developed; and you will remember that at the end it pointed to the
possibility that matter in the stars might be compressed to a density
much transcending our terrestrial experience. This called back to mind
the strange message of the Companion of Sirius. It could no longer
be dismissed as obvious nonsense. That does not mean that we could
immediately assume it to be true; but it must be weighed and tested
with a caution which we should not care to waste over a mere nonsense
jingle.
It should be understood that it was very difficult to explain away
the original message as a mistake. As to the mass being ⅘ths of the
sun’s mass there can be no serious doubt at all. It is one of the very
best determinations of stellar mass. Moreover, it is obvious that the
mass must be large if it is to sway Sirius out of its course and upset
its punctuality as a clock. The determination of the radius is less
direct, but it is made by a method which has had conspicuous success
when applied to other stars. For example, the radius of the huge star
Betelgeuse was first calculated in this way; afterwards it was found
possible to measure directly the radius of Betelgeuse by means of
an interferometer devised by Michelson, and the direct measurement
confirmed the calculated value. Again the Companion of Sirius does not
stand alone in its peculiarity. At least two other stars have sent us
messages proclaiming incredibly high density; and considering our very
limited opportunities for detecting this condition, there can be little
doubt that these ‘white dwarfs’, as they are called, are comparatively
abundant in the stellar universe.
But we do not want to trust entirely to one clue lest it prove false
in some unsuspected way. Therefore in 1924 Professor Adams set to
work again to apply to the message a test which ought to be crucial.
Einstein’s theory of gravitation indicates that all the lines of the
spectrum of a star will be slightly displaced towards the red end of
the spectrum as compared with the corresponding terrestrial lines. On
the sun the effect is almost too small to be detected having regard to
the many causes of slight shift which have to be disentangled. To me
personally Einstein’s theory gives much stronger assurance of the real
existence of the effect than does the observational evidence available.
Still it is a striking fact that those who have made the investigation
are now unanimous in their judgement that the effect really occurs on
the sun, although some of them at first thought that they had evidence
against it. Hitherto Einstein’s theory has been chiefly regarded by
the practical astronomer as something he is asked to test; but now the
theory has a chance to show its mettle by helping us to test something
much more doubtful than itself. The Einstein effect is proportional to
the mass divided by the radius of the star; and since the radius of the
Companion of Sirius is very small (if the message is right) the effect
will be very large. It should in fact be thirty times as large as on
the sun. That lifts it much above all the secondary causes of shift of
the lines which made the test on the sun so uncertain.
The observation is very difficult because the Companion of Sirius
is faint for work of this kind, and scattered light from its
overpoweringly brilliant neighbour causes much trouble. However, after
a year’s effort Professor Adams made satisfactory measurements, and he
found a large shift as predicted. Expressing the results in the usual
unit of kilometres per second, the mean of his measurements came to 19,
whilst the predicted shift was 20.
Professor Adams has thus killed two birds with one stone. He has
carried out a new test of Einstein’s general theory of relativity, and
he has shown that matter at least 2,000 times denser than platinum is
not only possible but actually exists in the stellar universe.[13]
This is the best confirmation we could have for our view that the sun
with a density 1½ times that of water is still very far indeed from
the maximum density of stellar matter; and it is therefore entirely
reasonable that we should find it behaving like a perfect gas.
I have said that the observation was exceedingly difficult. However
experienced the observer, I do not think we ought to put implicit trust
in a result which strains his skill to the utmost until it has been
verified by others working independently. Therefore you should for the
present make the usual reservations in accepting these conclusions.
But science is not just a catalogue of ascertained facts about the
universe; it is a mode of progress, sometimes tortuous, sometimes
uncertain. And our interest in science is not merely a desire to hear
the latest facts added to the collection; we like to discuss our hopes
and fears, probabilities and expectations. I have told the detective
story so far as it has yet unrolled itself. I do not know whether we
have reached the last chapter.
