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By R. C. Temps, G. E. Aiken

Compania de Acero del Pacifico, S.A., the sole Chilean steel producer, is adding to the expanding Chilean economy with development of the El Algarrobo mine. Expected to go on stream early in 1962, Algarrobo is a conventional open pit mine that will include facilities for ore extraction, crushing and screening, rail transport to the harbor at Huasco, modern ship-loading equipment and maintenance shops. CAP anticipates producing 1.38 mil- lion tons annually of high-grade ore for national and world market consumption. Chilean and North American management and engineering teams combined more than a decade ago in the financing and building of CAP'S Huachipato integrated steel plant. A similar performance is being achieved in northern Chile near the town of Vallenar with the opening of a 50-year supply of iron ore from the Algarrobo deposit. This successful intra-American undertaking deserves special mention in these times when some U.S. foreign assistance programs must be defended, particularly with respect to Latin America. North American financial participation in Algarrobo, through the Export-Import Bank of Washington, represents the greatest portion of the $24 million being invested.

Jan 3, 1962

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

IN general, fatty acids or their alkali salts do not cause clean quartz to float. However, the presence of multivalent ions, such as the alkaline-earth metal ions and heavy-metal ions, can activate quartz and thus make it respond to soap flotation. The mechanism of activation and soap flotation of quartz has been studied.1-4 The problem was attacked by making flotation tests rather than by careful adsorption measurements on suspensions of ground quartz in solutions containing the activator and the collector. Attempts have been made to determine the adsorption of barium ion and calcium ion on quartz. The results have only qualitative value as the analytical methods were not adequately precise. Artificial radioactivity and progress in radioactivity detection have introduced a new analytical tool, which can have a sensitivity several orders of magnitude greater than that of other methods.5-6 In the experimental work described in this paper the radioactive tracers, barium 140 and carbon 14, were employed. Lauric acid was synthesized, having a radioactive carbon atom and was used with Ba140 to study the adsorption of barium and laurate ions from aqueous solution on ground quartz. Flotation tests, using the vacuum flotation technique,4 were run in conjunction with the adsorption experiments. The object of this investigation was to understand better the reaction mechanism of barium activation and soap flotation of quartz. Methods and Materials Quartz Sample Preparation: Lumps of hand picked quartz, washed free of stains, were reduced in size to -20 mesh in laboratory crushers. The product was boiled in concentrated hydrochloric acid to remove the abraded iron. The cleaned product then was ground dry in a laboratory porcelain mill, using siliceous pebbles, to pass through a 200 mesh screen. The ground product was deslimed by sedimentation at 37 microns. This -200 mesh +400 mesh material was subjected again to boiling with concentrated hydrochloric acid, followed by washing with distilled water and further desliming. The cycle was repeated until no trace of iron could be detected in the wash liquor. During the final washing, the pH of the wash water was checked to insure the complete removal of the acid from the mineral. The quartz then' was rinsed with conductivity water. The resulting product was dried in a drying oven and stored in mason jars. The impurities (spectrographic) were as follows: Al, 0.01 to 0.001 pct; Li, Mg, Mn,, Na, each less than 0.001 pct; Fe and Cu not detected. The specific surface of the quartz sample was determined by the krypton gas adsorption method.7 The average of two measurements was 881 sq cm per g. The calculated specific surface for 37/74 micron quartz particles, using a surface factor of 1.96,8 is 900 sq cm per g. This is in good agreement with the measured value of 881 sq cm per g. Beta-Counting Method: The radioactive isotope of barium used in the experimental work was barium 140. It has a sufficiently long half-life, 12.8 days, emits high-energy beta particles (up to 1.0

