SECT.xm.] THEORY OF THE TIDES. 103 



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 conse- 

 quently 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 cir- 

 cumstances. It follows therefore 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 formulae 

 which determine the difference of the 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. 



Oscillations of the third kind are the semdiurnal tides so 

 remarkable on our coasts. They are occasioned by the 

 combined action of the sun and moon ; but, as the effect of 

 each is independent of the other, they may be considered 

 separately. 



The particles of water under the moon are more attracted 

 than the centre of gravity of the earth, in the inverse ratio 

 of the square of the distances. Hence they have a tendency 

 to leave the earth, but are retained by their gravitation, which 



