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By Warren E. Wilson

PRESENT-DAY design of launders is essentially an art depending to a marked degree upon the experience of the designer, whose problem is that of determining the dimensions of a conduit that will transport the pulp within the physical limitations of the plant and in the most economical manner. This paper has been prepared in an effort to place launder design upon a more scientific basis. A method is developed from elementary principles and presented in a form that may be used directly by the designer in determining launder dimensions.. The equations that are developed are believed to represent an advance over older ones, in that they give due consideration to all the pertinent variables, either including them in the analysis or showing that they may be neglected within the limits of applicability of the equations. Experimental data from several sources are used in evaluating the coefficients that are not determined in the mathematical analysis. On the basis of the material presented, it is concluded that launders may be designed with a much greater degree of accuracy than previously believed possible, when due consideration is given to all the factors involved in the problem. However, a great deal of work still remains to be done in the laboratory before a complete answer to all the questions in launder design can be made available. HISTORY OF LAUNDER DESIGN Among the references1-11 are cited accounts of many experiments that have been conducted in an effort to advance the knowledge of the flow of liquid-solid mixtures in flumes and pipes. With three notable exceptions, this work was carried on in such a manner that the results have limited value in solving the general problem, since not all the pertinent variables were measured and controlled. The exceptions are found in the works of Blue,6 Gilbert,7 and Blatch,11 who exercised great care in controlling and measuring all the significant quantities involved in the experimentation. It is notable that much of the work done by men directly connected with the mineral industries1-4 lacks somewhat in completeness, owing apparently to preconceived notions concerning the factors that determine the flow. For example, many measurements on flow in pipes and flumes carrying liquid-solid mixtures determined only the slope and percentage of solids, with no mention of size of particles, depth of flow, roughness of channel or specific gravity of solids. Material in current handbooks8,9 and textbooks is based largely on the experimental work cited above. Although most discussions of the topic-include statements that the results to be obtained by using the data presented are limited by the fact that all variables have not been considered, it is

Jan 1, 1943

Page Foreword. By Edmund M. Wise..................... 3 A.I.M.E. Officers and Dircctors...................... 4 Institute of Metals Division Officers and Committees............ 7 Institute of Metals Division Annual Award Certificate............ 8 Institute of Metals Division Lectures and Lecturers............. 9 Photograph of E. H. Dix, Jr., Institute of Metals Division Lecturer...... 10 PAPERS Acceleration of the Rate of Corrosion by High Constant Stresses. By E. H. Dm, JR. (Institute of Metals Division Lecture, T. P. 1204).......... 11 Variation of Internal Friction with Grain Size. By Clarence Zener and R. H. Randall. (T.P. 1146, with discussion) .............41 Changes in Damping Capacity during Annealing of Alpha Brass. By John T. NoRton. (T.P. 1168, with discussion)................49 An Electron Diffraction Study of Anodic Films. By R. A. HarrinQton and H. R. Nelson. (T.P. 1158).....................62 Determination of Orientations by Etch Pits. By Charles S. Barrett .and L. H. Levenson. (T.P. 1171, with discussion).............76 Process of Precipitation from Solid Solution, I—A Crystallographic Mechanism for the Aluminum-copper Alloys. By Carl H. Samans. (T.P. 1186). . . 85 Age-hardening of Aluminum Alloys, IV — Discussion of the Theory. By WilTJam L. Fink and Dana W. Smith. (T.P. 1083, with discussion). . . 95 Structure of Aluminum after Compression. By Charles S. BaRREtt and L. H. evensonON. (T.P. 1104, with discussion)................112 Recrystallization Texture of Aluminum after Compression. By ChaRlEs S. BarRett. (T.P. 1141, with discussion)................128 Plastic Deformation and Recrystallization of Aluminum Single Crystals. By J. A. Collins and C. H. Mathewson. (T.P. 1145, with discussion) . . . 150 Recovery and Recrystailization in Long-time Annealing of 70-30 Brass. By S. E. Maddigan and A. I. Blank. . (T.P, 1166, with disonssion).....170 Correlation of Deformation and Recrystallization Textures of Rolled 70-30 Brass. By R. M. Brick. (T.P. 1144, with discussion).........193 Tensile Deformation of Critically Oriented Brass Crystals. By H. L. Burghoff. (T.P. 1149).............................214 Recrystallization of Lead. By Paul A. Beck. (T.P. 1101, with discussion). . 222 Simple Method of Thermal Analysis Permitting Quantitative Measurements of Specific and Latent Heats. By Cyril Stanley Smith. (T.P. 1100, with discussion).............................236 Metallographic Study of Internal Oxidation in the Alpha Solid Solutions of Copper. By Frederick N. Rhines. (T.P. 1162, with discussion). . . . 246

