Table 11.6 shows the local sea and Table 11,7 shows the disturbance from a 

 distance. Corresponding values of Tables 11.6 and 11.7 add up the values 

 graphed by the solid lines in figure 11.22. Table 11,6 corresponds to the solid 

 lines continued by the dashed lines where appropriate. The maximum value 

 for a given k and the minimum value are underlined in Table 11.6. Note that 

 the minimum continues quite smoothly into that region where the swell is not 

 present. 



Confidence bounds on the sums around circles 

 Liet the sums of the corresponding entries in Tables 11.6 and 11.7 be de- 

 signated by D]jQ. Each value of Dj^g can be thought to have 19(A/36) degrees of 

 freedom if the variation between nearby values of U^r, s) is not too rapid. For 

 example, if a square in the U{r5 s) plane were cut in half, then each half would 

 be assigned the value U(ri, s)/2 and 19/2 degrees of freedom. The degrees of 

 freedom of the sum of the two values would then be 



12 

 2 



[(U(r,s)/2+ U(r,s)/2)|^ 



(U(r, s)/2)2+ (U(r, s)/2)2 

 or 19j and the sum of the two E values would again be U(r, s). 



For the sum around a circular ring, this caji be generalized to give the 

 degrees of freedom for a AE value corresponding to those frequencies be- 

 tween 2iT(k --4)/96 and 2ir(k +-4)/96, The equation for the degrees of free- 

 dome is then given by equation (11.15). 



(11.15) f„12^ ^^e-^ke^ 



" 4 36 |-2qD^2^] 



The factor of 4 enters in the denominator of equation (11.15) because only 



every fourth value of the spectral estimates is independent. 



204 



