generally moving with different speeds, the normal spectrum of a binary
system consists of two distinct superposed spectra, the two spectra
shewing different shifts which correspond to the speeds of the two
components. From the observed orbits of the two components of a binary
system, an astronomer might proceed to calculate with what speeds these
components would move in the direction of the line of sight, and could
then predict to what extent the two spectra ought to be displaced
if the light from the system were analysed in a spectroscope; the
spectroscope would of course confirm his prediction.
It is more instructive to imagine the reverse process. Suppose that on
analysing the light from a star, the astronomer obtains a composite
spectrum in which two distinct spectra shift rhythmically backwards
and forwards about their normal position. The fact that there are two
spectra tells him that he is dealing with a binary system; if the
rhythmic shift repeats itself every two years, he knows that its orbit
takes two years to complete. He studies the star by direct vision and
finds it is a binary system in which the constituents revolve about one
another every two years.
He examines another spectrum, and finds that it shifts rhythmically
every two days. On looking directly at this star he can only see a
single point of light. There must, of course, be two stars, but the
mere fact that they get around one another in so short a time as two
days proves that they must be very close to one another, and he need
feel no surprise that his telescope has failed to separate the image
into two distinct points of light. Systems of this kind, which the
spectroscope shews to be binary, but the telescope usually shews as
a single point of light, are called “spectroscopic binaries.” Over a
thousand such systems are known.
If the astronomer tries to construct the orbit of such a system from
the spectroscopic observations alone, he finds himself in difficulties.
His observations only tell him the velocities along the line of
sight, and these depend both on the actual speed and on the degree of
foreshortening; the same velocity may arise either from a big orbit in
a plane nearly at right angles to the line of sight, or from a much
foreshortened little orbit. It is impossible to calculate the actual
orbit or the weights of the stars from spectroscopic observation alone.
[Illustration: Fig. 5. The little orbit _AA′_ and the big orbit _BB′_
give the same velocities along the line of sight _CE_.]
ECLIPSING BINARIES. There is one exception. Suppose that a star’s light
is seen to diminish in amount at regular intervals and subsequently
to return to its original strength. The obvious interpretation of the
diminution of light is that one component of the system is eclipsing
the other, and this can only happen if the orbit is so completely
foreshortened that its plane passes through, or at least very close
to, the earth. In such a case it is possible to reconstruct the whole
orbit, and thence to calculate the weights of the two components. Not
only so, but the length of time during which the eclipses last tells
us the actual sizes of the two components, so that it is possible to
draw a complete picture of the system. Diagrams of the dimensions and
orbits of two typical eclipsing binaries are shewn in fig. 6; these
are drawn to the same scale, this being indicated by the small circle
representing the sun.
[Illustration: Fig. 6. Components and orbits of Eclipsing Binaries.]
When no eclipse occurs in a spectroscopic binary, we do not know how
much foreshortening to allow for, but we can obtain a general idea
of the weights of the components by assuming an average degree of
foreshortening. If we assume different degrees of foreshortening in
turn, we shall find that the computed weights come out least when the
plane of the orbit is assumed to pass through the earth—i.e. when the
orbits are computed as though the system were an eclipsing one. Thus
although we cannot discover the actual weights of the components of a
non-eclipsing binary, we can always state limits above which they must
lie, namely the weights computed as though the system were an eclipsing
one. In this way, we know that the two components of Plaskett’s star
must have more than 75 and 63 times the weight of the sun.
VARIABLE STARS
The majority of stars shine with a perfectly steady light, so that we
can say that a star is of so many candle-power. The sun, for instance,
emits a light of 3·23 × 10²⁷ candle-power.
Yet there are classes of exceptional stars in which the light flickers
up and down. In some, as in the eclipsing binaries just described, the
light-fluctuations are quite regular, repeating themselves with such
precision that the stars might well be used as time-keepers. In others
the fluctuations, though not perfectly regular, are nearly so, while
still others exist in which the fluctuations appear at present to be
completely irregular, although no doubt the changes in these will be
reduced to law and order in due course. For our present discussion, the
various types of irregular variables are not of great importance.
CEPHEID VARIABLES. The really interesting stars are those of a certain
class of regular variable, generally called “Cepheid variables,”
after their prototype δ Cephei. The physical nature of these stars
and the mechanism of their light-fluctuation is still far from being
understood; competing theories are in the field which we need not
discuss at this stage (see p. 223 below).
Whatever their mechanism may be, observation shews that these stars
possess a certain definite property, which proves to be of the utmost
value. This being so, we may accept it gratefully without troubling as
to its why and wherefore. The perfectly regular light-fluctuations of
the eclipsing binaries would make them suitable for time-keepers even
though we did not understand the mechanism behind these fluctuations.
In the same way the fluctuations of Cepheid variables have a quality
which makes them valuable as measuring-rods with which to survey the
distant parts of the universe. In brief, this property is that we can
deduce the intrinsic brightness of these stars, and so their distances,
from their observed light-fluctuations.
The light-fluctuations are so distinctive as to make the stars easy
of detection. There is a rapid increase of light, followed by a slow
gradual decline; then again the same rapid increase and slow decline as
before. It is as though someone were throwing armfuls of fuel on to a
bonfire at perfectly regular intervals.
One other class of variable stars, generally known as “long-period
variables,” shews somewhat similar light-fluctuations, but the two
classes are easily distinguished by their very different periods of
light-fluctuation. The Cepheid variable completes its cycle in a time
which may be a few hours, or may be days or weeks, but is never more
than about a month, whereas the long-period variable generally requires
about a year.
Fig. 7 shews the light curves of typical variable stars of the
different classes. In each diagram the progress of time is represented
by motion across the page from left to right; the higher the
fluctuating curve is above the horizontal line at any instant, the
brighter the star at that instant.
Out near the boundary of the galactic system is a cluster of stars
known as the Lesser Magellanic Cloud (Plate XXI, p. 214), in which
Cepheid variables occur in great profusion. In 1912, Miss Leavitt of
Harvard found that the light of the brighter Cepheids in this cloud
fluctuated more slowly than the light of the fainter ones. Whatever
was responsible for turning the stellar lights up and down, acted more
rapidly for feeble than for brilliant lights. The apparent brightnesses
of a number of Cepheids at varying distances would of course depend
only in part on their intrinsic brightness or candle-power, but the
stars in the Magellanic Cloud are all, nearly enough, at the same
distance from the earth. Thus differences in the apparent brightnesses
of stars in this cloud must represent real differences of intrinsic
brightness, and Miss Leavitt’s discovery could be stated in the form
that the period of light-fluctuation of a Cepheid depended on its
candle-power. Although this was only proved for the Cepheids in the
Magellanic Cloud, it must be true for all Cepheids wherever they are,
for it is inconceivable that we could make a star’s light fluctuate
more slowly or more rapidly merely by altering its distance from us—by
ourselves receding from it, in fact.
