96 OSCILLATIONS IN THE OCEAN. SECT. XIII. 



with an angle equal to twice the angular rotation of the earth, 

 and consequently happen twice in twenty- four hours (N. 157). 

 The first afford no particular interest, and are extremely small ; 

 but the difference of two consecutive tides depends upon the 

 second. At the time of the solstices this difference, which ought 

 to be very great according to Newton's theory, is hardly sensible 

 on our shores. La Place has shown that the discrepancy arises 

 from the depth of the sea, and that if the depth were uniform 

 there would be no difference in the consecutive tides but that 

 which is occasioned by local circumstances. It follows, there- 

 fore, that, as this difference is extremely small, the sea, considered 

 in a large extent, must be nearly of uniform depth, that is to 

 say, there is a certain mean depth from which the deviation is 

 not great. The mean depth of the Pacific Ocean is supposed to 

 be about four or five miles, that of the Atlantic only three or 

 four, which, however, is mere conjecture. Possibly the great 

 extent and uniformly small depth of the Atlantic over the tele- 

 graphic platform may prevent the difference of the oscillations 

 in question from being perceptible on our shores. From the 

 formulae which determine the difference of these consecutive 

 tides it is proved that the precession of the equinoxes and the 

 nutation of the earth's axis are the same as if the sea formed one 

 solid mass with the earth. 



The oscillations of the third kind are the semi-diurnal tides 

 so remarkable on our coasts. In these there are two phenomena 

 particularly to be distinguished, one occurring twice in a month, 

 the other twice in a year. 



The first phenomenon is, that the tides are much increased in 

 the syzigies (N. 158), or at the time of new and full moon : in 

 both cases the sun and moon are in the same meridian ; for when 

 the moon is new they are in conjunction, and when she is full 

 they are in opposition. In each of these positions their action is 

 combined to produce the highest or spring tides under that meri- 

 dian, and the lowest in those points that are 90 distant. It is 

 observed that the higher the sea rises in full tide, the lower it is 

 in the ebb. The neap tides take place when the moon is in 

 quadrature. They neither rise so high nor sink so low as the 

 spring tides. It is evident that the spring tides must happen 

 twice in a month, since in that time the moon is once new and 

 once full. Theory proves that each partial tide increases as the 



