STELLAR EVOLUTION
------------------------------------------------------------------------
BY THE SAME AUTHOR.
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CLIMATE AND TIME IN THEIR GEOLOGICAL RELATIONS: A Theory of
Secular Changes of the Earth’s Climate. By JAMES CROLL,
of H. M. Geological Survey of Scotland. With Maps and
Illustrations. 12mo. Cloth, $2.50.
DISCUSSIONS ON CLIMATE AND COSMOLOGY. By JAMES CROLL, LL.D.,
F.R.S. With Chart. 12mo. Cloth, $2.00.
------------------------------------------------------------------------
STELLAR EVOLUTION
AND ITS RELATIONS TO
GEOLOGICAL TIME
BY
JAMES CROLL, LL.D., F.R.S.
AUTHOR OF ‘CLIMATE AND TIME,’ ‘CLIMATE AND COSMOLOGY,’ ETC.
NEW YORK
D. APPLETON AND COMPANY
1889
------------------------------------------------------------------------
_Authorized Edition._
------------------------------------------------------------------------
PREFACE.
[Illustration]
There are two, and only two, conceivable sources from which the
prodigious amount of energy possessed by our sun and solar system can
possibly have been derived. Not only are these two sources radically
distinct in their essential nature, but both are admitted to be real and
not merely hypothetical sources of energy. The one source is
gravitation; the other, the source discussed in the present volume, a
source to which attention was directed some twenty years ago. A most
important distinction between these two sources is this: the amount of
energy available from the former can be accurately determined, but such
is not the case in regard to the latter. We can tell with tolerable
certainty the greatest amount of energy which gravitation could possibly
have conferred on the sun and solar system; but we have, at present, no
means of assigning a limit to the possible amount which might have been
derived from the other source. It may have been equal to that which
gravitation could afford, or it may have been twofold, fourfold, or even
tenfold that amount.
We have evidently in this case a means of determining which of the two
sources will ultimately have to be adopted as the source to which the
energy of our solar system must be referred. For if it can be proved
from the admitted facts of geology, biology, and other sciences, that
the amount of energy in the form of heat which has been radiated into
space by the sun during geological time is far greater than the amount
which could possibly have been derived from gravitation, this will
undoubtedly show that gravitation cannot account for the energy
originally possessed by our system.
The First Part of the volume is devoted to the consideration of what I
believe to be the probable origin of meteorites, comets, and nebulæ, and
of the real source from which our sun derived his energy. The facts
which support the theory here advocated, together with the light which
that theory appears to cast upon those facts, are next considered; and
it will be found, I think, that the theory has been very much
strengthened by the recent important spectroscopic researches of Mr.
Lockyer and others in reference to the constitution of nebulæ. The
Second Part of the work deals with the evidence in support of the theory
derived from the testimony of geology and biology as to the age of the
sun’s heat. The Third, and last, Part has been devoted to questions
relating to the pre-nebular condition of the universe, and the bearing
which these have on theories of stellar evolution. Several subjects
introduced in this part are only very briefly treated. These will,
however, be considered at greater length in a future volume,
“Determinism, not Force, the Foundation-stone of Evolution,” a work of a
more general and abstract character, which was commenced many years ago.
PERTH: _January 2, 1889_.
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CONTENTS.
[Illustration]
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PART I.
_THE IMPACT THEORY OF STELLAR EVOLUTION._
PAGE
CONSIDERATION OF THE FACTS WHICH SUPPORT THE THEORY, AND OF
THE LIGHT WHICH THE THEORY APPEARS TO CAST UPON THE FACTS 12
I. Probable Origin of Meteorites 12
II. Motion of the Stars; how of such different velocities,
and always in straight lines 14
III. Motion of the Stars not due to their mutual attractions 14
IV. Probable Origin of Comets 17
V. Nebulæ 18
1. Origin of Nebulæ 18
2. How Nebulæ occupy so much space 18
3. Why Nebulæ are of such various shapes 19
4. Broken fragments in a Gaseous mass of an
excessively high temperature the First stage of a
Nebula 19
5. The Gaseous condition the Second stage of a Nebula 24
6. The Gaseous condition Essential to the Nebular
Hypothesis 25
7. The mass must have possessed an excessive
temperature 26
8. Gravitation could, under no possible condition,
have generated the Amount of Heat required by the
Nebular Hypothesis 27
9. Condensation the Third and last stage of a Nebula 30
10. How Nebulæ emit such feeble Light 30
VI. Binary Systems 32
VII. Sudden Outbursts of Stars 33
VIII. Star Clusters 34
IX. Age of the Sun’s Heat: a Crucial Test 34
PART II.
_EVIDENCE IN SUPPORT OF THE THEORY
FROM THE AGE OF THE SUN’S HEAT._
TESTIMONY OF GEOLOGY AND BIOLOGY AS TO THE AGE OF THE SUN’S
HEAT 37
Testimony of Geology: Method employed 39
The Average Rate of Denudation in the Past probably not much
greater than at the Present 44
How the Method has been applied 47
Method as applied by Professor Haughton 50
Method as applied by Mr. Alfred R. Wallace 51
Method as applied directly 52
Evidence from “faults” 53
Time required to effect the foregoing amount of Denudation 62
Age of the Earth as determined by the Date of the Glacial
Epoch 64
Testimony of Biology 65
PART III.
_EVIDENCE IN SUPPORT OF THE THEORY
FROM THE PRE-NEBULAR CONDITION OF
THE UNIVERSE._
Professor A. Winchell on the pre-nebular condition of matter 71
Mr. Charles Morris on the pre-nebular condition of matter 75
Sir William R. Grove on the pre-nebular condition of matter 78
Evolution of the Chemical Elements, and its Relations to
Stellar Evolution 80
Sir Benjamin Brodie on the pre-nebular condition of matter 84
Dr. T. Sterry Hunt on the pre-nebular condition of matter 85
Professor Oliver Lodge on the pre-nebular condition of matter 87
Mr. William Crookes on the pre-nebular condition of matter 90
Professor F. W. Clarke on the pre-nebular condition of matter 98
Dr. G. Johnstone Stoney on the pre-nebular condition of
matter 99
THE IMPACT THEORY IN RELATION TO THE FOREGOING THEORIES OF
THE PRE-NEBULAR CONDITION OF MATTER 102
The Theories do not account for the Motion of the Stars 105
The Theories do not account for the Amount of Heat required 106
Evolution of Matter 107
Objection considered 109
Can we on Scientific grounds trace back the Evolution of the
Universe to an Absolute First condition? 110
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STELLAR EVOLUTION.
