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By S. M. Wu, R. L. Stone, T. D. Tiemann

The dissolution of silica from quartz in sodium hydroxide solutions was investigated by statistical methods. A second-order predicting equation was developed with 28 experiments expressing the dissolution of silica as a function of the variables quartz size, time, temperature and sodium hydroxide concentration. With this equation a comprehensive picture of the dissolution reaction was gained which included the effect on extraction of each variable and their interactions, fractional extractions, reaction rates and activation energies. A previous investigation of the extraction of silica from low grade siliceous iron ore by digestion in sodium hydroxide solutions presented the extraction as a function of time, temperature and sodium hydroxide concentration.' The present paper is an outgrowth of the previous work and develops by a mathematical analysis the functional relationship between the extraction of silica and time, temperature, sodium hydroxide concentration and particle size. Relatively pure quartz was used in this study in order that the basic quartz-sodium hydroxide reaction could be studied without the influence of other constituents that are commonly found in iron ores. The functional relationship between the dissolution

Jan 1, 1965

By Albert Sauveur

THE senior author of this paper has expressed the belief that when gamma iron transforms into alpha iron on reaching the A3 point, each gamma grain does not change bodily into one or more alpha grains but that the alpha phase forms first at the boundaries and along the crystallographic planes of the austenite grains.1 To quote: On cooling through the point A, at about 900° C., iron passes from the gamma condition to a. new allotropic form generally designated as alpha. This transforma¬tion, however, is not instantaneous. There are good reasons for believing that it begins at the grain boundaries and along the octahedral planes of the crystals and that it progresses until each grain of gamma iron is changed into a grain of alpha iron, the resulting structure being similar to that of gamma iron. Were it possible to retain at room temperature pure iron but partially transformed, it seems probable that a Widmanstättian structure, or rather, as later explained, a martensitic structure would be observed (Fig. 1), consisting of alpha iron at the boundaries and at the octahedral planes, and of a groundmass of gamma iron. In order to confirm, if possible, the accuracy of that view, a number of experiments were conducted. Polished samples of electrolytic iron were heated in a vacuum, maintained in the gamma range for several hours and quenched in different media. It was hoped by such means to produce and retain on the polished surfaces a pattern which would reveal the mechanism of the allotropic transformation. The samples were placed in evacuated quartz tubes, heated to 1000° C. and held 2 hr. at that temperature. The tubes were then immersed in the quenching bath. Iced brine and liquid air were used first. The polyhedral austenitic structure existing at the time of immersion was very clearly revealed (Fig. 2). This is generally ascribed to iron volatilizing at the grain boundaries.

Jan 1, 1929

By AIME AIME

IN many countries the lack of liquid petroleum supplies has centered interest upon the hydrogenation of coal and coal tars for the preparation of motor fuel. In the United States, hydrogenation has been of greater interest for grading up low-value petroleum fractions to the more valuable volatile fuels and for the preparation of a variety of premium products, including aviation gasolines, solvents, Diesel fuels, and lubricating oils. Chemically, the basic reason for this process is that, as shown in Table 1, the ratio of hydrogen to carbon (H/C ratio) in available raw materials is quite different from that characterizing the products sought.

Jan 1, 1936

By C. V. O. Hughes

Florida phosphate operations are unique in the ways standard mining equipment is made to meet specialized problems. Hydraulic mining and transportation has evolved in meeting three such special problems: 1) surface mining of a shallow, poorly consolidated but wet material; 2) high pro¬duction rates, necessary because of low prices for phosphate rock in a highly competitive market; and 3) preparation of the value-bearing rock, or matrix, for washing and flotation. The magnitude of the problems is better appreciated if the reader understands the size of operations in the area. The Florida phosphate field produces and ships about 10 million tons per year of phosphate rock. All of this has to be concentrated to its shipping grade, either by scrubbing and screening or by flotation.

