pressure recorder becomes larger and larger with increasing depth. 
In fact a little investigation shows that there will be crests ob- 
served in the pressure at the depth, z = -h, when an actual trough 
of the sea surface is passing overhead. Additional investigation 
of these formulas will be left to the reader. 
The pressure recorded at a depth, z, below the sea surface (z 
is negative) can be found from the following arguments. The free 
surface is given by equation (11.1), and it can also be represented 
by the limit of a partial sum as in the second expression in equa- 
tion (11.1). For each term in the partial sum, the pressure contri- 
bution to the total pressure for that partial sum is found by simply 
inserting pg exp(( Money) 2/8) for each cosine term in equation 
(11.2). A term for the static pressure is also needed. 
The limiting form is then given by the Gaussian Lebesgue Power 
Integral in the second expression in equation (11.2). The pressure 
at each point below the sea surface thus involves the contribution 
of each of the elemental waves passing overhead modified by the 
appropriate damping effect with depth. 
Pressure is usually only recorded at one fixed point. From the 
results of the first part of Chapter 10, the pressure at the point, 
X,Y, at any fixed depth, z, is given by equation (11.3). Thus 
the pressure as a function of time alone is Gaussian. A given 
pressure record can be analyzed for its power spectrum in the same 
way that a wave record of the sea surface can be analyzed for its 
power spectrum. The pressure power spectrum, [ACH ie, is related 
to the power spectrum for the free surface, [A(y age by equation 
(11.4). Given either one, the other can be found from the 
