90 THEORY OP THE TIDES. SECT. XIII. 



Both the height and time of high water are thus per- 

 petually changing ; therefore, in solving the problem, it 

 is required to determine the heights to which the tides 

 rise, the times at which they happen, and the daily vari- 

 ations. 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 di- 

 ameter, the nearer the body, and the more intense its 

 action on the sea; but the greater the decimation, 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 cov- 

 ered by the sea, are very far from according with obser- 

 vation. 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, amid 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 

 investigation 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 probabilities, it is a happy supplement to the 

 ignorance and weakness of the human mind. Thus 

 the problem of the tides does not admit of a general 

 solution. It is, indeed, necessary to analyze 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 modified by the 

 extent and depth of the sea, and the peculiar circum- 

 stances of the place. 



Since the disturbing action of the sun and moon can 

 only become sensible in a very great extent of water, 