Jan 1, 1940

Page Foreword. By Edmund M. Wise..................... 3 A.I.M.E. Officers and Dircctors...................... 4 Institute of Metals Division Officers and Committees............ 7 Institute of Metals Division Annual Award Certificate............ 8 Institute of Metals Division Lectures and Lecturers............. 9 Photograph of E. H. Dix, Jr., Institute of Metals Division Lecturer...... 10 PAPERS Acceleration of the Rate of Corrosion by High Constant Stresses. By E. H. Dm, JR. (Institute of Metals Division Lecture, T. P. 1204).......... 11 Variation of Internal Friction with Grain Size. By Clarence Zener and R. H. Randall. (T.P. 1146, with discussion) .............41 Changes in Damping Capacity during Annealing of Alpha Brass. By John T. NoRton. (T.P. 1168, with discussion)................49 An Electron Diffraction Study of Anodic Films. By R. A. HarrinQton and H. R. Nelson. (T.P. 1158).....................62 Determination of Orientations by Etch Pits. By Charles S. Barrett .and L. H. Levenson. (T.P. 1171, with discussion).............76 Process of Precipitation from Solid Solution, I—A Crystallographic Mechanism for the Aluminum-copper Alloys. By Carl H. Samans. (T.P. 1186). . . 85 Age-hardening of Aluminum Alloys, IV — Discussion of the Theory. By WilTJam L. Fink and Dana W. Smith. (T.P. 1083, with discussion). . . 95 Structure of Aluminum after Compression. By Charles S. BaRREtt and L. H. evensonON. (T.P. 1104, with discussion)................112 Recrystallization Texture of Aluminum after Compression. By ChaRlEs S. BarRett. (T.P. 1141, with discussion)................128 Plastic Deformation and Recrystallization of Aluminum Single Crystals. By J. A. Collins and C. H. Mathewson. (T.P. 1145, with discussion) . . . 150 Recovery and Recrystailization in Long-time Annealing of 70-30 Brass. By S. E. Maddigan and A. I. Blank. . (T.P, 1166, with disonssion).....170 Correlation of Deformation and Recrystallization Textures of Rolled 70-30 Brass. By R. M. Brick. (T.P. 1144, with discussion).........193 Tensile Deformation of Critically Oriented Brass Crystals. By H. L. Burghoff. (T.P. 1149).............................214 Recrystallization of Lead. By Paul A. Beck. (T.P. 1101, with discussion). . 222 Simple Method of Thermal Analysis Permitting Quantitative Measurements of Specific and Latent Heats. By Cyril Stanley Smith. (T.P. 1100, with discussion).............................236 Metallographic Study of Internal Oxidation in the Alpha Solid Solutions of Copper. By Frederick N. Rhines. (T.P. 1162, with discussion). . . . 246

Jan 1, 1940

Organization Place Date 1919 National Drainage Congress St. Louis, Mo. Nov. 11-13 American Mining Congress St. Louis, Mo. Nov. 1.7-21 Canadian Mining Institute Vancouver, B. C. Nov.. 26-28 American Society of Mechanical Engineers:.... New York, N. Y. Dec. 2-5 American Institute of Chemical Engineers Savannah, Ga. Dec. 3-6 Geological Society of America...; Boston, Mass. Dec. 29-31. American Society of Heating and Ventilating 1920 Engineers New York, N. Y. Jan. Mining and Metallurgical Society of America ... New York, N. Y. Jan. 13. American Institute of Min. and Met. Engineers... New York, N. Y. Feb. 16-19 American Ceramic Society Philadelphia, Pa. Feb. 23-26

