§ 16

Until comparatively recent times, until, in fact, the full dawn of modern science, the tides ranked amongst the greatest of nature's mysteries. And, indeed, what agency could be invoked to explain this mysteriously regular flux and reflux of the waters of the ocean? It is not surprising that that steady, rhythmical rise and fall suggested to some imaginative minds the breathing of a mighty animal. And even when man first became aware of the fact that this regular movement was somehow associated with the moon, was he much nearer an explanation? What bond could exist between the movements of that distant world and the diurnal variation of the waters of the earth? It is reported that an ancient astronomer, despairing of ever resolving the mystery, drowned himself in the sea.

The Earth Pulled by the Moon

But it was part of the merit of Newton's mighty theory of gravitation that it furnished an explanation even of this age-old mystery. We can see, in broad outlines at any rate, that the theory of universal attraction can be applied to this case. For the moon, Newton taught us, pulls every particle of matter throughout the earth. If we imagine that part of the earth's surface which comprises the Pacific Ocean, for instance, to be turned towards the moon, we see that the moon's pull, acting on the loose and mobile water, would tend to heap it up into a sort of mound. The whole earth is pulled by the moon, but the water is more free to obey this pull than is the solid earth, although small tides are also caused in the earth's solid crust. It can be shown also that a corresponding hump would tend to be produced on the other side of the earth, owing, in this case, to the tendency of the water, being more loosely connected, to lag behind the solid earth. If the earth's surface were entirely fluid the rotation of the earth would give the impression that these two humps were continually travelling round the world, once every day. At any given part of the earth's surface, therefore, there would be two humps daily, i.e. two periods of high water. Such is the simplest possible outline of the gravitational theory of the tides.

The actually observed phenomena are vastly more complicated, and the complete theory bears very little resemblance to the simple form we have just outlined. Everyone who lives in the neighbourhood of a port knows, for instance, that high water seldom coincides with the time when the moon crosses the meridian. It may be several hours early or late. High water at London Bridge, for instance, occurs about one and a half hours after the moon has passed the meridian, while at Dublin high water occurs about one and a half hours before the moon crosses the meridian. The actually observed phenomena, then, are far from simple; they have, nevertheless, been very completely worked out, and the times of high water for every port in the world can now be prophesied for a considerable time ahead.

The Action of Sun and Moon

It would be beyond our scope to attempt to explain the complete theory, but we may mention one obvious factor which must be taken into account. Since the moon, by its gravitational attraction, produces tides, we should expect that the sun, whose gravitational attraction is so much stronger, should also produce tides and, we would suppose at first sight, more powerful tides than the moon. But while it is true that the sun produces tides, it is not true that they are more powerful than those produced by the moon. The sun's tide-producing power is, as a matter of fact, less than half that of the moon. The reason of this is that distance plays an enormous rôle in the production of tides. The mass of the sun is 26,000,000 times that of the moon; on the other hand it is 386 times as far off as the moon. This greater distance more than counterbalances its greater mass, and the result, as we have said, is that the moon is more than twice as powerful. Sometimes the sun and moon act together, and we have what are called spring tides; sometimes they act against one another, and we have neap tides. These effects are further complicated by a number of other factors, and the tides, at various places, vary enormously. Thus at St. Helena the sea rises and falls about three feet, whereas in the Bay of Fundy it rises and falls more than fifty feet. But here, again, the reasons are complicated.

§ 17

Origin of the Moon

But there is another aspect of the tides which is of vastly greater interest and importance than the theory we have just been discussing. In the hands of Sir George H. Darwin, the son of Charles Darwin, the tides had been made to throw light on the evolution of our solar system. In particular, they have illustrated the origin and development of the system formed by our earth and moon. It is quite certain that, long ages ago, the earth was rotating immensely faster than it is now, and that the moon was so near as to be actually in contact with the earth. In that remote age the moon was just on the point of separating from the earth, of being thrown off by the earth. Earth and moon were once one body, but the high rate of rotation caused this body to split up into two pieces; one piece became the earth we now know, and the other became the moon. Such is the conclusion to which we are led by an examination of the tides. In the first place let us consider the energy produced by the tides. We see evidences of this energy all round the word's coastlines. Estuaries are scooped out, great rocks are gradually reduced to rubble, innumerable tons of matter are continually being set in movement. Whence is this energy derived? Energy, like matter, cannot be created from nothing; what, then, is the source which makes this colossal expenditure possible.

