the wave does not enter the formula o It is sufficient to recall that 

 as the wave breaks there exists a practically constant relation between 

 its length and its heighto For this reasonj the wave height. A, ad- 

 equately represents all the characteristics of the wave at this moment. 



The formula of Seftores Castro and Briones isj 



in which the slope T ^ cot ao 



The fact that one arrives at formiilas somewhat similar in form 

 by two procedures so different is highly satisfactory and indicates 

 that if we have not reached the definite truth we approximate it 

 closelyo Which of these provisional truths approximates most nearly 

 the definite truth? 



Dispensing with inopportune and perhaps biased modesty, I must 

 state that the equation which I have formulated satisfies me even 

 more than that of Senores Castro and Briones, which I have used in 

 various projects o 



In the first place the formula which we have just determined does 

 not require any adjustment in its coefficients or exponents to con- 

 form to reality o The theoretically derived equation fits more than 

 satisfactorily all the phenomena observed and tested. 



The formula of Senores Castro and Briones, tells us that for 

 1 =00 J p must be 0, which is to say that even the finest sand main- 

 tains itself when the slope is almost horizontal independently of the 

 violence of the wave. This at first sight might appear certain, 

 since it is the case of beaches which might be thought of as resembl- 

 ing rock-fill dikes whose stones are the light grains of sand, but it 

 is not so in reality » The analogy is not complete inasmuch as al- 

 though the grains of sand of the beaches move, those which leave one 

 spot are replaced by those which flow in from anothero On the con- 

 trary, if the sea carries away stones of a rock-fill they are not re- 

 placed naturally by others and damage occurs o 



The stones of rock-fill must be permanently fixed whatever may 

 be the violence of the surge of the waves, and consequently there 

 must be some minimum weight required however gentle the slopes 



The derived formula gives precisely the minimum weights correspond- 

 ing to each wave height when a s Oo This weight is 



/^^.;^= ^^'^ 



(d-J)^ 



It is the weight necessary to insure that the stones are not lifted 

 when the breaking wave falls over them„ However gentle the slope, 

 if the stones are lifted, they would be displaced along the slope 

 under successive and repeated wave attack and start the failure of 

 the dike. 



13 



