SSCT. 5] 



LONG OCEAN WAVES 



653 



"' Taking the dimensions of the Kealaikahiki channel. It is possible that the resonances 

 are associated with the Auau channel between the islands of Maui and Lanai. 



A. Frequency 



The table is in order of descending values of the frequency of the lowest 

 spectral peak. Values vary from 6.5 c/ks (period 0.043 h = 2.5 min) over the 

 narrow, steep shelf of Guadalupe Island to 0.09 c/ks (period 3.1 h) over the 

 broad gentle shelf of Argentina, We have implied here (and earlier) that these 

 spectral bands are governed by the dimensions of the shelf. The most simple- 

 minded model is that of a standing wave with an antinode at the shore line, 

 and a node at the edge of the continental shelf {x = A, Fig. 6). For the funda- 

 mental node the period is four times the travel time from a; = to a; = ^ . Let h{x) 

 be the depth and C = \/{gh) the phase velocity. Then 



To = 4 



/o- 



To 



dx 

 W) ^ 



VJgH') 



SA 



dh 



= 4 



Vgh VgilH') 



g_ 



H' 



A 



(1) 



Any of the three forms of the equation (1) proves useful. Note that the resonance 

 would be the same for a shelf of width A and constant depth IH'. The calcula- 

 tion presumes a coastal inclination, s', over the shelf, and neglects the bottom 