[Illustration]
PART I.
_THE IMPACT THEORY OF STELLAR EVOLUTION._
Upwards of twenty years ago[1] the theory—or, I should rather say, the
hypothesis—was advanced[2] that our sun was formed from a hot gaseous
nebula produced by the colliding of two dark stellar masses; and that,
as the stars are suns like our own, they in all likelihood had a similar
origin. The probability of this theory has been very much strengthened
by the facts, both astronomical and physical, which have accumulated
since the theory was enunciated. Before proceeding to the consideration
of these facts, and the conclusions to which they lead, it will be
necessary to give a statement of the fundamental principles of the
theory.
[Footnote 1: _Philosophical Magazine_, May 1868; _Climate and Time_,
chap. xxi.; _Quarterly Journal of Science_, July 1877; _Phil. Mag._,
July 1878; _Climate and Cosmology_, chaps. xvii. xviii. and xix.]
[Footnote 2: I prefer to use the term “theory,” with the above
understood qualification, viz. a theory in its hypothetical stage.]
In the theory here discussed the truth of the nebular hypothesis, which
begins by assuming the existence of a solar nebulous mass, is taken for
granted. The present theory deals not so much with the nebulous mass
itself as with the _formation_ of the nebula, and with those causes
which led to its formation. For convenience of reference, and to prevent
confusion, I have called it the “Impact Theory,” by which name it may be
distinguished, on the one hand, from the nebular theory, and, on the
other hand, from the meteoric theory, and all other theories which
regard gravitation as the primary source of the solar energy.
The theory starts with the assumption that the greater part of the
energy possessed by the universe exists or is stored up in the form of
the motion of stellar masses. The amount of energy which may thus be
stored up is startling to contemplate. Thus a mass equal to that of the
sun, moving with a velocity of 476 miles per second, would possess, in
virtue of that motion, energy sufficient, if converted into heat, to
maintain the present rate of the sun’s radiation for 50,000,000
years.[3] There is nothing extravagant in the assumption of such a
velocity. A comet, for example, having an orbit extending to the path of
the planet Neptune, approaching so near the sun as to almost graze his
surface in passing, would have a velocity within 86 miles of what we
have assumed. Twice this assumed velocity would give 200,000,000 years’
heat; four times the velocity would give 800,000,000 years’ heat; and so
on.
[Footnote 3: Pouillet’s estimate of the rate of solar radiation is here
taken.]
We are at perfect liberty to begin by assuming the existence of stellar
masses in motion; for we are not called upon to explain how the masses
obtained their motion, any more than we have to explain how they came to
have their existence. If the masses were created, they may as likely
have been created in motion as at rest; and if they were eternal, they
may as likely have been eternally in motion as eternally at rest.
Eternal motion is just as warrantable an assumption as eternal matter.
When we reflect that space is infinite—at least in thought—and that, for
aught we know to the contrary, bodies may be found moving throughout its
every region, we see that the amount of energy may be perfectly
illimitable.
But, illimitable as the amount of the energy may be, it could be of no
direct service while it existed simply as the motion of stellar masses.
The motion, to be available, must be transformed into heat: the motion
of translation into molecular, or some other form of motion. This can be
done in no other way than by arresting the motion of the masses. But how
is such motion to be arrested? How are bodies as large as our earth,
moving at the rate of hundreds of miles per second, to have their motion
stopped? According to the theory this is effected by _collision_: by
employing the motion of the one body to arrest that of the other.
Take the case of the formation of our sun according to the theory.
Suppose two bodies, each one-half of the mass of the sun, moving
directly towards each other with a velocity of 476 miles per second.
These bodies would, in virtue of that velocity, possess 4149 × 10^{38}
foot-pounds of energy, which is equal to 100,000,000,000 foot-pounds per
pound of the mass; and this, converted into heat by the stoppage of
their motions, would suffice to maintain, as was previously stated, the
present rate of the sun’s radiation for a period of 50,000,000 years. It
must be borne in mind that, while 476 miles per second is the velocity
at the moment of collision, more than one-half of this would be derived
from the mutual attraction of the two bodies in their approach to each
other.
Coming in collision with such a velocity, the result would inevitably be
that the two bodies would shatter each other to pieces. But, although
their onward motions would thus be stopped, it is absolutely impossible
that the whole of the energy of their motions could be at once converted
into heat; and it is equally impossible that it could be annihilated.
Physical considerations enable us to trace, though in a rough and
general way, the results which would necessarily follow. The broken
fragments, now forming one confused mass, would rebound against one
another, breaking up into smaller fragments, and flying off in all
directions. As these fragments receded from the centre of dispersion
they would strike against each other, and, by their mutual impact,
become shivered into still smaller fragments, which would in turn be
broken up into fragments yet smaller, and so on as they proceeded
outwards. This is, however, only one part of the process, and a part
which would certainly take place, though no heat were generated by the
collisions.
A far more effective means of dispersing the fragments and shattering
them to pieces would be the expansive force of the enormous amount of
incandescent gas almost instantaneously generated by the heat of
collision. The general breaking up of the two masses and the stoppage of
their motions would be the work of only a few minutes, or a few hours at
most. The heat evolved by the arrested motion would, in the first
instance, be mainly concentrated on the surface layers of the broken
blocks. The layers would be at once transformed into the gaseous
condition, thus enveloping the blocks and filling the interspaces. It is
difficult to determine what the temperature and expansive force of this
gas would at the moment be, but evidently it would be excessive; for,
were the whole of the heat of the arrested motion distributed over the
mass, it would, as has been stated, amount to 100,000,000,000
foot-pounds per pound of the mass—an amount sufficient to raise 264,000
tons of iron 1° C. Thus, if we assume the specific heat of the gas to be
equal to that of air (viz. ·2374), it would have a temperature of about
300,000,000° C. or more than 140,000 times that of the voltaic arc.
I hardly think it will be deemed extravagant to assume that at the
moment after impact the temperature of the evolved gas would be at least
as great as here stated. If we assume it to be so, it is obvious that
the broken mass would, by the expansive force of the generated gas, be
dispersed in all directions, breaking up into fragments smaller and
smaller as they knocked against one another in their progress outwards
from the centre of dispersion; and these fragments would, at the same
time, become gradually converted into the gaseous state, and gradually
come to occupy a space as large as that embraced in our solar system. In
the course of time the whole would assume the gaseous condition, and we
should then have a perfect nebula—intensely hot, but not very luminous.
