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By Albert A. Mathews

OUTCROPS of gypsum rock near the present site of the city of Gland Rapids, Mich., were known to fur traders early in the nineteenth century. However, the deposits seemed without value and were not worked for some time. So far as cat1 be learned, Michigan gyp- sum was first used by a plasterer who settled in Grand Rapids in 1834 as a member of its fourteenth white family. In building a house for one of the early traders, be used some otnamental stucco mouldings manufactured from the local gypsum deposits for decorations in the gables and around some circular windows. The gypsum was broken out with a hammer, ground in an Indian corn mill, and burlled in a caulclron kettle,. After two attempts, the ornaments were successfully set, and remained on the house until it was destroyed by fire in 1850.

Jan 1, 1936

By H. L. Gilbert, C. T. Anderson, W. J. Kroll

In a previous paper,' the use of a split graphite tube resistor as a heater element for high-temperature furnaces has been described. The principal advantages of this type of construction are: I. The quadruple resistance or voltage compared with the top-bottom clamp resistor furnace. 2. Free expansion of the resistor. 3. The ease of protection from oxidation by air. 4. The firmness by which it may be held in the compact split clamp. This construction appeared to be well adapted for the fusion of high melting metals which require fusion in a vacuum. Zirconium metal had previously been melted at the Albany Laboratory of the Bureau of Mines in a vacuum arc furnace on a water-cooled plate, using a movable tungsten top electrode.% When larger furnace capacities were desired, this type of construction proved to have its limitations as the largest tungsten rods available were about 7/8 in. in diameter. The supply of direct current of high amperage for producing the desired arc characteristics was also not available. Considerable difficulty was also found in compensating the atmospheric pressure on the flcxible tubing of the movable electrodc, at the same time keeping its movement sufficiently free to enable the striking of an arc on any part of the metal briquet. Among the various materials used for the electrodes in conducting experiments in the vacuum arc furnace was graphite. It was found that zirconium fused in a graphite cup with a carbon arc was contaminated to only 0.2 pct carbon. It was therefore decsed to melt zirconium directly in graphite crucibles. A high-frequency furnace was first used in the attempt to melt the zirconium in graphite crucibles. The high-frequency heating coil was placed outside a silica tube which was evacuated by means of an oil diffusion pump backed up by a mechanical pump. The graphite crucible was thoroughly degassed at 19oo"C before use. Considerable difficulty was experienced in operating at such temperatures in vacuo because, as shown by Zintl,3 carbon vapor formed and reacted with silica accortling to the reaction: SiO² + C = SiO + CO. The silicon monoxide which is volatile at these high temperatures reacted with the zirconium, thereby contaminating it with silicon and oxygen. The presence of carbon monoxide was detected by means of a gas discharge tube placed in the vacuum system as indicated by the pale blue glow of the tube as soon as carbon vapor started to react with the hot silica. The reaction between the carbon vapor and hot silica was avoided by the use of split cylindrical molybdenum shields which were inserted between the graphite crucible

Jan 1, 1949

By L. A. Roe, John Jan

Iodine is a soft, lustrous, grayish-black nonmetallic element with a density of 4.9. It is the least active of the four members of the halogen family. The other members are, in order of increasing activity, bromine, chlorine, and fluorine. Iodine is a solid at ordinary temperatures, while bromine is a liquid and chlorine and fluorine are gases. Iodine melts at 113°C and volatilizes at 184.4°C to a blue-violet gas with an irritating odor. It occurs in nature only as iodates and iodides or other combined forms. It was discovered by Bernard Courtois in France in 1811, who noticed its presence as an unknown substance in crude soda ash obtained from burning seaweed. Gay-Lussac recognized it as a new element and named it iode, from the Greek word "ioeides or iodes" for violet color (MacMillan, 1970). The world production is not known with any great certainty, but it is probably between 25 and 35 million lb per year, of which about 30% is consumed in the United States. Geology and Mineralogy Iodine compounds occur as a minor constituent as a mineral in the Chilean nitrate deposits and in solution in brines and seawater. According to the US Geological Survey, it is the 47th most abundant element in the earth's crust. The minerals lautarite, Ca (I03)3 (calcium iodate), and dietzeite, Cat (103)2 (CrO4), (calcium iodate-chromate) are found in Chilean nitrate deposits which are located in Antofagasta and Tarapaca provinces on the eastern slope of the coast range in a desert area. Various brines contain iodine compounds. Seawater contains about 0.05 ppm of iodine and some seaweeds will extract and accumulate it up to 0.45% on a dry basis. Some coals in West Germany also contain iodine compounds. The known and potential sources of iodine reported in 1968 are given in Table 1. Table 2 lists estimated world iodine reserves. Iodine has been recovered from brines in Java, Indonesia, France, England, and the USSR. Iodine has also been recovered from seaweed in Ireland, Scotland, France, Japan, Norway, and the USSR. The indicated reserves and future resources of iodine are large but have never been adequately measured. Analysis Iodine as the free element can be detected by the characteristic blue color it gives to a starch solution. Quantitatively it is determined as the free element by titration with standard thiosulfate solutions using starch as an indicator. Colorimetric methods are also applicable. Markets and Prices Iodine and its compounds are generally marketed in the form of: iodine, crude; iodine, resublimed; calcium iodates; calcium iodide; potassium iodide, sodium iodide, and numerous organic compounds. Product Specifications Crude iodine, World market: 99-99.5% 12. Crude iodine, US produced, average: 99.8% 12. Crude iodine, USP XVII Specs: not less than 99.8% percent I2. Resublimed iodine is usually 99.9% and ACS specifications call for not over 0.005% total bromine and 0.020% nonvolatile materials (Anon., 1971). Prices, c.i.f. United States, for iodine have been steadily increasing from $1.18 per lb of crude in 1967 to $6.37-7.27 in January 1981 (Anon., 1981). In 1980 the price of iodine increased by 50%.

