KENNELLY. — OSCILLATING-CURRENT CIRCUITS. 409 



denser oppositely, in such a manner as to check the oscillation. The 

 oscillations will take place about a condition of voltage equilibrium, 

 such that the emf. of the discharging condenser is equal and opposite 

 to the sum of the emfs. in the other condensers. If the quantity nec- 

 essary to flow through the circuit in order to attain the condition of 

 emf. equilibrium is </<. coulombs, then 



(^0 — <le) Si = qe {^2 + ^a), volts (71) 



or qe = Qo . ^^ ■ — = ^0 -• coulombs (72) 



^'i -f- S2 -r Ss s 



This is the oscillatory part of the charge in Si. The remainder would 

 reside permanently in the condensers, if there were no dielectric 

 leakage. 



Since the passage of qe coulombs attains the point of equilibrium 

 about which oscillation takes place, the first swing, neglecting damping, 

 carries 2 qe coulombs through the circuit. 



Of the initial stock of energy Wq = Qo\/2 joules, the portion sub- 

 ject to oscillation is, neglecting damping, 



This portion is alternately electric and magnetic energy. The re- 

 mainder persists in the electric form, disregarding leakage. 



If the impressed voltage E', instead of being applied initially to the 

 component condenser Si, were appHed initially to the equivalent resul- 

 tant condenser s of Figure 1, whose elastance is the sum of the com- 

 ponent elastances, the charge taken by s would be 



Qo = Qo -} coulombs (74) 



and the energy of the charge would be 



w'o= ^^"07 joules (75) 



But we have seen that these are precisely the amounts of oscillation- 

 charge and oscillation-energy available in the case of the charged 

 component condenser. Hence we obtain the following rule for the 



