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By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

By K. G. Black, B. P. Faulkner

Laboratory batch flotation rests are used for comparison of the floatability of ores and for comparison of the effect of various treatments on ore floatability. Although it is difficult to predict exact recoveries for continuous flotation on the basis of batch tests, considerable quantitative information can be obtained through their use. A simple method is presented which provides a convenient means of quantitatively evaluating results from laboratory batch tests. The information obtained is in the form of a discrete flotation rate distribution, which, if desired, can be used directly in a simulation of continuous flotation. Equation of Batch Flotation The validity for batch flotation of the first-order kinetic equation is accepted: [ ] where k is flotation rate of a class of articles and W (t) is weight of particles of the class in cell at time t. Thus, at time t, the fraction of the original amount of the class of particles still remaining in the cell is [ ] where W (0) is weight of class of particles in cell at time zero. If there are several classes of particles in the cell, each with its own flotation rate, k4, the fraction of the particles remaining is [ ] where W (t) is now the total weight of n classes, a, being the original fraction of W (0) belonging to the ith class. Accordingly, [ ] [Fig. 1] shows the result of a typical batch test. Such result can be characterized by a set of particle classes, each set described by a flotation rate, [ki,] and a corresponding fractional magnitude, [ai.] [ ] Multiple Regression Equation Eqs. 3 and 4 may be combined to give

Jan 1, 1973

By Gerald Edmunds, M. L. Fuller

The development of "fiber" or preferred orientations, during the plastic deformation of metals, and the relation of such structures to the anisotropic characteristics of worked metals has become a subject of common knowledge among metallurgists. Very little has been published, however, relative to variations existent throughout the cross-sections of rolled strips,1 and the influence that such variations may have. This paper presents such a study on a rolled zinc alloy.2 The significance of small differences in surface structure is shown in relation to bending properties. Experience with zinc and its alloys has shown that the outer radius of the bend, which is subject to tensile deformation, is the common region of failure. In considering relations of structural characteristics to bending properties it will suffice, therefore, to consider the ease and possible extent of tensile deformation resulting from various orientations. It is necessary in this connection to assume that on the average the individual crystals of a polycrystalline material act substantially as if their movements were unobstructed by the surrounding grains. This assumption is not strictly valid, but the error involved is unlikely to affect seriously the qualitative conclusions derived from its use. The mechanism of the plastic deformation of zinc crystals has been described by Mark, Polanyi and Schmid3 and by Mathewson and Phillips14 and is regarded as being accomplished by block movements or * Investigator, Rolling Mill Section, Research Division, New Jersey Zinc Co. f Investigator, X-ray Laboratory, Research Division, New .Jersey Zinc Co. 1 Variations of structure throughout the cross-section of wire have been reported in the literature. 2 This alloy contained, in addition to zinc, 1.0 per cent copper and 0.01 per cent magnesium. Its crystal form is hexagonal close packed, the sarne as that of pure zinc. 3 H. Mark, M. Polanyi and E. Schmid: Vorgange bei der Dehrlung von Zink-kristallen. Zlsch. f. Phys. (1922) 12, 58. 4 C, H. Mathewson and A. J. Phillips: Plastic Deformation of Coarse-grained Zinc. Proc. Inst. Met. Div., A. I. M. E. (1927) 143. C. H. Mathewson: Twinning in Metals. Proc. Inst. Met. Div., A. I. M. E. (1928) 7. The results of a further study of plastic deformation of zinc as related to twin-