_Unknown Atoms and Interpretation of Spectra_
It should be understood that this matter of enormous density is
not supposed to be any strange substance--a new chemical element
or elements. It is just ordinary matter smashed about by the high
temperature and so capable of being packed more tightly--just as more
people could be squeezed into a room if a few bones were broken. It
is one of the features of astronomical physics that it shows us the
_ordinary_ elements of the earth in an _extraordinary_
state--smashed or ionized to a degree that has either not been
reproduced or has been reproduced with great difficulty in the
laboratory. It is not only in the inaccessible interior of the star
that we find matter in a state outside terrestrial experience.
Here is a picture of the Ring Nebula in Lyra (Fig. 8).[14] It is taken
through a prism so that we see not one ring but a number of rings
corresponding to different lines of the spectrum and representing the
different kinds of atoms which are at work producing the light of the
nebula. The smallest ring, which is rather faint (marked by an arrow),
consists of light produced by the helium atoms in the nebula--not
ordinary helium but smashed helium atoms. It was one of the great
laboratory achievements of recent times when Professor A. Fowler in
1912 succeeded in battering helium atoms in a vacuum tube sufficiently
to give this kind of light, already well known in the stars. Two other
rings are due to hydrogen. With these three exceptions none of the
rings have yet been imitated in the laboratory. For instance, we do not
know what elements are producing the two brightest rings on the extreme
right and left respectively.
We are sometimes asked whether any new elements show themselves in
the stars which are not present or are not yet discovered on the
earth. We can give fairly confidently the answer No. That, however,
is not because everything seen in the stars has been identified with
known terrestrial elements. The answer is in fact given not by the
astronomer but by the physicist. The latter has been able to make out
the orderly scheme of the elements; and it transpires that there are
no gaps left for fresh elements until we come to elements of very high
atomic weight, which would not be likely to rise into the atmosphere of
a star and show themselves in astronomical observation. Every element
carries a number, starting with hydrogen which is No. 1, and going up
to uranium which is No. 92.
[Illustration: Fig. 8. THE RING NEBULA IN LYRA]
[Illustration: Fig. 9. HYDROGEN--THE BALMER SERIES]
And what is more, the element carries its number-plate so conspicuously
that a physicist is able to read it. He can, for instance, see that
iron is No. 26 without having to count up how many known elements
precede it. The elements have been called over by their numbers, and up
to No. 84 they have all answered ‘Present’.[15]
The element helium (No. 2) was first discovered by Lockyer in the
sun, and not until many years later was it found on the earth.
Astrophysicists are not likely to repeat this achievement; they cannot
discover new elements if there aren’t any. The unknown source of the
two rings close together on the right of the photograph (a bright ring
and a fainter ring) has been called _nebulium_. But nebulium is
not a new element. It is some quite familiar element which we cannot
identify because it has lost several of its electrons. An atom which
has lost an electron is like a friend who has shaved off his moustache;
his old acquaintances do not recognize him. We shall recognize nebulium
some day. The theoretical physicists are at work trying to find laws
which will determine exactly the kind of light given off by atoms in
various stages of mutilation--so that it will be purely a matter of
calculation to infer the atom from the light it emits. The experimental
physicists are at work trying more and more powerful means of battering
atoms, so that one day a terrestrial atom will be stimulated to give
nebulium light. It is a great race; and I do not know which side to
back. The astronomer cannot do much to help the solution of the problem
he has set. I believe that if he would measure with the greatest care
the ratio of intensity of the two nebulium lines he would give the
physicists a useful hint. He also provides another clue—though it is
difficult to make anything of it--namely, the different sizes of the
rings in the photograph, showing a difference in the distribution of
the emitting atoms. Evidently nebulium has a fondness for the outer
parts of the nebula and helium for the centre; but it is not clear what
inference should be drawn from this difference in their habits.
The atoms of different elements, and atoms of the same element in
different states of ionization, all have distinctive sets of lines
which are shown when the light is examined through a spectroscope.
