If the arc is supplied by an alternator of low inductance, and soft or
cored carbons are employed to produce a steady and silent arc, the
potential difference of the carbons periodically varies in a manner
not very different from that of the alternator on open circuit. If,
however, hard carbons are used, the alternating-current arc deforms
the shape of the alternator electromotive force curve; the carbon P.D.
curve may then have a very different form, and becomes, in general,
more rectangular in shape, usually having a high peak at the front.
The arc also impresses the deformation on the current curve. Blondel
in 1893 (_Electrician_, 32, p. 161) gave a number of potential and
current curves for alternating-current arcs, obtained by the Joubert
contact method, using two movable coil galvanometers of high
resistance to measure respectively potential difference and current.
Blondel's deductions were that the shape of the current and volt
curves is greatly affected by the nature of the carbons, and also by
the amount of inductance and resistance in the circuit of the
alternator. Blondel, W. E. Ayrton, W. E. Sumpner and Steinmetz have
all observed that the alternating-current arc, when hissing or when
formed with uncored carbons, acts like an inductive resistance, and
that there is a lag between the current curves and the potential
difference curves. Hence the _power-factor_, or ratio between the true
power and the product of the root-mean-square values of arc current
and carbon potential difference, in this case is less than unity. For
silent arcs Blondel found power-factors lying between 0.88 and 0.95,
and for hissing ones, values such as 0.70. Ayrton and Sumpner stated
that the power-factor may be as low as 0.5. Joubert, as far back as
1881, noticed the deformation which the alternating-current arc
impresses upon the electromotive force curve of an alternator, giving
an open circuit a simple harmonic variation of electromotive force.
Tobey and Walbridge in 1890 gave the results of a number of
observations taken with commercial forms of alternating-current arc
lamps, in which the same deformation was apparent. Blondel in 1896
came to the conclusion that with the same alternator we can produce
carbon P.D. curves of very varied character, according to the material
of the core, the length of the arc, and the inductance of the circuit.
Hard carbons gave a P.D. curve with a flat top even when worked on a
low inductance alternator.
The periodic variation of light in the alternating-current arc has
also been the subject of inquiry. H. Görges in 1895 at Berlin applied
a stroboscopic method to steady the variations of illuminating power.
Fleming and Petavel employed a similar arrangement, driving the
stroboscopic disk by a synchronous motor (_Phil. Mag._, 1896, 41). The
light passing through slits of the disk was selected in one particular
period of the phase, and by means of a lens could be taken from any
desired portion of the arc or the incandescent carbons. The light so
selected was measured relatively to the mean value of the horizontal
light emitted by the arc, and accidental variations were thus
eliminated. They found that the light from any part is periodic, but
owing to the slow cooling of the carbons never quite zero, the minimum
value happening a little later than the zero value of the current. The
light emitted by a particular carbon when it is the negative, does not
reach such a large maximum value as when it is the positive. The same
observers made experiments which seemed to show that for a given
expenditure of power in the arc the alternating current arc in general
gives less mean spherical candle-power than the continuous current
one.
[Illustration: FIG. 7.]
The effect of the wave form on the efficiency of the
alternating-current arc has engaged the attention of many workers.
Rössler and Wedding in 1894 gave an account of experiments with
alternating-current arcs produced by alternators having electromotive
force curves of very different wave forms, and they stated that the
efficiency or mean spherical candle-power per watt expended in the arc
was greatest for the flattest of the three wave forms by nearly 50%.
Burnie in 1897 gave the results of experiments of the same kind. His
conclusion was, that since the light of the arc is a function of the
temperature, that wave form of current is most efficient which
maintains the temperature most uniformly throughout the half period.
Hence, generally, if the current rises to a high value soon after its
commencement, and is preserved at that value, or nearly at that value,
during the phase, the efficiency of the arc will be greater when the
current curve is more pointed or peaked. An important contribution to
our knowledge concerning alternating-current arc phenomena was made in
1899 by W. Duddell and E. W. Marchant, in a paper containing valuable
results obtained with their improved oscillograph.[1] They studied the
behaviour of the alternating-current arc when formed both with solid
carbons, with cored carbons, and with carbon and metal rods. They
found that with solid carbons the arc P.D. curve is always
square-shouldered and begins with a peak, as shown in fig. 7 (a), but
with cored carbons it is more sinusoidal. Its shape depends on the
total resistance in the circuit, but is almost independent of the type
of alternator, whereas the current wave form is largely dependent on
the machine used, and on the nature and amount of the impedance in the
circuit; hence the importance of selecting a suitable alternator for
operating alternating-current arcs. The same observers drew attention
to the remarkable fact that if the arc is formed between a carbon and
metal rod, say a zinc rod, there is a complete interruption of the
current over half a period corresponding to that time during which the
carbon is positive; this suggests that the rapid cooling of the metal
facilitates the flow of the current from it, and resists the flow of
current to it. The dotted curve in fig. 7 (b) shows the current curve
form in the case of a copper rod. By the use of the oscillograph
Duddell and Marchant showed that the hissing continuous-current arc is
intermittent, and that the current is oscillatory and may have a
frequency of 1000 per second. They also showed that enclosing the arc
increases the arc reaction, the front peak of the potential curve
becoming more marked and the power-factor of the arc reduced.