Jan 1, 1952

INTRODUCTION Data available on prophyry copper occurrences in the Andean, Caribbean, Appalachian, and Cordilleran orogens may be categorized in a manner to suggest a hypothetical evolution for deposits that occur in the western hemisphere. A classification of de- posits is also suggested. A classification dependent on internal structure of a porphyry copper deposit would lead to two broad categories, breccia pipe and stockwork models. A classification of this type is examined herein but it is not universally accepted in the literature. Modeling based on igneous petrography as well as metasomatism attendant with the sulfide mineralization is more widely accepted by economic geologists whose evaluation of porphyry systems is influenced by the presence or absence of a phyllic zone. Lowell and Guilbert model deposits ordinarily include a phyllic zone, whereas those of the diorite model do not. Position of the phyllic zone in the alteration sequence is a significant ore guide. Should the phyllic zone be absent, dependence on alteration zoning to identify metallization is weakened. Presence or absence of the phyllic zone therefore is a significant parameter in the economic evaluation of a porphyry copper deposit (Hollister. et al., 1975). The Lowell and Guilbert (1970) model commonly includes a phyllic zone in quartz- bearing rocks. Parameters of both calc-alkalic and the quartz monzonite models mentioned elsewhere in this volume are sufficiently close to the Lowell and Guilbert (1970) model that it should be expanded to encompass them. The diorite model remains separate and distinct because deposits of this type are characterized by an absence of quartz in the pluton, commonly highly gold: copper ratios, low molybdenum content, and regular absence of sericite in the alteration zones. Therefore, for the benefit of those

Jan 1, 1978

By Robert V. Whitman

INTRODUCTION Ideally, this paper should start by citing examples of slope failures in open pit mines during earthquakes. I do not know of any such examples, although - since my search of the literature has not been exhaustive - such examples may well exist. However, there certainly are many examples of devastating earthquake-induced landslides, and there is no reason why such landslides cannot occur at large open pits. Moreover, many of the actual earthquake-induced landslides have seriously affected mining operations in one way or another. Hence, this paper will treat earthquake-induced landslide phenomena in general, in the hope and expectation that the reader can apply this general knowledge to the specific problems associated with open pit mining. Ultimately, of course, the aim is to predict the likelihood of the occurrence of earthquake-induced landslides, and to delineate steps which can be taken to minimize the possibility of their occurrence. These aims can be achieved only imperfectly at the present time, for our knowledge concerning earthquake-induced landslides is still in an embryonic stage. Nonetheless, much useful knowledge does exist. In order to understand and apply this knowledge, it is necessary to: 1. Review the nature and extent of actual earthquake-induced landslides; 2. Have a grasp of the basic terminology and concepts of seismology; 3. Study the fundamentals of probability-based seismic risk analysis; 4. Appreciate the way in which earth materials behave during earthquake loadings; and 5. Have a general knowledge of the methods currently available for analyzing the dynamic response of slopes. Much of this paper is devoted to this necessary background. Information of practical use in connection with various classes of slope stability problems is assembled in the final sections. LANDSLIDES DURING PAST EARTHQUAKES Almost every earthquake in mountainous country, strong enough to be reported in the literature, has caused at least some landslides and rockfalls. Unless these slides or falls damage

Jan 1, 1971

By T. D. Yensen, N. A. Ziegler

The elements aluminum,' arsenic,2 silicon,3 tin2 and vanadium,~.~ when used in relatively small amounts as alloying elements, seem to have a beneficial effect on the magnetic properties of iron—i. e., they increase the maximum permeability and decrease the coercive force—whereas there are definite indications that boron,5 carbon,6 nitrogen: oxygen," phosphorus16 sulfur6 and titaninum,~ as well as the metals of and adjacent to the ferromagnetic group, nickel,~ cobalt,1° copper," and manganese,% have a detrimental effect on these properties. The effects of calcium4 and magnesium4 are small, if any, while the effect of chromium12 in small amounts is unknown and in large amounts is generally detrimental. WeveR's Classification13 All chemical elements may be divided into three classes based on their effect on the allotropic transformation points of iron. Class 1 contains the nonmetallic elements (except phosphorus) and these lower the A3 point and raise the A4 point. Class 2 contains the common metals and

