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By S. R. Krogh, T. O. Olsen

Analytical expressions for the breakage rate as functions of mill charge, mill speed, particle size, ball diameter, and ball load are derived, using idealized models for probability of breakage (Gaudin and Meloy), energy distribution (Mempel), and arithmetic mean of effective ball energy (Langemanns). Computational results using the theoretical equations are compared to experiments. The equations enable simulation of ball mill grinding at different grinding conditions.

Jan 1, 1973

By Gordon M. Matheson, Charles V. Logie

The current state-of-the-art design of mine pillars can be grouped into empirical and numerical design techniques. Numerical design techniques are based on sophisticated computational techniques which analyze the stresses and strains through the interstices of a pillar. Empirical techniques are less exact, but have been widely used, particularly for coal mine pillar design, because of their ease of computation. Over the years numerous empirical equations have been proposed to calculate the ultimate strength of coal mine pillars. This paper presents a review of the various equations which are most frequently utilized and examines the fundamental assumptions, limitations and applicability of the design formulae. The review intends to provide the practicing mining engineer with an understanding of the assumptions and mathematical basis of each equation to aid in the selection of the criteria most applicable to his specific design problems. Recommendations are made of the empirical equations that are presently most acceptable for design.

Jan 1, 1983

By D. Constantinides

In 1981 a Zn-Ag-Pb deposit was discovered in the vicinity of Molai, Greece. Subsequently, it was determined to be of the Kuroko type. The geology of various areas in the southeast Peloponnesean Peninsula is similar to that of the Molai deposit. Since favorable geologic criteria are present, absent, or unknown in varying degrees in all areas, it was deemed necessary to classify and rank the prospective areas according to the level of information available. For each level of information, an ore discovery model based on pragmatic exploration criteria was developed, enabling the favorability of occurrence to be calculated for each area. A Monte Carlo simulation was used to calculate the probabilities, the input data consisting of quantitative and qualitative estimates of the geologic criteria for each area. Three levels of information were modeled : Level A consisted of 9 criteria, level B of 12 criteria, and level C of 20 criteria. The three levels of information were tested on the Molai area. The results exceeded expectations, showing the gen¬eral trends which control mineralization at the lowest level of information. With an increase in the level of information, geological trends become more evident and a differentiation can be made between areas containing Cu mineralization, exhibiting a low probability, and areas likely to contain Zn-Ag-Pb mineralization. The models were then applied to the neighboring areas - only level A and B were available.

Jan 1, 1986

By V. Miller

Highly variable milling procedures within a geologically complex porphyry copper deposit owned by Kennecott Corp. in Nevada made it necessary to estimate copper recovery and concentrate grade in areas where actual test data was lacking. Estimation was made by first determining the relationships between desired metallurgical properties and the ore's petrology-copper mineral type, rock type, and copper grade. This relationship was then combined with previously estimated rock type, mineral type, and copper grade data in the mineral block model to predict milling properties.

Jan 1, 1985

By George Lehman

THE Inspiration Consolidated Copper Co. had an orebody at Miami, Ariz., of close to 100,000,000 tons of low-grade copper ore, and the method of mining this ore most profitably was of great importance. The selection of a method was practically limited to a "top-slicing," a "shrinkage-stope" or a "caving" method. The "top-slicing" method would give a high extraction of the developed ore, at a high mining cost, and the ?shrinkage-stope" or "caving" methods ) a lower extraction of, the developed ore, at a lower mining cost. ORE-DRAWING TESTS To decide on the method to be used it was necessary to know about what extraction of the ore could be obtained by the "shrinkage-stope" or "caving" methods. As no definite information regarding the question was available at the time, C. E. Mills, the general manager, thought that some information could be obtained by experimenting in drawing ore, covered with capping, from an experimental box. Some work had already been done along these lines by W. C. Browning for the Inspiration Copper Co. and by myself for the Live Oak Development Co. The idea was to represent as nearly as possible, in the experimental box, the conditions within an area of caved stopes of caved ore all ready for drawing. That is, the area was supposed to represent a semibroken mass with the capping above it in the same condition and ready to follow the ore downward as it was drawn out of the chutes under the ore. To represent the above condition, in the experimental box, crushed ore from the mine was placed in it to a given height, and red barren capping from the mine was placed on top of the ore.

