408 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



falls to a final value of— 1000 volts. The other graphs in Figure 11 

 remain unaltered. 



The charging oscillations of a simple circuit containing resistance 

 differ only from the discharging oscillations with the same resistance, 

 in regard to phase direction, and to the absolute numerical values of 

 the condenser potential u, condenser charge q, and condenser energy W^^. 



Condensers and E-eactances in Series. 



If we have a circuit (Figure 16), containing a plurality of condensers, 

 or of reactances, or of both, in simple series, containing also resistances, 

 and subject to charging or discharging oscillations, we may compute 

 the behavior of the system as follows : 



Let / = sum of the individual joulean resistances, (ohms). 

 /' = sum of the individual hertzian resistances, (ohms). 

 r = r' + r" = the sum of all the individual resistances, (ohms). 

 s = si -\- .% + Sz etc., the sum of the individual elastances. (darafs). 

 / = /i + 4 + ^3 etc., the sum of the individual inductances, (henrys). 



Then if we have only 

 charging oscillations to 

 consider, under the ac- 

 tion of a constant im- 

 pressed emf E', inserted 

 between terminal TT, we 

 may replace the multiple 

 element system by the 

 equivalent single ele- 

 ment system of Figure 1 

 with resistance r, elas- 

 tance .% and inductance I. 

 Discharging Oscilla- 

 tions of Condenser in 

 Simple Series Circuit of 

 Multiple Elements. — 

 Let one of the condens- 

 ers, say Si, Figure 16, be 

 initially charged with a 

 quantity (^i coulombs 

 to an initial potential 

 Qi'^i volts, the rest of the system being without charge. Then, 



l4X/(9 



(>XfO' 



Figure 16. Simple series oscillation circuit of 

 composite elements. Inductances in dekahcniys. 



after release, the discharge of condenser Si will charge the other con- 



