770 Sir Oliver Lodge on the Transmission 



result is that the loss o£ energy per half swing is 



SttVZ 2 

 3K\ 3 



and the loss per second therefore 



\~tT ) •(^) 2 'Tpr = energy radiated per second 



by an electric radiator of moment el. It is easy to get this 

 by integrating the flow of energy per unit area, EH/47T, all 

 over the surface of a large sphere. 



For a magnetic or closed circuit radiator, of moment fin AC, 

 a similar expression can be written with vjfi instead of v/K. 



This may be thrown into various convenient forms (see 

 Lodge and Howard, Phil. Mag. July 1889), and the form I 

 prefer in practice is in terms of the mean square of current 

 supplied to the aerial : 



Radiation Power . . ,„/ height \2 



in kilowatts =4 ( am P ere8 > 2 ( wave-length ) ' " < o) 



because the current in an aerial can be measured with an 

 ammeter — if necessary a sensitive^hot-wire instrument heavily 

 shunted, — and the radiation power can thus be calculated. 

 Another way of measuring the current would involve the 

 use of a flowing-water calorimeter; which I propose to try 

 for this purpose. 



The main uncertainty about the data is an estimate of the 

 effective height of the upper capacity area which shall pro- 

 perly enter as a factor into the aerial's electric moment el ; 

 unless indeed there is also a lower capacity area thoroughly 

 insulated from the ground: for the effective height must 

 partly depend on the perfection or imperfection of the earth- 

 connexion and the quality of the soil. If the earth were a 

 perfect conductor the effective height would be twice the 

 apparent height. In practice there is generally some inter- 

 mediate value characteristic of the circumstances of the 

 station. 



To establish the above very handy expression for the 

 energy actually radiated per second, proceed thus : — 



The magnetic field close to a linear Hertz oscillator is 



tt e l n ■ n 



J± = — ^-cosn^sm u; 

 r* 



which corresponds to an oscillating current of strength 

 en cos nt and length I. 



