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By T. MacDONALD

ATHOUGH flotation has been a commercial process for over twenty years, the last two years have witnessed a sudden and phenomenal increase in our knowledge of how to separate minerals heretofore not considered amenable to flotation at all. As remarked by Professor Locke in the January issue. "Either commercial or laboratory flotation is reported on zircon, ilmenite, carnotite, kyanite, scheelite, chromite, fluorite, feldspar, cassiterite, wolframite, barite, and clay. Attractive patents on soap flotation are U. S. Nos. 2,000,656 and 2,040.187. A survey by Ralston in the February E. & M. J. adds many other minerals to this impressive list. The simple but pregnant fact is that any mineral can be coated, directly or indirectly, with a water-repellent coating, and since this is true, it follows that any mineral can be floated. Fundamentally, this is no new discovery, where, for instance, is the mineral that cannot he washed from a pair of dirty hands by means of soap and water, given the absence of refractory greases or oils which would have no proper place in flotation ?

Jan 1, 1937

By Joseph Jensen

THE history of the normal oil field is supposed to show an oil graph stalting high in flush production, descending more or less steeply into the curve of settled production and dropping gradually to the vanishing point of economical operation. Together with this at somewhere in the early history of the field, there appears from a vanishing point a graph showing the production of water. During the period of settled production this graph rises higher and, toward the close, unless extensive work is done in the line of correction, rises far above the oil graph to where the cost of operation terminates profitable pumping. Fields that start out with a high relative content of water are generally very short lived. Fields that never develop a water problem are exceedingly rare.

Jan 1, 1930

By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.' These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar's cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967

By Elwood G. Haney, R. N. Parkins

Stress corrosion cracking of two heats of 18 pct Ni maraging steel in rod form immersed in an aqueous solution of 0.6N NaCl at pH 2.2 has been studied on un-notched specimens stressed in a hard tensilf machite. Austenitizing temperature in the range 1830 to 1400 F has been shown to have a marked influence on the propensity to crack, the loulest austenitizing- temperature producing the greatest resistance to failure. In the nzosl susceptible conditions, the cracks followed the original austenile grain boundaries; but when tlze steels zcere heal treated to inproze their resistance to stress corrosion, the cracks becatne appreciably less branched and slzouqed significant tendencies to become trans granular. Electron metallography of the steels indicated the presence of snzall particles, possibly of titanium carbide, along- the prior austenite grain boundaries and these particles u:ere more readily detectable in the structures that were most susceptible to cracking. Crack propagation rates, which appeared to be dependent upon applied stress and structure, were usually in tlze reg-ion of 0.5 mm per hr and may, therefore, be e.xplained on tlze basis of a purely electrochetnical ,nechanism. However, there is some ezliderzce from fractography that crack extension may be assisted by ttlechanical processes. Anodic stit)zulation reduced the tiwe to fracture, although cathodic currents of small magnitudes delayed cracking-; further increase in cathodic current resulted in a sharp drop i,n fracture litne, possibly due to the onset of hydrogen ewbrittlement. THE use of the high strength maraging steels, with their attractive fracture toughness characteristics, is restricted because of their susceptibility to stress corrosion cracking in chloride solutions. Although this limitation has resulted in investigations of the stress corrosion susceptibilities of these steels, there have been few systematic studies aimed at defining the various parameters that determine the level of susceptibility. It is the case that the usual tests have been performed with the object of defining some stress or time limit, on unnotched or precracked specimens, within which failure was not observed,' but while such results may be of some use in design considerations, they are necessarily concerned only with the steels as they currently exist and not with their improvement to render them more resistant to stress corrosion failure. This omission may be considered unfortunate because the indications are that stress corrosion in maraging steels shows dependence on structure in following an intergranular path, and since experience with other systems of intergranular stress corrosion crack- ing is that susceptibility may be varied by modifying heat treatments, a similar effect may be expected with maraging steels. It is sometimes from such observations that a fuller understanding of the mechanism of stress corrosion crack propagation begins to emerge, leading in time to the development of more resistant grades of material. The present work was undertaken to study only one aspect of the influence of heat treatment upon the cracking propensities of the 18 pct Ni maraging steel, namely the effect of austenitizing temperature, although certain ancillary measurements and experiments have been undertaken. EXPERIMENTAL TECHNIQUES Most of the measurements were made on a steel, A, having the analysis shown below, although a few results were obtained on a steel, B, having a slightly different composition. Both steels were supplied in the austenitized condition, A as 3/8-in-diam rod and B as 1/2-in.-diam rod. Cylindrical tensile test pieces were machined from the rods: the overal length was 2 1/2 in., the gage length 1 in. and the diameter 0.128 to 0.136 in. The stress corrosion tests were carried out with the specimens strained in tension in a hard beam testing machine, the necessary total strain being applied to the specimen over a period of about 30 sec, after which the moving crosshead was locked in position and the load allowed to relax as crack propagation proceeded; the load relaxation was recorded. The load was applied after the specimen had been brought into contact with the corrosive solution, the latter being contained in a polyethylene dish having a central hole through which the specimen passed, leakage being prevented by the application of a film of rubber cement. The specimen was in contact with the solution for over half of its gage length and the solution was exposed to the air during testing. The solution was prepared from distilled and deionized water to which NaCl was added, 0.6N, and the pH adjusted to 2.2 by HCl additions. The composition of the solution