As its temperature diminished, the nebulous mass would begin to
condense, and ultimately, according to the well-known nebular
hypothesis, pass through all the different phases of rings, planets, and
satellites into our solar system as it now exists.
I am glad to find that the theory, in one of its main features, has been
adopted by Sir William Thomson,[4] the highest authority we have on all
points relating to the source of the sun’s heat.
[Footnote 4: Lecture on “The Probable Origin, the Total Amount, and the
Possible Duration of the Sun’s Heat,” delivered at the Royal Institution
on January 21, 1887, and published in _Nature_ of 27th of the same
month. The lecture was afterwards published with considerable additions
and alterations in the _Proceedings of the Institution_ vol. xii. It is
from this that my quotations are taken.]
“We cannot,” says Sir William, “help asking the question, What was the
condition of the sun’s matter before it came together and became hot?
(1) It may have been two cool, solid masses, which collided with the
velocity due to their mutual gravitation; or (2), but with enormously
less of probability, it may have been two masses colliding with
velocities considerably greater than the velocities due to their mutual
gravitation.”
He adopts the first of these suppositions. “To fix the idea,” he
continues, “think of two cool, solid globes, each of the same mean
density as the earth, and of half the sun’s diameter, given at rest, or
nearly at rest, at a distance asunder equal to twice the earth’s
distance from the sun. They will fall together and collide in exactly
half a year. The collision will last for about half an hour, in the
course of which they will be transformed into a violently agitated
incandescent fluid mass flying outward from the line of the motion
before the collision, and swelling to a bulk several times greater than
the sum of the original bulks of the two globes. How far the fluid mass
will fly out all around from the line of collision it is impossible to
say. The motion is too complicated to be fully investigated by any known
mathematical method; but with sufficient patience a mathematician might
be able to calculate it with some fair approximation to the truth. The
distance reached by the extreme circular fringe of the fluid mass would
probably be much less than the distance fallen by each globe before the
collision, because the translational motion of the molecules
constituting the heat into which the whole energy of the original fall
of the globes becomes transformed in the first collision is probably
about three-fifths of the whole amount of that energy. The time of
flying out would probably be less than half a year, when the fluid mass
must begin to fall in again towards the axis. In something less than a
year after the first collision the fluid will again be in a state of
maximum crowding round the centre, and this time probably even more
violently agitated than it was immediately after the first collision;
and it will again fly outward, but this time axially towards the places
whence the two globes fell. It will again fall inwards, and after a
rapidly subsiding series of quicker and quicker oscillations it will
subside, probably in the course of two or three years, into a globular
star of about the same dimensions, heat, and brightness, as our present
sun, but differing from him in this, that it will have no rotation.”[5]
[Footnote 5: _Proceedings of the Royal Institution_, vol. xii. p. 15.]
This is precisely what I have been contending for during the past twenty
years, with the simple exception that I assume, according to his second
supposition, that the “two masses collided with velocities considerably
greater than the velocities due to mutual gravitation.” Sir William
admits, of course, my supposition to be quite a possible one, but
rejects it on the supposed ground of its improbability. His reasons for
this, stated in his own words, are as follows:
“This last supposition implies that, calling the two bodies A and B for
brevity, the motion of the centre of inertia of B relatively to A must,
when the distance between them was great, have been directed with great
exactness to pass through the centre of inertia of A; such great
exactness that the rotational momentum or moment of momentum after
collision was no more than to let the sun have his present slow rotation
when shrunk to his present dimensions. This exceedingly exact aiming of
the one body at the other, so to speak, is, on the dry theory of
probability, exceedingly improbable. On the other hand, there is
certainty that the two bodies A and B at rest in space if left to
themselves, undisturbed by other bodies and only influenced by their
mutual gravitation, shall collide with direct impact, and therefore with
no motion of their centre of inertia, and no rotational momentum of the
compound body after the collision. Thus we see that the dry probability
of collision between two neighbours of a vast number of mutually
attracting bodies widely scattered through space is much greater if the
bodies be all given at rest than if they be given moving in any random
directions and with any velocities considerable in comparison with the
velocities which they would acquire in falling from rest into
collision.”
Sir William here argues that the second supposition is far less probable
than the first, because, according to it, the motion of the one body
relatively to the other must, in order to strike, be directed with great
exactness. The result, in such a case, is that collision will rarely
occur; whereas, according to the first supposition, the two bodies
starting from a state of rest will, by their mutual gravitation,
inevitably collide. According to the second hypothesis they will
generally miss; according to the first they will always collide.
I have been led to a conclusion directly opposed to Sir William’s. The
fact, that, according to the second supposition, collisions can but
rarely occur is one reason, amongst others, why I think that supposition
to be true; and the fact that, according to the first supposition,
collisions must frequently occur is also one reason, amongst others, why
I think it very improbable that it can represent the true condition of
things.
It by no means adds anything to the probability of the first supposition
to assert that, according to it, such collisions will occur readily and
frequently. On the contrary, it would show that the supposition was the
less likely to be true. If the collisions were insufficient in
character, the fewer of them that occurred, the better; for the result
of such collisions would simply be a waste of the potential energies of
the universe. We should in this case have an innumerable host of
imperfect suns without planets, or with at most only one or two, and
these at no great distance from the luminary. There would thus be
evolved a universe without any grand planetary systems. There is still
another objection to the supposition. The same gravitating force which
makes the dark bodies liable to come into collision with each other
must, of course, make them equally liable to come into collision with
the luminous bodies, and with our sun amongst the rest. Our sun would,
accordingly, be at the mercy of any of those masses which might happen
to come within the reach of its attractive influence. It would pull the
mass towards it, and a collision would be inevitable, unless it so
happened that a transverse motion of the sun itself might enable it to
escape destruction. Even in such a case it could not by any means manage
to get rid of the entangling mass.
