ELECTROMOTIVE FORCES OF THE ELECTRIC ARC. 321 



At frequencies above 90,000 the power-factor is + 1, therefore the excursions of the 

 P.D. and current obey OHM'S law, and the impedance of the arc is equal to its true 

 resistance. So that the true resistance of an arc, 3 millims. long, between 11 millims. 

 solid " Conradty Noris" carbons, and through which a current of 9 '91 amperes is 

 flowing, is 3*81 ohms. 



The P.D. between the terminals of the arc, accounted for by ohmic drop in the arc, 

 is therefore 37 '8 volts out of an observed P.D. arc of 49 '8 volts, so that there appears 

 to be a red back electromotive force opposing the flow of the currents in this arc of 

 12 volts. 



Considering next Curve II. for both cored carbons, the power-factor at the lowest 

 frequency of 250 per second has a positive value of + O'f>7 and increases 

 asymptotically, as in the case of solid carbons, until it is practically +1 at a 

 frequency of 15,000, and remains unity within the limits of experimental errors up to 

 the highest frequency tried of 50,000 -^ per second, the impedance becoming 

 practically constant, as with solid carbons. 



Therefore tlie, true resistance of fin arc 3 millims. !</>/,</, bet tree it I 1 mil limn, cored 

 " Conradty Noris" carbons, and t/ir.nif/li tchic/i, a current of 10 amperes is flowing, is 

 2'54 ohms, and the back E.M.F. is IG'i) volts, calculated in the same way as for solid 

 carbons. 



Finally, therefore, arcs between either solid or cored carbons have both back 

 E.M.F. and resistance, and the true values of these quantities differ greatly from 

 those usually assigned to them. 



In order to test whether the II. M.S. value of the added alternating current affected 

 the values obtained for the impedance and power-factor, the testing current was 

 varied over the range 0*030 ampere to 0*130 ampere, and the impedance and power- 

 factor were found to be constant within the limits of experimental error. 



It is of interest to enquire how the results obtained by Messrs. FRITH and RoDGERS 

 can be explained by the aid of these curves. The quantity that they measured and 

 called the resistance of the arc was really the impedance of the arc and a certain 

 resistance together, less the impedance of the resistance part alone. From fig. 2, 

 p. 311, using the same notation as before and assuming II non-inductive, 



PVC = V B C + P A V A C, or PV/C = U + P.J A . 



The quantity measured by Messrs. FRITH and RODGKRS was V/C II. 



In the case of solid carbons at their frequencies, about 100 ^ per second, P A is 

 roughly 1, and a little consideration shows that under these conditions P was 

 practically + 1, so that the quantity they called the resistance of the solid arc was 

 P A I A , or the product of the power-factor into the impedance of the arc, which is 

 evidently a negative quantity for frequencies under 1950 per second with the 

 solid arc investigated in Curves I. As they did not use the same make or size of 

 carbons as those used in this paper, it is impossible to make an accurate comparison 



VOL. cm. A. 2 T 