Jan 1, 1969

By J. G. Richardson, J. W. Graham

The purpose of this paper is to present the results of theoretical and experimental studies of water imbibition. The imbibition processes are involved in recovery of oil from stratified and fractured-matrix formations in natural water drives and water flooding. An understanding of the role of inhibition in implementing the recovery of oil from such formations is deemed essential to proper control of these reservoirs to achieve maximum recovery. The theoretical studies involved development of the differential equations which describe the spontaneous imbibition of water by an oil-saturated rock. The dependence of the rate of water intake by the rock on the permeability, interfacial tension, contact angles, fluid viscosities and fluid saturatiorls is discussed. A few experiments were performed using core samples to determine the effects of core length and presence of a free gas suturation. The role of water imbibition in recovery of oil from a fractured-matrix reservoir by water flooding was investigated by use of a laboratory model. This model was scaled to represent one element of a frac-tured-matrix formation. Water floods were made at various rates with several fracture widths. Interpretations were made of the behavior expected in a system containing many matrix blocks. The presence of a free gas sntu.ration was found to reduce the rate of water imbibition. In the reservoir prototype of the fractured-matrix model, water imbibition rather than direct displacement by water was the dominant mechanism in the recovery of oil at low rates. INTRODUCTION Imbibition may be defined as the spontaneous taking up of a liquid by a porous solid. The spontaneous process of imbibition occurs when the fuid-filled solid is immersed or brought in contact with another fluid which preferentially wets the solid. In the process of wetting and flowing into the solid, the imbibing fluid displaces the non-wetting resident fluid. Common examples of this phenomenon are dry bricks soaking up water and expelling air, a blotter soaking up ink and expelling air and reservoir rock soaking up water and expelling oil. As increasingly better lithological descriptions have been made of the characteristics of petroleum-bearing formations, it has become obvious that imbibition phenomena which were once considered laboratory curiosities are of practical importance. For instance, in reservoirs composed of water-wet sand strata of different permeability in intimate contact, the tendency of water to channel through the more permeable stratum is offset by the tendency for water to imbibe into the tight sand and expel oil into the coarse sand. Also, in fractured-matrix formations the tendency of water to channel through the fractures is offset by water-wet matrix blocks. As some imbibition of the water into the of the largest fields in the world are fractured-matrix reservoirs, it has become increasingly important to understand all the factors involved in the imbibition process. Examples of fractured-matrix reservoirs are the Spraberry field in West Texas which produces from a fractured sandstone', the giant Kirkuk field in Iran', the Dukhan field in Qatar, Persian Gulf2, and the Masjid-I-Sula-main and the Haft-Kel fields in Southwestern Iran, which produce from fissured limestone3. Research into recovery of oil from fractured-matrix formations was stimulated by the rapid decline of oil productivity of wells in the Spraberry formation. One result of this research was the water imbibition process developed by the Atlantic Refining Co.4 Another idea was that much of the Spraberry oil could be recovered by conventional water-flooding procedures5. Subsequently, pilot floods were conducted in this field to test the feasibility of these ideas. It was felt that an understanding of the role played by imbibition processes in displacement of oil from a fractured-matrix reservoir could not be obtained from field data alone because of the many complicating factors and uncertainties involved. Therefore, theoretical and laboratory studies were undertaken to provide this understanding. Study of the equations which describe the linear, countercurrent imbibition process provided an insight into the role of various factors in the process, such as the permeability of rock and inter-facial tension. In addition to the theoretical studies, imbibition experiments were conducted with core samples to determine the effect on the rate of imbibition of such variables as core length and free gas saturation. The principal experimental studies were conducted by water flooding a scaled model of an clement of a frac-tu red-matrix reservoir to evaluate

