previous chapter. The nature of the continuous spectrum, the be- 
havior of the wave train as it travels along, and its variation 
with n will be described. 
Spectrum 
The part of the continuous spectrum which was used in the 
integral form of the solution is given as b*(a) in equation (5.23). 
The second form, in terms of a, can be obtained with the use of 
equation (5.4), if n is an integer. As #! approaches 2r/T or as 
a@ approaches zero, the spectrum has an indeterminate form, but the 
application of standard methods shows that the value of b*(a) ap-= 
proaches ATn/m at this point. Thus for larger values of n, the 
contribution to the spectrum near values which are equal to values 
associated with the apparent local period becomes large compared 
to other values of the spectrum. 4s n approaches infinity, how- 
ever, the spectrum does not reduce to one infinitely high spike 
as in the problem in Chapter 4. The actual behavior of the spect- 
rum is shown in the graphs of b*(a) which are shown in figure 6. 
If n equals a small value as in the top graph of figure 6, the 
spectrum is a smooth curve with important contributions for all 
Spectral values. Such a disturbance of the sea surface would tra- 
vel only a short distance and rapidly die out. In the bottom graph 
of figure 6, there are three different scales on the ordinate, 
(b(a')), and abscissa (a'), axes. The inner scales apply for n = 
10. If n is increased by a factor of ten, the ordinate scale is 
increased by a factor of 10 and the abscissa scale is decreased by 
a factor of 10 as in the middle set of scales. Thus, the important 
part of the spectrum is increasingly concentrated near wp = anr/T, 
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