686 



BARBER AND TUCKER 



[chap. 19 



used but has several disadvantages : it records the distance to the nearest point 

 on the sea surface, and may thus miss steep crests ; it loses echoes when the 

 water is aerated, which often happens during storms ; it can also lose echoes 

 when a swell is passing over an otherwise calm sea, since there may be no wave 

 facets pointing in the correct direction to reflect sound to the transducer. The 

 alternative principle, which is the one usually used, is to measure the pressure 

 on or near the sea-bed as the waves pass overhead. The theoretical relationship 

 between the amplitude P of the pressure fluctuations (measured in equivalent 

 head of water) and the amplitude A of the surface elevation can be derived by 



1.30 

 1.26 

 1.22 

 1.18 

 1.14 

 1. 10 

 1.06 

 1.02 

 0.98 

 0.94 



1.15 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 



Theoretical attenuotion coefficient P/A 



0.9 



1.0 



Fig. 10. The ratio of theoretical to actual pressure-change amplitudes on the sea-bed 

 plotted against the theoretical attenuation factor. (After Draper, 1957, Fig. 3. By 

 courtesy of the Journal.) 



slight extension of the theory given in Lamb's Hydrodynamics, for example, 

 but seems to have been first quoted in the required form by Seiwell (1948). It is 



PjA = cos,h.k{h — z) I cosh kh, 



(13) 



where h is the depth of water, z is the depth of the measuring instrument, and 

 k = 27T/wavelength ; also a^ = gk tanh kh, where o- = 27r/wave period. 

 If the recorder is on the sea-bed, 



z = h and therefore P/A = sech kh. 



(14) 



Various attempts have been made to check this relationship experimentally, 

 but good agreement has never been found. Draper (1957), for example, finds 



