1242 THE BELL SYSTEM TECHNICAL JOURNAL SEPTEMBER 1953 



Table II — Ratio rlz for Local Circuitry at Contacts 



Initial Voltage 



r 

 z 



100 

 0.56 



150 

 0.65 



200 

 0.55 



230 

 0.41 



250 

 0.55 



300 

 0.30 



360 

 0.40 



400 

 0.40 



460 

 0.48 



and (3) measurements were made of the terminal voltage across the 

 main condenser at the end of the multiple discharges, from records 

 similar to Fig. 7, which, according to our analysis, is equal to v. For 

 these values of v Equation 6 was used to compute r/z. The results are 

 given in Table II. Each value of r/z in this table is the average of 3 to 

 6 values obtained by the different methods described above. In all cases 

 rjz was between 0.4 and 0.7. This indicates that the local contact cir- 

 cuitry is oscillatory. For our circuit, c was measured at 7.8 X 10~^^ 

 farad and if ^ is assumed to ke 2 X 10~^ henry, the computed resistance 

 r is 20 to 35 ohms. This is about 500 times greater than the dc resistance 

 of the same circuit. With this concept of the local contact circuitry v 

 was well defined and was then possible to perform some checks of the 

 main analytical relations presented in this paper with new measure- 

 ments and with measurements previously published. 



Comparison of Theory with Measurements: 



(1) Voltage drop across main condenser: In Fig. 7(B) is shown the 

 voltage drop across the main circuit condenser as a function of time for 

 L = 10"' henry, C = 1100 X 10"'' farad and Vo = 220 volts. Line (a) 

 was measured and Line (b) was computed using Equation 4(b). The 

 value of V used was obtained from Equation 6. Good agreement is in- 

 dicated. 



(2) Limiting circuit conditions for obtaining a steady arc: It was 

 pointed out in a previous section of this paper that a steady arc can be 

 established only if the maximum current reached during the multiple 

 discharge period is equal to or greater than the arc initiation current. 

 Equations 5(a) and 5(b) are expressions for the limiting circuit induc- 

 tance and the limiting initial voltage respectively. Equation 5(b) was 

 used to compute the hmiting voltage for a set of circuit conditions for 

 which measurements were made and published. Reference 3. In Table 

 IV Column 3 of this reference measured values of the limiting voltage 

 Vo were presented. A comparison of measured and computed Vo are 

 given here as Table III. It may be pointed out that the deviations be- 

 tween measurements and calculations are of the order of the measured 



