"periods" is ever solved, it will be possible to determine the p.d.f. 

 of the "wave lengths" by using the same theory on the new spectrum. 

 Aerial photographs, if the scale is known, would be useful in the 

 determination of the probability distribution of the "wave lengths" 

 empirically. 



Observations which show that the formula given above is more nearly 

 correct for the average "wave length" than is the classical formula 

 are cited by Dearduff (1953). He states that "the observed wave lengths 

 were as a whole much smaller than the calculated lengths based on the 

 usual formula." The value which was obtained from the analysis of 

 observations made from Nantucket Lightship was half of the value 

 which would be obtained using the classical formula. 



The theory on which equation (37) is based assumes that ripples 

 on top of the more dominant cycles are not counted in the measurement 

 of the "wave lengths". The crest must be above sea level and the trough 

 must be below sea level before the wave can be counted. A ripple or 

 perturbation riding on top of a larger wave should not be counted. When 

 such values are counted their effect is to decrease the average wave 

 length to a value even less than the one given by equation (37). 



2. Explanation of Theory of Equation (37) 



There is an idea prevalent in current wave theory that a wave 

 record can be broken up into pieces of one wave per cycle and that 

 each oscillation can be treated as if it were a sine wave with the use 

 of the classical formulas for the piece. 



The theory can be sketched briefly as follows; Given a wave record 

 as on the bottom of figure 6, the record is broken up into pieces at 

 each zero up- cross and each fragment is treated as if it were a piece 

 of a sine wave with a true period equal to the length in time of the piece 

 and with an amplitude equal to one-half the crest-to-trough height of the 

 piece. If the above assumptions were correct, then the wave record 

 could be represented mathematically as the sum of a number of 

 functions of the form sketched on the top of figure 6. 



Such a representation is obviously absurd. If such a fragment were 

 generated in a wave tank, it would alter in form completely before it 

 could travel even a few feet. A Fourier analysis of one of the pieces 

 shown in figure 6 would show it to be composed of a very broad Fourier 

 spectrum of frequencies so that it would not be correct to apply the 

 "period" T. to one of the pieces. Such a small piece of a sine wave is 

 not the same thing as a sine wave. 



37 



