upon attempting to find the average potential energy in the 
system when the wave groups overlap in time. 
The Lebesgue Power Integral for the Gaussian case of a sta- 
tionary time series eliminates these difficulties because it em- 
ploys a function which is (apart from a constant) directly related 
to the average potential energy in the wave record. Methods of 
wave record analysis based upon this integral do not depend upon 
the entire wave record, upon the time the record was made, or 
upon the existence of groups of waves in the record. The analysis 
of the wave records is therefore much simpler, and the interpre- 
tation of results is much easier. The formulation of the wave 
record as a Lebesgue Power Integral is not a complete solution 
to the problems because such a record lasts PORE and theoreti- 
cally at least, only has a meaning for an infinitely long record. 
It should be noted that it is not necessary to include a 
section on energy considerations in this chapter. The potential 
energy averaged over time at the point and time of observation 
is given by the area under the forecasted power spectrum multiplied 
by p2/4, and the very nature of the filters employed shows that 
all of the energy is accounted for. 
Fourier Integral theory was employed in order to find the 
filter manetiions for the forecasting diagrams since they are all 
based upon the results of Chapter 5. The Fourier Integral solu- 
tion gave the effect of the finiteness of the record on the infin- 
itely long record as represented by one of the terms of a partial 
sum which in the limit gave the Lebesgue Power Integral. 
In conclusion for this chapter, the most realistic results 
= WAL 
