Time and Tide: A Romance of the Moon

Let us look at the earth-moon system. The law of the conservation of moment of momentum may, with sufficient accuracy for our present purpose, be interpreted to mean that the total quantity of spin in the system remains unaltered. In our system the spin is threefold; there is first the rotation of the earth on its axis, there is the rotation of the moon on its axis, and then there is the orbital revolution of the moon around the earth. The law to which we refer asserts that the total quantity of these three spins, each estimated in the proper way, will remain constant. It matters not that tides may ebb and flow, or that the distribution of the spin shall vary, but its total amount remains inflexibly constant. One constituent of the total amount—that is, the rotation of the moon on its axis—is so insignificant, that for our present purposes it may be entirely disregarded. We may therefore assert that the amount of spin in the earth, due to its rotation round its axis, added to the amount of spin in the moon due to its revolution round the earth, remains unalterable. If one of these quantities change by increase or by decrease, the other must correspondingly change by decrease or by increase. If, therefore, from any cause, the earth began to spin a little more quickly round its axis, the moon must do a little less spin; and consequently, it must shorten its distance from the earth. Or suppose that the earth's velocity of rotation is abated, then its contribution to the total amount of spin is lessened; the deficiency must therefore be made up by the moon, but this can only be done by an enlargement of the moon's orbit. I should add, as a caution, that these results are true only on the supposition that the earth-moon system is isolated from all external interference. With this proviso, however, it matters not what may happen to the earth or moon, or what influence one of them may exert upon the other, no matter what tides may be raised, no matter even if the earth fly into fragments, the whole quantity of spin of all those fragments would, if added to the spin of the moon, yield the same unalterable total. We are here in possession of a most valuable dynamical principle. We are not concerned with any special theory as to the action of the tides; it is sufficient for us that in some way or other the tides have been caused by the moon, and that being so, the principle of the conservation of spin will apply.

Were the earth and the moon both rigid bodies, then there could be of course no tides on the earth, it being rigid and devoid of ocean. The rotation of the earth on its axis would therefore be absolutely without change, and therefore the necessary condition of the conservation of spin would be very simply attained by the fact that neither of the constituent parts changed. The earth, however, not being entirely rigid, and being subject to tides, this simple state of things cannot continue; there must be some change in progress.

I have already shown that the fact of the ebbing and the flowing of the tide necessitates an expenditure of energy, and we saw that this energy must come either from that stored up in the earth by its rotation, or from that possessed by the moon in virtue of its distance and revolution. The law of the conservation of spin will enable us to decide at once as to whence the tides get their energy. Suppose they took it from the moon, the moon would then lose in energy, and consequently come nearer the earth. The quantity of spin contributed by the moon would therefore be lessened, and accordingly the spin to be made up by the earth would be increased. That means, of course, that the velocity of the earth rotating on its axis must be increased, and this again would necessitate an increase in the earth's rotational energy. It can be shown, too, that to keep the total spin right, the energy of the earth would have to gain more than the moon would have lost by revolving in a smaller orbit. Thus we find that the total quantity of energy in the system would be increased. This would lead to the absurd result that the action of the tides manufactured energy in our system. Of course, such a doctrine cannot be true; it would amount to a perpetual motion! We might as well try to get a steam-engine which would produce enough heat by friction not only to supply its own boilers, but to satisfy all the thermal wants of the whole parish. We must therefore adopt the other alternative. The tides do not draw their energy from the moon; they draw it from the store possessed by the earth in virtue of its rotation.

We can now state the end of this rather long discussion in a very simple and brief manner. Energy can only be yielded by the earth at the expense of some of the speed of its rotation. The tides must therefore cause the earth to revolve more slowly; in other words, the tides are increasing the length of the day.

The earth therefore loses some of its velocity of rotation; consequently it does less than its due share of the total quantity of spin, and an increased quantity of spin must therefore be accomplished by the moon; but this can only be done by an enlargement of its orbit. Thus there are two great consequences of the tides in the earth-moon system—the days are getting longer, the moon is receding further.

