especially when one notes the way in which y is defined. 



The values of R, range from 0.983 to 0.847 and the average value is 

 0.918. Thus over 90 percent of the angular variation on the average is ex- 

 plained, by the values of c^ and -y , . The values of R range from 0,991 to 

 0,882 and the average value is 0,955. Over 95 percent of the angular variation 

 is explained, on the average, by the values of Ci, y-,i ^z ^^^ "VZ" The erratic 

 behavior of the other coefficients is explained as an attempt to fit the sampling 

 variation of the data. 



The graphs of c,, y-,, Cyt and y2 ^o "-^t vary as a function of k very 

 rapidly. It would not be difficult to express them as somewhat smoothed func- 

 tions of k (and hence |ji.) over the range of k from 11 to 27. The result would 

 then be given by equations (11,29). (1L30), {1L31) and (11.32). 



(11.29) c^ = CjV) 



(11.30) Y^=>^j^*(Hl) 



(11.31) C2 = C2*(ix) 



(11.32) Y^^^Z*^!^) 



The directional spectrum could then be defined analytically as a function 



of frequency and direction by equation (11.33) in which precautions would have 



to be taken to insure that the square bracket on the right was always positive. 



2 2y 2^2 

 (1L33) [A(ia,e)]2 = |^^l-i— ^ ■ -^t^ + c^*(tx)cos(2(0-yj^*(|a.))) 



+ C2*([Ji) cos(4(G-Y2*(fx)))] 



Also f|jj,j 0) would have a miniraum in the first quadrant as a function of G 



232 



