﻿Radiation from Bent Antenna?. 599 



of which was 1/5 metres and the horizontal part 60 metres 

 long. In other words, his ratio of horizontal to vertical was 

 as much as 40 : 1, and the greatest ratio in my experiments 

 was only 19 : 1. This entirely confirms Mr. Marconi's 

 remark, loc. cit. that " in order that the effects should be 

 well marked it is necessary that the length of the horizontal 

 conductors should be great in proportion to their height 

 above the ground/'' This is only another way of saying that 

 the magnetic moment of the oscillator must not be small 

 compared with the electric moment. This is achieved by 

 making the length of the horizontal portion of the antenna 

 large compared with that of the vertical portion. 



One point of great interest in the family of polar curves 

 above mentioned is that the minimum radius always lies near 

 to 105°, reckoned from a zero opposite to the direction in 

 which the free end of the antenna points. In the mathe- 

 matical theory given by the writer (Proc. Roy. Soc. vol.lxxviii. 

 p. 7, 1906) it is shown that for a doubly bent insulated 

 antenna azimuthal angle (6) of minimum force is given by 

 the expression 



COS0=-^y- . — , 



where (f> is the electric moment of the oscillator, M the 

 magnetic moment, v the velocity of radiation, m = Ztt/X, and 

 r is the distance between radiator and receiver. 



Now cf> = Q 8: a n d M == IBy S~ = Qn &y Sz, 



where Q is the maximum end charge of the oscillator and 



n^lTr/T. 



But v = n[m. Hence we have 



2£r=s 



M ~ m8y ' 



and 'A— - ^ — ^ — 



m~r 8y 2ir-r Sy ~ '20 r ' 8y ' 



Mr. Macdonald has shown (see 'Electric Waves') that in 

 the case of a linear oscillator the emitted wave-length is 

 2*5 times the total length. Hence for our case 



X = 2'5(2fy + &r) = 7*5fy. 



Therefore we have for the bent oscillator with three equal 

 branches 



cos#= s - =0'375\/V. 

 o r 



2R 2 



