treated as if every other one was independent, and since they are distributed 

 according to Chi Square with f degrees of freedom, the point on the CCS 

 curve is approximately distributed according to Chi Square with 



i2 



(10.2) 



Nk = i 



60 



S AE, 



,n=k 



H/ 



degrees of freedom (see Pierson [1954]). Then the confidence bands accord*; 

 ing to Tukey for large N are approximately given by multiplying the point on 

 the CCS curve by 



10 and 10 



The observed CCS curve is shown in figure 10.4 as plotted on the theo- 

 retical family of curves given by Pierson, Neumann and James [1955]. The 

 agreement for some CCS curve slightly in excess of 18 knots is quite strik- 

 ing although the agreement is not perfect. I 



1 



The CCS curve is too high at the frequency side of the scale. This 

 may in part be due to the summation of white noise errors at high frequencies. 

 Also if the pole surges back and forth in the long period waves, it may en- 

 counter shorter period chop while moving back in a trough in such a way 

 as to falsely assign their height contribution to a higher frequency. 



144 