Jan 1, 1983

By B. F. Fackenthal

For the past year we have had in use at the Durham furnace a set of hollow pig-patterns made of iron, which have given such satis factory results that I think a description of them would be of interest to the members of the Institute. Before the introduction of these iron patterns, we used the ordi nary wooden patterns, made in the usual way with straps of iron along the sides to protect the corners from wearing off. The size and shape of these wooden patterns are shown in Fig. 1. When the patterns were new, the pigs weighed about 130 pounds each, and were uniform in size, and the moulding was clean. But constant use soon wore the patterns away; and at the end of a few months, the pigs had become, in consequence, so much lighter that the moulding, daily, of several additional beds was necessary to accommodate the same quantity of iron. As the patterns wear away, the moulding becomes ragged and the pigs rough. Moreover, wooden patterns are often destroyed by fire. I have known an entire set to be destroyed by a break-out of iron. The iron pattern which I have designed is free from all the objections to the wooden pattern, being not only more durable, but, in the long run, far cheaper. The iron pattern having the same shape and size as the wooden one, is made of the best flange-iron, of No. 13 gauge. After the sheets have been cut to the proper size, three heats are required for the flanging. At the first heat, each piece is stamped in a cast-iron form, which gives the proper shape to the bottom part of the pat-

Jan 1, 1889

By J. Jolly, R. V. Wheeler

This short note on the probable character of the organic sulfur compounds in coal can do no more than indicate lines of research. We have no new experimental work to describe, nothing comparable in value with the careful studies of American coals by Powell and Parrl and Yancey and Frazer. A study of the manner in which sulfur compounds exist in British coals (and their behavior on heat treatment) is rendered increasingly necessary by the fact that the British reserves of good coking coals of reasonably low sulfur content are fast being depleted. We believe that it is essentially by a study of the modes of formation, occurrence, and decomposition of the various types of inorganic and organic sulfur compounds in coal that it will be possible, with hope of success, to attack the problem of purifying coals, otherwise eminently suitable for coking, from these objectionable ingredients. Sulfur, so far as is at present known, does not normally occur in the free state in the coal conglomerate, but is chiefly distributed, irregularly, in three forms : 1. As primary constituents of the coal conglomerate, organic in nature and probably associated with those molecular complexes that have resulted from the degradation of the proteins of the plant tissues responsible for the formation of the coal mass. These constituents can be classed as "organic sulfur." 2. As metallic sulfides, e.g., iron pyrites. 3. As metallic sulfates, e.g., calcium sulfate and ferrous sulfate. (The occurrence of these compounds varies with the occurrence and degree of degradation of class 2.) It is usually found that sulfur compounds of class 3, the metallic sulfates, are present in coal in small proportions only, amounting to about 1 or 1.5 per cent. of the total sulfur. The compounds in classes 1 and 2 are therefore of more importance. Class 1 alone will receive considera-

Jan 1, 1925

By Blair R. Benner

This paper describes the installation and operation of a Texas Nuclear on-line silica analyzer (NOLA) coupled with a Leeds and Northrup Microtrac particle-size monitor (Microtrac) at U.S. Steel's Minntac taconite concentrator. An automatic sampling system provides the NOLA with samples of final concentrate. After the sample is analyzed for silica by the NOLA, it is pumped to the Microtrac for size and surface area measurement. A sample is analyzed every six minutes, providing the control room with the silica concentration, the percent passing 270, 400, and 500 mesh, and an equivalent Blaine surface area number. When fed a slurry of final concentrate containing between 20 and 70% solids and 5 to 6% silica, the NOLA analysis is within ±0.2% of the wet chemistry silica. The agreement between the Microtrac output and standard screen analyses is ±1.2% at 270 mesh; ±1.5% at 400 mesh, and ±2% at 500 mesh. The poorer disagreement at the finer sizes is mainly due to inaccuracies in screening at 400 and 500 mesh. The agreement between Microtrac surface area a d laboratory Blaine surface area is about 9 ±80 cm 2/g. These instruments provide rapid and reliable feedback information to the concentrator and feed forward information to the agglomerator.

