Chapter VI: Front Matter (6)

Electric arcs may be classified into continuous or alternating current arcs, and open or enclosed arcs, carbon arcs with pure or chemically impregnated carbons, or so-called flame arcs, and arcs formed with metallic or oxide electrodes, such as magnetite. A continuous current arc is formed with an electric current flowing always in the same direction; an alternating current arc is formed with a periodically reversed current. An open arc is one in which the carbons or other material forming the arc are freely exposed to the air; an enclosed arc is one in which they are included in a glass vessel. If carbons impregnated with various salts are used to colour or increase the light, the arc is called a chemical or flame arc. The carbons or electrodes may be arranged in line one above the other, or they may be inclined so as to project the light downwards or more in one direction. In a carbon arc if the current is continuous the positive carbon becomes much hotter at the end than the negative, and in the open air it is worn away, partly by combustion, becoming hollowed out at the extremity into a _crater_. At the same time the negative carbon gradually becomes pointed, and also wears away, though much less quickly than the positive. In the continuous-current open arc the greater part of the light proceeds from the highly incandescent positive crater. When the arc is examined through dark glasses, or by the optical projection of its image upon a screen, a violet band or stream of vapour is seen to extend between the two carbons, surrounded by a nebulous golden flame or aureole. If the carbons are maintained at the right distance apart the arc remains steady and silent, but if the carbons are impure, or the distance between them too great, the true electric arc rapidly changes its place, flickering about and frequently becoming extinguished; when this happens it can only be restored by bringing the carbons once more into contact. If the current is alternating, then the arc is symmetrical, and both carbons possess nearly the same appearance. If it is enclosed in a vessel nearly air-tight, the rate at which the carbons are burnt away is greatly reduced, and if the current is continuous the positive carbon is no longer cratered out and the negative no longer so much pointed as in the case of the open arc.

Carbons.

Davy used for his first experiments rods of wood charcoal which had been heated and plunged into mercury to make them better conductors. Not until 1843 was it proposed by J. B. L. Foucault to employ pencils cut from the hard graphitic carbon deposited in the interior of gas retorts. In 1846 W. Greener and W. E. Staite patented a process for manufacturing carbons for this purpose, but only after the invention of the Gramme dynamo in 1870 any great demand arose for them. F. P. É. Carré in France in 1876 began to manufacture arc lamp carbons of high quality from coke, lampblack and syrup. Now they are made by taking some specially refined form of finely divided carbon, such as the soot or lampblack formed by cooling the smoke of burning paraffin or tar, or by the carbonization of organic matter, and making it into a paste with gum or syrup. This carbon paste is forced through dies by means of a hydraulic press, the rods thus formed being subsequently baked with such precautions as to preserve them perfectly straight. In some cases they are _cored_, that is to say, have a longitudinal hole down them, filled in with a softer carbon. Sometimes they are covered with a thin layer of copper by electro-deposition. They are supplied for the market in sizes varying from 4 or 5 to 30 or 40 millimetres in diameter, and from 8 to 16 in. in length. The value of carbons for arc lighting greatly depends on their purity and freedom from ash in burning, and on perfect uniformity of structure. For ordinary purposes they are generally round in section, but for certain special uses, such as lighthouse work, they are made fluted or with a star-shaped section. The positive carbon is usually of larger section than the negative. For continuous-current arcs a cored carbon is generally used as a positive, and a smaller solid carbon as a negative. For flame arc lamps the carbons are specially prepared by impregnating them with salts of calcium, magnesium and sodium. The calcium gives the best results. The rod is usually of a composite type. The outer zone is pure carbon to give strength, the next zone contains carbon mixed with the metallic salts, and the inner core is the same but less compressed. In addition to the metallic salts a flux has to be introduced to prevent the formation of a non-conducting ash, and this renders it desirable to place the carbons in a downward pointing direction to get rid of the slag so formed. Bremer first suggested in 1898 for this purpose the fluorides of calcium, strontium or barium. When such carbons are used to form an electric arc the metallic salts deflagrate and produce a flame round the arc which is strongly coloured, the object being to produce a warm yellow glow, instead of the somewhat violet and cold light of the pure carbon arc, as well as a greater emission of light. As noxious vapours are however given off, flame arcs can only be used out of doors. Countless researches have been made on the subject of carbon manufacture, and the art has been brought to great perfection.

