Resistance of the "Electric Arc. 349 



quickly the thickness of its image as projected on the distant 

 screen, before the piece of carbon had time to burn. 



For each set of experiments a particular current was de- 

 cided on : the carbons were put successively at different 

 distances apart and the resistance in the circuit varied until 

 the prearranged current was flowing through the arc, when 

 instantly the actual projected distance between the carbons on 

 the screen was read off and the difference of potentials between 

 the carbons in volts ; or the resistance in the circuit external 

 to the lamp could be left fixed, and the carbons gradually 

 withdrawn until the prearranged current was flowing through 

 the arc, when, as before, the projected length of arc and the 

 difference of potentials between the carbons was read off. A 

 large number of experiments were made in this way with a 

 Brush machine for currents varying between 5 '5 and 10*4 

 amperes, the distances between the carbon points from to one 

 and a quarter inch, and the difference of potential varying 

 from to 140 volts, the carbons being 0*24 inch thick. The 

 result when plotted gave a curve similar to that shown in fig. 2 

 (p. 350), horizontal distances representing distances between 

 the carbon points, and vertical distances the difference of poten- 

 tials between the carbons. For all the currents approximately 

 the same curve was ob J ained — a result to be expected, seeing 

 that the first investigation showed that the difference of 

 potentials between two carbons necessary to produce an arc 

 depended almost entirely on the distance between them, and 

 hardly at all on the strength of the current. The equation to 

 the curve we find to be approximately as follows : — 



E = 63 + 55a-63xl0- 10a , 



where E is the difference of potentials in volts between the 

 carbons, and a the distance between their points in inches. 

 It will be seen that at first the difference of potentials 

 necessary to maintain the arc increases rapidly with the 

 distance, and that at a distance of about one tenth of an inch 

 it is about 60 volts. From this the curve bends rapidly up 

 to a point corresponding with a distance between the carbons 

 of about one quarter of an inch ; and for greater distances 

 between the carbons than one quarter of an inch, the increase 

 of difference of potentials becomes nearly proportional to the 

 increase of distance, being about 54 volts per inch increase. 



This law is very like that found by Mr. C. F. Yarley for 

 the discharge through a vacuum-tube, which was that the 

 current was proportional to the difference of potentials 

 minus a constant; for this is equivalent to saying that, cceteris 

 paribusjthe difference of potentials necessary to produce a fixed 



Phil. Mag. S. 5. Vol. 15. No. 95. May 1883. 2 C 