By Samuel H. Dolbear

THE value of a mine is basically dependent on its capacity to yield profits. Since the ore must be mined, treated, and sold, some of it in various future years. there is a risk involved as to future costs, selling price, and working conditions. It cannot be expected that the economic condition existing at the time of valuation will continue unchanged for long periods in the future. During the past 20 years, mineral production in the United States has been conducted under a changing economy in many respects more exacting than that applied to other businesses. There have been increased production incentives, technical aid, exploration of privately owned mineral deposits by government at federal expense, and liberal loans for development and equipment, with risk partially assumed by government.. Some of these benefits have been counterbalanced by price ceilings, consumption controls, and stimulation of competition from foreign producers who have been offered the same advantages extended to American operators. For the present, mines will operate under a government policy directed toward reducing federal aid and control. The tenure of this change will depend upon future elections and the status of foreign relations. War and threat of war are now of the most vital significance to the mineral industries. Other factors which influence cost of production, markets, and price of mine output might be classified as Acts of God or Acts of Government. In some countries expropriation and the difficulty of exporting earnings or investment returns are risks that must be considered by foreign capital. Recognizing that this retards American investment in foreign countries, the Mutual Security Agency offers insurance against such expropriation and guarantees the convertibility of capital and profits. Since it is impossible to predict with certainty either cost of production or selling prices of metals for long periods, some assumptions must be made as to profits in the future. The basic assumption must be that the price of the company's product will vary in proportion to changes in operating cost. There is often a lag in this reaction, however, for prices of minerals are generally more sensitive to declines and less sensitive to increases than are costs. This reflects in part the resistance of labor to downward wage revision and a corresponding alertness in realizing its share of price advances. Some labor contracts include automatic adjustments to metal prices. Notwithstanding the complexity of the, problems involved and the difficulty of weighing their effect on value, such risks may be appraised with reasonable accuracy and a rate of earnings adopted that is compatible with the risk. It is, of course, possible to revert to a yardstick of value such as the commodity dollar, which has been advocated from time to time, but while revaluation in 1933 disturbed public confidence, the theoretical gold dollar continues to be the standard of greatest stability. Its gain or loss in purchasing power is reflected ultimately in cost of production and selling price of the mine product. At present 35 dollars are allocated to one ounce of gold. Measurement of Risk In the application of the Hoskold and most other formulae, a yearly dividend rate commensurate with the risk involved is set aside out of annual earnings. If the risk is great, this rate may be 15 to 25 pct of the amount invested. The remainder is placed in a sinking fund invested in safe securities such as high grade bonds or conservative equities, and the interest or dividends from these securities are added to the sinking fund. The sum of these sinking fund payments and the compounded interest at the end of the mine life is taken as the value of the mine. Admittedly the decision as to the size of the risk rate is the most difficult element in valuation and one requiring the most exacting consideration. It is necessary to look years ahead in an effort to determine future costs, market prices, demand, competition which may develop, including that of substitutes, and other influences common to the mine and to the region in which it is situated. Another phase of risk is the enactment of unfavorable legislation, taxes, and what appears to be an alarming spread of nationalization and expropriation. Capital is sometimes borrowed from the government to finance strategic production. Such loans may be collectable only out of production and involve no liability otherwise. Valuation in these cases must recognize the effect of such a reduction in liability. Offsetting some of these risks are the possibilities of mechanization and other cost-reducing discoveries, improvements in mining and treatment methods, new uses for minerals and metals, and normal growth of markets. In this paper, the terms risk rate, dividend rate, and speculative rate are synonymous. Safe rate and redemption rate are also used interchangeably. These alternatives are used here because they are commonly found in the literature on mine valuation. In Michigan, the State Tax Commission has long employed a risk rate of 6 pct in its valuation of iron mines. There the outline of reserves is well established and operating costs and conditions are based on adequate experience. The following comment on rates appears in the report of the Minnesota Interior commission on Iron Ore Taxation submitted to the Minnesota Legislature of 1941.1 Most engineers agree that 7 percent for the specu-lative rate is "an absolute minimum". C. K. Leith in

Jan 1, 1954

By George W. Mitchell

THE property of Eureka Corp. Ltd. is located in the approximate geographic center of Nevada, 2 miles from Eureka, the county seat. The great sources of power, the Colorado, Snake, and Salmon Rivers and the rivers of northern California, are 300 to 500 miles distant, and no lines serve areas closer than 150 miles. Fuel for diesel and steam generation is available in Utah, 300 to 400 miles to the east. Eureka's railhead is 80 miles north where two trunk lines cross the county. A spur line serves Ely, 77 miles east. Good highways connect Eureka to the railheads. Activity in the Eureka mining district began in the early 1870's. The oxidized high grade lead-sil-ver-gold ore terminated against the footwall of the Ruby Hill fault, and in 1890 the main operations ceased. In 1938 Eureka Corp. Ltd. discovered ore in the hanging wall of the fault by diamond drilling. The history of Eureka in the late 1800's indicates that there was some water at 600 to 800 ft in the old workings, probably accumulations above the water table which did not seriously interfere with mining operations. Both the Locan and Richmond shafts were sunk to a level below the table, but apparently the only serious difficulty with water occurred in the Locan. The steam pump used when the last work was done on the 1200 level in 1923, many years after exhaustion of the main orebodies, is still installed on the Locan 900 level. The capacity was about 500 gpm, lifting 750 ft to the 100 level, which connected with the surface. In addition to this. bailers were used to keep the 1200 level free of water. It is said that pumping in 1923 lowered the water in the Holly shaft, about a mile and a half away, but this seems doubtful. The pumping was of short duration because no ore was found. When work at the new Fad shaft was started in 1941 Eureka Corp. Ltd. engineers were fully aware of the probability of encountering water in large volume. Their primary exploration and development had to be carried on at the 2250 level. The first water was encountered at 300 ft. This was undoubtedly surface drainage in the bedding of the Pogonip limestone and was less than 100 gpm. The fractured, loose Hamburg dolomite at the water table was not well cemented, and relatively little water, 300 gpm, percolated through it with difficulty. At 1350 ft well-cemented dolomite containing some open fractures was encountered. These fractures produced the first water of consequence, 750 gpm. At 1700 ft the volume was 1000 gpm increasing to the maximum during shaft sinking, 1600 gpm, at the 2000 level. Secret Canyon shale, a dry formation, was entered at 2100 ft, where a concrete water ring was placed to catch all of the water. The volume decreased rapidly to a constant flow of 1200 gpm. Below 2100 ft the shaft and stations remained in the shale and water was not a problem. Several faults of moderate displacement, including the reverse Martin fault, had been intersected during the traversing of 1000 ft of wet Hamburg, but no undue quantities of water were encountered. Observations in the diamond drill holes in the ore zone area showed a rapid lowering of the water table. The shaft was flooded when it left the dry shale and entered the water-bearing Eldorado dolomite on the 2250 level, crossing a fissure which paralleled the Martin fault. High pressure water doubled the volume then being pumped. Pipe failure through a water door bulkhead was a contributing factor. Immediately following this flooding in March 1948 preparations were made to recover the shaft as rapidly as possible by increasing power and pump capacities as needed. Measurements before flooding indicated the water could be lowered at a fast rate. However, the water table did not recede as rapidly as expected and volumes required to lower the water in the shaft were higher. Obviously the size of the main water channel on the 2250 level was increasing because of erosion, allowing greater volumes to enter the workings and draining beyond the cone originally being drained during shaft sinking. Eroded material was being deposited in the shaft below the 2250 level in serious proportions. In December 1948 a second flooding of the Fad shaft was allowed for the purpose of reassessing existing conditions and studying alternate methods of attack. The detailed geology of the Eureka mining district, see Fig. 1, has been described during the past 75 years by many geologists.' Only the general features and those which seem to affect the drainage problem will be discussed. The old ore zone, mined between 1870 and 1890, is located in a wedge-shaped block of Eldorado dolomite between the footwall of the Ruby Hill fault and the underlying Prospect Mountain quartzite, see Fig. 2. Production of high grade oxidized lead ore containing high values in gold and silver has been variously estimated at $50 to $90 million. The tonnage mined was probably close to 1,500,000, nearly all of which was found above the water table. The new ore, discovered by diamond drilling in the hanging wall of the Ruby Hill fault, is a flat-

