equilibrium in a gaseous celestial body of so low a density that the
law of gases may be applied to it. That is only permissive for gases
or for mixtures of gases whose density does not exceed one-tenth of
that of water or one-fourteenth of the actual density of the sun.
The pressure in the central portions of such a mass of gas would,
of course, be greater than the pressure in the outer portions, just
as the pressure rises as we penetrate from above downward into our
terrestrial atmosphere. If we imagine a mass of the air of our
atmosphere transferred one thousand metres higher up, its volume will
increase and its temperature will fall by 9.8° C. (18° F.). If there
were extremely violent vertical convection currents in the air, its
temperature would diminish in this manner with increasing altitude; but
internal radiation tends to equalize these temperature differences.
The following calculation by Schuster concerning the conditions of a
mass of gas of the size of the sun is based on Ritter’s investigation.
It has been made under the hypothesis that the thermal properties of
this mass of gas are influenced only by the movements in it, and not by
radiation. The calculation is applied to a star which has the same mass
as the sun (1.9 × 10^{33} grammes, or 324,000 times the mass of the
earth), and a radius of about ten times that of the sun (10 × 690,000
km.), whose mean density would thus be 1000 times smaller than that of
the sun, or 0.0014 times the density of water at 4° C. In the following
table the first column gives the distance of a point from the centre
of the star as a fraction of its radius; the density (second column)
is expressed in the usual scale, water being the unit; pressures
are stated in thousands of atmospheres, temperatures in thousands
of degrees Centigrade. The temperature will vary proportionately
to the molecular weight of the gas of which the star consists; the
temperatures, in the fourth column of the table, concern a gas of
molecular weight 1—that is to say, hydrogen gas dissociated into
atoms, as it will be undoubtedly on the sun and on the star. If the
star should consist of iron, we should have to multiply these latter
numbers by 56, the molecular weight of iron; the corresponding figures
will be found in the fifth column.
Temperature in
Distance from Density Pressure in 10^3 10^3° Cent.
centre atmospheres Hydrogen Iron
0 0.00844 852 2460 137,500
0.1 0.00817 807 2406 134,600
0.2 0.00739 683 2251 126,100
0.3 0.00623 513 2007 112,400
0.4 0.00488 342 1707 95,600
0.5 0.00354 200 1377 77,100
0.6 0.00233 100 1043 58,400
0.7 0.00136 40 728 48,800
0.8 O.00065 12 445 24,900
0.9 0.00020 1.7 202 11,300
1.0 0.00000 0 0 0
Schuster’s calculation was really made for the sun—that is to say,
for a celestial body whose diameter is ten times smaller, and
whose specific gravity is therefore a thousand times greater than
the above-assumed values. According to the laws of gravitation and
of gases, the pressure must there be 10,000 times greater, and the
temperature ten times higher, than those in our table. The density of
the interior portions would, however, become far too large to admit
of the application of the gas laws. I have therefore modified the
calculations so as to render them applicable to a celestial body of ten
times the radius of the sun or of 1080 times the radius of the earth;
the radius would then represent one-twenty-second of the distance
from the centre of the sun to the earth’s orbit, and the respective
celestial body would have very small dimensions indeed if compared to a
nebula.
The extraordinarily high pressure in the interior portions of the
celestial body is striking; this is due to the great mass and to the
small distances. In the centre of the sun the pressure would amount to
8520 million atmospheres, since the pressure increases inversely as the
fourth power of the radius. The pressure near the centre of the sun is,
indeed, almost of that order. If the sun were to expand to a spherical
planetary nebula of a thousand times its actual linear dimensions (when
it would almost fill the orbit of Jupiter), the specific gravity at
its centre would be diminished to one-millionth of the above-mentioned
value—that is to say, matter in this nebula would not, even at the
point of greatest concentration, be any denser than in the highly
rarefied vacuum tubes which we can prepare at ordinary temperatures.
