HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 939 



circles are to be attributed to differences between the electrodes, probably 

 in the effective mean diameter. For observations in the active condition 

 the solid circles of Fig. 2 are consistently higher than the open circles, but 

 the opposite is true for measurements upon inactive surfaces. This reversal 

 is not significant; it was brought about by an accident which necessitated 

 rewelding the thermocouple to the moving electrode after the measure- 

 ments upon the active surfaces had been completed and before the measure- 

 ments upon the inactive surfaces. In earlier preliminary tests there was no 

 difference of this sort; one must conclude that the welding operation altered 

 the moving electrode. (In the case of the plots at the left of Fig. 3 below, 

 some of the data were taken before the rewelding operation and some after.) 



The continuous curves drawn on the lower half of Fig. 2 have the ordi- 

 nates Wex/B for the positive electrode and W(l — €x)/B for the negative, 

 where W is the total energy per closure represented by the horizontal lines 

 at the top of the figure and €x is the fraction of the energy flowing down the 

 positive electrode. (0.5 < e^ < 1). The energy lost by the positive to the 

 negative electrode by conduction per closure is clearly (co — ex)W. The 

 temperature difference between the wires near the point of contact is (W/B) 

 (2ex — 1) and, from analogy with the electrical formula for the spreading 

 resistance of a circular contact of diameter /, the heat flow from one elec- 

 trode to the other per second is found by multiplying this temperature 

 difference by Ikx and the heat flow per closure by further dividing by 60. 

 Equating the two expressions for heat flow one obtains ex = (60 Bea + Ikx)/ 

 (60 B + 2lkx). The curves drawn on Fig. 2 have shapes determined by this 

 expression with the two parameters €o and / chosen to fit the experimental 

 points. The resulting values of €o and / are: €o = 0.58, / = 11 X 10~^ cm 

 for the inactive electrodes and €o = 0.57, / = 3.3 X 10""* cm for the active 

 electrodes. 



If the area of contact were truly circular and the contacting electrodes 

 were crossed cy finders of perfect cross-section, these values of / would be 

 simply related by elastic theory to the forces F holding the electrodes 

 together when they are in contact. The formula^ is / = [6FD(1 — 'i^)/E]^ 

 where D is the diameter of the wires, E is Young's modulus for platinum 

 and V is Poisson's ratio. If we take^ E = 13 X 10^ gm/cm^, the above values 

 of / correspond respectively to forces of 5 and 0.1 grams weight. No signifi- 

 cance can, of course, be attached to these values of force other than to ob- 

 serve that they are not wildly unreasonable. 



The average lapse of time between the end of each arc and contact of 



5 A. E. H. Love, "The Mathematical Theory of Elasticity," Cambridge, fourth edition, 

 1927, page 197, equation 56. 



« R. Holm, "Electric Contacts," Hugo Gebers, Stockholm, 1946, p. 389. 