Jan 1, 1984

By E. S. Tankins, G. R. Belton

A simple solution model, based upon the formation of molecular species, is developed for strongly electronegative dilute solutes in liquid binary-metallic solvents. Two approximations are considered for the relative concentrations of the species: the random and the quasi-chemical. Equations are presented for the partial molar free energy, enthalpy, and entropy of mixing of the solute. An experimental study has been made of equilibrium in the reaction H2 6) +0 (dissolved) = H2O(g))for the liquid Cu-Co alloys. The standard free energy of solution of oxygen is presented as a function of composition for the alloys at 1550°C and as a function of temperature for five of the alloys. The experimental results for these alloys and also for Cu-Ni alloys are shown to be in reasonable agreernent with the theory in the random approximation. A knowledge of the thermodynamic behavior of dilute solutes in liquid metals and alloys is of importance in understanding and designing refining and alloy-making processes. Accordingly, several attempts have been made to derive suitable solution models to forecast the effect of a third component on the activity coefficient of such a solute in a metal. Alcock and Richardson' reviewed the literature prior to 1958 and also showed that a regular solution model gave a reasonable description in the case of metallic solutes but failed to account for the behavior of the more electronegative solutes sulfur and oxygen. These same authors2 later modified their model by using the quasi-chemical approximation3 to calculate the average composition of the first coordination shell surrounding each solute atom. This modified model was shown to lead to a better qualitative description of the behavior of the electronegative solutes; however, quantitative agreement with experimental data for oxygen in alloys could only be achieved by assuming a very small coordination number. The authors concluded that the major source of error in the model was the assumption that pairwise interaction energies were independent of composition. Substitutional and interstitial random solution models by Wada and saito4 are essentially similar to the first model except that the required interchange energies were derived from the modified solubility parameter equation of Mott, instead of from experimental binary data. Most recently Hoch5 has presented a statistical model for interstitial solutions and has applied the model to the Fe-C-O system. However, as the various interaction energies needed in the model had to be derived from the ternary data, the model does not promise well as a means of forecasting ternary behavior. Each of the above models carries the assumption that the strongly electronegative solutes have the same configurational environment as metallic solutes; i.e., the solute can be treated as a substitutional or interstitial atom in a quasi-crystalline lattice and is surrounded by a normal coordination shell of solvent atoms. There are, however, a number of facts which suggest that this is unlikely. First, the heats of solution are large, being more typical of molecule formation rather than alloying. For example, the heats of solution of monatomic oxygen and sulfur in liquid iron are -90 kea16,8 and -74 kea1,7, 8 respectively. These are to be compared with maximum heats of solution of metallic solutes in liquid iron of about -13 keal (silicon is an exception with -28.5 kea17). The large depression of the surface tension of liquid iron by trace amounts of the electronegative solutes oxygen, sulfur, and selenium9 suggests, by analogy with aqueous systems, the possible existence of polar molecules in the liquid. The effect of these solutes is at least three orders of magnitude greater than normal metal solutes.10 As has been pointed out by Richardson,11 the electron affinities and ionization potentials of oxygen and sulfur are such that it is likely that they exist in metallic solution as negatively charged ions. If this is so, and it is assumed that electrostatic forces play an important role in determining the configuration, it is unlikely that the stable configuration will be that of an isolated ion surrounded by a symmetrical coordination shell of solvent ions. It is more likely that the energy of the system would be lowered by the formation of solute-solvent screened dipoles. The above arguments suggest the formation of "molecular species" between solute and solvent atoms. The idea of the existence of molecular species in such solutions is not new, however', for Marshall and chipman12 have explained in a semi-quantitative manner the C-O equilibrium in liquid iron by postulating the species CO. Chen and Chip-man13 interpreted their measurements on the Cr-O equilibrium in iron in terms of the species CrO. Zapffe and sims14 have also postulated the existence of such species in liquid-iron alloys.

Jan 1, 1965

By R. I. Jaffee, H. R. Ogden, D. J. Maykuth

IN THE past year, Jaffee and Campbell&apos; and Finlay and Snyder2 reported on the mechanical properties of titanium-base alloys, some of which were in the same ranges of composition as are covered in this paper. In this paper, evidence confirming that given by Finlay and Snyder on the effects of carbon, oxygen, and nitrogen on titanium will be presented; and, in addition, new data will be given on the effects of these elements on the flow properties and phase transformation of titanium. Materials and Preparation of Alloys The preparation and general properties of iodide titanium have been adequately described elsewhere.&apos; , As-deposited iodide titanium rod, prepared at Battelle, of Vickers hardness less than 90 was employed as the base metal in the present work. This was the same material as that used by Finlay and Snyder.2 The probable analysis reported by them for standard quality metal holds here also: N 0.005 pct, 0 0.01 pct, C 0.03 pct, Fe <0.04 pct, A1 <0.05 pct, Si <0.03 pct, and Ti 99.85 pct. Carbon was added in the form of flake graphite supplied by the Joseph Dixon Crucible Co. Oxygen was added in the form of c.p. grade TiO, powder, produced by J. T. Baker Chemical Co. Nitrogen was added in Ti3N4 powder, supplied by the Remington Arms Co. Individual ingots weighed 7 or 8 g. Carbon, oxygen, or nitrogen was added by placing the corresponding powder in a capsule made from as-deposited iodide titanium rods and melting the capsule with the balance of the charge. The charge was are-melted with a tungsten electrode on a water-cooled copper hearth under a partial vacuum of very pure argon (99.92 pct minimum). Melting was practically contamination free. Vick-ers hardness increases of less than 10 points were normal for unalloyed iodide titanium control melts. Nitrogen analyses of are-melted iodide titanium showed a nitrogen content of 0.005 pct, about the same as is present in the as-deposited rod. No tungsten pickup was found in a melt of iodide titanium analyzed for tungsten. Weight losses in melting nitrogen-free alloys were very small and varied consistently from nil to 0.015 g (0 to 0.2 pct). This permitted the use of nominal composition for these alloys. Chemical analyses made for carbon, which can be analyzed conveniently by combustion methods, justified this procedure. Where nitrogen was added, considerable splattering took place. Here it was necessary to analyze for nitrogen by the Kjeldahl method. The ingots were hot rolled at 850°C to about 0.045 in. thick. After hot rolling, the strips were descaled by mechanical grinding, and then given a cold reduction of 5 to 10 pct to insure a uniform thickness throughout the length of the specimen. The edge strips and the tensile strips were annealed in a vacuum of 1x10-4 mm Hg pressure for 3 1/2 hr at 850°C and furnace cooled. Methods of Investigation Hardness Measurements: At least five Vickers hardness measurements were taken using a 10-kg load on each sample in the following conditions: (1) top and bottom of each ingot, (2) top and bottom surface of as-rolled and annealed sheet, and (3) on cross-section of annealed sheet and all quenched specimens. Tensile Tests: Tensile tests were conducted on Baldwin-Southwark testing machines having load ranges of 600 or 2000 lb. Tests were made on 1-in. gauge-length specimens, 3 1/4-in. overall length, 1/2 in. wide, 0.040 in. thick, with a reduced section 1 1/4 in. long and 0.250 in. wide. Two SR-4, A-7 strain gauges, one mounted on each side of the specimen, were used to measure the strain over a limited range to determine the modulus of elasticity. After the modulus of elasticity readings had been taken, load vs. strain readings were taken, using only one strain gauge, at increments of 0.0001 in. until the yield points were passed and then at 0.001-in. increments to the limit of the strain-gauge indicator (0.02 in.). Strain readings above 0.02 in. per in. were taken every 0.01 in., using dividers to measure the strain between the 1-in. gauge marks until the maximum load had been reached. Crosshead speed, when using the SR-4 gauges, was 0.005 in. per min, and, when using dividers, 0.01 in. per min. Flow Curves: Flow curves were determined using the true stress-true strain data obtained during the tension test. The usefulness of this type of information has been dealt with very adequately elsewhere by L. R. Jackson,&apos; J. H. Hollomon,6 and many others. Flow curves of true stress vs. true strain could be converted to the more conventional cold-work curve of 0.2 pct offset yield strength vs. percentage of cold reduction by means of the transformation, 1/1 = 1/1-R, where R is the fraction reduction in cold working. Thus, the true strains corresponding to percentage reduction can be calculated, and the 0.2 pct offset yield strengths scaled off the — 6 curve by taking the true stresses corresponding to the values of 6 + 0.002 strain. Heat Treatment: For the transformation studies, the alloys were heat treated in a horizontal-tube furnace using a dried 99.92 pct argon atmosphere, and quenched into water. Essentially no contamination was found after several hours of heat treatment at temperatures up to 1050°C. Metallography: Specimens were prepared in the

