d.) on the prolongation of the jetty the height ratio is 

 almost unity. 



II. ASYMPTOTIC FORMULAE 



1. In the geometric shadow one may substitute for f(u) the 

 following equivalent expression when ut and u~ are smaller than -2 



, - iTr(l/4+-u & /Z) 



flu) = 



WYF 



f(u) = 



4 trV l 



In this case 



r l 3j n d ± e 

 Z 



i rr(J/ 4 + u'A) 



_ { £££_ cos (9 a — q) 



and _g*l£C casfa+S) 



/ (u 2 )e 



have the same phase 5 the relative height then becomes; 



1 , 1 





sin Qg+Q 



-+ 



Sin -Sa 



e n -e 



Along the jetty where 9=0 one has 

 2a = _L 1 



2^-Vr 9inh 



(2) 



(3) 



(4) 



2„. On the geometric shadow, where vl-, = 0, then f (u]_) = l/2, 

 and starting at u£ <C — 2 , the relative height of the wave is 

 furnished by the modulus of the complex expression 



A = 0.5 + 



1 



4rr^- sine. 

 3* Outside the geometric shadow: 



(a) when u^ is greater than 2, one may write 



20 



