It will thus be seen that the arc, considered as a conductor, has the
property that if the current through it is increased, the difference
of potential between the carbons is decreased, and in one sense,
therefore, the arc may be said to act as if it were a _negative
resistance_. Frith and Rodgers (_Electrician_, 1896, 38, p. 75) have
suggested that the resistance of the arc should be measured by the
ratio between a small increment of carbon potential difference and the
resulting small increment of current; in other words, by the equation
dV/dA, and not by the ratio simply of V:A. Considerable discussion has
taken place whether an electrical resistance can have a negative
value, belonging as it does to the class of scalar mathematical
quantities. Simply considered as an electrical conductor, the arc
resembles an intensely heated rod of magnesia or other refractory
oxide, the true resistance of which is decreased by rise of
temperature. Hence an increase of current through such a rod of
refractory oxide is accompanied by a decrease in the potential
difference of the ends. This, however, does not imply a negative
resistance, but merely the presence of a resistance with a negative
temperature coefficient. If we plot a curve such that the ordinates
are the difference of potential of the carbons and the abscissae the
current through the arc for constant length of arc, this curve is now
called a _characteristic curve_ of the arc and its slope at any point
the instantaneous resistance of the arc.
Other physical investigations have been concerned with the intrinsic
brightness of the crater. It has been asserted by many observers, such
as Blondel, Sir W. de W. Abney, S. P. Thompson, Trotter, L. J. G. Violle
and others, that this is practically independent of the current passing,
but great differences of opinion exist as to its value. Abney's values
lie between 39 and 116, Trotter's between 80 and 170 candles per square
millimetre. Blondel in 1893 made careful determinations of the
brightness of the arc crater, and came to the conclusion that it was 160
candles per square millimetre. Subsequently J. E. Petavel found a value
of 147 candles per square millimetre for current densities varying from
.06 to .26 amperes per square millimetre (_Proc. Roy. Soc._, 1899, 65,
p. 469). Violle also, in 1893, supported the opinion that the brightness
of the crater per square millimetre was independent of the current
density, and from certain experiments and assumptions as to the specific
heat of carbon, he asserted the temperature of the crater was about
3500° C. It has been concluded that this constancy of temperature, and
therefore of brightness, is due to the fact that the crater is at the
temperature of the boiling-point of carbon, and in that case its
temperature should be raised by increasing the pressure under which the
arc works. W. E. Wilson in 1895 attempted to measure the brightness of
the crater under various pressures, and found that under five
atmospheres the resistance of the arc appeared to increase and the
temperature of the crater to fall, until at a pressure of 20 atmospheres
the brightness of the crater had fallen to a dull red. In a later paper
Wilson and G. F. Fitzgerald stated that these preliminary experiments
were not confirmed, and their later researches throw considerable doubt
on the suggestion that it is the boiling-point of carbon which
determines the temperature of the crater. (See _Electrician_, 1895, 35,
p. 260, and 1897, 38, p. 343.)
[Illustration: FIG. 6.]
Alternating current arc.
The study of the alternating-current arc has suggested a number of new
experimental problems for investigators. In this case all the factors,
namely, current, carbon P.D., resistance, and illuminating power, are
periodically varying; and as the electromotive force reverses itself
periodically, at certain instants the current through the arc is zero.
As the current can be interrupted for a moment without extinguishing
the arc, it is possible to work the electric arc from an alternating
current generator without apparent intermission in the light, provided
that the frequency is not much below 50. During the moment that the
current is zero the carbon continues to glow. Each carbon in turn
becomes, so to speak, the crater carbon, and the illuminating power is
therefore symmetrically distributed. The curve of illumination is as
shown in fig. 3. The nature of the variation of the current and arc P.D.
can be examined by one of two methods, or their modifications,
originally due to Jules Joubert and A. E. Blondel. Joubert's method,
which has been perfected by many observers, consists in attaching to the
shaft of the alternator a contact which closes a circuit at an assigned
instant during the phase. This contact is made to complete connexion
either with a voltmeter or with a galvanometer placed as a shunt across
the carbons or in series with the arc. By this arrangement these
instruments do not read, as usual, the root-mean-square value of the arc
P.D. or current, but give a constant indication determined by, and
indicating, the instantaneous values of these quantities at some
assigned instant. By progressive variation of the phase-instant at which
the contact is made, the successive instantaneous values of the electric
quantities can be measured and plotted out in the form of curves. This
method has been much employed by Blondel, Fleming, C. P. Steinmetz,
Tobey and Walbridge, Frith, H. Görges and many others. The second
method, due to Blondel, depends on the use of the _Oscillograph_, which
is a galvanometer having a needle or coil of very small periodic time of
vibration, say (1/2000)th part of a second or less, so that its
deflections can follow the variations of current passing through the
galvanometer. An improved form of oscillograph, devised by Duddell,
consists of two fine wires, which are strained transversely to the lines
of flux of a strong magnetic field (see OSCILLOGRAPH). The current to be
examined is made to pass up one wire and down the other, and these wires
are then slightly displaced in opposite directions. A small mirror
attached to the wires is thus deflected rapidly to and fro in
synchronism with the variations of the current. From the mirror a ray of
light is reflected which falls upon a photographic plate made to move
across the field with a uniform motion. In this manner a photographic
trace can be obtained of the wave form. By this method the variations of
electric quantities in an alternating-current arc can be watched. The
variation of illuminating power can be followed by examining and
measuring the light of the arc through slits in a revolving stroboscopic
disk, which is driven by a motor synchronously with the variation of
current through the arc.