MRS. IL AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
335 
The fall of P.D.—Q P—is more complex. It depends principally on how much of 
the extra carbon volatilised by the larger current remains between the carbons, and 
how much escapes along them. When the carbons have short thick ends more will 
remain than when they have long pointed ones, and as the ends of the carbons are 
thicker, with the same current, the longer the arc, a 
small increase of current will diminish the resistance of 
the arc more, the longer the arc. But the blunting of 
the carbons, which is a rapid affair when the arc is short, 
takes place more and more slowly as it is lengthened, till | 
at last the addition of a millimetre or so to the length of ^ 
the arc makes practically no difference in the shapes of | 
the carbons. Hence the diminution of resistance due ^ 
to the addition of SA to the current increases rapidly at q 
first, when the arc is short, and more and more slowly 
as the arc lengthens, till finally it becomes practically 
constant ; and hence also, Q R—the fall of P.D. accom¬ 
panying this diminution—increases more and more slowly 
as the arc is lengthened. Thus, while the rise of P.D.—P Q—increases at a constant 
rate as the arc is lengthened, the fall, Q R, increases at a diminishing rate. While 
the arc is so short, therefore, that Q II increases more rapidly than P Q when l is 
increased, the whole fall of P. D.—P S—will increase, with the length of the arc, or, 
since P S is — SV and SA is the same for all the lengths of arc, — SV/SA increases 
as the arc is lengthened. When the arc is so long that P Q increases faster 
than Q R, P S, and, therefore, — SV/SA will diminish as the arc is lengthened. 
Between the two stages there must be a length ot arc for which — SV/SA is a 
maximum. The curve connecting — SV/SA with l for a constant current, with solid 
carbons, must, therefore, be of the form ABC (fig. 18 ), and there seems to he no 
reason why , with very long arcs, SV/SA should not actually become positive, with 
superimposed alternating currents of comparatively low frequency, even with solid 
carbons. 
The curves connecting SV/SA with /, when cored carbons are used, must resemble 
the curve for solid carbons, ABC (fig. 18), but must be higher up the figure 
(D E F, G H K) when one carbon is cored, and still higher up (M N P) when both 
are cored. Also, since a change in the specific resistance of the arc must have more 
effect on the value of SV/SA the longer the arc, the distance between the curves for 
cored carbons and the curve for solid carbons must increase as the arc is lengthened, 
as it is made to do in fig. 18. 
Curves very similar to those in figs. 16 and 18 were obtained by Messrs. Frith and 
Rodgers, in 1896, by actual measurements of SV/SA. Other measurements that 
they carried out at the same time coincide with some of the other deductions I have 
made concerning the influence of cores on the value of SV/SA. Hence, experience, as 
