MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
313 
remains constant. In dealing with a superimposed alternating current there is, of 
course, no sudden increase and diminution, everything is gradual. The three changes 
of P.D. do not, therefore, act separately—they overlap. At any moment, for instance, 
when the current is increasing say, the increase may be considered due to the 
addition of successive small increments of current, so that the P.D. has a tendency to 
rise on account of the last added increment of current, to fall on account of the 
diminution of resistance due to the last but one, and to rise on account of the 
re-shaping of the carbons following the last but two. If the frequency of the 
alternating current is very low indeed, so that the current changes very slowly, all 
three of these tendencies will be in force at each moment, and the actual change 
of P.D. will be the resultant of the three. If the frequency is so high that the 
shapes of the carbons never change at all, but so low that the area of the volatilising 
surface can alter, only the first two tendencies will be operative; while, if the 
frequency is so high that the area of the volatilising surface remains constant, the 
resistance of the arc will not alter at all, the current and P.D. will increase and 
diminish together and proportionately, and, unless the arc contains a variable back 
E.M.F., SV/SA will measure the true resistance of the arc. 
The influence of the frequency of the alternating current on the magnitude and 
sign of SV/SA is traced in fig. ( J. PR represents the time occupied by one complete 
alternation, whatever that time maybe. If, for instance, the frequency is 50 complete 
alternations per second, PR represents one-fiftieth of a second; if the frequency is 
5000, PR represents one-five thousandth of a second. PSQTR represents the time 
change of current with any frequency. When the alternations are so slow that the 
arc remains normal, the change of P.D., SV, for a given small change of current, WS 
say, is the resultant of three such changes as BC, CD, and DE (fig. 7), and it is in 
the opposite direction from the change of current. The P. D. time curve is something 
like PXQYR (fig. 9) therefore, and SV/SA is the mean of such ratios as ZX/WS, and 
is therefore negative. 
When the frequency is raised, so that the carbons never have time to alter their 
shapes completely before the current changes, the third variation, DE, (fig. 7, p. 310) 
is smaller than with the normal arc, so that 8 V is greater negatively, and SV/SA 
must, therefore, have a larger negative value than when the arc is normal, and such 
a curve as PXjQY^t would be the P.D. time curve in this case. 
When the frequency was so high that the carbons never altered their shapes at 
all, but the volatilising surface underwent the maximum alteration, the third 
variation (DE fig. 7) would be absent altogether, and therefore SV would undergo 
the greatest change it was susceptible of in the opposite direction to the change of 
current, so that PX 2 QY 2 R is then the P.D. time curve,, and SV/SA has then its 
maximum negative value, and is the mean of such ratios as Z 2 X 2 /WS. 
With a further increase of frequency, the area of the volatilising surface would 
never have time to change completely, so that SV would be the resultant of two 
vol. cxcix.— a. 2 s 
