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By H. J. O’Donnell, B. C. Parks

IN 1930 the late Dr. Reinhardt Thiessen set up a method of microscopic analysis and type classification of coal that has since been followed as standard practice in the coal-petrography laboratory of the Bureau of Mines. Thiessen's terminology which designated the constituent parts of coal in terms of botanical origin was introduced in 1920.l The technique, however, of preparing a completely representative series of thin sections from a column sample of coal for use in making quantitative determinations of coal components with a microscope was developed about 10 years later by Thiessen and coworkers G. C. Sprunk and H. J. O'Donnell.2 Complete thin-section analyses subsequently have been made of 126 column samples of various ranks and types of American coals. The data and information were assembled from these thin-section studies and published in a large number of reports dealing chiefly with investigations of the coking and hydrogenation properties of certain American coals. In the years following adoption of Thiessen's method, a considerable amount of work was done in collecting column samples of many coals, making routine thin-section analyses of these, interpreting the results, and finding practical application for the information in other fields of coal research. The many reports and papers covering the work in coal petrography, however, offer very little discussion that can be considered as critical appraisal of the technique. Criticism outside the Bureau most often has voiced questioning opinions concerning the accuracy of the method used of measuring coal components microscopically and classifying the coal into arbitrary types on the basis of the quantitative determinations. The principal purpose of this paper is to discuss in some detail and present data showing the results of certain investigative work done in the petrography laboratory on the accuracy of the Bureau's method of microscopic measurement of components in coal thin sections. Data from microscopic analyses on file made by G. C. Sprunk and H. J. O'Donnell were freely used in the investigation, and a table of columnar analyses from an unpublished manuscript by Sprunk is included in this paper for reference. In the course of the experimental work a method was developed for measuring instrumentally with a planimeter the components shown in micrographs of selected thin sections. Measuring coal components with a planimeter furnished useful information for studying the accuracy of microscopically measuring the same components in thin sections. PETROGRAPHIC COMPONENTS AND TYPE CLASSIFICATION OF COAL Thiessen considered coal to be composed of two visibly different major components present in various types of coal in greatly varying proportions. He named

Jan 1, 1948

By George A. Grandy, D. W. Fuerstenau

Simulation of nonlinear grinding systems is discussed in the context of the size-discretized batch-grinding model. A linear approximation of environment-dependent (or nonlinear) selection functions is postulated for systems which exhibit feed grinding orders less than unity. For this, a convex linear combination of zero and first-order selection function forms is used to obtain an analytical solution that can be used for simulation. An example in which marked nonlinear behavior occurs is rod-mill grinding. Accordingly, a series of grinding experiments was carried out in a batch laboratory rod mill to test these techniques; agreement between experiment and the model was found to be very good. Recently, significant progress has been made in the simulation of linear grinding systems by using a population balance mathematical model. Herbst and Fuer-stenaul presented a parameter estimation scheme that can be used with the size-discretized batch-grinding model, and Gumtz and Fuerstenau3 have extended these techniques to the simulation of locked-cycle grinding. Grandy et aL." summarized the simulation of linear systems and noted important alternate solutions to the batch-grinding equation. Kelsall et a1.'-" discussed the dynamic simulation of linear batch grinding, as well as linear open and closed-circuit grinding. In all of these, the key word is linear, which certainly restricts the engineer trying to simulate a variety of grinding systems. This paper discusses an approach for the simulation of non-linear grinding systems, particularly those which exhibit grinding orders less than unity. Experimentally, dry rod-mill grinding is used to evaluate the technique presented. Batch Grinding Model The size-discretized batch-grinding model has been discussed in detail by Mika et al.'.' and by Herbst and Fuerstenau,' and therefore, will only be briefly developed here. The model is formulated by making a differential mass balance of each size fraction in such a manner that the equation parameters are precisely defined in terms of selection and breakage functions,' which can be either calculated'.' or estimated1 from experimental data. The model is phenomenological because it averages all stress-application events in the system and, therefore, does not distinguish the manner in which individual particles are stressed.' For this average environment, the resistance of all particles in a size fraction to breakage is defined by that size-frac-tion's selection function; and when fracture occurs from an average event, the breakage product size distribution is defined again by that size-fraction's breakage function. The model is deterministic and is derived in terms of a continuous time variable and a discretized size variable,' i.e., the n mass fractions associated with the n defined size intervals (see Table 1 for nomenclature).