The pressure would likewise be greatly diminished—namely, to about six
millimetres only, near the centre of the gaseous mass. The temperature,
however, would be rather high near the centre—namely, 24,600° C., if
the nebula should consist of atomatic hydrogen, and fifty-six times
as high again if consisting of iron gas. Such a nebula would restrain
gases with 1.63 times the force which the earth exerts. Molecules of
gases moving outward with a velocity of about 18 km. (11 miles) per
second would forever depart from this atmosphere.
The estimation of the temperature in such masses of gases is certainly
somewhat unreliable. We have to presume that neither radiation nor
conduction exert any considerable influence. That might be permitted
for conduction; but we are hardly justified in neglecting radiation.
The temperatures within the interior of the nebula will, therefore, be
lower than our calculated values. It is, however, difficult to make any
definite allowance for this factor.
If the mass of the celestial body should not be as presumed—for
instance, twice as large—we should only have to alter the pressure and
the density of each layer in the same proportion, and thus to double
the above values. The temperature would remain unchanged. We are hence
in a position to picture to ourselves the state of a nebula of whatever
dimensions and mass.
Lane has proved, what the above calculations also indicate, that the
temperature of such nebula will rise when it contracts in consequence
of its losing heat. If heat were introduced from outside, the nebula
would expand under cooling. A nebula of this kind presumably loses
heat and gradually raises its own temperature until it has changed
into a star, which will at first have an atmosphere of helium and of
hydrogen like that of the youngest stars (with white light). By-and-by,
under a further rise of temperature, the extremely energetic chemical
compounds will be formed which characterize the interior of the sun,
because helium and hydrogen—which were liberated when the nebula was
re-formed and which dashed out into space—will diffuse back into the
interior of the star, where they will be bound under the formation of
the compounds mentioned. The atmosphere of hydrogen and of helium will
disappear (helium first), the star will contract more and more, and the
pressure and the convection currents in the gases will become enormous.
There will be a strong formation of clouds in the atmosphere of the
star, which will gradually become endowed with the properties which
characterize our sun. The sun behaves very differently from the gaseous
nebulæ for which the calculations of Lane, Ritter, and Schuster hold.
For when the contraction of a gas shall have proceeded to a certain
limit, the pressure will increase in the ratio 1: 16, while the volume
will decrease in the ratio 8: 1, provided there be no change in the
temperature. When the gas has reached this point and is still further
compressed, the temperature will remain in steady equilibrium. At still
higher pressures, however, the temperature must fall if equilibrium
is to be maintained. According to Amagat, this will occur at 17° C.
(290° absolute) in gases like hydrogen and nitrogen, which at this
temperature are far above their critical points, and at a pressure of
300 or 250 atmospheres. When the temperature is twice as high on the
absolute scale, or at 307° C., twice the pressure will be required.
We can now calculate when our nebula will pass through this critical
stage, to which a lowering of the temperature must succeed. Accepting
the above figures, we find that half the mass of the nebula will fill
a sphere of a radius 0.53 of that of the nebula. If the mass were
everywhere of the same density, half of it would fill a sphere of 0.84
of this radius. When will the interior mass cross the boundary of the
above stage, while the exterior portions still remain below this stage?
That will be at about the time when the nebula in its totality will
pass through its maximum temperature. We will now base our calculations
on the temperatures which apply to iron in the gaseous state; for in
the interior of the nebula the mean molecular weight will at least be
56 (that of iron). We shall find that the pressure at the distance 0.53
will be about 177,000 atmospheres, and the temperature approximately
71 million degrees—_i.e._, 245,000 times higher than the absolute
temperature in the experiments of Amagat. The specified stage will
then be reached when the pressure will be 245,000 times as large as
250 atmospheres—viz., 61 million atmospheres. As, now, the pressure
is only 177,000 atmospheres, our nebula will yet be far removed from
that stage at which cooling will set in. We can easily calculate that
this will take place when the nebula has contracted to a volume about
three times that of our sun. The assertion which is so often made
that the sun might possibly attain higher temperatures in the future
is unwarranted. This celestial body has long since passed through the
culminating-point of its thermal evolution, and is now cooling. As the
temperatures which Schuster deduced were no doubt much too high, the
cooling must, indeed, have set in already in an earlier stage. But
stars like Sirius, whose density is probably not more than one per
cent, of the solar density, are probably still in a rising-temperature
stage. Their condition approximates that of the mass of gas of our
example.
