agreement of the measured data with theory. Since the theoretical 

 velocity correction for the effect of wave steepness contains two 

 functions, f(d/t) and f(H/L), another comparison was made to determine 

 the relative effect of these two functions. This was done by comput- 

 ing the velocity with only f (H/L) included from 



,2 



C T' = C HaO 



>+m 



(3) 



The correlation coefficients for C^' and C m were computed and are 

 shown in Table 3. From these correlation coefficients and the graphs 

 shown in Figures 1A, IB, 3A and 3B, it can be seen that the f(H/L) 

 parameter does not have enough effect on the theoretical wave velocity 

 to change the statistical correlation coefficient in relation to the 

 correlation coefficient between C h _q and C m . Therefore, the f(d/L) 

 parameter has the predominant effect in making the correlation 

 coefficient poorer for the Beach Erosion Board data and better for the 

 University of California data, using the correlations between C ra and 

 C|| = as a reference. 



The effect of f (d/L) on the theoretical wave velocity is more 

 readily apparent from a plot of f(d/L) versus (d/L) M0RIS0N shown in 

 Figure U. If the University of -California data are considered, the 

 range of d/L is 0.0959 to 1.3U2. Over most of this range, f(d/L) 

 is 1.0, but varies from 9.8 to 1.0 over a comparatively small part 

 of the range. This has the effect of making the theoretical velocities 

 slightly larger as a whole (Figure 2b), and making the correlation 

 between Cj, and C m higher than the correlation between Cjj_q. anci ^m» 

 The range of d/L for the Beach Erosion Board data is from 0.036 to 0.25k and 

 and f(d/L) varies from 398 to 1.3, which introduces too large a 

 correction for wave s teepness and the wsve velocities are over corrected 

 (Figure 2A) . The over correction of the wave velocities is also 

 revealed in the lowered correlation coefficient between dp and C m 

 when compared to the correlation between 0^.0- and ^m* 



It is interesting to note that in both Figures 1A and IB, which 

 compare C m and Ch_o there is a decided tendency for the predicted 

 velocities to be too small, indicating that some correction toward 

 larger predicted velocities is needed. 



The conclusions which can be drawn from this study are: 



1. The Airy theory predicts wave velocities well enough 

 for most purposes, but is inadequate if accuracy in 

 the order of 1% is desired. 



2. The Stokes, Theory, neglecting f(d/L), gives negligible 

 improvement over the Airy Theory. 



3. The Stokes Theory, including f(d/L), significantly im- 

 proves upon the Airy Theory for 0.1^ d/L ^ 0.U and 

 overcorrects the wave velocity for d/L ^ 0.1. 