[Illustration: Light Curve of Eclipsing Binary (β Aurigae)]
[Illustration: Light Curve of Irregular Variable (RS Ophiuchi)]
[Illustration: Light Curve of Cepheid Variable(ν Lacerbae)]
[Illustration: Light Curve of Long-Period Variable (ο Ceti)
Fig. 7. Light Curves of typical Variable Stars of different classes.]
Professor Hertzsprung of Leiden and Dr Shapley, then of Mount Wilson
Observatory, were quick to seize upon the implications of this
discovery. If two Cepheids _A_, _B_ in different parts of the sky
are found to fluctuate with equal rapidities, then their intrinsic
candle-powers must be equal. Thus any difference in their apparent
brightness must be traceable to a difference in their distances from
us. If _A_ looks a hundred times as bright as _B_, then _B_ must be at
ten times the distance of _A_. In the same way, a third Cepheid _C_
may prove to be at ten times the distance of _B_. We now know that _C_
is a hundred times as remote as _A_. And if _D_ can be found ten times
as distant as _C_, we know that _D_ is a thousand times as remote as
_A_. So we can go on constructing and ever extending our measuring-rod;
there is no limit until we reach distances so great that even Cepheid
variables, which are exceptionally bright stars, fade into invisibility.
So far we have only considered the comparative distances of Cepheids.
The absolute distances of many of the nearer Cepheids have, however,
been determined by the parallactic method already explained—i.e. by
measuring their apparent motion in the sky, resulting from the earth’s
motion round the sun. Taking any one of these stars as our original
Cepheid _A_, we can step continually from one Cepheid to another, and
so calculate the absolute distances of all the Cepheid variables in the
sky.
In this way the observed relation between the period of fluctuation
and the brightness of Cepheid variables—commonly known as the
“period-luminosity law”—can be made to provide a scale on which the
absolute luminosity, or candle-power, of a Cepheid can be read off
directly from the observed period of its light-fluctuations. The
Cepheid variables may be regarded as lighthouses set up in distant
parts of the universe. We can recognise them, just as a sailor
recognises lighthouses, by the quality of their light. We can read off
their candle-power from the period of their observed light-fluctuations
as easily as the sailor could read off the candle-power of a lighthouse
from an Admiralty chart. The apparent brightness of the Cepheid informs
us as to its distance from us[7].
[7] For instance, Cepheids whose light fluctuates in a period of 40
hours have approximately a luminosity 250 times that of the sun,
and so are of 8 × 10²⁹ candle-power; a period of ten days indicates
a luminosity 1600 times that of the sun, or a candle-power of 5·17
× 10³⁰, and so on. If a star in a distant astronomical object is
observed to fluctuate with a period of ten days, and the quality of
its fluctuations shew it to be a Cepheid variable, we know that its
actual candle-power must be 5·17 × 10³⁰. Its apparent brightness is
observed to be that of a star of, say, magnitude 16, which, stripped
of technicalities, means that we receive as much light from it as
from a single candle at a distance of 570 miles. The difference
between one candle and 5·17 × 10³⁰ candles accordingly corresponds to
the difference between 570 miles and the distance of the object in
question, whence, since light falls off as the inverse square of the
distance, we calculate that the distance of the object must be
___________
√5·17 × 10³⁰ × 570 miles
or about 220,000 light-years.
It would be difficult to over-estimate the importance of all this to
modern astronomical science. It means that a method has been found for
surveying, if not the whole of the universe, at least those parts of it
in which Cepheid variables are visible. Actually this last reservation
is unimportant, for Cepheid variables are very freely scattered in
space. Naturally the method is of most value for the exploration of
the most distant parts of the universe; here it achieves triumphant
success where other methods fail completely. The parallactic method
begins to fail when we try to sound distances of more than about a
hundred light-years. The apparent path in the sky, which a star at
this distance describes, in consequence of the earth’s motion round
the sun, is of the size of a pin-head two miles away. With all their
refinements, modern instruments find it difficult enough to detect so
small a motion as this, and it is practically impossible to measure it
with accuracy. The “period-luminosity” law measures the distances of
objects up to a million light-years away, with a smaller percentage of
error than is to be expected in the parallactic measures of stars only
a hundred light-years away.
SOUNDING SPACE
This by no means exhausts the list of modern methods of surveying
space. Any standard type of astronomical object, which is easily
recognisable and emits the same amount of light no matter where it
occurs, provides an obvious means of measuring astronomical distances,
for when once the intrinsic luminosity of such an object has been
determined, the distance of every example of it can be estimated from
its apparent brightness.
Cepheid variables of assigned periods provide the most striking
instance of such standard objects, but three others are available,
although they are not so generally useful as Cepheids. First comes
another type of variable star, the “long-period variables” already
mentioned, which are generally similar to Cepheids except that their
light fluctuates much more slowly. These stars are intrinsically far
more luminous even than Cepheids, many of them being 10,000 times
as luminous as the sun. They are accordingly visible at enormous
distances, and may ultimately be found to provide a means of sounding
depths of space at which even Cepheids are lost to sight.
Next come “novae” or new stars. Every now and then an ordinary star in
the sky suddenly bursts out in a phenomenal blaze of light, shining
with perhaps a thousand times its original brilliance. The cause of
these violent outbursts is still a matter for debate, and no thoroughly
convincing explanation has as yet been given. A study of comparatively
near novae has, however, provided information as to the luminosity of
the average nova when at its brightest, and as novae appear in various
parts of the sky, and particularly in the extra-galactic nebulae, they
provide a rough means of measuring stellar and nebular distances.
Blue stars provide yet another method. These are exceedingly luminous,
and they vary but little in intrinsic luminosity. Moreover, the
luminosity of any particular star can generally be estimated fairly
closely from the quality of the light it emits, by methods which will
be explained later. This makes it possible to determine the distances
of blue stars, and so of course of the astronomical objects in which
they occur.
Still two other methods of a different kind may be briefly mentioned.
Dr W. S. Adams, Director of Mount Wilson Observatory, and others have
found that certain definite peculiarities in the spectra of certain
classes of stars convey information as to the intrinsic brightness of
the star emitting them; with this information it is easy to estimate
the star’s distance from its apparent brightness. This is commonly
described as the method of Spectroscopic Parallaxes.
Finally the diffuse cloud of nebular matter which is spread through
interstellar space (p. 30) is found to affect the quality of light
travelling through it, so that a star’s spectrum gives an indication of
the amount of cloud through which the light of the star has travelled,
and this again provides a rough means of estimating distances inside
the galactic system.
