212 PRINCIPLES OF STRATIGRAPHY 



increase in the length of the period, therefore, means an increase in 

 the orbital velocity, which, if the wave height also increases, must 

 increase still further.* 



Wave velocity {DsiYis-iy: 12^) does not depend so much on 

 the orbital velocity as on the rate at which the crest position is 

 assumed by successive parts of the water, and this rate depends 

 chiefly on the depth to which orbital oscillations are felt in the 

 water body, so that the progress of the wave increases with the 

 increase in the depth affected. 



* The following formulae copied from Krummel (42 : p) serve to show the 

 relationship which exists between height and length of wave, its period, orbital 

 and translatory velocity in deep water. In all these: 



r = radius of orbit of water particles. 



h = half the wave height, i. e., its heig];it above mean surface. 



H = entire wave height (bottom of trough to top of crest). 



v = orbital velocity of water particles in meters per second 



Z = depth of water (in meters) from mean surface. 



X = wave length in meters. 



c = translatory velocity or wave velocity (meters per second) 



r = wave period in seconds. 



V = 3.1416. 



g = velocity of a free falling body at the end of the first second (9.81 m.). 



I The relation between the period of the wave t and the wave length X 

 is T = \ ~~ X 



TI The relation between the wave velocity c and the period r is 



2 TT 



T = c 



g 



III The relation between wave velocity c and wave length X is 



c = 



i 



2 IT 



IV The relation between wave velocity and size (radius) of the orbit r is 



c = \/g r 



V The relation between wave period r and the radius of the orbit r is 



'|/i 



VI The relation between velocity c and period r is 



2ir 



VII Given velocity or period the wave length is therefore 



\ 2 IT ., g , 

 A = c- or T- 



g 2 TT 



VIII The orbital velocity v is found according to the formula 



h 

 v = c — 



r 



