86 THEORY OF THE TIDES. SKCT. XIH. 



flattened at the poles ; but the action of the sun and 

 moon, especially of the moon, disturbs the equilibrium of 

 the ocean. If the moon attracted the center of gravity 

 of the earth and all its particles with equal and parallel 

 forces, the whole system of the earth and the waters 

 that cover it would yield to these forces with a common 

 motion, and the equilibrium of the seas would remain 

 undisturbed. The difference of the forces and the ine- 

 quality of their directions alone disturb the equilibrium. 



It is proved by daily experience as well as by strict 

 mathematical reasoning, that if a number of waves or 

 oscillations be excited in a fluid by different forces, each 

 pursues its course and has its effect independently of 

 the rest. Now in the tides there are three kinds of 

 oscillations depending on different causes, and producing 

 their effects independently of each other, which may 

 therefore be estimated separately. 



The oscillations of the first kind, which are very small, 

 are independent of the rotation of the earth ; and as they 

 depend upon the motion of the disturbing body in its 

 orbit, they are of long periods. The second kind of 

 oscillations depends upon the rotation of the earth, 

 therefore their period is nearly a day. The oscillations 

 of the third kind vary with an angle equal to twice the 

 angular rotation of the earth, and consequently happen 

 twice in twenty-four hours (N. 152). 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. From the formula 3 , which 