Jan 1, 1951

By H. L. Gilbert, C. Travis Anderson, W. J. Kroll

IN a previous paper,1 the use of a split graphite tube resistor as a heater element for high-temperature furnaces has been described. The principal advantages of this type of construction are: I. The quadruple resistance or voltage compared with the top-bottom clamp resistor furnace. 2. Free expansion of the resistor. 3. The ease of protection from oxidation by air. 4. The firmness by which it may be held in the compact split clamp. This construction appeared to be well adapted for the fusion of high melting metals which require fusion in a vacuum. Zirconium metal had previously been melted at the Albany Laboratory of the Bureau of Mines in a vacuum arc furnace on a water-cooled plate, using a movable tungsten top electrode.2 When larger furnace capacities were desired, this type of construction proved to have its limitations as the largest tungsten rods available were about 7/8in. in diameter. The supply of direct current of high amperage for producing the . desired arc characteristics was also not available. Considerable difficulty was also found in compensating the atmospheric pressure on the flexible tubing of the movable electrode, at the same time keeping its movement sufficiently free to enable the striking of an arc on any part of the metal briquet. Among the various materials used for the electrodes in conducting experiments in the vacuum arc furnace was graphite. It was found that zirconium fused in a graphite cup with a carbon arc was contaminated to only 0.2 pct carbon. It was therefore decided to melt zirconium directly in graphite crucibles. A high-frequency furnace was first used in the attempt to melt the zirconium in graphite crucibles. The high-frequency heating coil was placed outside a silica tube which was evacuated by means of an oil diffusion pump backed up by a mechanical pump. The graphite crucible was thoroughly degassed at 1900°C before use. Considerable difficulty was experienced in operating at such temperatures in vacuo because, as shown by Zintl,3 carbon vapor formed and reacted with silica according to the reaction: Si02 + C = SiO + CO. The silicon monoxide which is volatile at these high temperatures reacted with the zirconium, thereby contaminating it with silicon and oxygen. The presence of carbon monoxide was detected by means of a gas discharge tube placed in the vacuum system as indicated by the pale blue glow of the tube as soon as carbon vapor started to react with the hot silica. The reaction between the carbon vapor and hot silica was avoided by the use of split cylindrical molybdenum shields which were inserted between the graphite crucible

Jan 1, 1948

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1&apos;2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:&apos; Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal&apos;3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.&apos; Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By P. G. Shewmon, F. N. Rhines

