284 
NATURE 
[JuLy 20, 1899 
At the Congress at Chicago in 1893 Prof. Ayrton (Zhe 
Electrician, 1895, vol. xxxiv. pp. 336-7) first drew attention to 
the region of instability indicated by the dotted portions of the 
curves. At the same time he pointed out in Fig. 2, shown at 
Chicago, that whether the P.D. was descending as the current 
increased for, say, a 4 mm. arc, or was ascending for, say, a 0’5 
mm. arc, it became quite constant for wide variations of current 
with a hissing arc. 
And, lastly, by a comparison of Fig. 2 with Fig. 3 he brought 
out the fact that the largest current that would flow silently 
with any given length of arc was increased by using thicker 
carbons; for the carbons in Fig. 3 have about twice the 
diameter of those in Fig. 2, and while the largest silent current 
for, say, the 2mm. arc in Fig. 2 is 15°5 amperes, that for the 
same length of are in Fig. 3 is about 49 amperes, or more than 
three times as great. 
Returning now to the subject of the dotted lines in Figs. 1, 
2 and 3, it is plain that these divide the curves into two per- 
fectly separate parts, governed by different laws. For to the 
left of the dotted part the lines are all curved, and curved 
differently according as so/éd positive carbons are used as in 
Fig. 1, or coved as in Figs. 2 and 3, showing that with silent 
arcs the P.D. varies as the current varies, and that the law of 
variation is different with solid and cored carbons. To the 
right, on the other hand, the lines are all straight, and more or 
less parallel to the axis of current, whether the positive carbon 
is solid or cored, showing that with Azssdzg arcs the P.D. is the 
same for a given length of arc and a given pair of carbons, 
whatever current is flowing, and that this law is true whether 
the carbons be cored or solid. In fact, when the arc begins to 
hiss some complete and sudden break-down appears to occur, 
upsetting all the laws that have governed it while it was silent, 
and making cored and solid carbons behave alike. : 
Thus, our subject divides itself quite naturally into two dis- 
tinct portions, the one dealing with the arc when the break- 
down is imminent, but before it has actually occurred—dealing, 
that is to say, with the points at which the current is the largest 
that will flow silently—the A7ssézg points as I shall call them ; 
and the other dealing with the arc after the break-down has 
occurred, and when, therefore, the arc is really hissing. 
An examination of Fig. 1 shows that the hissing points lie 
well on the curve A BC; that curve may, therefore, be taken 
to embody the laws connecting the P.D. between the carbons, 
the current, and the length of the arc, at the Azsstng poents, for at 
least all those lengths of are given by the curves in Fig. 1. The 
most important of these laws concerns the current at the Azssing 
point, the largest sz/ent current. 
It is quite plain, from Fig. 1, that although this current in- 
creases as the length of the arc increases, yet it does not 
increase at the same rate as the length of the arc. For each 
millimetre added to the length of the arc involves a smaller and 
smaller addition to the largest silent current; so that finally a 
current must be reached which will not increase appreciably 
however much the arc is lengthened, always supposing that the 
law continues to hold for such long arcs. Hence, on this sup- 
position, for each pair of carbons the current that will sustain 
a normal silent arc has a maximum value, and any current 
greater than, this will make the arc hiss, however long it 
may be. 
Other laws concerning the arc when on the point of hissing 
and when actually hissing can be deduced directly from Figs. 
I, 2 and 3, but as these do not bear directly on the cause of 
hissing, the mathematical proofs of them may with advantage 
be omitted from the present article. Some of these laws may, 
however, be summed up as follows :— 
If V be the P.D. in volts between the carbons at the hissing 
point for an arc of 7 millimetres, and if V’ be the constant P.D. 
between the carbons for a hissing arc of the same length, then 
V =40°05 + 2°49 /, 
V'=29°25+2°75 /, 
and consequently 
V-V’=10'8 -—0'26/, 
which shows that ¢he longer the arc the less ts the P.D. between 
the carbons diminished when tt changes from silence to hissing, 
The numerical coefficients in the above equations naturally 
refer only to the carbons I used in my experiments, but the Zaws 
expressed by the equations must be true for a// direct current 
open arcs of lengths not differing very greatly from those I 
used, and burning between solid carbons. 
