CHAPTER II. Time and Tide in the Solar System

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.

Symmetrical Nebula in Piscium, M 74.]

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.