Oscillatory Discharges. 641 



amount of electricity which could not be discharged by the 

 spark itself, was found to be constantly negligible, i. e. 

 always inferior to the hundredth part of the initial charge. 



Disposable Energy and its Distribution in the 

 Circuit of Discharge. 



42. The work done in imparting the potential V to the con- 

 denser of capacity C would represent the energy effectively 

 disposable, and should accordingly be found again in the 

 discharge, but for the part dissipated in the dielectric, outside 

 of the metallic circuit and the spark. 



This dissipation of energy may reach sensible values in 

 condensers with solid dielectric, and, as a matter of fact, there 

 exists no reliable method of calculating it. In fact the methods 

 used for ordinary alternating currents of industrial machines 

 cannot be applied to the present case, and WulFs * method, 

 based upon the determination of the damping-coefficient 

 of the amplitude of oscillations, as derived from the residual- 

 charge curves, and of the theoretical decrement, as calculated 

 from the potential-differences corresponding to two successive 

 maxima, does not give results of sufficient accuracy. But 

 with our researches this inconvenience was reduced to a 

 minimum by the use of air- condensers, or at the least was 

 certainly of an order of magnitude inferior to the unavoidable 

 errors of the calorimetrical measurements. 



Another portion of energy, not found again in the circuit 

 either, is that radiated by electromagnetic waves. 



The theory of oscillatory discharge allows of this part of the 

 energy being calculated, as it affords a means of comparing 

 the intensity i of the current traversing the wires of the 

 discharge-circuit — supposed parallel and at the distance d 

 from one another — with the intensity i' observed in the 

 air-cylinder, having one of the wires as axis and half of the 

 distance d between the two wires as radius of the bases. The 

 ratio between i and i' (see Drude, Fhysik d. Aethers, p. 369) 

 is given by 



i/_ _ U 2 

 i ~T 2 c 2 ' 



These calculations cannot, it is true, be applied to our 

 experimental arrangements ; but it may still be observed 

 that they may give account of the order of magnitude of the 

 portion of energy dissipated. If, for instance, it be observed 

 that in the experiments performed by us the value of Tc, 

 that is the wave-length, is always superior to 600 m.: and 



* Wien. Ber. cv. II a, p. 6(57 (1890). 



