neighboring trench below sea level. Perturbations and smaller waves 

 such as the one at T3 in figure 5 are not counted if they do not pass 

 through sea level. 



The first danger which will make the observation less useful is a 

 tendency to ignore the low waves. The observer in tabulating the heights 

 of the passing waves may see many low waves and, because they appear 

 insignificant compared to the more dominant waves, may fail to write 

 them down. The average of the recorded values is then greater than 

 the average of all the values, and since the nature of the omitted waves 

 in unknown, the two values cannot be related. 



The observer must therefore .attempt to record the heights of all 

 the waves that pass the point of observation if the observed values are 

 to approximate the distribution given by equation (1). 



This can be done, but it is difficult to do because almost invariably 

 the observer will omit the low waves from such tabulations. Emphasis 

 on this point and its importance may, in time, nnake it possible to obtain 

 a complete sample of wave heights. If not, the theory of a truncated 

 distribution can be used to avoid this difficulty in a way which will be 

 discussed later. 



3. The Average Height 



After a sufficient number of heights has been recorded, the 

 average height is the simplest and most useful statistic which can be 

 computed from the data. 



Even in a sea, if the heights are a correct estimate of E, the ampli- 

 tudes are distributed according to equation (1). 



Consider figure 2. The first wave height equals ^ + ^ . The second 

 wave height equals f + ^4. ^^'^ ^° °^> therefore the average wave 

 height is given by equation (7)'. 



{C+C)+ (C+C) + ---+(C + £ ) 2N ^ 



N '^ t.:| N 



Even if the successive amplitudes combine to give height values 

 unrelated to the target distribution, the average wave height is still 

 equal to twice the average wave amplitude, and, under the assumption 

 that the amplitudes are from a target distribution, the value of E 

 can be estimated. 



11 