Jan 1, 1932

By C. H. Li, J. Washburn, E. R. Parker

Yield stress in single crystals of zinc was shown to be dependent on prior annealing temperature and rate of cooling after annealing. Rate of strain hardening beyond the yield was not sensitive to annealing procedure. A tentative mechanism for the effect was discussed. COMPARATIVE mechanical tests of metal single crystals generally show a large scatter of results. Many factors may contribute to this variation. The present investigation was undertaken to evaluate the influence of two factors not ordinarily considered of major importance—annealing temperature and cooling rate after annealing. Since plastic properties of crystals are thought to depend on the presence of lattice imperfections, it follows that a variation in properties should result from differences in the distribution and density of these imperfections. Furthermore, in the light of current theories of interaction between edge dislocations and lattice vacancies,' it seems possible that annealing temperature and subsequent rate of cooling might play a part in this distribution. Analysis of the effect of these variables on plastic properties may lead to a better understanding of the annealed state. Single crystals of zinc which have been strained in simple shear undergo complete recovery of mechanical properties upon subsequent annealing. This behavior is useful because a single specimen can be used repeatedly, thus eliminating the uncontrollable variables introduced by the use of many crystals. The test section of the crystals used for these experiments was a cylinder 1/8 in. thick with a cross-sectional area of about 1/3 sq in. The specimens were acid-machined from spherical single crystals 1 in. in diameter in such a way that the slip plane (0001) was at right angles to the axis of the cylinder. In testing, a shear stress was applied along one of the slip directions, [2110] in the (0001) plane.' All crystals, unless otherwise noted, were grown in a helium atmosphere from molten 99.99 pct pure Horse Head Special Zinc. Fig. 1 is a family of curves obtained from one crystal. Each curve was obtained by deforming the crystal to 10 pct strain at a rate of 3 pct per min, following an anneal of 1 hr at 260°C. The strain direction was reversed every other time so that no progressive change in shape of the specimen took place during the series of tests. Since the stress-strain curve was reproducible within a fairly narrow range under the same conditions of annealing, it was then possible to determine the effect of changes in annealing conditions. A crystal was tested repeatedly as previously described but the annealing temperature and rate of cooling preceding each test were varied (Fig. 2). Two cooling rates were used, approximately 30°C per min and 3°C per min. Annealing was conducted at three temperatures, 200°, 300°, and 400°C. For a given annealing time and rate of cooling the room temperature flow stress was higher the higher the annealing temperature. The increase in flow stress was small as the annealing temperature was increased from 200° to 300°C but rose rapidly when the annealing temperature was raised from 300" to 400°C. Faster cooling from the high temperature produced an even greater strengthening of the crystal. The curves were obtained in the order indicated by the numbers. The stress level associated with a certain annealing treatment was, within the limits of scatter, always the same regardless of the

Jan 1, 1954

By M. Gensamer

IT has been suggested by a number of people that it would be worth while for some one to attempt to summarize or condense the proceedings of this symposium. This task has fallen to me as organizer and co-chairman. Its difficulty will be appreciated by anyone who attempts to read the whole proceedings. It is therefore with trepidation that I offer the following digest. In recent years there has been a renewal of interest in America on this subject of the cohesive strength of materials, and a growing appreciation of the need for a better theory of cohesion failure. The theories of elastic action and plastic action are well developed, particularly the former. The theory of plastic action is still in the course of development, but it is well along. Plastic action is terminated by cohesion failure and what is needed is a theory that will tell us when to expect the cohesion failure. In the past it has generally been assumed that cohesion failure will occur when a critical value of the maximum tensile stress has been reached. Many experiments have shown that this is not strictly true, and this symposium concerns itself with the failures of this simple hypothesis, and with the efforts that have been made to devise a more satisfactory theory. The most active contributor in recent years to knowledge in this field is Dr. McAdam, and he was asked to open the symposium with a summary or condensation of his papers and views. Undoubtedly it is presumptuous to attempt a still greater condensation, but perhaps it will be useful, because even his contribution to this symposium contains no summary, no concise statement of just what his contribution has bees. Dr. McAdam makes two main points. The first is that the cohesive strength is not a single valued quantity, but that it is a function of all three principal stresses and hence must be represented diagrammatically by a surface in a three-dimensional figure. Dr. McAdam has attempted so to delineate the cohesion limit, basing his

Jan 1, 1944

By Arthur C. Spencer

In extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,' it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity, applied to an elastic brittle mass offering strung resistance to deformation, produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45' to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45. This general conclusion, resting upon analytical mechanics, is completely supported by the results obtained by DaubrBe2 in experiments upon the deformation of wax and resin prisms under compression. Let us then first consider one of Daubree's diagrams. In the case illustrated in Fig. 1, four sets of fractures in two approximately right-angled pairs (that is to say, in conjugate sets) were produced by endwise compression of a square cross-sectioned prism. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45o. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism, and place it between two fixed and