[Illustration: PLATE IX _Dominion Astrophysical Observatory, B. C._
The Globular Cluster _M_ 13 in Hercules]
GLOBULAR CLUSTERS. The law of Cepheid luminosity was first used by
Hertzsprung to estimate the distance of the Lesser Magellanic Cloud,
the study of which had been responsible for the original discovery of
the law. Shapley subsequently used it to determine the distances of
the rather mysterious groups of stars known as “Globular Clusters.”
A typical example of these is shewn in Plate IX. About 100 of these
clusters are known and they all look pretty much alike, except for
differences in apparent size. Even these latter can be traced mainly
to differences of distance, so that the globular clusters are probably
almost identical objects, and Plate IX might almost be regarded as a
picture of any one of them. Cepheid variables abound in them all.
Shapley found the nearest globular cluster, ω Centauri, to lie at a
distance of about 22,000 light-years, the furthest, N.G.C. 7006, being
about ten times as remote, at a distance of 220,000 light-years. At
such distances the parallactic method of measuring distances would of
course fail hopelessly. The parallactic orbit of a star at 220,000
light-years’ distance is about the size of a pin-head held at a
distance of 4000 miles; no telescope on earth could detect, still less
measure, such an orbit.
The mere figure of 220,000 light-years can convey but little conception
of the distance of this remotest of star-clusters from us. We may
apprehend it better if we reflect that the light by which we see the
cluster started on its long journey from it to us somewhere about the
time when primaeval man first appeared on earth. Through the childhood,
youth and age of countless generations of men, through the long
prehistoric ages, through the slow dawn of civilisation and through the
whole span of time which history records, through the rise and fall
of dynasties and empires, this light has travelled steadily on its
course, covering 186,000 miles every second, and is only just reaching
us now. And yet this enormous stretch of space does not carry us to the
confines of the universe; we shall now see that in all probability it
has barely carried us to the confines of the galactic system.
[Illustration: Fig. 8. The arrangement of the Globular Clusters.]
Shapley has mapped out the complete system of the globular clusters,
and finds that they occupy an oblong region, lying on both sides of
the plane of the Milky Way, its greatest diameter of about 250,000
light-years lying in this plane, and its two transverse diameters being
considerably shorter. The sun is nearer to the edge of this oblong
region than to its centre, which explains why all the globular clusters
appear in one half of the sky, as Hinks first noted in 1911. The
general arrangement is shewn in fig. 8. The page of the book represents
the plane of the Milky Way, the various dots representing the points
in this plane which are nearest to the different clusters, so that the
diagram exhibits the system of globular clusters as they would appear
to an observer out in space who viewed the galactic plane “full-on.”
All the globular clusters except N.G.C. 7006 lie within a circle of
about 125,000 light-years’ radius, having its centre at about 50,000
light-years from the sun.
[Illustration: PLATE X _E. E. Barnard_
The Region of ρ Ophiuchi]
THE ARRANGEMENT OF THE GALACTIC SYSTEM. Although the matter has long
been one of vigorous controversy, it is now becoming clear that the
region of space mapped out by these globular clusters approximately
coincides with that occupied by the galactic system itself. Herschel
and Kapteyn appear to have been in error in supposing the centre of the
galactic system to be in the neighbourhood of the sun; a considerable
accumulation of evidence indicates that it lies in a massive star-cloud
in the constellations of Ophiuchus and Scorpio. Dr Shapley and Miss
Swope, at Harvard Observatory, have recently determined the distance
of this star-cloud from the sun as 47,000 light-years, which places it
almost exactly at the centre of the system of globular clusters, as
shewn in fig. 8. There is what Shapley describes as a “local system” of
fairly bright stars surrounding the sun, and the error of identifying
this with the main galactic system has apparently been responsible for
a large part of the confusion which has hitherto beset the problem
of the architecture of the galaxy. This local system has the same
flattened shape as the main system, but it does not lie exactly in
the plane of the Milky Way, being inclined at an angle of about 12
degrees to it. The sun appears to lie very near to the plane of the
central plane of the system; recent determinations place it about 100
light-years to the north of this plane. Fig. 9 shews a cross-section of
the system, as it is now imagined to lie.
[Illustration: Fig. 9. Diagrammatic scheme of cross-section of the
Galactic System. The sun is at the head of the arrow.]
We have already compared the shape of the galactic system to that of
a wheel. It obviously could not retain this shape if the stars which
formed it were standing still in space. For the gravitational pull
of the inner stars would cause the outermost stars—the rim of the
wheel—to fall inwards, and the system would end as a confused jumble
of stars somewhere in the vicinity of the hub of the wheel. In 1913,
Henri Poincaré, Professor of Mathematics at the Sorbonne, suggested
that the galactic “wheel” might escape this fate if it were in a state
of rotation. Just as the earth’s motion saves it from falling into the
sun, and the moon’s motion saves it from falling on to the earth, so,
Poincaré suggested, the stars which form the rim of the wheel might be
saved from falling into the hub, by a motion of rotation of the whole
wheel. A rough calculation suggested that it would be necessary for the
wheel to rotate at the rate of a complete revolution about every 500
million years.
Naturally it is no simple matter to detect so slow a rotation. It was
first suspected to occur in the following way. We know that when a
spinning-top or gyroscope is set in rapid rotation, a considerable
force is needed to twist the top or gyroscope about in space. This is
the principle of the gyroscopic compass such as is used to steer ships.
A gyroscope, a sort of big steel spinning-top, is started spinning with
its two ends pivoted in a swinging frame. No matter how the ship turns,
the motion of the gyroscope keeps the frame pointing away in the same
direction, and by the help of this fixed direction the ship is kept on
its course. Now the solar system has many of the properties of a huge
spinning-top, the revolutions of the planets corresponding to the spin
of the top. As there is no twist impressed on this “spinning-top” from
outside, its axis of rotation must always point in the same direction,
thus providing a sort of “gyroscopic compass” to give us our bearings
in space.
In 1913 Charlier believed he had found that this “gyroscopic compass”
was turning round against the distant background of the Milky Way, at
the rate of a complete rotation every 370 million years, a period which
subsequent measurements increased to 530 million years. Eddington then
suggested that it might be the background rather than the gyroscopic
compass that was turning, the Milky Way actually rotating in the way
imagined by Poincaré, and at just about the rate which Poincaré had
calculated.
Recent investigations by Oort, Plaskett, Lindblad and others prove
beyond doubt that such a rotation really occurs, although it is not of
the simple “cart-wheel type” we have so far discussed. In the solar
system the innermost planets move more rapidly than the outermost: they
must necessarily do so if the motion of each planet is to counteract
the sun’s attraction. In the same way, if the rotational motion of the
galaxy is to counteract the gravitational attraction of its innermost
stars, its inner parts must rotate more rapidly than its outermost.