Jan 1, 1931

By Clifford Wilson

SCREENED pipe is designed with the view of restraining the fine, free-running sands of the production zone from entering oil wells. Its successful use is dependent on a number of factors. The nature and effects of some of these factors can be determined through experiment and observation, but some of the elements that have a distinct bearing on the use of screened pipe can be evaluated only by estimate. The important subsurface conditions which affect the use of screened pipe are: 1. Depth of production zone. 2. Extent of production zone. 3. Reservoir pressure. 4. Character and relative quantity of oil and gas. 5. Character of sediments a. Consolidation of beds. b. Variation in beds. c. Grain-size gradation of sands. d. Free-running characteristics of sand from different levels. Aside from the use. of mechanical equipment and tools, the measures to be taken in the installation of screened pipe involve: 1. Size of liner. 2. Length of liner. 3. Design and mesh of screen. 4. Portion of liner to be screened. 5. Manner of setting liner. 6. Preparation of or washing of the well before or during the setting of the screen. 7. Manner of bringing in the well. 8. Manner of flowing the well. Values applicable to the actual subsurface conditions that exist at any well can only be approximated. The accuracy of the estimate will be measured by the amount and quality of the evidence at hand and the personal factor of ability to interpret the evidence fairly, whether

Jan 1, 1932

By E. D. Gardner

The tide of increasing demand for metals turned during early 1949, with resultant lower prices. The production of the principal metals was less than in 1948. The problem of high unit costs, however, was held over from 1948. With the lower prices for metals, greater efforts are being made to reduce operating costs. The labor supply was adequate during the latter half of the year in most districts. The force has been reduced at most mines; some mines were idle during part of the year because of strikes, and others ceased operations on their own account. In the main, labor efficiency increased during the year in underground metal mines. Efforts are being made generally to improve labor relations. Green men hired in the time of the scarcity of skilled miners are becoming better trained. The supervisory personnel of most mines is cost conscious, and the planning of operations has been improved. Overhead costs are being scrutinized. The trend toward mechanization underground continued strong. Mining technology rapidly is becoming a problem of handling materials. Surface miners, underground miners and miners of metals, nonmetallics, and coal can learn much Gardner from each other. A mine, however, may become overmechanized. The capital charges against new equipment may exceed the saving in labor costs where sufficient daily tonnage is not handled.

Jan 1, 1950

By Walter Harvey Weed

CONTENTS. [ ] INTRODUCTION. THIS paper deals with certain ore-deposits whose structural features or mineral contents (or both) result, directly or indirectly, from igneous intrusions and their after-effects. It is largely a discussion of contact metamorphic ore-deposits based upon the physical changes in rocks due to contact action. It involves a classification of ore-deposits only so far as is abso-

Jan 1, 1913

By J. H. Nead

OBJECT THE experiments herein described were undertaken with a view to investigating thoroughly the influence of carbon on the tensile and impact physical properties of carbon steel. The original comprehensive plan included investigation of a series of steels with varying carbon contents over a wide range of heat treatments. These were to be studied as to their static tensile qualities, and also their resistance to shock as measured by the Charpy impact bending test. A thorough metallographic examination was likewise included in the schedule. The Charpy tests and the metallographic examination have not been completed to date, and are accordingly withheld for another report. All heat treatments, however, have been made, and the static tensile tests have been completed. A description of the procedure of the experiment and the results thus far obtained are therefore reported herein. CONCLUSIONS No attempt is made to draw general conclusions from these experiments, but the curves and the data are submitted as being of general importance and wide applicability.

