﻿Radiation from Bent Antennce. 597 



in the writer's Paper to the Royal Society ("A Note on the 

 Theory of Directive Antennae or Unsymmetrical Hertzian 

 Oscillators/'' Proc. Roy. Soc. Lond., ser. A, vol. lxxviii. p. 1). 



If 8z be the length of the side perpendicular to the bisect- 

 ing lino on which r is measured, and if we consider the oscil- 

 lation in this one side only, then on the same principles it can 

 be shown that the maximum magnetic (h) and electric (e) 

 forces at distances r from the oscillation taken in the same 

 directions as H and E are given by 



7 I8z , 



Uz a J"** 1 -. l 



At distances such that mr is large compared with unity, all 

 these forces vary inversely as the distance, and E = H and e = h. 



Also H//< = »iS// = 2tt8///\. 



Hence when using the bent earthed oscillator as in the 

 experiments here described, it is clear that the field at a 

 distance r from the centre, not small compared with the 

 wave-length, taken in the direction in which the free end of 

 the oscillator points, is to the field in the opposite direction 

 at an equal distance in the ratio of h — H to h + H., that is in 

 the ratio of \—2~$y to X-f-27rS//. 



Under the assumption here made as to the equality of the 



current at all points of the oscillator, the quantity By is the 



length of the horizontal part of the oscillator. In comparing 



the theory with the practical results, we must notice that the 



value to be assigned to Sy will always be very much less than 



the actual length of the horizontal part, because the actual 



magnetic moment of the bent oscillator is always much less 



than the product of the lengths of its vertical and horizontal 



portions and the maximum current at the earthed end. A 



consideration of all the circumstances shows that the By in 



the formula may, as a first approximation, be taken to be 



half the length of the horizontal portion of the antenna, 



whilst the wave-length in the present case was about five 



times the total length. Accordingly, in the case of the 

 © © ^ - 



antenna 10 feet long bent over so that 7 feet were horizontal, 

 the theory would predict that the ratio of the two magnetic 

 forces H and h should be in the ratio of 2ir x 3i to ox 10 or 

 22 to 50 ? and the ratio of the fore and aft fields or radiation 

 Phil. Mag. S. G. Vol. 12. No. 72. Dec. 1906. 2 R 



