316 
MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
The next point D, is obtained from Mr. Dubdell’s work. In his remarkable 
paper* on “Rapid Variations in the Current through the Direct Current Arc,” he 
said, “ I tried to record the transient rise in P.D. for the solid arc by means of an 
oscillograph, the sudden increase of the current being obtained by discharging a 
condenser through the arc. This experiment was successful, and a transient rise in 
P.D. was observed, the P.D. and current increasing together, hut only for about 
1/5000 second.” It is clear from this that SV/SA must at least begin to be positive 
with a frequency of 2,500 complete alternations per second; and D where OD = 2,500 
may be taken to be the point near which 8V/SA changes its sign. 
To the right of D the curve must continue to rise, as indicated in fig. 10, more and 
more slowly, as it approaches the horizontal line whose distance from the axis of 
frequency represents the value of SV/SA which is the true resistance of the arc. The 
curve must finally become asymptotic to this line, since when once a frequency is 
nearly reached with which the alternating current does not practically affect the 
resistance of the arc, increasing the frequency will not alter the value of SV/SA. 
My equation above shows that the resistance of the particular 2-millim. 10-ampere 
normal arc under discussion cannot be greater than 4'63 ohms, nor less than 0'62 
ohm ; for if there is no back E.M.F., 
38-88 + 2-07 x 2 11-66 + 1054 x 2 
10 + 100 
= 4-63 
and if there is the largest possible back E.M.F., viz., 38'88 -f 
11-66 
A 
volts (for it is 
impossible to imagine that terms involving the length of the arc can belong to a back 
17' T\/T XT’ \ x. 2'07 X 2 , 10 ‘ 54 >< 2 A ™ 
E.M.F.), then r= 1Q + ——— = 0-62. 
100 
Thus the curve cannot rise higher than the horizontal line SV/SA = 4'63, and it 
must rise at least as high as SV/SA = 0‘62. Consequently, as the lower curve in 
fig. 10 shows, the true resistance of this particular arc could not be measured with 
a superimposed alternating current having a frequency of less than at least 8000 
complete alternations per second, even if there were a back E.M.F. as great as 
40 volts. And if, as I have suggested, the back E.M.F. is zero, or at least very 
much smaller than 40 volts, the frequency would have to be many times as high for 
SV/SA to be on the horizontal part of the curve, i.e., for the alternating current not 
to alter the resistance of the arc. 
The Form of the P.D. Time Curve indicates whether the Resistance of the Arc is 
Affected by the superimposed Alternating Current or Not. 
The final test as to the frequency being high enough not to affect the resistance of 
the arc must, of course, be the finding, with the same root mean square value of the 
* ‘ Journal of the Institution of Electrical Engineers,’ vol. 30, p. 232. 
