TIME AND TIDE IN THE SOLAR SYSTEM
Early ideas of cosmogony—The Laplacian hypothesis—Tidal
friction in the earth-moon system—Its application by Kelvin
to the question of the earth’s antiquity—Its application
by Sir G. Darwin to the history of the moon and the date
of its birth—Difficulties in the way of the Laplacian
hypothesis—The Planetesimal hypothesis—The origin of the
ancestral solar nebula and its transformation into the solar
system—Early stages of the earth’s history.
Speculative fancies concerning the origin of the world form the subject
matter of many of the earliest writings on record, and throughout the
intellectual history of mankind the problem has proved to be one of
supreme fascination. It was not, however, until quite recent times
that the efforts of imagination gave place to reasoned hypotheses,
tempered by a more sober regard for physical probabilities. At first,
on having attained the status of a science, geology steadfastly
refused to consider seriously the cosmogonic fantasies then current.
It was Hutton, who by advocating the direct observation of nature in
place of the old scholastic arguments, first delivered geology from
the inevitable wranglings that would necessarily have arisen from so
premature a discussion of the beginning of things. Cosmogony, in spite
of this, continued to receive attention from workers in other sciences,
and while to-day we are still unable from geological facts alone to
trace back with confidence the details of the earth’s beginning, yet
the uncertainty which justified Hutton in entirely disregarding the
earth’s genesis no longer exists. Astronomy, physics, and chemistry
have all contributed to the elucidation of what may be called the
prehistoric period, and have done much to remove our modern ideas from
the dangerous quicksands of speculation.
It is becoming more and more evident that many of the fundamental
problems of geology can be solved only with reference to the processes
involved in the making of the earth and in its subsequent evolution.
The dynamic agencies at work to-day are genetically the outcome of the
ancestral forces which first moulded our planet, and theoretically, the
tectonics and constitution of the earth’s crust should lead back to
a more complete understanding of its initial condition. But the mind
of man is impatient of delay; shrewd guesses are made and gradually
adjusted to known facts, with the result that many geological doctrines
are founded not on observation alone, but also in part on fundamental
hypotheses.
During the 19th century scientific thought was powerfully influenced
by the achievement of Laplace, for it was he who first presented the
famous Nebular hypothesis in a consistent and acceptable form. Previous
thinkers, notably Buffon in 1745, and Kant in 1755, had put forward
similar generalisations, but they fell into certain errors which
Laplace escaped, and their expositions lacked the completeness and
authority which his mathematical genius guaranteed. In the _Système
du Monde_, published in 1796, Laplace attempted to trace the gradual
evolution of the solar system from a spheroidal nebula, under the
normal operation of natural laws. He started with a hot gaseous nebula
of lens-like shape extending beyond the present orbit of the outermost
planet and rotating slowly in the same direction as that of the sun.
The average density of such a nebula would be about ¹/₂₅₀,₀₀₀,₀₀₀
that of ordinary air. As Laplace explicitly states that the sun was
already foreshadowed in the nebula as a strongly condensed central
nucleus, the outer atmosphere must have been of inconceivable tenuity,
a condition maintained only by intense heat. Through the loss of this
heat by radiation, and under the influence of its own gravitation, the
nebula would slowly contract. In accordance with the laws of dynamics,
contraction would necessarily be accompanied by a compensating increase
in the rate of rotation. At a certain stage, the centrifugal force at
the Equator would balance the attraction of gravity, and a ring of
gas would be left behind. The same process of ring separation would
afterwards be repeated from time to time as contraction progressed,
and each ring being inherently unstable, would rupture, ultimately
forming a spheroidal mass with the requisite directions of rotation and
revolution. The Asteroids, a group of tiny planets revolving in the
zone between Mars and Jupiter, probably represent a ring which failed
to coalesce into a single planet. In their newly-born condition the
planets were still hot and gaseous, and by the operation of the same
mechanical agencies on a smaller scale most of them detached a second
generation of rings, and these having aggregated in turn became the
satellites. The great central nucleus, continuing to contract after the
last planetary ring had been abandoned, became the sun.