Jan 1, 1954

By E. A. Breitenbach

A computer program has been developed to afford rapid and complete quantitative log analysis for exploration and production decisions. The computation consists of automatic selection of tops and bottoms of porous intervals from the digitized data, and then point-by-point calculations within each selected interval. Nearly all log types can be analyzed. This paper presents the calculation techniques found to be appticable to machine evaluation and gives examples of their use. INTRODUCTION As the quantitative interpretation of well logs entails repetitive use of charts and equations, it is natural that digital computer programs would be written. A Universal Log Interpretation Computer Program (ULICP) has been developed to afiord rapid and complete analysis for exploration and production decisions. Application of this program enables the log analyst to: (I) apply rapid quantitative log analysis for exploration and production decisions on either a field, a well or on a single zone basis; (2) apply concepts of interpretation requiring detailed numerical analysis; (3) analyze all porous intervals on each log, rather than a few selected zones, and complete the analysis in less time than previously required. Computations are reported for every digitized point in each zone; (4) use empirical techniques applicable to a given area as an integral part of the computation; (5) experiment with the empirical coefficients and exponents in the interpretation equations to find the best possible solution; and (6) automatically plot both the original and computed data to scales analogous to the field prints. The primary utility of a log interpretation program stems from its ability to do an overwhelming amount of work with very little man-power. If a calculation procedure or thought process can be formalized to the extent that step-by-step logic can be written, a computer program can be developed that follows this logic. The major question is one of economics. A feasibility study of the costs for such a program indicates that digital processing is economical primarily as a means of increasing the productivity of the log analyst. In effect, the probability of missing productive intervals in any well, because of a lack of time to do detailed calculations, is greatly reduced. The nucleus of ULICP is programmed to compute large sections of a suite of logs by selecting zones automatically and then performing all pertinent computations on a data point by data point basis within each zone.'.' An entire suite of logs can be processed in this manner with very little manual intervention. Sufficient programming logic is available so that each log analyst can request computations pertinent to his area. These requests are made by simple additions or deletions of information on the input header cards. Hence, the log analyst is always in complete control of the computation process. The evaluation of a suite of logs requires pre-editing, digitization, computation, presentation of results and interpretation. Work by the log analyst is reqilired only in pre-editing and interpretation. Thus, he is allowed more time for comprehensive interpretation, rather than calculation. For continuity, the discussion of ULICP is organized sequentially: pre-editing, digitization, computation and presentation of results. DISCUSSION PRE-EDITING The extent of pre-editing prior to computation is dependent on the format of the original data. For analog prints, it requires inspection, correlation and editing of the logs, plus the entering of required data an special forms. For digitized data such as magnetic tape field recordings, only the special forms are necessary. The process for analog prints will be given here. The inspection and correlation process involves the selection of sections for digitization and the correlation of the traces to a common depth. To decrease the cost of digitization, traces that exhibit large variations in shale formations can be redrawn to a non-zero baseline. The next step is to enter all pertinent data on the input header cards. The header cards presently used for ULICP are presented as Figs. 1 through 6. Cards 1, 2, 3 and 4 (Fig. 1) are defined as the Main Header Cards. They describe the particular well for output identification and give basic information. Cards 5 through 15 (Figs. 2 through 6) are defined as the Block Header Cards. As such, they define the log types and the interpretation parameters for the block of data immediately following. Cards 1 through 10 are required for every computer run. Cards 11 through 14 pertain only to nuclear logs. Card 11 is required if any nuclear log is supplied, and cards 12 through 14 are required only when gamma-ray, density or neutron log data, respectively, are supplied. Card 15 (Fig. 6) must be supplied when cross-plot calculations are required. Either two- or three-component

