56 Dr. 0. Lodge on Electric Radiation, 



He omits the dielectric constant K, because lie supposes Q 

 expressed in electrostatic units, but it is better to make ex- 

 pressions independent of arbitrary conventions. 



So the loss of energy per second, being jt- times the above, 



is 



167rXQl) 2 v 

 3KA, 4 ; 



and this therefore is the radiation power. 



For a given electric moment, Q/, the radiation intensity 

 varies therefore as the fourth power of the frequency, i. e. 

 inversely as the fourth power of the linear dimensions of the 

 oscillator, as Fitzgerald some time ago pointed out. 



But inasmuch as different oscillators will not naturally be 

 charged to the same electric moment, but will rather be 

 charged to something like the same initial difference of 

 potential, as fixed by the sparking interval between their 

 knobs, it will be better to write Q = SV, and to insert the 

 full expression for X. 



Doing so, we get for the radiation activity at any instant 

 when the maximum difference of potentials at the terminals 

 isV, 



7T 4 S 2 Y 2 / 2 V V 2 



H: 



3tt 4 KS 2 LV - 

 Y*Kv 



sK^iog^y 2 



/ 4/\2 / 4/ \ 2 ' 



12 (log |) 12^(!og|) 



an expression roughly almost independent of the size of the 

 oscillator. Quite independent of it if the length and thick- 

 ness of its rod portion are increased proportionately. 



(The factor fiv may always be interpreted as 30 ohms 

 whenever convenient.) 



Thus all oscillators, large and small, started at the same 

 potential, radiate energy at approximately the same rate ; 

 short stout ones a little the fastest. 



But the initial energy of small oscillators being small, of 

 course a much greater proportional effect is produced in 

 them, and the radiation ceases almost instantaneously, their 

 energy being dissipated in a very few vibrations. On the 

 other hand, oscillators of considerable capacity keep on much 

 longer ; and with very large ends, as in Leyden jars, the loss 



