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By J. A. Dos Santos

High angle conveyor (HA C) systems in open-¬pit mining offer many advantages over the traditional, truck only, haulage systems. These include superior energy efficiency, less dependency on petroleum products, less sensitivity to inflation, less excavation for the amount of ore recovered, and less ramp construction and maintenance costs. Various high angle conveying systems and the corresponding characteristics of the high angle conveyor are illustrated. Discussion includes the range of HAC systems from the low capacity (up to 1.8 kt/h or 2000 stph), low lift (10.7 to 36.6 m or 35 to 120 ft), continuously mobile to the moderate capacity (1.8 to 3.6 kt/h or 2000 to 4000 stph), moderate lift (36.6 to 76.2 m or 120 to 250 ft), intermittently mobile to the high capacity (greater than 3.6 kt/h or 4000 stph), high lift (greater than 76.2 m or 250 ft), semimobile. Combinations of the above as required for the various open-pit mining operations are also discussed.

Jan 1, 1985

NEW MEMBERS The following list comprises the names of those persons who became members during the period of June 10, 1918, to July 10, 1918. ALLPORT, JAMES H., Cons. Engr Barnesboro, Pa. ANDERSON, G. E., Engr., Exploration Dept., American Smelt. & Refin. Co.,Tucson, Ariz. BAKER, HARRY A., Capt., Co. M, 53d Pioneer Infantry, Camp Wadsworth, Spartanburg, S. C. BEALL, ROBERT STEPHENS, Supt., Empire Zinc Co. (of Colorado), Canon City, Colo. BLAYLOCK, SELWYN GWILLYM, Mina & Met. Engr., Asst. Gen'l Mgr., Cons. Min. & Smelt. Co. of Canada, Ltd., Trail, B. C., Canada. BOTTERILL, THOMAS CLARK, Min. Engr., Belmont Surf Inlet Mines, Ltd., Surf Inlet, B. C., Canada. BOWMAN, MAURICE Asst. Supt., New Idria Quicksilver Min. Co., Idria, San Benito Co., Cal. BROOKS, EARL W Chief En r. Inland Collieries Co. Harmarville Pa. BROWN, DEWITT W Chief Chem., Prime Western Spelter Co., Iola, Kansas BUISSON, ARTHUR Min. Engr., Dept. of Mines, Sussex St., