i22 On the Resistance of the Electric Arc. 



Our former methods were not suitable for working with 

 a frequency lower than 7, for at this frequency the needles of 

 the voltmeter and ammeter began to vibrate with the alter- 

 nating current. This vibration of the needles was made use 



dY 

 of in the following way, to indicate the sign of the ^x at 



frequencies lower than 7. The Gramme alternator used in 

 the previous method was run as a rotatory transformer. By 

 adjusting the continuous current passing through this trans- 

 former, and hence its speed, any desired frequency could be 

 obtained down to as low as one complete alternation in 

 2 seconds. By an arrangement of mirrors the needles and 

 scales of both ammeter and voltmeter could be observed 

 simultaneously. In this way it could be seen whether the 

 two needles were at any instant vibrating in the same or in 

 opposite directions. It is evident that if the needles are 

 vibrating in phase, that is if an increase of P.D. is accom- 



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 panied by an increase of current, then — r must be positive ; 



while if they are vibrating out of phase, that is if an increase 

 of P.D. is accompanied by a decrease of current, then it is 

 negative. With this arrangement, solid carbons at any fre- 

 quency gave a negative resistance. With cored carbons, how- 

 ever, we found as we expected, that above a certain frequency 

 the resistance ivas positive, while below this frequency the method 



dV 

 gave a negative value for -j-r. The critical frequency was 



found by observing the point at which the swing of the needles 

 was uncertain, being sometimes in phase and sometimes out 

 of phase. At this point the frequency was 1*8, at 1*9 the 

 sign was certainly positive, and at 1*7 was negative. This 

 result was obtained with all arcs whose resistance as given by 

 our curves was positive (with one exception mentioned below), 

 and was not obtained with any whose resistance was negative. 

 In the case of arcs whose curves cross the zero line, the 

 transition from positive to negative, as shown by the disap- 

 pearance of the critical frequency, was well shown and 

 corresponded with the crossing of the zero line. As an 

 example, we ran an arc with Brush carbons +11 mm. 

 cored — 9 mm. solid at 10 amperes, the curve for which is 

 marked B in fig. 1, PI. V. It will be noticed that this curve 

 crosses the zero line twice, at 55 volts and again at 41*3 



olA. 

 volts : at 60 volts we found the sign of the -^r, as shown 



by the swing of the needles, to be positive at frequencies 