THE determination of the self-diffusion coefficient of magnesium has been made possible recently by discovery1-1 of a radioactive isotope, Mg28 having a half-life of 21.3 hr,1 and subject to manufacture in useful quantity. In the present research this material was condensed from the vapor phase upon a surface of high purity magnesium. The progress of diffusion of the tracer atoms into polycrystalline magnesium was followed by machining layers and measuring the change in the intensity of radiation as a function of the distance of each layer from the surface. The self-diffusion coefficient was found to be 2.1 X 10-8 sq cm per sec at 627°C, 3.6 X 10-9 sq cm per sec at 551°C, and 4.4 X 10-10sq cm per sec at 468°C; the activation energy is about 32,000 cal per mol. Experimental Procedure Since there was no other published measurement of a diffusion velocity in any magnesium-base material, is was necessary to employ a number of new experimental techniques. The short half-life of Mg28 made it necessary to complete the entire experimental procedure within three or four days. This meant that the work had to be done where a cyclotron was readily accessible and that all operations, prior to the diffusion heat treatment, had to be so designed as to minimize their time requirements. Unusual problems were imposed also by the chemical reactivity of magnesium, its high vapor pressure, and the fact that no satisfactory method for elec-trodepositing magnesium on magnesium is presently available. Finally, the machining and handling of the easily air-borne radioactive-magnesium chips involved certain health hazards, resulting in the need for further experimental restrictions. Preparation of Mg28 The Mg28 was produced in the Carnegie Institute of Technology syncrocyclotron by the neutron spallation of chlorine.5 his involved bombarding a 2 gram crystal of high purity NaCl with a beam of 350 mev protons for a period of 2 hr, after which the crystal was dissolved in warm water and the Mg28 was concentrated and purified by chemical means (see Appendix). About 50 microcuries of Mg28 thus were obtained in the form of magnesium oxinate (8 hydroxyquin-olatc?), which was ignited in air to produce MgO. This in turn was reduced to magnesium metal vapor, by the method of Russell, Taylor, and Cooper," in the vacuum apparatus shown schematically in Fig. 1. Here the essential part is a tantalum ribbon, slightly dished to receive the MgO. The ribbon, pre- viously outgassed at high temperature, is heated to about 1700°C by passing an electric current through it, whereupon tantalum oxide is formed, magnesium vapor is released almost instantaneously, and condensed partly upon the diffusion sample. Diffusion-Sample Preparation: Hot-extruded magnesium rod, 21/32 in. round was used in making the diffusion specimens. The magnesium analyzed as follows: 0.004 pct Al, 0.027 pct Fe, 0.040 pct Mn, 0.0004 pct Cu, 0.0002 pct Ni, and less than 0.01 pct Ca, 0.0004 pct Pb, 0.0011 pct Si, 0.001 pct Sn, and 0.001 pct Zn. A brief study of the crystal texture of this material revealed a sharp fiber texture with the (001) plane roughly parallel to the extrusion axis. Cylindrical samples 1/2 in. long by 5/8 in. were machined from this rod, the end faces dressed on 3/0 emery, and lightly etched with 20 pct HC1 in water. These samples then were annealed for at least twice the intended time of diffusion, at the intended diffusion temperature, in order to stabilize the grain structure at about 1 mm average diameter. The annealing treatments were conducted in argon in the same apparatus and in the same manner as the subsequent diffusion treatments, which will be described presently. Thus, a strain-free plane surface was produced, but there remained a layer of MgO which had largely to be removed before the layer of Mg28 was deposited. Most of this layer was taken off by two light passes over 3/0 emery paper. The balance of the oxide and a thin layer of metal were then removed by etching 5 to 10 min in 4 pct nital (4 pct HNO3 and 96 pct ethyl alcohol) made with absolute alcohol. There followed immediately three quick rinses in: 1-49 1/2 pct methanol, 49 1/2 pct acetone, and 1 pct formic acid, 2-50 pct methanol and 50 pct acetone, and 3-pure benzene. This procedure is essentially that of Sturkey.7 The resulting surface, which was of almost elec-tropolished brightness, remained plane and was free of cold work. It could be kept clean by storing under benzene, or in a desiccator; short exposure

Jan 1, 1955

By G. S. Brooks

The tendency of the oxides of such metals as aluminum, zinc, chromium, and calcium to form compounds at high tempera tures with iron oxide is well established by past investigation. Data of this reaction, as developed in laboratory research, have been contributed by Burleigh, Hofman, and Wells, in America, and by many others abroad. A partial bibliography of the subject is appended. From these authorities we learn that the ferric oxide here has the function of an acid, giving in the case of ZnO a zinc ferrite, with a normal composition of ZnOFe2O3 This formation of zinc ferrite particularly affects the success of such processes as leaching or magnetic separation, and thus becomes practically important to the metallurgist. But the meager existing data do not entirely agree; and quantitative results from muffle-practice are conspicuously absent. Furthermore, it being of some general importance to the zinc smelter in both roasting and reduction, the following few notes of operations oil a commercial scale are contributed: I. Physical Properties of Zinc Ferrite. As formed for the most part synthetically by investigators, zinc ferrite exhibits characteristic physical properties, such as octahedral crystals, dark color, and a density over 5, together with a slight magnetic attractability. In examining with the microscope many products of mechanical muffle-roasting kilns, it is, however, impossible to find individual grains which can be identified as consisting entirely of zinc ferrite. The variety of colors, especially where each grain of blende was mechanically free from marcasite, rather conveys the impression of a partial ferritization of the grain. One side or end, for example, may often have the hard, dense surface and dark red to black color of the ferrite, while the balance shows the usual light yellowish brown of a normal iron-free blende.