These points are so important that I shall try and illustrate them in another way, which will show, at all events, that one and both of these tidal phenomena commend themselves to our common sense. Have we not shown how the tides in their ebb and flow are incessantly producing friction, and have we not also likened the earth to a great wheel? When the driver wants to stop a railway train the brakes are put on, and the brake is merely a contrivance for applying friction to the circumference of a wheel for the purpose of checking its motion. Or when a great weight is being lowered by a crane, the motion is checked by a band which applies friction on the circumference of a wheel, arranged for the special purpose. Need we then be surprised that the friction of the tides acts like a brake on the earth, and gradually tends to check its mighty rotation? The progress of lengthening the day by the tides is thus readily intelligible. It is not quite so easy to see why the ebbing and the flowing of the tide on the earth should actually have the effect of making the moon to retreat; this phenomenon is in deference to a profound law of nature, which tells us that action and reaction are equal and opposite to each other. If I might venture on a very homely illustration, I may say that the moon, like a troublesome fellow, is constantly annoying the earth by dragging its waters backward and forward by means of tides; and the earth, to free itself from this irritating interference, tries to push off the aggressor and to make him move further away.

Fig. 2.

Another way in which we can illustrate the retreat of the moon as the inevitable consequence of tidal friction is shown in the adjoining figure, in which the large body E represents the earth, and the small body M the moon. We may for simplicity regard the moon as a point, and as this attracts each particle of the earth, the total effect of the moon on the earth may be represented by a single force. By the law of equality of action and reaction, the force of the earth on the moon is to be represented by an equal and opposite force. If there were no tides then the moon's force would of course pass through the earth's centre; but as the effect of the moon is to slacken the earth's rotation, it follows that the total force does not exactly pass through the line of the earth's centre, but a little to one side, in order to pull the opposite way to that in which the earth is turning, and thus bring down its speed. We may therefore decompose the earth's total force on the moon into two parts, one of which tends directly towards the earth's centre, while the other acts tangentially to the moon's orbit. The central force is of course the main guiding power which keeps the moon in its path; but the incessant tangential force constantly tends to send the moon out further and further, and thus the growth of its orbit can be accounted for.

We therefore conclude finally, that the tides are making the day longer and sending the moon away further. It is the development of the consequences of these laws that specially demands our attention in these lectures. We must have the courage to look at the facts unflinchingly, and deduce from them all the wondrous consequences they involve. Their potency arises from a characteristic feature—they are unintermitting. Most of the great astronomical changes with which we are ordinarily familiar are really periodic: they gradually increase in one direction for years, for centuries, or for untold ages; but then a change comes, and the increase is changed into a decrease, so that after the lapse of becoming periods the original state of things is restored. Such periodic phenomena abound in astronomy. There is the annual fluctuation of the seasons; there is the eighteen or nineteen year period of the moon; there is the great period of the precession of the equinoxes, amounting to twenty-six thousand years; and then there is the stupendous Annus Magnus of hundreds of thousands of years, during which the earth's orbit itself breathes in and out in response to the attraction of the planets. But these periodic phenomena, however important they may be to us mere creatures of a day, are insignificant in their effects on the grand evolution through which the celestial bodies are passing. The really potent agents in fashioning the universe are those which, however slow or feeble they may seem to be, are still incessant in their action. The effect which a cause shall be competent to produce depends not alone upon the intensity of that cause, but also upon the time during which it has been in operation. From the phenomena of geology, as well as from those of astronomy, we know that this earth and the system to which it belongs has endured for ages, not to be counted by scores of thousands of years, or, as Prof. Tyndall has so well remarked, “Not for six thousand years, nor for sixty thousand years, nor six hundred thousand years, but for æons of untold millions.” Those slender agents which have devoted themselves unceasingly to the accomplishment of a single task may in this long lapse of time have accomplished results of stupendous magnitude. In famed stalactite caverns we are shown a colossal figure of crystal extending from floor to roof, and the formation of that column is accounted for when we see a tiny drop falling from the roof above to the floor beneath. A lifetime may not suffice for that falling drop to add an appreciable increase to the stalactite down which it trickles, or to the growing stalagmite on which it falls; but when the operation has been in progress for immense ages, it is capable of the formation of the stately column. Here we have an illustration of an influence which, though apparently trivial, acquires colossal significance when adequate time is afforded. It is phenomena of this kind which the student of nature should most narrowly watch, for they are the real architects of the universe.

The tidal consequences which we have already demonstrated are emphatically of this non-periodic class—the day is always lengthening, the moon is always retreating. To-day is longer than yesterday; to-morrow will be longer than to-day. It cannot be said that the change is a great one; it is indeed too small to be appreciable even by our most delicate observations. In one thousand years the alteration in the length of a day is only a small fraction of a second; but what may be a very small matter in one thousand years can become a very large one in many millions of years. Thus it is that when we stretch our view through immense vistas of time past, or when we look forward through immeasurable ages of time to come, the alteration in the length of the day will assume the most startling proportions, and involve the most momentous consequences.

