WAVES 



217 



The radius of the orbit p may be calculated according to the follow- 

 ing fomiula of Bertin (quoted by KruiTimel-42 -.6) 



he 



or log — 

 h 



2 TT m — 

 \ 



where h is the half height of the waves (radius of orbit on surface); 

 e the basis of the natural logarithms (2.718); z the depth of water 

 in meters from the mean surface, X the wave length and m the 

 modulus of the common system of logarithms (0.4342944819), while 

 TT — 3.1416. 



JVavcs ill SJiallozv Water. "When waves run into shoaling 

 water their period remains unchanged, their height increases, and 

 their velocity and length decrease. The height increases because the 

 wave energy at any given point is spent upon a lessening depth of 

 water. The velocity decreases because the forward propagation 



ro Rw/» Rj) 



FaRWATUs. 



05?AW>J3Aa 



a^jAvvxoAa 



Fig. 33. Diagrams showing the change in the orbit described by the moving 

 particles of the waves as they approach the shore, and their direc- 

 tion of movement. (After Davis.) 



of wave disturbance is slower in shallow than in deep water. The 

 wave length decreases because the forward waves are more re- 

 tarded than the following waves. The period is unchanged because, 

 at any given point, one wave is as much delayed in arrival as 

 another. 



"On a steep-sloping beach the waves may wash up and down 

 without breaking; then the orbit is a narrow ellipse, much inclined 

 forward ; directly on the beach the orbit is practically a line coinci- 

 dent with the slope of the beach ; and here the water rises as it 

 advances and falls as it recedes. This relation of rise and fall to 

 forward and backward motion is not found where the orbit is an 

 oval. If the orbit is a vertical ellipse, rise goes with the last half 

 of recession and the first half of advance ; fall goes with the last 

 half of advance and the first half of recession." This is illustrated 

 by the "square frames" fitted to different forms of orbit in the 

 above diagrams (Fig. 33) given by Davis. 



"On a gradually shoaling bottom, swell changes to surf or break- 

 ers close to shore. The height of the wave increases, its front 



