completely in ten hours, and 31.4 hours after the start of the 
wave system at x equal to zero the component would no longer be 
present. Similar remarks can be made about each bar in the dia- 
grame When the various bars of the diagram overlap the sea surface 
is the sum of the various Sinusoidal terms indicated. Sine waves 
of different periods will sometimes add to a maximum and sometimes 
cancel to a minimum. In fact, there will be a point of phase re- 
inforcement every 100 seconds in this model. The maximum wave 
heights present are therefore just the sums of the amplitudes of 
the components. The peak amplitudes are shown above the dispersion 
diagram as a function of time along with the periods which go to 
make up the peak heights. 
The forerunners of swell discussed in the literature are 
clearly shown in this model. This swell will be more regular than 
the original model waves. What is of more interest is the trail- 
ing end of short period waves which is not discussed or emphasized 
as much in the literature. The waves which arrive after 42 hours 
will have periods less than the apparent period in the original 
storm, and the question as to why they are not observed more often 
arises. 
Alternate formulations 
The results shown by equations (6.14) through (6.17) can be 
obtained in an alternate form by finding the spectrum of equation 
(6.4), and by making an approximation to the integration to be 
carried out. The alternate derivation is given by Pierson [1951] 
in another paper. 
An exact solution can also be found by the substitution of 
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