WAVES 



417 



of propagation, but oscillate with uniform angular velocity about a mean 

 position, in a vertical plane parallel to that direction. In deep water the 

 orbit of a particle near the surface is sensibly circular, and the wave form 

 is trochoidal. In shallower water the orbit becomes approximately 

 elliptical with the major axis horizontal. In either case the particles in 

 the surface have the largest orbits, the extent of the motion diminishing 

 as the depth below the surface increases. The vertical motion diminishes 

 more rapidly than the horizontal motion, so that the deeper a particle 

 the flatter is its orbit. In deep water the maximum diameter of the orbit 

 diminishes in geometrical progression as the depth below the surface 

 increases in arithmetical progression. The following table 1 gives the 

 maximum horizontal and vertical displacements of the particles at 

 different depths for waves whose lengths are respectively equal to, and ten 

 times as great as the depth of the water they are traversing, the greatest 

 horizontal displacement of the particles at the bottom being represented 

 by unity. 



Depth below 

 surface. 



At surface . 

 10 depth . 

 20 . 

 3.0 . 



'40 . 

 60 . 

 80 . 

 At bottom . 



The motion of the particles in a wave of oscillation in fairly deep 

 water is shown in Fig. 184c. Those particles in the crest of the wave 

 move forward in the direction of propagation ; those in the trough 

 move backwards; while those at the mean level have simply vertical 

 motion. 



Velocity, Length, and Height of Waves of Oscillation in Deep Water. 

 Taking the surface particles to describe circular orbits of radius r with 



Airy, " Tides and Waves," Table IV. 



JLA, 



B E 