Let us first look back. There was a time when the day, instead of being the twenty-four hours we now have, must have been only twenty-three hours, How many millions of years ago that was I do not pretend to say, nor is the point material for our argument; suffice it to say, that assuming, as geology assures us we may assume, the existence of these æons of millions of years, there was once a time when the day was not only one hour shorter, but was even several hours less than it is at present. Nor need we stop our retrospect at a day of even twenty, or fifteen, or ten hours long; we shall at once project our glance back to an immeasurably remote epoch, at which the earth was spinning round in a time only one sixth or even less of the length of the present day. There is here a reason for our retrospect to halt, for at some eventful period, when the day was about three or four hours long, the earth must have been in a condition of a very critical kind.

It is well known that fearful accidents occasionally happen where large grindstones are being driven at a high speed. The velocity of rotation becomes too great for the tenacity of the stone to withstand the stress; a rupture takes place, the stone flies in pieces, and huge fragments are hurled around. For each particular grindstone there is a certain special velocity depending upon its actual materials and character, at which it would inevitably fly in pieces. I have once before likened our earth to a wheel; now let me liken it to a grindstone. There is therefore a certain critical velocity of rotation for the earth at which it would be on the brink of rupture. We cannot exactly say, in our ignorance of the internal constitution of the earth, what length of day would be the shortest possible for our earth to have consistently with the preservation of its integrity; we may, however, assume that it will be about three or four hours, or perhaps a little less than three. The exact amount, however, is not really very material to us; it would be sufficient for our argument to assert that there is a certain minimum length of day for which the earth can hold together. In our retrospect, therefore, through the abyss of time past our view must be bounded by that state of the earth when it is revolving in this critical period. With what happened before that we shall not at present concern ourselves. Thus we look back to a time at the beginning of the present order of things, when the day was only some three or four hours long.

Let us now look at the moon, and examine where it must have been during these past ages. As the moon is gradually getting further and further from us at present, so, looking back into past time, we find that the moon was nearer and nearer to the earth the further back our view extends; in fact, concentrating our attention solely on essential features, we may say that the path of the moon is a sort of spiral which winds round and round the earth, gradually getting larger, though with extreme slowness. Looking back we see this spiral gradually coiling in and in, until in a retrospect of millions of years, instead of its distance from the earth being 240,000 miles, it must have been much less. There was a time when the moon was only 200,000 miles away; there was a time many millions of years ago, when the moon was only 100,000 miles away. Nor can we here stop our retrospect; we must look further and further back, and follow the moon's spiral path as it creeps in and in towards the earth, until at last it appears actually in contact with that great globe of ours, from which it is now separated by a quarter of a million of miles.

Surely the tides have thus led us to the knowledge of an astounding epoch in our earth's past history, when the earth is spinning round in a few hours, and when the moon is, practically speaking, in contact with it. Perhaps I should rather say, that the materials of our present moon were in this situation, for we would hardly be entitled to assume that the moon then possessed the same globular form in which we see it now. To form a just apprehension of the true nature of both bodies at this critical epoch, we must study their concurrent history as it is disclosed to us by a totally different line of reasoning.

Drop, then, for a moment all thought of tides, and let us bring to our aid the laws of heat, which will disclose certain facts in the ancient history of the earth-moon system perhaps as astounding as those to which the tides have conducted us. In one respect we may compare these laws of heat with the laws of the tides; they are both alike non-periodic, their effects are cumulative from age to age, and imagination can hardly even impose a limit to the magnificence of the works they can accomplish. Our argument from heat is founded on a very simple matter. It is quite obvious that a heated body tends to grow cold. I am not now speaking of fires or of actual combustion whereby heat is produced; I am speaking merely of such heat as would be possessed by a red-hot poker after being taken from the fire, or by an iron casting after the metal has been run into the mould. In such cases as this the general law holds good, that the heated body tends to grow cold. The cooling may be retarded no doubt if the passage of heat from the body is impeded. We can, for instance, retard the cooling of a teapot by the well-known practice of putting a cosy upon it; but the law remains that, slowly or quickly, the heated body will tend to grow colder. It seems almost puerile to insist with any emphasis on a point so obvious as this, but yet I frequently find that people do not readily apprehend all the gigantic consequences that can flow from a principle so simple. It is true that a poker cools when taken from the fire; we also find that a gigantic casting weighing many tons will grow gradually cold, though it may require days to do so. The same principle will extend to any object, no matter how vast it may happen to be. Were that great casting 2000 miles in diameter, or were it 8000 miles in diameter, it will still steadily part with its heat, though no doubt the process of cooling becomes greatly prolonged with an increase in the dimensions of the heated body. The earth and the moon cannot escape from the application of these simple principles.

