﻿Radiation from Bent Antennae, 603 



of the transmitting antenna. It is obvious that if </> = 0, then 

 H varies as cos 6, assuming a constant value for the distance r, 

 and since the current in the receiving antenna varies as H, it 

 follows that the plotting of the current for various azimuths 

 of the sending antenna gives us a polar cosine curve con- 

 sisting of two circles with perimeters in contact at the origin. 

 If, however, M = 0, then H is constant for constant values of 

 r and the polar curve is a circle with centre at the origin. 

 For various intermediate ratios of M to </> the polar curve 

 takes some irregular figure-of-8-shape as depicted. 



The similarly shaped polar curves which Mr. Marconi has 

 given (loc. cit.) for the current in the receiving antenna 

 when a bent receiving antenna is swivelled round its earthed 

 end are, however, to be explained in a slightly different 

 manner. If a receiving antenna is employed which is partly 

 vertical and partly horizontal, then, when acted upon by a 

 similar or even a vertical transmitting antenna, there are 

 three sources of electromotive force in the receiving wire : — 



1st. That due to the action on the vertical part of the 

 receiving wire of the electric force of the incident wave 

 which is perpendicular to the earth's surface. 



2nd. That due to the cutting of the vertical part of the 

 receiving wire by the magnetic force of the incident wave 

 which is parallel to the earth's surface. 



3rd. That due to the magnetic-force lines passing under 

 the horizontal part of the receiving wire being alternately 

 reversed in direction, aided by the wave-length being roughly 

 equal to 4 times the length of that wire. 



The total E.M.F. is the vector sum of these three separate 

 E.M.F.s. The numerical values of (1) and (2) are equal, 

 and (1) is proportional to the minimum" radius of the polar 

 curve in the direction 105° to 110°. 



It is not difficult to show that when the receiving antenna 

 has its free end pointing anywhere in the semicircle which 

 lies nearest to the sending station, the E.M.F. (3) is opposed 

 in direction to E.M.F. (2), and for a certain azimuth these 

 nullify each other. Hence the minimum radius of the polar 

 curve is proportional to E.M.F. (1). Again, since (1) and 

 (2) differ in phase by 90°, it follows that the receiver current. 

 when the free end of the receiving wires bears 90° from the 

 shortest line connecting the stations, is proportional to the 

 vector sum of E.M.F. (1) and E.M.F. (2). 



On the other hand, when the free end of the receiving wire 

 points away from the sendiug station, the current in it is 

 proportional to the vector sum of E.M.F. (1) and the scalar 

 sums of (2) and (3). 



