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[Illustration: FIG. 117.--Tide-gauge for recording local tides, a pencil moved up and down by a float writes on a drum driven by clockwork.]
The first thing to be done by any port which wishes its tides to be predicted is to set up a tide-gauge, or automatic recorder, and keep it working for a year or two. The tide-gauge is easy enough to understand: it marks the height of the tide at every instant by an irregular curved line like a barometer chart (Fig. 117). These observational curves so obtained have next to be fed into a fearfully complex machine, which it would take a whole lecture to make even partially intelligible, but Fig.
118 shows its aspect. It consists of ten integrating machines in a row, coupled up and working together. This is the "harmonic analyzer," and the result of passing the curve through this machine is to give you all the constituents of which it is built up, viz. the lunar tide, the solar tide, and eight of the sub-tides or disturbances. These ten values are then set off into a third machine, the tide-predicter proper. The general mode of action of this machine is not difficult to understand.
It consists of a string wound over and under a set of pulleys, which are each set on an excentric, so as to have an up-and-down motion. These up-and-down motions are all different, and there are ten of these movable pulleys, which by their respective excursions represent the lunar tide, the solar tide, and the eight disturbances already analyzed out of the tide-gauge curve by the harmonic analyzer. One end of the string is fixed, the other carries a pencil which writes a trace on a revolving drum of paper--a trace which represents the combined motion of all the pulleys, and so predicts the exact height of the tide at the place, at any future time you like. The machine can be turned quite quickly, so that a year's tides can be run off with every detail in about half-an-hour. This is the easiest part of the operation. Nothing has to be done but to keep it supplied with paper and pencil, and turn a handle as if it were a coffee-mill instead of a tide-mill. (Figs. 119 and 120.)
[Illustration: FIG. 118.--Harmonic analyzer; for analyzing out the constituents from a set of observational curves.]
My subject is not half exhausted. I might go on to discuss the question of tidal energy--whether it can be ever utilized for industrial purposes; and also the very interesting question whence it comes. Tidal energy is almost the only terrestrial form of energy that does not directly or indirectly come from the sun. The energy of tides is now known to be obtained at the expense of the earth's rotation; and accordingly our day must be slowly, very slowly, lengthening. The tides of past ages have destroyed the moon's rotation, and so it always turns the same face to us. There is every reason to believe that in geologic ages the moon was nearer to us than it is now, and that accordingly our tides were then far more violent, rising some hundreds of feet instead of twenty or thirty, and sweeping every six hours right over the face of a country, ploughing down hills, denuding rocks, and producing a copious sedimentary deposit.
[Illustration: FIG. 119.--Tide-predicter, for combining the ascertained constituents into a tidal curve for the future.]
In thus discovering the probable violent tides of past ages, astronomy has, within the last few years, presented geology with the most powerful denuding agent known; and the study of the earth's past history cannot fail to be greatly affected by the modern study of the intricate and refined conditions attending prolonged tidal action on incompletely rigid bodies. [Read on this point the last chapter of Sir R. Ball's _Story of the Heavens_.]
[Illustration: Fig. 120.--Weekly sheet of curves. Tides for successive days are predicted on the same sheet of paper, to economise space.]
I might also point out that the magnitude of our terrestrial tides enables us to answer the question as to the internal fluidity of the earth. It used to be thought that the earth's crust was comparatively thin, and that it contained a molten interior. We now know that this is not the case. The interior of the earth is hot indeed, but it is not fluid. Or at least, if it be fluid, the amount of fluid is but very small compared with the thickness of the unyielding crust. All these, and a number of other most interesting questions, fringe the subject of the tides; the theoretical study of which, started by Newton, has developed, and is destined in the future to further develop, into one of the most gigantic and absorbing investigations--having to do with the stability or instability of solar systems, and with the construction and decay of universes.
These theories are the work of pioneers now living, whose biographies it is therefore unsuitable for us to discuss, nor shall I constantly mention their names. But Helmholtz, and Thomson, are household words, and you well know that in them and their disciples the race of Pioneers maintains its ancient glory.
NOTES FOR LECTURE XVIII
Tides are due to incomplete rigidity of bodies revolving round each other under the action of gravitation, and at the same time spinning on their axes.
