Fig. 4. 1(6) and two mutually perpendicular 

 reference lines 



Two Perpendicular Headings 



Suppose we take the same intensity field, 1(6), and measure it twice with a linesir array, once with 

 the array pointed North/South and once with the array pointed East/West (or any arbitrary pair of per- 

 pendicular headings) (See Fig. 4). We can dissect field I{d) exactly as before into two components, /^ 

 and /q, which are, respectively, symmetric and anti-symmetric with respect to the North/South axis. 



1(6) -1^(6) +1^(6). (7) 



Now we can take both of these components and dissect each one of them into two components 

 with respect to the second (East/West) axis, thus: 



1,(6) = I^(d) ^ 1^(6). 



(8) 



Because of the perpendicularity of the two measurement axes, the two components /^^ cind I^ both 

 retain their symmetry with respect to the North/South axis, and the two components I^ cind I^ both 

 retain their anti-symmetry with respect to the North/South axis. We have thus dissected the field into 

 four components, i.e., 



1(6) = 1^(6) + 1^(6) + 1^(6) + 1^(6) (9) 



such that each of the four components is either symmetric or anti-symmetric with respect to each of 

 the measurement sixes. 



Now, when we place the array parallel to the North/South axis, we measure 



M^(6) = 1^(6) + 1^(6). (10) 



Similarly, when we place the array in an East/West orientation, we measure 



M^O) = IJ6) + 1^(6). (11) 



893 