Under certain conditions (as in the nebulae) these appear as bright
lines; but more often they are imprinted as dark lines on a continuous
background. In either case the lines enable us to identify the element,
unless they happen to belong to an atom in a state of which we have
had no terrestrial experience. The rash prophecy that knowledge of the
composition of the heavenly bodies must be for ever beyond our reach
has long been disproved; and the familiar elements, hydrogen, carbon,
calcium, titanium, iron, and many others, can be recognized in the most
distant parts of the universe. The thrill of this early discovery has
now passed. But meanwhile stellar spectroscopy has greatly extended its
scope; it is no longer chemical analysis, but physical analysis. When
we meet an old acquaintance there is first the stage of recognition;
the next question is ‘How are you?’ After recognizing the stellar
atom we put this question, and the atom answers, ‘Quite sound’ or
‘Badly smashed’, as the case may be. Its answer conveys information
as to its environment--the severity of the treatment to which it is
being subjected--and hence leads to a knowledge of the conditions of
temperature and pressure in the object observed.
Surveying the series of stars from the coolest to the hottest, we can
trace how the calcium atoms are at first whole, then singly ionized,
then doubly ionized--a sign that the battering becomes more severe as
the heat becomes more intense. (The last stage is indicated by the
disappearance of all visible signs of calcium, because the ion with two
electrons missing has no lines in the observable part of the spectrum.)
The progressive change of other elements is shown in a similar way. A
great advance in this study was made in 1920 by Professor M. N. Saha,
who first applied the quantitative physical laws which determine the
degree of ionization at any given temperature and pressure. He thereby
struck out a new line in astrophysical research which has been widely
developed. Thus, if we note the place in the stellar sequence where
complete calcium atoms give place to atoms with one electron missing,
the physical theory is able to state the corresponding temperature or
pressure.[16] Saha’s methods have been improved by R. H. Fowler and
E. A. Milne. One important application was to determine the surface
temperatures of the hottest types of stars (12,000°—25,000°), since
alternative methods available for cooler stars are not satisfactory
at these high temperatures. Another rather striking result was the
discovery that the pressure in the star (at the level surveyed by the
spectroscope) is only ¹⁄₁₀₀₀₀th of an atmosphere; previously it had
been assumed on no very definite evidence to be about the same as that
of our own atmosphere.
We commonly use the method of spectrum analysis when we wish to
determine which elements are present in a given mineral on the earth.
It is equally trustworthy in examining the stars since it can make no
difference whether the light we are studying comes from a body close
at hand or has travelled to us for hundreds of years across space. But
one limitation in stellar work must always be remembered. When the
chemist is looking, say, for nitrogen in his mineral, he takes care to
provide the conditions which according to his experience are necessary
for the nitrogen spectrum to show itself. But in the stars we have
to take the conditions as we find them. If nitrogen does not appear,
that is no proof that nitrogen is absent; it is much more likely that
the stellar atmosphere does not hit off the right conditions for the
test. In the spectrum of Sirius the lines of hydrogen are exceedingly
prominent and overwhelm everything else. We do not infer that Sirius
is composed mainly of hydrogen; we infer instead that its surface is
at a temperature near 10,000°, because it can be calculated that that
is a temperature most favourable for a great development of these
hydrogen lines. In the sun the most prominent spectrum is iron. We do
not infer that the sun is unusually rich in iron; we infer that it
is at a comparatively low temperature near 6,000° favourable for the
production of the iron spectrum. At one time it was thought that the
prominence of hydrogen in Sirius and of metallic elements in the sun
indicated an evolution of the elements, hydrogen turning into heavier
elements as the star cools from the Sirian to the solar stage. There is
no ground for interpreting the observations in that way; the fading of
the hydrogen spectrum and the increase of the iron spectrum would occur
in any case as the result of the fall of temperature; and similar
spurious appearances of evolution of elements can be arranged in the
laboratory.
