Chap. 10] 



ELECTRICAL METHODS 



687 



Elliptical polarization may be readily demonstrated if it is assumed that 

 the additional field differs from the original field in respect to both direction 

 and phase by 90°. If the time variation of the two fields is represented 

 in two vertical planes at right angles to each other (Fig. 10-35) and if the 

 main field is assumed to have the larger amplitude and the interfering 

 field the smaller one, the length of the resultant vector I will be equal to 

 the maximum amplitude A of the larger field at the instant 1, since the 

 amplitude of the second field is zero. At the instant 2 the amplitude of 



Fig. 10-35. Elliptical polarization of an electric field when its components are 90° 

 out-of-phase and differ in direction by 90°. 



the larger field has decreased; the amplitude of the smaller field has in- 

 creased; and their resultant is given by the length and direction of the 

 vector 11. At the instant 3, the resultant field is given by the length of 

 vector III. At the instant 4, the amplitude of the larger field is zero. 

 Hence, the vector IV has the length B and is at right angles to the vector I. 

 The same phenomenon recurs in the three remaining quadrants. A line 

 connecting the ends of the vectors is an ellipse. 



The variation of the field amplitude with horizontal direction was pre- 

 viously represented by two adjoining circles (Fig. 10-33). If this pro- 



