SEQUEL TO THE EPOCH OF NEWTON". 461 



■ponding to those which the equilibrium theory gives, could be con- 

 sidered only as a conjecture, till the comparison with observation was 

 made. It was, however, a natural conjecture ; since the waters of the 

 ucean are at every moment tending to acquire the form assumed in the 

 equilibrium theory : and it may be considered likely that the causes 

 which prevent their assuming this form produce an effect nearly con- 

 stant for each place. Whatever be thought of this reasoning, the 

 conjecture is confirmed by observation with curious exactness. The 

 laws of a great number of the tidal phenomena — namely, of the Semi- 

 mensual Inequality of the Heights, of the Semi-mensual Inequality 

 of the Times, of the Diurnal Inequality, of the effect of the Moon's 

 Declination, of the effect of the Moon's Parallax — are represented 

 very closely by formulae derived from the equilibrium theory. The 

 hydrodynamical mode of treating the subject has not added any 

 thing to the knowledge of the laws of the phenomena to which the 

 other view had conducted us. 



We may add, that Laplace's assumption, that in the moving fluid 

 the motions must have a 2 ) P > iodicity corresponding to that of the 

 forces, is also a conjecture. And though this conjecture may, in some 

 cases of the problem, be verified, by substituting the resulting expres- 

 sions in the equations of motion, this cannot be done in the actual case, 

 where the revolving motion of the ocean is prevented by the intrusion 

 of tracts of land running nearly from pole to pole. 



Yet in Mr. Airy's Treatise On Tides and Waves (in the Encyclo- 

 pedia Melropolitana) much has been done to bring the hydrodynamical 

 theory of oceanic tides into agreement with observation. In this ad- 

 mirable work, Mr. Airy has, by peculiar artifices, solved problems 

 which come so near the actual cases that they may represent them. He 

 has, in this way, deduced the laws of the semi-diurnal and the diurnal 

 tide, and the other features of the tides which the equilibrium theory 

 in some degree imitates ; but he has also, takiug into account the effect 

 of friction, shown that the actual tide may be represented as the tide 

 of an earlier epoch ; — that the relative mass of the moon and sun, as 

 inferred from the tides, would depend upon the depth of the ocean 

 ( Art. 455) ; — with many other results remarkably explaining the ob- 

 served phenomena. He has also shown that the relation of the cotidal 

 lines to the tide waves really propagated is, in complex cases, very 

 obscure, because different waves of different magnitudes, travelling in 

 different directions, may coexist, and the cotidal line is the compound 

 result of all these. 



