The value of Chi Square is 23.1 with eight degrees of free- 
dom. It is highly improbable that such a distribution could 
come from a normal distribution. But note that it is the very 
last value in the sum which makes the sum so high. If this 
last term is omitted Chi Square is 7.8, and the sample could 
have come from a normal distribution 34 out of 100 times if 
chosen at random. 
The departure from the Gaussian case can be explained on 
the basis of the actual non-linearity of the sea surface. Be- 
cause of the non-linearity, crests are higher and troughs are 
lower than in a surface described by the Gaussian case. The 
peak values of the crests are what have produced the high value 
of Chi Square. It was pointed out in the second chapter that 
little could be done about the essential non-linearity of the 
sea surface, and these histograms show remarkable agreement with 
the hypothetical Gaussian case within the limits of the lineari- 
zation assumption. 
The potential energy of an actual wave record averaged over 
time can be computed by squaring the wave record and averaging 
over time. Such a computation would require rather leneeie 
computations. The histograms show that E ax can be estimated 
easily be taking the second moment about the mean (square of 
the variance) of a sample of one hundred or so points from the 
record. The computations involved would be considerably less 
than by the other method, and the reliability of the estimate 
would depend on the size of the sample, on the magnitude of 
Enax? 2nd on the function E( jy). The value of Enax and of P.E. 
=o 
