SECT. XIII. OSCILLATIONS IN THE OCEAN. 95 



deed, if so heavy a body as water were to move at the rate of 

 1000 miles an hour, it would cause universal destruction, since 

 in the most violent hurricanes the velocity of the wind is little 

 more than 100 miles an hour. Besides, it is evident that no 

 ship could either sail or steam against it. When the water is 

 shallow, however, there is a motion of translation in the water 

 along with the tide. 



In the deep ocean the undulating motion consists of two dis- 

 tinct things an advancing form and a molecular movement. 

 The motion of each particle of water is in an ellipse lying wholly 

 in the vertical plane ; so that, after the momentary displace- 

 ment during the passage of the wave, they return to their places 

 again. The resistance of the sea-bed is insensible in deep water ; 

 but when the tidal wave, which extends to the very bottom of 

 the ocean, comes into shallow water with diminished velocity, the 

 particles of water moving in vertical ellipses strike the, bottom, 

 and by reaction the wave rises higher ; and that being continually 

 repeated, as the form moves on the wave rises higher and higher, 

 bends more and more forward, till at last it loses its equilibrium, 

 and then both form and water roll to the shore, and the elliptical 

 trajectories of the particles, which in deep water were vertical, 

 incline more and more, till at length they become horizontal. 

 The distance from the shore at which the water begins to be 

 translated depends upon the depth, the nature of the coast, and 

 the form of the shore. Mr. Scott Russell has demonstrated that 

 in shallow water the velocity of the wave is equal to that which 

 a heavy body falling freely by its gravity would acquire in 

 descending through half the depth of the fluid. 



It is proved by daily experience, as well as by strict mathe- 

 matical reasoning, that, if a number of waves or oscillations be 

 excited in a fluid by different forces, each pursues its course and 

 has its effect independently of the rest. Now, in the tides there 

 are three kinds of oscillations, depending on different causes, and 

 producing their effects independently of each other, which may 

 therefore be estimated separately. The oscillations of the first 

 kind, which are very small, are independent of the rotation of 

 the earth, and, as they depend upon the motion of the disturbing 

 body in its orbit, they are of long periods. The second kind of 

 oscillations depend upon the rotation of the earth, therefore their 

 period is nearly a day. The oscillations of the third kind vary 