Jan 1, 1971

By A. H. Daane, J. J. Hanak, F. H. Spedding

IN the study of the rare earths at the authors' laboratory, methods have been devised for preparing pure rare earths and many of their properties'- have been determined. Very little information is found in the literature on the properties of europium metal, which is the scarcest of the naturally occurring rare earths. Since we have recently prepared europium in appreciable quantities, we are in a position to describe the method of preparation and some of the properties of this metal. Metallic europium was first prepared by Klemm and Bommera who heated a mixture of potassium and EuC1, in vacuo, and obtained a mixture of europium metal and KC1. Trombe4 electrolyzed a molten salt bath containing NaC1, KC1 and EuC1, and collected the europium in a molten cadmium electrode as a cadmium alloy. The cadmium was subsequently removed by distillation but the properties of the residue indicate that pure europium was not obtained. McCoy attempted to prepare europium by distilling mercury from europium amalgam, but the stability of the Eu-Hg intermetallic compounds prevented a complete separation of the two elements. The preparation of very pure europium was suggested by previous work in this laboratory1,4 in which ytterbium and samarium were prepared by heating the respective sesquioxides with lanthanum metal turnings to 1450°C in vacuo and distilling ytterbium and samarium from the mixtures. Subsequently, small test experiments showed that europium also could be prepared by this method. A more detailed version of this method was used in the work described in this paper. Klemm and Bommer3 found by X-ray analysis that the metal had a body-centered cubic (bcc) structure with a lattice constant a, = 4.582 ± 0.00A (converted from kX units), with a bulk density of 5.30 g per cu cm. They found europium to be weakly ferromagnetic. Spedding, et al,7 found a,, to be 4.606 ± 0.001A. Barrett' showed that the bcc structure persists throughout the temperature range 5 to 3000K with a, at 5, 78, and 300°K being 4.551 ± 0.003, 4.551 ± 0.004 and 4.577 ± 0.001A, respectively. Trombe1 described europium as being iron gray, malleable, about as hard as neodymium and not attacked by cold water. He estimated the melting point to be between 1100 and 1200°C. Previous work in this laboratory indicated that the pure metal corrodes rapidly in air and reacts with cold

Jan 1, 1959

By S. C. Sun, A. M. Gaudin

This paper presents the results of a. study of the relationship of the electrokinetic or zeta potential to flotation phenomena. The relationship is established on the experimental evidence that mineral behavior in flotation and in cataphoresis is generally governed by the chemical properties and amount of the reagents adsorbed at mineral surfaces. Cataphoresisl-5 or electrophoresis is the name given to the movement of a charged particle in a liquid medium under the influence of an applied electric field. Mineral behavior in cataphoresis, as indicated by the magnitude and sign of its ionic charge, can be represented by the term zeta potential. In this paper, the zeta potential represents the difference in potential between the immovable liquid layer attached to the surface of a solid particle and the movable liquid layer in the body of the liquid, and is the result of the tendency of ions on the surface of the particle and within the liquid boundary layer to establish a condition of equilibrium. A high positive zeta potential means that the mineral surface is dominated by cations, a high negative zeta potential indicates domination by anions, and a low zeta potential indicates that the surface is influenced almost equally by cations and anions. In terms of observed quantities the zeta potential is given by the relation _ 4µ(300)² Z= kx in which z is the zeta potential expressed in in volts, µ the viscosity of the solution in poises, u the velocity of particles in centimeters per second, x the impressed potential gradient in volts per centimeter, and k the dielectric constant of the solution in c.g.s. units. A convenient source for the derivation of the equation is the book by Thomas. The term zeta coefficient is an expression coined to denote the difference between the magnitude of the zeta potential of a mineral suspended in solution A, and that of the same mineral suspended in solution B, which consists of solution A and an additional chemical agent, but is at the same pH. For example, the difference between the zeta potential of galena particles in distilled water and that in any chemical solution at the same pH is a zeta coefficient. Or, when the zeta potential of a mineral particle is measured first in distilled water, then in a mixture of water and copper sulphate, and finally in a mixture of water, copper sulphate and xan-thate, we can calculate the zeta coefficient

