power spectrum of the wave record taken of the free surface by equa- 
tion (12.20). Given either one and given the depth of the water, 
and the depth of the instrument, the other can be computed except 
for the high spectral components lost by filtering due to depth due 
to the fact that the pressure recorder simply will not respond to 
minute variations in the pressure field. 
At the bottom, z equals minus H, and equation (12.20) becomes 
equation (12.21). The pressure record recorded by a pressure re- 
corder on the bottom is therefore some segment of one of the infin- 
itely long records which result from the limit of a partial sum such 
as those discussed in Chapter 7. 
Wave refraction in the transition zone 
The refraction of the short crested Gaussian waves which have 
been derived in the previous chapters is an extremely complicated 
problem. The basic theory which has been derived by Sverdrup and 
Munk [1944], Johnson, O'Brien, and Isaacs [1948], arthur [1946], 
Eckart [1951], and Arthur, Munk and Isaacs [1952], is correct, but 
it applies only to one pure sine wave of constant period. The theory 
needs to be placed upon a somewhat firmer theoretical basis as pointed 
out by Pierson [195la], and the results of Eckart [1951] are a first 
step in this direction. 
The theory of wave refraction is at the level of theoretical 
development which was attained by the theory of optics before the 
work of Luneberg [1944, 1947] in optics. That is, wave refraction 
theory has been derived not from the basic hydrodynamic equations, 
but by a series of approximations and assumptions about the nature 
of the motion of a pure sine wave over a bottom of variable depth. 
BH 
