ELECTROMOTIVE FORCES OF THE ELECTRIC ARC. 325 



testing current was 100,000 per second with solid arcs, and 26,000 ^ with cored 

 arcs. In every experiment the power-factor of the arc was also determined, and 

 found equal to + 1 to within the limits of experimental error, except for a very few 

 small current arcs whose resistance was so high that the power-factor could not he 

 measured with any certainty. 



In the Curves III. and IV. there is plotted, besides the resistance of the arc and 

 the P.D. between its terminals, the back E.M.F., calculated as the difference between 

 the P.D. and the product of the direct current into the resistance, or ohmic drop in 

 the arc. 



The resistance of both the cored and the solid arcs increases with decrease of the 

 direct current, apparently tending to become infinite for current zero. The back 

 E.M.F. of the solid arc first decreases with increase of current and then slightly 

 increases again, having a minimum of 11 '3 volts at about (! amperes. With cored 

 carbons the back E.M.F. increases with increase of current, from 12 '2 volts at 

 1 ampere to 18 '5 volts at 20'8 amperes. It is curious to note that the back E.M.F. 

 of solid arcs is larger than that of cored arcs for .small currents, the reverse being 

 the case with the larger currents. 



As the back E.M.F. does not vary much for any of the ares, the whole of the 

 values observed being between 11 "2 volts and 18'f> volts, the high P.D.'s required to 

 maintain very small-current solid arcs is mainly due to the resistance of the arc, and 

 not to the change in its back E.M.F. 



The connection between the resistance r and the current A for the cored arc, length 

 3 millims., between 11-millim. " (Jonradty Noris " carbons, can be approximately 

 expressed over the range from 1'5 amperes to '20 amperes by the very simple relation 

 (r + 0'25)A = 29. 



For the solid arc, length 3 millims., between 11-millim. " Conradty Noris" carbons, 

 no such simple relation seems to exist; but the curve may be approximately repre- 

 sented over the range I'D amperes to 11 amperes by the relation r = 33'5A~' -|-42A"~~. 



Effect of Vdryinc] the Arc Lenyfh. 



The direct current through the arc being kept constant, the connection between 

 the back E.M.F., the resistance, and the length, is given in Curves V. and VI. 



With both solid and cored arcs the effect of increasing the length is to increase the 

 resistance, though not proportionately to the length, the curve between resistance 

 and length being very similar to that between P.D arc and length. This latter 

 curve is generally assumed to be a straight line, but such is not the case over 

 the wide range of lengths 1 millim. to 30 millims. used in these experiments 

 (see Appendix I.). 



The back E.M.F. of the solid arc is nearly independent of the length, dropping 

 slightly to a minimum at 4 millims. and then rising again. With the cored arc the 

 back E.M.F. decreases with increase of length. 