Jan 1, 1947

By A. M. Gaudin, S. C. Sun

This paper presents the results of a. study of the relationship of the electrokinetic or zeta potential to flotation phenomena. The relationship is established on the experimental evidence that mineral behavior in flotation and in cataphoresis is generally governed by the chemical properties and amount of the reagents adsorbed at mineral surfaces. Cataphoresisl-5 or electrophoresis is the name given to the movement of a charged particle in a liquid medium under the influence of an applied electric field. Mineral behavior in cataphoresis, as indicated by the magnitude and sign of its ionic charge, can be represented by the term zeta potential. In this paper, the zeta potential represents the difference in potential between the immovable liquid layer attached to the surface of a solid particle and the movable liquid layer in the body of the liquid, and is the result of the tendency of ions on the surface of the particle and within the liquid boundary layer to establish a condition of equilibrium. A high positive zeta potential means that the mineral surface is dominated by cations, a high negative zeta potential indicates domination by anions, and a low zeta potential indicates that the surface is influenced almost equally by cations and anions. In terms of observed quantities the zeta potential is given by the relation _ 4µ(300)² Z= kx in which z is the zeta potential expressed in in volts, µ the viscosity of the solution in poises, u the velocity of particles in centimeters per second, x the impressed potential gradient in volts per centimeter, and k the dielectric constant of the solution in c.g.s. units. A convenient source for the derivation of the equation is the book by Thomas. The term zeta coefficient is an expression coined to denote the difference between the magnitude of the zeta potential of a mineral suspended in solution A, and that of the same mineral suspended in solution B, which consists of solution A and an additional chemical agent, but is at the same pH. For example, the difference between the zeta potential of galena particles in distilled water and that in any chemical solution at the same pH is a zeta coefficient. Or, when the zeta potential of a mineral particle is measured first in distilled water, then in a mixture of water and copper sulphate, and finally in a mixture of water, copper sulphate and xan-thate, we can calculate the zeta coefficient

Jan 1, 1947

By H. D. Newell

THERE has been much research and commercial development in recent years in the use of chromium and nickel in steels of various types, including those intended for high-temperature service. By "high-tem-perature steels" are meant those specifically designed for service at ele-vated temperatures in steam plants, oil refineries and other industries where high-temperature operations are conducted. This paper is devoted to some preliminary data on the effect of silicon on certain of the most popular chromium-molybdenum steels now being used in quantity by the refining industry and includes a short statement on the influence of copper in steels intended for high-temperature service.

Jan 1, 1937

Jan 1, 1953

By J. P. Pritchard, J. T. Pierce, O. G. Slay

This paper discusses the results of a technology-evaluation program to ascertain the feasibility of a piotornask-photoresist technology developed for fabrication of multiple-layer thin-film superconductive circuitry. The uehicle selected for this evaluation was a 120-bil associative data processor requiring a set of nine photomasks to define a similar number of patterned material layers of lead, tin, and polymer insulation. A total circuit area of 4 sq in. involved 2500 actitle and 12,000 passive crossings. Several short-free, electrically continuous specimens were satisfactorily completed under this program. Problems encountered in the preparation and use of the requi-ed set of Photomasks are discussed, as also are the problets of providing suitable external connections. A major retarding factor in the development of the superconducting thin-film cryotron technology for many years was the absence of batch fabrication means yielding necessary device density and count per substrate for practical applications. Early workers in the field desired only limited numbers of devices to permit careful study of discrete devices and representative circuitry integrating logic and memory capabilities. For these purposes mask stencils could be formed to selectively control the placement of materials, sequentially vapor-deposited in vacuum, to form the multilayer structure. In general a distinct pattern was required for each material layer; therefore, mechanical provisions were required to change not only the material source, but the patterning mask as well, before each deposition. All deposition steps were preferably performed in a single evacuation of the deposition chamber. Thus the means for storing, transporting, and registering masks and sources with respect to the substrate existed and were operated within the vacuum environment. In the authors' experience, the approach was and remains serviceable for preliminary device study, but was not extensible to an economical manufacturing method by virtue of the difficulties inherent in mask stencil preparation and use, and the capital investment implicit in the mechanization requirements. Since the commercial attraction of the cryotron technology stems principally from its potential for economical batch fabrication, the authors' program has placed major emphasis on fabrication methods. A highly useful method has evolved through adaptation