On this hypothesis the earth was originally a hot fluid globe with
a heavy atmosphere consisting of the vapours of its more volatile
constituents. As it contracted it rotated faster and faster, until a
limiting velocity was attained which allowed the separation of the
ring which ultimately condensed to form the moon. At a later stage the
earth began to solidify and the crust first made its appearance. The
lighter igneous rocks, the granites and corresponding lavas, presumably
formed the outer layers, while beneath this zone the more basic magmas
arranged themselves in the order of their density. When cooling had
sufficiently progressed, the waters condensed to form the oceans, and
with the emergence of the lands, denudation began for the first time
and the earth’s historical period was inaugurated.
At the time of the birth of the moon the rotatory velocity of the
earth must have been very rapid compared with that of the present day,
and an obvious deduction is that the earth has gradually slowed down
in the course of its history—in spite of the accelerative effect of
contraction—and is probably still being retarded. From a comparative
study of ancient and modern eclipses, Dunthorne demonstrated in 1749
that the earth appeared to be losing time. More than a century later,
Adams showed from a revision of all the data, that the loss amounted to
22 seconds in a century, although he was careful to point out that the
assumptions on which his calculation was based were themselves not
securely founded. It was Kant who started the idea that the ceaseless
operation of tidal friction would tend to bring about this result. Long
afterwards Kelvin indicated the way in which tidal retardation might be
applied to estimate the date of the earth’s solidification. He supposed
that the form then assumed by the earth had survived in its essential
features throughout geological history. Subsequent diminution of the
rate of rotation was not considered to be attended by a corresponding
change of oblateness. Granting this assumption, the present figure
of the earth ought to inform us of the rate of rotation under which
it would be in fluid equilibrium at the time of consolidation. After
making these concessions to speculation, Kelvin safeguarded himself by
assigning wide limits to the earth’s age. His maximum estimate was a
liberal 1000 million years, but he further stated his opinion that if a
much higher antiquity than 100 million years were demanded, the polar
flattening and equatorial bulging should be more marked than we find
them.
These conclusions were necessarily somewhat vague, and based as they
were on a very questionable assumption, they were readily susceptible
to damaging criticism. It is known from the concordant evidence
afforded by seismic, geo-physical, and astronomical phenomena that
the earth is essentially solid throughout with a rigidity more than
twice that of steel. So far our conception of the earth is similar to
Kelvin’s, but the postulate that such a body could resist rotational
changes without modification in shape, cannot now be granted. As a
whole the earth tends to conform to the laws of fluids, though its
response may be tardy and the alteration of form may lag considerably
behind the ultimate cause. This being so, it would be more correct to
refer Kelvin’s time limits to the period of “lag” rather than to the
period of the earth’s history as a solid globe.
Sir G. Darwin’s departure from the ring conception of Laplace in the
case of the moon, and his alternative theory of the moon’s origin and
history are well known. Tracing back to their logical conclusions the
effects of tidal friction in the earth-moon system, he has developed
one of the most fascinating romances in the domain of cosmogony.
Unfortunately it is impossible to apply any definite dates to the
critical stages of this history, if for no other reason than the
imperfection of our present lunar and tidal theories. His lower
estimate of the time which has elapsed since the disruptive catastrophe
lies between 50 and 60 million years, but the actual time would
certainly be much greater. Indeed, Darwin himself, referring to the
problem of cosmical time after the advent of radium and the overthrow
of the older standards, wrote, “I feel with some degree of confidence
that if the tidal theory shall ultimately be condemned it will not meet
its execution on the score of lack of time.” A recent discussion of
the problem by Prof. Chamberlin and his colleagues is unfavourable to
Darwin’s view. After a careful study of the rate of tidal retardation
they show that the lengthening of the day is of the order of one second
in 500,000 years, and that if the physical condition of the earth has
remained essentially as at present, at least 220,000 million years must
have elapsed since the day occupied 20 of our present hours and the
month 29 such days. Yet just after the birth of the moon, as outlined
by Darwin, day and month were alike in duration, each being equal to
about three of our present hours. It must be confessed that, after all,
we know but little of the moon’s history with certainty.
