3. Effect of Proper Current of the River Itself.—A river has also to deliver a large amount of water into the sea during a single oscillation of the tide, and its own proper current is superposed on the tidal currents. Hence in actual rivers, while the resultant current continues to flow up-stream after high water is reached, with falling water-level, it ceases flowing before mean water-level is reached; and while the resultant current ebbs down-stream after low water, it generally continues to ebb with the rising tide for some time after mean water is reached, the downward stream, in fact, lasting longer than the upward one. The moments at which currents change will differ in each river according to the depth, the time and the extent of the rise and fall at the mouth and the volume of water delivered by the river; but in every case the tide rises more quickly than it falls, so that the time-interval from low water to high water is shorter than from high to low.
4. Natural Change in Shape of a Wave Advancing into Shallow Water.—The demonstration is too technical to be included here, but it can be proved analytically that a wave progressing up a river must change its shape so that the front slope gets increasingly steeper, and the rear slope more gradual. If this steepening of the front slope be carried to an extreme, the wave would present the form of a wall of water, but the mere advance into shallow water would not by itself suffice to produce so great a change of form without the aid of the natural current of the river, which cooperates with this change in the shape of a wave as it runs into shallow water, so as to exaggerate the steepness of the front slope. When, as is the case for many rivers, the estuary contains broad flats or shoals of mud or sand which are nearly dry at low water, the tide sometimes rises so rapidly, especially if the mouth of the estuary be funnel-shaped, that the wave becomes a wall of water, and is then properly called a "bore". Let us note briefly the way in which Hangchow Bay affords typical circumstances of this sort, so that we there have a most striking case of this interesting phenomenon.
The Physiography of Hangchow Bay
Hangchow Bay, or the estuary of the Ch'ien-tang River, has a very marked funnel shape. From Yangtse Cape (the extremity of Pu Tung Peninsula) on the north to Ketau Point on the south is considerably over sixty miles, while the distance between banks at a point thirty miles farther west is approximately only half of this and in twenty miles more has again been reduced by half, so that along the meridian of Chapu it is only about eighteen miles wide. From Ketau Point in a line approximately northeast there extends for over eighty miles a chain of rugged islands, beginning on the south with Chusan,