Two spheres revolving round each other can only remain spherical if rigid; if at all plastic they become prolate. If either rotate on its axis, in the same or nearly the same plane as it revolves, that one is necessarily subject to tides.
The axial rotation tends to carry the humps with it, but the pull of the other body keeps them from moving much. Hence the rotation takes place against a pull, and is therefore more or less checked and retarded. This is the theory of Von Helmholtz.
The attracting force between two such bodies is no longer _exactly_ towards the centre of revolution, and therefore Kepler's second law is no longer precisely obeyed: the rate of description of areas is subject to slight acceleration. The effect of this tangential force acting on the tide-compelling body is gradually to increase its distance from the other body.
Applying these statements to the earth and moon, we see that tidal energy is produced at the expense of the earth's rotation, and that the length of the day is thereby slowly increasing. Also that the moon's rotation relative to the earth has been destroyed by past tidal action in it (the only residue of ancient lunar rotation now being a scarcely perceptible libration), so that it turns always the same face towards us. Moreover, that its distance from the earth is steadily increasing.
This last is the theory of Professor G.H. Darwin.
Long ago the moon must therefore have been much nearer the earth, and the day was much shorter. The tides were then far more violent.
Halving the distance would make them eight times as high; quartering it would increase them sixty-four-fold. A most powerful geological denuding agent. Trade winds and storms were also more violent.
If ever the moon were close to the earth, it would have to revolve round it in about three hours. If the earth rotated on its axis in three hours, when fluid or pasty, it would be unstable, and begin to separate a portion of itself as a kind of bud, which might then get detached and gradually pushed away by the violent tidal action. Hence it is possible that this is the history of the moon. If so, it is probably an exceptional history. The planets were not formed from the sun in this way.
Mars' moons revolve round him more quickly than the planet rotates: hence with them the process is inverted, and they must be approaching him and may some day crash along his surface. The inner moon is now about 4,000 miles away, and revolves in 7-1/2 hours. It appears to be about 20 miles in diameter, and weighs therefore, if composed of rock, 40 billion tons. Mars rotates in 24-1/2 hours.
A similar fate may _possibly_ await our moon ages hence--by reason of the action of terrestrial tides produced by the sun.
THE TIDES, AND PLANETARY EVOLUTION
In the last lecture we considered the local peculiarities of the tides, the way in which they were formed in open ocean under the action of the moon and the sun, and also the means by which their heights and times could be calculated and predicted years beforehand. Towards the end I stated that the subject was very far from being exhausted, and enumerated some of the large and interesting questions which had been left untouched. It is with some of these questions that I propose now to deal.
I must begin by reminding you of certain well-known facts, a knowledge of which I may safely assume.
And first we must remind ourselves of the fact that almost all the rocks which form the accessible crust of the earth were deposited by the agency of water. Nearly all are arranged in regular strata, and are composed of pulverized materials--materials ground down from pre-existing rocks by some denuding and grinding action. They nearly all contain vestiges of ancient life embedded in them, and these vestiges are mainly of marine origin. The strata which were once horizontal are now so no longer--they have been tilted and upheaved, bent and distorted, in many places. Some of them again have been metamorphosed by fire, so that their organic remains have been destroyed, and the traces of their aqueous origin almost obliterated. But still, to the eye of the geologist, all are of aqueous or sedimentary origin: roughly speaking, one may say they were all deposited at the bottom of some ancient sea.
The date of their formation no man yet can tell, but that it was vastly distant is certain. For the geological era is not over. Aqueous action still goes on: still does frost chip the rocks into fragments; still do mountain torrents sweep stone and mud and _debris_ down the gulleys and watercourses; still do rivers erode their channels, and carry mud and silt far out to sea. And, more powerful than any of these agents of denudation, the waves and the tides are still at work along every coast-line, eating away into the cliffs, undermining gradually and submerging acre after acre, and making with the refuse a shingly, or a sandy, or a muddy beach--the nucleus of a new geological formation.
Of all denuding agents, there can be no doubt that, to the land exposed to them, the waves of the sea are by far the most powerful. Think how they beat and tear, and drive and drag, until even the hardest rock, like basalt, becomes honeycombed into strange galleries and passages--Fingal's Cave, for instance--and the softer parts are crumbled away. But the area now exposed to the teeth of the waves is not great.