It is rather probable that the chemical elements have much the same
relative abundance in the stars that they have on the earth. All the
evidence is consistent with this view; and for a few of the commoner
elements there is some positive confirmation. But we are limited to the
outside of the star as we are limited to the outside of the earth in
computing the abundance of the elements, so that this very provisional
conclusion should not be pressed unduly.
_Spectral Series_
To illustrate further this kind of deduction, let us consider the
spectrum shown in Fig. 9 and see what may be learnt from it. With a
little trouble we can disentangle a beautifully regular series of
bright lines. The marks above will assist you to pick out the first few
lines of the series from the numerous other spectra mixed up with it.
Noticing the diminishing spacing from right to left, you will be able
to see that the series continues to the left for at least fifteen lines
beyond the last one marked, the lines ultimately drawing close together
and forming a ‘head’ to the series. This is the famous Balmer Series of
hydrogen, and having recognized it we identify hydrogen as one of the
elements present in the source of the light. But that is only the first
step, and we can proceed to further inferences.
Professor Bohr’s theory of the hydrogen atom teaches us that each line
of the series is emitted by an atom in a different state. These ‘states
of excitation’ can be numbered consecutively, starting from the normal
state of the hydrogen atom as No. 1. The light emitted in the first
few states comes into the part of the spectrum not reproduced here, and
the first line in our picture corresponds to state No. 8. Counting to
the left from this you will recognize the successive lines without much
difficulty up to state No. 30. Now the successive states correspond to
more and more swollen atoms, that is to say, the planet electron[17]
makes a wider and wider circuit. The radius (or more strictly the
semi-axis) of its orbit is proportional to the square of the number of
the state, so that the orbit for state No. 30 is 900 times larger than
the orbit for the normal atom No. 1. The diameter of the orbit in No.
30 is approximately a ten-thousandth of a millimetre. One inference can
be drawn immediately--the spectrum shown in Fig. 9 was not produced in
any terrestrial laboratory. In the highest vacuum that can be used in
terrestrial spectroscopy the atoms are still too crowded to leave room
for an orbit so large as this. The source must be matter so tenuous
that there is vacant space for the electron to make this wide circuit
without colliding with or suffering interference from other atoms.
Without entering into further detail we can conclude that Fig. 9 is a
spectrum of matter more rarefied than the highest vacuum known on the
earth.[18]
It is interesting to notice that, whereas throughout most of the
picture the lines are shown on a dark background, at the extreme left
the background is bright; the change occurs just at the point where the
Balmer Series comes to an end. This background of light is also due to
hydrogen and it is caused in the following way. The swollen atoms in
state No. 30 or thereabouts are perilously near the bursting-point,
so it is natural that along with them there should be atoms which
have overstepped the limit and burst. They have lost their planet
electrons and are occupied in catching new ones. Just as energy is
required in order to wrench away an electron from an atom, so there
will be superfluous energy to be got rid of when the atom tames a wild
electron. This superfluous energy is radiated and forms the bright
background referred to. Without entering into technicalities of the
theory, we can see that it is appropriate that this light from the
burst atoms should appear in the spectrum immediately beyond the lines
from the most swollen atoms, since bursting is a sequel to overswelling.
