374 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



where J = y'— 1, the quadrantal operator. 

 The reactance —j^c of the condenser at the same frequency will be 



. ^ .1 .s 



C(x) 0> 



ohms (2) 



D E 



nmnnnnmnnr) 



where s = 1/c is the elastance of the condenser in darafs.^ 



Discharging and Charging Oscillations. — An oscillatory circuit may 

 be excited into activity either when energy is added to it, or when energy 



is withdrawn from it. In the former 

 case charging oscillations, and in the 

 latter case discharging oscillations are 

 produced. Thus the circuit may be 

 initially devoid of electric or magnetic 

 energy, and a certain constant potential 

 dift'erence of Uq volts, as from a storage 

 battery, may be inserted in the circuit 

 between the terminals TT, Figure 1. 

 The condenser will then be charged 

 by an oscillatory process, or series of 

 charging oscillations. 



Again, the condenser may be initially 

 charged to a potential difference of (Jo 

 volts, and allowed to discharge by short- 

 circuiting the terminals TT. Dis- 

 charging oscillations will then be 

 produced. Or, the condenser may be 

 initially without charge, but the in- 

 ductance DE (Figure 1) may be charged by allowing a steady current 

 of /o amperes to pass through it from some external source. If then 

 the gap TT be closed, and the source of charging current is suddenly 

 withdrawn sparklessly, discharging oscillations will be produced in the 

 circuit. 



Discharging oscillations may even be considered as taking place in an 

 active initially energised circuit, in the limiting case where the circuit 

 is assumed to be resistanceless ; so that energy ceases to be dissipated 

 during the discharge. 



In any of the above cases, the circuit selects the frequency of free 



• Prof. V. KarapetofF seems to have been the first writer to have had the 

 courage to print the useful term daraf as a unit of elastance the reciprocal of 

 2i farad. "The Electric Circuit, " Ithaca, N. Y. 1910, p. 72. See also "Elec- 

 trical Papers," O. Heaviside, 1892, Vol. 2, p. 125. 



TT 



a 



d ^ c tt 



h^wYrznmnnnnr— -1 



0- G 



Figure 1. Diagram of con- 

 nections of simple oscillating- 

 current circuit, and schematic 

 representation of the same. 



