of a large Accumulator. 195 



was evidently necessary to blow out the flaming discharge in 

 order to see if oscillations followed the pilot discharge. The 

 first experiment was made with 2500 cells arranged in series ; 

 and the flaming discharge was much lessened both by the 

 reduction in the number of cells and by a suitable arrangement 

 for blowing it out. On developing the photographs it was 

 found that the discharge was an oscillatory one ; for as many 

 as Hve or six clearly defined oscillations followed the first, or 

 pilot discharge. The number of cells was then doubled ; and, 

 although more difficulty was experienced with the flaming dis- 

 charge, oscillations were again obtained. 



On the supposition that each cell of the battery can be 

 regarded as a leaking condenser ; and that it is equivalent in 

 capacity to a condenser shunted by a resistance equal to that 

 of the electrolyte, we can treat such a cell as a conducting 

 condenser under the influence, during discharge, of a periodic 

 current. The analysis of this well-known case is as follows.* 

 Let ABC and AEC be two circuits, the circuit ABC being 

 a shunt to the circuit AEC, which contains a condenser E. 



Let L be the coefficient of self-induction of ABC, R its 

 resistance, C the capacity of the condenser in the circuit 

 AEC and r the resistance of the wires leading to the plates of 

 the condenser. 



Then if i is the current through ABC and x the charge on 

 the plate nearest to A 



- + R^ = r -j- + -. 



at at c 



Since each of the quantities is equal to the electromotive force 

 between A and C. 



If ^ = COS pt, /ja 9 + R axi 



then x— y. r-j sin (pt + a) 



(it*?). 1 



whei*e a = tan * -^ + tan 1 — rv 

 K rpC 



dx VLyTlr . , ^ ; 



Hence -j- — —f- cos (pt + a). 



at i o 



4- r 



c v 



Thus the maximum current along AEC is to that along 

 ABC as 



VLV + R 2 is to f | s 



+ r\ 

 "P 

 Or if we neglect the resistance r of the leading wires, as 



VLy + R 2 : 7t-j or neglecting L, as — -. 



* See Elements of Electricity and Magnetism, Prof. J. J. Thomson, p. 431. 



