entire transcendental function capable of satisfying equation 
(11.27) and equation (11.24) for greater than pw, if it is to 
have a value for all p or it must be identically zero for » 
greater than some value. The functions given in the examples in 
Chapter 9 satisfy equation (11.27) [and therefore (11.19) and 
(11.16)]. When they were manufactured, condition (11.24) was not 
known. It might be an interesting problem for the reader to see 
if they satisfy equation (11.24) for all values of yp Ke 
The use of autocorrelation functions 
The non-normalized autocorrelation function given in eauation 
(10.26) was used to find the power spectrum. In its own right 
it is an extremely important function in wave theory because it 
permits short range predictions of what the next few waves will 
be like. The non-normalized autocorrelation function of a wave 
record dies down to zero for large values of p and it is very small, 
for example, for p equal to about 180 seconds for a power spectrum 
from a "sea" record. This means that what occurs at the point of 
observation three minutes after, say, a crest passes that point has 
very little to do with the fact that a crest passed three minutes 
ago. Stated another way, it is impossible to predict whether a 
erest or a trough will be passing the point of observation three 
Minutes after a given time of observation. Note that the power 
spectrum of the wave system tells us a great deal about the whole 
wave record, about the characteristics of the record, and about 
the "sea" and "swell" properties. However nothing can tell us the 
exact shape of the wave record three, ten, twenty or thirty minutes 
into the future. 
19 
