KENNELLY. 



OSCILLATING-CURRENT CIRCUITS. 



411 



or hyperbolic angular velocity O of the currents in the circuit.* In 

 the case of a circuit resistance r = 500 ohms, the hyperbolic angular 

 velocity will be ii = 1936.492 hyperbolic radians per second, as shown 

 at OPQ, Figure 17. 



Analytically, O = V-^"^ — Wq"^ hyp. radians/sec. (76) 



and the h3T)erbolic period T of the current and p. d. is 2 tt/O seconds. 



^V 



t 

 ^^-/ 





J, =. /y. StcoruU'* P 

 C)xboTi,aT\.tta.L Ttm.e ■Foxto*' 



> y . c 







^yO xroiti 

 Jyidiat Dtstipcdm ED. 



Figure 17. Stationary vector-diagrams of hyperbolic angular velocity, 

 impedance, and discharging jjotential difference in a simple non-oscillating 

 condenser circuit with ultraperiodic resistance. 



Similarly, the .^-triangle of Figure 17 has a base AB = p = r/2 = 

 250 ohms, and a side ylC equal to the resistanceless oscillatory im- 

 pedance Vis = 158.1138 ohms, as in Figures 4 and 12. The remaining 

 side CB opposite to the angle i/' and perpendicular to A C, represents 

 the non-oscillatory or hyperbolic reactance 193.6492 ohms Operating 

 upon the Z triangle by multiplication with 5.164 amperes, the initial 

 vector-current, we obtain the T/ triangle DEF, Figure 17. 



* For the first publication of the conception of hyperbolic angular velocity 

 of discharges in ultraperiodic circuits, we are indebted to Dr. Alexander 

 INIacfarlane. See appended Bibliography. 



