TIDES

The alternate rise and fall of the waters of the ocean. The moon is the principal agent in the production of the tides; but they are modified, both with respect to their height and the times at which they happen, by the action of the sun. The effect of the planets is inappreciable. The attractive force of a body on a distant particle of matter varying inversely as the square of the distance, the particles of the earth on the side next the moon will be attracted with a greater, and those on the opposite side with a smaller force, than those which are situated intermediately. The gravitation towards the earth's centre of the particles nearest the moon will therefore be diminished, and consequently, if at liberty to move among themselves, they will rise above the general level. In 1236 TIDES. like manner, the moon's attraction on the most distant particles being le than on the central ones, their relative gravitation towards the centre will also be diminished, and the waters will consequently be heaped up on the side of the earth which is turned away from the moon. Hence if the earth were at rest, the ocean would take the form of an oblong spheroid, with its longer axis pa ing through the attracting body; and it may be shown from theory that the spheroid would be in equilibrium under the influence of the moon's attraction, if the longer semi, axis exceeded the shorter by about 58 inches. But in consequence of the rapid rotation of the earth about its axis, the spheroid of equilibrium is never fully formed; for before the waters can tiike their level, the vertex of the spheroid has shifted its position on the earth's surface, in consequence of which an immensely broad and very flat wave is formed, which follows the motions of the moon at some interval of time. In the open sea the time of high water is, in general, from two to three hours after the moon's transit over the meridian either above or below the horizon. The tidal wave, it is to be observed, is entirely different from a current: the particles of water merely rise and fall; but except when the wave pa es over shallows, or approaches the shore, there is little or no progre ive motion. 1 he waters of the ocean are affected in a similar manner by the action of the sun, under the influence of which they have a tendency to a ume at every instant the form of an elongated spheroid; but although the attractive force of the sun is immensely greater than that of the moon, yet, by reason of the greater distance of the sun, the difference of the effect on particles situated on opposite sides of the earth (on which difference the phenomena depend) is very much le . The solar tides are therefore comparatively small with respect to the lunar tides, and, in fact, are never perceived as distinct phenomena, but become sensible only from the modifications which they produce in the heights and times of those which primarily depend on the moon. At the syzygies, when the sun and moon come to the meridian together, the tides are, ceteris paribus, the highest; at the quadratures, or when the sun and moon are 90° distant, the tides are least. The former are called spring tides, the latter neap tides. Although we are not in po e ion of data to enable us to compute the exact height either of the spring or neap tides, yet their relative heights in the open ocean probably correspond very nearly to the ellipticities of the spheroids of equilibrium that would be formed under the action of the two bodies exerted separately. Now the ellipticity of the aqueous spheroid formed by the moon's action is about five feet, and the ellipticity of that formed by the sun's action about two feet; therefore, the spring and neap tides being the surA and difference of the separate effects, the average spring tide will be to the average neap in the ratio of about 7 to 3. See Gravitation. By reason of the ellipticity of the orbits the distances of the sun and moon from the earth are continually changing; and the theorj' of attraction proves that the efficacy of either body in disturbing the waters of the ocean is inversely proportional to the cube of its distance. Hence it is found that if the mean efficacy of the sun be represented by 20, the influence of the sun's action will vary between the extremes of 19 and 21, and and that of the moon's between 43 and 59. The highest spring tide will therefore be to the lowest neap as 59-1-21 to 43 — 19; that is, as 80 to 24, or as 10 to 3. Another effect of the solar action is observed in the times at which high water takes place from day to day. In the spring and neap tides the time of high water is not altered by the sun's action, the solar and huiar tides being synchronous in the former case, and the time of actual low water being that of solar high water in the latter; but in the intermediate tides the time of actual high water is accelerated or retarded. In the first and third quarters of the moon, the solar wave is to the westward of the lunar one; and cohsequently the observed tide, which is the result of the combination of the two waves, will be to the westward of the place it would occupy if the moon acted alone, and the time of high water will therefore be accelerated. In the second and fourth quarters, the general effect of the sun is to produce, for a like reason, a retardation in the time of high water. This result of the combined action of the two attracting bodies is what is usually termed the priming and lagging of the tides, and it is most remarkable about the time of new and full moon. It is to be observed, however, that the effect now described is modified to some extent by the inertia of the water. The greatest and least tides do not happen exactly at the times of new and full moon; but at least two, and commonly three tides after, even at places directly exposed to the general tide of the ocean. In consequence of the greater amount of impre ed force, the acceleration of the lunar tide is greater than that of the solar; whence it may happen that when the lunar tide occurs two or three hours after the transit of the moon. [s. 1249]