Jan 12, 1915

By C. L. Mantell

ALTHOUGH SO common and well known a metal, tin is really a less abundant element than many of those less familiar and usually ranked with the scarce or rare elements, such as cerium, yttrium, lithium, beryllium., titanium, zirconium and vanadium. The color of tin is white, with a slightly bluish tinge. When it is compared with nickel, the latter metal is brown. When placed alongside of tin, chromium is definitely blue. Tin is whiter than silver or zinc. Exceedingly thin films of tin show various shades of brown by transmitted light. The metal has a brilliant luster, and when mirror-polished, has high light reflectivity. The luster depends to a large extent upon the pouring temperature at which the metal is cast. If the temperature be, too high, iridescent colors may show on the surface. These are the result of oxide film formation. If the pouring temperature be too low, the surface is dull. Small amounts of foreign metals, such as lead, arsenic, antimony and iron, decrease the luster of tin and impart a yellowish tinge to the metal. The structure is decidedly crystalline. The cast metal is a mass of crystals. When a bar of tin is bent, it emits a characteristic creaking sound. This is called the "cry" of tin, resulting from the grinding of the crystals one against the other during the bending of the metal. Tin metal may lose its crystalline structure by cold working, but grain growth occurs rapidly under the influence of heat. Metal which has been cast at a low temperature may become amorphous as the result of mechanical work. If such material be heated to temperatures well. below the melting point, say at 110° C. for a half hour or for a few minutes at 150° C. recrystallization occurs. If the surface of tinned plate, tin foil, or tin metal in cast form be etched with hydrochloric acid containing a little free chlorine, attack occurs at the intercrystalline faces. The surface shows patterns resembling the frost flowers on window panes in winter. The etched appearance is called moiré metallique. Fine dendritic surface crystals of tin may be obtained by casting the metal on a surface of polished steel. In commercial tin plate, the intercrystalline boundaries are shown by fine grooves or channels, which result from the method

Jan 1, 1929

By Edward Wichers

THE purpose of this paper is to set forth the matters of principal interest in connection with work done in the past few years on the purification of the metals of the platinum group, including the study and modification of methods already in the literature and the development of new procedures. For the most part, the results will be given in summary form, reserving the publication of detailed data and directions for a forthcoming paper to be issued by the Bureau of Standards. In recent years increasing interest has been shown in the preparation of the pure platinum metals, both by those concerned with the manufacture of the metals and their alloys for scientific and industrial purposes and those who are engaged in the study of the chemical or physical properties of the elements. The purification of the metals usually has been regarded as a matter so involved and difficult as to require the attention of specialists. It is hoped that this paper will show that any of the metals can be prepared in any desired degree of purity by relatively simple straightforward chemical methods. For the most part, it is thought that the methods given are suitable for small-scale refineries as well as for the laboratory; also, that they will bring the time required for the purification of any of the metals within reasonable limits. The new procedure suggested for purifying platinum should prove to be much shorter than any methods described in the literature.

Jan 1, 1928

By F. F. Aplan

The past year has been another year of vigorous fundamental research in mineral processing as evidenced by the active publication of results, particularly in Germany, Japan, United Kingdom, United States and USSR. It was also noteworthy for several significant meetings and conferences. The Basic Science sessions at the AIME Annual Meeting continued to attract an increasing audience and the sessions were especially notable for the active discussion of papers. The third Engineering Foundation Conference on Particulate Matter Systems,1 chaired by F. F. Aplan, was held in Milwaukee in August and attracted over 100 experts from five continents. Sessions at this week-long conference covered comminution, particle characterization, separation of fine particles, fluid-solid separations as applied to pollution control, flotation kinetics, particle-particle interactions and particle agglomeration. This popular conference will be continued under John Karpinski of Bethlehem Steel Corp. as 1968 chairman.

Jan 2, 1968

Why should I pay $8.50 an hour for dealer repairs when my own mechanics work for $3.50?" The numbers vary, but that's the argument most contractors use to justify doing their own repairs. They don't realize it, but they're probably losing big money. For instance, it takes nearly a quarter of a million dollars in tools alone to equip a shop comparable to an average equipment dealer's facilities. A contractor must buy a lot of expensive, specialized tools he seldom uses, or else settle for the inefficiency of having repairs done by his mechanics with relatively unsophisticated tools. His building soaks up money in rent, maintenance insurance, taxes. His mechanics demand good wages. It even costs money when mechanics aren't repairing equipment. Mechanics get full wages for slack periods and cleanup time, too. This doesn't count as service manhours, but it's still part of the total repair cost. To help contractors uncover these hidden expenses and find out the true cost of owning a shop, some equipment dealers have devised a do-it-yourself "shop cost analysis form."

