there might be long stretches of the original record which do 
not show any groups. 
If equation (3.10) is applied to7 (t) instead of 17 ,(t), 
there is a much better chance that the potential energy of the 
representative wave record will be apvroximately equal to the 
potential energy of the actual wave record. However, the wave 
grouo chosen and the time interval,T, might not be representative 
of the entire wave record. 
There are several other, not so important, ways in which 
the actual wave record could be analyzed which would yield a 
discrete spectrum. For example, it could be assumed that a ten 
or twenty minute length of record repeats itself periodically 
every ten or twenty minutes. Such an analysis would be carried 
out along the lines of the one described above. The harmonics 
would not become appreciable until n was of the order of forty- 
five or fifty. The analysis would be even more tedious than 
the one described above, and the results would not be too amen- 
able to theoretical work. The portion of the wave record studied 
would be repeated exactly, but the record and its representation 
would not agree outside of the time interval studied. 
It could also conceivably happen that a wave record was com- 
posed of discrete spectral components which were irrational. For 
example, 7 (t) = cos 2rt//2 + sin 27t//3 is not periodic. There 
is no time interval, T , such that 7 (t) = (t+T). Sucha 
representation for the free surface would be called an almost 
periodic function. For additional theoretical considerations, 
reference is made to the book by Bohr [1947] on the subject. 
= Ail = 
