Benjamin and Feir 



obtained equations governing extremely gradual — but not necessarily- 

 small — variations in wave properties, and showed that these equations 

 are of elliptic type if kh > 1.363 (a result also obtained by Lighthill in 

 the case of deep-water waves, kh -» oo) but are hyperbolic if kh < 1.363. 

 On the whole there is a nice accord among the results of Whitham's, 

 Lighthill's, and the present authors' theories, and the available experi- 

 mental results fit well into the established picture. 



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498 