Jan 9, 1916

By B. Yu, H. M. Lee, R. P. Gardner

Some preliminary results are given on the use of radioactive tracers for implementing the mechanistic approach to flotation. The process studied is an industrial one for the cleaning of sand for the production of glass. The radioactive tracers employed are those produced from intrinsic elements in the sand by neutron irradiation in a nuclear reactor. The results indicate that the technique will be useful for the determination of flotation simulation mechanistic model parameters on operating industrial processes without interruption of their normal operation.

Jan 1, 1980

By François Robert

The rate of new mineral discoveries in Canada has been declining in the last two decades. In response to the challenge and to stagnating investments in mining-related R&D, twenty Industry partners, supported by PDAC and Natural Resources Canada, established in 2010 the Exploration Innovation Consortium (EIC). This Consortium seeks to promote the discovery of new resources in Canada through coordination and sponsorship of industry-focused innovative and collaborative research and technology development, as well as training and education in mineral exploration. The two main themes of the integrated R&D program focus on exploration targeting in Deep and Mature Environments and in Remote and Covered Terranes.

May 1, 2011

By M. E. Nicholson

IT has been suggested by a number of investigators, I including Hume-Rothery and Raynor,' that certain intermediate phases in metal systems take on interstitial crystal structures because of an appropriate ratio of radii of the two atoms. If the size factor is an important parameter in determining whether or not an intermediate phase will have an interstitial structure, then it would appear reasonable that the relative sizes of interstitial atoms should have a direct relation to their solubilities in interstitial compounds. It was on such a basis that Petch,' in his discussion of the cementite structure, concluded that nitrogen is the only possible element which could replace carbon. Recent X-ray studies by Jacka indicate that the solid solubility of nitrogen in cementite is negligible. If this is the case, then on the basis of size factor it would not be expected that any element can replace carbon in FeaC, since according to Schwarzkopf and Kieffer4 the covalent atomic radii of nitrogen, carbon, and boron are 0.71, 0.76, and 0.87A, respectively. Nevertheless, Vogel and Tammann in 1922 indicated that a quasi-binary relation exists between the interstitial compounds FeaC and Fe2B and that the solid solubility of boron in FeaC at approximately 1150°C is 1.4 pct B by weight. Because of the apparent disagreement between theory and experiment, the solid solubility of boron in FeaC has been reinvestigated. In addition, the influence of boron on the saturation magnetic moment (per gram) and Curie temperature of cementite was determined. Experimental Procedure A series of Fe-B-C alloys which varied in boron content from 0 to 5.4 wt pct B were prepared by arc melting a 50-g ingot using carbonyl iron, Ache-son AUC graphite, and Cooper grade A boron for starting materials. The composition of these alloys is listed in Table I and shown graphically in Fig. 1. The samples represented by the solid circles were used for X-ray analysis and Curie temperature measurements; by the squares, samples used for quantitative metallography; and by the triangles, samples used for saturation magnetic moment measurements and Curie temperature measurements. After arc melting and subsequent quenching from 1000°C, so that all phases in the resulting microstructure were brittle, one half of the 50-g ingots were pulverized until a powder was obtained which was less than 100 mesh. These powders were then homogenized in evacuated Vycor capsules at 1000°C for 24 hr and water quenched. Although the homogenized powder had sintered somewhat, it was suitable for saturation magnetic moment and Curie temperature determinations, for which the 60 to 100-mesh fraction of the powder was used. For X-ray analysis the homogenized powder was crushed again until a 300-mesh powder was obtained. After crushing, the powder was mixed with Alundum of approximately the same grit size to prevent sinter-

Jan 1, 1958

By S. Chander, D. W. Fuerstenau

Hallimond tube flotation, contact angle measurements, electrokinetics, and electrode potential measurements have been used to investigate the natural floatability of molybdenite. The effect of surface pretreatment and the role of hydrogen, hydroxyl, molybdate, and calcium ions on the flotation of molybdenite has been studied. The surface potential of molybdenite has been suggested to be controlled by HMoO[ ] and MoO4= surface species whose properties are strongly influenced by pH. Calcium ions, which appear to be specifically adsorbed, are able to reverse the zeta potential of molybdenite. The experimental results have been analyzed in terms of the Derjaguin model of wettability, namely in terms of van der Waals and electrical double layer interactions and hydration effects at interfaces.