Jan 1, 1956

By H. W. Maynor, C. J. McHargue

DURING the course of an investigation of materials suitable for use as thermocouples at elevated temperatures by one of the authors, several nlolybdenum-rhenium alloys were prepared. Micrographs of an annealed alloy containing 25 pct Re (intended concentration; analysis not obtained) showed a number of twins, Fig. 1, suggesting a face-centered cubic structure. This note reports the structure and recrystallized wire texture of an alloy containing 25 wt pct Re. Alloys were prepared from 99.9 pct Mo (Fansteel Metallurgical Corp.) and rhenium obtained from the University of Tennessee (purity unreported). Powders were combined and briquetted at 56,000 psi and sintering was carried out at 2400°C for 5 hr in vacuum. Ingots so prepared were swaged at 982.2" to 1037.8oC into wires 0.036 in. diameter, a reduction in diameter of 85.6 pct. These wires were vacuum-annealed 1 hr at 2000°C. A North American Philips 114.59 mm powder camera and nickel-filtered copper radiation were used for structure determination. For the texture determination a Laue-type camera was used with zirconium-filtered molybdenum radiation and, because of the high background, aluminum foil was mounted next to the film. Exposures were taken with the wire perpendicular to the X-ray beam and tilted by 10". It was found that the X-ray pattern could be indexed on the basis of a face-centered cubic structure. Because of difficulties associated with obtaining a good X-ray pattern for this material, accurate parameter determinations were not made. An indicated parameter value of 3.70A was obtained. The X-ray data are given in Table I. The annealed wire texture was observed to be a sharp [111] texture. The spread about this fiber axis was k8" at the surface of the 0.036 in. wire. The annealed wire textures of aluminum have been reported as retention of the [Ill] deformation texture for anneals below 500°C and a new [1121 texture for anneals above 600°C.1 In copper wires, with a [Ill] plus [loo] deformation texture, results indicate a retention of this texture for annealing at lower temperatures and new components or the disappearance of components for annealing at higher temperatures.' The presence of the strong [I111 texture in the molybdenum-rhenium alloy after a 2000 °C anneal suggests that the deformation texture was the same. Acknowledgment The wires used in this study were prepared and heat-treated at the Institute for Atomic Research, and Ames Laboratory, Iowa State College, and the authors wish to express their thanks to the Institute for allowing the use of the material and permission to publish the results.

Jan 1, 1954

By K. N. Weaver

In the early 1950's the cement industry began putting a new emphasis on geology. This article points up some of the industry's raw materials problems that geologists are uniquely qualified to handle. Portland cement can be made from relatively abundant industrial minerals and rocks, and this may explain why cement producers placed little emphasis on geology during the early days of the industry. After World War 11, however, the industry began to recognize the need for geological exploration and some of the larger companies began to build a permanent geological staff. This development has its roots in: 1) The rapid expansion of the industry. After World War II and continuing into the early 1950's the demand for cement far exceeded the production capacity. This placed a great deal of pressure on the producers to enlarge capacity at their plants and to develop new sites. 2) The closing of many cement plants due to inadequate raw materials. Producers feared lack of raw materials due to inadequate exploration and evaluation. 3) An ever increasing pressure for upgrading of the quality of portland cement, necessitated upgrading the quality of raw materials. 4) The increasingly large capital investment needed to build new cement plants required a higher degree of accuracy in reserve calculation. These reasons are more or less self explanatory and will not be elaborated on. They are outlined to illustrate the probable evolution of thought among cement management to justify the development of a geological staff. In the author's personal experience the geologist must continually readjust to changing conditions within the industry. For example, cement production capacity grew so rapidly that today production is only about 70% to 75% of rated capacity (73.8% in 1963). Therefore, whereas the geologist's function during the active expansion of capacity was primarily one of exploration, one of his major functions today is the development of existing reserves. This assumes of course that reserves at existing plants have been proven to be adequate in terms of the company's reserve policy. Through the proper development of raw materials, the geologist can markedly influence quality control, production and long range planning. Examples of several of the operations of Medusa Portland Cement Co. will illustrate how proper attention to geologic detail pays off in the above areas. Because limestone is the major raw material of port-land cement, the examples will be concerned with it. DEVELOPMENT OF GEOLOGIC DETAIL One of the prime objectives of an exploration or development project should be the establishment of the stratigraphy and structure of the deposit. The basic tool for exploration and development is still the core drill, and the geologist must gain a maximum amount of information from a minimum amount of drilling. In order to obtain this objective the following is essential: 1) Adequate detailed geologic logging of cores. The core is first logged and separated into lithologically distinct units. In order to make the lithologic breaks as meaningful as possible, representative pieces of core (not all) are etched in dilute HCI. This removes the "drill polish", brings out the structure of the rock and indicates the proportion of dolomite and argillaceous material because dolomite and argillaceous material etch in relief. In this way the lithologic breaks become clearer and one gains a general idea of the chemical makeup before analysis. This method of logging lessens the probability of including two types of stone, e.g. limestone and dolomite into the same sample for chemical analysis. 2) Representative sampling for chemical analysis. After logging, the lithologic units are sampled for chemical analysis. A representative analysis can be obtained by extracting a 1-in. sample for every foot of core. For example, a lithologic interval of 10 ft to 20 ft would yield ten 1-in. samples taken at 11 ft, 12 ft, 13 ft... and 20 ft. These samples are then crushed, pulverized and split into a sample for chemical analysis. This sampling method represents a significant saving of time over splitting the entire core. 3) Preparing the core as a record. Because of the expense of storage and the difficulty of handling large amounts of core, only representative samples of each lithologic unit are saved for reference. An

