940 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



the electrodes at or near the place where the arc occurred can be calculated 

 from the velocity of the moving electrode at contact and the average sepa- 

 ration of the electrodes when the arc took place. Measurements of this 

 separation have been made earlier J Rough calculation of the local tempera- 

 tures of the electrodes near the point of contact, making use of this average 

 elapsed time, have shown that when contact is made these local tempera- 

 tures are still far above the mean temperatures at the ends of the wires 

 (perhaps higher by 10°C). The local temperatures reach the mean tem- 

 peratures in a time which is very short in comparison with 1/60 second, 

 and thus the conduction of heat from the positive to the negative electrode 

 due to this local high temperature is not corrected for by the extrapolations 

 of the curves of Fig. 2. This correction can be made by obtaining AT meas- 

 urements for different electrode velocities and extrapolating to zero velocity. 

 Such data are plotted in Fig. 3. It is obvious that the curves of the lower 

 half of this figure must become horizontal as they approach zero velocity, 

 but no other theoretical deduction has been made regarding their shapes. 

 The differences between the AT values at the velocities of the data of Fig. 2 

 and at zero velocity are the required corrections, and these are written 

 down on Hne 2 of Table 1. The correction seems to be small (0.001°C), 

 or perhaps zero, for the active electrodes (right-hand side of Fig. 3) but 

 amounting to about d= 0.005°C for the inactive electrodes (left-hand side). 

 That the former should be smaller than the latter is in line with our knowl- 

 edge that an arc between electrodes which are approaching each other will 

 occur when they are farther apart if the electrodes are active than if they 

 are inactive.*^ 



The values of ^Tq after applying the corrections of line 2 of Table I are 

 written down on line 3. On line 3 are given also (columns 2) measured values 

 of Ar for inactive electrodes in a circuit containing an inductance of 10 X 

 10~* h which completely prevented any arcing. On line 4 are values of the 

 energy dissipated upon the electrodes per closure calculated from the ^Tq 

 values of line 3. One must still consider corrections due to radiation and con- 

 vection losses from the surfaces of the wires and radiation loss from the arc 

 itself. These are taken up one at a time in the following paragraphs. 



If the only correction were due to radiation from the surfaces of the warm 

 wires, the heat put into the end of a wire per second w would be related to 

 Aro by the equation 



w = kwATo/L + HAATq/3, (1) 



where k is thermal conductivity, co , L and A are respectively the cross- 

 sectional area, length and surface area of the wire, and H = 4^0 (re, the 



' L. H. Germer, Jl.App. Phys. September 1951, Table I, line 3. (in press) 