All this risk, in so far as gravitation is concerned, would have been
completely averted if an original projected velocity of some thirty or
forty miles per second had been conferred on the dark mass; for, in this
case, the attractive force of the sun would fail to arrest its motion,
and the mass would pass onward through space, never to return. This
simple conception of an original motion removes entirely those
objections which, we have seen, besets the supposition we have been
considering. With such a motion, not only would the risk to our solar
system be removed, but the collisions between the dark bodies themselves
would be a matter of rare occurrence; and hence the energy of the
universe would be conserved. And when a collision did happen it would be
on a grand scale, and the result would be not an imperfect sun without
planets, but an incandescent nebula, out of which, by condensation, a
complete solar system would be evolved. In fact, within the whole range
of cosmical physics, I know of nothing more impressive in its sublime
simplicity than this plan, by which the stability and perfection of the
universe is thus secured. How vast the ends—how simple the means!
CONSIDERATION OF THE FACTS WHICH SUPPORT THE THEORY, AND OF THE
LIGHT WHICH THE THEORY APPEARS TO CAST UPON THE FACTS.
I. _Probable Origin of Meteorites._
Recent researches establish beyond doubt that stars, nebulæ, comets and
meteorites, do not differ much from our earth in their chemical
constitution. Meteorites, it is true, differ in their physical
characteristics from ordinary rock such as is found on the earth’s
surface. But it is possible, if not probable, that the earth’s interior
mass “may,” as Sir Henry Roscoe remarks, “partake of the physical nature
of these metallic meteorites, and that if we could obtain a portion of
matter from a great depth below the earth’s surface we should find it
exactly corresponding in structure as well as in chemical composition
with a metallic meteorite, and the existence of such interior masses of
metallic iron may go far to explain the well-known magnetic condition of
our planet.”[6] I think there can be little doubt that, were our earth
broken up into small fragments, and these scattered into space, it would
probably be impossible to distinguish them from ordinary meteorites. The
two would be so like in character that one can hardly resist the
conviction that meteorites are but the fragments of sidereal masses
which have been shattered by collision. That meteorites are broken
fragments is the opinion expressed by Sir William Thomson, who says
“that he cannot but agree with the common opinion which regards
meteorites as fragments broken from larger masses, and that we cannot be
satisfied without trying to imagine what were the antecedents of those
masses.” The theory we have been considering appears to afford an
explanation of their antecedents. According to it, they are broken
fragments of two dark stellar masses which were shattered to pieces by
collision. After what has been stated concerning the production of the
gaseous nebulæ out of which our solar system was formed, it must be
regarded as highly improbable, if not impossible, that the whole of the
fragments projected outwards with such velocity should be converted into
the gaseous condition. Multitudes of the smaller fragments, especially
those towards the outer circumference of the nebulous mass, meeting with
little or no obstruction to their onward progress, would pass outwards
into space with a velocity which would carry them beyond the risk of
falling back into the nebula. They would then continue their progress in
their separated forms as meteorites. If this be their origin, then
meteorites are the offspring of sidereal masses, and not their parents,
as Mr. Lockyer concludes.
[Footnote 6: _Manchester Science Lectures_, Fifth Series, p. 31.]
These meteorites must be of vast antiquity, for if they are fragments of
the dark bodies then they must be not only older than our solar system,
but older than the nebula from which that system was formed. Some of
them, however, may have come from other systems. They are fragments
which may yet cast some light on the history of the dark bodies.
Comets, bodies which in many points seem allied to meteorites, probably
have, as we shall shortly see, a similar origin.
II. _Motion of the Stars; how of such different velocities, and always
in straight lines._
It will be only when the two bodies, coming from contrary directions,
collide with equal momentum that the entire motion will be stopped. But
in the case of stellar masses moving, as it were, at random in every
direction this is a condition which will but rarely occur. Accordingly,
in most cases the resulting stars will have more or less motion. In
short, the stars should, according to the theory, be moving in all
directions and with all varieties of velocity. Further, it follows that
these motions ought to be in perfectly straight lines, and not in
definite orbits of any kind. So far as observation has yet determined,
all these conditions seem to be fulfilled. Sometimes it will happen that
the two bodies will strike each other obliquely. In this case the
resulting star, both as to the direction and velocity of its motion,
will, to a large extent, be the resultant of the two concurrent forces.
III. _Motion of the Stars not due to their Mutual Attractions._
According to the theory the absolute motion of the stars is due, not to
the influence of gravity, but to motions which originally belonged to
the two component masses out of which the star arose; motion regarding
the origin of which science can no more inform us than it can regarding
the origin of the masses themselves. There is strong presumptive
evidence that the motion of the stars is due to this cause. We know that
there are stars which have a far greater velocity than can result from
gravitation, such, for example, as the star 1830 Groombridge, which has
a velocity of 200 miles per second. Suppose, with Professor Newcomb,
that the number of stars belonging to the universe amounts to
100,000,000, and that these have, on the average, five times the mass of
the sun, and are spread out in a layer across which light requires
30,000 years to pass. Then computation shows that, unless the attractive
power of the whole were sixty-four times greater than it really is, it
could not have conferred on Groombridge the motion which it possesses,
or arrest it in its onward course.[7] We are therefore forced, as
Professor Newcomb remarks, to one of two alternatives, viz.: “Either the
bodies which compose our universe are vastly more massive and numerous
than telescopic examination seems to indicate, or 1830 Groombridge is a
runaway star, flying on a boundless course through infinite space, with
such momentum that the attraction of all the bodies of the universe can
never stop it.”
[Footnote 7: Newcomb’s _Astronomy_, p. 487, English edition, 1878.]
As regards the theory we are discussing, it is the same which
alternative is taken, for both are equally favourable. If the former,
then, according to the theory that stellar heat had its origin in
collision, it is presumptive evidence that space is occupied by dark
bodies far more numerous and massive than the luminous ones which the
telescope reveals. If the latter, viz. that the star has a velocity
which never could have been produced by attraction, “then,” as says
Professor Newcomb, “it must have been flying forward through space from
the beginning, and, having come from an infinite distance, must now be
passing through our system for the first and only time.” The probability
is, however, that the star derived its motion from the source from which
it derived its light and heat; namely, from the collision of the two
masses out of which it arose. If the star is ever to be arrested in its
onward course, it must be by collision; but such an event would be its
final end.
There are other stars, such as 61 Cygni, ε Indi, Lalande 21258, Lalande
21185, μ Cassiopeiæ, and Arcturus, possessed of motions which could not
have been derived from gravity. And there are probably many more of
which, owing to their enormous distances, the proper motions have not
been detected. α Centauri, the nearest star in the heavens, by less than
one-half, is distant twenty-one millions of millions of miles; and there
are, doubtless, many visible stars a thousand times more remote. A star
at this distance, though moving transversely to the observer at the
enormous rate of 100 miles per second, would take upwards of thirty
years to change its position so much as one second, and consequently
1,800 years to change its position one minute. In fact, we should have
to watch the star for a generation or two before we could be certain
whether it was moving or not.
