assigned the values 



' 1200 1200 ' 1200 ' 



on both, the horizontal and vertical axes (1200 = 30 x 2 x 20). 



A simpler system of notation will be used by assigning the values 0, 

 1, . . . , , etc. to the spectral coordinates just as the values of k were used 

 in studying the wave pole spectrum. 



Then R is given by R* times 1200/2it5 and it becomes 



1200(k 'h^ 



(11.13) R = 2 



(96)^^(5.12) 



= 0.025429(k--|)2 ?= C(k --|)2. 



The values of R for k - -^ an.d k + -t determine two concentric circles. 

 The total contribution to the value of E of all estimates within these two 

 circles should correspond to the value determined from the wave pole 

 spectrum except for residual errors of white noise and curvature. To esti- 

 mate this, the value of one half of the area between the inner circle and the 

 outer circle is needed. 



The area of the inner circle is 



7r[C(k-^)2] 

 and the area of the outer circle is 



4c(k + i)^]^, 



One half of the difference is the area of one half the circular ring as given by 



194 