Special manuals must be consulted for further information (see
especially a treatise on _Carbon making for all electrical purposes_,
by F. Jehl, London, 1906).

Physical phenomena.

The physical phenomena of the electric arc are best examined by forming a carbon arc between two carbon rods of the above description, held in line in a special apparatus, and arranged so as to be capable of being moved to or from each other with a slow and easily regulated motion. An arrangement of this kind is called a _hand-regulated arc lamp_ (fig. 4). If such an arc lamp is connected to a source of electric supply having an electromotive force preferably of 100 volts, and if some resistance is included in the circuit, say about 5 ohms, a steady and continuous arc is formed when the carbons are brought together and then slightly separated. Its appearance may be most conveniently examined by projecting its image upon a screen of white paper by means of an achromatic lens. A very little examination of the distribution of light from the arc shows that the illuminating or candle-power is not the same in different directions. If the carbons are vertical and the positive carbon is the upper of the two, the illuminating power is greatest in a direction at an angle inclined about 40 or 50 degrees below the horizon, and at other directions has different values, which may be represented by the lengths of radial lines drawn from a centre, the extremities of which define a curve called the _illuminating curve_ of the arc lamp (fig. 5). Considerable differences exist between the forms of the illuminating-power curves of the continuous and alternating current and the open or enclosed arcs. The chief portion of the emitted light proceeds from the incandescent crater; hence the form of the illuminating-power curve, as shown by A. P. Trotter in 1892, is due to the apparent area of the crater surface which is visible to an eye regarding the arc in that direction. The form of the illuminating-power curve varies with the length of the arc and relative size of the carbons. Leaving out of account for the moment the properties of the arc as an illuminating agent, the variable factors with which we are concerned are (i.) the current through the arc; (ii.) the potential difference of the carbons; (iii.) the length of the arc; and (iv.) the size of the carbons. Taking in the first place the typical direct-current arc between solid carbons, and forming arcs of different lengths and with carbons of different sizes, it will be found that, beginning at the lowest current capable of forming a true arc, the potential difference of the carbons (the arc P.D.) decreases as the current increases. Up to a certain current strength the arc is silent, but at a particular critical value P.D. suddenly drops about 10 volts, the current at the same time rising 2 or 3 amperes. At that moment the arc begins to _hiss_, and in this hissing condition, if the current is still further increased, P.D. remains constant over wide limits. This drop in voltage on hissing was first noticed by A. Niaudet (_La Lumière électrique_, 1881, 3, p. 287). It has been shown by Mrs Ayrton (_Journ. Inst. Elec. Eng._ 28, 1899, p. 400) that the hissing is mainly due to the oxygen which gains access from the air to the crater, when the latter becomes so large by reason of the increase of the current as to overspread the end of the positive carbon. According to A. E. Blondel and Hans Luggin, hissing takes place whenever the current density becomes greater than about 0.3 or 0.5 ampere per square millimetre of crater area.

The relation between the current, the carbon P.D., and the length of
arc in the case of the direct-current arc has been investigated by
many observers with the object of giving it mathematical expression.

Let V stand for the potential difference of the carbons in volts, A
for the current through the arc in amperes, L for the length of the
arc in millimetres, R for the resistance of the arc; and let a, b, c,
d, &c., be constants. Erik Edlund in 1867, and other workers after
him, considered that their experiments showed that the relation
between V and L could be expressed by a simple linear equation,

V = a + bL.

Later researches by Mrs Ayrton (Electrician, 1898, 41, p. 720),
however, showed that for a direct-current arc of given size with solid
carbons, the observed values of V can be better represented as a
function both of A and of L of the form

c + dL
V = a + bL + ------.
A

In the case of direct-current arcs formed with solid carbons, Edlund
and other observers agree that the arc resistance R may be expressed
by a simple straight line law, R = e + fL. If the arc is formed with
cored carbons, Mrs Ayrton demonstrated that the lines expressing
resistance as a function of arc length are no longer straight, but
that there is a rather sudden dip down when the length of the arc is
less than 3 mm.

The constants in the above equation for the potential difference of
the carbons were determined by Mrs Ayrton in the case of solid carbons
to be--

11.7 + 10.5L
V = 38.9 + 2.07L + ------------.
A

There has been much debate as to the meaning to be given to the
constant a in the above equation, which has a value apparently not far
from forty volts for a direct-current arc with solid carbons. The
suggestion made in 1867 by Edlund (_Phil. Mag._, 1868, 36, p. 358),
that it implied the existence of a counter-electromotive force in the
arc, was opposed by Luggin in 1889 (_Wien. Ber._ 98, p. 1198), Ernst
Lecher in 1888 (_Wied. Ann._, 1888, 33, p. 609), and by Franz Stenger
in 1892 (_Id._ 45, p. 33); whereas Victor von Lang and L. M. Arons in
1896 (_Id._ 30, p. 95), concluded that experiment indicated the
presence of a counter-electromotive force of 20 volts. A. E. Blondel
concludes, from experiments made by him in 1897 (_The Electrician_,
1897, 39, p. 615), that there is no counter-electromotive force in the
arc greater than a fraction of a volt. Subsequently W. Duddëll (_Proc.
Roy. Soc._, 1901, 68, p. 512) described experiments tending to prove
the real existence of a counter-electromotive force in the arc,
probably having a thermo-electric origin, residing near the positive
electrode, and of an associated lesser adjuvant _e.m.f._ near the
negative carbon.

This fall in voltage between the carbons and the arc is not uniformly
distributed. In 1898 Mrs Ayrton described the results of experiments
showing that if V1 is the potential difference between the positive
carbon and the arc, then

9 + 3.1L
V1 = 31.28 + --------;
A

and if V2 is the potential difference between the arc and the negative
carbon, then

13.6
V2 = 7.6 + ----,
A

where A is the current through the arc in amperes and L is the length
of the arc in millimetres.

The total potential difference between the carbons, minus the fall in
potential down the arc, is therefore equal to the sum of V1 + V2 = V3.

22.6 + 3.1L
Hence V3 = 38.88 + -----------.
A

The difference between this value and the value of V, the total
potential difference between the carbons, gives the loss in potential
due to the true arc. These laws are simple consequences of
straight-line laws connecting the work spent in the arc at the two
electrodes with the other quantities. If W be the work spent in the
arc on either carbon, measured by the product of the current and the
potential drop in passing from the carbon to the arc, or vice versa,
then for the positive carbon W = a + bA, if the length of arc is
constant, W = c + dL, if the current through the arc is constant, and
for the negative carbon W = e + fA.

In the above experiments the potential difference between the carbons
and the arc was measured by using a third exploring carbon as an
electrode immersed in the arc. This method, adopted by Lecher, F.
Uppenborn, S. P. Thompson, and J. A. Fleming, is open to the objection
that the introduction of the third carbon may to a considerable extent
disturb the distribution of potential.

The total work spent in the continuous-current arc with solid carbons
may, according to Mrs Ayrton, be expressed by the equation

W = 11.7 + 10.5L + (38.9 + 2.07L)A.

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.)

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.

The general phenomena of the alternating-current arc are as follow:--

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.

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.

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).

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].

Let r denote the radius PT of the zone of the sphere, then

r = R cos [theta].

Hence the area of the zone swept out by PQ is equal to

2[pi]R cos [theta] ds = 2[pi]R² cos [theta] d[theta]

in the limit, and the total quantity of light falling on the zone is
equal to the product of the mean intensity or candle-power I in the
direction AP and the area of the zone, and therefore to

2[pi]IR² cos [theta] d[theta].