Thus the sun ought to be overtaking those stars which lie outside it
on the galactic wheel, while being itself overtaken by those which
lie inside it. Such an overtaking motion is fairly easy to detect.
A careful analysis of observed stellar motions has disclosed such a
motion, shewing that the galaxy as a whole is in rotation in precisely
the way just described, the inner parts rotating most rapidly.
The hub of this gigantic wheel lies almost exactly in the direction
which Shapley assigned to the centre of the galaxy from his study of
the globular clusters. Its distance from the sun, which cannot yet be
determined with any great accuracy, is probably somewhere about 37,000
light-years. To within the limits of accuracy which are at present
attainable, this places the centre of the galactic wheel at the centre
of the system of globular clusters (see fig. 8, p. 64). In the vicinity
of the sun, the galactic wheel performs a complete revolution in a
period of about 230 million years, and this endows the stars near
the sun with a motion through space at a speed of nearly 200 miles a
second, arising from the rotation of the galaxy alone.
With these data, it is possible to weigh the stars of the galactic
system _en masse_. Individual stars far away from the centre of the
galactic system must be describing orbits under the gravitational
pull of the system as a whole, the pull which prevents the stars from
scattering away into space, and so keeps the galactic system in being.
The aggregate of these orbital motions produces the general rotation
of the galaxy which we have just discussed. And from the figures just
mentioned, it can be calculated that the total weight of matter inside
the sun’s orbit must be about that of 240,000 million suns. Part of
this may of course arise from interstellar dust or gas. Nevertheless,
as the average star weighs considerably less than the sun, the total
number of stars in the galactic system may well be of the order of
400,000 million. This estimate of course includes all stars, dark as
well as luminous, but there are reasons for believing that the number
of dark stars is comparatively small (see p. 269 below).
Other estimates of the number of stars in the galaxy have been made,
generally lower than the foregoing. Two estimates by Lindblad, for
instance, give the total weight of the galaxy as 110,000 and 180,000
million suns respectively.
Again we are confronted with the difficulty of visualising such large
numbers. With perfect eyesight on a clear moonless night we can see
about 3000 stars. Imagine each of these 3000 stars to spread out into
a complete sky-full of 3000 new stars, and we are contemplating 9
million stars, which is still only the number visible in a telescope
of 5 inches aperture. We probably cannot ask our imagination to play
the same trick for us a second time, but if it can be persuaded
to do so, and if we can think of each of these 9 million stars as
again generating a whole sky-full of stars, we still have only
27,000 million stars within our purview—a number which is still far
below any permissible estimate of the total number of stars in the
galactic system. Or again, let us notice that the number of stars
photographically visible in the 100-inch telescope, namely 1500
million, is about equal to the number of men, women and children in
the world. Each inhabitant of the earth—each man, woman and child
living in the five continents or travelling on the seven seas—can
be allowed to choose his own particular star, and can then repeat
the process tens, and more probably hundreds, of times without going
outside the galactic system.
After this we can still go exploring outside the galactic system and
find more and ever more stars. The galactic system, with its hundreds
of millions of stars, no more contains all the stars in space than one
house contains all the inhabitants of Great Britain. There are millions
of other houses and millions of other families of stars.
THE EXTRA-GALACTIC NEBULAE. We have already spoken of the faint
nebulous objects which Herschel described, somewhat conjecturally, as
“island universes.” These are the other houses in which other families
of stars are to be found. The most powerful of modern telescopes shew
that they consist, in part at least, of huge clouds of stars. Just as
a powerful microscope shews that a puff of cigarette smoke, in spite
of its appearance of continuity, consists of a cloud of minute but
quite distinct particles, so a powerful modern telescope breaks up the
light from the outer regions of these nebulae into distinct spots of
light; the nebula is resolved into a cloud of shining particles, just
as the Milky Way was in Galileo’s tiny telescope of three centuries
ago. Plate XI shews an example; it represents a magnification of a
small area in the top left-hand corner of the Great Nebula _M_ 31
in Andromeda already shewn in Plate IV (p. 30), and the resolution
into distinct spots of light is unmistakable. We know that some at
least of these spots of light are stars, because we recognise them as
Cepheid variables, their light shewing the unmistakable characteristic
fluctuations of the familiar Cepheid variables nearer home. The other
shining particles are of comparable brightness and shew about the range
of brightness above and below that of the Cepheids which is needed to
justify us in supposing that they are ordinary stars.
[Illustration: PLATE XI _Mt Wilson Observatory_
Magnification of a part (left-hand top corner) of the Great Nebula _M_
31 in Andromeda, which is shewn complete in Plate IV (p. 30)]
[Illustration: PLATE XII _Mt Wilson Observatory_
Magnification of the central region of the Great Nebula _M_ 31 in
Andromeda]
From the observed periods of fluctuation of their Cepheid variables, in
combination with the other methods just explained, Dr Hubble of Mount
Wilson Observatory has recently found that even the nearest of these
nebulae, namely the nebula _M_ 33 shewn in Plate XX (p. 213), is so
remote that light takes some 850,000 years to travel from it to us. The
Great Nebula _M_ 31 in Andromeda (p. 30) is at the slightly greater
distance of about 900,000 light-years. This abundantly proves that
these nebulae lie right outside the galactic system, justifying the
term “extra-galactic” nebulae.
One might attempt to estimate the total number of stars in these
nebulae by counting those visible in a selected average small area, but
more precise methods are available. Just as we have supposed that the
outermost stars in the galactic system are describing orbits under the
gravitational attraction of the galaxy as a whole, so we must suppose
that the outermost stars in a nebula are describing orbits under the
gravitational attraction of the main mass of the nebula; the forces
which keep them from running away from the nebula are similar to those
which keep the earth moving in its orbit round the sun. If so, we can
weigh the nebulae, precisely in the same way as we weigh the sun (p.
44) or the galactic system (p. 69). Dr Hubble in this way estimates
that the weight of the Great Nebula _M_ 31 in Andromeda, shewn in Plate
IV, must be about 3500 million times that of the sun, while the nebula
N.G.C. 4594 in Virgo, shewn in Plate XV (p. 204), must have about 2000
million times the weight of the sun. In general it seems likely that
each of the extra-galactic nebulae contains about enough matter to make
some 2000 million stars.
