SBCT. XIII. THEORY OF THE TIDES. 87 



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 semidiurnal 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 at- 

 tracted than the center 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 is diminished by this tendency. 

 On the contrary, the moon attracts the center of the 

 earth, more powerfully than she attracts the particles of 

 water in the hemisphere opposite to her ; so that the 

 earth has a tendency to leave the waters, but is retained 

 by gravitation, which is again diminished by this tendency. 

 Thus the waters immediately under the moon are drawn 

 from the earth, at the same time that the earth is drawn 

 from those which are diametrically opposite to her, in 

 both instances producing an elevation of the ocean of 

 nearly the same height above the surface of equilibrium; 

 for the diminution of the gravitation of the particles in 

 each position is almost the same, on account of the dis- 

 tance of the moon being great in comparison of the ra- 

 dius of'the earth. Were the earth entirely covered by 

 the sea, the waters thus attracted by the moon would 

 assume the form of an oblong spheroid whose greater 

 axis would point toward the moon ; since the columns of 

 water under the moon, and in the direction diametrically 

 opposite to her, are rendered lighter in consequence of 

 the diminution of their gravitation ; and in order to pre- 

 serve the equilibrium, the axes 90 distant would be 

 shortened. The elevation, on account of the smaller 

 space to which it is confined, is twice as great as the 

 depression ; because the contents of the spheroid always 

 remain the same. If the waters were capable of assum- 

 ing the form of equilibrium instantaneously, that is the 

 form of the spheroid, its summit would always point to 

 the.inoon notwithstanding the earth's rotation. But on 