Jan 1, 1967

By R. W. Raymond

There is apparently no end to the doubts, inconsistencies and absurdities in which the courts of our mining States and Territories are involved in their attempts to apply to conditions of ever-increasing complexity the provisions of our anomalous mining law. In previous papers, I have called this statute " the law of the apex," because it based upon that vague, novel and mysterious condition the most important grant of title. But the apex is scarcely a more essential feature than the end-lines and the side-lines; for the rights which it may confer may be limited in various ways by these; so that we have, in many a case, the most ridiculous result that the United States, in return for the money of a citizen, conveys to him with much solemnity, under its broad seal, nobody knows what, bounded nobody can tell how. A decision recently made at Butte by Judge De Wolfe, of the United States District Court of Montana, in the case of King et al. vs. The Amy and Silversmith Mining Company, furnishes a fresh illustration of this criticism. The diagram on the following page, constructed without precise regard to courses and distances, simply to assist in the statement of the essential features of the case, will, 1 hope, make clear the principles . involved : The plaintiff occupies a location (the Nonconsolidated) adjoining on the north the defendant's location, a b c d (the Amy), and the disputed mining-ground lies, let us say, in depth under the point W, that is, on the dip of the vein, VD, but not under the surfacelocation, a b c d. The defendant has the prior title, and claims this ground under its extra-lateral right. It is admitted that the apex does not cross the end-line, a d, and does cross the side-line, a b. Whether it crosses, at the other end of the location, the end-line, b c

Jan 1, 1889

By Frederick M. Becket, Russell Franks

In a recent article,l which described the softening effect of columbium in plain high-chromium steels, the authors stated that their investigations had shown columbium to be also a particularly valuable inhibitor of intergranular corrosion in steels of the 18 per cent chromium, 8 per cent nickel type. It is the purpose of the present paper to record some of the results obtained through the introduction of columbium to the austenitic chromium-nickel steels. The damaging effects of this type of corrosion have become so widely known as to restrict considerably the applications of the steels under consideration, and therefore there is little question of the importance of the goal to be attained. Numerous contributions concerning the susceptibility of the austenitic chromium-nickel steels to intergranular corrosion have appeared during the past few years, and among others who have dealt constructively with the subject are such well-known authors as Strauss and Houdremont of Germany, Hatfield of England, and Bain in the United States. Different theories have been propounded as to the cause of intergranular corrosion, and various remedial measures have been proposed, the majority of which involve the use of addition agents. Titanium is the addition agent at present most generally employed, as suggested by Houdremont and modified as described by Bain, Aborn and Rutherford. Little has been published on the effects of holding these steels for long periods at the relatively lower temperatures in the presence of corroding media, and the effects have mot been fully realized by producer and consumer.

Jan 1, 1934

By G. K. Manning, C. H. Lorig

TWO metallurgical tools have acquired wide use within the past several years as a means of studying the transformation characteristics of steel. One is a technique used first by Bain and Davenport for determining the transformation characteristics of a steel at constant temperature; the second is the end-quench hardenability test. Constant-temperature transformation curves like those of Bain and Davenport have done much to rationalize the metallography of steel; however, in commercial practices, constant-temperature transformation is seldom encountered, therefore only rarely can such curves be directly applied. The real reason for the determination of such curves lies in the fact that they provide a way of thinking about transformation that is both convenient and productive. The end-quench hardenability test is a more practical means of studying transformation, for, by correlating positions on the hardenability bar with shapes of different masses, an almost direct application of the results can be made. Unfortunately, the end-quench test, though practical, can do very little toward improving the metallurgists' way of thinking about transformation. These two metallurgical tools, dealing with precisely the same phenomenon, should be very closely associated in metallurgists' minds. Actually, they are frequently pushed into separate mental corners and considered as being more or less distinct and unrelated. The reason for this is that no strong connecting link between them has been developed. An attempt is sometimes made to relate these two tools by projecting the critical cooling rate on the isothermal transformation plot as illustrated in Fig. I. The critical cooling rate is considered as a constant rate-though in practical applications, cooling rates are never constant—and this constant cooling rate is given uniform significance from the Ae temperature down to the temperature of initial transformation. A little thought indicates the errors of such a procedure. Certainly the time interval spent just below point A of Fig. I cannot be as effective in promoting nucleation as is the time interval spent just above point B. Yet the procedure represented in Fig. I considers all the time spent between temperatures A and B to be just as effective in promoting nucleation as though all the time were spent at temperature B. Furthermore, change the shape of the isothermal curve between points B and C in any way desired, and the required critical cooling rate is not changed one iota. This cannot possibly be true. Such a way of thinking about critical cooling rates not only is incapable of giving any results that are quantitatively satisfactory but is likely to give very misleading qualitative results.

