If we designate by Hp the depth of the tee of the slope and by 

 Lp, hp, Kp the characteristics* of the wave over the depth Hp; by H 

 the depth of the point on the slope that we are considering, and by L, 

 h, K, etc., the corresponding characteristics of the wave, and if, for 

 the reasons presented, we admit the conservation of energy, one deduces 

 immediately: 



h = 



"p 4 



where 



p =Vk JIsL and Pp - -/^ 



a 



deduced from the approximate curve 



k p /ST , 

 V a p 



of figure 22 of the cited report, or from its corresponding table, 

 pages 32 and 33. 



The approximate curve can be utilized, neglecting the breaking 

 factor /b^~ because the action of breaking is so very rapid that 



Vb— 



there is insufficient time for its effects to be really produced 

 before breaking, and even if this should not be entirely so, as the 

 said effects are very similar for all breakings, on being neglected 

 they would remain implicitly in the coefficients N, determined by 

 direct observation of the phenomena. 



With respect to the generalization of the formula, mentioned at 

 the beginning of this study, it is proper to note that for some 

 years it has been refined on the basis of the following reasoning j 

 and that, although this reasoning also supposes some simplifications, 

 the final result we get will confirm, on comparison with an actual 

 case (always the final test in technology), that the degree of ap- 

 proximation is also sufficient for practical applications. 



The maximum horizontal particle velocity o f th e wave (on 

 breaking under its limiting conditions, v n = Vgh,*^ being the 

 principal cause of the removal of the stones of the breakwaters, the 

 effects of the maximum orbital velocity, also horizontal, correspond- 

 ing to any depth 



ft r 



_T 



ttBoth these notations and the others can be found in our report pre- 

 sented to the fourth communication of the Second Section of the 

 XVII International Congress of Navigation. 

 *-*See the cited booklet of July 1938, or its translation, and the 

 aforementioned report to the Lisbon Congress. 



8 



