406 PROCEEDINGS OF THE AMERICAN ACADEMY. 



discharge for r = and then determine w by the stationary vector- 

 diagram of Figure 7, taking the full resistance r into account. 



Upon the axis —XOX of reference, Figure 15, lay off the initial 

 value O/q of the current in the reactance, at the instant of release, 

 assumed in this case to be 6.3246 amperes. The initial energy in the 

 reactance will be ll^l'l = 2 joules. Lay off an angle XOl^ = 90o — i>, 

 and a vector initial current Iq = I^ cosec ^ = 8.165 amperes. All of 

 the diagrams in Figures 7 and 12 now apply. The 6^ diagram gives 

 us the initial position of the condenser p. d. vector OU^, = 1291 

 volts. The projection of this on —XOX is 0U^ = 0, corresponding 

 to the uncharged condition of the condenser. OE^ is the initial posi- 

 tion of the vector inductive emf. in the reactance, and the initial self- 

 inductance emf in the circuit is OE^ = 1264.9 volts propelling the 

 discharging current. The initial Ir drop in the circuit coincides in 

 phase with /q, and taken negatively, extends to Olt^ = 1633 volts. 

 The projection of this on —XOX g\we^ an initial Ir emf in the circuit 

 of 1264.9 volts just equilibrating the emf. of self-induction. The 

 entire vector system is to be considered as starting to rotate at angular 

 velocity w. If the diagram is to include the effects of damping, then 

 each vector must rotate in an equiangular spiral of angle ^ as indi- 

 cated in Figure 8. But if we apply independent damping factors, the 

 vectors in Figure 15 may rotate in circles as undamped quantities. 



It will be seen that Figure 15 corresponds to Figure 8 except that it is 

 advanced tt — c/) in phase. Thus a given energy charge discharged from 

 the condenser, in this case 2 joules, with an initially uncharged reac- 

 tance, will give rise to precisely the same rotative vector-diagram as the 

 same energy discharged from the reactance, except in regard to the 

 phase of the diagram. The rotative diagrams of U, I, P, and W will 

 also be the same in either case ; except that in the rotating and rolling 

 vector-diagram Figure 14, N3I and NC interchange in significance, 

 NM being the reactance-energy vector in one case and the condenser- 

 energy vector in the other. 



Simultaneous Discharghig Oscillations from Condenser and Reac- 

 tance. — It is possible for a circuit like that of Figure 1, containing 

 resistance, inductance, and capacity in simple series, to be released 

 with an electric charge in the condenser, and an independent magnetic 

 charge in the coil. The discharge which follows is then in part a con- 

 denser discharge, and in part a reactance discharge. If we know the 

 initial charges, we can obtain the vector-diagram of the discharge by 

 determining the w-diagram of the system (Figure 7) and then making 

 two separate rotative vector-diagrams, one, like Figure 8, for the dis- 



