MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
309 
proportional to a constant plus a term which varies directly with the current. 
Dividing by A 2 , we obtain to, the resistance of the mist, 
0136 , 2-86 
TO = — - + 
A 
A 2 
Combining this with f the resistance of the vapour him on p. 306, we have for the 
total resistance of the normal arc an expression of the form 
/ + to = — + — • 
But I have shown* that an equation of the form 
V = a + bl + c -^~ 
exactly fits not only all the numerous measurements that I have myself made ot 
simultaneous values of the P.D. between the carbons, the current, and the length of 
the arc, but also all the similar experiments made by other observers when both 
carbons are solid. When l, the length of the arc, is constant, this equation becomes 
where y and 8 are constants, 
resistance of an arc, 
Hence, dividing by A, we have, for the total apparent 
Thus, by considering only the way in which the resistances of the vapour film and 
of the carbon mist respectively must vary with the current, we arrive at an equation 
for the resistance of exactly the same form as is obtained by dividing by the current 
the values found experimentally for the P.D. between the carbons. So that instead 
of an arc consisting of a circuit of low resistance combined with a back E.M.F., it may 
well be that its apparent resistance, i.e., the ratio of V to A, is its true resistance; 
or it may be that, if there is any back E.M.F. at all, it is very much smaller than has 
hitherto been supposed. 
Both the Resistance of the Arc and the P.D. between the Carbons depend not only on 
the Current and the Length , but also on How Lately a Change has been made in 
Either and on What that Change teas. 
The whole resistance of the arc depends on the cross-sections of the vapour film 
and the mist, and on the distance between the carbons. Now I have shown that 
* ‘ The Electric Arc,’ p. 186. 