Jan 1, 1906

By W. M. Weigel

LESS advances in the technology of non-metallic minerals than for several years past mark 1931, and the cause is easily found. The universal depression and decreased markets for non-metallic as well as other mineral commodities has forced the producers to cut out all unnecessary expense and reduce operating costs to a minimum in order to keep going, even on a reduced output, and to prevent insolvency. The result. has been that but 'little research has been carried on, and such as has been completed has in but few cases been put into commercial practice on account of the expense involved in new equipment and plant changes. The trend in the industry has been more economic than technologic, and the greatest effort put on market studies and sales attempts to expand markets and scrutiny of present operating 'practice leading to reduction of cost of production. This tendency has been increased by highly competitive conditions and the buyer's market which has prevailed and to the fact that price has been a greater factor than quality in placing orders. Only in cases where improvements in technology would immediately and effectively reduce costs or where in special cases there was but little competition with almost a monopoly control has actual technical development taken place.

Jan 1, 1932

By Stephen H. Stow

A relationship exists between the color and the chemical composition of the pebbles from the Bone Valley Phosphate Formation. Darker-colored pebbles are relatively high in iron oxide and relatively low in calcium phosphate when compared to lighter-colored samples; the brown color of the phosphate pebbles can be correlated with their iron content and the black and gray colors with their organic carbon content.1,3 It was anticipated that the darkness of a phosphate sample might be quantitatively measured by a simple reflectivity test and that the amount of reflected light could be correlated with the chemical composition of the rock, especially with the elements which cause the color and darkness of the Florida phosphates. Twenty-one samples of production grade phosphate rock from Hillsboro County, Fla., were studied. All samples were ground to -200 mesh for reflectivity tests and analyses. All analyses are accurate to well within ±2% of the reported value, except for aluminum and organic carbon, which are accurate to only ±15% of the reported amount. Reflectivity measurements were taken with a model 610 Photovoltmeter for tri-stimulus amber, blue and green, and white lights. Experimental procedures and data are available upon request. Results Table 1 contains linear correlation coefficients (LCC) for the element-reflectance relationships for the samples. The top portion of the table refers to the LCC between the percent of light reflected off the samples and the percent of a given element (or its oxide) as analyzed. In the lower portion of the table the LCC refers to the relationship between the same reflectance data and the chemical analyses which have been corrected on the basis of 0% acid insoluble material (chiefly quartz) in the phosphate rock. Each LCC presented in Table I is computed for the 14 coarser samples exclusive of the seven concentrates since the concentrate samples appear to have anomalous reflectivities upon comparison with the coarser grades. Only the most significant LCC for each element is presented in graphical form. Discussion of Data Iron: [Fig. 1] is a graph of the relationship between iron and reflectivity (LCC = - 0.98). A good correlation with Fe2O3, is expected due to the relationship between the tan (or brown) color and the abundance of iron oxide, the principal mode of occurrence of iron in Florida phosphates.8 Note the location of the seven triangles which repre-

Jan 1, 1972

By Otto W. Nuttli

THE magnetic method of prospecting is well suited to determination of faulting in the basement rock. In addition to establishing the horizontal position of the fault, it often furnishes valuable information concerning the depth and amount of faulting. Consider a simple case of a vertical fault, represented in cross-section in Fig. 1. Let A A' represent the plane of observation (ordinarily the surface of the earth), and BB'B"B"' the upper surface of the basement. Assume that the sedimentary rocks are nonmagnetic, so that the magnetic susceptibility of the material above the basement is zero. Let k indicate the susceptibility of the basement rock, c the density contrast between it and the neighboring sedimentary rocks, and the amount of vertical displacement. Fig. 1 shows the material, indicated by cross- hatching, which gives rise to the magnetic anomaly. In most cases it can be assumed that is small compared to the thickness of the sedimentary rocks. The semi-infinite, rectangular slab of rock of susceptibility k, density contrast , and thickness t may then be replaced by a semi-infinite sheet CC' of mass t per unit area at depth 2 (the mean depth of the slab). Nettleton 1 states that this approximation results in an error of less than 2 pct for the computed gravitational field intensity when t is as great as 2/2 and decreases rapidly for smaller values of t. By a theorem of Poisson, the magnetic field intensity can be determined readily from the gravitational field. The theorem states that W = (I/) • (U/i) i1 [1] where W is the magnetic potential associated with the structure, I is the intensity of magnetization which is assumed to have the direction of the inducing field, ? is the constant of gravitation, the density contrast, U the gravitational potential associated with the structure, i the direction of the inducing magnetic field, and i1 a unit vector in that direction. The multiplication indicated in Eq. 1 is