Jan 1, 1967

By E. T. Turkdogan, M. T. Hepworth, R. P. Smith

The permeability of oxygen in 0 iron in the tempera-ture range 700" to 900 C and in 6 iron at 1450°C was determined by the rate of internal oxidation of iron, containing -0.1 pct Al. The solubility of oxygen in zone-refined iron was determined by equilibration with hydrogen-water vapor gas mixtures at 1450" and 1510°C; oxygen solubilities , for iron in equi1ibriu.rn with molten oxide, are found to be 66 and 83 ppm for these two temperatures, respectively. The diffusivity of oxygen in iron at 14500C3 as calculated from the permeability and solubility data, is (4.1 * 0.6) x 10 "B sq cm per sec. OXYGEN is one of the most common impurities present in iron or steel, mainly in the form of oxide inclusions. In the study of many metallurgical problems concerning solid iron, it is often desirable to know with a reasonable accuracy the solubility and diffusivity of oxygen over a wide temperature range. The solubility of oxygen in solid iron has been the subject of numerous studies yielding highly discordant results as seen for example from the literature surveys made by Meijering &apos; and Schenck et a1.&apos; As shown by Kitchener et aL3 and by Sifferlen, the high oxygen solubilities reported by many investigators are the result of oxidizable impurities which are often present in iron. In addition, there have been experimental problems associated with icaccuracy of oxygen analysis of iron containing less than 100 ppm 0. A number of studies have been made on the permeability of oxygen in a and y iron using Fe-Si, Fe-Mn, and Fe-A1 alloys in the internal-oxidation experiments.1&apos;2&apos;5&apos;6 However, no direct measurements have been made of the diffusivity of oxygen in iron. In the present work two sets of experimental measurements were made: permeability and solubility studies at 1450" and 1510°C and permeability studies only in the range 700 to 900°C. In both sets of permeability measurements slab-shaped specimens containing small predetermined amounts of aluminum in solution were exposed at constant temperature to gas mixtures of hydrogen, water vapor, and argon for varying times. These specimens were quenched, sectioned, and examined for oxygen penetration by metallographic observation of aluminum oxide particles which formed. From these data, it is possible to calculate the ratio of the diffusivity of oxygen in iron, D, to the equilibrium constant K for the reaction Hz(g) * O (dissolved in iron) = H,O(g). EXPERIMENTAL Permeability Measurements at 1450°C. An ingot of vacuum-carbon deoxidized iron containing 0.086 pct A1 was prepared, using commercial "Type lO4A Plas-tiron"; after hot rolling, specimens were machined into slabs a by 2 by 2 in. The impurity contents were: S, P < 0.002 pct; C, Mn < 0.01 pct; each of all other Usual impurities < 0.004 pet. The amount of oxide inclusions in this material, determined by a bromine-methyl acetate extraction, corresponded to about 20 ppm 0 in the iron which agreed well with the results of vacuum-fusion analysis. Each specimen was annealed at 1450°C for 1 hr in purified hydrogen, polished to a smooth surface, and then introduced into a controlled oxidizing atmosphere in a recrystallized alumina tube at 1450°C. The constant temperature zone (*3"C) was about 3 in. in length. The gas composition was controlled by mixing argon with hydrogen (using calibrated constant-head flow meters) and passing the mixture through a column of a mixture of oxalic acid dihydrate and 10 pct anhydrous oxalic acid, to establish a required water-vapor content in the gas mixture. The temperature of the oxalic acid dihydrate column was controlled by a thermostat. The total gas flow was in the range 800 to 1000 cu cm per min. The exit gas from the reaction tube was passed through a weighing bottle containing a desiccant, to cross-check the degree of water-vapor saturation, which for all experiments was about 97 pct of those derived from the data of Baxter and Lansing.1 For a typical experiment, a specimen was introduced into the furnace in a stream of dry argon and hydrogen. The specimen was then rapidly raised by a Pt-Rh alloy wire into the hot zone and allowed to reach the reaction temperature, at which time the oxidizing gas mixture was introduced. The oxygen potentials employed were sufficient to oxidize aluminum but not to cause liquid iron oxide to form. After a specified time, the experiment was ended by dropping the specimen onto a water-cooled copper block at the bottom of the reaction tube. The depth of the internally oxidized zone, hereafter called the "case", was determined by sectioning the specimen at right angles to the long direction. The section was then examined under a microscope equipped with a micrometer stage. In general, the oxide particles were fairly uniform in size and distribution, forming a reasonably well-defined interface between the oxidized and unoxidized region. A typical cross section as observed at X30 is shown in Fig. 1. A thermal macroetch was used in one selected specimen to delineate the case. A cross section of a previously oxidized slab was polished and reheated at 1450°C in a hydrogen atmosphere for about 10 min. Upon quenching, the surface relief shown in Fig. 2 was produced; causes of this effect are unknown. Permeability Measurements Below 900°C. A slightly

Jan 1, 1967

By F. W. Davis

SOME idea may be gained of the tremendous consumption of refractories by the open-hearth steel manufacturers from a statement made by A. T. Green at a meeting reported by T11.e Industrial Chemist of London, as follows: "At a very progressive steel plant in the Midlands, with a battery of five open-hearth furnaces working. twelve months and making 3000 tons of steel per week, the cost of refractories per ton of steel produced averages about $0.50 for the actual open- hearth casting and $0.12 for those operations incidental to the rolling of the metal." .These figures, when translated into the annual tonnage of steel, represent a very considerable expenditure.