Let us first speak of the earth. There are multitudes of volcanoes in action at the present moment in various countries upon this earth. Now whatever explanation may be given of the approximate cause of the volcanic phenomena, there can be no doubt that they indicate the existence of heat in the interior of the earth. It may possibly be, as some have urged, that the volcanoes are merely vents for comparatively small masses of subterranean molten matter; it may be, as others more reasonably, in my opinion, believe, that the whole interior of the earth is at the temperature of incandescence, and that the eruptions of volcanoes and the shocks of earthquakes are merely consequences of the gradual shrinkage of the external crust, as it continually strives to accommodate itself to the lessening bulk of the fluid interior. But whichever view we may adopt, it is at least obvious that the earth is in part, at all events, a heated body, and that the heat is not in the nature of a combustion, generated and sustained by the progress of chemical action. No doubt there may be local phenomena of this description, but by far the larger proportion of the earth's internal heat seems merely the fervour of incandescence. It is to be likened to the heat of the molten iron which has been run into the sand, rather than to the glowing coals in the furnace in which that iron has been smelted.

There is one volcanic outbreak of such exceptional interest in these modern times that I cannot refrain from alluding to it. Doubtless every one has heard of that marvellous eruption of Krakatoa, which occurred on August 26th and 27th, 1883, and gives a unique chapter in the history of volcanic phenomena. Not alone was the eruption of Krakatoa alarming in its more ordinary manifestations, but it was unparalleled both in the vehemence of the shock and in the distance to which the effects of the great eruption were propagated. I speak not now of the great waves of ocean that inundated the coasts of Sumatra and Java, and swept away thirty-six thousand people, nor do I allude to the intense darkness which spread for one hundred and eighty miles or more all round. I shall just mention the three most important phenomena, which demonstrate the energy which still resides in the interior of our earth. Place a terrestrial globe before you, and fix your attention on the Straits of Sunda; think also of the great atmospheric ocean some two or three hundred miles deep which envelopes our earth. When a pebble is tossed into a pond a beautiful series of concentric ripples diverge from it; so when Krakatoa burst up in that mighty catastrophe, a series of gigantic waves were propagated through the air; they embraced the whole globe, converged to the antipodes of Krakatoa, thence again diverged, and returned to the seat of the volcano; a second time the mighty series of atmospheric ripples spread to the antipodes, and a second time returned. Seven times did that series of waves course over our globe, and leave their traces on every self-recording barometer that our earth possesses. Thirty-six hours were occupied in the journey of the great undulation from Krakatoa to its antipodes. Perhaps even more striking was the extent of our earth's surface over which the noise of the great explosion spread. At Batavia, ninety-four miles away, the concussions were simply deafening; at Macassar, in Celebes, two steamers were sent out to investigate the explosions which were heard, little thinking that they came from Krakatoa, nine hundred and sixty-nine miles away. Alarming sounds were heard over the island of Timor, one thousand three hundred and fifty-one miles away from Krakatoa. Diego Garcia in the Chogos islands is two thousand two hundred and sixty-seven miles from Krakatoa, but the thunders traversed even this distance, and were attributed to some ship in distress, for which a search was made. Most astounding of all, there is undoubted evidence that the sound of the mighty explosion was propagated across nearly the entire Indian ocean, and was heard in the island of Rodriguez, almost three thousand miles away. The immense distance over which this sound journeyed will be appreciated by the fact, that the noise did not reach Rodriguez until four hours after it had left Krakatoa. In fact, it would seem that if Vesuvius were to explode with the same vehemence as Krakatoa did, the thunders of the explosion might penetrate so far as to be heard in London.

There is another and more beautiful manifestation of the world-wide significance of the Krakatoa outbreak. The vast column of smoke and ashes ascended twenty miles high in the air, and commenced a series of voyages around the equatorial regions of the earth. In three days it crossed the Indian ocean, and was traversing equatorial Africa; then came an Atlantic voyage; and then it coursed over central America, before a Pacific voyage brought it back to its point of departure after thirteen days; then the dust started again, and was traced around another similar circuit, while it was even tracked for a considerable time in placing the third girdle round the earth. Strange blue suns and green moons and other mysterious phenomena marked the progress of this vast volcanic cloud. At last the cloud began to lose its density, the dust spread more widely over the tropics, became diffused through the temperate regions, and then the whole earth was able to participate in the glories of Krakatoa. The marvellous sunsets in the autumn of 1883 are attributable to this cause; and thus once again was brought before us the fact that the earth still contains large stores of thermal energy.

