the Gaussian case has been presented by Tukey and Hamming 
[1949]. For the non-Gaussian case very little is known. 
Paraphrasing Tukey, it can be said that "This restriction to 
Gaussian (wave records) will presumably not be a serious hindrance 
to our analysis of actual (wave records) which will be non- 
Gaussian to a greater or less extent, if we use the quantitative 
expressions for the fluctuations as warning signs, and realize 
that fluctuations larger than those predicted by Gaussian theory 
are likely. The recommended procedures (in the paper) are known 
to be good for Gaussian (wave records). For moderately non- 
Gaussian cases, the analogy with simple problems suggests that 
the procedures will be quite good." For wave records the 
modifying effects of non-linearity must be kept in mind, at 
least in a qualitative sense. Tukey (personal communication) 
Says that the values of Chi Square given before are just what 
one might expect from random noise and that the better results 
for the pressure records show that the system is non-linear in 
the high frequency components. 
If the qualifications and explanations in the above section 
are taken into consideration, it can be concluded that the best 
possible known way to represent a wave record and consequently 
the sea surface as a function of time at a fixed point is given 
by the Gaussian case of the Lebesgue Power Integral. Any portion 
of a record of the sea surface as observed as a function of time, 
if the sea surface is in a stationary state, can therefore be 
thought of as a segment of one of the statistical ensemble of 
functions which would result from the indicated limiting process 
= 146% 
