the value of K and K + dK. 
The representation of wave records by the Gaussian case of 
the Lebesgue Power Integral 
If a portion of an actual wave record is to be represented 
by equations (7.1) through (7.10) and (7.27) through (7.32), 
then it must, at least, approximate the properties of the inte- 
gral, and satisfy equations (7.33) and (7.34). One property 
of the integral is that 7 (t) never repeats itself. Another 
is that if a time interval t is chosen, which is large enough 
to eliminate autocorrelation effects, then the values of the 
heights of the sea surface measured at tis tit Fy ay 2T .acee 
and so on, will be distributed according to equation (7.34). 
Herein lies the fault of the models in Chapter 6. For different 
ty in this model, (since it was assumed that the groups were 
spaced T units apart plus or minus a small deviation) the values 
of 7 (t) will not all have the same probability distribution 
and therefore the model is not Gaussian. 
It is very easy to test a wave record to see if the dis- 
tribution of points chosen from 7(t) at time intervals suffi- 
ciently great is Gaussian. The test has been made on some actual 
amplitude wave records and on some pressure records. Some re- 
sults of the tests are given in figure 14. 
The first histogram in figure 14 is from a wave height record 
obtained with the Beach Erosion Board Tmetrenene described by 
Caldwell [1948], which was located on the pier at Long Branth, 
New Jersey. It shows that the distribution is not quite Gaussian 
because the median value of the histogram is below zero and the 
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