654 



ELECTRICAL METHODS 



[Chap. 10 



a phase shift of 27r/10. For the sake of illustration, the horizontal com- 

 ponent is shown at right angles to the direction of propagation (Y) while 

 actually, in the radio surface wave, the horizontal component is in the 

 plane of propagation (X). This, however, does not change the resulting 

 phenomenon or the equations given later. 



If for each instant the position of the resultant vector is constructed 

 and then the ends of the vectors are projected on one plane, they lie on 

 the circumference of an ellipse. The maximum vertical and horizontal 

 components are tangents to this ellipse, and its tilt angle depends on the 

 ratio of the two components as well as their relative phase shift. As 

 shown below, the ratio of major and minor axes of this eUipse may be 

 measured conveniently in the field. If their ratio (see Fig. 10-19) 6/a 



Posihon of maximum 

 /s/gna/ of anfenna 



Direction of I a 



>- I *' 



Propogofion 



Fig. 10-19. Ellipse of polarization and receptor with rotatable antenna to measure 

 compression and obliquity of this ellipse (adapted from Eeldman). 



is designated by r, the ratio of the horizontal and vertical components is 

 given by 



■ /XV ^ (r^- Dsin^tA + l 

 \Z/ (r2 - 1) cos2 ,A + 1 ' 



(10-18c) 



wherd ^ is the tilt angle of the ellipse. 



The following equation" for the relation between phase shift <p, tilt 

 angle ^, and intensity ratio, follows from the geometry of the ellipse : 



cos fp — \ tan 2^ ( = — 



(M) 



(10-18d) 



An apparatus for the determination of these quantities is illustrated in 

 Fig. 10-19. It consists of a receiver with a rotatable double L antenna 



" Derived on p. 690. 



