TIDES. 275 TIDE WATERS. motion in such a canal. It can be shown mathe- matically that the speed at which such a wave would travel depends simply on the depth of the canal. The deeper the canal, the greater the speed of the wave. This is, of course, very important, and sliows what a perfectly free wave would do under such simplified conditions. It can even be computed that if the canal were I3^j, miles deep, the wave would travel round the earth in exactly twenty-four hours. Now, it is the tendency of the sun and moon to set such a free wave in motion at each instant of time; and tliese go on traveling along more or less like the supposed simple wave in the canal. If the ocean were 13'ji miles deep, the waves would have a period of one day: and the new free waves forming all the time would reinforce the old ones, leading to an enormous tidal accumulation. Fortunate- ly, the ocean is much less than 13S4miles deep, and the waves travel much more slowly than once a day. It ma}- happen, tlierefore, that as the waves travel around the earth, their speed may be such that we shall find a wave hollow instead of a wave crest under the moon. Thus, the modification of the equilibrium theory by the wave motion may at times completely reverse things, giving us low tide when we should ex- pect high tide. We may carry the canal idea a step further, with a remarkably interesting result. Suppose the whole surface of the earth were covered with a series of canals parallel to the equatorial canal. Then, as we approach the pole, the canals will be shorter, since the equatorial circumference of the earth is longer than it is in any other latitude. Tlius the waves in high latitudes would not have so far to go as the waves in low latitudes, and so might tend to reinforce each other as ex- plained above. So we might have 'inverted' tides in the equatorial regions and direct ones in the polar regions : and in some intermediate latitude there would be, as Darwin says, "very great tides, the nature of which cannot be speci- fied exactly." This would occur, as we have seen, where the earth's circumference is short enough to permit a free wave to go all around in about twenty-four hours. These dynamical considerations of wave motion in canals lead to results bearing some sort of resemblance to the actual observed phenomena of nature. It should be noted, of course, that the foregoing considera- tions refer to theoretical conditions such as ■would exist if the earth were simply covered with a layer of water. But the actual facts of nature are so different that they modify very greatly the theoretical tidal action of the sun and moon. So large a part of the terrestrial sur- face is covered by land that the free motion of tidal waves is seriously impeded. It is therefore impossible to predict the times of high water accurately from theoretical considerations alone. Fortunately, the practical prediction of the time of high water for any place can be effected by analyzing a long series of tidal observations made at the place in question. This method of pro- cedure has been in use for many years, and we now possess tidal tables for all principal sea- ports accurate enough for the purposes of navi- gation. An interesting modification of ordinary tides occurs in rivers. Here the tidal rise appears of course as a strong current running up-stream, where the ocean level outside the river-mouth has been raised. At times this tidal current advances with a high and dangerous wave crest (called a bore), and it may acquire velocity enough to raise the water-level in the river con- siderabl}' above that of the ocean outside. Phe- nomena of this kind, and indeed all tidal phe- nomena, are partly modified by the configuration of the coast line and the depth of water. TIDE WATERS. Waters subject to the ebb and How of the tides. The term is of legal sig- nificance because synonymous in the common law with 'navigable waters,' in relation to which were developed the system of rules defining the rights and obligations of transportation and commerce thereon. The open sea is the common property of all nations (see High Seas) and the rights of a particular nation thereon are restricted to the marginal belt of a marine league. (See Ter- ritorial Waters.) By the rules of the common law still prevailing in England, both the title and dominion of the sea. and of all rivers and arms of seas where the tide ebbs and flows, and of all lands below high-water mark, including both the shore and the soil under such waters, are vested in the Crown for the public benefit. Tidal waters are public highways, but non-tidal waters, though actually navigable, are subject to private ownership, the riparian owners hold- ing title to the middle of the stream, subject to the paramount right of the public use for navi- gation. In the United States the physical fea- tures of the coimtry and its dual political organ- ization rendered a strict application of the com- mon-law rule inexpedient, and the law in regard to inland streams not subject to tides varies some- what in this regard in the difl'erent State juris- dictions. Prior to the adoption of the Constitu- tion, the colonies existing as separate political entities had exercised full sovereignty. While under the Constitution the Federal Government possesses exclusive jurisdiction over dealings with foreign nations and in the regulation of inter- state commerce (Article I. § viii. sub. 3), yet the title and dominion of tidal waters and lands remains prima facie vested in the several States abutting thereon for the public benefit, subject only to the paramount right of navigation, which, whether of foreign or interstate commerce, is under the governance of the general Government. In this respect also the rights of the original thirteen States and of those later admitted are the same, and as to the territory acquired subsequent to the adoption of the Con- stitution, the title and dominion of such tidal lands and waters passes to the United States for the benefit of the whole people, but impressed with a trust for the several States ultimately created out of said territory, except in cases where grants have been made by the sovereignty exercising jurisdiction prior to its acquisition by the United States, or where said lands are subject to trusts requiring other disposition. Such were the rules laid down in regard to the territory of California acquired from Jlexico. Yet it has been some- times held that Congress has the power, whenever necessary and proper, to grant lands below high- water mark in tidal waters in territories belong- ing to the United States. In Canada it has been decided that the Saint Lawrence River and the Great Lakes are public navigable waters and are not subject to