Jan 1, 1965

By E. C. Burke, W. R. Hibbard

Plastic deformation in magnesium single crystals was studied by tensile tests at room temperature utilizing an improved preparation and testing technique. Consistent critical resolved shear stress values for basal slip were obtained. The advent of pyramidal slip at room temperature was rationalized upon the basis of grip constraints. A bend-twinning hypothesis was advanced as an explanation of mechanical twinning which occurs as a complex stress-relief mechanism. INVESTIGATIONS of the plastic deformation of magnesium have been limited to the determination of the fundamental kinetics which may be summarized as follows: 1—Twinning on the {102).l 2— Slip on the (001) plane in the [loo] direction at room temperature.' 3—Slip on the {101) or {102) plane in the [loo] direction above 225°C." 4—Critical resolved shear stresses for basal slip in tension at room temperature of 83 g per sq mm with a variation from 57 to 127 g per sq mm." Bakarian' studied the compression of thin wafers of magnesium single crystals and classified the components of the deformation mechanisms as follows: 1—The Basal field: (001) at an angle of less than 20" to the compression surface. Fracture along {101} or slip on (001) followed by {101} fracture. 2—The prism field: (001) at an angle greater than 60" to the compression surface. Twinning on the {102) generally occurring during the early stages of loading, basal slip in the areas of original orientation and (001) slip within twins. 3—The central field: (001) at angles greater than 20" but less than 60" to the compression surface. Slip on the (001). 4—The critical resolved shearing stress for {101} slip above 225°C was 400 g per sq mm. Observations of mechanical twins in hexagonal close-packed metals have been summarized by numerous investigatorsb-' emphasizing a lateral or rotational atomic adjustment, in addition to the pure twinning shear, and the importance of reorienting the basal plane to a position more favorable for continued slip, rather than the resulting small dimensional changes. Criterion for the operative twinning planes has not been clearly established. Schmid and Boas hurmised that an energy condition related to the atom movements is the determining factor. MillerQ bserved that twinning stresses in zinc crystals decreased as the amount of prior deformation increased. Preparation of Specimens Magnesium single crystals % in. in diam x 8 in. long were grown from the melt under an argon atmosphere in a gradient furnace similar to that described by Jillson." Magnesium containing 0.018

Jan 1, 1953

By Baxter C. Madden

Stress corrosion is defined and certain examples are illustrated. A number of test methods, to determine the resistance of materials to stress corrosion, are being developed at Wright Field. The criterion as to the validity of a method is stated. Three types of specimens and the method of stressing each type are described. Five different corrosive conditions are set forth. The results of tests to date, although too few for any general conclusions to be arrived at, are presented. The program for the continuation of the investigation is indicated. A bibliography is included. The development of the method of loading a cantilever-type specimen, so that a nearly constant stress at a large deflection may be realized, is presented as Appendix I.

