have the same properties as required in Chapter 9 for the analogous 
functions in that chapter. The subscript H's have been added to 
emphasize the fact that, given [E,(p ,©)] offshore in deep water, 
then Ey ( # 99) is an unknown function unless the refraction proper- 
ties of the transition zone are given. 
The potential function is given by equation (12.17). [ioe CE oul 
is the power spectrum of the waves in water of depth, H. It cannot 
be found from the theories given in Chapter 10, although appropriate 
modifications of the formulas given therein would yield correct re- 
sults. 
As a function of time at a fixed point, these equations can 
be treated just as in Chapter 10. The record as a function of time 
is Gaussian and the results of Chapter 7 again apply. Boyle ) is 
by analogy equal to Boy(H 91/2). As before, [ALC WE is the inte- 
gral over 0 of Berg arch ahr 
Ti.e pressure at a depth, z, produced by a short crested Gaussian 
sea surface on the surface of a layer of water of depth, H, is given 
by equation (12.18). It reduces to the results given in Chapter 
1l as the depth approaches infinity. 
The pressure at a fixed point in the x,y plane as a function 
of z and t is given by equation (12.19). The equation can be de- 
rived by the use of the methods of Chapter 10. For a fixed value 
of zy, a pressure record as a function of time is therefore Gaussian 
and can be analyzed for its pressure power spectrum in the same way 
that a wave record can be analyzed. 
The power spectrum of the pressure record for a pressure re- 
corder at any depth (not necessarily the bottom) is related to the 
6S) 
