WAVES 415 



the plane forming its rear face is increased, and under this pressure the 

 plane moves forwards, heaping up the water ahead of it. When the 

 column has been raised to its greatest height, at the crest of the wave, it 

 presses equally on both front and rear planes, accelerating the velocity of 

 the column ahead, retarding that behind, and so increasing its own width 

 until it finally comes to rest at its original level. Each successive column 

 is in turn displaced forward in the direction of transmission, and the 

 result is that a volume of water equal to that of the wave is displaced in 

 this direction. The motion of each particle is very approximately a semi- 

 ellipse, with its major axis horizontal, horizontal displacements being 

 uniform, and vertical displacements proportional to the distance above 

 the bottom of the channel. 

 Velocity of Propagation. Imagine the wave propagated in a stream 



Direction of Propagation . 



FIG, 184s. 



running in the opposite direction with such uniform velocity V as to keep 

 the wave form stationary relative to the banks. 



Then if h be the original depth of water ; k the height of wave ; V 

 the velocity at the crest of the wave (Fig. 184fi) 



h 



we have V = V 



h 



Applying Bernoulli's equation to the surface filaments where the 

 pressure is constant 



1 + 