Jan 1, 1945

By S. S. Clarke

THE opening of zinc-lead ore bodies in the lower chert beds of the Tri-State district, locally called sheet-ground deposits, [ ] presented several new economic operating problems to be solved before the low-grade deposits could be mined profitably. Drilling was the first high-cost problem and loading and haulage difficulties followed. At this time, the sheet-ground mines are producing about 2000 tons per day. GEOLOGY The geology and ore deposits of the Tri-State district have been covered in detail by [ ] Fowler and Lyden.* Briefly, the sheet-

Jan 1, 1942

By S. Beatty

RECENT experimental results' on the superconductive properties of vanadium indicate that the magnetic behavior of the metal is greatly affected by internal strains caused by mechanical work, and particularly by oxygen and nitrogen impurities. These result in an increase in the hardness of the metal such that metallurgists' have used hardness as a measure of the impurities. An increase in the impurities should also be reflected in a change of lattice parameter with increasing impurity content. The lattice parameter of vanadium prepared by the thermal decomposition of the iodide has been determined by two workers. Neuburger3 obtained a value of a, =3.0338 ± 0.0003A for the body-centered cubic lattice by means of the powder method. The work of Katelaar is referred to by van Arkel4 in which a value of a0 = 3.025 is given. Four samples were used for this investigation. Sample A, the vanadium of the highest purity in the group, was obtained by means of the thermal decomposition of vanadium diiodide and deposited on a 3 mil diam tungsten filament in the form of crystals. The second sample, labeled B, was obtained by the calcium reduction of the pentaoxide at a sufficiently high temperature to give a melt. A third sample, C, was obtained in the same manner as B but remelted in a pure argon atmosphere. The last sample, D, was prepared by the calcium reduction method and the fine powdered vanadium was then sintered by means of applied heat and pressure. Samples A, B, and C were thus essentially free of mechanical strain in their preparation. Sample D was annealed in a high vacuum at 800°C. The samples were prepared for X-ray diffraction analysis such that all additional strain by cold work or by contamination with oxygen and nitrogen was kept at a minimum. Powder obtained from filings was deemed unsuitable since this would require annealing to get rid of the cold work. A heat treatment up to 1000°C at 10-6 m pressure might still increase the impurity content by means of adsorbed oxygen from residual gas in the vacuum chamber. The most satisfactory samples were prepared for back-reflection film techniques. Samples were cut to size, etched with hydrobromic acid, and mounted in Bakelite. They were then lightly polished on 3-0 paper and lightly etched. Chemical and Hardness Analysis of Samples Spectrographic analyses were made of the four samples and indicated similar metallic impurities for the group. The major metallic impurity in each sample was iron, which was less than 0.01 pct. The sum of the other metallic impurities was approximately 0.1 pct. The carbon content was assumed low by virtue of the methods of sample preparation. The principal impurity difference between the samples was in the oxygen and nitrogen content.

