equilibrium theoi)-, from its fundamental assumption, is confessedly 

 inadequate as an explanation of the causes and motions of the tides ; 

 indeed, Airy goes so far as to style it " a most contemptible theory " 

 and " grossly imperfect. '' Nevertheless, it has been of the greatest 

 value ; for, whilst rejecting the processes on which they are founded, 

 men of science till recently have agreed in using its results in discus- 

 sing tidal observations. 



With a few exceptions, no continued series of observations were 

 made on the tides till about a century ago ; but since the progress of 

 the theoiy has rendered it able to grapple with masses of observations, 

 and reduce them to law, it has become necessarj- to obtain accurate 

 and multiplied observations. 



For this purpose a self-registering tide gauge has been in use for 

 many years past ; its essential features are a vertical narrow cjlinder, 

 sunk to a certain depth, so as to exclude the action of surface waves ; 

 a float attached to a piston rod working easily within the cylinder, 

 and communicating a properly proportioned vertical movement to a 

 tracing pencil ; and lastly, a band of paper, which, by suitable 

 mechanism, is made to travel uniformly past the pencil. A curve is 

 thus traced on the paper, whose abscissse represent the line, and its 

 ordinates the height of the tide ; a graphical record can thus be 

 obtained of the tide wave at any port. 



Newton and Bernouilli had, as we have seen, considered the ocean 

 as in equilibrium, at every instant, under the forces animating 

 it. Thoroughly dissatisfied with this assumption, Laplace 

 resolved, in 1772, to investigate the motions of the ocean, as 

 caused by the attractions of the earth and heavenly bodies, by the 

 pressure thence resulting among the particles of water them- 

 selves, and by the earth's rotation. He assumed that the earth is 

 entirely covered by a shallow ocean, of evanescent density, and also 

 that the depth is equal throughout any particular parallel of latitude. 



His ultimate solution shewed him that the oscillation of the ocean 

 is the sum of oscillations of three kinds, corresponding respectively 

 to the tides of long period, the diurnal, and the semi-diurnal tides of 

 the equilibrium theory. The investigations of Laplace constitute what 

 is known as the dynamical theory of the tides, and would be 

 sufficient, had he done nothing else, to place him among the greatest 

 of mathematicians. But the dynamical, notwithstanding its vast 



