or, when the wave breaks, the trochoid transforms itself into an 

 elliptical cycloid resulting in the maximum molecular velocity 



/^.C^^/f^ -^-.y^ 



Consequently, the maximum orbital velocity of the molecules of water 

 as the wave breaks is: 



(A = total height of the wave and is approximately equal to the depth 

 in which the wave breaks )« The parabola ON (Figure U) described hy 

 the crest molecules in falling shows that MN = A, Moreover, the 

 slopes which cause the wave to break at must pass near the point P 

 situated at the depth Ao Figure 4 has been drawn with attention to 

 these considerations and illustrates clearly the perceptibly normal 

 incidence of the wave when breaking over the various slopes of rock- 

 fill dikes o 



Having tested this normality, we now suppose (Figure 5) that a 

 stone rests on any plane whatsoever and that a normal intermittent 

 current envelopes the stone. There will be two instants when the 

 stone may separate from the plane, tending to be elevated in the 

 direction opposite to the current of the streamo These instants are, 

 the initial, see Figure 5-A, when the first liquid molecules of the 

 stream strike the plane, and the final. Figure 5-B, when the upper 

 face of the stone emerges through the end of the stream. 



In the initial instant the pressure over the upper face of the 

 stone will be in terms of head, as has been indicated previously, i:l£ 

 and over the plane and lower face of the stone, will be: S 



s 



The stone then will tend to lift from the plane under the action of 

 an upward pressure of approximately: 



S ~ S ~ S 



In the final instant the dynamic pressure over the upper face of the 

 stone as it emerges from the stream will be zero, and over the lower 

 face will equal approximately 



s 



and the stone will tend to lift from the plane » 



These two conditions, initial 1, and, final 2, Figure 6, are also 

 produced in the case of a stone situated on a slope beaten by breaking 

 waves o For the same reasons noted above the stone tends to lift from 

 the slope upon which it rests. 