Jan 1, 1953

By B. J. Nelson, F. N. Rhinos

Studies upon the rates of oxidation of copper alloys containing small quantities of the alloying elementsl,2 have shown that steady growth of the scales at predictable rates is limited to a small concentration range and to oxidation at temperatures above 600°C., whereas unpredictable and erratic oxidation behavior is found with alloys containing larger additions and at low temperatures. The latter effect appears to be associated with modifications in the geometric disposition of the oxides. At low concentrations of the baser elements in copper, simple oxidation behavior is typified by the formation of two distinguishable zones of oxidation: (I) a subscale composed of discrete particles of the oxide of the alloying element embedded in substantially pure copper and (2) an external scale composed of cuprous oxide (with a very thin layer of cupric oxide on the outside) containing particles of the alloying element distributed throughout, but most profusely near the metal surface (see Fig. 2, top). Where this type of structure obtains, the process of oxidation is believed to be implemented, and its rate controlled, by the diffusion of the reacting elements through a' continuous matrix phase; i.e., through the alpha (metallic) phase of the subscale and alloy and through the cuprous oxide of the external scale. Copper is presumed to diffuse outward through the cuprous oxide layer to the external surface, where it reacts to form more cuprous oxide.3 Oxygen is delivered at the oxide-metal interface in the form of cuprous oxide, which may either react with the alloying element to deposit its oxide at the inner limit of the external scale or dissolve in the pure copper that remains at the surface of the metal after it has become depleted in its oxidiza-ble alloying elements. Both oxygen and the alloying element are pictured as diffusing through the metal, the oxygen inward and the alloying element outward. Where the two diffusion streams meet in sufficient concentration the oxide of the subscale is precipitated. If the oxygen pressure in the surrounding atmosphere is just below the pressure necessary to maintain cuprous oxide undecomposed, no cuprous oxide can be formed; some of the oxide of the alloying element may form upon the external surface, if its decomposition pressure is below that of cuprous oxide, and a normal sub-scale appears. This condition is achieved experimentally by enclosing the alloy with cuprous oxide together with an excess of copper. At temperatures from 600°C. downward, the precipitated oxides tend to accumulate at the grain boundaries of the alpha phase where a relatively small volume establishes a partial barrier to the diffusion of the reactants- Similarly, large volumes of Precipitated oxides tend to deposit in various patterns that may be expected to

Jan 1, 1944

By F. N. Rhinos, B. J. Nelson

Studies upon the rates of oxidation of copper alloys containing small quantities of the alloying elementsl,2 have shown that steady growth of the scales at predictable rates is limited to a small concentration range and to oxidation at temperatures above 600°C., whereas unpredictable and erratic oxidation behavior is found with alloys containing larger additions and at low temperatures. The latter effect appears to be associated with modifications in the geometric disposition of the oxides. At low concentrations of the baser elements in copper, simple oxidation behavior is typified by the formation of two distinguishable zones of oxidation: (I) a subscale composed of discrete particles of the oxide of the alloying element embedded in substantially pure copper and (2) an external scale composed of cuprous oxide (with a very thin layer of cupric oxide on the outside) containing particles of the alloying element distributed throughout, but most profusely near the metal surface (see Fig. 2, top). Where this type of structure obtains, the process of oxidation is believed to be implemented, and its rate controlled, by the diffusion of the reacting elements through a' continuous matrix phase; i.e., through the alpha (metallic) phase of the subscale and alloy and through the cuprous oxide of the external scale. Copper is presumed to diffuse outward through the cuprous oxide layer to the external surface, where it reacts to form more cuprous oxide.3 Oxygen is delivered at the oxide-metal interface in the form of cuprous oxide, which may either react with the alloying element to deposit its oxide at the inner limit of the external scale or dissolve in the pure copper that remains at the surface of the metal after it has become depleted in its oxidiza-ble alloying elements. Both oxygen and the alloying element are pictured as diffusing through the metal, the oxygen inward and the alloying element outward. Where the two diffusion streams meet in sufficient concentration the oxide of the subscale is precipitated. If the oxygen pressure in the surrounding atmosphere is just below the pressure necessary to maintain cuprous oxide undecomposed, no cuprous oxide can be formed; some of the oxide of the alloying element may form upon the external surface, if its decomposition pressure is below that of cuprous oxide, and a normal sub-scale appears. This condition is achieved experimentally by enclosing the alloy with cuprous oxide together with an excess of copper. At temperatures from 600°C. downward, the precipitated oxides tend to accumulate at the grain boundaries of the alpha phase where a relatively small volume establishes a partial barrier to the diffusion of the reactants- Similarly, large volumes of Precipitated oxides tend to deposit in various patterns that may be expected to