NO. 1551, VOL. 60] 
From Fig. 1 it might be supposed that, given the length of 
the arc, the increase of current that abruptly occurs on the arc 
starting hissing was as definite for that length of arc as the 
diminution in the P.D. And this, for a long time, I imagined 
to be the case. But while trying to find out what law connected 
the smallest hissing current with the length of the arc, I saw 
that the value of that current really depended on the circuit 
outstde the arc. I found, in fact, that when the largest silent 
current for any length of are changes to the smallest hissing 
current for the same length of arc, the value of that smallest 
hissing current depends on the E.M.F. of the dynamo ov/y. 
The smaller that E.M.F. is, the greater will be the smallest 
hissing current for any given length of arc, while if the E.M.F. 
of the dynamo could be made infinite, the smallest hissing cur- 
rent and the largest silent current would be equal; that is to 
say, when the arc began to hiss the P?.D. between the carbons 
would drop, but the current would remain quite unchanged. 
Thus it is possible, by choosing suitable E.M.F.s, to make 
the sudden smallest hissing current have any value greater 
than that of the largest silent current for the same length of arc. 
In 1889 Luggin found, by measuring the fall of potential 
between each carbon and the arc, that the principal part of the 
diminution of P.D. caused by hissing took place at the junction 
of the positive carbon and the arc. Some experiments of the 
same sort that I made about three years ago, using arcs varying 
between £ mm. and 6 mm., gave the same result. 
For the lengths of are dealt with, I found that hissing caused 
a mean fall of about 9°7 volts in the total P.D. between the 
carbons, and a mean fall of about 6°3 volts in the P. D. between 
the positive carbon and the arc. Hence of the whole diminution 
of the P.D, between the carbons caused by hissing, about two- 
thirds took place at the junction of the positive carbon and 
the arc. 
Further, my experiments showed that very little of the re- 
mainder of the diminution, if any, was due to a diminished fal] 
in the P.D. between the are and the negative carbon ; there- 
fore this remaining diminution must be attributed to a lowering 
of the resistance of the arc itself. We may sum up these results 
as follows :— 
Of the total diminution of the P.D. between the carbons 
caused by hissing, about two-thirds takes place at the junction 
of the posttive carbon and the arc, and the remaining third 
seems to be due to a lowering of the reststance of the arc ztself. 
We now pass from the consideration of the electrical 
measurements of the arc to the appearance of the crater, arc, 
and carbons. 
Every alteration of the current and of the distance between 
the carbons naturally produces a corresponding modification of 
all parts of the arc, but until the value of the current attains a 
certain magnitude, which depends only on the length of the are 
with a given pair of carbons, this change is one of degree 
merely, and not of character. A greater current simply pro- 
duces a larger crater, a larger arc, and longer points to the 
carbons. When the special current is reached, however, a 
change, which is no longer simply one of degree, takes place 
in that white-hot depression at the end of the positive carbon — 
from which most of the light of the arc is derived—the crater, © 
as it is called. Instead of presenting a uniformly. bright surface 
to the eye, this becomes partly covered with what appear to be 
alternately bright and dark bands, sometimes radial like the 
spokes of a wheel, sometimes in one or more sets of concentric 
circles, sometimes oscillating, sometimes rotating round different 
centres in opposite directions. The directions of rotation or 
oscillation and whole positions of the images change continu- 
ally, and the motion grows faster and faster as the current is 
increased. 
When the current is so much increased that the motion 
becomes too fast for the eye to detect, the are begins to hum, 
and then, as Mr. Trotter (Proc. Noy. Soc., vol. lvi. p. 262) 
first showed in 1894, it rotates at the rate of from 50 to 450 
revolutions per second. 
As soon as hissing begins the whole appearance of the crater 
changes again; a sort of cloud seems to draw in round a part 
of it, moving from the outer edge inwards, and varying con- 
tinually in shape and position. Sometimes but one bright spot 
is left, sometimes several, but always the surface is divided into 
bright and dull parts, giving it a mottled appearance, as 1s 
slightly indicated in (6) Fig. 4. If, then, the current be 
diminished, so that the arc becomes silent again, the whole 