Jan 1, 1947

By G. K. Manning, C. H. Lorig

TWO metallurgical tools have acquired wide use within the past several years as a means of studying the transformation characteristics of steel. One is a technique used first by Bain and Davenport for determining the transformation characteristics of a steel at constant temperature; the second is the end-quench hardenability test. Constant-temperature transformation curves like those of Bain and Davenport have done much to rationalize the metallography of steel; however, in commercial practices, constant-temperature transformation is seldom encountered, therefore only rarely can such curves be directly applied. The real reason for the determination of such curves lies in the fact that they provide a way of thinking about transformation that is both convenient and productive. The end-quench hardenability test is a more practical means of studying transformation, for, by correlating positions on the hardenability bar with shapes of different masses, an almost direct application of the results can be made. Unfortunately, the end-quench test, though practical, can do very little toward improving the metallurgists' way of thinking about transformation. These two metallurgical tools, dealing with precisely the same phenomenon, should be very closely associated in metallurgists' minds. Actually, they are frequently pushed into separate mental corners and considered as being more or less distinct and unrelated. The reason for this is that no strong connecting link between them has been developed. An attempt is sometimes made to relate these two tools by projecting the critical cooling rate on the isothermal transformation plot as illustrated in Fig. I. The critical cooling rate is considered as a constant rate-though in practical applications, cooling rates are never constant—and this constant cooling rate is given uniform significance from the Ae temperature down to the temperature of initial transformation. A little thought indicates the errors of such a procedure. Certainly the time interval spent just below point A of Fig. I cannot be as effective in promoting nucleation as is the time interval spent just above point B. Yet the procedure represented in Fig. I considers all the time spent between temperatures A and B to be just as effective in promoting nucleation as though all the time were spent at temperature B. Furthermore, change the shape of the isothermal curve between points B and C in any way desired, and the required critical cooling rate is not changed one iota. This cannot possibly be true. Such a way of thinking about critical cooling rates not only is incapable of giving any results that are quantitatively satisfactory but is likely to give very misleading qualitative results.

Jan 1, 1947

By S. B. Christy

Jan 1, 1902

Balancing the prodigious iron ore deposits of Western Australia are the equally vast coal resources of the Bowen series of eastern Queensland. The Bowen series is a Permian basin stretching 500 miles in a north-south line. The beginning of what will be large scale mining of the Kianga-Moura coalfields in Dawson Valley was made by the Australian company of Thiess Bros. in July 1961. Then Peabody Coal Co. of St. Louis, Mo., joined Thiess. Later, Mitsui & Co. Ltd. received a 20% interest in the firm Thiess, Peabody, Mitsui Coal Pty. Ltd. Rtitsui was to lend the company money for development. Queensland Parliament, by special act, granted the company exclusive franchise over the Kianga-Moura coalfield, an area of 350 square miles. The rights do not include other minerals. The company is to have a 120-mile railroad completed to Gladstone or some other port in seven years. It must produce at least 500,000 long tons of coal annually until the line is built, after which production is to be upped to 2 million tons. By December 1962, these arrangements were completed.

Jan 10, 1964

By Albert J. Phillip

Jan 1, 1947

By Albert J. Phillip

Jan 1, 1947

By A. C. Dittrick

THE Simon-Carves washer, originally known as the Baum jig washer, was first built in Europe about 1892. It was probably the first washer to use intermittent pressure of air on water in one part of the wash box to obtain water pulsations in another part. This type of washer was also the first to successfully clean various sizes in the same unit. Previous practice was to size closely before washing. Today there are several large firms abroad, and a few in the United States, that are constructing the Baum type washer. The design of all is practically the same, their differences being only in details. In 1928, the Hanna Coal Co. first gave consideration to the question of coal cleaning. It was believed at that time that by efficient removal of so-called noncombustibles appearing in the Pittsburgh No. 8 seam, certain markets that had been lost due to poor preparation might be recovered. Mechanical cleaning and mechanical loading were under consideration. This type of cleaning was considered the most practical means of removing impurities in the sizes below 4 in. It was decided to adopt mechanical cleaning and develop a system of mechanical loading that would be successful on No. 8 coal.