Jan 1, 1914

By Francis F. Lucas

Jan 1, 1931

By L. W. Saperstein, Y. J. Wang

The development of computer programs to solve complex ventilation networks has reached a point of refinement where these programs become a necessary tool of the ventilating engineer. Such a program is presented. This program has an increased efficiency over its predecessors; it also includes the important facility of fixed quantity branches. This is in addition to the earlier capabilities of free-splitting, internal or external fans, and natural ventilation pressures. The program is written in Fortran IV with double-precision arithmetic and is listed here. Sample problems with input and output are also given. The recent, and presumably continuing, official interest in mine safety is bound to result in more stringent control requirements for ventilation. Anticipating this requirement, the Dept. of Mining, The Pennsylvania State University, has developed a computer program for the solution of complex mine ventilation networks. It is the opinion of this department that the program has sufficient merit to warrant its use in normal industrial operating conditions. Although the undergraduate mining engineering students of this department are routinely trained to use the program, it was felt that this training did not present a fast enough means of dissemination; consequently, this paper was written. The conception of the program is not new;1; however, the present version incorporates features that changes it from a scientific endeavor to a useful operating tool. These features include those of earlier programs, such as free-splitting, external or internal fans, and natural ventilation processes plus the important ability of handling fixed quantity branches, and of increased efficiency giving reduced cost. The facility for fixed quantities will be discussed in more detail. The solution of any network depends upon satisfying Kirchchoff&apos;s laws. These state that the sum of flow at any junction is zero, and that the sum of the pressure drop in branches totals the pressure drop in the mesh constituted by those branches, that is that the pressure drop around any mesh is zero. The terminology is derived from Synge," and is, in fact, that used by Topologists. A branch is any airway of uniform characteristics; a junction is where two or more airways meet (the minimum number of two airways is useful for describing the point where a low resistance airway changes into a high resistance one due to some physical constriction); a mesh is a path, along some branches, that returns on to itself, but does not need to traverse the same branch twice in order to do so; and a tree describes all those branches in a network which, while connected through all the junctions, do not form any meshes. Obviously the branches-in-tree are open-ended and can be shown to be one less than the number of junction (J-1). The branches-out-of-tree, also called basic branches, are equal to the number of basic meshes and are M = N — J + 1, where M is the number of meshes and N is the number of branches. The major difference between this network and an electrical one is that the law attributed to Atkinson for pressure drop is utilized rather than Ohm&apos;s law. Atkinson stated that the pressure drop (potential) is equal to a resistance factor multiplied by the quantity squared. This is written H = RlQlQ where H is the head loss. Q? is written in this factored fashion so that H will always have the same sign as Q. A negative sign is used to indicate that flow in a branch is opposite to that of its containing mesh. A mesh takes the direction of its basic branch. Utilizing Atkinson&apos;s law in Kirchchoff&apos;s second law and bearing in mind that the first law must remain satisfied, the program will determine all quantities, or head losses as they are related, for the branches of the network. The program uses a Geuss-Seidel form of in-teration, starting from an arbitrary Q and using a correction factor of the type first suggested by Professor Hardy Cross&apos; that will handle the nonlinear equation of Atkinson&apos;s law. A fuller description of the interative process is included in Wang and Hartman.&apos; Iteration continues until the correction factor is less than or equal to a preset error (E) or until a maximum number of iterations (MAXIT) have been reached. Utilizing an E of 50 cfm, sample problems have had rapid solutions. Rapidity of solution is also ensured by the method of selecting meshes and basic branches. This is done by the computer, which chooses the highest resistance branches, fixed quantity branches, and those containing fans, as basic branches. Natural ventilation pressures are handled as fans of constant pressure and may be assigned to any branch. The computer will generate a fan characteristic by polynominal fitting if a few operating points from the desired fan are input. A fan may be placed in any branch of the network, except those with fixed quantities. The strength of the present program over its earlier versions is its ability to handle fixed quantity branches. This means that certain branches can have their quantity determined, or preset, by the ventilating engineer. Operating under this constraint, the program will analyze the network and output the pressure change necessary to achieve this desired quantity. A call for positive head loss would require an auxiliary fan; negative head loss would require a regulator. This represents a powerful tool for the ventilating engineer who must insure that certain quantities of air pass across the operating faces or through working stopes. McPherson6 suggested that a ventilation program would be useful for determining in advance which branches were receiving inadequate air, and that subsequent calculations would then indicate the necessary corrections. The present program makes these corrections. Thus the mine manager can know immediately the consequences of changes to his system;

