Electromagnetic Waves round the Earth. 377 



R ohms (including radiation resistance), a current I 2 will be 

 set up in it of the approximate amount (Ruedenberg) 



l 2= lu (14a) 



The reradiated energy is here accounted for by including in 

 R 2 the radiation resistance of the receiving system. 



The ratio of the current amplitudes or R.M.S. currents in 

 the receiver to the same quantity in the transmitting antenna 

 (all quantities relating to the transmitter have suffix 1 and 

 to the receiver suffix 2) is therefore 



I2 _ 300 v 2ir x j \ <x l h l ct 2 h 2 -(3xie 



i\~ 20tt p lX / s inea"~W~ e 

 or, when the earth's circumference is taken as 40,000 kilo- 

 metres, this reduces to 



23-94 



where all lengths are in kilometres, I 2 and I x are expressed 

 in the same units, R 2 is in ohms and 6 in radians. 



If the linear distance d in kilometres is introduced be- 

 tween the transmitter and receiver, measured along the great 

 circle, the last factor occurring in (15) can also be written 

 - Q-Q0376d 

 xi ' 



This formula gives the ratio of the received antenna current 

 to sender antenna current under the assumption of a perfectly 

 insulating atmosphere and a perfectly conducting earth. 



A similar formula for the case of a plane is 



I2 _Q 7 - « 1 /t 1 . <L.Jl 2 



where d is the linear distance between the oscillator and 

 resonator. Formula (15), in which only the first term of 

 the series in (8) is employed, is valid over the whole sphere 

 with the exception ot 1, a zone near the sender such that 

 d< 140 \/\ (otherwise more terms of the series in (8) have 

 to be employed) ; and 2, with the exception of a zone near 

 the sender's antipodes where diffraction zones occur, as 

 explained above. 



A comparison of formula (15) with experimental obser- 

 vations must now decide whether actual wireless trans- 

 mission is established by diffraction only, the atmosphere 

 being assumed to be a perfect insulator. 