Jan 1, 1956

By Lawrence Addicks

ONE of the properties of copper, which has done much to give it its present prominent place among the useful metals, is its electrical conductivity, a property which has now become the chief criterion of 'the value of the commerical product. In pursuance of that distinctively American principle that, 1' the best is none too good," metal of the highest conductivity is usually called for even where such extreme purity is of no advantage, for instance, in the making of brass and other alloys. The average brass-founder feels nervous unless his copper is so very pure that it shows a conductivity of 99 or 100 per cent., while the character of the zinc used is usually overlooked in his anxiety. Electrolytic refining has made it possible to produce copper of a' very high degree of purity, the metallic impurities averaging but a few thousandths of 1 per cent.; oxygen, usually present in the form of cuprous oxide, bringing the total up to about a tenth of 1 per cent. The published data bearing upon the relationship between chemical purity and electrical conductivity is, however, very scant,' nearly all the work that has been done having dealt with alloys carrying considerable quantities of the foreign elements. In this paper I have brought together the results of experiments extending over a period of several years that have been carried out with the idea of determining the amount of various elements which would lower the conductivity 3 or 4 per cent.-a series of impure coppers rather than alloys. There are many precautions necessary to keep the conditions

Mar 1, 1905

By D. Mizer, J. B. Clark

In a recent investigation of the entire magnesium-yttrium phase diagram, Gibson and Carlsonl report the maximum solid solubility of yttrium in magnesium as 8.0 wt pct Y at 1050°F (565°C). However, independent studies of the precipitation in magnesium-yttrium alloys, 2 conducted prior to the publication of the above phase diagram, indicated a greater solid solubility of yttrium in magnesium. Accordingly, the magnesium-rich region of the diagram was re-investigated to determine more accurately the liqui-dus, solidus, and solvus of the magnesium solid solution in this system. Metallography and thermal analysis were chosen as the best corroboratory methods for accurately determining this region of the diagram. A magnesium-yttrium master alloy was prepared from yttrium of 99.9 pct purity and singly sublimed magnesium of 99.9 pct purity. Subsequently, the twelve magnesium-yttrium alloys shown in Fig. 1 were prepared using standard alloying procedures for magnesium. Metallographic samples of the alloys were heat treated under an SO, atmosphere in an electric furnace capable of control within ±3oF of the desired temperature. Alloy samples for the metallographic determination of the solvus, and for the precipitation studies were solution treated at 1000° F for 16 hr. Subsequent aging times for the solvus determination varied from a minimum of 6 hr for the higher temperatures up to 816 hr for lower temperatures. Periods of 30 min at temperature were used to generate liquation for the metallographic placement of the solidus and eutectic horizontal. The liquidus and the eutectic horizontal were determined by thermal analysis. Simple time-temper- ature heating and cooling curves were obtained from 10-g alloy samples heated and cooled in a well-insulated electric furnace. An Iron-Constantan thermocouple was placed in direct contact with the sample. The thermocouple did not contaminate the alloy sample since metallographic examination showed that the alloy melt did not wet or attack the thermocouple. The heating and cooling rates were approximately 5 to 8OF per min. The standard metallographic procedures for magnesium were used in polishing and etching the magnesium-yttrium alloys studied. Glycol etchant* was etchant was used to reveal precipitate in the solvus determination. The redetermined magnesium-rich region of the magnesium-yttrium diagram is shown in Fig. 1. The

