312 
MRS. II. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
of measuring the resistance by means of a small superimposed alternating current. 
Such a method has been employed by many experimenters, but the results have 
not shared the similarity of the methods ; for while von Lang and Arons found, in 
1887, that the arc had a 'positive resistance, Messrs. Frith and Lodgers, in 1896, 
found that it had a negative one with solid carbons. 
We shall now see the reason of this disparity, and first it may be well to recall 
shortly the reasoning on which the method is based.. 
The equation Y = E + A r may be taken to represent the connection between the 
P.D. between the carbons, the current, and the length of the arc, whether it has a 
variable E.M.F., a constant E.M.F., or none at all. For in the first case E will be 
variable, in the second constant, and in the third zero. In any case SY/SA = r, 
only when such a small quick change is made in V and A that neither E nor r is 
made to vary by it. 
Instead of a single small quick change of current, the experimenters superimposed 
a small alternating current on the direct current of the arc, and measured the average 
value of SY/SA, or its equivalent. Obviously, if the alternating current left the 
resistance and any back E.M.F. that might exist in the arc unaffected, this was 
a true measure of the resistance of the arc. But if the alternating current changed 
both or either of these, then instead of being equal to r y we should have 
if there is a back E.M.F., and if both it and the 
resistance varied with the alternating current; 
if there is a back E.M.F., and if it alone varied; 
if there is no back E.M.F., or if the resistance alone 
varied. 
None of the experimenters, as far as I am aware, applied any but a few imperfect 
tests to see whether the alternating currents they employed affected the resistance 
of the arc or not, and it was, I believe, because the resistance teas affected, in every 
case, that such diverse results were obtained. The low frequency of the alternations 
was the probable source of error, for I shall now show that, with a given root mean 
square value of the alternating current, the average value of SY/SA varies not only 
in magnitude, hut even in sign, with the frequency of that current. 
Effect of the Frequency of the Superimposed Alternating Current on the 
Value and Sign of SY/SA. 
I have shown (p. 310) that when a sudden increase of the current is made and 
maintained the P.D. has three successive stages of variation. It first rises (BC, fig. 7), 
then falls (CD), then rises again (DE), but not so high as before, and after this it 
SY 
SA 
r 8E , A Sr 
r +sX + A sX 
hV 
SA 
= r + 
SE 
SA 
SY 
SA 
— r + A 
Sr 
SA 
