320 MR. W. DUDDELL ON THE RESISTANCE AND 



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for the relative calibration of the thermo-galvanometer. From these values the 

 impedance of the arc lamp I A = I B , V A /V E , and the power-factor of the arc lamp, 

 P A = (V* - V A 2 - V E 3 )/2V A V U , were calculated. 



In order to obtain from these values the impedance and power-factor of the arc 

 itselj, a small correction had to be applied to I A for the resistance and self-induction 

 of the loop formed by the frame of the lamp and the carbons, and also to P A for the 

 self-induction of R which had previously been determined. To make these small 

 corrections, it was necessary to assume that the alternating current had a sine-wave 

 form, which was approximately the case. 



As a check on the method of experiment and on the calculation and correction of 

 results, the impedance and power-factor of the platinoid resistance, described on p. 317, 

 which had a resistance of 3'499 ohms and a self-induction of about 3 X 10~ 8 henry, 

 were determined, the experiment and calculations being performed in the same manner 

 as for the arc. The values obtained were : impedance 3'50 ohms, power-factor 0'999, 

 which show that the method was satisfactory in this case. 



Results Obtained by Varying the Frequency. 



The fundamental experiment of this investigation into the resistance of the electric 

 arc consists, as has already been explained, in varying the frequency of the super- 

 imposed alternating testing current, in order to determine whether with a sufficiently 

 high frequency the condition of the arc will remain unchanged, the value of the 

 resistance being then measured at this frequency. The criterion that the conditions 

 of the arc remain unchanged has been shown to be that the power-factor of the arc 

 as measured with the superimposed alternating current must be unity. The true 

 resistance will then be equal to the impedance. 



The results of the experiments on the effect of varying the frequency on the power- 

 factor and the impedance for solid and cored* arcs are represented graphically in 

 Curves I. and II. (Plate 2). 



With solid carbons the power-factor at 250 per second is 0'91. On increasing 

 the frequency it decreases numerically until it vanishes and changes sign at 1,950 ~- 

 per second, the waves of superposed alternating P.D. and current being then 90 out 

 of phase. With further increase of frequency the power-factor increases rapidly at 

 first, then more and more slowly, becoming asymptotic to -f- 1, and finally practically 

 attains this value at a frequency of 90,000 -- per second ; above this frequency the 

 power-factor is, within the limits of experimental error, equal to + 1 up to the 

 highest frequency attained, namely, 120,000 -~ per second. The impedance of the 

 solid arc increases with increase of frequency from 0'97 ohm at 250 to 3'8 ohm at 

 a frequency of 90,000 -*- per second, above which it remains practically constant. 



"Solid" and "cored" arc mean respectively arc between two solid carbons and between two cored 

 carbons. 



