for Uy equal to ten thousand om, the true value will lie between 
thirteen thousand om@ and eight thousand cm* ninety percent of 
the time. 
The reliability of a seven minute wave record 
Seven minute long samples of a function related to 7 (t), 
namely P(t), are taken every four hours at Long Branch, New Jersey 
by a pressure recorder in approximately thirty feet of water.* 
Spectral components with periods less than 3.5 seconds will not 
show up in the records. A At of 1.7 seconds is therefore the 
value which will exclude aliases and eliminate dangers from that 
feature of the analysis. There are 420 seconds in a seven minute 
wave record and therefore N is 246. If m is chosen to be twenty, 
then one band would cover periods from 7.14 to 4.56 seconds. The 
value of f would be 24, and approximately 90% of the time the true 
value of the power in the band would lie between 1.8 times and .63 
times the estimated value. The same possible error could occur 
for the estimate of each of the bands, and the total power in the 
record can also be incorrect. 
These results are not too surprising. Consider again the 
records shown in figure 12. The records are over one hour long. 
One tenth of the record is about seven minutes long. It is evident 
from the records that strips seven minutes long can be found which 
would yield much smaller values for the simple estimate of the 
number, E ,» than would be obtained from the estimate over the 
max 
entire record. Similarly, much higher values could also be found. 
It is therefore necessary to conclude that the data which can be 
*See the next two chapters. 
2 285 & 