Let I0 stand for the mean spherical candle-power, that is, let I0 be
defined by the equation

4[pi]R²I0 = 2[pi]R[Sigma](Iab)

where [Sigma](Iab) is the sum of all the light actually falling on
the sphere surface, then

1
I0 = -- [Sigma](Iab)
2R

[Sigma](Iab)
= ------------ I_(max)
2RI_(max)

where I_(max) stands for the maximum candle-power of the arc. If,
then, we set off at b a line bH perpendicular to DE and in length
proportional to the candle-power of the arc in the direction AP, and
carry out the same construction for a number of different observed
candle-power readings at known angles above and below the horizon, the
summits of all ordinates such as bH will define a curve DHE. The mean
spherical candle-power of the arc is equal to the product of the
maximum candle-power (I_(max)), and a fraction equal to the ratio of
the area included by the curve DHE to its circumscribing rectangle
DFGE. The area of the curve DHE multiplied by 2[pi]/R gives us the
_total flux of light_ from the arc.

Owing to the inequality in the distribution of light from an electric
arc, it is impossible to define the illuminating power by a single
number in any other way than by stating the mean spherical
candle-power. All such commonly used expressions as "an arc lamp of
2000 candle-power" are, therefore, perfectly meaningless.

Photometry of arc.

The photometry of arc lamps presents particular difficulties, owing to the great difference in quality between the light radiated by the arc and that given by any of the ordinarily used light standards. (For standards of light and photometers, see PHOTOMETER.) All photometry depends on the principle that if we illuminate two white surfaces respectively and exclusively by two separate sources of light, we can by moving the lights bring the two surfaces into such a condition that their _illumination_ or _brightness_ is the same without regard to any small colour difference. The quantitative measurement depends on the fact that the illumination produced upon a surface by a source of light is inversely as the square of the distance of the source. The trained eye is capable of making a comparison between two surfaces illuminated by different sources of light, and pronouncing upon their equality or otherwise in respect of brightness, apart from a certain colour difference; but for this to be done with accuracy the two illuminated surfaces, the brightness of which is to be compared, must be absolutely contiguous and not separated by any harsh line. The process of comparing the light from the arc directly with that of a candle or other similar flame standard is exceedingly difficult, owing to the much greater proportion and intensity of the violet rays in the arc. The most convenient practical working standard is an incandescent lamp run at a high temperature, that is, at an efficiency of about 2½ watts per candle. If it has a sufficiently large bulb, and has been _aged_ by being worked for some time previously, it will at a constant voltage preserve a constancy in illuminating power sufficiently long to make the necessary photometric comparisons, and it can itself be compared at intervals with another standard incandescent lamp, or with a flame standard such as a Harcourt pentane lamp.

In measuring the candle-power of arc lamps it is necessary to have
some arrangement by which the brightness of the rays proceeding from
the arc in different directions can be measured. For this purpose the
lamp may be suspended from a support, and a radial arm arranged to
carry three mirrors, so that in whatever position the arm may be
placed, it gathers light proceeding at one particular angle above or
below the horizon from the arc, and this light is reflected out
finally in a constant horizontal direction. An easily-arranged
experiment enables us to determine the constant loss of light by
reflection at all the mirrors, since that reflection always takes
place at 45°. The ray thrown out horizontally can then be compared
with that from any standard source of light by means of a fixed
photometer, and by sweeping round the radial arm the photometric or
illuminating curve of the arc lamp can be obtained. From this we can
at once determine the nature of the illumination which would be
produced on a horizontal surface if the arc lamp were suspended at a
given distance above it. Let A (fig. 10) be an arc lamp placed at a
height h( = AB) above a horizontal plane. Let ACD be the illuminating
power curve of the arc, and hence AC the candle-power in a direction
AP. The illumination (I) or brightness on the horizontal plane at P is
equal to

AC cos APM/(AP)² = FC/(h² + x²), where x = BP.

