740 TIDES sensible under the simple supposition of an un- interrupted ocean covering the earth's surface, becomes very considerable under the actual cir- cumstances of the case. The depth of the sea varies so much, and the form of its basin, taken as a whole, is so interrupted by the land, that it may be doubted whether, were the action of the sun and moon at once suspended, their tide waves would perform even a single revo- lution with any sort of regularity. Hence it follows that the tides for the time being may be considered as almost completely command- ed by the then actual positions and proximities of the sun and moon, the free oscillations of the sea in its bed being quite subordinate to the forced wave generating them. In consequence (as is always the case in forced oscillations), every periodicity in the action of the forcing cause is propagated in the oscillations, and re- cords itself in the recorded height of the tide on every point of the coast, but at each point at a greater or less interval from the culmina- tion of the sun or moon, according to its local position and the more or less circuitous course taken by the tide wave to reach it, which spe- cial observation can alone determine. This interval is called the establishment of the place. The close relation which the times of high water bear to the times of the moon's passage shows that the moon's influence in raising the tides must be much greater than the sun's. In fact, while the whole attraction of the sun upon the earth far exceeds that of the moon, yet, owing to the greater proximity of the latter, the difference between its attraction at the centre of the earth and at the nearest or most remote points of its surface, which pro- duces the tides, is about 2$ times as great as the difference of the sun's attraction at the same points. There will be two complete lunar tides in every lunar day of 24h. 52m., and also two complete solar tides in every mean solar day. These are known as the semi-diurnal tides, and constitute the principal fluctuations of the sea level. When the sun and moon are in conjunction or opposition, at the time of new or full moon, the effects of both combine to produce the spring tides, when high water is higher and low water is lower than at mean tides by the amount of the solar tide. At quadratures the high water of the sun will combine with the low water of the moon to produce a less fall, and the low water of the sun with the high water of the moon to pro- duce a less rise, than at mean tides ; and we have the neap tides, the range of which is less than the mean range by the amount of the solar tide. Thus, at New York, the rise and fall at syzygies is 5-4 ft., at quadrature 3-4 ft,, the former being the sum, the latter the differ- ence of the lunar and solar tides ; whence we obtain for the effect of the moon 4-4 ft., and for that of the sun 1 ft., or a -ratio of 44 to 10. This proportion does not prove to be the same in all parts of the world, and even varies considerably in places not far distant from each other. At Boston the heights are 11 "3 and 8 - 5 ft. respectively, giving a proportion of 7 to 1. On the Atlantic coast of the United States it averages about 5 to 1, while on the E. side of the Atlantic ocean, on the coasts of France and England, it is in many parts 3 to 1. These differences are to be ascribed to the fact that the shore and harbor tides which we observe have in every instance acquired a greater mag- nitude than the ocean tides, and have been modified in form by the varying slope of the bottom and configuration of the shores. A simple comparison of the range of spring and neap tides will not serve, therefore, as a cor- rect measure of the relative effect of the sun and moon, and hence for a determination of the mass of the moon, which can only be de- rived from those data by a profound mathe- matical analysis. The next variation of the tides to be considered is that dependent on the moon's decimation. Were the moon constant- ly in the plane of the equator, the highest points of the tide waves would also be in that plane, and would consequently produce a series of equal tides at any place either N. or S. of the equator. But it is evident that when she ascends to the north, the vertex of the tide wave will tend to follow her, giving the high- est point of one tide in the northern, and the 1 highest point of the opposite tide in the south- ern hemisphere. Consequently, when the moon has a northern declination, the tide at any place in the northern hemisphere caused by her upper transit will be higher than that caused by the lower transit. This variation in the heights has a period of one lunar day, and is called the diurnal inequality; it reaches its maximum when the moon is at its greatest northern or southern decimation, and disap- pears when it is on the equator, and conse- quently has a half-monthly period. The va- riations of height from this cause produce a corresponding inequality in the times of high water. The sun's declination affects the tides in a similar manner, but the amount of the disturbance is very small, and its period ex- tends over half a year. Yet in lon'g series of observations its effect is well marked, both in height and time. The diurnal inequality de- pending on the moon's declination is on the other hand quite sensible, and in many places constitutes a prominent or even the chief fea- ture of the tides, as on the Pacific coast of North America and in the gulf of Mexico, to the peculiarities of which we shall recur here- after. If the tides arrive at the same place by two different channels, and one of them is retarded behind the other by six hours, in consequence of travelling a longer route or in shallower water, the semi-diurnal tides will l>e destroyed by an interference of the waves, that is, by the high water of one being superim- posed on the low water of the other ; the di- urnal inequality, however, will not be de- stroyed, but merely modified in height and time, leaving a single tide in the lunar day
