complete freedom in subsequent theoretical and practical work. 
Numerical methods for the determination of [A(#)]° from a sample 
from a stationary time series 
Ocean wave records are obtained on both coasts of the United 
States and in England. A few are or have been analyzed by Deacon 
[1949], Barber and Ursell [1948], and Klebba [1946,1949] with the 
aid of mechanical-electrical wave analyzers. Others are being or 
have been analyzed by Seiwell [1949, 1950, 1950] and Seiwell 
and Wadsworth [1949] and Rudnick [1949] by autocorrelation methods. 
Two have been analyzed by Tukey and Hamming [1949].* All the rest 
of the wave records have suffered the inglorious fate of being 
analyzed for "significant" height and period. Given the "signifi- 
cant" height and period, it is usually impossible even to estimate 
the average potential energy (in part, because the records are 
pressure records). Infact, from the two numbers which result, it 
is impossible to tell if the waves are all from one source, and 
in general it is frequently difficult to tell whether the record 
was of a "sea" or of a "swell." 
The numerical methods of analysis of stationary time series 
or "temporarily homogeneous" time series (tukey) as derived and pre- 
sented by Tukey [1949] and Tukey and Hamming [1949] are the basis 
for a correct analysis of wave records because they are the only 
methods in which the errors of the analysis can be precisely de- 
fined by statistical methods. Any analysis of a short section of 
*These results will be discussed in greater detail in a later 
chapter. It suffices to say now that the error in Seiwell's 
interpretation was that he failed to consider the whole auto- 
correlation function of the records he studied. They actually 
die down to zero if carried out far enough with a long enough re- 
cord. The wave analyzer records of the records he studied are more 
realistic than his interpretation. 
= 2 70n= 
