Dr. 0. Lodge on Electric Radiation. 57 



of energy by radiation is often but a small fraction of that 

 turned into heat by the frictional resistance of the circuit. 

 The expression for the radiating power may be compared 



V 2 

 either with the form -|SV 2 or with the form ^- > an ^ the loss 



of energy may be said to be like a static capacity of 

 30 earth quadrants 5556 microfarads 



6 ( log ?T ' ( lo *4T 



charged to the potential Y, being discharged once a second ; 

 or like the heat produced per second in a resistance of 



360 



/ 4/\ 2 



( ^°£ 1 ) omns > navm g a difference of potential V be- 

 tween its ends. The duration of the discharge must there- 

 fore be exactly comparable to the time a wire of this resistance 

 would take to equalize the potential of the oscillator-ends 

 initially charged to the same difference of potential. 



For the small oscillator used in the optical experiments 



41. 

 here recorded, the value of log y is approximately 4\ ; hence 



the equivalent resistance is 7250 ohms. And, since the 

 initial difference of potential is, say, 26,400 volts, the power 

 of the initial radiation is 96,000 watts or 128 horse-power. 



At this rate the whole original stock of energy (5400 ergs) 

 would be gone in the two-hundred millionth of a second, i. e. 

 in the time of 1\ vibration ; but of course the energy really 

 decays logarithmically. The difference of potential at any 

 instant being given by 



-V^ff' that 1S , V = V . *s, 



where R is the above 7250 ohms plus the resistance of the 

 spark and of the oscillator itself to these currents. The 

 resistance of the spark is probably but a dozen, or perhaps a 

 hundred, ohms; that of the small oscillator is about \/ ' (Ir) 

 ohms, where r is its ordinary resistance to steady currents 

 expressed in ohms, and I is its length in centimetres. This, 

 therefore, is utterly negligible ; practically the whole of its 

 energy goes in radiation. For the big oscillator the resist- 

 ance is about \/(-3o^) ; and so for a linear oscillator in 

 general the dissipation resistance may be considered as simply 



H = 360 (logj) 2 ohms. 