Jan 1, 1962

By P. A. Laxen, H. R. Spedden

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.'*' Study of the adsorption of sodium from an aqueous solution oftheon quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained."." Three main factors which appeared likely to affect the adsorption of sodium are: l—concentration of sodium in the solution, 2—concentration of onotherof cations in the solution, and 3—anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in thesethe amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxyl-ion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory' except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying." To minimize the laborious preparation of quartz, experiments were made to determine .whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na" activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot 11) and 2000 (lot 111) as determined by the Bloecher method." Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.' It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß+ radiation and a 1.30 mev r radiation. The decay scheme is illustrated in the following equation: ß+ NaR-------'8'77NeZ2 3 years The /3 radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang.R The original active material was 1 ml of solution containing 1 millicurie of Na" as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen." In brief, it included the following steps: 1—Ascertainment of linearity between concentration of Na" and activity measured. 2—Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3—Taking precautions to avoid evaporation of water during centrifuging

Jan 1, 1953

By P. A. Laxen, H. R. Spedden

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.'*' Study of the adsorption of sodium from an aqueous solution oftheon quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained."." Three main factors which appeared likely to affect the adsorption of sodium are: l—concentration of sodium in the solution, 2—concentration of onotherof cations in the solution, and 3—anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in thesethe amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxyl-ion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory' except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying." To minimize the laborious preparation of quartz, experiments were made to determine .whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na" activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot 11) and 2000 (lot 111) as determined by the Bloecher method." Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.' It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß+ radiation and a 1.30 mev r radiation. The decay scheme is illustrated in the following equation: ß+ NaR-------'8'77NeZ2 3 years The /3 radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang.R The original active material was 1 ml of solution containing 1 millicurie of Na" as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen." In brief, it included the following steps: 1—Ascertainment of linearity between concentration of Na" and activity measured. 2—Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3—Taking precautions to avoid evaporation of water during centrifuging

Jan 1, 1953

By R. C. Ernrnons, Ray Wilcox

RECENTLY completed experimental work, carried out in the department of geology at the University of Wisconsin, aiming at a prevention of silicosis in industry has been reported in the American Mineralogist. A vast amount of work on silicosis has been reported in the literature, the clinical aspects having been especially well covered. A host of critical observations have been made on the variations in the nature of the silicosis problem in different environments, and a great deal of valuable experimental work has helped to clarify these observations. At present a greater amount of information of a critical sort is available than ever before, which affords a more sound basis for interpretive thought. It has been observed in industry that essentially pure silica dust gives rise to silicosis. Jones would modify this conclusion to place the responsibility on sericite, a silicate mineral present in the siliceous dust. Material such as granite dust, which carries a high free silica (quartz) content, is also a silicosis hazard. But sericite, too, is usually present in granite. In general it is widely believed that silicosis is caused by the presence in the lung of silicic acid regardless of the source. This view is adopted here.

