314 
MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
such changes as BC and CF, say, (fig. 7) only ; SY/SA would therefore have a smaller 
negative value than with the lower frequency last mentioned, and the curve denoting 
the time change of P.D. might again be PX^YjPt, or it might be PX 3 QY 3 R, if the 
frequency were high enough. When the frequency was so great that the two P.Ds., 
BO and CD (fig. 7) were exactly equal, the P.D. would not alter at all when the 
current was changed, SY/SA would be zero, and the straight line PQB would be the 
time change of P.D. curve. When the frequency was further increased, the change 
of P.D. would be-the resultant of two such changes as BC, CG (fig. 7), the total change 
of P.D. would therefore he in the same direction as the change of current, the P.D. 
Fig 9. Suggested curves connecting current and P.D. with time for different frequencies of the same 
small superimposed alternating current, when the direct current and length of the arc are constant. 
time curve would be like PX t QY 4 R, and SY/SA would be + Z^Xy'WS. Finally, 
when the frequency was so great that the area of the volatilising surface never 
altered at all, the change of P.D. would be BC (fig. 7) alone, the P.D. time curve 
would be PX-QYJt, SY would be Z-X-, and SY/SA, or Z-X-/WS would measure the 
true resistance of the arc, even if there is a back E.M.F. in the arc, unless that back 
E.M.F. varies with the current. 
