Resistance of the Electric Arc. 421 



except for short arc-lengths indicated a negative resistance *, 



we find that with both carbons cored the resistance is always 



positive. With a view to elucidating this point, we repeated 



Mr. Mather's experiments using both carbons cored, and 



8V 

 found the ~-r- negative as shown by the following table: — 



Brush Carbons. Both cored. 



+ 11 mm. —9 mm. 



Arc taking 9 amperes at 43 volts. 

 Resistance in circuit about 5 ohms. 



Resistance 











introduced. 



Volts. 



8V. 



Amperes. 



SA. 



+ '5 



44-8 



+ 1-8 



8-10 



- '90 



+ •4 



44-2 



+ 1-2 



8-30 



- -70 



+ •3 



44 



+ 1-0 



8-45 



- -55 



+ •2 



43-7 



+ *7 



8-62 



- -38 



+ •1 



43-3 



+ *3 



8-75 



- -25 



-•1 



42-8 



- -2 



9-20 



+ -20 



-•2 



42-4 



- -6 



9-38 



+ -38 



-•3 



42-0 



-1-0 



9-60 



+ -60 



-•4 



41-6 



-1-4 



9-85 



+ -85 



-•5 



41-1 



-1-9 



10-08 



+ 1-08 



In the curves connecting the P.D. between the carbons and 

 the current^ each point is obtained by taking the readings of 

 ammeter and voltmeter after the arc has been made to burn 

 for a very considerable time at constant current and arc-length, 

 so that one may say that the u frequency " is zero. In this 

 case, the resistance, if deduced from the slope of these curves, 

 would be negative both for cored and for solid carbons. In 

 Prof. Ayrton's original method, although the readings are 

 taken as quickly as possible, still the "frequency" is small 

 compared with the lowest frequency we have hitherto used, 

 and both the carbons and the arc may have time to alter before 

 the ammeter and voltmeter can be read. This method would 

 lead to the same conclusion as before, viz. that the resistance 

 of the arc is always negative. Our measurements, however, 

 with frequencies as low as 7*5 gave a positive resistance for 

 arcs using cored carbons. Hence it seems that there must 

 be a critical frequency, above which the resistance has a 

 positive value which is independent of the frequency, and 

 below which it appears to have a negative value, and further, 

 that this frequency must lie between 7*5 and 0. 



* Mrs. Ayrton does indeed rind that for cored carbons at short lengths 

 the curves slope slightly upwards, thus indicating a positive resistance, 



Phil Mag. S. 5. Vol. 42. No. 258. Nov. 1896. 2 H 



