as Radiators in Wireless Telegraphy, 679 



such a closed circuit also radiates energy, and we can derive 

 a similar formula for the radiation to that given by Hertz 

 for the open circuit. The author has shown that if M is 

 the maximum magnetic moment of such a closed circuit *, 

 viz., the product of its area S and the maximum value of the 

 alternating current (reckoned in electromagnet measure) in 

 it ; and if \ is the wave-length of the radiation emitted by it, 

 and E the radiation in ergs per period, then for the magnetic 

 oscillator we have 



E -^5x^ (9) 



Bat by definition M = AS/10, and if the current is sinoidal 

 a = A/\/2, hence we have 



E = 10'4~. ....... (10) 



Furthermore, if the oscillations are persistent the power in 

 watts W radiated is given by 



W=31,200^ (11) 



The formulae (8) and (11) can be written in the form 



w=4xio- 38 sv^( cio t c irr tic ) 



(12) 



oscillator). 



These last two formulae show us that in the case of the 

 open or electric oscillator the power radiated varies as the 

 square of the current in it, and as the square of the frequency, 

 whereas in the case of the closed or magnetic oscillator it 

 varies as the square of the current but as the fourth power of 

 the frequency. Accordingly, in the case of the magnetic 

 oscillator the radiation is small unless the frequency is very 

 high. 



For the purposes of theory, it is most convenient to consider 

 a closed oscillatory circuit as made up of a series of Hertzian 

 or dumbbell oscillators placed in series with their electric 

 poles of opposite sign overlapping. We can then easily 

 determine the nature of the electric and magnetic field 

 produced by it by the summation of those due to the 

 •elementary oscillators. As the writer has given lately in 

 another place a discussion of the problem and furnished the 

 expressions for the electric and magnetic forces at any point 



* See ' The Electrician,' vol. lix. p. 936 (1907). A series of articles on 

 4 'The Elementary Theory of Electric Oscillators,'' by J. A. Fleming. 



2 Z 2 



