amount of light emitted by each, and if their diversity of apparent
magnitude were due principally to the greater distance of the fainter
stars, then the brightness of a star would enable us to form a more or
less approximate idea of its distance. But the accumulated researches
of the past seventy years show that the stars differ so enormously in
their actual luminosity that the apparent brightness of a star affords
us only a very imperfect indication of its distance. While, in the
general average, the brighter stars must be nearer to us than the
fainter ones, it by no means follows that a very bright star, even of
the first magnitude, is among the nearer to our system. Two stars are
worthy of especial mention in this connection, Canopus and Rigel. The
first is, with the single exception of Sirius, the brightest star in
the heavens. The other is a star of the first magnitude in the
southwest corner of Orion. The most long-continued and complete
measures of parallax yet made are those carried on by Gill, at the Cape
of Good Hope, on these two and some other bright stars. The results,
published in 1901, show that neither of these bodies has any parallax
that can be measured by the most refined instrumental means known to
astronomy. In other words, the distance of these stars is immeasurably
great. The actual amount of light emitted by each is certainly
thousands and probably tens of thousands of times that of the sun.
Notwithstanding the difficulties that surround the subject, we can at
least say something of the distance of a considerable number of the
stars. Two methods are available for our estimate--measures of parallax
and determination of proper motions.
The problem of stellar parallax, simple though it is in its conception,
is the most delicate and difficult of all which the practical
astronomer has to encounter. An idea of it may be gained by supposing a
minute object on a mountain-top, we know not how many miles away, to be
visible through a telescope. The observer is allowed to change the
position of his instrument by two inches, but no more. He is required
to determine the change in the direction of the object produced by this
minute displacement with accuracy enough to determine the distance of
the mountain. This is quite analogous to the determination of the
change in the direction in which we see a star as the earth, moving
through its vast circuit, passes from one extremity of its orbit to the
other. Representing this motion on such a scale that the distance of
our planet from the sun shall be one inch, we find that the nearest
star, on the same scale, will be more than four miles away, and
scarcely one out of a million will be at a less distance than ten
miles. It is only by the most wonderful perfection both in the
heliometer, the instrument principally used for these measures, and in
methods of observation, that any displacement at all can be seen even
among the nearest stars. The parallaxes of perhaps a hundred stars have
been determined, with greater or less precision, and a few hundred more
may be near enough for measurement. All the others are immeasurably
distant; and it is only by statistical methods based on their proper
motions and their probable near approach to equality in distribution
that any idea can be gained of their distances.
To form a conception of the stellar system, we must have a unit of
measure not only exceeding any terrestrial standard, but even any
distance in the solar system. For purely astronomical purposes the most
convenient unit is the distance corresponding to a parallax of 1",
which is a little more than 200,000 times the sun's distance. But for
the purposes of all but the professional astronomer the most convenient
unit will be the light-year--that is, the distance through which light
would travel in one year. This is equal to the product of 186,000
miles, the distance travelled in one second, by 31,558,000, the number
of seconds in a year. The reader who chooses to do so may perform the
multiplication for himself. The product will amount to about 63,000
times the distance of the sun.
[Illustration with caption: A Typical Star Cluster--Centauri]
The nearest star whose distance we know, Alpha Centauri, is distant
from us more than four light-years. In all likelihood this is really
the nearest star, and it is not at all probable that any other star
lies within six light-years. Moreover, if we were transported to this
star the probability seems to be that the sun would now be the nearest
star to us. Flying to any other of the stars whose parallax has been
measured, we should probably find that the average of the six or eight
nearest stars around us ranges somewhere between five and seven
light-years. We may, in a certain sense, call eight light-years a
star-distance, meaning by this term the average of the nearest
distances from one star to the surrounding ones.
To put the result of measures of parallax into another form, let us
suppose, described around our sun as a centre, a system of concentric
spheres each of whose surfaces is at the distance of six light-years
outside the sphere next within it. The inner is at the distance of six
light-years around the sun. The surface of the second sphere will be
twelve light-years away, that of the third eighteen, etc. The volumes
of space within each of these spheres will be as the cubes of the
diameters. The most likely conclusion we can draw from measures of
parallax is that the first sphere will contain, beside the sun at its
centre, only Alpha Centauri. The second, twelve light-years away, will
probably contain, besides these two, six other stars, making eight in
all. The third may contain twenty-one more, making twenty-seven stars
within the third sphere, which is the cube of three. Within the fourth
would probably be found sixty-four stars, this being the cube of four,
and so on.
Beyond this no measures of parallax yet made will give us much
assistance. We can only infer that probably the same law holds for a
large number of spheres, though it is quite certain that it does not
hold indefinitely. For more light on the subject we must have recourse
to the proper motions. The latest words of astronomy on this subject
may be briefly summarized. As a rule, no star is at rest. Each is
moving through space with a speed which differs greatly with different
stars, but is nearly always swift, indeed, when measured by any
standard to which we are accustomed. Slow and halting, indeed, is that
star which does not make more than a mile a second. With two or three
exceptions, where the attraction of a companion comes in, the motion of
every star, so far as yet determined, takes place in a straight line.
