ON WAVES. 347 



its surface, arising from the height of o, tends to retard the motion of P, 



and as the accelerating force is diminished the retardation increases, the 



whole action of the column p being continually to retard the plane P ; and 



if the diminution of force take place in the same succession as the original 

 increments, the diminution of the velocity of P will take place in a manner 

 similar to that df its original increase, and it will finally be brought to rest 



when the column n has regained its level. 



The same succession of conditions takes place in the plane which separates 

 any two successive elementary columns ; first of all the posterior surface of the 

 plane is pressed by a higher column than itself, tending to increase its height 

 and increased velocity, and having reached the maximum, the anterior surface 

 is thereafter pressed by a water column of greater height than the posterior 

 surface, retarding its velocity, and finally bringing it into a state of rest. 

 Thus the forces and motion of each elementary plane are repetitions of the 

 forces and motions of the original disturbing plane by which the wave was 

 generated. 



The power employed in wave genesis is therefore expended in raising to 

 a height equal to the crest of the wave, each successive water column ; each 

 water column, again descending, gives out that measure of power to the next 

 in succession, which it thus raises to its own height. The time employed in 

 raising a given column to this height, and in its descent and communication 

 of its own motion to the next in succession, constitutes the period of a wave, 

 and the number of such columns undergoing different stages of the process at 

 the same time measures the length of a wave. 



During the anterior half of the wave the following processes take place. 

 The generating force communicates to the adjacent column through its pos- 

 terior bounding plane, a pressure ; this pressure moves the posterior plane 

 forward, the water in the column is thereby raised to the height due to the 

 velocity, and the pressure of this water column communicates to the anterior 

 bounding plane also a velocity and a pressure in the same direction ; there- 

 fore the accelerating force produces a given motion of translation in the 

 whole column a height of column due to that velocity, and an approximation 

 of the anterior forces of the column to each other ; these are all the forces 

 and the motions concerned in the matter. The motive power thus stored 

 during the anterior half of the wave is restored in the latter half wave length 

 thus : the column raised to its greatest height presses on both its posterior 

 and anterior surface, on the anterior surface it presses forward the anterior 

 column, tending to sustain its velocity and maintain its height ; on the poste- 

 rior column its pressure tends to oppose the progress and retard the velocity 

 of the fluid in motion, and thus retarding the posterior and accelerating the 

 anterior surface, widens the space between its own bounding planes until it 

 repose once more on the original level. 



The Wave a Vehicle of Power. — The wave is thus a receptacle of moving 

 power, of the power required to raise a given volume of water from its place 

 in the channel to its place in the wave, and is ready to transmit that power 

 through any distance along that channel with great velocity, and to replace it 

 at the end of its path. In doing this the motion of the Avater is simple and 

 easily understood, each column is diminished in horizontal dimension and 

 increased proportionally in vertical dimension, and again suffered to regain its 

 original shape by the action of gravity. There is no transference of indivi- 

 dual particles through, between and amongst one another, so as to produce 



