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taken to be the boiling-point of carbon. That carbon is volatilized in the arc is undoubtedly a fact. The surface of the crater has the appearance of boiling ; the hissing noise occurring with excessive current density is similar to that produced by violent boiling of water, and may result from the same cause, though carbon, like arsenic, vaporizes directly from the solid state. Carbon consumption goes on in a vacuum, although at a slower rate than in air, and the vapor thus formed condenses on the sides of the inclosing chamber. These facts all go to show that carbon is actually evaporated. Such being the case, the temperature of the surface of the carbon would naturally remain stationary at this boiling-point, like the temperature of boiling water at atmospheric pressure, whatever the heat applied. The temperature of the negative carbon, except at its extreme point, is considerably lower than that of the positive. The difference is due to the fact that the larger part of the energy is transformed into heat at or near the surface of the positive carbon. This is evident from the relative appearance of the two electrodes and is demonstrated experimentally by measuring the distribution of potential between the carbons. The most reliable observations show that about 40 volts drop occurs between the positive and the arc stream, with only 24 volts in the stream and 24 volts between the stream and the negative carbon.
The temperature of the space between the carbons may be much higher than that of the surface in the same way that steam can be superheated above the point at which it is evaporated, there being, in fact, no limit to the possible rise in temperature. Since the current is conducted by the highly heated vapor present, it is to be expected that such a conductor will be heated by the passage of a current the same as a solid or a liquid.
Theory. - It is evident that the amount of carbon vaporized at the positive crater forming the arc stream will vary with the current, therefore the resistance of the arc, which varies inversely with its cross-section, varies inversely with the current. In this respect the arc is totally unlike solid or liquid conductors, whose resistance is independent of the current, other conditions remaining the same. Hence Ohm's law in its general form is inapplicable to the arc stream.
The fact that the phenomena at the arc are more or less reversible, since the vaporized carbon can again be converted into the solid state by condensation, points to the existence of a counterelectro-motive force, and since the temperature of the vaporization is constant, or nearly so, the counter electro-motive force should also be constant, which appears to be the case. Physicists have long sought to isolate and determine this experimentally, and it would seem that such a definite physical problem could easily be solved ; but there are peculiar difficulties, which up to the present time have rendered all methods and results questionable. There are great difficulties connected with retaining the arc, whose carbons are constantly changing, at a constant condition, and a long time is required to permit the arc to assume a stationary state. Further, the depth of the crater, and consequently the true length of the arc, is very hard to measure at any given moment. Again, the resistance varies with the length of the arc and in some inverse ratio with the current. Add to this the difficulty of securing pure carbons whose density, electrical conductivity, and heat conductivity are uniform throughout, and the utter impossibility of retaining the counter-electro-motive force after the current which induces it has ceased to flow, and the difficulties become more apparent. By indirect methods an approximate value of 35 to 394 volts has been arrived at for arcs of 10 amperes and 45 volts and pure carbons. . The indications point to a counterelectro-motive force at the arc, variable with the current and other conditions. In fact, it is very likely that it consists of a combination of two or perhaps more separate electro-motive forces; one due to the volatilization of the carbon, another due to the thermoelectric effect at the positive carbon, and perhaps still another thermo-electric potential at the negative carbon.
Voltage dependent on Boiling Point. — From what has already been said, it seems probable that whatever tends to raise the boiling point of carbon will likewise raise the voltage required to maintain an arc, a conclusion confirmed by experiment. Increase of atmospheric pressure, other conditions being constant, increases the arc voltage. Similarly we should be able to reduce the voltage by lowering the vaporizing point of the crater, an effect which is found to result when more volatile substances, such as the salts of the earth metals, are introduced, usually in the form of a core.
Resistance. — The resistance of an arc, like that of any other conductor, increases with its actual length, and diminishes with its cross-section. The length of an arc usually given is the apparent length; that is, the distance from the edge of the crater to the tip of the negative. The true length is, of course, the distance from the bottom of the crater to the tip of the negative. A case may easily be imagined where, owing to the varying depth of the crater, the apparent length might be diminished yet the actual length increased. Failure to distinguish between these two is apt to result in misleading conclusions. The cross-section of the arc varies at different points between the carbons, since it has a tendency to spread out from electric repulsion, which causes its section to be greatest about midway between the carbon points. The arc stream tends to spread out farther as the carbons are drawn apart. The area of the crater, which is, of course, one end of the arc stream, has been found by Ayrton to vary approximately according to this law : D = .128 x .15 A ; where D is the diameter in inches, and A is the current expressed in amperes.
