average "period", and the result is that the average "wave length" 

 is less than what would be computed from the average "period" 

 by the use of the classical formula. When this effect is corrected for 

 the short-crestedness of the waves, the result is equation (37) for a 

 fully developed sea. 



As part of the erroneous method of wave analysis depicted in figure 

 6, it is frequently assumed that the "wave length" of the wave which 

 passed during the time interval, T., is given by 



L. = 5.12 T. (38) 



J J 



in deep water or by an appropriately modified equation in shallow water. 

 This assumption is obviously dependent upon the assumption that the 

 zero which passes at the start of the "cycle" does not disappear before 

 the zero which passes at the close of the "cycle" finally arrives, and 

 upon the assumption that a new zero does not form between the first 

 zero and the point of observation and the old zero before the second 

 recorded zero passes. (Siniilar remarks could be made about crests.) 

 Since the wave forms of actual ocean waves do not propagate without 

 change of shape, and since the crests of actual ocean waves are not 

 conservative, these assumptions are not valid and the formula cannot 

 be used. 



The average of the "wave lengths" as computed from the individual 

 "periods" is always greater than the average "wave length" computed 

 from the average "period", ajid even this latter value is too big. 



Although it is unknown, suppose that the p.d.f. has the typical 

 properties of all p.d.f. 's in that it gives the probability that a "period" 

 within a band of "periods" will be observed. 



The p.d.f. of the "periods" is then g (T)dT with the properties that 



~ ~ (39) 



g(T)= for T<0, ^ ' 



g(f) > for f >0, (40) 



'CO 



^"'^ f g(T)ciT = | 



(41) 



The average "period" then equals 



00 



j= Tg (t )dT . 



Jo 



(42) 



41 