Jan 1, 1971

By D. C. Reynolds

Recent experiments with II-VI compounds have shown that they hazle considerable potential for laser applications over a broad region of the optical spectrum. It may be possible to cover the spectrum continuously from 3200A (ZnS) to the far infrared (CdHg:Te) since HgTe is a semimetal. At this writing laser action has been observed in ZnS, Zn0, CdS, CdSe, CdS:Se, CdTe, and some of the CdHg:Te alloys. Of particular interest are those lasers operating in the zlisible and near ultraciolet regzons of the spectrum where detectors of high sensitivity are available. The lasing transitions in II-VI compounds are bound exciton transitions some of which have been identified in auxiliary experiments. High efficiencies and low thresholds for lasing hare been achieved almost exc1usively in plutelet-type crystals. The greater crystalline quality exhibited by the phtelet-type material is shown to result from the crystal growth habit. Phonon scattering- of conduction electrons to the ground-state exciton is discussed ill relution to Lou thresholds and high efficiencies for lasing- observed in the CdS:Se solid solutions. The first successful semiconductor laser operation was achieved in the III-V compounds. It is possible to choose a material in this group that will operate between approximately 0.65 and 8.5 . There are at least two reasons why one would like to have a laser operating at shorter wavelengths. First, it would be easier to experiment with a laser operating in the visible region of the spectrum, and also more desirable to have high-in tensity visible light sources. Second, the most sensitive photomul-tiplier detectors are available in the visible and near ultraviolet regions of the spectrum. It is known that II-VI compounds are direct-band-gap semiconductors and as such offer the potential of operating at any specified wavelength between 3200 (ZnS) and 7772A (CdTe). Light emission from II-VI compounds has been the subject of numerous investigations for many years. These investigations were all primarily concerned with noncoherent emission. It has been only recently that coherent emission from these compounds has been observed. To date, laser operation has been demonstrated in CdS, CdSe, and the solid solutions of CdS:Se, ZnS, ZnO, and CdTe. These compounds cover an appreciable portion of the optical spectrum from the ultraviolet to the near infrared. In considering laser applications, the use of lasers in communication&apos;s systems offers many desirable features. In any operation of this type one must consider the losses in transmitting the radiation from the source to the detector. Atmospheric absorption in the visible and near ultraviolet is variable and greater than in certain regions of the infrared. It might be concluded that for long-range communication systems an infrared laser operating in a spectral region that is coincident with a transmission window in the atmosphere would be preferable. However, one cannot overlook the possibility of operating a system in the sensitive region of a highly sensitive photomultiplier detector or other light-amplifying system. LASER CONSIDERATIONS To produce a source of coherent radiation it is necessary to achieve a population inversion. In the case of semiconducting materials it is necessary to raise the electrons from one energy state to a higher-energy state relative to it. In semiconductors, this population inversion can be achieved by three different techniques: 1) Current Injection. This technique uses a p-n junction biased in the forward direction. Large numbers of electrons are injected from the n region into the p region, and recombination occurs close to the junction. An inverted population is obtained in this region and the recombination radiation propagates parallel to the junction. This type of pumping has been used in the GaAs junction-type lasers but has not been successfully employed in the II-VI compounds. 2) Optical Pumping. In this case, one uses photons to obtain a population inversion by exciting electrons to higher-energy states. The pump sources are flash lamps or arc lamps and, occasionally, other laser sources when such sources have the appropriate energy for exciting the electrons. The disadvantage of this type of pumping is that flash lamps put out a rather broad spectrum of radiation, whereas the laser material has a rather narrow region of absorption. This results in an inefficient process. Laser sources provide efficient pump sources but the number of usable wavelengths is limited. 3) Electron Beam Pumping. In this technique, the laser sample cavity is bombarded with electrons having energies in the range from approximately 10 to a few hundred kv. The bombarding radiation excites electrons from valence to conduction band states in the semiconductor, giving rise to an inverted population. This type of pumping has been used successfully in several 11-VI compounds.

Jan 1, 1968

By T. A. Ring

The bed filtration of colloidal particles has been modeled by performing a differential particle balance. The balance considered the localized particle deposition rate to be the sum of three rate resistances: mass transfer to a region near the surface, adhesion onto a partially filled surface, and resuspension from a partially filled surface. The differential particle balance equations, one for the free particles and one for the adhered particles, were solved by a finite difference algorithm. Results of this model are compared to experimental filter breakthrough curves.

Jan 1, 1985

Impact Transition Temperatures of Some Pearlite-Free Mild Steels As Affected by Heat Treatments in the Alpha Range H. P. Tardif (Canadian Armament Research and Development Establishment, Quebec)—Mr. Josefsson is to be congratulated for his study of a most difficult subject and for the theories proposed to explain the re- sults. One point which, however, might not have received proper attention is that of the shape of the stress-strain curve at the yield point of quenched and furnace-cooled specimens and of specimens strain aged