Hence if the candle-power curve of the arc and its height above the
surface are known, we can describe a curve BMN, whose ordinate PM will
denote the brightness on the horizontal surface at any point P. It is
easily seen that this ordinate must have a maximum value at some
point. This brightness is best expressed in _candle-feet_, taking the
unit of illumination to be that given by a standard candle on a white
surface at a distance of 1 ft. If any number of arc lamps are placed
above a horizontal plane, the brightness at any point can be
calculated by adding together the illuminations due to each
respectively.

The process of delineating the photometric or polar curve of intensity
for an arc lamp is somewhat tedious, but the curve has the advantage
of showing exactly the distribution of light in different directions.
When only the mean spherical or mean hemispherical candle-power is
required the process can be shortened by employing an integrating
photometer such as that of C. P. Matthews (_Trans. Amer. Inst. Elec.
Eng._, 1903, 19, p. 1465), or the lumen-meter of A. E. Blondel which
enables us to determine at one observation the total flux of light
from the arc and therefore the mean spherical candle-power per watt.

Street arc lighting.

In the use of arc lamps for street and public lighting, the question of the distribution of light on the horizontal surface is all-important. In order that street surfaces may be well lighted, the minimum illumination should not fall below 0.1 candle-foot, and in general, in well-lighted streets, the maximum illumination will be 1 candle-foot and upwards. By means of an illumination photometer, such as that of W. H. Preece and A. P. Trotter, it is easy to measure the illumination in candle-feet at any point in a street surface, and to plot out a number of contour lines of equal illumination. Experience has shown that to obtain satisfactory results the lamps must be placed on a high mast 20 or 25 ft. above the roadway surface. These posts are now generally made of cast iron in various ornamental forms (fig. 11), the necessary conductors for conveying the current up to the lamp being taken inside the iron mast. (The pair of incandescent lamps halfway down the standard are for use in the middle of the night, when the arc lamp would give more light than is required; they are lighted by an automatic switch whenever the arc is extinguished.) The lamp itself is generally enclosed in an opalescent spherical globe, which is woven over with wire-netting so that in case of fracture the pieces may not cause damage. The necessary trimming, that is, the replacement of carbons, is effected either by lowering the lamp or, preferably, by carrying round a portable ladder enabling the trimmer to reach it. For the purpose of public illumination it is very usual to employ a lamp taking 10 amperes, and therefore absorbing about 500 watts. Such a lamp is called a 500-watt arc lamp, and it is found that a satisfactory illumination is given for most street purposes by placing 500-watt arc lamps at distances varying from 40 to 100 yds., and at a height of 20 to 25 ft. above the roadway. The maximum candle-power of a 500-watt arc enclosed in a roughened or ground-glass globe will not exceed 1500 candles, and that of a 6.8-ampere arc (continuous) about 900 candles. If, however, the arc is an enclosed arc with double globes, the absorption of light would reduce the effective maximum to about 200 c.p. and 120 c.p. respectively. When arc lamps are placed in public thoroughfares not less than 40 yds. apart, the illumination anywhere on the street surface is practically determined by the two nearest ones. Hence the total illumination at any point may be obtained by adding together the illuminations due to each arc separately. Given the photometric polar curves or illuminating-power curves of each arc taken outside the shade or globe, we can therefore draw a curve representing the resultant illumination on the horizontal surface. It is obvious that the higher the lamps are placed, the more uniform is the street surface illumination, but the less its average value; thus two 10-ampere arcs placed on masts 20 ft. above the road surface and 100 ft. apart will give a maximum illumination of about 1.1 and a minimum of about 0.15 candle-feet in the interspace (fig 12). If the lamps are raised on 40-ft. posts the maximum illumination will fall to 0.3, and the minimum will rise to 0.2. For this reason masts have been employed as high as 90 ft. In docks and railway yards high masts (50 ft.) are an advantage, because the strong contrasts due to shadows of trucks, carts, &c., then become less marked, but for street illumination they should not exceed 30 to 35 ft. in height. Taking the case of 10-ampere and 6.8-ampere arc lamps in ordinary opal shades, the following figures have been given by Trotter as indicating the nature of the resultant horizontal illumination:--

