For a simple sine wave, the formulas, L= CT, and L = gT I Ztr imply 

 a lso tha t L = ZirC /g, C = V^gL/ZTr, C = gT/2Tr , T =V'2Td_/g, and T = 

 •>/2"T C / g . Thus if L or C or T is observed, the other two quantities can 

 be computed from it. In table 6, the comparison shows that C could not 

 be predicted from either T or L. The value of L. when computed from C 

 is much too low. When L is computed from T the NACHI observations 

 agree, but the computed wave length is considerably greater than the 

 observed wave length in the_MIKUMA observations. Whenthe formula for 

 the average wave length E, in terms of the average period, T, namiely 

 L = TgT I Zir, is applied to the MIKUMA observations, the period of 

 13 seconds yields a value of 2/3 of 264 meters or 176 meters as 

 compared to an observed wave length of 180 meters. The second set 

 of observations yields a value of 184 meters as compared to an observed 

 value of 200 meters. The percentage error with respect to the observed 

 average wave length is about 2% with the new formula and 47% with the 

 classical formula in the first case. In the second case, the errors are 

 8% and 38 %, respectively. 



It is most interesting that two of these four sets of observations 

 obtained in 1935 should agree with the newly derived formula. Since the 

 other two do not, it can be added that observations in a towing tank in 

 which Gaussian waves were generated, confirm, the theoretical basis of 

 the derivation of the new formula.* 



Wooding (1955) has derived an approximate joint probability distri- 

 bution for wave annplitude and frequency (period) in random noise, and he 

 has applied the results to the interpretation of wave observations. The 

 results show that the time interval between the successive upcrosses in 

 a wave record has a higher probabiliy of being large if the wave is high 

 than if the wave is low. Thus the average time interval between 

 successive crests of the one-third highest waves shouldbe greater than 

 the average time interval between all the crests. Or, stated another way, 

 the significant "period" is greater than the average "period." 



It should be possible to derive a formula for the significant "period" 

 in terms of a theoretical wave spectrum using the results of Wooding 

 (1955). If an average wave length were obtained using the "significant" 

 period and the classical formula, the error would be even greater than 

 that obtained by using the classical formula and the "average" period. 



In view of the difficulty of observing the significant wave height 

 discussed in this paper, it is believed that the observation of a true 



* See Lewis (1954). 



49 



