942 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



open electrodes when the arc is over and ?' = 15 (for platinum)^"' is the arc 

 voltage assumed to be strictly constant during the life of each arc which is 

 very closely true. The energy left in the circuit after an arc is over is CVl/2. 

 The total energy dissipated in the circuit is C[Vl/2 - (Fo - Vi)v - Vl/2] 

 during the arc, plus CVi/2 afterwards. When closure occurs without an 

 arc (conditions 2) the total initial energy CVo/2 is dissipated in the cir- 

 cuit. Some of the circuit energy appears in the electrode wires and is meas- 

 ured, as shown by the numbers of lines 7 and 8 of columns 2. It can probably 

 be safely assumed that the fraction of the circuit energy which appears in 

 the electrode wires is the same whether or not there is an arc. With this 

 assumption, and knowledge of Vi and v, we can use the data of columns 2 

 and 3 to calculate two parameters, 77, the fraction of the circuit energy 

 which appears in the electrode wires, and 6, the fraction of the arc energy 

 which is dissipated upon the positive electrode for the active condition. 

 The data of columns 1 are not to be used with those of columns 2 and 3 

 because of a different electrical circuit and in consequence a different (and 

 no doubt larger) value of rj. 



Quantities of interest are defined here: 

 total energy eo = CVJ2 

 arc energy ea = C{Vo — Vi)v 

 energy which is measured | arc, Ca + 17(^0 — ^a) 



(true value) | no arc, r}eo 



factor by which all energy measurements are in 

 error (i.e., experimental error) ^ 



fraction of arc energy at positive electrode 6 

 values obtained | arc, positive electrode, w+ 

 by measurement | arc, negative electrode, w_ 

 I no arc, total energy, wq 

 From the way these definitions have been given it is clear that 



Wo = ^eo 



w+ = ^UaO + (eo — ea)r//2] 

 These equations yield 



^ = \(w+-\- W-)eo — (eo — e^w^jeoCa 

 rj = 'Woea/{{w+ + W-)eo — (eo — ea)wo] 

 = [2w+ - (eo - ea)^]/2^ea. 



The known numerical values of C, Fo, Vi and v give, in ergs, eo = 80, Ca = 

 67.5, circuit energy dissipated during an arc = 11.25, circuit energy dis- 



" Reference 1, Table II, page 957. 