Jan 1, 1935

By N. J. Grant, H. Brunner

This paber is concerned with the determination of equations relating elongation to the amount of shear taking place both along grain boundaries and in slip planes of poly crystalline aggregates during creep. Certain discrepancies with previously used equations are pointed out. Grain boundaries were observed to become serrated during creep, but it is shown that this does not necessarily prevent further grain boundary sliding. Direct obser-vations of subgrain boundary ingration lead to the conclusion that this migration facilitates sliding along serrated grain boundaries. It is bointed out that the state of stress at triple boints is still unknown. MOST of the mechanisms of deformation contributing to elongation are shear processes, such as slip, kinking, grain boundary sliding, and twinning. For quantitative investigations of individual deformation mechanism it is necessary to know the equation which permits the calculation of speci-tnen elongation from measured amounts of shear. This calculated elongation must then be compared with the observed total elongation. The authors' special interest concerned grain boundary sliding during creep. Although this subject has already been investigated quantitatively by McLean,' Rachinger,' and Fazan, Sherby, and Dorn, calculations indicated that none of the equations used thus far to relate shear with elongation were sufficiently well founded. A basic study of this relationship was thus made and the results of this study (which do not entirely agree with those previously used) are presented. Most of the ideas set forth apply not only to grain boundary sliding but to other mechanisms of shear as well. THE SPEAR-ELONGATION RELATIONSHIP Basic Models—The relationship between shear and elongation is trivial in the simplest case of shear, which is shown in Fig. l(a). The vector A; designates the displacement across the shear interface, and Au, and Aut are its components parallel and normal to the tensile direction, respectively. It is evident that the specimen elongation due to shear is equal to the longitudinal component of the shear vector, and it should be noted that the normal component does not contribute to the elongation of the specimen (there are, of course, two normal components in a three-dimensional model). The model shown in Fig. l(b) may be applied to mechanical twinning and to subgrain boundary tnigration. In this case the width (h) of an already existing shear band increases by the migration of an interface, but the shear angle y (angle of mis-orientation in the case of a subgrain boundary) remains constant. The geometrical relationships indicated in Fig. l(b) permit this case to be reduced to the one shown in Fig. l(a). For the resulting elongation A6 we find: where AV/V = fraction of the volume of the specimen swept by migrating interfaces , and 1 = length of specimen. Thus, assuming for example that the angle of mis-orientation is 1 deg, and that P = 45 deg, we find that the specimen elongates 0.87 pct of its length if the entire volume of the specimen is swept once by such a subgrain boundary. An example of deformation by migration of subgrain boundaries is shown in Fig. 2. The specimen shown was repolished after 9.8 pct creep strain and the test then continued for another \ pct. Since the shear vector has, in general, a component normal to the surface, subgrain boundary migration results in the formation of an inclined band delineating the region swept by the subgrain boundary. These inclined bands become clearly visible when observed with oblique illumina-

Jan 1, 1960

BLOCK CAVING HAS BEEN DEVELOPED to a high degree of efficiency in the last two decades and more particularly since World War II. At the Jeffrey mine of Canadian Johns-Manville Co., in the Eastern Townships of Quebec, several innovations have increased production and decreased costs. Asbestos ore is produced at the rate of 10,000 tpd from an underground operation supplemented by a large open pit that has been mined since 1881. The orebody consists of asbestos veins in a fractured and serpentinized peridotite. Hardness and structural strength of rock vary from soft shear zones at one extreme to a small amount of hard granitic inclusions at the other. In general the ore is weak and deteriorates on exposure to air, so that it is difficult to maintain underground openings for any period of time. Permanent workings are lined with concrete and temporary ones are driven mini- mum size and supported with steel sets as required.

Jan 5, 1954

By G. O. Prickett, P. Somasundaran

An experimental progmm based on statistical principles is used for optimizing a flotation operation for the separation of minerals. In this case, flotation of sylvite from sylvinite ore with amine and starch as the flotation reagents was studied to find the optimum reagent levels at various slime levels. The experiments were first done on a two-level three-factor design. Analysis of the results showed that the interactions between various factors were significant. Hence, a first-order linear model of the flotation response would not be accurate. The two-level three-factor design was expanded into a composite design in order to test the fit of a higher-order model. Data were treated to obtain an expression for flotation response as a function of the different variables, to predict the optimum reaaent levels at various slime levels, and also to determine the path of steepest ascent. Tests around the predicted optimum and along the path of the steepest ascent were done until a near-optimum region was obtained. Exploration of the nature of the response surface in that region established the actual location of the maximum response. The optimum amine level was found to be 0.20 lb of amine per ten of ore at all slime levels, while the optimum starch level varied as a function of the slime present. Computer access at the laboratory by means of a teletype terminal on a commercial time-sharing system enabled efficient and accurate treatment of experimental data. The efficiency of experimental investigations can be improved significantly by the use of experimental design and data analysis based on statistical principles. The common approach used in experimental research is to study a property of a system as a function of "one-variable-at-a-time". Several authors'-4 have pointed out the inadequacy and deceptiveness of this method. Results obtained for the effects of a variable on the measured response of the system using

Jan 1, 1970