Jan 1, 1973

The October issues* of the Journals of the three AIME Societies carried a brief resume of the historical development of various technical and professional organizations which in some immediate or remote way affect the individual member of AIME. This resume was presented by the Institute Committee on Inter-Engineering Society Cooperation. Recently, several plans have evolved designed as a first step to provide a so-called "unity organization" for the entire engineering profession. Almost all of the plans involve Engineers' Joint Council, Engineers' Council for Professional Development, and National Society for Professional Engineers in some way or other. Hence our committee is presenting to our membership a resume of the recent activities of the two umbrella organizations and of NSPE. More detailed information on any of these organizations may be obtained from annual reports published by the organizations.

Jan 2, 1961

By Michael B. Bever, John R. Anderson

Carbon may affect the alloys of copper in several ways. Provided an alloying element does not oxidize preferentially, even minute quantities of carbon dissolved in liquid alloys of high copper content will form insoluble carbon oxide gases under oxidizing conditions. Gas porosity in castings of high-copper alloys can originate in this way. In certain alloys of low copper content carbon may have considerable solubility and may be an effective deoxidizer. In these alloys carbon will tend to suppress porosity. Carbon that is dissolved in the molten alloy is likely to be retained in the solidified metal. The effects of carbon on the physical properties of the metal are determined by the form in which it is present. Depending on the alloying elements and also on the cooling rate, carbon may precipitate as graphite, may form a carbide or may remain in solid solution on cooling. As solid copper does not dissolve a measurable amount of carbon, a carbon-bearing solid solution can occur only if the copper is alloyed with a large excess of an element that forms such a solution. The effect of graphite or of carbides on the properties of an alloy will depend on the size and distribution of the precipitated particles. As Hensel pointed out in discussion,' the formation of an alloy carbide may interfere with the age-hardening properties of a copper alloy. One would also expect that the presence of carbides or of graphite will under certain conditions promote corrosion or high-temperature failure in nonferrous alloys. Since carbon has an effect on the soundness of castings and affects the structure and behavior of solid copper alloys, its solubility in the liquid alloys is of practical importance. The isothermal change of carbon solubility with alloy composition is of interest from a theoretical standpoint. The binary alloys of copper with manganese and with nickel are used industrially and serve as a base for more complex alloys. The solubility of carbon in each of these metals is known, but its solubility in their alloys has not been determined. Earlier Data The solubility of carbon in molten pure copper is about o.oooi pct at II00°C and 0.0004 pct at 1475°C.l Various authors2""6 have published data on the solubility of carbon in molten manganese. There is agreement on a value of about 6.7 pct in the temperature range r2170 to 1245°c This solubility value corresponds to the formula Mn3C. It increases very little with increasing temperature. Corson7 states that carbon is soluble in copper-manganese alloys and that the

Jan 1, 1947

By John R. Anderson, Michael B. Bever

Carbon may affect the alloys of copper in several ways. Provided an alloying element does not oxidize preferentially, even minute quantities of carbon dissolved in liquid alloys of high copper content will form insoluble carbon oxide gases under oxidizing conditions. Gas porosity in castings of high-copper alloys can originate in this way. In certain alloys of low copper content carbon may have considerable solubility and may be an effective deoxidizer. In these alloys carbon will tend to suppress porosity. Carbon that is dissolved in the molten alloy is likely to be retained in the solidified metal. The effects of carbon on the physical properties of the metal are determined by the form in which it is present. Depending on the alloying elements and also on the cooling rate, carbon may precipitate as graphite, may form a carbide or may remain in solid solution on cooling. As solid copper does not dissolve a measurable amount of carbon, a carbon-bearing solid solution can occur only if the copper is alloyed with a large excess of an element that forms such a solution. The effect of graphite or of carbides on the properties of an alloy will depend on the size and distribution of the precipitated particles. As Hensel pointed out in discussion,' the formation of an alloy carbide may interfere with the age-hardening properties of a copper alloy. One would also expect that the presence of carbides or of graphite will under certain conditions promote corrosion or high-temperature failure in nonferrous alloys. Since carbon has an effect on the soundness of castings and affects the structure and behavior of solid copper alloys, its solubility in the liquid alloys is of practical importance. The isothermal change of carbon solubility with alloy composition is of interest from a theoretical standpoint. The binary alloys of copper with manganese and with nickel are used industrially and serve as a base for more complex alloys. The solubility of carbon in each of these metals is known, but its solubility in their alloys has not been determined. Earlier Data The solubility of carbon in molten pure copper is about o.oooi pct at II00°C and 0.0004 pct at 1475°C.l Various authors2""6 have published data on the solubility of carbon in molten manganese. There is agreement on a value of about 6.7 pct in the temperature range r2170 to 1245°c This solubility value corresponds to the formula Mn3C. It increases very little with increasing temperature. Corson7 states that carbon is soluble in copper-manganese alloys and that the