Jan 1, 1944

AT the fall meeting of the Iron and Steel Division, Oct. 4, 1934, in New York, a symposium was held on Slag Control in the Making of Iron and Steel. The chairman was J. H. Nead and the vice chairman, G. B. Waterhouse. The latter presided at both morning and afternoon sessions. The papers and discussions were presented in the order in which they appear on the following pages. To meet space requirements, much of this material has been considerably condensed. CONTENTS [ ]

Jan 1, 1935

By M. Lastra, A. Cruz, J. Menacho

The use of phosphates was studied as a way of purifying acidic copper leach solutions for direct electrowinning. The addition of 2.5 gpl phosphorus to plant solutions originally containing 6.25 gpl Fe (III) at pH 2 0 reduced the iron concentration by one half. Under identical conditions, but without phosphorous additions, the iron concentration was reduced by less than 1 gpl. Any residual phosphorous had no undesirable impact on electrowinning. The concentration ratio of Fe (III) to phosphorous which provides maximum iron elimination was determined. Higher ratios bring about a redissolution of the iron precipitate. Several ways of controlling iron with phosphates are discussed. These take advantages of more rapid and complete iron precipitation at lower pH levels.

Jan 1, 1980

By P. Payson

INTERGRANULAR corrosion in corrosion-resistant chromium-nickel steels has been widely discussed in the last few years. So far as the author knows, nothing has been published which definitely shows that this tendency can be eliminated, although suggestions have been made that a remedy is possible if certain specifications are satisfied. Strauss, Schottky and Hinueber1 suggested an increase in chromium content to an extent that would prevent the impoverishment of chromium on carbide precipitation sufficient to cause impaired corrosion resistance in the matrix. Pilling2 suggested an increase in nickel, so that the stability of the austenite matrix would be increased. Aborn and Bain,3 say that "intergranular attack-may be eliminated by preventing carbide precipitation (e. g., by lowering the carbon content or somehow raising its solubility) or by precipitating it permanently under conditions which will not remove chromium from solid solution so drastically at any points." In a later paper Aborn and Bain4 state that many different metallic elements, tungsten, vanadium, copper, aluminum, molybdenum, titanium and zirconium, have been added in small per-centages to increase the stability of these alloys, but that it has been reported that according to the copper sulfate test these added elements act only to retard the intergranular corrosion, and that increased nickel and chromium contents have similar effects. Newell5 showed that the lower the quenching temperature before reheating, the less severe was the intergranular attack.

Jan 1, 1932

By N. W. Perry

Some months ago a gentleman gave me a handful of minerals which he had collected in an arroyo, or dry stream-bed, that ran through the town of Ramos, State of San Luis Potosi, Mexico, as a sample of the class of ore that might be expected in the mines of that section. I was, however, familiar with those mines and their ores, and cast the pebbles aside as of no interest. I afterwards returned to Mexico and took charge of two groups of mines, one in the State of Zacatecas, and the other in the town of Ramos, State of San Luis Potosi. While I was thus engaged, it was a very frequent occurrence for parties to bring me specimens of rock, ores, etc., for my opinion on them; and one day a man brought me a half-dozen or more small pieces of a very black shiny mineral, desiring to know what it was. I did not recognize it, and desired him to give me the specimens for analysis, which he promised to do in a day or two. He never did give them to me, for he lost them ; but he said there were plenty more where these came from—at Ramos—and he could get them at any time for me. I thought no more of the matter until after my return to this country, when, one day, in looking over some of my old " trash," I came across the specimens at first referred to as having been cast aside so carelessly. I noticed two distinct minerals among the pebbles : one being erubescite or tetrahedrite, the predominating mineral of the mines of Ramos, and the other a hard black shining mineral, the same that I had wished to analyze in Mexico. On testing for hardness I was surprised that it scratched topaz with some degree of ease, thus placing it above 8 in the scale of hardness. Trying it with a corundum, I sometimes succeeded in scratching it, but at other times it would scratch the corundum, and at still other times neither would produce the slightest effect on the other. Crystallized topaz would be ground to a powder in attempting to scratch the black mineral, without abrading it in the slightest. It must, therefore, be placed at 9 in the scale of hardness. It is of the deepest opaque black, not unlike pitch-blende in ap-

