SECT, xui.] EFFECTS OF DECLINATION. 107 



Theory and observation show that each partial tide increases 

 as the cube of the apparent diameter, or of the parallax of 

 the body which produces it, and that it diminishes as the 

 square of the cosine of the declination of that body (N. 154). 

 For, the greater the apparent diameter, the nearer the body, 

 and the more intense its action on the sea ; but the greater 

 the declination, the less the action, because it is less direct. 



The periodic motions of the waters of the ocean, on the 

 hypothesis of an ellipsoid of revolution entirely covered by 

 the sea, are very far from according with observation. This 

 arises from the very great irregularities in the surface of the 

 earth, which is but partially covered by the sea ; from the 

 variety in the depths of the ocean, the manner in which it 

 is spread out on the earth, the position and inclination of 

 the shores, the currents, and the resistance the waters meet 

 with : causes impossible to estimate, but which modify the 

 oscillations of the great mass of the ocean. However, amidst 

 all these irregularities, the ebb and flow of the sea maintain 

 a ratio to the forces producing them sufficient to indicate 

 their nature, and to verify the law of the attraction of the 

 sun and moon on the sea. La Place observes that the in- 

 vestigation of such relations between cause and effect, is no 

 less useful in natural philosophy than the direct solution of 

 problems either to prove the existence of the causes, or to 

 trace the laws, of their effects. Like the theory of proba- 

 bilities, it is a happy supplement to the ignorance and weak- 

 ness of the human mind. Thus the problem of the tides 

 does not admit of a general solution. It is indeed necessary ' 

 to analyse the general phenomena which ought to result 

 from the attraction of the sun and moon, but these must be 

 corrected in each particular case by local observations mo- 

 dified by the extent and depth of the sea, and the peculiar 

 circumstances of the place. 



Since the disturbing action of the sun and moon can only 

 become sensible in a very great extent of water, the An- 

 tarctic Ocean is the principal source of our tides. A succes- 