The planetary nebulæ are vastly more voluminous. The immense space
which these celestial bodies may occupy will be understood from the
fact that the largest among them, No. 5 in Herschel’s catalogue,
situated near the star B in the Great Bear, has a diameter of 2.67
seconds of arc. If it were as near to us as our nearest star neighbor,
its diameter would yet be more than three times that of the orbit
of Neptune; doubtless it is many hundreds of times larger. This
consideration furnishes us with an idea of the infinite attenuation
in such structures. In their very densest portions the density cannot
be more than one-billionth of the density of the air. In the outer
portions of such nebulæ the temperature must also be exceedingly low;
else the particles of the nebula could not be kept together, and only
hydrogen and helium can occur in them in the gaseous state.
Yet we may regard the density and temperature of such celestial bodies
as gigantic by comparison with those of the gases in the spirals of the
nebulæ. There never is equilibrium in these spirals, and it is only
because the forces in action are so extraordinarily small that these
structures can retain their shapes for long periods without noticeable
changes. It is, probably, chiefly in those parts in which the cosmical
dust is stopped in its motion that meteorites and comets are produced.
The dust particles wander into the more central portions of the
nebulæ, into which they penetrate deeply, owing to their relatively
large mass, to form the nuclei for the growth of planets and moons. By
their collisions with the masses of gases which they encounter, they
gradually assume a circular movement about the axis of rotation of the
nebula. In this rotation they condense portions of the gases on their
surface, and hence acquire a high temperature—which they soon lose
again, however, owing to the comparatively rapid radiation.
So far as we know, spiral nebulæ are characterized by continuous
spectra. The splendor of the stars within them completely outshines the
feeble luminosity of the nebula. The stars in them are condensation
products and undoubtedly in an early stage of their existence;
they may therefore be likened to the white stars, like the new star
in Perseus and the central star in the ring nebula of the Lyre.
Nevertheless, it has been ascertained that the spectrum of the
Andromeda nebula has about the same length as that of the yellow stars.
That may be due to the fact that the light of the stars in this nebula,
which we only seem to see from the side, is partly extinguished by dust
particles in its outer portion, as was the case with the light of the
new star in Perseus during the period of its variability.
Our considerations lead to the conclusion that there is rotating about
the central body of the nebula an immense mass of gas, and that outside
this mass there are other centres of condensation moving about the
central body together with the masses of gas concentrated about them.
Owing to the friction between the immigrated masses and the original
mass of gas which circulated in the equatorial plane of the central
body, all these masses will keep near the equatorial plane, which will
therefore deviate little from the ecliptic. We thus obtain a proper
planetary system, in which the planets are surrounded by colossal
spheres of gas like the stars in the Pleiades (Fig. 52). If, now, the
planets have very small mass by comparison with the central body—as
in our solar system—they will be cooled at an infinitely faster rate
than the sun. The gaseous masses will soon shrink, and the periods of
rotation will be shortened; but for those planets, at least, which are
situated near the centre, these periods will originally differ little
from the rotation of the central body. The dimensions of the central
body will always be very large, and the planets circulating about it
will produce very strong tidal effects in its mass. Its period of
rotation will be shortened, while the orbital rotation of the planets
will tend to become lengthened. Thus the equilibrium is disturbed;
it is re-established again, because the planet is, so to say, lifted
away from the sun, as G. H. Darwin has so ingeniously shown with
regard to the moon and the earth. Similar relations will prevail in
the neighborhood of those planets which will thus become provided with
moons. Hence we understand the peculiar fact that all the planets move
almost in the same plane, the so-called ecliptic, and in approximately
circular orbits; that they all move in the same direction, and that
they have the same direction of rotation in common with their moons and
with the central body, the sun. It is only the outermost planets, like
Uranus and Neptune, in whose cases the tidal effects were not of much
consequence, that form exceptions to this rule.