Jan 1, 1970

By Betty J. Laswell, Gerald W. Laswell

Rotary drilling in modern open-pit mining is usually considered the lead phase which not only establishes the production rates but frequently limits them. From this viewpoint alone, the drilling phase must be maximized. The drill phase is the step that permits all the other operational phases to function within their design limits. This means that, in most cases, the drill is literally run to destruction to ensure that the shovel will be able to smoothly and consistently load a manageably size muck, the haul trucks can carry a balanced load without having a boulder dropped through the bed, and the crusher can devour constant rock size.

Jan 8, 1978

By Robert Henderson

Several very interesting articles have been written on the caving system of mining, but most of these papers have dealt separately with the slusher system or the chute and grizzly system. In this paper, a comparison will be made of the two methods, both of which are being used at the Climax mine. The mine is on the Continental Divide, in central Colorado, at an altitude of approximately 11,500 ft. above sea level. The long, cold winters, characteristic of the high Rockies, create a number of operating problems not usually found in other mining areas. The Ore Body The Climax ore body is just east of the Mosquito fault. This structural deformation has brought the granite on the east against the sedimentary rocks on the west. The ore occurs in an intensely altered granite and schist around a silicified granite core. The ore is in a highly fractured zone of moderate silicification. The principal mineral, molybdenite, is found in these fractures. Barren dikes of granite porphyry cut through the ore body and core with no apparent regularity. The grade of the ore is fairly uniform and gradually decreases toward the footwall core and also into the hanging-wall granite. The footwall and hanging wall are determined entirely by assays. The ore body is roughly dome-shaped, with the apex truncated at the surface. It is covered to varying depths with talus. A horizontal section of the ore body on the Phillipson level appears as an annular ellipse surrounding the footwall core. The ring of ore varies in width from 300 ft. to as much as 800 ft. The north-south axis of the core is about 1200 ft. and the east-west axis is about 1800 ft. In the ore zone, the rock is sufficiently strong to maintain reasonably large openings, and openings larger than haulage drifts usually have to be supported. The ore is cut by a great many fractures and shears and breaks into rather large blocks when caved, necessitating considerable secondary blasting. The waste that overlies the ore body breaks relatively fine in comparison with the size of the blocks of the caved ore and tends to run through the broken ore in the cave, causing dilution unless the draw is carefully controlled. Mining Systems For several years the ore was mined by the chute and grizzly system, a system that differs from that used in other caving mines only in the size of openings and equipment. In the chute and grizzly system, main haulage laterals were driven along the footwall core and also along the hanging wall. Between these laterals, at

Jan 1, 1946

By C. B. Dudley

In October, 1878, and again in February, 1881, I had the honor to make public, through the medium of the American Institute of Mining Engineers, the results of an extended study of steel rails which had been in service, and which mere taken for the purpose from the tracks of the Pennsylvania Railroad Company. These studies appeared in three papers. In the first of these papers the question. what kind of steel is least liable to fracture or disintegration in the track, was the principal one considered. In the second paper the question discussed was, does the power of steel to resist wear increase with the hardness ? In the third paper the relation between wear and the chemical and physical properties of the metal was the principal point considered. The general results arrived at, or the cooclusions reached, were, as follows: 1. That a mild steel is less liable to fracture, and if properly made, less liable to crushing or disintegration in the track than a harder steel. 2. That the wearing-power of steel in rails not only does not increase as hardness increases, but, on the contrary, diminishes; or, in other words, that a mild steel gives less loss of metal under the same service than a hard steel. These conclusions may be briefly stated in a single sentence—namely, in rails mild steel is not only less liable to fracture and disintegration in the track, but it also gives longer life, or wears more slowly under the same traffic; than harder steel. It is perhaps hardly necessary to add that by mild steel is meant steel