The resistance of the 10-ampere arc is it to ļ an ohm for arc lengths from about to to an g of an inch in length. Houston and Kennelly give 5 ohms per inch as a rough general value.
Carbons. — There are two classes of carbons used in arc lighting, solid and cored. They may be of any diameter. For the sizes usually employed the average resistance is 0.15 ohms per foot
Solid carbons vary according to their purity, molecular structure, and hardness. Cored carbons are solid except for a hole running axially through the carbon, filled with some material more soft and volatile than the remaining carbon — being usually a mixture of carbon and some metallic salt.
Object of Core. The object of this core is first to decrease the voltage for a given length of arc, as already explained, or to increase the length for a given voltage. This has the initial effect of reducing any irregularity in carbons or the feeding mechanism to a less percentage of the whole length. Further, the core, by affording a plentiful supply of vapor, tends to maintain a stable condition of the arc. It also keeps the arc located in one spot, and prevents the tendency to travel irregularly around the carbon due to the arc seeking the path of least resistance. When this traveling occurs it gives rise to an objectionable flicker, owing to the shadow
of the carbons being shifted in different directions, and to the variations of energy which occur faster than the mechanism can follow. A core may be employed also to modify the color of the light, as for instance to produce a yellowish tinge due to the well-known sodium flame. With these facts in mind, we can explain many phenomena found in arcs as used in practice.
Carbon Consumption. — With similar carbons placed vertically one over the other, the relative consumption will depend on the amount carried off by :
Volatilization and electrolytic action.
When carbons of different diameters are used, their life increases roughly in proportion to their sectional area, barring the oxidation of the air. The latter is frequently reduced, and the conductivity of the carbon increased, by plating about nine-tenths of their cylindrical surface with a thin layer of copper, leaving the tip uncoated; but the primary object of the plating is to reduce the contact resistance of the carbon.
Volts and Amperes. — The volts and amperes required depend greatly upon circumstances; but for the open arcs usually employed, the amperes range from six to ten, and the volts from forty-two to fifty-two: a common value would be 47 volts and 9.6 amperes. In search-light projectors much heavier currents are frequently employed, from 50 to 150 or 200 amperes, with voltages from 48 to 53. With these heavy currents, the carbons become hotter, and are oxidized farther back from the ends, resulting in longer points.
Physical Phenomena. — The positive carbon wastes away electrolytically inside of the crater, and by the action of the air outside of the crater, causing it to waste away about twice as rapidly as the negative in the open arc. The negative carbon is consumed by oxidation of the air alone, according as its temperature is increased by the carbon particles deposited on it, and by the heat reverberated from the positive crater. The closer the positive approaches the negative, the greater will be its roasting effect on the latter. With very short arcs, the deposit of graphitic carbon upon the negative accumulates faster than it wastes away, so that it forms a nib or second point on the top of the negative which finally
crumbles away. This action may or may not be accompanied by a hissing noise.
Carbon turns to Graphite. Carbon that has been exposed to the heat of the arc turns to graphite. The hard pencils of solid carbon used for high-tension lamps will not mark paper before being used. After having been burned a few minutes the tip of the negative will write black like a pencil, and even the point of the positive will show some graphite.
Electrical Relations. — With both solid and cored carbons a point may be reached when the voltage will be constant if the arc length and current are kept the same. This is called the stationary state. In Fig. 259 the relation of the voltage to
current is plotted for several apparent arc lengths with both carbons cored. It will be noted that with short arcs, less than ay inch long, the voltage rises as the current increases, due to the increased CR drop. With arcs longer than a inch, on the other hand, the voltage falls with increasing current, due to the expansion of the long arc, whose larger cross-section more than compensates for the drop caused by increasing current. This, at one time, gave rise to a theory that the arc had a negative resistance, an entirely unwarranted conclusion. For arcs of is inch, the spreading action of the stream exactly counterbalances the increase current; so that for this arc length the voltage remains constant within wide Auctuations of current. In arcs shorter than d' inch the stream has no room to spread laterally. Another reason for