322 MR. W. DUDDELL ON THE RESISTANCE AND 



between the results obtained. Taking arcs of tbe same lengtb and current between 

 "Apostle," "Brush" and " Carre " carbons, the mean of the value of what Messrs. 

 FRITH and RODGERS called the resistance of the arc is about 0'79 ohm, and this 

 agrees very well with the value of P A I A obtained by extra-polating Curves I. back to 

 about 100 -r- per second. So that this curve explains both the sign and the value of 

 the so-called negative resistance of the solid arc. 



With cored carbons, P A will only be about + - 5 at 100 frequency. The value of 

 P is unknown, but is certainly less than unity, so that the quantity measured by 

 Messrs. FRITH and RODGERS for cored carbons must be less than P A I A . By extra- 

 polation from Curves X., the value of P A I A at 100 frequency for cored " Conradty 

 Noris " carbons is about + 0'5 ohm. Owing to the indefinite nature of cored carbons, 

 this value cannot be expected to agree very well witli those obtained by Messrs. 

 FRITH and RODGERS for carbons of other makers. Taking arcs of the same length, 

 and current as that used in Curves II., the values given by Messrs. FRITH and 

 RODGERS for different makes are: "Apostle," 0'03 ohm; "Brush," 0'59 ohm; 

 " Carre," 0'55 ohm. The two latter values agree with the value 0'5 of P A I A deduced 

 from the curves for " Conradty Noris " carbons to a higher degree of accuracy than 

 might reasonably be expected, whereas the disagreement in the case of " Apostle " 

 carbons, as measured by Messrs. FRITH and RODGERS, seems to indicate that their 

 result is in some way abnormal, possibly due to some accidental impurity in the core. 



The critical frequency of 1 '8 ^ per second observed by MESSRS. FRITH and 

 RoDGERS for the cored arcs, at which the quantity they measured changes sign, 

 evidently corresponds with the power-factor changing sign, so that the curve between 

 power factor and frequency would cut the zero line at a frequency about 1'8 per 

 second, and it is evident that at lower frequencies it would become negative, an 

 increase of current being accompanied by a decrease in P.D. The curves for the 

 cored arc, if they could be obtained down to sufficiently low frequencies, would 

 therefore lie similar to those obtained for the solid arc. The great difference 

 between the solid and cored arcs lies in the much greater quickness with which the 

 conditions of the former can vary, corresponding to any change, however small, in 

 the current through the arc. The relative sluggishness of the cored arc is probably 

 due to the presence in its vapour column of saline matter derived from the core. 



The fact that the solid arc lias a negative power-factor at frequencies below the 

 critical frequency of 1950 - indicates that the arc is under these conditions supplying 

 power to the alternating current circuit, and that this is the fact can easily be shown 

 experimentally by connecting a wattmeter so as to measure the power supplied to 

 the solid arc by the alternating current, when it will be found that at low frequencies 

 the solid arc is actually supplying poiver to the alternate-current circuit, ivhile at 

 frequencies above the critical value the alternate-current circuit supplies power to the 

 arc. This observation is of course not in any way at variance with the principle 

 of conservation of energy, since the alternating energy given out by the arc is 