Jan 1, 1947

By A. L. Holley

The existence of iron ore and anthracite coal in the neighborhood of Providence, R. I., baa long been known, chiefly as a geological fact; that these materials, so near to each other and to tidewater, are of such a good quality and are present in such large quantity, as to have seriously raised the question of establishing blast furnaces there, was a surprising fact to me; and I have thought that the few notes I have lately gathered on the subject would be of interest at this partly New England meeting. The coal field referred to has an area of above 400 square miles, and is found throughout the belt of transition rocks extending from Newport Neck to Mansfield, Massachusetts. It underlies the cities of Providence and Newport, and the towns of Middletown, Portsmouth, Jamestown, Warwick, Barrington, Cranston, North Provi-

Jan 1, 1879

By C. M. McKinney

Sulfur content data from Bureau of Mines routine analyses of 1,060 United States crude oils were used with crude oil production data for the years 1956-66 to prepare tables and charts that illustrate the volume and percentage distribution according to sulfur content of crude oil produced in 10 geographical areas of the United States. Similar relationships for foreign crude oils based on analyses of 201 crude oils and production during 1966 are illustrated for Africa, Canada, Middle East, and South America. Tables are included giving field name, sulfur content, geologic name and age of producing formation, depth of producing formation, and production during 1966 for 882 United States crude oils and 201 .foreign crude oils. Between 1955 and 1966 the average sulfur content of crude oils produced in the United States decreased from 0.73 to 0.67 percent.

Jan 1, 1967

By J. A. Solomon, H. E. Shafer

As a result of the great demand for metallic aluminum and the scarcity of domestic bauxite, numerous processes have been proposed and developed to extract the oxide of this metal (Al2o3) from clays, shales, and other low-grade raw materials.1-4 An exploratory study was made to extract alumina with sulfuric acid from relatively impure coal-associated draw-slate and to establish an optimum calcination temperature for maximum recovery. Draw-slate is the term used to describe the hard, slaty material directly overlying many coal seams and may range from a few inches to a few feet in thickness. Alumina content of these draw-slates may range from as low as 15% to over 35%. Although the following results are limited in scope, some of the data should prove beneficial for further work. Coal-associated clay, shale, and gob heretofore have been considered nuisance products; any successful alumina extraction process would greatly enhance the worth of these almost limitless resources. This research demonstrated that an optimum calcination temperature for alumina extraction could be established for a coal-associated draw-slate and that this temperature was lower than those suggested in previous work with unspecified clay types. It should be noted that slightly higher acid concentrations and somewhat finer particle sizes were used in this series of tests as compared to previous work. EXPERIMENTAL WORK Essentially, alumina extraction proceeded in four steps: 1) grinding, 2) calcining, 3) acid leaching, and 4) precipitating of aluminum sulfate. An initial series of reference tests to determine the optimum temperature of solubility for alumina was run using relatively pure kaolin. Kaolin forming clays are hydrous aluminum silicates of the approximate composition 2H2O A12O3 2SiO and kaolinite is the mineral that predominates in most kaolins. 5 The kaolin was ground to -30 mesh and subsequently calcined at temperatures ranging from 100°C to 700°C. Each sample was calcined for 1 hr in a muffle furnace and in turn subjected to sulfuric-acid leaching (H2SO4, 9 molar) for a 2-hr period. The filtrates were analyzed for the amount of dissolved alumina recovered.637 Also, each sample of leached or barren residue was