+-----------+------------+---------+------------------------+
| | | | Horizontal Illumination|
|Arc Current|Height above| Distance| in Candle-Feet. |
| in | Road | apart +-----------+------------+
| Amperes. | in Feet. | in Feet.| Maximum. | Minimum. |
+-----------+------------+---------+-----------+------------+
| 10 | 20 | 120 | 1.85 | 0.12 |
| 10 | 25 | 120 | 1.17 | 0.15 |
| 10 | 40 | 120 | 0.5 | 0.28 |
| 6.8 | 20 | 90 | 1.1 | 0.21 |
| 6.8 | 40 | 120 | 0.3 | 0.17 |
+-----------+------------+---------+-----------+------------+

As regards distance apart, a very usual practice is to place the lamps at spaces equal to six to ten times their height above the road surface. Blondel (_Electrician_, 35, p. 846) gives the following rule for the height (h) of the arc to afford the maximum illumination at a distance (d) from the foot of the lamp-post, the continuous current arc being employed:--

For naked arc h = 0.95 d.
" arc in rough glass globe h = 0.85 d.
" " opaline glob h = "
" " opal globe h = 0.5 d.
" " holophane globe h = 0.5 d.

These figures show that the distribution of light on the horizontal surface is greatly affected by the nature of the enclosing globe. For street illumination naked arcs, although sometimes employed in works and factory yards, are entirely unsuitable, since the result produced on the eye by the bright point of light is to paralyse a part of the retina and contract the pupil, hence rendering the eye less sensitive when directed on feebly illuminated surfaces. Accordingly, diffusing globes have to be employed. It is usual to place the arc in the interior of a globe of from 12 to 18 in. in diameter. This may be made of ground glass, opal glass, or be a dioptric globe such as the holophane. The former two are strongly absorptive, as may be seen from the results of experiments by Guthrie and Redhead. The following table shows the astonishing loss of light due to the use of opal globes:--

+--------------------------------------+-----+--------+-------+-------+
| | | Arc | Arc in| Arc |
| |Naked|in Clear| Rough |in Opal|
| | Arc.| Globe. | Glass | Globe.|
| | | | Globe.| |
+--------------------------------------+-----+--------+-------+-------+
| Mean spherical c.p. | 319 | 235 | 160 | 144 |
| Mean hemispherical c.p. | 450 | 326 | 215 | 138 |
| Percentage value of transmitted light| 100 | 53 | 23 | 19 |
| Percentage absorption | 0 | 47 | 77 | 81 |
+--------------------------------------+-----+--------+-------+-------+

By using Trotter's, Fredureau's or the holophane globe, the light may be so diffused that the whole globe appears uniformly luminous, and yet not more than 20% of the light is absorbed. Taking the absorption of an ordinary opal globe into account, a 500-watt arc does not usually give more than 500 c.p. as a maximum candle-power. Even with a naked 500-watt arc the mean spherical candle-power is not generally more than 500 c.p., or at the rate of 1 c.p. per watt. The maximum candle-power for a given electrical power is, however, greatly dependent on the current density in the carbon, and to obtain the highest current density the carbons must be as thin as possible. (See T. Hesketh, "Notes on the Electric Arc," _Electrician_, 39, p. 707.)

For the efficiency of arcs of various kinds, expressed by the mean hemispherical candle power per ampere and per watt expended in the arc, the following figures were given by L. Andrews ("Long-flame Arc Lamps," _Journal Inst. Elec. Eng.,_ 1906, 37, p. 4).

Candle-power Candle-power
per ampere. per watt.
Ordinary open carbon arc 82 1.54
Enclosed carbon arc 55 0.77
Chemical carbon or flame arc 259 5.80
High voltage inclined carbon arc 200 2.24

It will be seen that the flame arc lamp has an enormous advantage over other types in the light yielded for a given electric power consumption.

Arc lamp mechanism.

