Tidal force

“ This is the reason why the sun, although it exceeds the moon in mass more than 25,000,000 times, and is situated only about 400 times as far away from the earth, exercises comparatively so slight a tidal force on the water of the ocean. If the tidal force varied as the square of the distance, like the ordinary effects of gravitation, 82the tides produced by the sun would be more than 150 times as high as those produced by the moon, and would sweep New York, London, and all the seaports of the world to destruction. ”

“ It is strange that, while so much has been written and spoken about the possibility of turning the energy of the tides to account for power in the service of man, comparatively little attention has been paid to the problem of similarly utilising the wave-power, which goes to waste in such inconceivably huge quantities. Where the tidal force elevates and depresses the sea-water on a shore, through a vertical distance of say eight feet, about once in twelve hours, the waves of the ocean will perform the same work during moderate weather once in every twelve or fifteen seconds. ”

“ If there should be any fluid materials on the small satellite they must be distracted by the most terrific tides. It is certain that seas on its surface would be submitted to tidal forces at least thirty times as potent as those on the earth. ”

“ But the true explanation of the phenomenon is doubtless this: the tidal current runs strongest from west to east, and its power is greater in the more open channel or farther from the land. In other words its force increases southwards, and as the direction of the bank is from northwest to southeast, the size of the masses coming from the westward and thrown ashore must always be largest where the motion of the water is most violent. ”

“ Those who have encountered a tidal wave must have observed that the sea rises rather slowly, but the descent into the trough is steep. This is due to the fact that the water is lifted, possibly very slowly, under the action of a varying force, great at first, but dying out quickly, while the raised mass is urged downward by the constant force of gravity. ”

“ These instruments, although differing considerably in detail from the Indian predictor, are essentially the same in principle.
§ 9. Tidal Friction.—All solid bodies yield more or less to stress; if they are perfectly elastic they regain their shapes after the stresses are removed, if imperfectly elastic or viscous they yield to the stresses. We may thus feel certain that the earth yields to tide-generating force, either with perfect or imperfect elasticity. ”

“ With the gravitational Satellite's Velocity Retarded. law of force between the two bodies the retardation must prevail over the acceleration [13] The action of tidal friction may appear somewhat paradoxical, but it is the exact converse of the acceleration of the linear and angular velocity and the diminution of distance of a satellite moving through a resisting medium. ”

“ But as their huge bulks come nearer, the chains that bind them become stronger and stronger, and the tremendous pull of the one gargantuan fire ball on the other raises titanic tides of flame. Great streamers of gas shoot out, and all the space about is lighted by the flaming suns. The pull of gravity becomes more and more intense, and as the one circles the other, the tide is pulled up, and the mighty ball of fire, which, for all its existence has been practically motionless as far as rotation goes, begins to acquire a greater and greater rotational speed as the tidal drag urges it on. ”

“ In considering the effect of the natural forces still in operation during the many thousands of years during which they have been at work, it is necessary to bear in mind that the level of the sea has all along remained the same, except so far as it is varied by the rise and fall of the tide, and by the exceptional exaggerations of tidal movement caused by the wind. ”

“ This rise and fall of the waters along the coast, accompanied frequently by strong currents, are produced directly by the arrival in the shoal water of a pulsation of the ocean, which becomes a true onward-moving gravity wave as it nears the land. In the open sea the amplitude of the tidal undulations is but two or three feet, and their rate of travel in general 700 to 800 miles per hour. ”

“ Were it not for the inertia of the ocean and the resistance offered by the irregular continents, high tide would always exist exactly under the moon, and we should have high water at any place just at the time when the moon is in the south and crossing the meridian of that place. But while the inertia of the water tends to make all tides late, the irregular distribution of the land breaks up the tidal wave into so many wave-crests and greatly retards their progress. ”

“ 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 [Pg 380] pushed away by the violent tidal action. ”

“ The velocity of all tidal currents would also be greater than at present, and as the power of a current of water for transporting solid material held in suspension increases rapidly with the velocity, so we may infer that the efficiency of tidal currents as a vehicle for the transport of comminuted rocks would be greatly increased. It is thus obvious that tides with a rise and fall double in vertical height of those which we know at present would add a large increase to their efficiency as geological agents. ”

“ Though we have not yet put the tides into harness, yet tides are not idle. Work they will do, whether useful or not. In some places the tidal currents are scouring out river-channels; in others they are moving sand-banks. From a scientific point of view the work done by the tides is of unspeakable importance. To realize the importance, let us ask the question, Whence is this energy derived with which the tides do their work? The answer seems a very obvious one. If the tides are caused by the moon, the energy they possess must also be derived from the moon. ”

“ Tide is the vertical rise and fall of the water, and tidal current is the horizontal flow. The tide rises and falls, the tidal current floods and ebbs. The navigator is concerned with the amount and time of the tide, as it affects access to shallow ports. The navigator is concerned with the time, speed, and direction of the tidal current, as it will affect his ship’s position, speed, and course. ”

“ Progress of the Tide-wave over the Ocean and in the British Seas.—Sufficient tidal data would give the state of the tide at every part of the world at the same instant of time, and if the tide wave is a progressive one, like such wave as we may observe travelling along a canal, we should be able to picture mentally the motion of the tide-wave over the ocean and the successive changes in the height of water at any one place. ”

