MRS. H. AYRTON ON TIIE MECHANISM OF THE ELECTRIC ARC. 
315 
Thus, by applying the same alternating current, but with different frequencies, to 
a direct current arc, SY/SA can be made to have any value from a fairly large 
negative value to the true positive value. It is easy to see, therefore, how different 
experimenters might get very different values and even different signs for the 
resistance of the arc, when they measured it by means of a superimposed alternating 
current; and fig. 9 shows the imperative necessity of some rigorous proof that the 
alternating current has not affected the resistance of the arc before any such 
measurements can be accepted as final. I shall presently show how such a proof can 
be obtained, but first it will be interesting to see how, with an arc of given length, 
and with a given current flowing, the value of SY/SA is connected with the frequency 
of the alternating current, and what sort of frequency is required in order that the 
resistance of the arc shall not be affected by. this current. 
To find the Curve connecting SY/SA with the Frequency ofi the Superimposed 
Alternating Current , and to see with what Frequency SY/SA Measures the True 
Resistance of the Arc. 
Take an arc of 2 millims. with a direct current of 10 amperes flowing. For the 
arc to remain normal when the small alternating current is superimposed on it, the 
frequency must be practically zero, for each alternation must take many seconds 
instead of only a small fraction of a second. Now the equation I have found* 
between Y, A, and /, in the normal arc with solid Apostle carbons is 
Y 
38-88 -f 2-07^ + 
11 66 + 10-5Y 
A 
therefore the normal SY/SA = — ^ ^ ~|~ a ^ ^ = — 0 - 33, when l = 2, and A = 10. 
At 
The first point on the curve connecting SV/SA with the frequency of the alterna¬ 
ting current has, therefore, the co-ordinates 0, and — 0'33 (A, fig. 10). 
The value found for SY/SA by Messrs. Frith and -Rodgers]' with the same carbons, 
direct current, and P.D. was about — 0'8, more than double the normal value, which 
shows that the alternating current they superimposed was making the resistance of 
the arc vary to an extent that made the P.D. follow some such curve as PX 2 QY 2 R 
(fig. 9). They also found that varying the frequency from 7 to 250 complete alterna¬ 
tions per second made no difference in the value they obtained for SY/SA. Therefore 
the curve connecting SY/SA with the frequency must fall steeply from A, the point of 
no frequency, to B, the point for a frequency of 7, and must be practically horizontal 
from B to C (fig. 10). Hence Messrs. Frith and Rodgers’ observations cover the 
portion BC of the curve. 
* ‘ The Electric Arc,’ p. 184. 
t ‘ Phil. Mag.,’ 1896, vol. 42, Plate 5. 
