KENNELLY. — OSCILLATING-CURRENT CIRCUITS. 407 



charging condenser and the other, like Figure 15, for the discharging 

 reactance. These two vector-diagrams are now to be combined vector- 

 ially, into a new resultant vector-diagram, which will represent the 

 behavior of the mixed discharge. Since each of the component dia- 

 grams obeys the geometry of Figures 7 and 12, the resultant diagram 

 will also obey it. The rotative vector-diagrams i/, /, P, and W will 

 also follow, but the W diagram of Figure 13 will be ambiguous, except 

 in regard to the dissipated energy. 



It is evident, moreover, that since the energy of a simple resistance- 

 reactance-condensance oscillator exchanges harmonically from the elec- 

 tric to the magnetic form, after correcting for dissipation, any initial 

 state of assigned separate electric and magnetic energies must corres- 

 pond to some phase of a discharge from a certain single stock of energy, 

 electric or magnetic. 



Charging Oscillations of Circuit Containing Resistance. — If in the 

 circuit of Figure 1, assumed to possess resistance, and with no initial 

 charge, we insert a constant charging p. d. between the terminals t, t, 

 in such a direction as will cause a subsequent discharge to flow in the 

 positive sense of the arrow d e ; then both the charging emf and the 

 initial direction of the charging current must be reckoned negative, or 

 in the sense e, d. The charging vector-diagram will then be the same 

 as that of Figure 8, with a phase difference of 180**, or read upside 

 down. The stationary vector-diagrams of Figures 7 and 12 apply as 

 before, as well as the rotative vector-diagrams of Figures 13 and 14. 

 In the last-named, however, the condenser energy Oc must be counted 

 from c to 0, or in the reversed direction, since the energy in the con- 

 denser is initially nil and increases to its final full value. 



We may consider that Figure 8 is the vector-diagram of a charging 

 condenser system in which the constant impressed emf. between the 

 terminals t t (Figure 1) is positive, or in the direction of the arrow d e. 

 If as before c = 4 X 10~® farad ; r = 200 ohms ; / = 0.1 henry and 

 B = 1000 volts, we first find w^ = 1581.14 radians per second as in 

 Figure 3, then the angle ^, and m = 1581.14 \50" 46', as in Figure 7. 



We then lay off OU^^E= 1000 volts in Figure 8 and OTl^= OU. 



cosec ^\- — (^ = 1291 \39" 14' volts. This is the vector charging p. d. 



The vector current follows from Figure 7 as 8.165 amperes, and the 

 vector emf. of self-induction symmetrical with Of/p in regard to the 

 current. The graphs of Figures 10 and 11 then apply as before, except 

 that in Figure 1 1 the p. d. must be read from the top line as zero, since 

 the potential of the condenser at d, Figure 1, commences at zero and 