IV. _Probable Origin of Comets._
Great difficulty has been experienced in accounting for the origin of
comets upon the nebular hypothesis. They approach the sun from all
directions, and their motions, in relation to the planets, are as often
retrograde as direct. Not only are their orbits excessively elliptical,
but they are also inclined to the ecliptic at all angles from 0° to 90°.
It is evidently impossible to account satisfactorily for the origin of
comets if we assume them all to have been evolved out of the solar
nebula, although this has been attempted by M. Faye and others. Comets
are evidently, as Laplace and Professor A. Winchell both conclude,
strangers to our system, and have come from distant regions of space. If
they belonged to the solar system they could not, says Professor
Winchell, have parabolic and hyperbolic paths. “Only a small portion of
the comets,” he remarks, “are known to move in elliptic orbits.”[8] This
assumption that they are foreigners will account for all the
peculiarities of their motions; but how are we to account for their
coming into our system? How did they manage to leave that system in
which they had their origin? If a comet have come from one of the fixed
stars trillions of miles distant, the motion by which it traversed the
intervenient space could not, possibly, have been derived from gravity.
We are therefore obliged to assume that the motion was a projected
motion. Comets, in all probability, have the same origin as meteorites.
The materials composing them, like those of the meteorites, were
probably projected from nebulæ by the expulsive force of the heat of
concussion which produced the nebulæ. Some of them, especially those
with elliptic orbits, may have possibly been projected from the solar
nebula.
[Footnote 8: _World Life._ p. 27.]
V. _Nebulæ._
It is a curious circumstance that the theory here advanced seems to
afford a rational explanation of almost every peculiarity of nebulæ, as
I have, on former occasions, endeavoured, at some length, to prove.[9]
[Footnote 9: _Philosophical Magazine_, July 1878; _Climate and
Cosmology_, Chap. xix.]
1. _Origin of nebulæ._—We have already seen that the theory affords a
rational account of the origin of nebulæ.
2. _How nebulæ occupy so much space._—It accounts for the enormous
_space_ occupied by nebulæ. It may be objected that, enormous as would
be the original temperature of the solar system produced by the primeval
collision, it would nevertheless be insufficient to expand the mass,
against gravity, to such an extent that it would occupy the entire space
included within the orbit of Neptune. But it will be perceived, from
what has already been stated regarding the dispersion of the materials
before they had sufficient time to assume the gaseous condition, that
this dispersion was the main cause of the gaseous nebula coming to
occupy so much space. And, to go farther back, it was the suddenness and
almost instantaneity with which the mass would receive the entire store
of energy, before it had time to assume even the molten, not to say the
gaseous, condition, which led to tremendous explosions, followed by a
wide dispersion of materials.
3. _Why nebulæ are of such varied shapes._—Although the dispersion of
the materials would be in all directions, it would, according to the law
of probability, very rarely take place uniformly in every direction.
There would generally be a greater amount of dispersion in some
directions than in others, and the materials would thus be carried along
various lines and to diverse distances; and, although gravity would tend
to bring the widely scattered materials ultimately together into one or
more spherical masses, yet, owing to the exceedingly rarified condition
of the gaseous mass, the nebulæ would change form but slowly.
4. _Broken fragments in a gaseous mass of an excessively high
temperature the first stage of a nebula._—From what has already been
shown, it will be seen that after the colliding of the two dark bodies
the first condition of the resulting nebula would be an enormous space
occupied by broken fragments of all sizes dashing against each other
with tremendous velocities, like the molecules in a perfect gas. All the
interspaces between those fragments would be entirely filled with a
gaseous mass, which, at its earliest stages at least, as in the case of
the solar nebula, would have a temperature probably more than one
hundred thousand times that of the voltaic arc. Whether such a mass
would be visible is a point which can hardly be determined, as we can
have no experience on earth of a gas at such a temperature.
That there are some of the nebulæ which appear to consist of solid
matter interspersed in a gaseous mass is shown by the researches of Mr.
Lockyer[10] and others. In fact, the theory is held by Professor
Tait[11] that nebulæ consist of clouds of stones—or meteor-swarms, as
Mr. Lockyer would term them—in an atmosphere of hydrogen, each stone of
which, moving about and coming into collision with some other, is
thereby generating heat which renders the circumambient gas
incandescent. In reference to this theory of Professor Tait, Mr. Lockyer
says that the phenomena of the spectroscope can be quite well explained
“on the assumption of a cloud of stones, providing always that you could
at the same time show reasonable cause why these clouds of stones were
‘banging about’ in an atmosphere of hydrogen.”[12] The theory, however,
does not appear to afford any rational explanation of this banging about
of the stones to and fro in all directions; for, according to it, the
only force available is gravitation, and this can produce merely a
motion of the materials towards the centre of the mass. Under these
conditions very little impinging of the stones against each other would
take place. But, according to the theory here adopted, we have an agency
incalculably more effective than gravity, one which accounts not merely
for the impact of the stones, but for their very existence as such,
inasmuch as it explains both what they are and whence they came.
[Footnote 10: _Proceedings of Royal Society_, vol. xliii. p. 117.]
[Footnote 11: _Good Words_ for 1875, p. 861.]
[Footnote 12: _Manchester Science Lectures._]
Mr. Lockyer has recently fully adopted Professor Tait’s suggestion as to
the nature and origin of nebulæ, and has endeavoured to give it further
development. He considers the nebulæ to be composed of sparse
meteorites, the collisions of which give the nebulæ their temperature
and luminosity. He divides the nebulæ into three groups, “according as
the formative action seems working towards a centre; round a centre in a
plane, or nearly so; or in one direction only.” As a result we have
globular, spheroidal, and cometic nebulæ.
_Globular nebulæ_ he accounts for in the following manner. “If we,” he
says, “for the sake of the greatest simplicity consider a swarm of
meteorites at rest, and then assume that others from without approach it
from all directions, their previous paths being deflected, the question
arises whether there will not be at some distance from the centre of the
swarm a region in which collisions will be most valid. If we can answer
this question in the affirmative, it will follow that some of the
meteorites arrested here will begin to move in almost circular orbits
round the common centre of gravity.