Jan 1, 1968

By Frederick M. Becket

DoctoR Albert Sauveur, distinguished scientist and Honorary Member of this Institute, predicted in the first Howe Memorial Lecture that the privilege of delivering' this annual address would be considered a highly significant honor. The intervening years have well borne out Sauveur's prophecy. I wish to assure the American Institute of Mining and Metallurgical Engineers that I also deeply appreciate this honor, recognizing at the same time the present and even more the future responsibilities with which it is accompanicd. Several of the previous lecturers had the good fortune to attend the classes of Professor Howc and to work in his laboratories. I was similarly favored, although in my instance and to my great regret the period was all too short. However, Howe's book, published in 1903, "Iron, Steel and Other Alloys," afforded me abundant opportunity to continue these studies. How well I remember the inspiration I derived from this famous book by Howe, the metallurgical master, pioneer, and educator! Remembering that Professor Howe contributed numerous papers to The Metallographist, a magazine supported from a technical point of view by the world's pioneers in metallography, I was curious a few days ago to learn the nature of Howe's early contributions to this magazine. The first paper by Howe in the first year of The Metallographist (1898) dealt with the allotropic theory; the second also treated of allotropy, and I quote the first sentence of that paper: The allotropic theory of the hardening of steel may, like so many other important theories, have to be accepted or rejected not on direct proof or disproof, but on the accumulation of circumstantial evidence for or against it. Howe's ability to stimulate others by his deep understanding and clarity of expression was truly remarkable; but just as striking was his intuitive judgment concerning the implications of metallurgical data in the arts and scienees. It therefore seems fitting that this lecture comprise a broad treatment of the subject chosen, rather than a closely documented thesis on any one phase of the problem; that in it attention be focused

Jan 1, 1938

By Frederick M. Becket

DoctoR Albert Sauveur, distinguished scientist and Honorary Member of this Institute, predicted in the first Howe Memorial Lecture that the privilege of delivering' this annual address would be considered a highly significant honor. The intervening years have well borne out Sauveur's prophecy. I wish to assure the American Institute of Mining and Metallurgical Engineers that I also deeply appreciate this honor, recognizing at the same time the present and even more the future responsibilities with which it is accompanicd. Several of the previous lecturers had the good fortune to attend the classes of Professor Howc and to work in his laboratories. I was similarly favored, although in my instance and to my great regret the period was all too short. However, Howe's book, published in 1903, "Iron, Steel and Other Alloys," afforded me abundant opportunity to continue these studies. How well I remember the inspiration I derived from this famous book by Howe, the metallurgical master, pioneer, and educator! Remembering that Professor Howe contributed numerous papers to The Metallographist, a magazine supported from a technical point of view by the world's pioneers in metallography, I was curious a few days ago to learn the nature of Howe's early contributions to this magazine. The first paper by Howe in the first year of The Metallographist (1898) dealt with the allotropic theory; the second also treated of allotropy, and I quote the first sentence of that paper: The allotropic theory of the hardening of steel may, like so many other important theories, have to be accepted or rejected not on direct proof or disproof, but on the accumulation of circumstantial evidence for or against it. Howe's ability to stimulate others by his deep understanding and clarity of expression was truly remarkable; but just as striking was his intuitive judgment concerning the implications of metallurgical data in the arts and scienees. It therefore seems fitting that this lecture comprise a broad treatment of the subject chosen, rather than a closely documented thesis on any one phase of the problem; that in it attention be focused

Jan 1, 1938

By Peter Beardmore, Michael B. Bever

The effects of the temperature of deformation and the degvee of deformation on the annealing spectrum of a Au-Ag alloy have been determined by vesistance measurements. Specimens were deformed in torsion at 4°, 78K and room temperature up to strains nd/l of about 1.0 and were isochronally annealed. Discrete annealing stages similar to those found for pure metals were observed. Stage A occurred below room temperature; the decrease in reszstance associated with this stage increased as the temperature of deformation was lowered or the strain was increased. Stage B manifested itself as an increase in resistance; this is attributed to the restoration of short-range order promoted by vacancy or vacancy aggregate migration. At temperatures above 48S0K, recrystallization or Stage C occurred. Stages A, B, and C in the annealzng curves of this alloy may be considered to correspond to Stages II, Ill, and V, respectively, in the terminology used to describe the annealing spectrum of pure metals. ThE annealing behavior after deformation below room temperature has been thoroughly investigated on pure metals, in particular gold and copper. The occurrence of several discrete stages in the annealing spectrum of these metals has been established, but the interpretation of some of these stages in terms of specific mechanisms is still controversial.' The annealing of alloys deformed below room temperature has been the subject of only a few investigations. In the investigation reported here, a Au-Ag alloy was annealed after deformation at and below room temperature. This continues a research program on the deformation and annealing behavior of Au-Ag alloys.2-8s EXPERIMENTAL PROCEDURE An alloy rod of composition 82.6 wt pct Au-17.4 pct Ag was reduced to wire, 0.0428 in. diam, by swaging and drawing. After a recrystallization treatment, the grain size was 0.031 mm, as obtained from the average linear intercept.7 The ends of wires about 6 in. long were flattened and sealed into short brass tubes with cold setting cement to form the grips of the torsion specimens. The equipment used for deformation has been described elsewhere.6 The specimens were deformed at room temperature, 78", and 4°K to various strains nd/l, where n is the number of turns, d the diameter of the specimen, and 1 its length between grips. The strain rate ?max was 0.1 min-' at the sur- face of the specimen except where noted otherwise. The specimens were annealed isochronally for 30 min at intervals of approximately 30°K from the temperature of deformation to approximately 800°K, except that after deformation at 4°K the lowest annealing temperature was 78°K. A potentiometric method was used to measure the resistance: all measurements were made at 78°K with the exception of some measurements at 4°K mentioned below. Data obtained with a single specimen yielded a complete annealing curve: in several cases duplicate specimens were used to confirm the reproducibility of the curves. Since the surfaces of the specimens were rough after deformation, their diameters could not be measured accurately. The resistance increments after deformation and annealing are therefore reported as percentages of the resistance of the same specimen measured after completion of the annealing, that is, after full recrystallization. The corresponding resistivity values can be calculated by obtaining the effective diameter of a deformed specimen from the ratio of its resistance after recrystallization to the true resistivity, which was determined with a smooth specimen of known dimensions. This method of calculation was used to obtain data shown in several of the figures. RESULTS AND DISCUSSION The isochronal annealing curves after deformation to various strains at 4", 78K, and room temperature are shown in Figs. 1, 2, and 3, respectively. The resistance increment of the as-deformed specimens as a function of strain is shown in Fig. 4. For the specimens deformed at 4°K. values measured at 78°K are plotted with the exception of those for the as-deformed