At the time of its announcement to the world the Laplacian theory was
remarkably in accordance with the knowledge of the time. But as further
discoveries were made, numerous inconsistencies and contradictions
arose. Not only were certain of the movements of the planets and
satellites found to be in a retrograde direction, but, besides these
awkward facts, at every stage of the postulated development of the
solar system insuperable mechanical difficulties appear which render
the truth of the hypothesis highly improbable. Finally, in the dynamics
of the system there are so many discrepancies between the requirements
of theory and the actual circumstances that Prof. Moulton and Dr. See
both insist that it could not have originated in the way that Laplace
imagined. The heavens have been diligently searched for nebulæ of
the Laplacian type, but no certain case has been observed. The vast
majority conform to the spiral type and to a nebula of this kind appeal
has been made in the recently developed Planetesimal hypothesis of
Chamberlin and Moulton.
[Illustration: FIG. 5.
Symmetrical Nebula in Piscium, M 74.]
[Illustration: FIG. 6.
Whirlpool Nebula in Canes Venatici, M 51.
SPIRAL NEBULÆ.]
The general structure of a spiral nebula is immediately suggestive
of tidal action. From a central nucleus two spiral arms emerge at
diametrically opposite points. Often they are beautifully defined
(Figs. 5, 6), but seen from the side they appear as discs of misty
light. In the arms nebulous knots and irregularities are generally
apparent, the precursors, perhaps, of a system of bodies analogous in
their distribution to the planets. To account for the existence of a
spiral form, conditions of extreme tidal distortion are suggested. In
the case of our ancestral sun such conditions would be brought about
by the close approach of another celestial body. As the stranger
drew near, the tidal stresses set up would gradually increase until
explosive outbursts of matter from the sun were projected in the
plane of attraction, one on the near side, another on the far side.
The result of the combined attractions of the two suns on the ejected
material would be to develop a spiral structure. An enormous number of
tiny planets or planetesimals would thus begin to circulate about the
sun, associated with scattered knots of larger dimensions which would
form the nuclei of the future planets and satellites. These knots would
at once begin to grow by coalescence at the expense of the vast numbers
of planetesimals associated with them in adjacent zones. Dynamically
the scheme is sound, and the many suggestive consequences which unfold
themselves explain away most of the difficulties which proved so
embarrassing to the Laplacian hypothesis. Into a discussion of these
advantages space does not allow us to enter, but it may be said that of
all the attempts to grapple with the fundamental problem of the genesis
of the solar system, the Planetesimal hypothesis appears to be the
most successful. It is to be welcomed, apart from its many convincing
features, if only because of its stimulation to the further study of
the early stages of earth history.
The earth began on this hypothesis as a nebular knot, and it has since
grown up to its present mass by the capture of outside planetesimals.
It is very unlikely that it was ever in a molten condition. Internal
heat arose in part from the condensation of the mass during the
period of its growth. The temperature would slowly rise until the
fusion point of certain of the constituents was reached and the
liquid tongues and pockets thus formed would then tend to move away
from the centre—the lighter and less viscous stony material being
squeezed upwards relatively to a network of the heavier and more rigid
metallic material. Once vulcanism had been initiated in this way the
process would continue until a highly metallic nucleus had collected.
Surrounding it there would gradually form a thick zone of silicate
rocks, the differentiation from the original heterogeneous mixture of
stony and metallic constituents being due to the selective fusion of
the former. In dealing with the question of the earth’s heat in a later
chapter, the value, and indeed the necessity of this conception will be
realised.
The atmosphere and oceans must have been derived from the planetesimals
themselves, and on analogy with rocks and meteorites, the planetesimals
would not be lacking in the raw material from which to evolve them.
Even now, the outer 70 miles of the earth’s crust would be competent to
supply all the nitrogen of the atmosphere, the water of the oceans
and the vast quantity of carbon-dioxide represented by limestones and
carbonaceous deposits. With the existence of an ocean and atmosphere,
a new factor in surface differentiation arose. Mechanical and chemical
denudation became possible, and the first sediments were deposited.
Although the earth’s growth had not yet ceased, all the agents occupied
in its subsequent development were now at work and its geological
history may be said to have definitely commenced.