74:2 TIDES spread over six hours either way, is nowhere very rapid. Where a bay or indentation of the coast presents its opening favorably to the tide wave, and decreases in width from the entrance toward its head, the tides rise 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 by which a portion of the horizontal motion is transferred into vertical motion, the velocity of the wave being at the same time retarded. This effect is stri- kingly illustrated by a generalization of the heights of the tides on the Atlantic coast of the United States, developed from the tidal ob- servations made in connection with the United States coast survey. That coast presents in its general outline three large bays : the great southern, from Cape Florida to Cape Hatteras ; the great middle, from Cape Hatteras to Sias- conset, Nantucket ; and the great eastern, from Siasconset to Cape Sable. Referring to the tide table given below, we find at Cape Florida a mean height of 1*5 ft., and as we follow the coast to the northward a gradually increasing height, reaching 7 ft. at Savannah entrance, then decreasing again, with an exception easily explained, to Cape Hatteras, where it is 2 ft. In the middle bay, following the stations on the coast, and omitting those on the bays and sounds, we have a less regular increase to 4'8 ft. at Sandy Hook, and a decrease to 2 '7 ft. at Menemsha bight on Nantucket island. The configuration of the eastern bay is less regular, and the correspondence of heights requires closer examination. The recess of Massachu- setts bay is well marked by the increase in height, reaching 10 ft. at Boston and Ply- mouth ; but the most striking effect of the convergence of shores and shoaling is exhibit- ed in the bay of Fundy. On a line across its mouth, at the Kennebec river as at Cape Sable, the mean height of tide is 8 ft., while at St. John's, K B., it rises 19 ft., and at Sackville in Cumberland basin, at the head of the bay, 36 ft., attaining to 50 ft. and more at spring tides. When the wave leaves the open sea, its front slope and its 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 be- comes long and gentle. Hence arise the cir- cumstances noticed in the early part of this article, and illustrated by reference to the Chesapeake bay. At the 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. 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 18 ft. takes place in an hour and a half, while the fall occupies 10 hours. As the wave advances over a shoal- ing bottom, a portion of the horizontal motion is transformed into vertical motion, by which the height of the wave is increased, the most rapid current approaches the greatest rise, and the interval between the stand and slack water is diminished. This exaggeration of the height and current is particularly remarkable when- ever the front of the advancing tide wave stretches across the mouth of an estuary with contracting borders, and extensive flats border- ing the channel near low-water level ; then it produces a bore, or sudden and violent wave of great height, which rushes forward with such impetuosity as to sweep everything be- fore it. Such is the ease at the head of the bay of Fundy ; likewise in the Hoogly river, in the bay of Bengal ; in the Dordogne, where it empties into the Garonne, on the coast of France ; and in the Severn river, where at spring tides a bore of 9 ft. in height rushes up stream. In the river Amazon, at the equinoxes (when the equatorial tide is at its maximum), during three consecutive days bores of 12 or 15 ft. high rush up the river with each high water ; so that along the course of the stream, up which for 200 m. from its mouth no fewer than eight tide waves are simultaneously ad- vancing, as many as five bores are sometimes at once in progress. It is easily seen that in the smaller seas, which have little or no com- munication with the ocean, as the Mediter- ranean, Black, and Caspian seas, and the North American lakes, the tides must be insensible, as the attraction of the moon is at all times very nearly the same for all parts of them. Near the W. end of the Mediterranean, as at Malaga, a small tide is observable, propagated from the Atlantic ocean through the straits of Gibraltar. Tides are also observable at Venice, but the observations have not been discussed so as to determine whether they arise from a small tide wave proper to the Mediterranean, magnified by travelling up the Adriatic sea, although insensible at its mouth, or whether they are variations due to the winds. Fluctu- ations of the sea level resembling those of the tides, and causing irregularities in the latter, are often produced by the winds, which in many places have a certain periodicity in their direction and force, as the land and sea breezes in the tropics. They come under considera- tion here only as complicating the study of the tidal phenomena. The existing theories, while they suffice for the explanation of the observed facts, are inadequate to the prediction of the phenomena at places where they have not been observed. This arises not from any defect in the principles upon which the theory is based, but from the difficulty of investigating mathe- matically the motion of fluids, under all the various circumstances in which the waters of the sea and of rivers are found, and from our ignorance of the configuration of the bottom of the sea. The equatorial sea being broken up into three great basins, and open water existing only to the southward of the three great continents, the tides are complicated in