Jan 1, 1970

By M I. Pownceby, N A. S Webster, R Pattel, N Ware

The decrease in quality of Australian iron ore, coupled with the demand for more efficient energy use, necessitates closer monitoring and optimisation of process conditions for iron ore sinter production. Sinter properties are correlated with the mineralogical content and traditionally, quality control has relied on methods such as Fe2+ determination, point counting via optical microscopy and automated electron beam techniques such as QEMSCAN; these can have a typical turnaround time of several days between sampling and reporting of results. As well, there is additional uncertainty around quantifying some of the complex mineralogical phases in sinter such as silico-ferrite of calcium and aluminium (SFCA) and SFCA-I, which are key phases influencing sinter quality. There is a clear need for the implementation of alternative analytical methodologies that offer a turnaround in hours or even minutes to provide information to accurately maintain production conditions.X-ray diffraction (XRD) is a technique widely used for the quantitative mineralogical phase analysis (QPA) of ores and processed materials in the iron ore industry. Partial least squares regression (PLSR) analysis methods have recently been suggested as an indicator of sinter Fe2+ content from powder XRD data without the need for rigorous and often time-consuming mineralogical analysis by the operator. In this study we provide results from the implementation of PLSR to predict the strength of iron ore sinter. Results are sourced from a well-constrained data set comprising strength properties (as quantified by a tumble index (TI)) from a series of compact laboratory test samples. Using this data set it was determined that PLSR has potential to be used as a method for calculation of sinter TI from powder XRD data and, therefore, process control.CITATION:Webster, N A S, Pownceby, M I, Ware, N and Pattel, R, 2017. Predicting iron ore sinter strength through X-ray diffraction analysis, in Proceedings Iron Ore 2017, pp 331–334 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 24, 2017

By T. M. Morris

R. T. Hukki (Finland Institute of Technology, Helsinki, Finland)—Two schools of thought are developing concerning the order of the rate of flotation. The paper by Morris is intended to show experimental evidence in favor of the first order rate. Arbiter, on the other hand, has presented an earlier paper" to demonstrate the validity of the second order rate equation. Unfortunately his method of plotting is open to criticism, as pointed out by Morris." A more sensitive method of plotting has been described by the writer,= whereby the data presented by Arbiter demonstrate the superiority of the second order plot. The general rate equation may be written in the following forms for the integrated first and second order equations: (A) t = -1/k In Co-R/Co (first order) [4] 1 (B) 1/t = - kCo + kCo2 1/R (second order) As a first approximation the value of Co may be taken as a unity, 100 pct or 1. Whether or not this is the case in all tests performed by Morris is impossible to judge, owing to the fact that the flotation times are extremely short, e.g. 150 sec in tests A. It would, indeed, be very interesting to know what the total recovery R would be after 1 hr of flotation, for example, instead of after 150 sec. Certainly there are circumstances when C, approaches unity within a very small margin of error. Morris has used the same approximation in his example D "since the feed to this cleaner

Jan 1, 1954