“The major axes of these orbits may be assumed to be not very diverse,
and we may further assume that, to begin with, one set will preponderate
over the rest. Their elliptic paths may throw the periastron passage to
a considerable distance from the common centre of gravity; and if we
assume that the meteorites with this common mean distance are moving in
all planes, and that some are direct and some retrograde, there will be
a shell in which more collisions will take place than elsewhere. _Now,
this collision surface will be practically the only thing visible, and
will present to us the exact and hitherto unexplained appearance of a
planetary nebula—a body of the same intensity of luminosity at its edge
and centre—thus putting on an almost phosphorescent appearance._
“If the collision region has any great thickness, the centre should
appear dimmer than the portion nearer the edge.
“Such a collision surface, as I use the term, is presented to us during
a meteoric display by the upper part of our atmosphere.”[13]
[Footnote 13: _Proc. of Royal Society_, vol. xliv. p. 5.]
_Spheroidal nebulæ_, he considers, are produced by the rotation of what
was at first a globular rotating swarm of meteorites.
_Cometic nebulæ_ are explained, he considers, “on the supposition that
we have either a very condensed swarm moving at a very high velocity
through a sheet of meteorites at rest, or the swarm at rest surrounded
by a sheet, all moving in the same direction.”
In an able and interesting work, which seems almost utterly unknown in
England,[14] Professor Winchell has advanced views similar to those of
Tait and Lockyer regarding the nature and origin of nebulæ. But he, in
addition, discusses the further question of the origin of those swarms.
I shall have occasion to refer to Professor Winchell’s views more fully
when we come to the consideration of the pre-nebular condition of the
universe.
[Footnote 14: _World Life, or Comparative Geology_, by Alexander
Winchell, LL.D., Professor of Geology and Palæontology in the University
of Michigan. Chicago: S. C. Griggs & Co. 1883.]
Amongst the first to advance the meteoric hypothesis of the origin and
formation of the solar system was probably the late Mr. Richard A.
Proctor. This was done in his work, “Other Worlds than Ours,” published
in 1870. “Under the continual rain of meteoric matter,” he says, “it may
be said that the earth, sun, and planets are _growing_. Now, the idea
obviously suggests itself that the whole growth of the solar system,
from its primal condition to its present state, may have been due to
processes resembling those which we now see taking place within its
bounds.” He further adds: “It seems to me that not only has this general
view of the mode in which our system has reached its present state a
greater support from what is now actually going on than the nebular
hypothesis of Laplace, but that it serves to account in a far more
satisfactory manner for the principal peculiarities of the solar system.
I might, indeed, go farther, and say that where those peculiarities seem
to oppose themselves to Laplace’s theory they give support to those I
have put forward.”[15] He then goes on to show the points wherein his
theory seems to him to offer a better explanation of those peculiarities
than that of Laplace.
[Footnote 15: _Other Worlds_, chap. ix.]
5. _The gaseous condition the second stage of a nebula._—The second
stage obviously follows as a necessary consequence from the first; for
the fragments, in the case under consideration, possess energy in the
form of motion, which, with the heat of their circumambient vapour, is
more than sufficient not only to convert the fragments into the gaseous
state, but to produce complete dissociation of the chemical elements.
The complete transformation of the first stage into the second must,
therefore, be simply a matter of time.
According to the laws of probability it may, however, sometimes happen
that the two original dark bodies will not collide with force sufficient
to confer on the broken fragments the energy required to convert them
all into the gaseous condition. The result in this case would, no doubt,
be that the untransformed fragments, drawn together by their mutual
attractions, would collide and form an imperfect star or sun, without a
planet. Such a star might continue luminous for a few thousands or
perhaps a few millions of years, as the case might be, when it would
begin to fade, and finally disappear. We have here an imperfect nebula,
resulting in an imperfect star. In short, we should have in those
stellar masses, on a grand scale, what we witness every day around us in
organic nature, viz. imperfect formations. Such occasional imperfections
give variety and add perfection to the whole. How dreary and monotonous
would nature be, were every blade of grass, every plant, every animal,
and every face we met formed after the most perfect model!
6. _The gaseous condition essential to the nebular hypothesis._—It is
found that the density of the interior planets of our solar system
compared with that of the more remote is about as five to one. The
obvious conclusion is that there is a preponderance of the metallic
elements in the interior planets and of metalloids in the exterior. It
thus becomes evident, as Mr. Lockyer has so clearly shown,[16] that when
our solar system existed in a nebulous condition the metallic or denser
elements would occupy the interior portion of the nebula and the
metalloids the exterior. Taking a section of this nebula from its centre
to its circumference, the elements would in the main be found arranged
according to their densities: the densest at the centre, and the least
dense at the circumference. If we compare the planets with their
satellites, we find the same law holding true. The satellites of
Jupiter, for example, have a density of about only one-fifth of that of
the planet, or about one twenty-fifth of that of our earth, showing that
when the planet was rotating as a nebulous mass the more dense elements
were in the central parts and the less dense at the outer rim, where the
satellites were being formed. Again, if we take the case of our globe,
we find, as Mr. Lockyer remarks, the same distribution of materials,
proving that when the earth was in the nebulous state the metallic
elements chiefly occupied the central regions, and the metalloids those
outer parts which now constitute the earth’s crust.
[Footnote 16: _Manchester Science Lectures._]
All these facts show that the _sifting_ and _sorting_ of the chemical
elements according to their densities must have taken place when our
solar system was in the condition of a nebula. But, further, it seems
impossible that this could have taken place had the materials composing
the nebula been in the solid form, even supposing that they had taken
the form of clouds of stones.
It is equally impossible that the nebula could have been in the fluid or
liquid state during this process. This is obvious, for the nebula must
then have occupied, at least, the entire space within the orbit of the
most remote planet. But our solar system in the liquid condition could
not occupy one-millionth part of that space. It is therefore evident
that the nebula must have been in the state of a gas, and a gas of
extreme tenuity.
7. _The mass must have possessed an excessive temperature._—There is
ample evidence, Mr. Lockyer thinks, to show that the temperature of the
solar nebula was as great as that of the sun at the present time. But I
think it is extremely probable that, in some of its stages, the nebula
had a very much higher temperature than that now possessed by the sun.
There must, during the sifting period, have been complete chemical
dissociation, so as to keep the metals and the metalloids uncombined,
and thus allow the elements to arrange themselves according to their
densities. The nebula hypothesis, remarks Mr. Lockyer, “is almost
worthless unless we assume very high temperatures, because, unless you
have heat enough to get perfect dissociation, you will not have that
sorting out which always seems to follow the same law.”
