308 MR. W. DUDDELL ON THE RESISTANCE AND 



phenomena. Therefore all methods which depend on the steady change 8V in the 

 potential difference V produced by a given steady change SA in the current A, that 

 is to say, which depend on an excursion on the steady curve between V and A, 

 however small it may be, simply measure the difference between the P.D.'s required 

 to maintain an arc with a current A and a distinct and different arc with a current 

 A Jt: SA, which is evidently no measure of either the resistance of the arc with 

 current A or with A ^ SA. 



If the measuring current SA is only applied for a short time 8t, it is necessary that 

 the energy supplied to or removed by it shall be so small as not to appreciably alter 

 the thermal conditions of the very small mass of gaseous and other material which is 

 taking part in the conduction of the current. How extremely short the time that 

 may elapse is will appear later ; for the present it is sufficient to point out that it 

 has been found that even in - 7-5-^0 second a change of 3 per cent, in the arc current 

 has appreciably altered the thermal conditions and the light emitted by the arc.* 



It thus appears that the only available methods of experimentally determining the 

 resistance and E.M.F. of the arc must be based on making the necessary change in 

 the main current, i.e., the measuring current, as small as possible, and on completing 

 the test so soon after making this change that none of the conditions of the arc will 

 have had time to appreciably alter before it is completed. 



The first method tried consisted in sending the oscillatory discharge from a 

 condenser through the arc, and recording by means of an oscillograph the variations 

 in the P.I), between the terminals of the arc and in the current through it. If the 

 frequency of the oscillatory discharge can be made so high that the conditions of the 

 arc are not in any way altered by it, then the wave-forms of the oscillatory part of 

 the P.D. and current will be similar curves and in phase if the arc possesses a true 

 resistance. This was not found to be the case with the oscillations used, which had 

 frequencies up to 5000 -^ per second, the current oscillation always lagging behind 

 the P.D. oscillation. 



At low frequencies and with solid carbon electrodes the oscillations were 180 out 

 of phase, and this difference was gradually reduced with increase in frequency to 

 below 90 at 5000 -r per second, and there were indications that this lag would 

 finally disappear if a much higher frequency were used, so that the conditions of the 

 arc were not altered by the oscillations. 



A largo number of experiments, some of which have been published in a paperf 

 before the Institution of Electrical Engineers, were made to determine the effect of 

 small rapid variations in current on the conditions of the arc itself. The conclusion 

 drawn from the above experiments was that a very much higher frequency than 

 5000 per second was necessary in order that the arc might not be affected by the 

 measuring current. 



* 'Journal of the Institution of Electrical Engineers,' 1901, vol. 30, p. 236. 

 t Ibid. 