Jan 1, 1930

By Allen Johnson

WITH a realization of the rapidly increasing importance of automatic stokers as a medium for domestic heating, the Anthracite Institute Labo-ratory has conducted extensive investigations, over a period of several years, to determine the various outstanding characteristics of stoker design and performance. The purpose of this paper is to summarize these findings as a guide to current practices. STOKERS INVESTIGATED One or more models of the underfeed stokers listed below were included in the various phases of this investigation: Beckley Gilkoal Burnwell Iron Fireman Combustioneer Motor Stokor Electric Furnace Man Norristown Super-Stoker Erie Heat Generator Whitney Fire Ball (Tests Incomplete.) Fuel Saver Principles of Construction.-The operating principle of the leading makes of underfeed stokers is similar (Fig. 1). A plungers, or slowly revolving worm2, conveys the buckwheat or rice sizes of anthracite to the center of a specially constructed tuyere pot where air is admitted to the coal. through suitable ports of varying design. As the fuel burns, it is slowly forced to the outside circumference of the tuyere by the pressure of the incoming coal; eventually the ash falls over the edge of the pot, either entirely by gravity or aided by mechanical sweepers. In at least one model, the entire firepot revolves. While various special details have been included in the design of a number of stokers, they do not affect the ,general principles as described above, and therefore have not been included in this discussion.

Jan 1, 1935

By George S. Rice

MANY studies on ground movement and subsidence have been carried on by members of the Institute during the past year, but only a few papers have reached maturity. Two of the mining schools of this country have continued their interest in ground movement research. At Columbia University School of Mines, Philip Bucky has continued his investigations, employing photoelastic methods and the use of his centrifugal apparatus for testing what he termed "the strength and behavior of mining structures." Helmut Landsberg, of The Pennsylvania State College, has developed a convergence recorder similar in principle to that used by the

Jan 1, 1936

By R. O. Williams

Measurements have been made of the internal energy of deformation in a Cu-A1 alloy and a Cu-Zn alloy as the deference between the work and the released heat. The method required the rapid compression of samples to reduce thermal interactions. The rate of energy storage is low initially but then becomes almost linear with strain. Both alloys stored about 60 cal per mole at a strain of 0.4 in the recrystallized condition. The fractional rate of storage increases at low strains reaching about 0.25 at a strain of 0.15 and then decreases slowly with increasing strains. As do pure metals, these alloys release appreciable energy immediately following deformation; in contrast with pure metals, however, the release continued for extended periods of time. This energy release is somewhat sensitive to the amount of deformation, the deformation temperature, and prior thermal & eatment. It is believed that this release is a composite of that observed in pure metals which has been attributed to dislocations and that due to the motion of vacancies which produces increased short-range order. IT is expected that changes brought about by deformation of a pure metal can be understood in terms of the three defects—dislocations, vacancies, and interstitials—along with the interactions possible between these defects. Frequently stacking faults are created and must also be considered. 1t is not immediately clear whether or not the stress fields which are created should be regarded as independent of dislocations. For alloys there is the important additional effect of atomic configuration, for example short-range order, which must also be considered and will, in general, interact with each of the above defects. While it is true that a complete understanding of pure metals is not yet possible, it would seem very valuable to establish the similarities and differences between pure metals and alloys. Such knowledge could contribute to the understanding of both. A study of the changes in internal energy resulting from deformation of two alloys is reported here. Although some information has been available for alloys almost as long as for pure metals, the volume of work has been substantially less. Sato&apos; and Quinney and Taylor&apos; were responsible for the earlier work, both using brass and annealing calorimetry. tizhnova&apos; studied stored energy in Cu-Ni alloys by a method somewhat similar to the one reported here. Bever and his co-workers have made extensive studies of Au-Ag alloys4&apos;5 and more recently CU-AU&apos;U&apos; using solution calorimetry. Clarebrough et a1.&apos; have recently studied brass using annealing calorimetry. EXPERIMENTAL METHOD The present results were obtained by the rapid, adiabatic compression of a sample about 1/4 in, diam by 1/2 in. long between two tungsten carbide hammers. A vacuum provided thermal isolation and oil provided effective lubrication between the sample and hammers. The increase in internal energy is the difference between the mechanical energy and the heat liberated within the sample. The mechanical energy was determined from the velocity of the hammers (calculated from the height through which the hammers traveled) and was essentially constant for each deformation cycle. The heat was determined from the temperature increase of the sample which was measured by an embedded thermocouple. Specific heat data were calculated from Neumann&apos;s rule using tabulated data for pure metals.9 Since the fraction of the energy which is stored is large compared to that for pure metals, specific heat data of high accuracy are not required. Successive increments of deformation were carried out by repeating the procedure, the limit being determined mostly by the decreasing accuracy caused by the increasing corrections and the decreasing storage of energy. About five cycles were used to give a true strain of about 0.5 while the time interval between cycles was 1 to 2hr.

