Oscillatory .Discharges. 635 



that evolved in the metallic part of the circuit. According 

 to his experiments — as Orgler * had found by a different 

 method — the resistance R of the spark should be represented, 

 in terms of its length I, by the relation 



R = AZ + B, 



A and B being constants. But the variations of the resist- 

 ance with the period of oscillation cannot be deduced from 

 Oardani's experiments. This goes to show that the experiments 

 so far performed, as above stated, fail to give the complete 

 solution of the problem. But, on the other hand, it may be 

 maintained that, in order to take account of the spark, one 

 would have to write the equation for the movement of the 

 electricity under the form 



Q clQ 7 _. AZQV 7 T dQ d*Q 7 7 - . 



differing from the one applying to the discharge in a wholly 

 metallic circuit by the term ivdt, representing the work 

 accomplished in the production of the spark. If iv could be 

 regarded as constant, the action of the spark would be per- 

 fectly equivalent to that of a resistance, and to would have to 



be comprised in the coefficient of ( — - ) dt. In that case the 



solution of (a) would differ from that of Thomson's equation 

 only by the different value of R, which then would represent 

 the combined resistance of the metallic circuit and the spark. 

 But the processes occurring in the spark are very complex, 

 and their nature is not known with certainty. 



One might maintain with Heydweiller f that the variation 

 of the resistance of the spark, after being rapid at the 

 beginning of the discharge, would proceed slowly, so that for 

 great resistances of the circuit after a relatively short 

 time a constant " regime " would be set up. But if this were 

 true, w would be such a function of t and R that (a) would 

 not be integrable ; hence this hypothesis cannot be tested by 

 experiment. 



It thus only remained to submit to new measurements 

 the resistance the spark offers under various conditions ; these 

 we made with our apparatus, the arrangement of which 

 enabled the total energy spent in the spark to be measured. 

 and to be compared with that spent at the same time in 

 tne metallic part, whose resistance R't, for oscillations of 



* Drude's Ann. i. p. 159 (1900). 

 f Wied. Ann. xliii. p. 310 (1891). 



