MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
325 
carbon were composed entirely of core, and the other, D E F, connecting the rise of 
P.D., due to the increase of the specific resistance, with the current. The curve 
connecting the true P.D. with the current is found by adding each ordinate of D E F 
to the corresponding ordinate of A B C, as indicated in the dotted line. Whether 
this resulting curve has the form G H Iv, or M N P, or Q B S (fig. 12) depends, 
evidently, upon the relation between the increase of the cross-section and the rise of 
specific resistance, i.e., on the relative structures and cross-sections of the core and 
the outer carbon. 
The fact, already obtained from Table IV., that, for the same current and length 
of arc, the vapour film, and, consequently, the crater, is smaller with a cored than 
with a solid positive carbon, explains why the arc can carry such a much larger 
current without hissing when the positive carbon is cored than when it is solid. For 
I have shown* that hissing is the result of that direct contact of the crater with the 
air which follows when the crater grows too large to cover the end only of the 
positive carbon and so extends along its sides, and this must happen with a smaller 
current the larger the crater is with a given current, i.e., it must happen with a 
smaller current when the positive carbon is solid than when it is cored. 
How the Change in the Cross-Sections of the Mist and the Vapour Film, due to 
a Change of Current, is Affected by Coring Either or Both Carbons. 
Consider next the facts concerning the influence of the cores on the values 
of SV/SA, when a small alternating current is superimposed on a direct current 
normal arc, that the resistance of the arc is affected by this superposition. Here we 
have to deal, not with the whole P.D. between the carbons, but with the change 
in that P.D. that accompanies a given small change of current, and I shall show that 
the effect of the core on this change must always be to add a positive increment 
to SV/SA, the amount of which depends on the value of the direct current, the 
length of the arc, and the frequency of the alternating current. 
The influence of the core on the value SV/SA is two-fold ; it alters the amount by 
which the cross-sections of the vapour film and the mist change, with a given change 
of current ; and it makes their specific resistances vary with the current. We will 
take each separately, the change of cross-section first. I shall call the part of SV/SA 
that depends on the change of cross-section SV r /SA, and the part that depends on 
the variation in the specific resistance 8V,./SA, so that 8V C /SA -f 8VyS A = SV/SA, 
I have already pointed out (p. 306) that if, when the current is increased, the ratios 
of the new cross-sections of the mist and the vapour film to the old are greater than 
* “The Hissing of the Electric Arc,” ‘Journal of the Proceedings of the Institution of Electrical 
Engineers,’ 1899, vol. 28, p. 400. 
