ox TIDES AND TIDAL ACTION IN HARBORS. 211 



not far distaut from each other. At Boston the heights are 11.3 and 

 8.5 feet, respectively, giving a proportion of seven to one. On the 

 Atlantic coast of the United States it averages about five to one, while 

 on the east side of the Atlantic Ocean, on the coasts of France and 

 England, it is in many parts as three to one. 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 magnitude than the ocean 

 tides, in consequence of the wave having passed over a sloping bottom 

 and having been greatly retarded by the effect of friction. A comparison 

 of the range of spring and neap-tides, therefore, will not serve as a 

 correct measure of the relative effect of the sun and moon, unless the 

 effect of friction were taken into consideration, which we are at i^resent 

 unable to do for want of a complete knowledge of the configuration of 

 the bottom. 



The interval between the moon's meridian x)assage and the time of 

 Ligh water is subject to a variation similar to that of the height. On 

 the day after the spring-tides, the top of the solar tide-wave will be 

 nearly an hour in advance of the lunar tide-wave, and the two waves 

 will combine to make high water earlier than the moon's alone would 

 bring it. It will continue to be earlier until the moon's transit is 

 later by three hours, or in the first octanr. It then falls back until it 

 is latest in the third octant, and again advances, until, at the next 

 spring-tides, it reaches its mean period. The mean of all the luni-tidal 

 intervals for half a month at a port its called its mean establishment, 

 which is used for finding the time of high water on any given day ; and 

 tables are constructed from observations at the principal ports for find- 

 ing the correction for semi-monthly inequality due to the moon's age. 

 Thus, for New York, the mean luni-tidal interval is 8h. 13m., and its 

 least and greatest values are 7h. 52m. and 8h. 35m. On the Atlantic 

 coast of the United States the range of this inequality is about three- 

 quarters of an hour ; on the coasts of France and Great Britain it often 

 exceeds one and a half hours. 



DIURNAL INEQUALITY. 



The next variation of the tides to be considered is that dependent on 

 the moon's declination. Were that body constantly 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 north or south of the equator. But it is evident that, when the 

 moon ascends to the north, the vertex of the tide-wave will tend to fol- 

 low it, giving the highest point of one tide in the northern, and the 

 highest point of the opposite tide in the southern, hemisphere. Conse- 

 quently, when the moon has a northern declination, the tide at any ])lace 

 in the northern hemisphere caused hx its upper transit will be higher 

 than that caused by its lower transit. (See diagram of diurnal inequal- 

 ity.) This variation in the heights has a period of one lunar day, and 