8. _Gravitation could, under no possible condition, have generated the
amount of heat required by the nebular hypothesis._—The nebular
hypothesis does not profess to account for the origin of nebulæ. It
starts with matter existing in space in the nebulous condition, and
explains how, by condensation, suns, planets &c. are formed out of it.
In fact, it begins at the middle of a process: it begins with this fine,
attenuated material in the process of being drawn together and condensed
under the influence of attraction, and professes to explain how, as the
process goes on, a solar system necessarily results. To simplify our
inquiry we shall confine our attention to the solar nebula, and consider
in the first place how far condensation may be regarded as a sufficient
source of heat.
A. _Condensation._—The heat which our nebula could have derived from
condensation up to the time that Neptune was detached from the mass, no
matter how far the outer circumference of the mass may have originally
extended beyond the orbit of that planet, could not have amounted to
over 1/7,000,000 of a thermal unit (772 foot-pounds) for each cubic
foot. It is perfectly obvious that this amount could not have produced
the dissociation required; and without the required dissociation Neptune
could never have been formed. Further, it is physically impossible that
the materials of which our solar system are composed could have existed
in the gaseous state in a cool condition prior to condensation. Unless
possessed of great heat, even hydrogen could not exist in stellar space
in the gaseous form; and far less could carbon, iron, platinum, &c.
Before Neptune could have been formed the whole of the materials of the
system must have possessed heat, not only sufficient to reduce them to
the gaseous state, but sufficient to produce complete dissociation. But
by no conceivable means could gravitation have conferred this amount of
heat by the time that the mass had condensed to just within the limits
of the orbit of Neptune.
B. _Solid globes colliding under the influence of gravity alone._—As we
have already seen, the view has been adopted by Sir W. Thomson that the
solar nebula may have resulted from the colliding of cold, solid globes
with the velocity due to their mutual gravitation alone. He states his
views as follows:
“Suppose, now, that 29,000,000 cold, solid globes, each of about the
same mass as the moon, and amounting in all to a total mass equal to the
sun’s, are scattered as uniformly as possible on a spherical surface of
radius equal to one hundred times the radius of the earth’s orbit, and
that they are left absolutely at rest in that position. They will all
commence falling towards the centre of the sphere, and will meet there
in 250 years, and every one of the 29,000,000 globes will then, in the
course of half an hour, be melted, and raised to a temperature of a few
hundred thousand or a million degrees Centigrade. The fluid mass thus
formed will, by this prodigious heat, be exploded outwards in vapour or
gas all round. Its boundary will reach to a distance considerably less
than one hundred times the radius of the earth’s orbit on first flying
out to its extreme limit. A diminishing series of out-and-in
oscillations will follow, and the incandescent globe, thus contracting
and expanding alternately, in the course, it may be, of 300 or 400
years, will settle to a radius of forty times the radius of the earth’s
orbit.”[17]
[Footnote 17: _Proceedings of Royal Institution_, vol. xii. p. 16.]
The reason which he assigns for the incandescent globe settling down at
a radius forty times that of the earth’s orbit is as follows: “The
radius of a steady globular gaseous nebula of any homogeneous gas is 40
per cent. of the radius of the spherical surface from which its
ingredients must fall to their actual positions in the nebula to have
the same kinetic energy as the nebula has.”
If the solar nebula thus produced would be swelled out into a spherical
incandescent mass with a radius 40 times the radius of the earth’s
orbit, simply because the globes fell from a distance of 100 times the
radius of that orbit, then for a similar reason the mass would have a
radius of 400 times that of the earth’s orbit had the globes fallen from
a distance of 1,000 times the radius, and 400,000 times if the globes
had fallen from a distance of 1,000,000 times the radius, and two-fifths
of any conceivable distance from which they may have fallen.
Supposing all this to be _physically_ possible, which it undoubtedly is
not, still the heat generated would not be sufficient; for, whatever the
radius of the nebula might be, its entire energy, both kinetic and
potential, is simply what is obtained from gravitation, and this, as we
have seen, is insufficient.
9. _Condensation the third and last condition of a nebula._—According to
the gravitation theory, condensation is the first stage of a nebula as
well as the last; for, according to it, gravity is the force which both
collects together the scattered materials and gives them their heat.[18]
Before condensation begins there can, according to the gravitation
theory, be no such thing as a nebula properly so called. The materials
exist, of course, but they do not exist in the form of a nebula.
According to the impact theory which I here advocate, condensation
cannot begin till after the nebula has begun to lose the heat with which
it was originally endowed.
[Footnote 18: Laplace held a more accurate view of the primitive
condition of the solar nebula. He considered that, owing to intense
heat, the solar mass became expanded to the limits of the remotest
planetary orbit of our system; that, in cooling, it began slowly to
condense; and that, as condensation went on, planet after planet became
detached from the mass. Laplace, however, offered no explanation of the
manner in which the primitive nebula obtained its heat.]
10. _How nebulæ emit such feeble light._—The light of nebulæ is mainly
derived from glowing hydrogen and nitrogen in a condition of extreme
gaseous tenuity; and it is well known that these gases are exceedingly
bad radiators. The oxyhydrogen flame, although its temperature is
surpassed only by that of the voltaic arc, gives a light so feeble as to
be scarcely visible in daylight. The small luminosity of nebulæ is,
however, mainly due to a different cause. The enormous space occupied by
those bodies is not so much due to the heat which they possess as to the
fact that their materials were dispersed into space before they had time
to pass into the gaseous condition; so that, by the time that this
latter state was assumed, the space occupied was far greater than was
demanded either by the temperature or by the amount of heat which they
originally received. If we adopt the nebular hypothesis of the origin of
our solar system, we must assume that our sun’s mass, when in the
condition of a nebula, extended beyond the orbit of the planet Neptune,
and consequently filled the entire space included within that orbit.