Jan 11, 1919

By M. B. Standing, D. L. Katz

Equilibrium data are reported on the composition and densities of coexisting vapor and liquid phases as a function of Pressure and temperature for four hydrocarbon systems prepared from crude oil and natural gas. The data were observed over a range of pressures from 1000 to 8220 Ib. per sq. in. and at temperatures ranging from 35' to 250°F. The compositions of the hydrocarbon systems were such that the critical temperatures of the mixtures were lower than the range of the investigation. Under these conditions, it is shown that the composition of the systems has a marked effect upon both the absolute value of the equilibrium constants and the change of the constants with pressure for the several components comprising the system. From weight-balance considerations, it has been possible to construct the partial phase diagram of a mixture of a 49.9" A.P.I. crude oil and natural gas having a gas-oil ratio of 3660 cu. ft. per barrel. Descriptions of the apparatus used, the analytical procedure, the material used, and the equilibrium measurements are included. A knowledge of the physical behavior of naturally occurring hydrocarbon mixtures is fundamental to the treatment of many problems in the production, transportation and rehing of petroleum. The recent discoveries of pools having formation pressures up to 7500 lb. per sq. in. and higher, and the development of full-scale equipment to operate at pressures of 5000 lb. per sq. in. or more have greatly increased the need for knowledge of the composition, temperature, pressure and density relationships of coexisting vapor and liquid hydrocarbon phases. The following paper presents the results of investigations upon 22 mixtures of natural gas and crude oil of known com~o~itio~ that had been brought to equilibrium under controlled conditions of temperature and pressure. Data are presented upon the densities and compositions of the coexisting vapor and liquid phases for four different systems containing hydrocarbon material having boiling points from minus 2 5S°F. to well over I000 F. The data were observed Over a pressure range from Iooo Ib. per Sq. in to 8220 lb. Per sq. in. and a temperature range from 35' to 2 50°F. The accepted method of computing the physical relationship between two coexisting phases of a hydrocarbon mixture is by use of the "equilibrium constant" K as proposed by Souders, Selheimer, and Brown. definition,

Jan 1, 1944

By M. B. Standing, D. L. Katz

Equilibrium data are reported on the composition and densities of coexisting vapor and liquid phases as a function of Pressure and temperature for four hydrocarbon systems prepared from crude oil and natural gas. The data were observed over a range of pressures from 1000 to 8220 Ib. per sq. in. and at temperatures ranging from 35' to 250°F. The compositions of the hydrocarbon systems were such that the critical temperatures of the mixtures were lower than the range of the investigation. Under these conditions, it is shown that the composition of the systems has a marked effect upon both the absolute value of the equilibrium constants and the change of the constants with pressure for the several components comprising the system. From weight-balance considerations, it has been possible to construct the partial phase diagram of a mixture of a 49.9" A.P.I. crude oil and natural gas having a gas-oil ratio of 3660 cu. ft. per barrel. Descriptions of the apparatus used, the analytical procedure, the material used, and the equilibrium measurements are included. A knowledge of the physical behavior of naturally occurring hydrocarbon mixtures is fundamental to the treatment of many problems in the production, transportation and rehing of petroleum. The recent discoveries of pools having formation pressures up to 7500 lb. per sq. in. and higher, and the development of full-scale equipment to operate at pressures of 5000 lb. per sq. in. or more have greatly increased the need for knowledge of the composition, temperature, pressure and density relationships of coexisting vapor and liquid hydrocarbon phases. The following paper presents the results of investigations upon 22 mixtures of natural gas and crude oil of known com~o~itio~ that had been brought to equilibrium under controlled conditions of temperature and pressure. Data are presented upon the densities and compositions of the coexisting vapor and liquid phases for four different systems containing hydrocarbon material having boiling points from minus 2 5S°F. to well over I000 F. The data were observed Over a pressure range from Iooo Ib. per Sq. in to 8220 lb. Per sq. in. and a temperature range from 35' to 2 50°F. The accepted method of computing the physical relationship between two coexisting phases of a hydrocarbon mixture is by use of the "equilibrium constant" K as proposed by Souders, Selheimer, and Brown. definition,

