384 PROCEEDINGS OF THE AMERICAN ACADEMY. 



cyclic condenser or inductance energy 7905.7/3162.3 — 2.5 joules. 

 The semi -system -energy would also be 2.5 joules. 



Charging Oscillations in a Simple Resistanceless OsciUating-Current 

 Circuit. — If with the system of Figure 1 initially unchanged, we sud- 

 denly impress upon the circuit, assumed resistanceless, between the 

 terminals TT, a. constant potential difference Uq, also assumed resist- 

 anceless, as from a storage battery of large cells, then both the condenser 

 and the inductance will be subjected to charging oscillations. In this 

 case, if the impressed p. d. U^ is the same as that already assumed for 

 the initial p. d. of the discharging condenser, the conditions represented 

 in Figure 5 will apply to the charging oscillations, except in regard to 

 phase, and to the meaning of the zero line 00. The sign of the oscilla- 

 tions will be reversed, or the phase displaced 180°, from those corres- 

 ponding to a p. d. of the direction Ou, Figure 5. That is, an impressed 

 p. d. having the + direction will set up from the start the same system 

 of oscillations as those from the discharge of a condenser impressing 

 a + direction of p. d. on the circuit. The zero line 00 of Figure 5, in 

 regard to p. d. and to condenser energy, instead of representing zero 

 p. d. and zero condenser energy, will also have to be interpreted re- 

 spectively in the charging case, as the constant value of impressed 

 p. d., and the mean energy of the condenser under the impressed p. d. 

 That is, the horizontal line through — 10 will be the zero line of p. d. 

 if the impressed p. d. is 1000 volts tending to make the condenser 

 p. d. positive. 



Simple Oscillating-Current Circuits Containing Resistance. 



When such a circuit as that shown in Figure 1 is allowed to dis- 

 charge through a known total resistance rohms, including both joulean 

 and hertzian resistances (all types that involve dissipation of power in 

 proportion to the square of the current), the first step is to find the 

 resistanceless angular velocity w of Figure 3, that is to determine the 

 angular velocity of discharge on the basis of no resistance (/• = 6). 

 Let this value of resistanceless angular velocity be denoted by w^. We 

 then proceed to determine the angular velocity w in the presence of 

 the actual resistance r. 



Let P = r/2 ohms (13) 



be the semi-resistance of the circuit, and 



T = l/p seconds (14) 



will then be a time-constant, which may, for convenience, be called the 

 oscillation time-constant of the circuit, as distinguished from the ordi- 



