In a strait or sound a nodal line is re duced to a no-tide point through the deflecting force described in § 6; around such a point the sequence of the tide is the reverse of that of the forces. If a no-tide point is due to the overlapping of two systems, the sequence de pends upon the tidal hours of the systems.
10. Peculiarities of distance be tween the Antarctic Continent and Australia be ing more nearly equal to the half length of a solar wave than of a lunar, causes the solar wave to be comparatively large along the south ern coast of Australia. The same is true, but in a lesser degree, for the region between the Antarctic Continent and South Africa. The distance from the Antarctic Continent to the Atlantic Coast of the United States being a lit tle more than one and one-half lunar wave lengths causes the ratio of the solar to the lunar• wave to be comparatively small along this coast. If the ocean oscillate differently for different constituents, we can readily see rea sons for considerable differences of epoch and so for remarkable of the tides.
If a tidal river be so shallow that the range of tide is a considerable fraction of the depth, ordinary wave-like oscillations of the water are no longer possible. The result is that as the wave progresses, the duration of the rise will be shortened and that of the fall lengthened. An extreme case results in a phenomenon called a bore — an advancing wall of water,' which may be several feet in height, flowing up the bed of a river. A bore (o.v.) occurs in the Petitco diac River, an affluent of the Bay of Fundy, its height at Moncton being three or four feet. Bores occur in several of the rivers of India, in several of western Europe, in the Amazon River, in the Tsien-tang Kiang and in Turn again Arm, Alaska. Various other peculiarities in the shape of the wave are due to the shal lowness of the water. A much contracted en trance to a bay not only reduces the range within, but alters the shape of the wave.
On the other hand, the range may increase as the tide passes up a funnel-shaped bay or estuary, and especially may this be the case when the bay has a large stationary oscillation related to the waters outside. The Bay of Fundy has at its head a spring range of nearly 50 feet, which fact depends upon both of these circumstances. But the large tides in Bristol
Channel, England, and in Bristol Bay, Alaska, are due chiefly to the contracting and shoaling of these bodies.
As a rule strong tidal currents occur in straits, tidal rivers, over shoals, and off capes.
Along the open coast and in the ocean at large, tidal currents generally set successively in all directions, the motion being elliptically harmonic or nearly so. This horizontal motion having two degrees of freedom is much harder to than is the tide, or motion defined by the rise and fall of the surface. Points at which the velocity ellipses or hydographs be come circles may be styled °circular points.° 11. Tides in the Earth's By these are meant the rise and fall experienced by the surface of the apparently solid earth due primarily to the tide-producing forces of the moon and sun acting upon the earth's crust and all matter within.
With the exception of § 5, we have made no mention of the attraction of the tidally dis turbed waters upon themselves because the density of water is only 2/11 that of the °solid° earth, and the depth of the ocean is but a small fraction of the earth's radius. In the produc tion of body tides not only is the direct disturb ing action of the tidal forces involved, but also the attraction of the matter, however, disturbed upon itself.
Let ag denote the rise and fall of the ocean's surface as measured from the earth's centre and expressed in terms of the earth's radius, a., the rise and fall of the surface of the °solid° earth similarly measured; then the actually observed rise and fall of the waters surface relatively to the land is = m. The value of as is required. From theoretical considerations of the direct and indirect effect of the tidal =.-- ° where a denotes the range of the equilibrium tide in an ocean of small density covering the earth, due to the direct action of the tidal forces; ke and are two moduli depending respectively upon the elasticity and internal constitution of the earth; leo denotes the range of the deformation in the surface of the °solid° earth due to the direct action of the tidal forces.