303 
MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC 
Or, since a fl- x is proportional to A, 
k 
A 
where k is constant; that is, A f the P.D. used in sending the current through the 
vapour film, is constant. 
Hence, no back E.M.F. at the crater is necessary to account for the great fall of 
potential between it and the arc, for tire film of high resistance vapour, whose 
existence I have suggested, could cause the P.D. between the positive carbon and 
the arc to remain constant, exactly as if this junction were the seat of a back E.M.F. 
The Apparent Negative Resistance of the Arc is caused by the True Positive 
Resistance diminishing more rapidly than the Current Increases. 
It has been mentioned (p. 301) that the specific resistance of the green flame is so 
high as to make it, to all intents and purposes, an insulator, so that nearly the whole 
of the current flows through the mist. It follows, therefore, that the resistance of 
an arc of given length must depend (apart from the resistance of the vapour film) 
simply on the cross-section of the carbon mist, which, as it appears purple in the 
image of the arc, can easily be measured. To see how this cross-section varies when 
the current is increased while the length of the arc is kept constant, I have drawn, 
in fig. 5, diagrams traced from actual images, after the arc had been burning long 
enough with each current and length for the P.D. between the carbons to have 
become quite constant, great care having been taken to trace as accurately as possible 
the exact limits of the purple centre and the green outer flame. 
The resistance of the carbon mist (as distinct from that of the vapour film) may be 
defined, practically, as being the resistance of that portion of the mist that lies 
between the parallel planes passing through the mouth of the crater and the tip of 
the negative carbon. 
The mean cross-section of the mist D 3 , given in column 3 of Table I., has been 
obtained by taking the means of the squares of the three lengths AB, CD, and EF. 
The next column, giving the ratio of D 3 to the current A, shows that the cross-section 
of the mist increases more rapidly than the current. Column 5 gives numbers pro¬ 
portional to the resistance of the mist, while columns 6 and 7 contain numbers 
proportional to the power spent in the mist, as obtained from these experiments and 
from the equation to be subsequently referred to. 
The mist carries practically the whole of the current, and, since D° increases moie 
rapidly than A (column 4), it follows that in the normal arc the resistance of the mist 
diminishes more rapidly than the current increases. But equation (2) above shows 
that the resistance of the vapour film varies inversely as the current. Hence, with 
