The subjoined cut, which shows the principal cotidal lines in the Indian and Atlantic oceans, is from Dr. Whewell's chart above men tioned, and contains tho modifications introduced in that which is given by Mr. Airy, in his Essay on `Tides and Waves,' in the' Encyclo paedia Metropolitans.' I In investigations relating to the tides, it is required to determine the form assumed by the surface of the water when the particles are subject to the actions of disturbing forces; and for this purpose it is convenient to assume that if no such forces existed, the earth would consist of a solid spherical nucleus within a body of water whose exterior surface is that of a sphere concentric with the nucleus. Let the circle cd represent the nucleus, and the circumference ob the sur face of the surrounding water in a plane passing through the centre of the earth, and the sun or moon at xi : then, in the theory indicated by Newton, the attraction of the celestial body will draw the particles of water towards it so that the surface 06 will assume the form a'1, ; at the same time the attraction exercised on the solid part ed will cause the latter to take the position c'd'. Thus at the same instant the stir face of the water at a' and b' is farther removed from the centre of the earth than it would be If there were no perturbation; while at e and f it is nearer the centre. If the celestial body were constantly in the plane of the equator, the summit of the elevated water would also be in that plane, and exactly or nearly under the body. A section of the spheroid of water passing through the poles of the equator and tho summit just mentioned would be an ellipse, and its periphery would coincide with the direction of a terrestrial meridian. By the diurnal rotation thus tide-wave, as it may bo called, would appear to move about the earth from east to west at the rate of above 1000 miles per hour at the equator ; and its positions at the end of every hour would constitute a series of cotldal lines Hence, if a small island at the terrestrial equator were to project above the surface of the water, it would arrive successively at the points a', e, G', f, a', so that in the time of a rotation of the earth on its axis with respect to the celestial body, there would occur at the Wand two states of high-water and two of low-water. The arrival of the island at the summit a', which would, if u were the moon, take place at the end of every 24 h. 50m. nearly, is called the diurnal tide; and that which takes place when the island arrives at the summit b', that is 12h. 25m. after the former, is called the senxidiurnal tide. By this theory there ought to be scarcely any tides near the poles, the water being always drawn from them towards the tropical regions; and the attractions at o' under the celestial body being greater than the attractions at 11, it should follow that the diurnal tide is greater than the acinidiurnal tide, neither of which cir cumstances, however, is conformable to observation.
If an island having a great extent from the equator towards the north and south were to intercept the tide-wave, the elevated water, passing round the extremities of the island, would on its western side form two waves, which would advance towards, and meet one another at the equator, making, at different places on the coast, high-water successively later, in the directions of their motions. And it is easy to conceive that the tide-wave of a great ocean will send branches into any seas which it may approach in its movement about the earth : such are called derived tides.
The combined actions of the sun and moon, when those luminaries are in conjunction or opposition, that is, at new or full moon, may be readily conceived to produce what are called spring-tides; and the diminution of each other's attractions when in quadratures, to produce the neap-tides. It may further be understood that, as the distances of the 81111 and moon from the earth vary by the ellipticity of the orbits, at the times when either of the celestial bodies is in perigee, its attrac tive power being greater than at other times, the tide-wave raised by it will attain a greater elevation than usual ; on the other hand, when in apogee, the high-water elevation must be the least.
The tides are greatly modified at any station or port by the position of the latter with respect to the equator, and by the declination of the sun and moon. The two summits of the great tide-wave are, at the same instant, diametrically opposite to one another; and if the latitude of the station were equal to the moon's declination on a given day, both moon and station being for example north of the equator, the summit of the wave would on that be at the station when the moon is in or near the zenith; but about twelve hours afterwards, the station, having described half the circumference of a circle about the earth's axis by the diurnal rotation, will be on the opposite of the meridian; and the summit of the wave, being on the southern side of the equator, will be at a distance from the station equal to twice the moon's declination; consequently the height of this tide will be much less than that of the former tide. The contrary phenomenon occurs when the moon and the station are on opposite sides of the equator.
Among the tide-waves with which we are best acquainted are those of the Indian and Atlantic oceans; and from the known times of high Water at different places, it is asqertained that the summit of a wave advances from the seas to the south of Australia into the Bay of Bengal, and towards the Persian Gulf, causing the hour of high-water to be successively later at the ports from Ceylon northwards, on both aides of the western peninsula of India. The summit of a single wave seems to extend from the mouth of the Red Sea, along the eastern coast of Africa, to the Cape of Good Hope, where it joins the tide-waves of the Atlantic. These advancing northwards, cause the time of high water to be successively later at the different ports on the western coast of Africa and Europe, and on the whole eastern coast of South and North America; so that the wave which at a certain instant is at the Cape, in 15 hours from that time is at the mouth of the English Channel and on the western coast of Ireland. This wave, being appa rently checked in its progress by the British Isles, divides itself into two principal branches, of which one flows up the Channel, and passing through the Straits of Dover, is off the mouth of the Thames in S hours from the time that it was at Brest. A small branch advances up St. George's Channel ; but the second principal branch of the wave flowing round the northern extremity of Scotland, proceeds slowly down the North Sea, and meets the first branch off the mouth of the Thames in 20 hours from the time that it was at the entrance of the Channel.
From Rio Janeiro to the Falkland Islands a wave summit seems to advance directly from east to west ; and from the form of the con tinent of South America, the high tide occurs successively later in going southward from Cape Frio, as if the wave came from the north.