In its outward motion the flying body deviates neither to the right nor
left. It is safe to say that, if any deviation is to take place,
thousands of years will be required for our terrestrial observers to
recognize it.
Rapid as the course of these objects is, the distances which we have
described are such that, in the great majority of cases, all the
observations yet made on the positions of the stars fail to show any
well-established motion. It is only in the case of the nearer of these
objects that we can expect any motion to be perceptible during the
period, in no case exceeding one hundred and fifty years, through which
accurate observations extend. The efforts of all the observatories
which engage in such work are, up to the present time, unequal to the
task of grappling with the motions of all the stars that can be seen
with the instruments, and reaching a decision as to the proper motion
in each particular case. As the question now stands, the aim of the
astronomer is to determine what stars have proper motions large enough
to be well established. To make our statement on this subject clear, it
must be understood that by this term the astronomer does not mean the
speed of a star in space, but its angular motion as he observes it on
the celestial sphere. A star moving forward with a given speed will
have a greater proper motion according as it is nearer to us. To avoid
all ambiguity, we shall use the term "speed" to express the velocity in
miles per second with which such a body moves through space, and the
term "proper motion" to express the apparent angular motion which the
astronomer measures upon the celestial sphere.
Up to the present time, two stars have been found whose proper motions
are so large that, if continued, the bodies would make a complete
circuit of the heavens in less than 200,000 years. One of these would
require about 160,000; the other about 180,000 years for the circuit.
Of other stars having a rapid motion only about one hundred would
complete their course in less than a million of years.
Quite recently a system of observations upon stars to the ninth
magnitude has been nearly carried through by an international
combination of observatories. The most important conclusion from these
observations relates to the distribution of the stars with reference to
the Milky Way, which we have already described. We have shown that
stars of every magnitude, bright and faint, show a tendency to crowd
towards this belt. It is, therefore, remarkable that no such tendency
is seen in the case of those stars which have proper motions large
enough to be accurately determined. So far as yet appears, such stars
are equally scattered over the heavens, without reference to the course
of the Milky Way. The conclusion is obvious. These stars are all inside
the girdle of the Milky Way, and within the sphere which contains them
the distribution in space is approximately uniform. At least there is
no well-marked condensation in the direction of the galaxy nor any
marked thinning out towards its poles. What can we say as to the extent
of this sphere?
To answer this question, we have to consider whether there is any
average or ordinary speed that a star has in space. A great number of
motions in the line of sight--that is to say, in the direction of the
line from us to the star--have been measured with great precision by
Campbell at the Lick Observatory, and by other astronomers. The
statistical investigations of Kaptoyn also throw much light on the
subject. The results of these investigators agree well in showing an
average speed in space--a straight-ahead motion we may call it--of
twenty-one miles per second. Some stars may move more slowly than this
to any extent; others more rapidly. In two or three cases the speed
exceeds one hundred miles per second, but these are quite exceptional.
By taking several thousand stars having a given proper motion, we may
form a general idea of their average distance, though a great number of
them will exceed this average to a considerable extent. The conclusion
drawn in this way would be that the stars having an apparent proper
motion of 10" per century or more are mostly contained within, or lie
not far outside of a sphere whose surface is at a distance from us of
200 light-years. Granting the volume of space which we have shown that
nature seems to allow to each star, this sphere should contain 27,000
stars in all. There are about 10,000 stars known to have so large a
proper motion as 10". But there is no actual discordance between these
results, because not only are there, in all probability, great numbers
of stars of which the proper motion is not yet recognized, but there
are within the sphere a great number of stars whose motion is less than
the average. On the other hand, it is probable that a considerable
number of the 10,000 stars lie at a distance at least one-half greater
than that of the radius of the sphere.
On the whole, it seems likely that, out to a distance of 300 or even
400 light-years, there is no marked inequality in star distribution. If
we should explore the heavens to this distance, we should neither find
the beginning of the Milky Way in one direction nor a very marked
thinning out in the other. This conclusion is quite accordant with the
probabilities of the case. If all the stars which form the groundwork
of the Milky Way should be blotted out, we should probably find
100,000,000, perhaps even more, remaining. Assigning to each star the
space already shown to be its quota, we should require a sphere of
about 3000 light-years radius to contain such a number of stars. At
some such distance as this, we might find a thinning out of the stars
in the direction of the galactic poles, or the commencement of the
Milky Way in the direction of this stream.