Attempts are sometimes made to explain volcanic phenomena on the supposition that they are entirely of a local character, and that we are not entitled to infer the incandescent nature of the earth's interior from the fact that volcanic outbreaks occasionally happen. For our present purpose this point is immaterial, though I must say it appears to me unreasonable to deny that the interior of the earth is in a most highly heated state. Every test we can apply shows us the existence of internal heat. Setting aside the more colossal phenomena of volcanic eruptions, we have innumerable minor manifestations of its presence. Are there not geysers and hot springs in many parts of the earth? and have we not all over our globe invariable testimony confirming the statement, that the deeper we go down beneath its surface the hotter does the temperature become? Every miner is familiar with these facts; he knows that the deeper are his shafts the warmer it is down below, and the greater the necessity for providing increased ventilation to keep the temperature within a limit that shall be suitable for the workmen. All these varied classes of phenomena admit solely of one explanation, and that is, that the interior of the earth contains vast stores of incandescent heat.

We now apply to our earth the same reasoning which we should employ on a poker taken from the fire, or on a casting drawn from the foundry. Such bodies will lose their heat by radiation and conduction. The earth is therefore losing its heat. No doubt the process is an extremely slow one. The mighty reservoirs of internal heat are covered by vast layers of rock, which are such excellent non-conductors that they offer every possible impediment to the leakage of heat from the interior to the surface. We coat our steam-pipes over with non-conducting material, and this can now be done so successfully, that it is beginning to be found economical to transmit steam for a very long distance through properly protected pipes. But no non-conducting material that we can manufacture can be half so effective as the shell of rock twenty miles or more in thickness, which secures the heated interior of the earth from rapid loss by radiation into space. Even were the earth's surface solid copper or solid silver, both most admirable conductors of heat, the cooling down of this vast globe would be an extremely tardy process; how much more tardy must it therefore be when such exceedingly bad conductors as rocks form the envelope? How imperfectly material of this kind will transmit heat is strikingly illustrated by the great blast iron furnaces which are so vitally important in one of England's greatest manufacturing industries. A glowing mass of coal and iron ore and limestone is here urged to vivid incandescence by a blast of air itself heated to an intense temperature. The mighty heat thus generated—sufficient as it is to detach the iron from its close alliance with the earthy materials and to render the metal out as a pure stream rushing white-hot from the vent—is sufficiently confined by a few feet of brick-work, one side of which is therefore at the temperature of molten iron, while the other is at a temperature not much exceeding that of the air. We may liken the brick-work of a blast furnace to the rocky covering of the earth; in each case an exceedingly high temperature on one side is compatible with a very moderate temperature on the other.

Although the drainage of heat away from the earth's interior to its surface, and its loss there by radiation into space, is an extremely tardy process, yet it is incessantly going on. We have here again to note the ability for gigantic effect which a small but continually operating cause may have, provided it always tends in the same direction. The earth is incessantly losing heat; and though in a day, a week, or a year the loss may not be very significant, yet when we come to deal with periods of time that have to be reckoned by millions of years, it may well be that the effect of a small loss of heat per annum can, in the course of these ages, reach unimagined dimensions. Suppose, for instance, that the earth experienced a fall of temperature in its interior which amounted to only one-thousandth of a degree in a year. So minute a quantity as this is imperceptible. Even in a century, the loss of heat at this rate would be only the tenth of a degree. There would be no possible way of detecting it; the most careful thermometer could not be relied on to tell us for a certainty that the temperature of the hot waters of Bath had declined the tenth of a degree; and I need hardly say, that the fall of a tenth of a degree would signify nothing in the lavas of Vesuvius, nor influence the thunders of Krakatoa by one appreciable note. So far as a human life or the life of the human race is concerned, the decline of a tenth of a degree per century in the earth's internal heat is absolutely void of significance. I cannot, however, impress upon you too strongly, that the mere few thousands of years with which human history is cognizant are an inappreciable moment in comparison with those unmeasured millions of years which geology opens out to us, or with those far more majestic periods which the astronomer demands for the events he has to describe.

An annual loss of even one-thousandth of a degree will be capable of stupendous achievements when supposed to operate during epochs of geological magnitude. In fact, its effects would be so vast, that it seems hardly credible that the present loss of heat from the earth should be so great as to amount to an abatement of one-thousandth of a degree per annum, for that would mean, that in a thousand years the earth's temperature would decline by one degree, and in a million years the decline would amount to a thousand degrees. At all events, the illustration may suffice to show, that the fact that we are not able to prove by our instruments that the earth is cooling is no argument whatever against the inevitable law, that the earth, like every other heated body, must be tending towards a lower temperature.