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BELL SYSTEM TECHNICAL JOURNAL 



(23), (25), (26), the formulas for the principal parameters relating to 

 the point a are, of course, 



2^2 -77p± 1^1 

 2^ = Wzp |i^| 



Z=X + tY 

 W=U + lV 

 z =x+iy 



Fig. 12 

 But, since the x'aj-axes are parallel to the XA F-axes, 



z = Z — Za. 

 Squaring (42) and taking the mean of the result gives 



I^ =Y^^- Za^ - IZZa. 



(39) 

 (40) 

 (41) 



(42) 



(43) 



Multiplying (42) by its conjugate ^ and taking the mean of the result 

 gives 



J^i = ]zp + |Za|2 - 2Re (ZZa). (44) 



Substituting (43) and (44) into (39), (40), (41) yields the desired for- 

 mulas expressing the principal parameters relating to the point a (Fig. 

 12) in terms of quantities relating to the point A. 



