Most wave records at the present time are not actual mea- 
surements of the free surface. They are measurements of the 
pressure at some depth below the free surface. In all but one 
known case, the depth is the bottom at a short distance (rela- 
tively speaking) from the shore. In this one case, the pressure 
was recorded by a submarine below the sea surface as reported 
by Ewing and Press [1949]. In terms of the equations employed 
herein, P = P(X),y,,z,,t) 1s known where usually z, is equal to 
- W(X yy), the depth of the water below the (X59Y5) point of 
installation of the instrument. 
From either 7 = 7 (X,,¥,,0,t) or P = P(X 6 sV59Z52t)s the 
problem is to find out what P = P(x - x) ¥Y - Ygs 25 By) 6 : 
i) =a) (Gs S85 3/ S sean 12) etal (Sane) WS WC = 5.5 = Nig) Bo 8) 
are like. The problem is not simple. In fact, with the given 
data, the problem cannot be solved. 
As a start, though, it is necessary to study what is most 
accurately known, namely either ) = 7) (X59¥590,t) or P = 
P(X 59Vo2259t)- The free surface will be used in this part of 
the discussion although the remarks can be modified so that they 
apply to the pressure. The question is, "What ways are there to 
analyze the free surface as a function of time?" 
Over time intervals of the order of days, 7 = 7) (t), at 
any fixed point, is not even remotely periodic. The amplitude 
of 7) may vary from small departures from zero to storm wave 
heights. The problem, then, is how to analyze 7 under the assump- 
tion that some property of 7) is preserved for time intervals of 
the order of twenty minutes or so, with the reservation that 
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