Jan 1, 1891

By Paul A. Bailly

2.1-1. The Exploration Function in the Mineral Industry. With regard to a new mine, exploration can be technologically defined as all the activities and evaluations necessary before an intelligent decision can be made establishing size, initial flowsheet, and annual output of the new extractive operation based on a certain mineral deposit. The activities that follow such a decision are called first development, then operation (90). Thus, in the U.S.A., exploration may continue in the technological sense after a mineral property has entered the "development stage" as defined for tax purposes. Regulations under Sections 1.615.1 and 1.616.1 of the U.S. Internal Revenue Code state that the "development stage" has been reached when "deposits of ore or other minerals are shown to exist in sufficient quantity and quality to reasonably justify commercial exploitation by the taxpayer" (95). There are, of course, many instances where additional later exploration discloses additional reserves which justify a plant much larger, more efficient and more profitable than the minimum feasible commercial operation. After a surface mine is put into operation, additional search generally will increase the reserves and thus warrant expansion of the rate of output and/or extend the life of the operation. The methods and techniques in such search are similar to those used in predevelopment exploration. This activity has produced a major part of new reserves for all mineral commodities but is not considered as exploration in the context of this chapter. The objective of exploration is, briefly stated, to find and acquire a maximum number of new economic mineral deposits with a minimum cost and in minimum time. The search must be so organized as to maximize the overall probability of discovering commercial mineral concentrations within a minimum time with the funds available. As shown by Celasun (27) these statements are neither adequate nor complete from a pragmatic point of view. Each actual exploration venture must define its objectives in terms of a minimum rate of return on investment for any deposit found

Jan 1, 1968

By David White

ATTENTION has been given to the sources and supply of the raw vegetal matter and. the conditions of its submission to the process of sedimentation. An original and most valuable review has been made of the more important or significant chemical compounds originally contained in the organic debris, and of the biochemical changes-undergone by the latter during deposition. Consideration also has been given to the factors controlling the selective biochemical decomposition, in whole or in part, of :this debris, and the deposition, as, sediments, of the undecomposed plant structures and compounds, together with more or less of the so-called "ulmic," or "humic," organic decomposition products in colloidal solution.1 BIOCHEMICAL CHANGES END IN PEAT FORMATION The biochemical process terminates in the peat stage of coal formation, and with the cessation of this process organic sedimentation is completed. All subsequent changes result from geological causes and conditions. The deposits are in the form of peats of different types, organic muds, oozes, etc. They are essentially uncompressed and are wholly unconsolidated, and their water content is great, amounting to over 85 per cent. near the surface of the deposit. Many of the chemical compounds remain as in the once living organisms; others are biochemically broken down and new ones formed.

Jan 2, 1925

By William B. Phillips

The possible sources of potash salts in the United States have been considered from many points of view during the last several years, but it is only within the last two or three months that the situation has become acute. We import from Germany, the only sourcc of large supply, more than $10,000,000 worth of potash salts annually, and this business has been badly crippled by the European war. If there was ever a time in our industrial existence when the necessity of providing for our own needs was more acute than it is now, we are not aware of it. One has only to study the price lists of chemicals sent out by the large supply houses to see the change wrought within a very short time. Whether or not these prices are to maintain for a considerable time, no one can say; but it appears to be probable that we shall not see prices materially lower for a period of uncomfortable length, to say the least. It is not my purpose at this time to discuss the various sources of supply of potash salts that have been suggested or recommended. Some of them might afford a pleasing relief but all of them combined would not affect the situation seriously. If we are to have our own sources of potash salts, they will have to compare, in some efficient manner, with the sources upon which we have drawn during the last 20 or 30 years; i.e., they must exist in minable quantities. It seems to me to be quite idle to speculate upon our domestic sources of potash if those sources are not of a character similar to those upon which we have so long depended. A few thousand or, perhaps, a few hundred thousand dollars' worth of chemically derived potash may be produced under the stress of present conditions, but when we consider that each year demands more than $10,000,000 worth, we must look to underground sources; we must look to mines similar to the famous Stassfurt and Halle deposits. If we cannot mine potash salts, we shall have to do without them for a while.