Jan 1, 1963

By J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young&apos;s modulus and a value of approximately 0.5 for Poisson&apos;s ratio. A value of % for Poison&apos;s ratio with finite Young&apos;s modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2&apos;3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By F. W. Bryan, D. H. Lynch

Introduction This paper is a general description of current central Florida phosphate mining, beneficiation, and product transportation. It is directed and believed to be of interest to engineers not familiar with this industry. Deposit: The phosphate deposits of central Florida are generally located in a five county area which includes Polk, Hillsborough, Hardee, Manatee, and DeSota counties. Geologically, the deposit is of marine origin and is identified as the Bone Valley formation. This formation is Pliocene to Recent in geological age and overlies a Miocene limestone formation known as the Hawthorn. The Bone Valley formation sediments are regionally characterized by equal proportions of apatite, quartz, and clay. The clay is predominantly of the mont-morillonite family. On a local scale, however, the proportions of these three major constituents vary considerably. The phosphate occurs as the apatite mineral (Ca 10F2(PO4)(6) and with the clay and sand, the minable ore is commonly referred to as matrix. This matrix is overlain by unconsolidated overburden of sand and sandy clays, ranging in depth from 10 to 45 ft. The matrix usually occurs in fairly horizontal continuous beds from 3 to 25 ft in thickness. The bedded limestone formation lies directly below the matrix and is generally well defined. The phosphate particles range from 3/4 in. to 200 mesh (Tyler) in size. The phosphate particles coarser than 14 mesh are called pebble phosphate and those less than 14 mesh are termed flotation feed which, when beneficiated, subsequently become concentrates. Through mining and beneficiation, phosphate quality is measured in BPL percent which stands for bone phosphate of lime units. In subsequent chemical manufacturing, the quality is indicated by P205 content. The deposit is economically characterized by various ratios such as tons of product per acre and cubic yards handled per ton of product. Magnesium, iron, and aluminum content are also considered in evaluating ore reserves. These elements are often critical to the chemical fertilizer processes. Presently, an ore body is considered economically minable if it meets the criteria shown in [Table 1]. These, of course, are general guidelines and specific costs and returns on investment must be considered in each case for acquiring reserves. On a new grass-root venture, a 20-30 year life is generally expected with a mineral recovery of 80%. History and Uses Phosphate mining in central Florida began around the turn of the century. However, in the early days, only pebble phosphate was produced until about 1930 when technology was available to beneficiate the -14 + 150 mesh particles. The -150 or -200 mesh material was discarded as it is today. The basic processes for beneficiation are washing, scrubbing, desliming, sizing, and flotation. These basic unit processes are essentially the same today although many improvements have been developed since the early days. Phosphate is used primarily in the production of high analysis fertilizer chemicals, typical of which are triple superphosphate, monoammonium phosphate (MAP), and diammonium phosphate (DAP). Phosphate is also used in the production of food preservatives, dyes for cloths, vitamin and mineral capsules, steel hardeners, gasoline and oil additives, toothpaste, shaving creams and soaps, bone china dishes, plastics, optical glass, photographic films, light filaments, water softeners, insecticides, soft drinks, road fill, and livestock feed supplements. Florida produces over 80% of the nation&apos;s marketable phosphate rock and one-third of the world production, according to the US Bureau of Mines. This amounted to approximately 35 million tons in 1975. Exports of Florida phosphate rock were to such countries as Canada, Japan, West Germany, Italy, and India, with Canada and Japan being the major users. Almost 95 o of all outbound cargo shipped through the port of Tampa is phosphate rock or related products. Beneficiation Following is a description of Agrico&apos;s new Fort Green beneficiation plant which is typical of the newer large capacity plants being built in the field. Agrico&apos;s Fort Green mine was completed in 1975 and is located in the southwest corner of Polk County and is directly adjacent to Manatee, Hillsborough, and Hardee Counties. With some minor differences, Fort Green is typical of a modern central Florida plant. The rated capacity is 3,000,000 plus tons of product per year and this varies according to the richness of the ore being handled. A simplified flowsheet is presented in [Figs.1 and 2]. This plant is served by three draglines of the 40-cu-yd class. The phosphate beneficiation is usually divided into three major functional steps: (1) washing and screening to produce a pebble product and flotation feed, (2) feed preparation and (3) flotation to produce concentrates. The typical plant is similarly divided into these three functional areas. Washer: Briefly, the slurried matrix is pumped from two draglines simultaneously at a combined rate of about 20,000 gpm at 2000 tph (solids) to rotary trommel screens sized to make a 7/8-in. separation. ([See Fig. 1]-) The trommel oversize is sent to hammermills where it is crushed and returned to the trommel screens, or pumped to tailings if minor impurities (Fe203, A1203, MgO) are too high. The trommel undersize is pumped to 14 mesh stationary (static) flat screens. The flat screen over¬size is subjected to three stages of 14 mesh vibrating screening and two stages of log washing in order to produce a final pebble product. The pebble product (+ 14 mesh material) is conveyed by belt conveyor to a large on-ground storage pile. Pebble product is reclaimed through a tunnel and loading system below