The fury of a winter storm may dash them a little higher than usual, but they cannot reach cliffs 100 feet high. They can undermine such cliffs indeed, and then grind the fragments to powder, but their direct action is limited. Not so limited, however, as they would be without the tides.
Consider for a moment the denudation import of the tides: how does the existence of tidal rise and fall affect the geological problem?
The scouring action of the tidal currents themselves is not to be despised. It is the tidal ebb and flow which keeps open channel in the Mersey, for instance. But few places are so favourably situated as Liverpool in this respect, and the direct scouring action of the tides in general is not very great. Their geological import mainly consists in this--that they raise and lower the surface waves at regular intervals, so as to apply them to a considerable stretch of coast. The waves are a great planing machine attacking the land, and the tides raise and lower this planing machine, so that its denuding tooth is applied, now twenty feet vertically above mean level, now twenty feet below.
Making all allowance for the power of winds and waves, currents, tides, and watercourses, assisted by glacial ice and frost, it must be apparent how slowly the work of forming the rocks is being carried on. It goes on steadily, but so slowly that it is estimated to take 6000 years to wear away one foot of the American continent by all the denuding causes combined. To erode a stratum 5000 feet thick will require at this rate thirty million years.
The age of the earth is not at all accurately known, but there are many grounds for believing it not to be much older than some thirty million years. That is to say, not greatly more than this period of time has elapsed since it was in a molten condition. It may be as old as a hundred million years, but its age is believed by those most competent to judge to be more likely within this limit than beyond it. But if we ask what is the thickness of the rocks which in past times have been formed, and denuded, and re-formed, over and over again, we get an answer, not in feet, but in miles. The Laurentian and Huronian rocks of Canada constitute a stratum ten miles thick; and everywhere the rocks at the base of our stratified system are of the most stupendous volume and thickness.
It has always been a puzzle how known agents could have formed these mighty masses, and the only solution offered by geologists was, unlimited time. Given unlimited time, they could, of course, be formed, no matter how slowly the process went on. But inasmuch as the time allowable since the earth was cool enough for water to exist on it except as steam is not by any means unlimited, it becomes necessary to look for a far more powerful engine than any now existing; there must have been some denuding agent in those remote ages--ages far more distant from us than the Carboniferous period, far older than any forms of life, fossil or otherwise, ages among the oldest known to geology--a denuding agent must have then existed, far more powerful than any we now know.
Such an agent it has been the privilege of astronomy and physics, within the last ten years, to discover. To this discovery I now proceed to lead up.
Our fundamental standard of time is the period of the earth's rotation--the length of the day. The earth is our one standard clock: all time is expressed in terms of it, and if it began to go wrong, or if it did not go with perfect uniformity, it would seem a most difficult thing to discover its error, and a most puzzling piece of knowledge to utilize when found.
That it does not go much wrong is proved by the fact that we can calculate back to past astronomical events--ancient eclipses and the like--and we find that the record of their occurrence, as made by the old magi of Chaldaea, is in very close accordance with the result of calculation. One of these famous old eclipses was observed in Babylon about thirty-six centuries ago, and the Chaldaean astronomers have put on record the time of its occurrence. Modern astronomers have calculated back when it should have occurred, and the observed time agrees very closely with the actual, but not exactly. Why not exactly?
Partly because of the acceleration of the moon's mean motion, as explained in the lecture on Laplace (p. 262). The orbit of the earth was at that time getting rounder, and so, as a secondary result, the speed of the moon was slightly increasing. It is of the nature of a perturbation, and is therefore a periodic not a progressive or continuous change, and in a sufficiently long time it will be reversed.
Still, for the last few thousand years the moon's motion has been, on the whole, accelerated (though there seems to be a very slight retarding force in action too).
Laplace thought that this fact accounted for the whole of the discrepancy; but recently, in 1853, Professor Adams re-examined the matter, and made a correction in the details of the theory which diminishes its effect by about one-half, leaving the other half to be accounted for in some other way. His calculations have been confirmed by Professor Cayley. This residual discrepancy, when every known cause has been allowed for, amounts to about one hour.