This is not the same thing as saying that each nebula already contains
2000 million stars. While many of these nebulae appear to consist
largely of clouds of stars, yet most of them contain also a large
central region which no telescopic power has so far succeeded in
resolving into distinct points. For instance, Plate XII shews the
central region of the Great Nebula in Andromeda magnified to the same
degree as the left-hand top corner shewn in Plate XI, and this is
clearly not resolved into stars in the same way as the outer regions
shewn in Plate XI. The whole of the nebula N.G.C. 4594 in Virgo, shewn
in Plate XV, also refuses to be resolved into separate stars. We shall
find reasons later (Chapter IV) for interpreting these central regions
as masses of gas which are destined in time to form stars, but have not
yet done so. We shall in fact find that the nebulae are the birthplaces
of the stars, so that each nebula consists of stars born and stars not
yet born. It is the total weight of stars already born and of matter
which is destined to form stars that aggregates 2000 million suns.
About 2,000,000 of these extra-galactic nebulae are visible in the
great 100-inch telescope. In general, they appear to be scattered
with a tolerable approach to uniformity through space, their average
distance apart being something of the order of 2,000,000 light-years,
although here and there this uniformity is broken by clouds and
clusters of nebulae. For instance, the sky is remarkably rich in
nebulae in the constellations of Virgo and Coma Berenices. Here a
cloud of about 300 nebulae is collected, according to Shapley, within
a space having only from 5 to 10 times the dimensions of the galactic
system, at a distance of some ten million light-years from the sun. The
same region of the sky appears also to contain three other and more
remote clouds. Shapley has suggested that our galactic system, the
Andromeda nebula and other near nebulae may constitute a similar cloud.
THE REMOTEST DEPTHS OF SPACE. Hubble estimates that the most distant of
the 2,000,000 nebulae revealed by the 100-inch telescope must be about
140 million light-years away from us. This is the greatest distance
which the human eye has so far seen into space. The 220,000 light-years
which formed the diameter of the galactic system seemed staggeringly
large at first, but we are now speaking of distances some 600 times
greater. For all but a 500th part of its long journey, the light by
which we see this remotest of visible nebulae travelled towards an
earth uninhabited by man. Just as it was about to arrive, man came into
being on earth, and built telescopes to receive it. So at least it
appears when viewed on the astronomical scale. Yet even this last 500th
part of the journey covers the lives of 10,000 generations of men,
through all of which, as well as through 500 times as great a span of
time, the light has been travelling steadily onward at 186,000 miles a
second.
There are so many faint nebulae at the very limit of vision of the
100-inch telescope, that it seems certain that a still larger telescope
would reveal a great many more. The 200-inch telescope, which it is
hoped will shortly be built, having twice the aperture of the present
100-inch, ought to probe twice as far into space, and so may perhaps be
expected to shew about eight times as many, or 16 million, nebulae.
THE STRUCTURE OF THE UNIVERSE
So far every increase of telescopic power has carried us deeper and
deeper into space, and space has seemed to expand at an ever-increasing
rate. We may well ask whether this expansion is destined to go on for
ever: are there any limits at all to the extent of space?
Even a generation ago, I think most scientists would have answered this
last question in the negative. They would have argued that space could
be limited only by the presence of something which is not space. We, or
rather our imaginations, could only be prevented from journeying for
ever through space by running up against a wall of something different
from space. And, hard though it may be to imagine space extending for
ever, it is far harder to imagine a barrier of something different from
space which could prevent our imaginations from passing into further
space beyond.
The argument is not a sound one. For instance, the earth’s surface
is of limited extent, but there is no barrier which prevents us from
travelling on and on as far as we please. A traveller who did not
understand that the earth’s surface is spherical, would naturally
expect that longer and longer journeys from home would for ever open up
new tracts of country awaiting exploration. Yet, as we know, he would
necessarily be reduced in time to repeating his own tracks. As a result
of its curvature, the earth’s surface, although unlimited, is finite in
extent.
THE THEORY OF RELATIVITY
Through his theory of relativity, Einstein claims to have established
that space also, although unlimited, is finite in extent. The total
volume of space in the universe is of finite amount just as the surface
of the earth is of finite amount, and for the same reason; both bend
back on themselves and close up. The analogy is valid and useful
only so long as we are careful to compare the whole of space to the
surface of the earth, and not to its volume. The volume of the earth is
also finite in amount, but for quite different reasons. A mole which
burrowed on and on through the earth in a straight line would come in
time to something which is not earth—it would emerge into the open
air; but we can go on and on over the surface of the earth without
ever coming to anything which is not the surface of the earth. The
properties of space are those of the surface, not of the volume, of the
earth.
As a consequence of space bending back into itself, a projectile or a
ray of light can travel on for ever without going outside space into
something which is not space, and yet it cannot go on for ever without
repeating its own tracks. For this reason it is probable that light
can travel round the whole of space and return to its starting point,
so that if we pointed a sufficiently powerful telescope in the right
direction in the midnight sky, we should see the sun and its neighbours
in space by light which had made the circuit of the universe. We should
not see them as they now are, but as they were many millions of years
ago. Light which had left the sun so long ago would have travelled
round almost the whole of space and then, just as it was about to
complete the circle, it would be caught in our telescope instead of
being allowed to start on its second journey round space.
This curvature of space has other functions than that which it performs
on the grand scale, of limiting the total volume of space. Before
Einstein’s day the curvatures of the paths of planets, cricket balls
and projectiles in general were all attributed to the pull of a “force”
of gravitation. The theory of relativity dismisses this supposed force
as a pure illusion, and attributes the curved paths of projectiles of
all kinds to their efforts to keep a straight track through a curved
space. This curved space is not, it is true, the ordinary space of the
astronomer. It is a purely mathematical and probably wholly fictitious
space, in which the astronomers’ space and the astronomers’ time
are inextricably bound together and enter as equal partners. To be
absolutely exact, there are four equal partners. The first three are
the three dimensions of ordinary space—breadth, width, and height,
or, if we prefer, north-south, east-west and up-down. The fourth is
ordinary time measured in a way appropriate to the way in which we
have measured our space (a year of time corresponding to a light-year
of space, and so on), and then multiplied by the square-root of -1.
This last multiplication by the square-root of -1 is of course the
remarkable feature of the whole affair. For the square-root of -1
has no real existence; it is what the mathematician describes as an
“imaginary” number. No real number can be multiplied by itself and give
-1 as the product. Yet it is only when time is measured in terms of
an imaginary unit of √(-1) years that there is true equal partnership
between space and time. This shews that the equal partnership is purely
formal—it is nothing but a convenient fiction of the mathematician.
Indeed had it been anything more, our intuitive conviction that time is
something essentially different from space could have had no basis in
experience and so would have vanished ere now.
These complications with respect to time need not concern us here; the
essential point is that Einstein’s theory of relativity teaches that
space ultimately bends back on itself like the earth’s surface, so that
the total amount of space is finite.
THE COSMOLOGY OF EINSTEIN. According to Einstein’s original theory, the
dimensions of space are determined by the amount of matter it contains.