In explanation of these phenomena various philosophers and astronomers
have advanced a theory which is known as the Kant-Laplace theory,
after its most eminent advocates. Suggestions pointing in the same
direction we find in Swedenborg (1734). Swedenborg assumed that our
planetary system had been evolved under the formation of vortices from
a kind of “chaos solare,” which had acquired a more and more energetic
circulating motion about the sun under the influence of internal
forces, possibly akin to magnetic forces. Finally a ring had been
thrown off from the equator, and had separated into fragments, out of
which the planets had been formed.
Buffon introduced gravitation as the conservational principle. In an
ingenious essay, “Formation des Planètes” (1745), he suggests that
the planets may have been formed from a “stream” of matter which was
ejected by the sun when a comet rushed into it.
Kant started from an original chaos of stationary dust, which under
the influence of gravitation arranged itself as a central body, with
rings of dust turning around it; the rings, later on, formed themselves
into planets. The laws of mechanics teach, however, that no rotation
can be set up in a central body, which is originally stationary, by
the influence of a central force like gravitation. Laplace, therefore,
assumed with Swedenborg that the primeval nebula from which our
solar system was evolved had been rotating about the central axis.
According to Laplace, rings like those of Saturn would split off, as
such a system contracted, and planets and their moons and rings would
afterwards be formed out of those rings. It is generally believed at
present, however, that only meteorites and small planets, but not the
larger planets, could have originated in this way. We have, indeed,
such rings of dust rotating about Saturn, the innermost more rapidly,
the outer rings more slowly, just as they would if they were crowds of
little moons.
Many further objections have later been raised against the hypothesis
of Laplace, first by Babinet, later especially by Moulton and
Chamberlin. In its original shape this hypothesis would certainly not
appear to be tenable. I have therefore replaced it by the evolution
thesis outlined above. It is rather striking that the moons of the
outermost planets, Neptune and Uranus, do not move in the plane of
the ecliptic, and that their moons further describe a “retrograde”
movement—that is to say, they move in the direction opposite to that
conforming to the theory of Laplace. The same seems to hold for the
moon of Saturn, which was discovered in 1898 by Pickering. All these
facts were, of course, unknown to Laplace in 1776; and if he had known
them he would scarcely have advanced his thesis in the garb in which
he offered it. The explanation of these facts does not cause any
difficulty. We may assume that the matter in the outer portions of
the primeval nebula was so strongly attenuated that the immigrating
planet did not attain a sufficient volume to have the large common
rotation in the equatorial plane of the sun impressed upon it by the
tidal effects. Charged only with the small mass of matter which they
met on their road, the planet and its moon, on the contrary, remained
victorious in the limited districts in which they were rotating. Only
the slow orbital movement about the central body was influenced, and
that adapted itself to the common direction and the circular orbit. It
is not inconceivable that there may be, farther out in space, planets
of our solar system, unknown to us, moving in irregular paths like the
comets. The comets, Laplace assumed, probably immigrated at a later
period into our solar system when the condensation had already advanced
so far that the chief mass of the nebular matter had disappeared from
interplanetary space.
Chamberlin and Moulton have attempted to show that the difficulties
of the hypothesis of Laplace may be obviated by the assumption that
the solar system has evolved from a spiral nebula, into which strange
bodies intruded which condensed the nebular mass of their surroundings
upon themselves. We have pointed out examples of how the nebula seems
to vanish in the vicinity of the stars, which would correspond to
growing planets, located in nebulæ.
In concluding this consideration, we may draw a comparison between the
views which were still entertained a short time ago and the views and
prospects which the discoveries of modern days open to our eyes.
Up to the beginning of this century the gravitation of Newton seemed
to rule supreme over the motions and over the development of the
material universe. By virtue of this gravitation the celestial bodies
should tend to draw together, to unite in ever-growing masses. In the
infinite space of past time the evolution should have proceeded so far
that some large suns, bright or extinct, could alone persist. All life
would be impossible under such conditions.
And yet we discern in the neighborhood of the sun quite a number
of dark bodies, our planets, and we may surmise that similar dark
companions or satellites exist in the vicinity of other suns and stars;
for we could not understand the peculiar to-and-fro motions of those
stars on any other view. We further observe that quite a number of
small celestial bodies rush through space in the shapes of meteorites
or shooting-stars which must have come to us from the most remote
portions of the universe.
