Although it is not impossible to obtain a negative value in a power spec- 

 trum computed according to the techniques described, it is highly improbable 

 that such consistent patterns of negative numbers should occur. Given that 

 the computations are correct, one possible explanation of what occurred is that 

 the original data have been distorted by some unknown and undetected source of 

 error to such an extent that they no longer represent a sample from a stationary 

 Gaussian process in two variables. (Another very disturbing possible conclusion 

 is that the ocean waves cannot be satisfactorily approximated by a stationary 

 Gaussian process in three variables. ) 



Moreover since the sum of all the values of U(r, s) must add up to the vari- 

 ance of the original data (in these figures), the negative values have the effect of 

 adding erroneous positive values to the already positive estimates ifi the other 

 parts of the figure. 



A study of the figures and the data shows that the gross features of the analy- 

 sis appear to be correct but that there seems to be a background distortion in the 

 pattern which is difficult to define precisely. 



Analysis of original results 



Various tests of the results were made at this point, and it soon became 



evident that there were serious discrepancies between the wave pole frequency 



spectrum and the average of the two directional spectra. The average of the 



sums of the values shown in the directional spectra (which in turn equals 



[Q(00)2 + Q(00)3]/[2(1.016)^]) should give a number which when corrected for 



possible sources of error should be nearly the same as one half the E value 



165 