Jan 1, 1944

By C. C. CONCANNON

POTASH is an essential. It is necessary as an ingredient in fertilizers or as a plant food, and certainly one of the great problems, and one of increasing gravity, is the maintenance of agricultural fertility that we may have adequate food supplies. When one thinks of potash one thinks of Germany. The first and most important deposits of soluble potash salts were found in Germany, and it was through Ger- man research and the application of a highly developed knowledge of chemistry that the value of these deposits was recognized and appreciated in the field of agricultural fertilization. The Germans knew that they had something of great value in their potash resources, not only because of the advantage derived from the extensive use of it in their own intensive farming operations at home, but also because of the pressing need for it on the part of other countries. Appreciating the economic value of this in international trade, they fostered the industry to the fullest extent and devoted much attention to well organized propaganda designed to bring out the essential need for potash of German origin throughout the world. Thus every one came to believe that potash was an essential commodity of only German origin and as such it held an extraordinary position in world trade prior to 1914.

Jan 1, 1926

COUNCIL OF EDUCATION OF AIME (Formerly Mineral Industry Education Division) Established as a Division January 15, 1932 Established as a Council February 26, 1957 John C Calhoun, Jr, Chairman 0 Cutler Shepard, Vice-Chairman Thomas A Read, Secretary-Treasurer Dept of Mining & Metallurgical Engrg University of Illinois Urbana, Illinois COUNCIL OF ECONOMICS OF AIME (Formerly Mineral Economics Division) Established as a Division December 15, 1948 Established as a Council February 26, 1957 Louis C Raymond, Chairman Lorin A Cranson, Vice-Chairman Henry T Mudd, Vice-Chairman Adam K Stricker, Jr, Vice-Chairman Paul F Yopes, Secretary-Treasurer U S Bureau of Mines Albany, Oregon

Jan 1, 1957

Organization Place Date 1917 American Electro-Chemical Society Detroit; Mich. May 2-5 American Waterworks Association Richmond, Va. May 7-11 American Institute of Electrical Engineers New York City May 18 America' Society of, Mechanical Engineers Cincinnati, Ohio May 22-25 American Iron and Steel Institute New York City May 25-26 ' Interstate Oil Mill Superintendents Association. Augusta, Ga. May (last wk.) Electric Power Club Hot Springs, Va. June 11-14 Society for the Promotion of Engineering Education .... Evansville, Ind. June 19-22. American Institute of Electrical Engineers Hot Springs, Va. June 25 American Society for Testing Materials Atlantic City, N. J. June 26-30

Jan 5, 1917

By AIME AIME

THE second session on geophysical prospecting at the February meeting of the Institute was a discussion of the mining law and the bearing of the new method of search on location of claims and assessment work thereon. Allen H. Rogers was chairman of the meeting, which he opened by reviewing the present law and the proposed changes. W. R. Ingalls commented (by letter) on the Arentz bill, as introduced into the House of Representatives in 1921 and the need for revision of the present mining law. L. W. Douglas explained (by letter) the bill that he introduced and which has been passed by the House. SAMUEL S. ARENTZ, Nevada: It is my opinion that if the American Institute of Mining and Metallurgical Engineers is to sell this proposition to the people in the West, they have to sell it to the lawyers, because, after all, they are heard loudly when it comes to speaking in Congress. One man tells the other, "This thing is a vicious piece of legislation"; it might not be, but they will pass it on if it affects them. If the Institute would impress on the people affected that we need a re-codification of the mining law and that such is necessary along certain lines; that things have changed during the past decade or two, so today instead of doing our prospecting alone through the sinking of a shaft, through a discovery that may be seen, we are now moving on to more modern means of discovery through geophysics, through the churn-drill, through geology, through geological inference, I think we could get somewhere.

