Chap. 10] 



ELECTRICAL METHODS 



691 



The amplitude variation of the electrical field in a horizontal plane, in 

 the case of elliptical polarization, differs from that for D.C. which was 

 previously represented by two circles (Fig. 10-33). Since elliptical polari- 

 zation may be assumed to result from a combination of two fields at right 

 angles to each other, their combined amplitude variation follows from a 

 superposition of two amplitude circles at right angles to each other. Since 

 in each circle the amplitude variation is represented by a cosine law, the 

 resultant ampUtude in a line connecting the probes OA (in Fig. 10-36) is 



OA = \/a^ cos2 a + 62 sin2 „. (10-26a) 



NummitJ Va/ttts: 



Fig. 10-36. Relations of amplitude, direction, phase, ellipse- and lemniscate 

 characteristics in A.C. potential fields (adapted from Ambronn). 



The phase b in the line OA with respect to the phase in the direction of 

 thq major axis may be calculated, though in practice the procedure is 

 reversed, since the phase difference is measured and the characteristics of 

 the ellipse are obtained from it. Assuming the elUpse to be known, a 

 tangent drawn from the point A will give points F and B. The normal 

 to the X axis through F intersects a circle drawn about with the radius a 

 in the point C. The direction of OC with respect to the x axis is the phase 

 angle in the line OA . These geometric relations may be expressed by the 

 following equations: 



(1) 



X = a cos o; 



(2) 



y = b sin 8. 



