degrees of freedom for each U,* if m = 20 were again used. 
Thus any attempt to put the peak under too powerful a micro- 
scope is doomed to failure unless a longer stretch of obser- 
vation is available. The length of the record, the spacing 
of the observations, and the lags used are ideally suited to 
show that there is essentially no power above 0.12 to 0.15 
cycles/second (at periods less than 8.3 to 6.6 seconds), but 
is‘not well suited to the detailed investigation of the structure 
of the peak. The 53-X record has been analyzed by Seiwell and 
Wadsworth in terms of a combination of 
(1) a single frequency, and 
(2) an auto regressive scheme as proposed by Kendall.... 
The latter scheme would involve a finite amount of power in the 
region 0.12 to 0.50 cycle/second now seen to contain at most 
a negligible amount. Almost any analysis containing simple 
auto-regressive components will similarly fail to fit the 
observed facts." 
The above analysis shows that the one second lags chosen and 
the number of lags made were quite inadequate to describe the power 
spectrum. At depths of the order of 78 feet, faith in hydrodynamic 
theory would tell us that all periods less than about 6 second would 
not be recorded by the pressure recorder and the spectra shown sure- 
ly confirm this fact since essentially 2/3 of the values obtained 
are zero. Note that for a lag of three seconds and for the same 
amount of work on a record three times as long, considerable val- 
uable information would have been obtained. 
Noise versus signal 
The problem of proving that a wave record contains one or 
several pure sine waves is analagous to a problem treated originally 
by Wiener [1949] in his famous book on communication theory. Con- 
sider an A.M. radio receiver a great distance from the transmitter. 
Let the detected signal, say, one of the notes in the chimes of 
100 