Jan 1, 1915

By F. C. Bond

SIZE of grinding media is one of the principal factors affecting efficiency and capacity of tumbling-type grinding mills. It is best determined for any particular installation by lengthy plant tests with carefully kept records. However, a method of calculating the proper sizes, based on correct theoretical principles and tested by experience, can be very helpful, both for new installations and for guiding existing operations. As a general principle, the proper size of the make-up grinding balls added to an operating mill is the size that will just break the largest feed particles. If the balls are too large the number of breaking contacts will be reduced and grinding capacity will suffer. Moreover, the amount of extreme fines produced by each contact will be increased, and size distribution of the ground product may be adversely affected. If the balls added are too small, grinding efficiency is decreased by wasted contacts that are too weak to break the particles nipped; these largest particles are gradually worn down in the mill by the progressive breakage of corners and edges. Ball rationing is the regular addition of make-up balls of more than one size. The largest balls added are aimed at the largest and hardest particles. However, the contacts are governed entirely by chance, and the probability of inefficient contacts of large balls with small particles, and of small balls with large particles, is as great as the desired contact of large balls with large particles. Ball rationing should be considered an adjunct or secondary modification of the principle of selecting the make-up ball size to break the largest particle present. Empirical Equation In 19521,2 the author presented the following emerical equation for the make-up ball size: B - ball, rod, or pebble diameter in inches. F = size in microns 80 pct of new feed passes. Wi - work index at the feed size F. Cs - percentage of mill critical speed. S — specific gravity of material being ground. D == mill diameter in feet inside liners. K - 200 for balls, 300 for rods, 100 for silica pebbles. Eq. 1 was derived by selecting the factors that apparently should influence make-up ball size selection and by considering plant experience with each factor. Even though Eq. 1 is completely empirical, it has been generally successful in selecting the proper size of make-up balls for specific operations. But an equation based on theoretical considerations should be used with more confidence and have wider application. The theoretical influence of each of the governing factors listed under Eq. 1 was accordingly considered in detail, as described below, and a theoretical equation for make-up ball sizes was derived. Derivation of Theoretical Equation Ball Size and Feed Size: The basis of this analysis is that the largest ball in a mill should be just sufficient to break the largest feed particle into several pieces, excluding occasional pieces of tramp oversize. In this article the size F which 80 pct passes is considered the criterion of the effective maximum particle feed size. The smallest dimension of the largest particles present controls their breaking strength. This dimension is approximately equal to F. As a starting point for the analysis it is assumed that a 1-in. steel ball will effectively grind material with 80 pct passing 1 mm, or with F- 1000µ or about 16 mesh. The breaking force exerted by a ball varies with its weight, or as the cube of its diameter R. The force in pounds per square inch required to break a particle varies as its cross-sectional area, or as its diameter squared. It follows that when a 1-in. ball breaks a 1-mm particle, a 2-in. ball will break a 4-mm particle, and a 3-in. ball a 9-mm particle. This is in accordance with practical experience, as well as being theoretically correct. Confirmation of this reasoning is supplied by the Third Theory of Comminution," which states that the work necessary to break a particle of diameter F varies as F. Since work equals force times distance, and the distance of deformation before breaka4e varies as F it follolvs that the breaking force should vary as F½ These relationships are expressed in Table I, with a 1-in. ball representing one unit of force and breaking a 1-mm particle. This establishes theoretically the general rule used in Eq. 1 that the ball size should vary as the square root of the particle size to be broken. Ball Size and Work Index: The work input W required per ton" varies as the work index Wi, and the

Jan 1, 1959