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the tidal wave. The time required for the transmission of the sea-waves from Simoda to San Francisco was twelve hours and thirty-six minutes. The distance being 4,500 miles, the transmission of the wave was at an average rate of 360 miles per hour. The theory of wave-motion teaches us that this velocity will be attained by a free-moving wave in a depth of 1,440 fathoms, which may be taken as the average depth of the Pacific Ocean between Japan and California. It will be observed that the crests of the waves occur at intervals of about twenty-three minutes, corresponding to a length, from crest to crest, of 150 miles. The height when the waves arrived at San Francisco was about eighteen inches from hollow to crest, the high waves caused by the original impulse having gradually flattened out to that form in their transmission across the ocean.
The great earthquake which occurred in Peru, in August, 1868, was likewise recorded on the tide-gauges at San Diego, San Francisco, and Astoria. The fluctuation of the ocean was so great in this instance as to be very sensible to casual observation, and was noted in Australia, at the Sandwich Islands, and at Kodiak, in Alaska. The data obtained from these observations, combined with the result before mentioned, indicate that the average depth of the Pacific Ocean is about 1,800 fathoms.
MOVEMENT OF TIDAL WAVES.
The waves above described, originating with an impulse at one definite point, and propagated freely through the ocean in every direction, with a velocity depending upon the square root of the depth of the sea, may serve as good illustrations of the manner in which tides are propagated through sounds, bays, and rivers. The following table gives the rate of motion for different depths: Depth in feet...... 10: Miles per hour ...........
12. 2 30.0
38. 7 .... 1,000 16
122, 3 ........... 6,000
299.5 That movement of the ocean, however, which we have designated by the name of tide-wave, does not partake of the nature of a wave in the common acceptation of the term, but it is rather to be conceived as a general movement of the water toward a point under the attracting body, and again away from it. Its periodicity is strictly dependent upon that of the attracting body. The velocity of the movement is about 1,000 miles per hour on the equator; it extends to the bottom of the ocean, the depth of which is inconsiderable compared with the radius of the earth. It is not attended by a sensible elevation of the water in midocean; and in this respect the characteristic of what we call a wave is absent. The movement may be likened to that of an impulse given to a very long rigid bar, as of iron. In this case, a sensible time will be
required for the transmission of the impulse from one end to the other, and during its transmission the particles will successively approach to each other, by which an infinitesimal elevation and subsidence, after the manner of a wave, will be produced. In the same way the trans
TIMES AND HEIGHTS OF TIDES ON ATLANTIC COAST OF UNITED STATES
mission of the movement through the incompressible water of the sea is attended with an infinitesimal elevation and recession; but when the movement reaches shallow water, in approaching the shores, the hori. zontal motion is partly translated into vertical motion upon the sloping bottom; and it is thus that the tides attain sensible vertical height.
Now, where a bay or indentation of the coast presents itself, opening favorably to the tide-wave thus developed, and decreases in width from its entrance toward its head, the tide rises higher and higher from the mouth upward. This is due to the concentration of the wave by the approach of the shores and to the gradual shoaling of the bottom.
This effect is strikingly illustrated by a generalization of the heights of the tides on the Atlantic coast of the United States. That coast presents, in its general outline, as represented in the annexed diagram, three large bays: the great southern, from Cape Florida to Cape Hatteras; the great middle, from Cape Hatteras to Nantucket; and the great eastern, from Nantucket to Cape Sable, now known as the Gulf of Maine. It will be seen that the tide-wave arrives at about the same time at the headlands, Cape Florida, Cape Hatteras, Nantucket, and Cape Sable, and that at those points the height is inconsiderable compared with the rise at the head of the several bays. Thus, at Cape Florida the mean rise and fall is only one and one-half of a foot; at Hatteras, but two feet; while at the intermediate entrance to Savannah it reaches seven feet, declining in height toward both capes. Again, at the head of the middle bay, in New York Harbor, it reaches five feet, while on the southeast side of Nantucket Island it is little over one foot. The configuration of the eastern bay is less regular, and the correspondence of heights is not so obvious. The recess of Massachusetts Bay is well marked, the increase in height reaching ten feet at Boston and Plymouth. Rolling on eastward along the coast of Maine, it constantly increases; but the most striking effect of the convergence of shores is exhibited in the Bay of Fundy. At St. John's the mean height of tide is niveteen feet, and at Sackville, in Cumberland Basin, tbirtysix feet, attaining to fifty feet and more at spring-tides.
When the ware leaves the open sea, its front slope and rear slope are equal in length and similar in form, but as it advances into a narrow channel, bay, or river, its front slope becomes short and steep, and its rear slope becomes long and less inclined. Hence arises the fact that at a station near the sea, the time occupied by the rise is equal to that occupied by the descent; but at a station more removed from the sea, the rise occupies a shorter time than the descent. Thus, in Delaware Bay and River we have the following relations of the duration and height of rise and fall:
An examination of this table will show, besides the marked increase in the height of the tide due to the contraction of the shores from the capes up to New Castle, a subsequent loss from friction in a narrow channel of nearly uniform character, and correspondingly a rapid propagation of the tide-wave through the deep water of the bay, and a comparatively slow movement along the narrower channel of the river. At the mouth of the bay the duration of rise exceeds that of fall by ten minutes, while at Philadelphia it is less by two hours forty-two minutes. When the tide is very large compared with the depth of water, this inequality becomes very great; thus, in the Severn River, at Newnham, above Bristol, England, the whole rise of eighteen feet takes place in one and a half hours, while the fall occupies ten hours.
The agency of tidal currents in producing changes in the entrances of bays and barbors is a subject of the first importance to commerce and navigation, and has received full attention in the prosecution of the American coast survey. The laws according to which the changes take place require to be studied by long-continued observation, and when the change is for the worse, the means of counteracting it must be pointed out.
As on the average the same amount of water moves inward and outward with the flood and ebb tides, we might readily suppose that the same amount of material is transported either way, and that no important change would take place in the configuration of the bottom. But the operation of the flood-stream is very different from that of the ebbstream. We have, as a general feature, an interior basin of some extent, communicating with the sea by a comparatively narrow passage. The flood-stream, therefore, running with considerable velocity through this channel, will, as it enters the basin, spread out and become slow, depositing the sand and mud it is charged with, and making extensive flats or sboals opposite the entrance. The ebb-stream runs slowly over the flats from all directions toward the opening without removing much of the deposit, and gradually concentrates in definite narrow channels, which it scoops out, and the depth of which will depend in a great de. gree on the proportion of the area of the basin to the outlet, or, in other terms, on the difference of level which will be reached during the ebb between the basin and the ocean, which determines the greatest velocity and transporting power reached by the ebb-stream.
On the bars of most of the sand-barred harbors on our southern coast, the place and direction of the channel are frequently changed during violent storms; when the direction of the waves happens to be oblique to that of the channel, or when the sea runs directly upon the channel, the depth of water may be considerably diminished for the time being by the sand rolled up by the waves. But in all these cases it is found that the normal depth is speedily restored by the scour of the ebb-tide, which
depends upon the unchanged factors of area and form of basin, height of tide, and character of the material forming the bar.
An interesting instance of this maintenance of the depth of channels from a determinate tidal basin is furnished by the effects of the obstructions placed in the channel over Charleston Bar during the war of the rebellion. On the accompanying diagram is seen the “stone fleet" sunk in the main channel, which at that time had twelve feet of water at low tide where the figure 7 indicates the present depth. There was, moreover, another channel, making out more to the southward, with