spectra obtained at different headings and the solution of a set of simul- 

 taneously linear equations. 



From the results of this present study, it can be stated that the method 

 proposed by Longuet-Higgins [1957] is not likely to be successful, especially 

 with respect to a sea. Since the data are taken at different times at different 

 headings, each record has a different sampling variation for each spectral 

 estimate. The various moments thus have wide sampling variation. 



Moreover, eighth moments are required to give any sort of definition 

 to the spectrum. For the true sea surface the eighth moment is entirely 

 determined by the capillary waves on the water. Some sort of filtering 

 action would be needed in the recording instruments to maintain pure gravity 

 wave conditions otherwise a problem in resolution would arise due to the 

 extreme range of wavelengths covered. The effect of such filters would have 

 to be incorporated in the theory. 



Even with the capillary waves filtered out there would be high frequency 

 error noise of some sort or another present in the data. In computing an 

 eighth moment, this noise would blow up beyond all recognition and com- 

 pletely obviate the value of the estimated moment. 



In contrast the methods used in this study effectively suppress high fre- 

 quencies whether real or due to errors in the data. Also various sources 

 of error which will undoubtedly be present in any method of recording waves 

 were isolated and removed. 



The very valuable results of Longuet-Higgins [1957] on the statistical 



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