The practical employment of the electric arc as a means of illumination is dependent upon mechanism for automatically keeping two suitable carbon rods in the proper position, and moving them so as to enable a steady arc to be maintained. Means must be provided for holding the carbons in line, and when the lamp is not in operation they must fall together, or come together when the current is switched on, so as to start the arc. As soon as the current passes, they must be moved slightly apart, and gripped in position immediately the current reaches its right value, being moved farther apart if the current increases in strength, and brought together if it decreases. Moreover, it must be possible for a considerable length of carbon to be fed through the lamp as required.

One early devised form of arc-lamp mechanism was a system of clockwork
driven by a spring or weight, which was started and stopped by the
action of an electromagnet; in modern lighthouse lamps a similar
mechanism is still employed. W. E. Staite (1847), J. B. L. Foucault
(1849), V. L. M. Serrin (1857), J. Duboscq (1858), and a host of later
inventors, devised numerous forms of mechanical and clockwork lamps.
The modern self-regulating type may be said to have been initiated in
1878 by the differential lamp of F. von Hefner-Alteneck, and the
clutch lamp of C. F. Brush. The general principle of the former may be
explained as follows: There are two solenoids, placed one above the
other. The lower one, of thick wire, is in series with the two carbon
rods forming the arc, and is hence called the _series coil_. Above
this there is placed another solenoid of fine wire, which is called
the _shunt coil_. Suppose an iron rod to be placed so as to be partly
in one coil and partly in another; then when the coils are traversed
by currents, the iron core will be acted upon by forces tending to
pull it into these solenoids. If the iron core be attached to one end
of a lever, the other end of which carries the upper carbon, it will
be seen that if the carbons are in contact and the current is switched
on, the series coil alone will be traversed by the current, and its
magnetic action will draw down the iron core, and therefore pull the
carbons apart and strike the arc. The moment the carbons separate,
there will be a difference of potential between them, and the shunt
coil will then come into action, and will act on the core so as to
draw the carbons together. Hence the two solenoids act in opposition
to each other, one increasing and the other diminishing the length of
the arc, and maintaining the carbons in the proper position. In the
lamp of this type the upper carbon is in reality attached to a rod
having a side-rack gearing, with a train of wheels governed by a
pendulum. The action of the series coil on the mechanism is to first
lock or stop the train, and then lift it as a whole slightly. This
strikes the arc. When the arc is too long, the series coil lowers the
gear and finally releases the upper carbon, so that it can run down by
its own weight. The principle of a shunt and series coil operating on
an iron core in opposition is the basis of the mechanism of a number
of arc lamps. Thus the lamp invented by F. Krizik and L. Piette,
called from its place of origin the Pilsen lamp, comprises an iron
core made in the shape of a double cone or spindle (fig. 13), which is
so arranged in a brass tube that it can move into or out of a shunt
and series coil, wound the one with fine and the other with thick
insulated wire, and hence regulate the position of the carbon attached
to it. The movement of this core is made to feed the carbons directly
without the intervention of any clockwork, as in the case of the
Hefner-Alteneck lamp. In the clutch-lamp mechanism the lower carbon is
fixed, and the upper carbon rests upon it by its own weight and that
of its holder. The latter consists of a long rod passing through
guides, and is embraced somewhere by a ring capable of being tilted or
lifted by a finger attached to the armature of an electromagnet the
coils of which are in series with the arc. When the current passes
through the magnet it attracts the armature, and by tilting the ring
lifts the upper carbon-holder and hence strikes the arc. If the
current diminishes in value, the upper carbon drops a little by its
own weight, and the feed of the lamp is thus effected by a series of
small lifts and drops of the upper carbon (fig. 14). Another element
sometimes employed in arc-lamp mechanism is the brake-wheel regulator.
This is a feature of one form of the Brockie and of the
Crompton-Pochin lamps. In these the movement of the carbons is
effected by a cord or chain which passes over a wheel, or by a rack
geared with the brake wheel. When no current is passing through the
lamp, the wheel is free to move, and the carbons fall together; but
when the current is switched on, the chain or cord passing over the
brake wheel, or the brake wheel itself is gripped in some way, and at
the same time the brake wheel is lifted so that the arc is struck.