376 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



t = from the position shown, to rotate positively in the plane U^IqEq 

 with the angular velocity w, as determined by formula (5). At any 

 time t seconds after the release of the discharge, the orthogonal pro- 

 jections on XOX of the three vectors OUo, OIq, and OE^^ will represent 

 the corresponding instantaneous values of the discharging p. d. at con- 

 denser terminals, the current strength, and the emf. of self-induction 

 in the coil. The vector discharging current therefore rotates in quadra- 



FiGURE 2. Rotative vector-diagram of simple resistanceless oscillating- 

 current circuit. 



ture between the two opposed and equal electromotive forces of dis- 

 charge and of self-induction, developing with them reactive power and 

 cyclic energy ; but with no dissipated energy, under the assumption of 

 negligible resistance. 



Figure 3 presents a series of stationary vectors ; w, Y, I, P, W. 

 The vector w is drawn in the —j direction, and with a length w = l/^/Vl 

 =■ \^s/l radians-per-second, according to formula (5). If we take, as 

 an example, a condenser of c = 4 microfarads {s = 0.25 megadarat), 

 charged to an initial p. d. of U^ = 1000 volts, and discharged through 

 a resistanceless inductance of ^=0.1 henry, we find w= 1581.14 

 radians per second, corresponding to a frequency of » = 251.646 cycles 

 per second, and a complete period of T = 0.003,974 second. 



Starting from the initial position of Figure 2, the subsequent position 

 of any vector in the system, after the lapse of t seconds, is determined 

 by multiplying the vector by 



€-{-M) — ^M — g-'v'S ~ £yi581.14<_ 



numeric Z (7) 