The more matter there is, the smaller space must be, and conversely;
space could only be of literally infinite extent if it contained
no matter at all. The problem of determining the extent of space
accordingly reduces to that of determining how much matter it contains.
We have no means of estimating how much matter may exist outside those
regions of space which are within the reach of our telescopes, but
within these regions matter seems to be fairly uniformly distributed in
the form of extra-galactic nebulae.
From the known weights of these, Hubble estimates that the mean density
of matter in space must be about 1·5 × 10⁻³¹ times that of water. On
the assumption that matter is distributed with this density through the
whole of space, including those parts which our telescopes have not
yet penetrated, we can calculate quite definitely that the radius of
space is 84,000 million light-years, or 600 times the distance of the
furthest visible nebula. The journey round space would take 500,000
million light-years, and if ever our telescopes shew us the solar
system from behind, we shall see it as it was 500,000 million years ago.
Thus, according to Einstein’s original theory, even the 140 million
light-years through which we can range with our telescopes form only
a small fraction of the whole of space—something like one part in a
thousand million. There is plenty of space still awaiting exploration.
It is perhaps not surprising. Mankind, who has been possessed of
telescopes for only 300 years out of the 300,000 of his residence on
earth, could hardly hope to discover the whole of space in so short a
time. Our astronomer-explorers are moving from island to island in the
small archipelago which surrounds their home in space, but they are
still far from circumnavigating the globe. And, just as the earliest
geographers tried to estimate the size of the earth, long before they
thought of circumnavigating it, from the curvature of a small part of
its surface, so astronomers are now trying to form estimates, although
necessarily vague, of the size of the whole universe from the curvature
of that part of it with which they are already acquainted.
The general theory of relativity has long passed the stage of being
regarded as an interesting speculation. It not only accounts for
phenomena of planetary motion before which Newton’s law of gravitation
failed, but it has predicted other phenomena—the apparent displacements
of stars near the sun at an eclipse, resulting from the light by which
we see them being bent as it passes through the sun’s gravitational
field, and a certain displacement of stellar spectra towards the red
end—which were entirely unsuspected when the predictions were first
made, but have subsequently been fully confirmed by observation. Indeed
the theory has by now qualified as one of the ordinary working tools
of astronomy. It has been used to measure the diameter of the small
faint star Sirius _B_, the companion to Sirius (p. 262), as well as
to discuss the nature of the stars at the centres of the “planetary
nebulae” (p. 323).
Nevertheless, the general theory of relativity does not lead up to
Einstein’s cosmology in a unique way. It is perfectly possible for
the former to be true and the latter false. The general theory of
relativity fixes the attributes of any small fraction of the universe
quite definitely, but leaves open several alternative ways in which
these small fractions can be pieced together to form a whole.
Einstein’s particular view of the cosmos cannot therefore claim the
prestige which attaches to the general theory of relativity as a whole.
And indeed for some years it fell somewhat into disfavour, and appeared
likely to be superseded by an alternative cosmology which de Sitter of
Leiden propounded and developed in some detail in 1917.
THE COSMOLOGY OF DE SITTER. Let us first try to understand the
essential differences between these two cosmologies.
Einstein’s cosmology supposes that the size of the cosmos is determined
by the amount of matter it contains. If it was decided, at the
creation, to create a universe containing a certain amount of matter
which was to obey certain natural laws, then space must at once have
adjusted itself to the size suited for containing just this amount of
matter and no more. Or, if the size of the universe and the natural
laws were decided upon, the creation of a certain definite amount of
matter became an inevitable necessity. De Sitter’s universe is less
simple, or, if we prefer so to put it, allowed more freedom of choice
in its creation. After the laws of nature had been fixed, it was still
possible to make a universe of any size, and to put any amount of
matter, within limits, into it. Looked at from the strictly scientific
point of view, Einstein’s universe has one element of arbitrariness
fewer than de Sitter’s universe, and to this extent it has the
advantage of simplicity.
On the other hand this simplicity is acquired at a price. The
fundamental corner-stone of the whole theory of relativity is the
equal partnership of space and time in the sense already explained.
Einstein’s cosmology gains its simplicity only at the expense of
supposing that this equality of partnership disappears when we
view the cosmos as a whole. It supposes that space and time are
indistinguishable (in the purely formal sense already indicated)
only to a being whose experience is limited to a small fraction of
the universe; they become utterly distinct for a being who can range
through the whole of space and time. It is not altogether clear how
much weight ought to be attached to this objection, if objection it
is. Real space and real time undoubtedly are distinct. Even if we
deny the reality of both, they still remain distinguishable as modes
of perception. What reproach, then, can it be to a cosmology that it
admits that, in the last resort, when the universe is contemplated
on the grand scale, space and time resolve themselves into distinct
types of entity? Somehow we knew it already, before ever we began to
contemplate the universe on the grand scale.
Whatever the answer to this last question may be, de Sitter’s cosmology
avoids all possible reproach by maintaining the equal partnership of
space and time, not only in individual fractions of the cosmos, but
throughout the cosmos as a whole. It will of course be understood that
we are still speaking of equal partnership in the purely formal sense
already explained, a light-year entering the cosmology on the same
footing as the square-root of -1 years. Even de Sitter’s cosmology does
not pretend that a light-year (9·46 million million kilometres) is the
same thing as twelve months.
Although Einstein’s main theory of relativity has been amply confirmed
by observation, the cosmological part of it did not predict any special
features such as permitted of a direct observational test. De Sitter’s
cosmology, on the other hand, predicted that the spectra of all distant
objects must shew a displacement towards the red, of amount depending
on the distance of the object. The equal partnership of space and time
results in the vibrations of the light-waves emitted by any specified
source being slower in distant than in near parts of the universe;
the stream of time rolls more rapidly just where we happen to be than
anywhere else. This sounds paradoxical at first, but examination shews
that it is not; de Sitter is not asking us to return to a geocentric
universe, because he shews that the inhabitant of a distant star would
also find that terrestrial atoms were keeping slower time than his own.
The paradox is completely resolved by the concept of the relativity of
all measures of space and time.
This displacement to the red as a result of mere distance is peculiar
to de Sitter’s cosmology. It is additional to the displacement which,
as all cosmologies agree, the spectrum of a moving body must shew as
the result of its motion, this latter being towards the red only if the
body is receding from the earth (p. 51). On de Sitter’s cosmology, the
two displacements are not entirely independent, for it is an essential
feature of this cosmology that near bodies should tend to move further
apart from one another. Just as bits of straw thrown together into a
stream tend to get separated as they float down the stream, so objects
in de Sitter’s universe move further apart as they float down the
stream of time.