[Illustration: FIG. 8.--Enclosed Arc Lamp.]
Enclosed arc lamps.
If a continuous-current electric arc is formed in the open air with a
positive carbon having a diameter of about 15 millimetres, and a
negative carbon having a diameter of about 9 millimetres, and if a
current of 10 amperes is employed, the potential difference between the
carbons is generally from 40 to 50 volts. Such a lamp is therefore
called a 500-watt arc. Under these conditions the carbons each burn away
at the rate of about 1 in. per hour, actual combustion taking place in
the air which gains access to the highly-heated crater and negative tip;
hence the most obvious means of preventing this disappearance is to
enclose the arc in an air-tight glass vessel. Such a device was tried
very early in the history of arc lighting. The result of using a
completely air-tight globe, however, is that the contained oxygen is
removed by combustion with the carbon, and carbon vapour or hydrocarbon
compounds diffuse through the enclosed space and deposit themselves on
the cool sides of the glass, which is thereby obscured. It was, however,
shown by L. B. Marks (_Electrician_ 31, p. 502, and 38, p. 646) in 1893,
that if the arc is an arc formed with a small current and relatively
high voltage, namely, 80 to 85 volts, it is possible to admit air in
such small amount that though the rate of combustion of the carbons is
reduced, yet the air destroys by oxidation the carbon vapour escaping
from the arc. An arc lamp operated in this way is called an enclosed arc
lamp (fig. 8). The top of the enclosing bulb is closed by a gas check
plug which admits through a small hole a limited supply of air. The
peculiarity of an enclosed arc lamp operated with a continuous current
is that the carbons do not burn to a crater on the positive, and a sharp
tip or mushroom on the negative, but preserve nearly flat surfaces. This
feature affects the distribution of the light. The illuminating curve of
the enclosed arc, therefore, has not such a strongly marked maximum
value as that of the open arc, but on the other hand the true arc or
column of incandescent carbon vapour is less steady in position,
wandering round from place to place on the surface of the carbons. As a
compensation for this defect, the combustion of the carbons per hour in
commercial forms of enclosed arc lamps is about one-twentieth part of
that of an open arc lamp taking the same current.
It was shown by Fleming in 1890 that the column of incandescent carbon
vapour constituting the true arc possesses a unilateral conductivity
(_Proc. Roy. Inst._ 13, p. 47). If a third carbon is dipped into the arc
so as to constitute a third pole, and if a small voltaic battery of a
few cells, with a galvanometer in circuit, is connected in between the
middle pole and the negative carbon, it is found that when the negative
pole of the battery is in connexion with the negative carbon the
galvanometer indicates a current, but does not when the positive pole of
the battery is in connexion with the negative carbon of the arc.
The arc as an illuminant.
Turning next to the consideration of the electric arc as a source of
light, we have already noticed that the illuminating power in different
directions is not the same. If we imagine an electric arc, formed
between a pair of vertical carbons, to be placed in the centre of a
hollow sphere painted white on the interior, then it would be found that
the various zones of this sphere are unequally illuminated. If the
points in which the carbons when prolonged would intercept the sphere
are called the poles, and the line where the horizontal plane through
the arc would intercept the sphere is called the equator, we might
consider the sphere divided up by lines of latitude into zones, each of
which would be differently illuminated. The total quantity of light or
the total illumination of each zone is the product of the area of the
zone and the intensity of the light falling on the zone measured in
candle-power. We might regard the sphere as uniformly illuminated with
an intensity of light such that the product of this intensity and the
total surface of the sphere was numerically equal to the surface
integral obtained by summing up the products of the areas of all the
elementary zones and the intensity of the light falling on each. This
mean intensity is called the _mean spherical candle-power_ of the arc.
If the distribution of the illuminating power is known and given by an
illumination curve, the mean spherical candle-power can be at once
deduced (_La Lumière électrique_, 1890, 37, p. 415).
[Illustration: FIG. 9.]
Let BMC (fig. 9) be a semicircle which by revolution round the
diameter BC sweeps out a sphere. Let an arc be situated at A, and let
the element of the circumference PQ = _ds_ sweep out a zone of the
sphere. Let the intensity of light falling on this zone be I. Then if
[theta] [asymp] the angle MAP and d[theta] the incremental angle PAQ,
and if R is the radius of the sphere, we have
ds = R d[theta];
also, if we project the element PQ on the line DE we have
ab = ds cos [theta],
:. ab = R cos [theta] d[theta]
and
Iab = IR cos [theta] d[theta].