Even supposing Neptune’s orbit to have been its outer limit, which,
obviously, was not the case, it would nevertheless have occupied
274,000,000,000 times the space it does at present. We shall assume, as
before, that 50,000,000 years’ heat was generated by the concussion. Of
course, there might have been twice or even ten times that quantity; but
it is of no importance what amount is in the meantime adopted. Enormous
as 50,000,000 years’ heat is, it yet gives, as we shall presently see,
only 32 foot-pounds of energy for each cubic foot. The amount of heat
due to concussion being equal, as before stated, to 100,000,000,000
foot-pounds for each pound of the mass, and a cubic foot of the sun at
his present density of 1·43 weighing 89 pounds, each cubic foot must
have possessed 8,900,000,000,000 foot-pounds. But when the mass was
expanded sufficiently to occupy 274,000,000,000 times its original space
(which it would do when it extended to the orbit of Neptune), the heat
possessed by each cubic foot would then amount to only 32 foot-pounds.
In point of fact it would not even amount to so much, for a quantity
equal to upwards of 20,000,000 years’ heat would necessarily be consumed
in work against gravity in the expansion of the mass, all of which
would, of course, be given back in the form of heat as the mass
contracted. During the nebulous condition, however, this quantity would
exist in an entirely different form, so that only 19 out of the 32
foot-pounds per cubic foot generated by concussion would then exist as
heat. The density of the nebula would be only 1/16,248,160 that of
hydrogen at ordinary temperature and pressure. The 19 foot-pounds of
heat in each cubic foot would thus be sufficient to maintain an
excessive temperature; for there would be in each cubic foot only
1/440,000 of a grain of matter. But, although the _temperature_ would be
excessive, the _quantity_ both of light and heat in each cubic foot
would of necessity be small. The heat being only 1/71 of a thermal unit,
the light emitted would certainly be exceedingly feeble, resembling very
much the electric light in a vacuum-tube.
VI. _Binary Systems._
The theory affords a rational explanation of the origin of binary stars.
Binary stars, in so far as regards their motion, follow also, of course,
as a consequence, from the gravitation theory. If two bodies come into
grazing collision, “they will,” says Sir William Thomson, “commence
revolving round their common centre of inertia in long elliptic orbits.
Tidal interaction between them will diminish the eccentricities of their
orbits, and, if continued long enough, will cause them to revolve in
circular orbits round their centre of inertia.”[19] This conclusion was
pointed out many years ago by Dr. Johnstone Stoney.
[Footnote 19: _Proceedings of Royal Institution_, vol. xii. p. 15.]
VII. _Sudden Outbursts of Stars._
The case of a star suddenly blazing forth and then fading away, such as
that observed by Tycho Brahe in 1572, may be accounted for by supposing
that the star had been struck by one of the dark bodies—an event not at
all impossible, or even improbable. In some cases of sudden outbursts,
such as that of Nova Cygni, for example, the phenomenon may result from
the star encountering a swarm of meteorites. The difficulty in the case
of Nova Cygni is to account for the very sudden decline of its
brilliancy. This might, however, be explained by supposing that the
outburst of luminosity was due to the destruction of the meteorites, and
not to any great increase of heat produced in the star itself. A swarm
of meteorites converted into incandescent vapour would not be long in
losing its brilliancy.
Mr. Lockyer thinks that the outburst was produced by the collision of
two swarms of meteorites, and not by the collision of the meteorites
with a previously existing star.[20]
[Footnote 20: _Proceedings of the Royal Society_, vol. xliii. p. 140.]
Amongst the millions of stars occupying stellar space catastrophes of
this sort may, according to the theory, be expected sometimes to happen,
although, like the collisions which originate stars themselves, they
must, doubtless, be events of but rare occurrence.
VIII. _Star Clusters._
A star cluster will result from an immensely widespread nebula breaking
up into a host of separate nuclei, each of which becomes a star. The
irregular manner in which the materials would, in many cases, be widely
distributed through space after collision would prevent a nebula from
condensing into a single mass. Subordinate centres of attraction would
be established, as was long ago shown by Sir William Herschel in his
famous memoir on the formation of stars;[21] and around these the
gaseous particles would arrange themselves and gradually condense into
separate stars, which would finally assume the condition of a cluster.
[Footnote 21: _Philosophical Transactions_ for 1811.]
IX. _Age of the Sun’s Heat: a Crucial Test._
When we come to the question of the age of the sun’s heat, and the
length of time during which that orb has illuminated our globe, it
becomes a matter of the utmost importance which of the two theories is
to be adopted. On the age of the sun’s heat rests the whole question of
geological time. A mistake here is fundamental. If gravitation be the
only source from which the sun derived its heat, then life on the globe
cannot possibly date farther back than 20,000,000 years; for under no
possible form could gravitation have afforded, at the present rate of
radiation, sufficient heat for a longer period. It will not do to state
in a loose and general way, as has been frequently done, that the sun
may have been supplying our globe with heat at its present rate for
20,000,000 or 100,000,000 years, for gravitation could have done no such
thing; a period of 20,000,000, not 100,000,000, years is the lowest
which is admissible on that theory. Not even that length of time would
be actually available; for this period is founded on Pouillet’s estimate
of the rate of solar radiation, which has been proved by Langley to be
too small, the correct rate being 1·7 times greater. “Thus,” as says Sir
W. Thomson, “instead of Helmholtz’s 20,000,000 years, we have only
12,000,000.” But the 12,000,000 years would not in reality be available
for plant and animal life; for undoubtedly millions of years would
elapse before our globe could become adapted for either flora or fauna.
If there is no other source of heat for our system than gravitation, it
is doubtful if we can calculate on much more than half that period for
the age of life on the earth. Professor Tait probably over-estimates the
time when he affirms “that 10,000,000 years is about the utmost that can
be allowed, from the physical point of view, for all the changes that
have taken place on the earth’s surface since vegetable life of the
lowest known form was capable of existing there.”[22] And this is
certainly about all that can ever be expected from gravitation;
mathematical computation has demonstrated that it can give no more. The
other theory, founded on motion in space—a cause as real as
gravitation—labours under no such limitation. According to it, so far at
least as regards the store of energy which may have been possessed by
the sun, plant and animal life may date back, not to 10,000,000 years,
but to a period indefinitely more remote. In fact, there is as yet no
known limit to the amount of heat which this cause may have produced;
for this depended upon the velocities of the two bodies at the moment
prior to collision, and what these velocities were we have no means of
knowing. They might have been 500 miles a second, or 5,000 miles a
second, for anything which can be shown to the contrary. Of course I by
no means affirm that it is as much as 100,000,000 years since life began
on our earth; but I certainly do affirm that, in so far as a possible
source of the sun’s energy is concerned, life may have begun at a period
as remote.
[Footnote 22: _Recent Advances in Physical Sciences_, p. 175.]