gives information on the correct spectral wave length to assign 
to each discrete spectral period. In equation (6.13), these 
wave lengths are assigned to the periods, and complete knowledge 
of the behavior of equation (6.3) at other x has now been obtained. 
Some of the waves are assigned to travel in the negative x di-, 
rection in order to obtain complete agreement with the results 
of Chapter 4. 
For a fixed t, the sea surface as described by equation 
(6.13) is periodic as a function of x. The wave lengths involved 
are given by L = et °/2nm=, and they decrease in length by one 
over the square of the integers. 
Alternate solution 
An alternate solution to equation (6.3) is also possible 
with the use of the results of Chapter 4. If, in equation (4.9), 
t - nt is substituted for t, and then if the equation is summed 
from n equals minus infinity to plus infinity, an alternate so- 
lution is the result. The alternate solution is horribly diffi- 
cult to evaluate and interpret. It represents a sort of blind 
alley with little practical application. The difficult terms 
and derivations of Chapter 4 would have to be analyzed and summed 
over many values of n before a result would be obtained. For 
comparison, in equation (6,13) for typical values of o andT, 
only about ten terms are important in the sum, and the evaluation 
and interpretation is quite simple. 
A finite train of regular wave groups 
In equation (6.12), for typical values of o , t , and T, the 
first term in parenthesis is negligible and it is therefore neglected 
= 32906:2 
