CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 297 



where 



2X1 Ci 



^"^ ^ = 2zr(7x 



Qo is the initial charge in the primary condenser Ci, and Li and Bi are 

 the inductance and resistance in the primary circuit. The curve, 

 which represents this equation, is, as is well known, a rise and fall of 

 current with respect to time, and is aperiodic or oscillatory according 

 as Ei^ is greater or less than AL-i/Ci. The critical resistance above 

 which the discharge is non-oscillatory is, for the circuits which were 

 used in this investigation, of the magnitude of 100 ohms. As will be 

 seen later, the average resistance of the gap is so low compared to this 

 quantity that the existence of no inverse current cannot be attributed 

 solely to the aperiodic nature of a discharge through a high resistance. 

 Moreover, if the average resistance were high enough to cause the dis- 

 charge to be aperiodic, the end of the discharge would be asymtotic to 

 the time axis. 



The resistance of the gap very rapidly drops from a very high value 

 at the start to a low value. Since the resistance is a function of the 

 current, and very probably a function of the time of which we have no 

 knowledge, it is impossible to derive any exact mathematical expres- 

 sion for the current curve. A consideration of the physical aspects 

 will, however, reveal to some extent the reasons for the shape shown. 

 If, in the differential equation for the primary circuit. 



di 

 the term ^i is suddenly decreased, it is evident that the term Lx -~ 



at 



will prevent at first a rapid change in current. This, in part, ex- 

 plains the slow rise of current as shown by the first part of the primary 

 wave form. As the discharge progresses the resistance becomes lower, 

 and the current increases, following more closely one of the expo- 

 nential discharge curves of low resistance. For reasons previously 

 given, the discharge stops as soon as the current becomes zero. 



(3) Ths Resistance of the Gap. 



It is interesting, by assuming an approximate expression for the 

 primary wave form, to calculate the change in resistance of the gap 