Jan 1, 1956

By William Y. Holland, Roger H. Cook

Dexter H. Reynolds (Chapman and Wood, Mining Engineers and Consulting Geologists, Albuquerque, N. M.)—A number of questions are raised by conclusions and inferences made in the above-mentioned paper. The more troublesome of these concern use of the various pozzolans to combat the deleterious effects of the alkali-aggregate reaction. The most alkali-reactive materials listed are opal and rocks containing opaline silica. The pozzolans mentioned specifically for use as amelioratives are opaline shales and cherts. These are stated to retard the expansion caused by the alkali-aggregate reaction. Another well-recognized pozzolan is diatomaceous earth, which consists principally of opaline silica. A pozzolan presumably owes its effectiveness to its high reactivity with the alkaline liquid phase of the concrete mix. It appears reasonable to expect that finely divided opaline silica added as a pozzolan would be more susceptible to reaction with the alkalies present than would larger particles of the same material. The authors report that work with high and low alkali cements indicates that in the presence of alkali-reactive materials, deleterious expansion depends upon the alkali content of the cement. The total effect, therefore, should be more or less independent of the amount of reactive aggregate present, and still more independent of its state of subdivision. The deleterious effects should, if anything, be aggravated by the addition of a finely divided, highly reactive pozzolan. Further, if the alkali-aggregate reaction is of great importance in the long-term soundness of concrete structures, the addition of a pozzolan to a concrete made with aggregate free from known deleterious materials would be a questionable procedure. The benefits reportedly accruing from such use of pozzolans are greater ultimate strength for a given cement content, increased resistance to deterioration by exposure to sulphate solutions and other mineral waters, and greater resistance to damage by wetting and drying and freezing and thawing. In view of the deleterious effects of highly reactive materials are these benefits ephemeral? The same considerations apply to another alkali-reactive material, chalcedony, which appears to consist of ultrafine-grained quartz, with opal absent in detectable amounts. Quartz flour is notably reactive chemically and physiologically (cf. Ref. 11 of Holland and Cook&apos;s paper), a fact borne out by its effectiveness as a pozzolan, which presumably might be expected to offset the deleterious effects of the presence of chalcedony in the aggregate. A second question of some importance concerns the reportedly highly deleterious reactivity of acidic and intermediate volcanic glasses, such as rhyolite, perlite, and pumice. Air entrainment is listed as one of the ameliorative measures to combat the deleterious effects of the alkali-aggregate reaction. The alkalic-silica gel formed by the reaction may expand into air bubbles and thus not cause appreciable expansion of the concrete mass. It would appear then that pumice and perlite, particularly perlites of the pumiceous types and other types after expansion, would also tend to counteract the expansion, since these materials consist largely of voids and air bubbles. Certainly this would be expected of structural concrete in which pumice or perlite is used as total aggregate. Finely ground pumice, perlite, and volcanic ash have been demonstrated to be active pozzolans (cf. Pumice as Aggregate for Lightweight Structural Concrete by Wagner, Gay, and Reynolds, Univ. of New Mexico Publications in Engineering No. 5, Albuquerque, 1950). In fact, the term pozzolan was first associated with finely divided pumice or volcanic ash. Such materials were used with hydrated lime as the sole cementitious agent in constructing public buildings, roads, and aqueducts by the ancient Romans. The deleterious alkali reactivity of the volcanic glass, itself containing several percent of the alkalies, apparently did not contribute to the remarkable state of preservation of those ancient structures, as exemplified by the Appian Way and the Pantheon Dome. Still a third question involves .the reactivity of constituents of concrete when exposed to various salt solutions. Resistance to. deleterious expansion and cracking as a result of contact with mineral waters and its relationship to the mineral content of the aggregate are not mentioned by the authors. Yet the phenomena pictured in Fig. 1, and especially in Fig. 2, appear very much like those caused by exposure to mineral waters. The deterioration of concretes exposed to sulphate waters is generally considered related to the chemical constituency of the cement itself, particularly to the relative amount of tricalcium alum-inate contained. Could not many of the ill effects presently blamed on alkali-aggregate reaction really have been caused by contact with sulphate or other salt-containing mineral waters? Or perhaps their use as mixing waters? May not the deleterious expansion be as much a function of the chemical makeup of the cement as it is of the mineral constituency of the aggregate? Would it not be just as important to use alkali-free mixing water as it is to use a low-alkali cement? It appears obvious that resistance of cements and concretes to sulphate and other salt solutions cannot be left out of account in discussion of deterioration of concrete structures with time. This factor may be of equal or even greater importance than the alkali-aggregate reaction, particularly for concrete subjected to wetting and drying cycles, such as airstrip paving, water-retaining dams, and highway structures. Another very important factor is called to attention on page 1022 of the article in Mining Engineering, October 1953, in that failure of concrete structures may result from poor construction practices and use of too high water-cement ratios. Both of these can contribute remarkably to decreased resistance to attack by sulphate waters, and presumably could have an equally remarkable effect upon extent of damage resulting from the alkali-aggregate reaction. From the above remarks it appears that while alkali-aggregate reaction may be an important factor in decreasing the useful. life of a concrete structure, it is not the only factor involved, and it may not be even a controlling factor. Likewise, many of the phenomena apparently associated with the alkali-aggregate reaction may have resulted from cond&apos;itions which had little relationship to the alkali-reactivity of a constituent of the aggregate. Certainly if alkali-aggregate reactivity is a major factor in bringing about early failure, one cannot help feeling anxiety concerning the future of the many concrete structures in this country and abroad in which pumice and perlite were used as total or partial aggregates. This anxiety can only be dispelled by calling to mind that among the best-preserved relics coming down to us from ancient times are structures made with mortars containing highly alkali-reactive aggregates.

Jan 1, 1955

By S. F. Shaw

In 1913, the Tiro General mine, at Charcas, S.L.P., Mexico, which had been making from 125 to 150 gal. of water per min., was allowed to become flooded, after all the pumps had been removed, and in 1918 the problem of unwatering it came up for solution. There are two vertical shafts, the Tiro General, 1390 ft., and the San Fernando, 1225 ft. in depth, with five connecting levels between them. The San Fernando shaft had been partly retimbered, while the Tiro General had been newly timbered from the collar to 1090 ft. in depth. It had been possible to place guides in only one compartment of the Tiro General, from the collar to the seventh or 850-ft. level, to which it was necessary to lower the water before station pumps could be installed. Soundings indicated that compartments in the Tiro General were open to 1082 and 428 ft., and in the San Fernando shaft to 471, 488, and 586 ft. The water had risen to a point 140 ft. below the collar of the Tiro General shaft.. Pumping Equipment The steam plant at the Tiro General shaft includes one 300-hp., one 150-hp. and one 100-hp. Erie City water-tube boiler, and two 160-hp. Heine water-tube boilers. All but one of these boilers were supposed to be in good shape, but it was soon discovered that six years of idleness in a climate that is foggy for several months of the year had left them in poor condition. The compressed-air plant comprises one Nordberg cross-compound compressor with piston displacement of approximately 2500 cu. ft.of free air compressed to 96 Ib. per sq. in.; and another Nordberg cross-compound with piston displacement of 1235 cu. ft. of free air, to the same pressure. The main pump station is on the seventh level where had been installed a Prescott pot-valve plunger pump with capacity of 200 gal. per min.; also a Gould triplex plunger pump with capacity of 135 gal. per min., driven by a 6 1/2 by 10 by 12 in. steam engine. From the lower levels, the water had been raised to the seventh level by small station pumps and sinking pumps.

Jan 1, 1920

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry&apos;s law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2&apos;= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,&apos; using Laitinen and Liu&apos;s&apos; value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,&apos; and the equations of Wagner and Werner,&apos; the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O&apos; and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies&apos; have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969