Removing the contribution of the dominant variable (Xl) from the 

 analysis (tables B32-B36) reveals the new dominance of another geometric 

 variable, XIO (water depth), which may be considered as a mediator for the 

 various process elements in the environment. 



Thus, ignoring XIO, it is seen that lag periods 2 and 5 are still 

 the most-influential on shoaling-zone slope, when the variables are taken 

 six at a time. Because variables X3 and X5 exhibit data redundancy with 

 those of X2 and Xk, as explained earlier, it is seen that wave period is 

 the important variable for measurement times weighted with those of high- 

 tide measurements (lag periods 2 and 5; tables B33 and B36), while wave 

 height (Xk) is most important in altering the slope for measurement times 

 weighted with those of low-tide measurements (tables B32, B3U, B35)- This 

 result of the least-squares analysis, if truly representative of high and 

 low-tide conditions, would be in keeping with the knowledge that waves of 

 a given period and height will exert a greater effect at a fixed point on 

 the bottom when the tide is low than when it is high (cf . Inman and Nasu, 

 1956, p. 30). The wave-height effect might then be diminished at high 

 tide to the extent that the only effect that is felt is the effect of 

 wave length (wave period) as it influences drag over the bottom. 



A study of the weakest combinations of the variables taken six at 

 a time shows (tables B37-B^l) that wave steepness and tidal-current veloc- 

 ity, which are both present in four of the strongest combinations for the 

 five lag periods are also present in these weakest combinations. The 

 only variables that are present in the strongest combinations of six at 

 a time (tables B27-B31), and present in none of the weakest combinations 

 for the corresponding lag periods, are mean size (Xl), wave length (X3), 

 wave height (X^), water depth (XIO), and water density (Xll) . 



Finally, reference to frequency tables bU2-B^6, for variables con- 

 sidered in combinations of six at a time, reveals that the distributions 

 of numbers of combinations by ^-SS-reductlon classes are polymodal for 

 lag periods 1, 3) ^^ and ^, but essentially unimodal for lag period 2, 

 Lag periods 3 and k exhibit four modes, while 1 and 5 exhibit three each. 

 One Inference is that sub-groups of variables that Influence the slope 

 to dissimilar degrees are somewhat segregated during lag periods 3 and k. 

 These sub-groups, however, if they are in fact semi-discrete in a physical 

 sense, each seem to influence the shoaling-wave-zone slope to about the 

 same degree during lag period 2. If true, it might be said that the com- 

 bination X2, X3, X5, X9, XIO, and X12 (table B33) is the most-significant 

 combination of variables to influence the foreshore slope and that this 

 influence is exerted between k and 8 hours prior to slope measurement. 

 Additional work with such frequency tables is planned. They are presented 

 in appendix B for the Interested reader and for future reference. 



Summary . — The bottom slope of the beach at 15th Street, some 250- 

 feet seaward of the breaker zone, may be thought of as being controlled 

 mostly by the following combination of six variables: average mean grain 

 size of the bottom materials, wave period, wave length, wave steepness. 



47 



