436 PROCEEDINGS OF THE AMERICAN ACADEMY. 



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

 five 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 discharge, 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 A E C he two circuits, the circuit ABC being a shunt 

 to the circuit A E C, which contains a condenser E. 



Let L be the coeflficient of self-induction oi A B C, R its resistance, C 

 the capacity of the condenser in the circuit A E C, and r the resistance of 

 the wires leading to the plates of the condenser. 



Then, if ^ is the current through A B C, and x the charge on the plate 

 nearest to A, 



\- It I ^ r — H . 



dt dtc 



Since each of the quantities is equal to the electromotive force between 



A and C. 



If Z = COSp^ (^^2 + ^2^2 



then X := -/—\ \T sin {p t + a), 



(^^-v)^ 



1 1 -^ P 1 



where a = tan '■ - ^^ + tan '■ 



R ^ rpC 



Hence ^^ = ^/W+^E cos (p t + a), 

 dt 1 



cy ^ 



Thus the maximum current along ^ ^ Cis to that along A B C o,^ 





V'L'p' + R' is to y 772-, + r\ 



c p 



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



1 Tt 



'\/ L-j}^ + R^ : -7- , or, neglecting L, as, -— . 

 Op 1 



G'p 



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