The explanation of these apparent deviations from what we may regard
as a necessary consequence of the exclusive action of gravity will
be found under two heads—in the action of the mechanical radiation
pressure of light, and in the collisions between celestial bodies. The
latter produce enormous vortices of gases about nebular structures in
the gaseous condition; the radiation pressure carries cosmical dust
into the vortices, and the dust collects into meteorites and comets and
forms, together with the condensation products of the gaseous envelope,
the planets and the moons accompanying them.
The scattering influence of the radiation pressure therefore balances
the tendency of gravitation to concentrate matter. The vortices of
gases in the nebulæ only serve to fix the position of the dust, which
is ejected from the suns through the action of the radiation pressure.
The masses of gas within the nebulæ form the most important centres of
concentration of the dust which is ejected from the sun and stars.
If the world were limited, as people used to fancy—that is to say,
if the stars were crowded together in a huge heap, and only infinite,
empty space outside of this heap, the dust particles ejected from the
suns during past ages by the action of the radiating pressure would
have been lost in infinite space, just as we imagined that the radiated
energy of the sun was lost.
If that were so, the development of the universe would long since
have come to an end, to an annihilation of all matter and of all
energy. Herbert Spencer, among others, has explained how thoroughly
unsatisfactory this view is. There must be cycles in the evolution of
the universe, he has emphasized. That is manifestly indispensable if
the system is to last. In the more rarefied, gaseous, cold portions of
the nebulæ we find that part of the machinery of the universe which
checks the waste of matter and, still more, the waste of force from
the suns. The immigrating dust particles have absorbed the radiation
of the sun and impart their heat to the separate particles of the
gases with which they collide. The total mass of gas expands, owing to
this absorption of heat, and cools in consequence. The most energetic
molecules travel away, and are replaced by new particles coming from
the inner portions of the nebulæ, which are in their turn cooled by
expansion. Thus every ray emitted by a sun is absorbed, and its energy
is transferred, through the gaseous particles of the nebulæ, to suns
that are being formed and which are in the neighborhood of the nebula
or in its interior portions. The heat is hence concentrated about
centres of attraction that have drifted into the nebula or about the
remnants of the celestial bodies which once collided there. Thanks to
the low temperature of the nebula, the matter can again accumulate,
while the radiation pressure, as Poynting has shown, will suffice
to keep bodies apart if their temperature is 15° C., their diameter
3.4 cm., and their specific gravity as large as that of the earth,
5.5. At the distance of the orbit of Neptune, where the temperature
is about 50° absolute and approximates, therefore, that of a nebula,
this limit of size is reduced to nearly one millimetre. It has already
been suggested (compare page 153) that capillary forces, which would
prevail under the co-operation of the gases condensed upon the dust
grains, rather than gravity, play a chief part in the accumulation
and coalescence of the small particles. In the same manner as matter
is concentrated about centres of attraction energy may be accumulated
there in contradiction to the law of the constant increase of entropy.
During this conservational activity the layers of gas are rapidly
rarefied, to be replaced by new masses from the inner parts of the
nebula, until this centre is depleted, and the nebula has been
converted into a star cluster or a planetary system which circulates
about one or several suns. When the suns collide once more new nebulæ
are created.
The explosive substances, consisting probably of hydrogen and helium
(and possibly of nebulium), in combination with carbon and metals, play
a chief part in the evolution from the nebular to the stellar state,
and in the formation of new nebulæ after collisions between two dark
or bright celestial bodies. The chief laws of thermodynamics lead to
the assumption that these explosive substances are formed during the
evolution of the suns and are destroyed during their collisions. The
enormous stores of energy concentrated in these bodies perform, in a
certain sense, the duty of powerfully acting fly-wheels interposed in
the machinery of the universe in order to regulate its movements and
to make certain that the cyclic transition from the nebular to the
star stage, and vice versa, will occur in a regular rhythm during the
immeasurable epochs which we must concede for the evolution of the
universe.