The eclipse occurred later than calculation warrants. Now this would have happened from either of two causes, either an acceleration of the moon in her orbit, or a retardation of the earth in her diurnal rotation--a shortening of the month or a lengthening of the day, or both. The total discrepancy being, say, two hours, an acceleration of six seconds-per-century per century will in thirty-six centuries amount to one hour; and this, according to the corrected Laplacian theory, is what has occurred.
But to account for the other hour some other cause must be sought, and at present it is considered most probably due to a steady retardation of the earth's rotation--a slow, very slow, lengthening of the day.
The statement that a solar eclipse thirty-six centuries ago was an hour late, means that a place on the earth's surface came into the shadow one hour behind time--that is, had lagged one twenty-fourth part of a revolution. The earth, therefore, had lost this amount in the course of 3600 365-1/4 revolutions. The loss per revolution is exceedingly small, but it accumulates, and at any era the total loss is the sum of all the losses preceding it. It may be worth while just to explain this point further.
Suppose the earth loses a small piece of time, which I will call an instant, per day; a locality on the earth will come up to a given position one instant late on the first day after an event. On the next day it would come up two instants late by reason of the previous loss; but it also loses another instant during the course of the second day, and so the total lateness by the end of that day amounts to three instants. The day after, it will be going slower from the beginning at the rate of two instants a day, it will lose another instant on the fresh day's own account, and it started three instants late; hence the aggregate loss by the end of the third day is 1 + 2 + 3 = 6. By the end of the fourth day the whole loss will be 1 + 2 + 3 + 4, and so on. Wherefore by merely losing one instant every day the total loss in _n_ days is (1 + 2 + 3 + ... + _n_) instants, which amounts to 1/2_n_ (_n_ + 1) instants; or practically, when _n_ is big, to 1/2n^2. Now in thirty-six centuries there have been 3600 365-1/4 days, and the total loss has amounted to an hour; hence the length of "an instant," the loss per diem, can be found from the equation 1/2(3600 365)^2 instants = 1 hour; whence one "instant" equals the 240 millionth part of a second. This minute quantity represents the retardation of the earth per day. In a year the aggregate loss mounts up to 1/3600th part of a second, in a century to about three seconds, and in thirty-six centuries to an hour. But even at the end of the thirty-six centuries the day is barely any longer; it is only 3600 365 instants, that is 1/180th of a second, longer than it was at the beginning. And even a million years ago, unless the rate of loss was different (as it probably was), the day would only be thirty-five minutes shorter, though by that time the aggregate loss, as measured by the apparent lateness of any perfectly punctual event reckoned now, would have amounted to nine years.
(These numbers are to be taken as illustrative, not as precisely representing terrestrial fact.)
What can have caused the slowing down? Swelling of the earth by reason of accumulation of meteoric dust might do something, but probably very little. Contraction of the earth as it goes on cooling would act in the opposite direction, and probably more than counterbalance the dust effect. The problem is thus not a simple one, for there are several disturbing causes, and for none of them are the data enough to base a quantitative estimate upon; but one certain agent in lengthening the day, and almost certainly the main agent, is to be found in the tides.
Remember that the tidal humps were produced as the prolateness of a sphere whirled round and round a fixed centre, like a football whirled by a string. These humps are pulled at by the moon, and the earth rotates on its axis against this pull. Hence it tends to be constantly, though very slightly, dragged back.
In so far as the tidal wave is allowed to oscillate freely, it will swing with barely any maintaining force, giving back at one quarter-swing what it has received at the previous quarter; but in so far as it encounters friction, which it does in all channels where there is an actual ebb and flow of the water, it has to receive more than it gives back, and the balance of energy has to be made up to it, or the tides would cease. The energy of the tides is, in fact, continually being dissipated by friction, and all the energy so dissipated is taken from the rotation of the earth. If tidal energy were utilized by engineers, the machines driven would be really driven at the expense of the earth's rotation: it would be a mode of harnessing the earth and using the moon as fixed point or fulcrum; the moon pulling at the tidal protuberance, and holding it still as the earth rotates, is the mechanism whereby the energy is extracted, the handle whereby the friction brake is applied.