as summarized by Simon Newcomb) that for these
stars the ratio ranges from 3·85 to 3·28, the former value being
found for regions near the Milky Way and the latter for regions
near the galactic poles. There is here evidence that even among
stars of the Durchmusterung (9·5 magnitude), a limit of the universe
has been reached, at least in the direction normal to the plane of
the Milky Way. For the higher magnitudes J. C. Kapteyn has
shown that the star-ratio diminishes still further.
In all investigations into the distribution of the stars in space
one fact stands out pre-eminently, viz. the existence of a certain
plane fundamental to the structure of the heavens.
This is the galactic plane, well known from the fact that
it is marked in the sky by the broad irregular belt of
milky light called the Galaxy or Milky Way. But it
The
Galactic
Plane.
is necessary to make a careful distinction between the galactic
plane and the Galaxy itself; the totter, though it is necessarily
one of the most remarkable features of the universe, is not
the only peculiarity associated with the galactic plane: Its particular
importance consists in the fact that the stars, bright as well
as faint, crowd towards this plane. This apparent relation of the
lucid stars to the Galaxy was first pointed out by Sir W. Herschel.
For the stars visible to the naked eye a very thorough investigation
by G. V. Schiaparelli has shown the relation in a striking manner.
He indicated on planispheres the varying density of distribution
of the stars over the sky. On these the belt of greatest density
can be easily traced, and it follows very closely the course of the
Milky Way; but, whereas the latter is a belt having rather sharply
defined boundaries, the star-density decreases gradually and continuously
from the galactic equator to the galactic poles. The
same result for the great mass of fainter stars has been shown by
Seeliger. The following table shows the density with which stars
brighter than the ninth magnitude are distributed in each of nine
zones into which Seeliger divided the heavens:—
| Galactic latitude | N. Pole to 70° N. |
70° N. to 50° N. |
50° N. to 30° N. |
30° N. to 10° N. |
10° N. to 10° S. |
10° S. to 30°S. |
30° S. to 50° S. |
50° S. to 70° S. |
70° S. to S. Pole | |
| Number of stars per square degree | 2·78 | 3·03 | 3·54 | 5·32 | 8·17 | 6·07 | 3·71 | 3·21 | 3·14 | |
The table, which is based on over 130,000 stars, shows that along
the galactic circle the stars are scattered nearly three times more
thickly than at the north and south poles of the Galaxy. What,
however, is of particular importance is that the increase is gradual.
No doubt many of the lucid stars which appear to lie in the Milky
Way actually belong to it, and the presence of this unique cluster
helps to swell the numbers along the galactic equator; but, for
example, the increased density between latitudes 30° to 50° (both
north and south) as Compared with the density at the poles cannot
be attributed to the Galaxy itself, for the Galaxy passes nowhere
near these zones. The star-gauges of the Herschels exhibit a
similar result; the Herschels counted the number of stars visible
with their powerful telescopes in different regions of the sky, and
thus formed comparative estimates of the density of the stars
extending to a very high magnitude. According to their results
the star-density increases continuously from 109 per square degree
at the poles to 2019 along the galactic equator. In general, the
fainter the stars included in the discussion the more marked is their
crowding towards the galactic plane. Various considerations tend
to show that this apparent crowding does not imply a really greater
density or clustering of the stars in space, but is due to the fact
that in these directions we look through a greater depth of stars
before coming to the boundary of the stellar system. Sir William
Herschel and afterwards F. G. W. Struve developed the view that
the stars are contained in a comparatively thin stratum bounded
by two parallel planes. The shape of the universe may thus be
compared to that of a grindstone
or lens, the sun being
situated about midway between
the two surfaces. Thus
the figure, represents a section
of the (ideally simplified) universe
cut perpendicular to
- ↑ This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