Jan 1, 1980

By F. R. Hensel

Up to the present time few attempts have been made to produce hard nonmagnetic materials by heat treatment of austenitic steels. The usual result has been to cause them to pass into the martensitic stage, thus destroying to a great extent the typical austenitic properties, since this involves a transition of a portion of the iron from a face-centered to a body-centered type of atomic arrangement. High-strength nonmagnetic materials such as might be provided by properly hardening austenite are required in the electrical industry for different machine parts. In Europe nonmagnetic retainer rings for restraining the end-turns of the rotor windings in turbo-alternators have been developed as a special application of high-strength austenite. In testing1 a 28,000-kva. three-phase Siemens turbogenerator running at 3000 r.p.m. at full load current, the losses in the short-circuit test were 450 kw. for the magnetic ring and 286 kw. for the nonmagnetic, and the difference should be attributable to the magnetic ring. The differences in temperatures during the same test are given in Table 1 and these show the advantage of a nonmagnetic over a magnetic retainer ring. Hardening in this case was obtained by cold working, such as hammering, rolling or some means for stretching the steel while at a temperature near 500" C. One means for stretching2 is to rotate the forged or rolled ring in a centrifugal machine so as to develop within it stress higher than

Jan 1, 1931

By G. Cartaud, F. Osmond

We have already devoted two previous memoirs to this question. In the firstL we collated and discussed the existing literature on the subject; in the second: we described the crystalline forms obtained by the reduction, at different temperatures, of ferrous chloride by hydrogen or by zinc-vapor. The conclusion from these researches was that the three allo-tropic states of iron—a, stable below A2; , stable between A2 and A3; and , stable above A3—all crystallize in the cubic system. The differences observed were such as are customarily encountered in the crystallographic records of many minerals of which allotropic varieties or isomerides are not known, and did not conform to the ordinary definition of polymorphism. It is, however, improbable that allotropic transformations, which are placed beyond doubt by a series of positive facts, do not involve some changes in the intimate structure. As a matter of fact, the crystals we did obtain were too small to allow of a precise examination, and this might introduce an element of uncertainty in the firm establishment of our conclusions. Professor H. Le Chatelier mas even led to think from some of our results that r-iron could very well be a rhom-bohedron simulating a cube, and not a true cube, and it will be remembered that the crystalline form of bismuth was for a long time incorrectly regarded as cubic. Allotropy does not, however, necessarily involve such a deduction. Without departing from the cubic system at all, a whole

Jan 1, 1907

By Ernest A. Hersam

The advantages of the tri-axial diagram in representing the composition of slags and silicates are well appreciated by many metallurgists. Prof. H. M. Howe* has pointed out the application of a fourth variable, in connection with the diagram, and has called attention to the usefulness of the general systern of tri-axial representation. In the discussion of Prof. Howe&apos;s paper, Mr. Firmstone† indicated how certain distances could be measured directly by projection. Prof. R. H. Thurston,‡ as early as 1877, had made use of a typtic model and of triangular diagrams, with contour-lines, rekrresenting varying physical properties corresponding to varying chemical composition. Still earlier, Prof. J. Willard Gibbs§ had used the diagram in similar work; and other scientists were thought by him to have preceded him in its use. During the period of nearly a quarter-century, following these early publications, there has been an ever-increasing use of graphic methods in numerous branches of scientific work, stimulated, in part, by the possibility of representation by three co-ordinates upon plane-surfaces. Yet the number of possible co-ordinates for graphic representation has always been, and always must be, insufficient to express many facts which are shown mathematically; while, without graphic representation, the involved nature of mathematical expression often fails to facilitate and promote research. The coming into use, therefore, of the fourth co-ordinate, permitting representation by four variables, marks but the beginning of some lines of research which could not well advance without this aid.

Jan 1, 1902

By R. E. Head, E. L. Tucker

Previous investigations of E. L. Tucker and R. E. Head&apos; related in particular to the effect of cyanogen compounds on galena, sphalerite, and pyrite, and their behavior in the presence of such compounds. The present contribution deals with the floatability of the copper minerals and of pyrite. All experiments were performed on minus 200-mesh material, the method of preparation being the same as that described in the previous article. Flotation tests were made in a small mechanically agitated machine of 50-gm. capacity designed in this laboratory by Gates and Jacobsen.2 General Naval Stores pine oil No. 5 and potassium xanthate were used in constant amount in all of the experiments; these agents were selected because of their present wide use in the flotation of copper minerals. Time additions were varied to secure four final hydrogen ion concentrations, namely, neutral, 0.0005 per cent. CaO, 0.003 per cent. CaO, and 0.02 per cent. CaO. The variation in lime addition was introduced to include the range of alkalinities employed in actual flotation practice. The minerals employed were the purest obtainable. Their analyses are shown in the following tabulation: Table 1.—Analyses of Minerals Employed in Experiments mineral Cu Fe Cao S MgO Insol. Chalcocite .............. 77 02 0.49 0.29 21.70 0.08 0.28 Chalcopyrite............. 34.50 29.20 0.23 34.10 0.07 1.42 Bornite................. 64.30 9.30 0.12 23.70 0.10 1.95 Pyrite....................... 36.90 1.12 49.70 .... 1.51

Jan 1, 1926