REFRACTION 



157 



refraction before it breaks than a lower one of the same length, because 

 it breaks in deeper water ; hence, it may break at a considerably greater 

 angle with the coast. 



Table 35. — The angles which breakers make with a straight shvre line, when all 

 bottom contours are parallel with the beach, for waves of different degrees of steepness 

 in deep water approaching the shore line at different initial angles. It is assumed 

 that the waves will break where the depth of water is 1.3 times the breaker height 



The alteration in the angle between a wave and the coast that results 

 from refraction is both gradual and cumulative, so that the crest be- 

 comes more and more strongly curved in toward the beach. Calcula- 

 tion of the precise shapes of such curves is complex, for it involves the 

 determination of the velocity of the wave at different points along its 

 crest at successive intervals of time, from which the successive posi- 

 tions of these points can be plotted. But the degree to which a wave 

 is refracted over straight and parallel bottom contours can be pic- 

 tured xoughly by laying its crest down as a series of short chords cross- 

 ing one contour of the bottom after another, at the angles indicated in 

 table 36, as has been done in figure 46, for a wave, the offshore ends of 

 which are at an angle of 70° with the coast line. 



Table 36. — The angles which waves (approaching at different initial angles) make 

 with a straight shore line in diminishing depths of water (relative to the length of 

 the wave in deep water) 



THE LOSS OF WAVE HEIGHT BY REFRACTION 



Refraction also affects the heights of waves, for when their inshore 

 ends are delayed, while their offshore parts continue to advance un- 

 checked, they are expanded sidewise — are stretched out as it were. 