“ In such cases, however, where the rivers flow into tidal seas, it is important to place the jetties sufficiently apart to avoid any loss of tidal influx, since the tidal flow assists the fresh-water discharge in keeping the outlet open; whereas, with rivers flowing into tideless seas, a moderate restriction of the width between the jetties increases the scour. ”

“ Enough sail had to be carried to give the ship ample steerage way when the walls of rushing water passed us, for incredible as it may seem to those who have not had the experience, the waves of the sea run at a speed far greater than anything afloat that sails. The tidal wave, theoretical at least, must have a speed of one thousand miles per hour in order that the tides may follow the attraction of the moon and girdle the earth each twenty-four hours; some speed even in these days of rapid travel. ”

“ The general effect is, however, that the friction of the tides makes the earth revolve more slowly; in other words, that part of the energy of rotation of the earth, so to speak, is consumed in rubbing against the tidal waters. All the work, therefore, that the tides do in undermining our cliffs, and washing away our beaches, is extracted by the sun and moon from the work stored up in the rotation of the earth. ”

“ The ocean tides are also immensely powerful, but the rise and fall of the water is so slight and so gradual in most places that an enormous plant is [175] required to obtain any appreciable amount of power. In certain regions, however, tidal power is actually in use to-day. ”

“ If the theory of the tides was to be the simple one so often described, then at every port noon should be the hour of high water on the day of the new moon or of the full moon, because then both tide-exciting bodies are on the meridian at the same time. Even if the friction retarded the great tidal wave uniformly, the high tide on the days of full or change should always occur at fixed hours ”

“ Hence, as the tides may be regarded as a machine doing work, we have to ascertain the origin of that energy which they are continually expending. It is at this point that we first begin to feel the difficulties inherent in the theory of tidal evolution. ”

“ But man, slow to take nature's constant hint of assistance, makes slight and irregular use of this power, in careening ships and getting them afloat when aground.
This power may be applied in various ways. A large body, of the heaviest materials that will float, may first be raised by it, and being attached to the end of a balance reaching from the land, or from a stationary support fastened to the bottom, when the tide falls the whole weight will be brought to bear upon the end of the balance. Also, when the tide rises, it may be made to exert a nearly equal force in the opposite direction. ”

“ Along the south coast from Land's End to Beachy Head the average velocity is 40 miles per hour, the rate reducing as the wave approaches Dover, in the vicinity of which the tidal waves from the two different directions meet, one arriving approximately twelve hours later than the other, thus forming tides which are a result of the amalgamation of the two waves. On the ebb tide the direction of the waves is reversed. ”

“ It is sometimes possible to effect the desired end by applying the power of the tide. A sea-wall judiciously thrown out will sometimes concentrate the tide into a much narrower channel. Its daily oscillations will be accomplished with greater vehemence, and as the tide rushes furiously backwards and forwards over the obstacle, the incessant action will gradually remove it, and the impediment to navigation may be cleared away. Here we actually see the tides performing a piece of definite and very laborious work, to accomplish which by the more ordinary agents would be a stupendous task. ”

“ The semi-synchronous oscillation of the Southern Ocean raises the magnitude of oceanic tides somewhat above these directly generated values.
Oceanic tides are true waves, not currents. Coast tides are currents. The momentum of the water, when the tidal wave breaks upon a continent and rushes up channels, raises coast tides to a much greater height—in some places up to 50 or 60 feet, or even more. ”

“ The general conceptions are even more different than the results, and the later theory is less concerned with the tides in oceans, which probably affect only our Earth, than with those of a planet in a fluid or viscous condition, which may still continue to some extent after the surface has become 126 partly solidified. He therefore studies the tide raising force, and the tendency to retardation of rotation, by the Sun on the planets, and by these on their satellites while still in a fluid state, tabulating some very striking results. ”

“ The stability theorems shewed in effect that the ordinary perturbations produced effects which sooner or later compensated one another, so that if a particular motion was accelerated at one time it would be retarded at another; but this is not the case with tidal friction. Tidal action between the earth and the moon, for example, gradually lengthens both the day and the month, and increases the distance between the earth and the moon. Solar tidal action has a similar though smaller effect on the sun and earth. ”

“ If the Straits were wide enough to admit the progress of the tidal wave there would be a rise and fall in the ports of the Mediterranean, but as they are not, only the tidal current rushes in and out twice every day. ”

“ But in the present condition of the globe, where the oceans are separated by continents and broken by islands, the progress of the tidal waves is obstructed, deflected, and wholly stopped in a great variety of ways and places, so that the hours, amount, and behavior of the tides are exceedingly varied in different regions, and are often very puzzling, forming one of the most difficult matters with which the practical navigator has to deal. ”

“ Three small islets are all that now remain of this once fertile district.25
The breakers of the ocean receive no small aid in their 67 work of destruction from the action of tides and currents which co-operate with the winds to keep the waters of the sea in constant motion. And though the winds may sleep for a time, the tides and currents are always actively at work, and never for a moment cease to wear away the land. But they are even more powerful auxiliaries as agents of transport. ”