points of observation. Finally, the forecasting diagrams explain 
in part the observed change from sea into swell and the decrease 
in wave height with distance traveled. 
Fourier Integral versus Lebesgue Power Integral 
The introductory chapter of this paper began with a quotation 
from Lamb which stated that the most general case consistent with 
the assumption that the potential function was a simple harmonic 
function in x could be solved by the use of Fourier's Integral 
theorem. Interesting, but not completely general, results were 
obtained in Chapters 4, 5, and 6 with the use of Fourier's Inte- 
gral theorem. Then suddenly strikingly realistic and completely 
general results were obtained by the use of a new integral referred 
to as the Lebesgue Power Integral. It would seem, at first approxi- 
mation, that Lamb was wrong in the quotation. 
This is not the case, however. Lamb was correct. If 7 (o,t) 
is given at x = 0 throughout the entire storm, no matter how conm- 
plicated the function, and if 7(0,t) is zero before and after the 
storm, then it is conceivably possible to find the Fourier spect- 
rum for the entire wave system, and to solve a much more complicated 
problem somewhat along the lines of the problems solved in Chap- 
ters 4 and 5. Such a procedure would be impossible in a practi- 
cal sense because of the length of the record and complexity of 
the function which would be required. 
For an actual wave record it would also not be possible to 
attack the problem along the lines employed in Chapter 6 where the 
wave system was treated as if it were composed of wave groups 
repeating at fairly regular intervals, since a difficulty arises 
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