Even if this were not found at the distance which we have supposed, it
is quite certain that, at some greater distance, we should at least
find that the region of the Milky Way is richer in stars than the
region near the galactic poles. There is strong reason, based on the
appearance of the stars of the Milky Way, their physical constitution,
and their magnitudes as seen in the telescope, to believe that, were we
placed on one of these stars, we should find the stars around us to be
more thickly strewn than they are around our system. In other words,
the quota of space filled by each star is probably less in the region
of the Milky Way than it is near the centre where we seem to be
situated.
We are, therefore, presented with what seems to be the most
extraordinary spectacle that the universe can offer, a ring of stars
spanning it, and including within its limits by far the great majority
of the stars within our system. We have in this spectacle another
example of the unity which seems to pervade the system. We might
imagine the latter so arranged as to show diversity to any extent. We
might have agglomerations of stars like those of the Milky Way situated
in some corner of the system, or at its centre, or scattered through it
here and there in every direction. But such is not the case. There are,
indeed, a few star-clusters scattered here and there through the
system; but they are essentially different from the clusters of the
Milky Way, and cannot be regarded as forming an important part of the
general plan. In the case of the galaxy we have no such scattering, but
find the stars built, as it were, into this enormous ring, having
similar characteristics throughout nearly its whole extent, and having
within it a nearly uniform scattering of stars, with here and there
some collected into clusters. Such, to our limited vision, now appears
the universe as a whole.
We have already alluded to the conclusion that an absolutely infinite
system of stars would cause the entire heavens to be filled with a
blaze of light as bright as the sun. It is also true that the
attractive force within such a universe would be infinitely great in
some direction or another. But neither of these considerations enables
us to set a limit to the extent of our system. In two remarkable papers
by Lord Kelvin which have recently appeared, the one being an address
before the British Association at its Glasgow meeting, in 1901, are
given the results of some numerical computations pertaining to this
subject. Granting that the stars are scattered promiscuously through
space with some approach to uniformity in thickness, and are of a known
degree of brilliancy, it is easy to compute how far out the system must
extend in order that, looking up at the sky, we shall see a certain
amount of light coming from the invisible stars. Granting that, in the
general average, each star is as bright as the sun, and that their
thickness is such that within a sphere of 3300 light-years there are
1,000,000,000 stars, if we inquire how far out such a system must be
continued in order that the sky shall shine with even four per cent of
the light of the sun, we shall find the distance of its boundary so
great that millions of millions of years would be required for the
light of the outer stars to reach the centre of the system. In view of
the fact that this duration in time far exceeds what seems to be the
possible life duration of a star, so far as our knowledge of it can
extend, the mere fact that the sky does not glow with any such
brightness proves little or nothing as to the extent of the system.
We may, however, replace these purely negative considerations by
inquiring how much light we actually get from the invisible stars of
our system. Here we can make a definite statement. Mark out a small
circle in the sky 1 degree in diameter. The quantity of light which we
receive on a cloudless and moonless night from the sky within this
circle admits of actual determination. From the measures so far
available it would seem that, in the general average, this quantity of
light is not very different from that of a star of the fifth magnitude.
This is something very different from a blaze of light. A star of the
fifth magnitude is scarcely more than plainly visible to ordinary
vision. The area of the whole sky is, in round numbers, about 50,000
times that of the circle we have described. It follows that the total
quantity of light which we receive from all the stars is about equal to
that of 50,000 stars of the fifth magnitude--somewhat more than 1000 of
the first magnitude. This whole amount of light would have to be
multiplied by 90,000,000 to make a light equal to that of the sun. It
is, therefore, not at all necessary to consider how far the system must
extend in order that the heavens should blaze like the sun. Adopting
Lord Kelvin's hypothesis, we shall find that, in order that we may
receive from the stars the amount of light we have designated, this
system need not extend beyond some 5000 light-years. But this
hypothesis probably overestimates the thickness of the stars in space.
It does not seem probable that there are as many as 1,000,000,000 stars
within the sphere of 3300 light-years. Nor is it at all certain that
the light of the average star is equal to that of the sun. It is
impossible, in the present state of our knowledge, to assign any
definite value to this average. To do so is a problem similar to that
of assigning an average weight to each component of the animal
creation, from the microscopic insects which destroy our plants up to
the elephant. What we can say with a fair approximation to confidence
is that, if we could fly out in any direction to a distance of 20,000,
perhaps even of 10,000, light-years, we should find that we had left a
large fraction of our system behind us. We should see its boundary in
the direction in which we had travelled much more certainly than we see
it from our stand-point.
