(9.47), (9.48), (9.65) through (9.70), and equations (7.55) and 
(7.56) (with R replacing x), is the most realistic forecast for- 
mula of all those that have been presented. The above formulas 
are the only ones out of over three hundred in this paper (so far) 
which are needed to carry out a wave forecast. Actually only 
two diagrams given by figures 24 and 25 are needed along with 
the concept of the Gaussian case of the Lebesgue Power Integral 
for short crested sea surface. All of the other attempts to 
represent the sea surface and to forecast ocean waves serve only 
to illustrate forcefully the inadequacy of the models employed. 
A system which depends on the gross characteristics of a storm 
at sea, namely its duration, width, and fetch, and on the properties 
of a very special integral has yielded results which explain all 
known properties of waves from a storm at sea by the use of the 
classical concepts of gravity wave theory. 
In actual practice, the square cutoff filter will be only a 
first approximation to the actual wave systems because the winds 
which produce the waves require time to build up to full amplitude 
and die down from full amplitude, and because of smoothing effects 
due to the finite time required for observation and the finite 
area which must be observed. The waves build up with the wind, 
and they have different characteristics at the edges of the storm 
and at the rear of the storm than they do at the center of the 
forward edge. The actual filterswill then be smoothed in some 
way with respect to the theoretical filters. Their actual nature 
awaits detailed analysis and study of the sea surface. 
me fay 