Whilst you have this photograph of the Balmer Series before you I
may take the opportunity of recounting the history of another famous
series. In some of the hottest stars a related series of lines known
as the Pickering Series was discovered in 1896. This is spaced on
precisely the same regular plan, but the lines fall half way between
the lines of the Balmer Series--not exactly half way because of the
gradually diminishing intervals from right to left, but just where
one would naturally interpolate lines in order to double their number
whilst keeping the spacing regular. Unlike the Balmer Series, the
Pickering Series had never been produced in any laboratory. What
element was causing it? The answer seemed obvious; surely these two
related series, one fitting half way between the other, must belong to
different modes of vibration of the same atom, hydrogen. That seemed to
be the only possible answer at the time; but we have learned more about
atoms since then. We may fairly argue that the ideal simplicity of
these two series indicates that they are produced by an atomic system
of the simplest possible type, viz. an atom with one planet electron;
but it must be remembered that this condition only tells us how the
atom is _clothed_, not what the atom is. The helium atom (or, for
that matter, the uranium atom) can on occasion masquerade in the scanty
attire of the hydrogen atom. Normal helium has two planet electrons;
but if one of these is lost, it becomes hydrogen-like and copies the
simple hydrogen system on a different scale. It is significant that the
Pickering Series appears only in the very hottest stars--in conditions
likely to cause loss of an electron. The difference between hydrogen
and hydrogen-like helium is firstly the difference of atomic weight;
the helium nucleus is four times as massive. But this scarcely affects
the spectrum because both nuclei are so massive that they remain almost
unshaken by the dancing electron. Secondly, the helium nucleus has
a double electric charge; this is equivalent to substituting in the
vibrating system a controlling spring of twice the strength. What can
be more natural than that the doubled force of the spring should double
the number of lines in the series without otherwise altering its plan?
In this way Professor Bohr discovered the real origin of the Pickering
Series; it is due to ionized helium, not to hydrogen.[19]
The heavy nucleus, whether of hydrogen or helium, remains almost
unshaken by the atomic vibration--almost, but not quite. At a later
date Professor A. Fowler succeeded in reproducing the Pickering
Series in the laboratory and was able to measure the lines with much
greater accuracy than could be achieved in stellar spectroscopy; he
was then able to show from his measures that the nucleus is not quite
irresponsive. It was a delicate double-star problem transferred to the
interior of the atom; or perhaps a closer analogy would be the mutual
influence of the sun and Jupiter, because Jupiter, having a thousandth
of the mass of the sun, disturbs it to about the same extent that the
light electron disturbs the hydrogen nucleus. Ionized helium is a
faithful copy of the hydrogen atom (on the altered scale) in everything
except the ‘shake’; the shake is less than in hydrogen because the
helium nucleus is still more massive and rock-like. The difference
of shake throws the Pickering Series of helium and the Balmer Series
of hydrogen slightly out of step with respect to one another; and by
measuring this misfit Professor Fowler was able to make a very accurate
determination of the shake and therefore of the mass of the electron.
In this way the mass of the electron is found to be ¹⁄₁₈₄₄th of the
mass of the hydrogen nucleus; this agrees well with the mass found
by other methods, and the determination is probably not inferior in
accuracy to any of them.
And so the clue first picked up in stars 300 light years away, followed
in turn by the theoretical and the experimental physicist, leads in the
end to the smallest of all things known.
_The Cloud in Space_
Having already considered the densest matter in the universe, we now
turn to consider the rarest.
In spite of great improvements in the art of exhausting vessels we
are still a long way from producing a _real_ vacuum. The atoms
in a vacuum tube before it is exhausted muster a formidable number
containing about twenty digits. High exhaustion means knocking off
five or six noughts at the end of that number; and the most strenuous
efforts to knock off one more nought seem ludicrously ineffective--a
mere nibbling at the huge number that must remain.
Some of the stars are extremely rarefied. Betelgeuse, for example, has
a density about a thousandth that of air. We should call it a vacuum
were it not contrasted with the much greater vacuosity of surrounding
space. Nowadays physicists have no difficulty in producing a better
vacuum than Betelgeuse; but in earlier times this star would have been
regarded as a very creditable attempt at a vacuum.
The outer parts of a star, and especially the light appendages such as
the solar chromosphere and corona, reach much lower densities. Also the
gaseous nebulae are, as their appearance suggests, extremely tenuous.
When there is space enough to put a pin’s head between adjacent atoms
we can begin to talk about a ‘real vacuum.’ At the centre of the Orion
nebula that degree of rarefaction is probably reached and surpassed.
A nebula has no definite boundary and the density gradually fades off.
There is reason to think that the fading off becomes slow at great
distances. Before we pass entirely out of the sphere of one nebula we
enter the sphere of another, so that there is always some residual
density in interstellar space.