The Earth Slowing down

The answer is simple, but startling. The source of tidal energy is the rotation of the earth. The massive bulk of the earth, turning every twenty-four hours on its axis, is like a gigantic flywheel. In virtue of its rotation it possesses an enormous store of energy. But even the heaviest and swiftest flywheel, if it is doing work, or even if it is only working against the friction of its bearings, cannot dispense energy for ever. It must, gradually, slow down. There is no escape from this reasoning. It is the rotation of the earth which supplies the energy of the tides, and, as a consequence, the tides must be slowing down the earth. The tides act as a kind of brake on the earth's rotation. These masses of water, held back by the moon, exert a kind of dragging effect on the rotating earth. Doubtless this effect, measured by our ordinary standards, is very small; it is, however, continuous, and in the course of the millions of years dealt with in astronomy, this small but constant effect may produce very considerable results.

But there is another effect which can be shown to be a necessary mathematical consequence of tidal action. It is the moon's action on the earth which produces the tides, but they also react on the moon. The tides are slowing down the earth, and they are also driving the moon farther and farther away. This result, strange as it may seem, does not permit of doubt, for it is the result of an indubitable dynamical principle, which cannot be made clear without a mathematical discussion. Some interesting consequences follow.

Since the earth is slowing down, it follows that it was once rotating faster. There was a period, a long time ago, when the day comprised only twenty hours. Going farther back still we come to a day of ten hours, until, inconceivable ages ago, the earth must have been rotating on its axis in a period of from three to four hours.

At this point let us stop and inquire what was happening to the moon. We have seen that at present the moon is getting farther and farther away. It follows, therefore, that when the day was shorter the moon was nearer. As we go farther back in time we find the moon nearer and nearer to an earth rotating faster and faster. When we reach the period we have already mentioned, the period when the earth completed a revolution in three or four hours, we find that the moon was so near as to be almost grazing the earth. This fact is very remarkable. Everybody knows that there is a critical velocity for a rotating flywheel, a velocity beyond which the flywheel would fly into pieces because the centrifugal force developed is so great as to overcome the cohesion of the molecules of the flywheel. We have already likened our earth to a flywheel, and we have traced its history back to the point where it was rotating with immense velocity. We have also seen that, at that moment, the moon was barely separated from the earth. The conclusion is irresistible. In an age more remote the earth did fly in pieces, and one of those pieces is the moon. Such, in brief outline, is the tidal theory of the origin of the earth-moon system.

The Day Becoming Longer

At the beginning, when the moon split off from the earth, it obviously must have shared the earth's rotation. It flew round the earth in the same time that the earth rotated, that is to say, the month and the day were of equal length. As the moon began to get farther from the earth, the month, because the moon took longer to rotate round the earth, began to get correspondingly longer. The day also became longer, because the earth was slowing down, taking longer to rotate on its axis, but the month increased at a greater rate than the day. Presently the month became equal to two days, then to three, and so on. It has been calculated that this process went on until there were twenty-nine days in the month. After that the number of days in the month began to decrease until it reached its present value or magnitude, and will continue to decrease until once more the month and the day are equal. In that age the earth will be rotating very slowly. The braking action of the tides will cause the earth always to keep the same face to the moon; it will rotate on its axis in the same time that the moon turns round the earth. If nothing but the earth and moon were involved this state of affairs would be final. But there is also the effect of the solar tides to be considered. The moon makes the day equal to the month, but the sun has a tendency, by still further slowing down the earth's rotation on its axis, to make the day equal to the year. It would do this, of course, by making the earth take as long to turn on its axis as to go round the sun. It cannot succeed in this, owing to the action of the moon, but it can succeed in making the day rather longer than the month.

Surprising as it may seem, we already have an illustration of this possibility in the satellites of Mars. The Martian day is about one half-hour longer than ours, but when the two minute satellites of Mars were discovered it was noticed that the inner one of the two revolved round Mars in about seven hours forty minutes. In one Martian day, therefore, one of the moons of Mars makes more than three complete revolutions round that planet, so that, to an inhabitant of Mars, there would be more than three months in a day.

- - - The End - - -

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