Jan 1, 1937

By H. E. Cline

A criterion for stability of a lamellar structure in two-phase alloys ulas derived froflr perturbation analysis of the steady-state solutions for eutectic growth. Both the mass and thermal diffusion were considered with boundary conditions for coupled lamellar growth. The concept of an effective liquidus slope was introduced. Excellent agreement was found with the experiments of Mollard and Flemings and the theory predicted a range of compositions on one side of the eulectic composition in which stable growth may occur with zero temperature gradient. The lamellar structure was found to be more stable than predicted by simple constitutional supercooling. The effect of impurity additions was also considered. DIRECTIONALLY solidified eutectic alloys may have a structure consisting of parallel plates or rods. It is important to know the range of composition and growth conditions that produce this ideal composite structure. Breakdown of the planar solid-liquid interface during growth may lead to a dendritic or cellular structure as in single-phase alloys. In the case of single-phase alloys, the concept of constitutional supercooling1 may explain breakdown, but in two-phase alloys the concept is no longer valid because the melting point is not given by the liquidus of one phase. Both phases must be considered in the mass and thermal diffusion problem. In the following theory a boundary condition at the solid-liquid interface was determined by using the steady-state equations of Jackson and ~unt' to relate the average temperature and composition of the liquid at the interface. Then a sinusoidal perturbation in the shape of the interface was introduced to test for stability as in the analysis of Mullins and ~ekerka.~ The wavelength of the important perturbation was assumed to be much larger than the lamellar spacing, h, and the perturbation was assumed not to change the lamellar spacing, A. Both the mass and thermal diffusion equation were used with averaged quantities at the boundary to determine whether the perturbation grows or shrinks in time. A stability criterion was determined by considering the case in which the perturbation remains stationary. An example of Pb-Sn alloys was used to illustrate the validity of this theory. I) THEORY A) Temperature at the Interface. The temperature of the interface in coupled two-phase growth is close to the eutectic temperature TE even for alloys off eutectic composition. It is assumed that the interface is in local equilibrium and one expects the temperature at the intersection of the liquid phase and the solid phases a and 0 to be near the eutectic temperature. The interface is undercooled because of curvature and the deviation of the composition in the liquid from the eutectic composition. The average interface temperature Ti for steady-state growth of a lamellar eutectic with a plane interface was determined by Jackson and Hunt' as given in their Eq. [17c]. Instead of using the ratio of the lamellar widths hp/h, as a parameter, the volume fraction of the 0 phase, +, will be used as it simplifies the algebra. The average interface temperature using this notation becomes: The average temperature of the interface depends on the volume fraction of the 0 phase, +, which may be related to the composition of the solid or the bulk composition of the liquid Co by: where C, and Cp are the average compositions of the solid phases. In steady-state growth, the composition of the solid is equal to the composition in the liquid far from the interface. The variation of the average interface temperature with composition is illustrated in Fig. 1 for the case of Pb-Sn alloys with a 10"4 cm lamellar spacing as calculated from Eqs. [I] and [2]. The interface temperature goes through a maximum at a composition near but not exactly at the eutectic composition. There is no reason why the composition corresponding to the maximum temperature should be equal to the eutectic

Jan 1, 1969

By J. R. Spencer

When supplies of high pressure mercury or other liquids are required in analytical work, it is convenient to have the source of supply at a relatively constant pressure and available in sufficient volume to satisfy the requirements of the apparatus in use. It is also desirable that the pressuring device be as simple and as inexpensive as possible and convenient to operate. This pump combined with a small storage reservoir containing gas under pressure has the attributes of (1) positive control of the maximum output pressure through the use of a regulator in the low pressure air supply; (2) an increasing capacity as the rate of withdrawal of mercury from the pressured system is increased; and (3) simplicity, requiring only the use of a lathe, drill press, and welding unit in its construction. DESCRIPTION Essential parts of the pump are shown in Fig. 1. In appearance the unlt is similar to the usual steam pump in common use in industrial applications although considerably smaller in size. The main differences lie in the area ratio of the air and mercury pistons and in the design of the air valve mechanism. Approximate diameters of these pistons are 4.25 in. to 0.375 in. respectively, giving an area ratio of about 130 to 1. The air piston (2) is attached to the end of shaft (4), with the mercury piston being merely a reduced extension of the shaft. Mercury intake and discharge to the pump are controlled by high pressure check valves that screw into the ports indicated at (6). Air supply is controlled by the valve assembly mounted on top of the

Jan 1, 1950

By A. P. Svenningsen

DURING the work at the test mill in Morenci, it was determined that a suitable feed for the ball mills could be made by a single pass through a short-head cone crusher. These crushers did not require a closed circuit delivering only a screen product to the mills, such as is the practice in some concentrators. By no means does this mean that the practice in these other concentrators is wrong, but just that the Morenci ore can be most economically crushed and ground in this manner. Therefore, the design of the secondary crushing plant was simply a problem of taking 25,000 tons of ore per 16 hour day from the primary crusher, this ore ranging in size from fine particles to 10 or 12 in., and reducing it to minus 3/4 in. Inasmuch as outages must be contended with in any crushing plant, it was assumed that the crusher would operate at full capacity for approximately only twleve hours per day, which is three-quarter capacity for the 16-hour shift. With this in mind, it was necessary to design a crushing plant which would average approximately 1600 tones per hour for the 16-hour day, or 2000 tons per hour for slightly over 12 hours per day.

