The wave from the southern ocean acts northward, from Tierra del Fuego and the Falkland Islands to the coast of Patagonia, and at Port St. Elena on that coast it occurs 12 hours later than at those islands.
On the western coast of America the tide travels from north to south, between Acapulco and the Straits of Magelhaens ; while from the former place it travels northwanle In the Pacific Ocean the general direction of the tide-wave is from east to west ; but the heights of the tides are small, not exceeding 2 feet at the islands of the South Sea.
It is observed however by Dr. Whewell (`PU. Trans.,' 1833), that tide must not be understood to be the tide which would be raised if the whole earth were covered with water, on account of the modifications produced by the form of the continent of South America. The most xisteni part of New South Wales, between 25° and 30' S. lat., has the Iiish-tide earlier than points which are situated towards the north or !with of that tract.
Peculiarities in tides, arising from the interference of tide-waves, occur in many different places. In the middle of the North Sea there is a considerable space within which the tide produced by the tide waves coming from the north and south takes places at one time. And Dr. Whewell states, on the authority of the late Captain Hewett, that about the Ower Shoal there is no sensible rise of the tide till 3 hours after the time of low-water ; but when the ebb stream has nearly ceased, there is a sudden rise of 6 or 6 feet ; so that nearly the whole rise of the tide occurs in the last three hours.
In 1740 the Aeaddrnie des Sciences offered a prize for the best memoir on the theory of tides : and the paper by Daniel Bernoulli on the flux and reflux of the sea shared it with those of Euler and Mac laurin. In that paper it is assumed that the water is kept in equilibrio between the attractions of its particles towards the earth's centre of gravity and the disturbing forces exercised by the sun and moon; and though the results of that theory are found to differ greatly from the observed phenomena, the theory itself is deserving of attention, since the analytical expressions which have been obtained by it first exhi bited the several phenomena distinctly from one another : those ex pressions consequently became guides to the observer or experimenter in his efforts to ascertain the true values of the particular effects which they represented.
The attraction exercised by the solid nucleus of the earth on a particle of water at any distance from its centre, being considered the same as it would be if all the matter of the nucleus existed in that centre, is represented by E being the mass of the earth and the square of the distance of a particle from the centre. But if x, y, and z are rectangular co-ordinates of a particle, the centre of the earth being the origin, we have + z'; and the partial differentials of the expression , relatively to x, y, and z, represent the effects of y + that attraction upon a particle in the directions of the three axes. If the attractions of the particles of water for each other are taken into consideration, there must be determined the attraction exercised upon a particle by all the water between the spherical nucleus and the ex terior surface (supposed to be spheroidal) of the surrounding fluid, and the expression for this attraction must be added to that for the solid.
The disturbing force of the sun or moon upon a particle of water is represented by being the mass of the celestial body and R the distance of the particle of water from it ; and the partial differentials of that expression relatively to x, y, and z give the values of the attrac tion in the direction of the coordinate axes : but the disturbing force exercised by the sun or moon on a particle of water being equal to the difference between its attraction on the particle and its attraction on the centre of the earth—the latter, which is represented by (n being supposed to be the distance between the centres of the earth and celestial body), is subtracted from the attraction exercised on the particle in the direction of one of the coordinate axes, supposed to be parallel to the line joining those centres, in order to have that difference. The attracting forces of the earth in the directions of the three axes being subtracted from the disturbing forces of the sun or moon in the same directions, there remain three terms which are usually represented by x, Y, and z. And since it has been demon strated by mathematicians that when a body is in equilibrie under the action of attracting forces, the expression xdx+ Ydy +zdz is an exact differential ; the form of the surface of equilibrium is determined by making the integral of the expression constant.