Jan 1, 1929

By C. B. Alcock, R. A. Oriani

Some simple models of solutions are described; these include the regular solution, the subregular solution, and the quasichemical model. The assunzption underlying these models, the physical signzficance thereof, and the experimental manifestations are discussed. Examples are presented from the fields of liquid and solid metallic solutions, liquid slags, mattes, liquid and solid ionic solutions, and mixed carbides to show under what conditions and for which systems these solution models are fair descriptions. The deviations of real solutions from the models are of theoretical interest. Some such deviations, both for dilute and for concentrated solutions, arc pointed out and their Physical sigtzzficance discussed. DURING the past half century there has been a gradual accumulation of thermodynamic data for systems of interest to the metallurgist. There remain many gaps in the data, however, and the metallurgist must often face the problem of estimation of thermodynamic quantities where measured values do not exist. One might hope that the experimental progress would be matched by theoretical advances which would make such estimations possible with a high degree of confidence. However, theoretical progress has been disappointingly slow even for the simplest kinds of solutions, and since the multicomponent systems in which the metallurgist is interested are very complex, one cannot expect theory to be of much help to the metallurgist. In this situation, therefore, it seems worthwhile to examine some simple models of solutions from two points of view: firstly, to see if such crude models represent the thermodynamic facts in as many types of solutions as possible sufficiently well for the needs of the metallurgist, and secondly to see what the deviations from such models show to be important for consideration by theorists. BOND ENERGY MODELS OF SOLUTIONS The simple models that we will examine from these points of view may be termed statistical models, in that they are concerned with the thermodynamic consequences of some simple assumptions about the energy of an assembly of atoms, molecules, or ions, and do not inquire into the physical basis of the interaction. The underlying assumption of these models is that the energy of an assembly of molecules (by which we include also atoms or ions) is given by the sum over all interaction energies of molecules taken two at a time; we will discuss only those models in which the pairwise interactions are restricted to those between nearest neighbors. Thus, in a pure substance of bond energy EAA, the internal energy (with respect to some specific reference state) will be expressed as NAA EAA where NAA is the number of nearest-neighbor pairs. A solution of molecules A and B will be characterized by NAA EAA + NBB EBB + NAB EAB where the Eij represent the bond energies of the nearest-neighbor i-j pairs. If one assumes that the EAA and EBB are the same in the pure components as in the solution, and that the coordination numbers in the two pure substances and in the solution are the same, then the energy of the solution with respect to the pure components (i.e., the energy of solution) is a function of the following linear combination of the bond energies: EAB - 1/2(EAA +EBB) = w. The thermodynamically ideal solution is defined as one in which the activity of each component is equal to the mole fraction of that component at all concentrations and all temperatures. It follows that

Jan 1, 1962

By Charles E. Heinrichs

IN the last decade one of our oldest and largest non-metallic metallic mineral industries has been the subject of persistent technical research, the results of which are another example of the benefits following the systematic application of scientific principles. The consequent improvement in the technique of phosphate recovery represents the greatest material advance in the industry since the discovery of phosphate in Florida in 1881. Moreover, these successes have stimulated interest and development in numerous other nonmetallic industries. Strange as it may seem, and despite the fact that the phosphate deposits of Giles County, Tennessee, together with those of Polk and Hillsborough Counties, Florida, have yielded more than 50,000,000 long tons in the last twenty years, the mineralogy of phosphates has been given scarcely any space in our technical literature. For many years it was the general consensus that these so-called phosphate rocks represented a physical mixture composed principally of tri-calcium phosphate, together with smaller quantities of calcium carbonate, calcium fluoride, iron phosphate, aluminum phosphate and other less important constituents. More recent investigations, however, led to the conclusion that these phosphates really represent a complex mineral in which calcium, iron, aluminum, phosphorus pentoxide, carbon dioxide, and fluorine all form a definite part of the molecule. Colony, after a careful study, utilizing chemical, microscopic, and X-ray diffraction methods, reported that American phosphates consist principally of calcium-carbono-phosphate of the staffalite type.