Jan 1, 1942

By J. Chipman, T. P. Floridis

The equilibrium of gaseous H2O-H2, mixtures with liquid iron is used to establish the activity coefficient of dissolved oxygen as log f o = — 0.20 [%O]. Discrepancies in earlier work are explained or eliminated. Additions of cobalt, molybdenum, tungsten, and platinum increase the activity coefficient of oxygen whereas copper and gold decrease it. THE importance of dissolved oxygen as a refining agent in liquid steel has led to a number of studies of its thermodynamic properties. It is the purpose of this paper to examine the effects of a number of alloying elements on the activity of oxygen in the steel bath. As a preliminary to the study of the effects of alloying elements, it seemed desirable to examine certain minor discrepancies in the published data on the properties of oxygen in simple iron-oxygen solutions. The activity and free energy of oxygen in liquid iron were studied by chipman1 in 1933 by means of the reaction h2(g)+-o = H2O (g);K; = PH2O/PH2[% O] [1] The data were in fairly good agreement with calculations from results on the similar reaction CO (g) + O- = CO2 (g); K2 =P CO2/P CO [% O] [2] which had been obtained by Vacher and Hamilton2 as an incidental part of their study of the reaction of carbon with oxygen dissolved in the melt. It was found that the equilibrium ratio k1 was not a true constant but varied with the oxygen concentration in the manner shown in Fig. 1, which is copied from the original paper. This early observation has been refuted in subsequent work but is confirmed in the present paper, and an explanation of the discrepancy can now be presented. In Fig. 1, the two points on the extreme right were disregarded in drawing the

Jan 1, 1959

COLUMBIA SECTION STANLY A. EASTON, Chairman, FREDERIC KEFFER, Vice-Chairman, L. K. ARMSTRONG, Secretary-Treasurer, P. 0. Drawer 2154, Spokane, Wash. D. C. LIVINGSTON FRANK A. Ross The first meeting of the Columbia Section was held on March 24, as a part of the 1916 Northwest Mining Convention which was held under the -auspices of the Spokane Mining Men's Club assisted by the Spokane Chamber of Commerce, the technical program being in charge of the Spokane Engineering and Technical Association assisted by the local sections of the A. I. E. E., A. S. C. E., and A. I. M. E. The program of the successive sessions was carefully arranged with view to its application to mining, and in addition to the technical program there were exhibits of ores, minerals, devices, etc., of interest to the delegates, who numbered over 500. A portion of the program was also arranged with special reference to the requirements of the prospector and miner. A reception, a banquet, a complimentary luncheon, a regular daily call' of the Stock Exchange, a visit to the High Schools and to one of the substations of the Washington Water Power Company and to the Union Iron Works kept the visitors entertained, the ladies being looked after by a special committee of ladies who held open house during the entire week. Several important resolutions were passed by the Convention and one by the Columbia Section, A. 1. M. E. With Stanly A. Easton, chairman, presiding, the Columbia Section, American Institute of Mining Engineers, occupied the time between 2.00 and 5.30 p.m., March 24th, the Moorish room of the Spokane hotel being filled with members and their guests. "The Apex Law and the Mineral Surveyor" was a paper presented by F. W. Callaway and generally dis-cussed because of its local application in the Coeur d'Alenes, the conclusions being reached after expensive litigation between two of the large mining operators in that district.

Jan 6, 1916

By Carl Henrich

I have read with particular interest that portion of the discussion by Anton Eilers referring to the high-lime (and also high-alumina) slags made by August Raht in 1881, while smelting the Horn Silver ores at Franklin, Utah. The two analyses of such slags, furnished by Mr. Raht to Mr. Eilers are: (a) Not determined in this analysis. (b) Not given in Mr. Eilers' paper. Oxygen ratio, A1 as base. I. 0 in acid: O in base:: 18.1:18.9:: 0.96:1 11. 0 in acid :O in base:: 18.7:17.5::1.06:1 Average: 18.4:18.15=1.01:l Oxygen ratio, AI as acid. I. O in acid: O in base: :23.2:13.8:: 1.68:1 11. O in acid: O in base::23.1:13.5:: 1.76:1 Average: 23.15:13.4 = 1.73:l By assigning to alumina the the of a base, Mr. Eilers deduces the formula 3Feo.-2SiOa + 4Cao.2SiO². The nearest approach to a simple formula expressing the average composition of these slags, which I can figure, is 9RO.Al2O3.6SiO2. Allowing a ratio of 4Feo : 5Cao, we have for this formula:

Jan 1, 1917