Thus on de Sitter’s theory a displacement of spectral lines to the red
cannot be interpreted as evidence either of motion or of distance; it
is a mixture of both. This does not mean that we have been altogether
wrong in deducing the velocities of stars in the galactic system from
the observed displacements of their spectral lines. No appreciable
displacement is produced by distance alone, unless this distance forms
an appreciable fraction of the radius of the universe. Systematic
displacements to the red are, it is true, observed in the spectra of
the most distant stars, but they are of very small amount. It is only
when we look to the remote extra-galactic nebulae that we can expect to
observe the effect in appreciable strength.
Now it has long been one of the outstanding puzzles of astronomy that
the spectra of the distant nebulae are uniformly displaced towards
the red. The observed displacements are not small. Interpreted as
velocities, many of them would represent speeds of over 1000 miles
a second. Humason has found that two faint nebulae N.G.C. 4860 and
4853 shew apparent speeds of recession of 4900 and 4600 miles a
second respectively. They are both members of a cloud of nebulae in
Coma Berenices (p. 72), which is probably at a distance of about 50
million light-years. Quite recently the spectrum of another very faint
nebula in Ursa Major has been found to indicate an apparent motion of
recession with a speed of 7200 miles a second. If de Sitter’s theory
is rejected, almost all the extra-galactic nebulae must be running
away from us with terrific, almost unimaginable, speeds. And the
further away they are the more precipitately they are increasing their
distance. Yet we can hardly reintroduce simplicity by adopting de
Sitter’s theory, and treating the whole apparent stampede of nebulae
as spurious, since this theory involves that the nebulae may well, in
actual fact, be running away from us, scattering being an inherent
property of objects in a de Sitter universe.
The fact that the spectra of the most distant nebulae shew these large
displacements provides a certain presumption in favour of the truth of
de Sitter’s cosmology; this at least explains them twice over, while
no other cosmology explains them at all. If we tentatively accept this
cosmology, then each observed spectral shift must be regarded as the
sum of two parts, one arising in the ordinary way from a recession of
the nebula, and the other arising merely from its distance.
A preliminary study by Dr Hubble has shewn that on the whole the
spectral displacements are largest for the most distant nebulae,
and that their amounts are roughly proportional to the distances
of the nebulae from us. If we interpret the whole of the observed
displacements purely as evidence of recession, we can calculate that
the radius of the universe is about 2000 million light-years, or some
fourteen times the distance of the furthest visible nebula. With so
large a radius of the universe, the further displacement resulting from
the mere distance of even remote nebulae is negligible, so that our
assumption that the displacements arise almost entirely from velocities
of recession receives _à posteriori_ vindication. If the observed
displacements of the nebular spectra had been strictly proportional
to their distances from us, we should have obtained a consistent
explanation of the observed facts by assuming that we lived in a de
Sitter universe having a radius of about 2000 million light-years.
THE EXPANDING UNIVERSE. It used to be thought that the cosmologies
of Einstein and de Sitter were antagonistic to one another, since
obviously no one universe could be an Einstein universe and a de
Sitter universe at the same time. A recent investigation by a Belgian
mathematician, the Abbé G. Lemaître, has put a different complexion on
the problem. In brief Lemaître has shewn that no universe could stay
permanently in the state considered by Einstein. A universe in this
state is an unstable structure; immediately it came into being it would
start to expand, and would not cease from expanding until it had become
a de Sitter universe. Even after this the expansion would continue, but
it would now become merged in the normal expansion of the de Sitter
universe, such as we have already considered.
In the light of these results, the question at issue is not whether our
universe is an Einstein universe or a de Sitter universe, but rather
how far it has travelled along the road which begins with an Einstein
universe and ends with a de Sitter universe. Whatever the answer may
be, we are led to suppose that at the beginning of time the nebulae
were much nearer to one another than they now are, that ever since
then they have obeyed their inherent tendency to scatter, or rather
the tendency of the flowing stream of time to scatter them, and that
they are now moving away from us, and from one another, with speeds
which are proportional to their distances. This is in accordance with
Hubble’s conclusion, that the apparent speeds of recession of the
nebulae are roughly proportional to their distances. From Hubble’s
data Eddington has calculated that the original Einstein universe must
have had a radius of about 1200 million light-years. If the apparent
speeds of recession of the nebulae had been found to be strictly
proportional to their distances, we could have explained everything by
supposing that we lived in an expanding universe, which had started
as an Einstein universe of 1200 million light-years’ radius, had now
expanded to something of the order of 2000 million light-years’ radius,
and was destined to go on expanding to all eternity.
This provides a simple and rather fascinating picture of the universe,
but there are many reasons against supposing that it is a true one.
In the first place, if we interpret the spectral displacements as
evidence of velocity alone, the speeds of the nebulae are probably very
far from being (as the foregoing picture would require) accurately
proportional to their distances from us. A group of three nebulae, all
believed to be at the same distance of about 50 million light-years,
differ by nearly 2000 miles a second in their speeds, which average
about 5000 miles a second. Oort has found a general tendency for the
speeds of very distant nebulae not to be strictly proportional to
their distances. At from 20 to 40 million light-years the apparent
divergences average 750 miles a second, but it is not clear how far
these result merely from inaccurate estimates of the distances of these
remote nebulae.
In the second place, if the observed spectral shifts represent mere
scattering, we can calculate the time since this scattering began; it
proves to be many thousands of millions of years. Enormous though such
a length of time is, it does not appear to be enough. We shall see
later (Chapter III) how time leaves its mark, its wrinkles and its grey
hairs, on the stars, so that we can guess their ages tolerably well,
and the evidence is all in favour of stellar lives, not of thousands
of millions, but of millions of millions, of years. If the nebulae owe
their present motions to mere scattering, then the stars must have
lived the greater parts of their lives before this scattering began.
Such a hypothesis seems too artificial for acceptance, at any rate so
long as any alternative is open.
Of course we must frankly admit that our estimates of stellar ages may
be found to need revision. Indeed they have been calculated on the
supposition that no appreciable scattering of the type required by de
Sitter’s cosmology has ever taken place. If not only the nebulae, but
also the stars composing the galactic system, were huddled together at
the beginning of time, our estimates of the lives of the stars would
have to be substantially shortened, and it is conceivable, although I
think very unlikely, that they could be reduced to lengths of the kind
we have just considered; they certainly could not be so reduced if the
original universe had a radius anywhere near to Eddington’s estimate of
1200 million light-years.
Nevertheless the cosmologies of de Sitter and Lemaître undoubtedly
require that the present-day universe must be expanding, that the
nebulae must be retreating both from one another, and from us, and that
their spectra must, as a consequence, shew displacements to the red.
But there is nothing to compel us to identify these displacements with
those actually observed. Many causes, other than motions of recession,
are capable of reddening spectral lines, and only after we have
deducted all the reddening due to these various other causes shall we
be in a position to say that the residue represents a true motion of
recession.