Jan 1, 1933

By N. J. Grant, Per Knudsen, J. T. Blucher

The fatigue behavior of three SAP alloys was studied in ternzs of strain rate and temperature, at high strains. The k values in the modified Manson-Coffin equation, Nk4 = C, were less than 0.5 under all test conditions, and change with strain amplitude for the lower-oxide alloys at about 2 pct strain. Lowest k values were near 0.25. Strain rate had no effect on life at 80 F, but had an increasingly greater effect with increasing temperature above 500". Life decreased with decreasing strain rate, above 500"F, and with increasing temperature. Ductility at fracture in a tension test was indicated to be an important factor in determining 1ife in these big+-strain tests with the SAP alloys. INEVITABLY, in the course of mechanical tests at elevated temperatures, particularly if significant time at temperature is involved, there are large changes in structure; these changes make it difficult to relate behavior patterns over ranges of temperature or strain rates at high temperatures. Such changes are to be expetted in low cycle fatigue at low strain rates and high temperatures. Accordingly, it was of great interest to examine the low cycle fatigue behavior of SAP / an aluminum oxide dispersion-strengthened aluminum, a type of alloy which had shown unusual structure stability to temperatures as high as 1000" to 1150°F and resisted recrys-tallization essentially to the melting temperature.'j3 Since the matrix is pure aluminum, there are no complications of averaging, agglomeration, or phase solution. It was also desirable to check the Manson-Coffin equation4?' for the SAP alloys, namely N~E~ = , where ep is the total plastic strain amplitude, k and C are constants, and N is the number of cycles to failure. Here, too, was an opportunity to check the roles of temperature and strain rate with a very stable material. Tavernelli and coffin6 had concluded that k had a value of about 0.5 for many alloys and C was equal to ~/2, where E is the fracture ductility determined from a static tension test. The results were obtained from low-temperature tests where creep and diffusion processes are unimportant. Manson7 found k = 0.6 fitted his data reasonably well; however, in later analyses of a large amount of low cycle fatigue data generated at room temperat~re@"~ he found k to vary from 0.6 for short lives to 0.21 for long-life fatigue tests. In the latter studies,89g Manson separated the total strain range into elastic and plastic components when he found that k was influenced by the nature of the strain. The use of EL (total strain) instead of EP (total plastic strain)4'5 makes a difference in the resultant k value. The ratio of changes with temperature, strain rate, and strain; further, there are the problems in the determination of the elastic strain. Based on these considerations, and the improved fit of points in a plot of by Wells and Sullivan,' is also utilized in these studies. Anderson and wahl,14 using commercial 1100 aluminum, and Blucher and Grant,15 using 99.99 pct pure aluminum, found an increase in life with increasing test temperature. Anderson and Wahl were the first to report low cycle fatigue results from SAP materials. With increasing temperature, the role of strain rate becomes more important. In this regard, care must be exercised to differentiate between frequency (wherein strain rate may vary from zero to a maximum in each cycle, sinusoidally, for example), and constant strain rate, as used in the present study, in a saw-tooth type cycle; in the latter case, the frequency is not specified but can easily be calculated from the strain and strain rate data. It has generally been found that life in low cycle fatigue tests decreases with decreasing frequency16 or with decreasing strain rate at elevated temperatures.15 Coffin,17 reviewing Eckel's work,16 also reported that k increased with decreasing frequency for acid lead, yielding values from 4.0 at a frequency fo 6.6 cycles Per day to 1-46 at a frequency of 7440 cycles per day; the value of k decreased to 0.58 at a frequency of 2.38 x lo6 cycles per day. EXPERIMENTAL PROCEDURE Three SAP alloys, of two nominal compositions, were tested. Alcoa supplied XAP 005 as 2-in.-diam extruded bar, of nominal composition A1-7 wt pct A1203. The Danish Atomic Energy Commission supplied SAP 930 (A1-7 wt ~ct Ala3) and SAP 865 (A1-13 wt pct Al&) manufactured by Swiss Aluminium Ltd., in the form Of $-in.-diam extruded rod. Metallographic comparison of the structures of XAP 005 and SAP 930 showed the former to have a more uniform oxide distribution. Button-head specimens were machined in the longitudinal direction of the bar with 0.4 in. gage length by 0.2 in. diameter, with a fillet radius of j-B in. After machining, the specimens were electropolished in a 1 to 4 mixture of perchloric acid to methanol to remove all machining marks. All test bars were in the as-extruded condition. The fatigue tests were performed on a hydraulically activated, axial strain machine, with complete reversal of strain.15 Test conditions were:

Jan 1, 1969

By JOHN R. SUMAN

TONIGHT I want to speak of the current problems and the postwar difficulties facing American industry. American industry has done an outstanding job in adjusting its operations to wartime necessity. The national income for 1942 was nearly $120,000,090,000 and of this outlay approximately $55,000,000,000 went for war material. The enormity of the expenditures for war material is indicated by the fact that the expenditures for war purposes alone were greater than the annual gross national income in the period 1931-34. This tremendous production job in turning out a record output of war products was accomplished by industry in spite of a large number of restraining and hampering influences, and I want to mention several of the more important problems.

Jan 1, 1943

By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961

CONTENTS PAGE MERRISS, M. H.-Direct Electrolysis of Black-copper Anodes of High Nickel-lead Content. Discussed by C. S. Witherell, C. P. Linville, G. E. Dalbey, M. H. Merriss 1 GRISWOLD, GEORGE G.-Calculating the Zinc for Desilverizing Lead Bullion by the Parkes Process. Discussed by C. S. Witherell, George G. Griswold, Milo W. Krejci, Lawrence Addicks, W. F. Gross, H. H. Alexander, A. F. Beasley, C. P. Linville 3 ALEXANDER, H. H. and STACK, J. R.-The Reduction and Refining of Tin in the United States. Discussed by Edward F. Kern, J. R.' Stack, R. L. Hallett, C. R. Hayward, William H. Bassett, R. C. Canby, H. G. S. Anderson 20 GREENAWALT, WILLIAM E.-Greenawalt Electrolytic Copper Extraction Process. Discussed by Stuart Croasdale, Colin G. Fink, Arthur L. Walker, Edward F. Kern, Henry A. Tobelmann, Oliver C. Ralston 26 BENEDICT, C. H. and KENNY, H. C.-Ammonia Leaching of Calumet and Hecla Tailings. Discussed by G. E. Dalbey, C. H. Benedict 34 RALSTON, OLIVER C.-Hydrometallurgy of Lead. Discussed by F. L. Bosqui, Jr., George D. Van Arsdale 34 TAINTON, U. C. and LEYSON, L. T.-Electrolytic Zinc from Complex Ores. Dis¬cussed by W. G. Woolf, C. A. Hansen 39 Direct Electrolysis of Black-copper Anodes of High Nickel-lead Content Discussion of the paper of M. H. MERRISS, presented; at the New York Meeting; February, 1924, and, issued, as Paper No. 1273-M, with MINING AND METALLURGY, September, 1923. C. S. WITHERELL, New- York, N. Y. (written discussion).-This paper is particularly valuable in that it gives the results of operations -carried out under conditions differing from standard practice. In the electrolytic refining of copper, as in other kinds of metal refining, it is occasionally necessary to treat extraordinary foul or complex material, in which cases 'it is valuable to know what other metallurgists have accomplished under similar conditions. As tapping the slimes-covered anodes brought the tank-voltage down to 0.45 to 0.50 volt, the counter electromotive force was, probably not more than 0.1 or 0.2 volt; hence the so-called polarization was, mainly,

Jan 6, 1924

By Clyde E. Williams, V. N. Krivobok, C. H. Herty

THE extreme effect of the depression on the steel industry is well illustrated by the fact that the amount of iron ore shipped from the Lake Superior district was the lowest in 47 years. Something over 3 1/2 million tons of ore was shipped in 1932, compared with over 65 million tons in 1929. It is not surprising then that practically no advancement in iron ore beneficiation has been made. Improved research and development work, however, was continued at the Michigan College of Mines in the survey of the lean iron ores of Michigan with reference to the possibility of their concentration; at the University of Minnesota in its large-scale jigging studies of Lake :Superior ores; and at Battelle Memorial Institute in the development of improved jigging of iron ores. The successful operation of the new Hadsel mill at a gold property in California gave such low grinding costs on a quartz ore as to give much encouragement in the iron ore industry for a cheapening of the cost of grinding lean ores for concentration.

