pected from table 1, but rather is X5 and X7 (H^/Lq and U^^) . The third 

 strongest doublet is X5 and XIO (a). Although these differ by only a 

 small percentage^ they are being taJsen here as ranked by the least-squares 

 procedure. 



The practice of inferring the relative rank of combinations of 

 variables from their rank when taken individually is generally not a sound 

 procedixre- Slope angle of the lower foreshore (Xl)^ for example, does 

 not appear (table 2) to contribute as much as fully six other variables 

 (Xs 2-7). The method of sequential multiregression analysis shows, however, 

 that Sjr. is present in the strongest triplet and remains prominent in several 

 of the stronger triplets. From an initial SS reduction of 5-11^^ when 

 considered individually, it is seen that in the presence of variables X5 

 and XT it contributes f\illy 6.^+8^ (table k) , for an increase in its origi- 

 nal value of only 1.37^- Thus, the strongest individual variable may be 

 influenced by other variables. However, when the grounds for accepting 

 the strongest variable on a physical basis are sound, it is conventionally 

 taken at face value, and the effects of other independent variables grouped 

 with it are expressed in terms of the added reduction contributed by the 

 combined variable. 



Continuing in table 3, we noted that the strongest triplet (Xl, X5, 

 Tj) now includes beach slope (Xl), another f\xndamental variable, which 

 ranked fully seventh in order of importance when the variables -^ere considered 

 individually (table 2). Table k indicates the change in the original ^ 

 SS reduction value of XI when in the presence of X^ and TJ . The value of 

 XI has increased some 1.37%v 



The strongest combinations of independent variables taken four at 

 a time is composed of XI, X3, X5, and X7. Interestingly, the original 

 SS-reduction value of X3 {26.k6iy table 2) has been reduced by 2U.92'/o 

 (table h) , in the presence of XI, X'3, and X7. This is largely because it 

 already occurs in variable X5. 



At this point it is instructive to rewrite the empirical laboratory 

 expressions found by Brebner and Kamphuis (I963, p. 22) to represent the 

 mean longshore-current velocity as they computed it: a) using Airy wave 

 theory, b) Snell ' s law for wave refraction (assuming a gently sloping plane 

 beach), and c) by expressing the wave parameters in terms of deep-water 

 values . 



V = 1.9 (g Sf)^/3 H^^/^ (Hq/Lq)^/^ (sin 1.65aQ +0.1 sin 3-300^) Energy (l) 



Approach 



V = U.O (g Sj^)^/^ Hq^/^ (Ho/Lq)"^/ (sin 1.6^^ + 0.1 sin S-SOa^) Momentum (2) 



Approach 



Assuming for the moment that there is a reasonable relationship 

 between the major factors that determine longshore-current velocity in 

 the laboratory and those that influence it in nature, we may look for the 

 position ef the combination of XI, X3, X5, and XIO in the ranking of % SS 



22 



