KUNGL. SV. VKT. AKADEMIENS HANDLINGAR. KAM) 47. \:<> 4. [5 



Assuming this as a fair mean valuc, we lind: 



(0D\ 



and the amplitude of the boundary wave will be: 



cagv? c . l()z 



^L>\ " 50.0,8 



sinh z// . , 



\<lk Ue-x 



0.25c./., 



apart from the integral: 



+ 00 



I j{'/.)e iy) dl 

 This at once may approximately be written 



To comply with the conditions for the theory, the ridge should neither be too high, 

 nor too steep. We might conveniently use the idea that /(/.) is concentrated, with a 



mean value of m meters, within an area of a definite ratio to the wave-length -. Let 



a 

 2~7r 



be this ratio; « will be not too small a number. We have 



,. ma 

 m I d/.= ■ — . 



so finally the amplitude will be 



. 25 c . a . m meters ; 



and this may well be an observable quantity, provided the theory will hold for suffi- 

 ciently large values of c and m. 



In accordance with a general supposition regarding the approximative treatment 

 of wave-motion in fluids, a »small » quantity in the investigation of the previous chapter 

 is one that might be neglected when compared to the velocity of propagation of the 

 waves produced. Thus, at least as far as regards points at some distance from the ridge, 

 the result obtained will be true ^7 c is small compared to the velocity of 'propagation of 



2t 

 boundary-waves of the period — . Assuming, at present, this to be the case, the contents 



of the preceding chapter may be summed up in the following statements: 