Jan 1, 1933

By Sherwin F. Kelly

THE geophysical scene shifts and alters, the emphasis changes, and new possibilities loom, but the tendency is always towards widening the field and deepening the analytical penetration. Seismic methods have had their heyday, the torsion balance is being displaced by the gravimeter, electrical methods are showing deeper penetration, soil analysis is the newest tool, and gamma-ray logging appears on the horizon. One of the striking features of re- cent geophysical work in the oil fields has been the marked decrease in the number of seismic crews employed. Although the percentage of company crews is believed to have increased appreciably. the sum total has fallen sharply, as shown by the figures for the Gulf Coast area. About two years ago probably over 100 seismic parties were operating there, whereas now there are only about 35. This decrease may be partly due to the low prices of petroleum with a consequent reluctance to spend money to increase crude-oil re- serves but more probably to the fact that reflection and refraction shooting have been carried on so extensively that they have been applied to a large pro- portion of the areas in which they may reasonably be expected to succeed. Some of the earlier enthusiasm, particularly over reflection prospecting, may have erred on the side of over- optimism; some of the present curtailment may be due to over pessimism; but in the opinion of various observers seismic work at the present rate seems to be at it- optimum. It nevertheless remains pre-eminent as a technique for detailing structures in areas where good reflections can be obtained and is the only method that will give accurate depth to definite beds. Results may be poor in certain areas but many regions still remain wherein it can be applied, so that plenty of structural mapping remains to be done by the reflection seismic method.

Jan 1, 1940

By John T., Ryan

THE subject assigned me, "Safety in Mining," is a very broad one and only the high spots can be covered in this short paper. As this is a meeting of the Coal Division, these remarks will be directed largely to coal mine safety, although the principles of safety and effective accident prevention methods are relatively the same in every branch of mining or industrial work. The coal mining industry should take pride in the part it has played in the development of the accident prevention movement, and there is ample proof for the statement that the first real organized accident prevention, work, both abroad and in this country, was con- ducted in the coal mining industry.

Jan 1, 1930

By Henry Mackay

THE interesting paper recently submitted by Messrs. Tobelmann and Potter' shows that chemical problems have developed which are of great interest in this new and important branch of metallurgy. Those who realize what a process of this kind really involves will agree that it deserves a better name than "leaching process." The word leaching conveys the idea that the copper is simply leached out of the ore with acid and then precipitated on iron; the chemistry of such a process would be of little interest. As, however, during the first year's operation of this plant 24,400,532 lb. (11,067,837 kg.) or about two-thirds of the produce, was electrolytic copper, while 7,992,033 lb., or about one-third, was cement copper, it would seem more appropriate to term the process electrochemical. It further appears, from the particulars given, that efforts have been made to have the entire production in the form of electrolytic copper. -This could be done if the chemistry of the problem were kept in balance, so that it would not be necessary to discard any solutions that carried copper and acid of commercial value. A process, such as that under consideration, in which the copper is precipitated from solution by electrolysis, the solvent being at the same time regenerated, is one that requires special chemical and electrochemical knowledge and experience if all the -copper in solution that has been extracted from the ore is to be successfully and economically produced as electrolytic copper. The object of this paper is to discuss, from the practical and theoretical standpoints, the chemical and electrochemical problems involved in the working of a process of this kind, and' which must be solved to keep it in chemical and electrochemical equilibrium. In such a process, if the chemical balance is maintained, a solution can be used alternately as a

Jan 9, 1919