and two with the smaller value referring to steep waves on 

 gently sloping beaches. The ratio d,/H, varies between one 

 and three, the sraaller value referring to a gently sloping 

 beach. 



Where a wave train approaches the coast at an angle the 

 direction of progress changes as the waves enter shallow water. 

 Since the velocity is less in shallow water, the part of the 

 wave which first reaches shallow water orogresses at a slower 

 rate than the part which is still in deec v;ater and consequent- 

 ly the wave front turns gradually until it becomes parallel to 

 the beach. The height of the waves will be less than that of 

 v'aves which advance directly against the coast as the energy 

 must be distributed over a greater length of beach. 



As a simple example consider a straight coast off whicn 

 the der)th contour lines are parallel. Call the energy of 

 the waves in deep ^'ater E , let a be the angle which the 

 wave crest in deep water forms with the coast line, and let 

 Qq be the angle with the coast line where d = L /25. Where 

 d = L' /25 the energy of the wave equals E cos ( €? - a^) , 

 and the wave height is 



&-^ 



V' 



H = H^Wcos i a^ - a^ 



because the wave height is proportional to the square root 

 of the energy. Thus, the reduction in height is small be- 

 cause even for {a - a ) = 45° 



OS 



V 



cos ( a - a ) = 0.84 



60 