Quite recently Dr Zwicky of Pasadena has suggested that gravitating
matter diffused through space may redden all light which passes through
the space. He gives dynamical reasons for his suggestion, calculates
the amount of spectral shift to be anticipated in the light reaching
us from the nebulae, and finds that it would account for practically
the whole of the observed shift. It is possible that the greater part
of the observed reddening of nebular light may be due to this or some
similar cause, only a small fraction representing true motions of
recession. If so, we can extend the age of the universe indefinitely,
and are free to assign to the stars the very great ages which the
evidence of general astronomy seems to demand. This we shall discuss
fully in Chapter III.
In de Sitter’s original form of this cosmology, light would take an
infinite time to travel round the universe, and this would prevent any
object being seen by light which had travelled the long way round.
This results from de Sitter having considered only the ideal case of
a universe entirely empty of all matter. With even a little matter in
the universe, the path of a ray of light would presumably bend back on
itself and return to its starting point after a finite time. It has
been quite seriously suggested that two faint nebulae (_h_ 3433 and
_M_ 83) may actually be our two nearest neighbours in the sky, _M_ 33
and _M_ 31, seen the long way round space. If so, we see the fronts of
two objects when we look at _M_ 33 and _M_ 31, and the backs of the
same two objects when we point our telescopes in exactly the opposite
directions and look at _h_ 3433 and _M_ 83. No doubt this is only a
conjecture, and perhaps rather a wild one, but many more startling
conjectures have been made in astronomy, and subsequently proved to be
true.
All these discussions of the structure of space are of course highly
speculative, but they agree in suggesting the general conclusion
that, if we cannot yet see the whole of space, we can at least survey
an appreciable fraction of it. Our astronomer-explorers may not as
yet have circumnavigated the globe, but they are perhaps discovering
America, and we can well imagine that even the next generation will
have completed the circumnavigation of space, and will think of a
finite but unbounded space in the same way, and with the same ease, as
we think of the finite but unbounded surface of the earth.
A MODEL OF THE UNIVERSE
We found it difficult enough to visualise the 4¼ light-years which
constitute the distance to the nearest star, so we may be well advised
not even to attempt to visualise this last distance of thousands of
millions of light-years, the conjectured circumference of the universe.
Yet we may try to see all these distances in proper proportion relative
to one another by the help of a model drawn to scale. We can escape the
effort of trying to imagine unimaginably great distances by keeping the
scale very small.
The earth, travelling 1200 times faster than an express train, makes
a journey of 600 million miles around the sun every year. Let us
represent this journey by a pin-head ¹/₁₆ of an inch in diameter. This
fixes the scale of our model; the sun has shrunk to a minute speck of
dust ¹/₃₄₀₀ of an inch in diameter, while the earth is a still more
minute speck which is too small to be seen at all even in the most
powerful of microscopes. On this scale the nearest star in the sky,
Proxima Centauri, must be placed about 225 yards away, and to contain
even the hundred stars nearest to our sun in space, the model must be a
mile high, a mile long and a mile wide.
Let us go on building the model. We may think of stars indiscriminately
as specks of dust, because their sizes vary about as much as the sizes
of specks of dust. In the vicinity of the sun we must place specks of
dust at average distances of about a quarter of a mile apart. In other
regions of space they are generally even farther apart, for, owing to
the presence of the “local cluster,” the immediate neighbourhood of the
sun happens to be a rather crowded part of the sky. We go on building
the model for hundreds of miles in every direction, and then, if we
are building in a direction well away from the galactic plane, the
specks of dust begin to thin out; we are approaching the confines of
the galaxy. In the galactic plane itself we build out for about 7000
miles before we come to the farthest globular cluster, and still we are
inside the galactic system. With our earth’s long yearly journey round
the sun as a pin-head the whole galactic system is about the size of
the American continent. It may be well to pause and try to visualise
the relative sizes of a pin-head and of the American continent, before
we go on with our mental model-building.
After we have finished the galactic system, we must travel about 30,000
miles before we begin to set up the next bit of our model, at any rate
if we are keeping it to scale. At this distance we place the next
family of stars, a family which is probably substantially smaller and
more compact than our own galactic family, but is comparable with it
both in size and in numbers. So we go on building our model—a family
of thousands of millions of stars every 30,000 miles or so—until we
have two million such families. The model now stretches for about four
million miles in every direction. This represents as far as we can
see into space with a telescope; we can imagine the model going on,
although we know not how nor where—all we know is that the part so far
built represents only a fraction of the universe.
Every galactic system or island universe or extra-galactic nebula
contains thousands of millions of stars, or gaseous matter destined
ultimately to form thousands of millions of stars, and we know of
two million such systems. There are, then, thousands of millions of
millions of stars within the range covered by the 100-inch telescope,
and this number must be further multiplied to allow for the parts of
the universe which are still unexplored. At a moderate computation, the
total number of stars in the universe must be something like the total
number of specks of dust in London. Think of the sun as something less
than a single speck of dust in a vast city, of the earth as less than
a millionth part of such a speck of dust, and we have perhaps as vivid
a picture as the mind can really grasp of the relation of our home in
space to the rest of the universe.
An alternative procedure would have been to construct our scale-model
by taking all the specks of dust in London and spreading them out
to the right distances to represent the various stars in space. The
average actual distances between specks of dust in London is a quite
small fraction of an inch; to get our model to correct scale, this
distance must be increased to about a quarter of a mile, even when
we are building the part which represents the crowded part of space
round the sun. If we build our model in this way, we obtain a vivid
picture of the emptiness of space. Empty Waterloo Station of everything
except six specks of dust, and it is still far more crowded with dust
than space is with stars. This is true even of the comparatively
crowded region inside the galactic system; it takes no account of the
immense empty stretches between one system of stars and the next. On
averaging throughout the whole of the model, the mean distance of a
speck of dust from its nearest neighbour proves to be something like 80
miles. The universe consists in the main not of stars but of desolate
emptiness—inconceivably vast stretches of desert space in which the
presence of a star is a rare and exceptional event.
Let us in imagination take up a position in space somewhere near the
sun, and watch the stars moving past with speeds about 1000 times
that of an express train. If space were really crowded with stars our
position would be as unenviable as if we sat down in the middle of
Regent Street to watch the traffic go by—our life, though thrilling,
would be brief. Yet, as exact calculation shews, the stellar traffic is
so little crowded that we would have to wait about a million million
million years before a star ran into us. Put in another form, the
calculation shews that any one star may expect to move for something
of the order of a million million million years before colliding with
a second star. The stars move blindly through space, and the players
in the stellar blind-man’s-buff are so few and far between that the
chance of encountering another star is almost negligible. We shall
see later that this concept is of the profoundest significance in our
interpretation of the universe.