112 Shallow Water Wave Transformation through External Factors 



in which K and E are the complete elliptic integrals of 1st and 2nd kind; the 

 deviation from the Lagrangian value j (gh) is very small for great wave 

 lengths. 



The extensive and detailed experiments of the Weber brothers (1825) 

 in their inadequate wave tank have been partly used by Thorade to attempt 

 a test of the theory. It has, however, been found that they do not suffice to 

 answer all problems. Most of the experimental series deal with shallow water 

 waves. Their velocity of propagation should correspond to the equation of 

 Laplace (p. 18) c = j (8/x)tanh^//. In the case of long waves, they would 

 have to conform to the equation by Lagrange c = j (gh). Krummel (1911, 

 vol. II, p. 22) has given the comparison with the values of Lagrange, whereas 

 Thorade (1931, p. 189) has given the comparison with the Lagrangian values. 



Table 16 gives a comparison between these observed values in the tanks 

 and velocities computed according to the equations by Laplace and Lagrange. 

 We can see that for increasing depth the Laplace formula is in better agreement 

 with observations. 



Table 16. Shallow water wave in Weber's wave tank 



A more recent long series of observations has been made from the Scripps 

 Institute of Oceanography at La Jolla (California), and Fig. 49 is a com- 



24 

 22 



20 



I 



~ 18 



10 



16 18 



C observed. 



20 22 

 ft/sec 



24 



26 



Fig. 49. Observed and computed wave velocitites in shallow water from observations at 

 the pier of the Scripps Institute of Oceanography, La Jolla, California. 