Jan 1, 1884

By Robert W. Hunt

HAVING devoted considerable time to the investigation of the Clapp-Griffiths converter and the metal produced in it, it may perhaps be of interest to the Institute to learn the conclusions which I have formed. Of course, it is well known that the stationary converter of small size is the very oldest type of vessel used in the pneumatic process. Hence it will be only necessary to call your attention to the points which are special features of the Clapp-Griffiths. This converter has a slag tap-hole, situated at such a height in relation to the metal under treatment that, when the cinder is formed and boils up as the blow progresses, it can run off and thus be removed from contact with the iron, and will also be out of the way when the decarbonized metal is tapped into the casting ladle and the manganiferous alloy added. The manner of shutting off the blast, when the process is completed and the metal is being tapped, is another distinctive feature. The tuyeres are situated around the sides of the vessel, and enter the interior some little distance above the bottom; they are provided with plugs through the centers of which there are small openings. When the blow is completed, these plugs are forced forward into the outer orifices of the tuyeres, thus shutting off the blast, excepting the small quantity' entering through the passages named. While this is sufficient to keep the metal from running into the tuyeres, it reduces to the minimum the action of the blast while the metal is being tapped. Of course, this is of great importance, as in an ordinary stationary converter any delay in getting open the tap-hole means overblowing, and even while the first part of the charge is running out the oxidation is in frill force. Duplicate or movable bottoms are used, thus more than doubling the possible output of the plant. The pressure of' blast is quite light, never ex-

Jan 1, 1885

By P. C. Kapur

A principal first-order and a minor summation term contribute to the solution to the discretized batch-grinding equation when formulated in cumulative retained mode. Depending on the inter relations hips between the selection and breakage parameters, the minor term may be advantageously modified in a number of ways. The reduced grinding equations thus obtained are solved by iterations to give relatively simple solutions which are tested against experimental data. The irn-plications and advantages of the reduced grinding equations are briefly discussed. In many instances, the trajectory of the particle-size distribution in a batch mill may be extracted from a set of particle mass balance equations as follows

Jan 1, 1971

By B. Ladanyi, B. Hoyaux

A first requirement for assessing the safety of a rock slope, either artificial or natural, particularly if the rock behaves in an elastic-brittle manner, is a propw knowledge of the distribution of stresses within the slope and their development with time and advancement of workings. There are a uumber of different methods that can be used, in principle, for obtaining this information, such as (1) stress measurement in situ, (2) photoelasticity,1 (3) analytical methods, and (4) numerical methods. In cases where the stress distribution cannot be obtained by classical analytical methods, as in the one considered herein, either photoelasticity or numerical methods are norrnally used. However, actually, due to the rapid development of high-speed computers, increasing preference is given to the numerical methods. Among the latter, the most successful ones, to date, for determining the stress distribution in slopes have been (1) the finite difference method,2-4 (2) the lumped parameter method,5 and (3) the finite element rnethod.6 However, for determining gravity stresses in a natural rock slope, only the finite difference method has been used until now.7,8 A solution of the same problem by the finite element method will be shown here in which a particular reference is given to the development of tensile fracture zones within the slope. FINITE ELEMENT METHOD The stress analysis using the finite element method originates from an extension of the matrix analysis of structures.9 It consists in decomposing a continuous medium, assumed herein to be homogeneous and isotropic,

Jan 1, 1972

By T. K. Matthews

Minerals are mined as a one-time crop, and the processing of one ton of ore results in there being one ton less to be recovered from the deposit. Although some minerals occur in greater abundance than others, they are to a greater or lesser degree exhaustible. Depletion Allowances One of the distinctive features of the mineral industries is the allowance for depletion. The depletion allowance is a much maligned and misunderstood principal of our tax structure. Although imperfect in design, it has nevertheless served as a constructive incentive for the development and expansion of the minerals industry.

Jan 1, 1969