We should not dismiss this branch of the subject without saying that
considerations are frequently adduced by eminent authorities which tend
to impair our confidence in almost any conclusion as to the limits of
the stellar system. The main argument is based on the possibility that
light is extinguished in its passage through space; that beyond a
certain distance we cannot see a star, however bright, because its
light is entirely lost before reaching us. That there could be any loss
of light in passing through an absolute vacuum of any extent cannot be
admitted by the physicist of to-day without impairing what he considers
the fundamental principles of the vibration of light. But the
possibility that the celestial spaces are pervaded by matter which
might obstruct the passage of light is to be considered. We know that
minute meteoric particles are flying through our system in such numbers
that the earth encounters several millions of them every day, which
appear to us in the familiar phenomena of shooting-stars. If such
particles are scattered through all space, they must ultimately
obstruct the passage of light. We know little of the size of these
bodies, but, from the amount of energy contained in their light as they
are consumed in the passage through our atmosphere, it does not seem at
all likely that they are larger than grains of sand or, perhaps, minute
pebbles. They are probably vastly more numerous in the vicinity of the
sun than in the interstellar spaces, since they would naturally tend to
be collected by the sun's attraction. In fact there are some reasons
for believing that most of these bodies are the debris of comets; and
the latter are now known to belong to the solar system, and not to the
universe at large.
But whatever view we take of these possibilities, they cannot
invalidate our conclusion as to the general structure of the stellar
system as we know it. Were meteors so numerous as to cut off a large
fraction of the light from the more distant stars, we should see no
Milky Way, but the apparent thickness of the stars in every direction
would be nearly the same. The fact that so many more of these objects
are seen around the galactic belt than in the direction of its poles
shows that, whatever extinction light may suffer in going through the
greatest distances, we see nearly all that comes from stars not more
distant than the Milky Way itself.
Intimately connected with the subject we have discussed is the question
of the age of our system, if age it can be said to have. In considering
this question, the simplest hypothesis to suggest itself is that the
universe has existed forever in some such form as we now see it; that
it is a self-sustaining system, able to go on forever with only such
cycles of transformation as may repeat themselves indefinitely, and
may, therefore, have repeated themselves indefinitely in the past.
Ordinary observation does not make anything known to us which would
seem to invalidate this hypothesis. In looking upon the operations of
the universe, we may liken ourselves to a visitor to the earth from
another sphere who has to draw conclusions about the life of an
individual man from observations extending through a few days. During
that time, he would see no reason why the life of the man should have
either a beginning or an end. He sees a daily round of change, activity
and rest, nutrition and waste; but, at the end of the round, the
individual is seemingly restored to his state of the day before. Why
may not this round have been going on forever, and continue in the
future without end? It would take a profounder course of observation
and a longer time to show that, notwithstanding this seeming
restoration, an imperceptible residual of vital energy, necessary to
the continuance of life, has not been restored, and that the loss of
this residuum day by day must finally result in death.
The case is much the same with the great bodies of the universe.
Although, to superficial observation, it might seem that they could
radiate their light forever, the modern generalizations of physics show
that such cannot be the case. The radiation of light necessarily
involves a corresponding loss of heat and with it the expenditure of
some form of energy. The amount of energy within any body is
necessarily limited. The supply must be exhausted unless the energy of
the light sent out into infinite space is, in some way, restored to the
body which expended it. The possibility of such a restoration
completely transcends our science. How can the little vibration which
strikes our eye from some distant star, and which has been perhaps
thousands of years in reaching us, find its way back to its origin? The
light emitted by the sun 10,000 years ago is to-day pursuing its way in
a sphere whose surface is 10,000 light-years distant on all sides.
Science has nothing even to suggest the possibility of its restoration,
and the most delicate observations fail to show any return from the
unfathomable abyss.
Up to the time when radium was discovered, the most careful
investigations of all conceivable sources of supply had shown only one
which could possibly be of long duration. This is the contraction which
is produced in the great incandescent bodies of the universe by the
loss of the heat which they radiate. As remarked in the preceding
essay, the energy generated by the sun's contraction could not have
kept up its present supply of heat for much more than twenty or thirty
millions of years, while the study of earth and ocean shows evidence of
the action of a series of causes which must have been going on for
hundreds of millions of years.
The antagonism between the two conclusions is even more marked than
would appear from this statement. The period of the sun's heat set by
the astronomical physicist is that during which our luminary could
possibly have existed in its present form. The period set by the
geologist is not merely that of the sun's existence, but that during
which the causes effecting geological changes have not undergone any
complete revolution. If, at any time, the sun radiated much less than
its present amount of heat, no water could have existed on the earth's
surface except in the form of ice; there would have been scarcely any
evaporation, and the geological changes due to erosion could not have
taken place. Moreover, the commencement of the geological operations of
which we speak is by no means the commencement of the earth's
existence. The theories of both parties agree that, for untold aeons
before the geological changes now visible commenced, our planet was a
molten mass, perhaps even an incandescent globe like the sun. During
all those aeons the sun must have been in existence as a vast nebulous
mass, first reaching as far as the earth's orbit, and slowly
contracting its dimensions. And these aeons are to be included in any
estimate of the age of the sun.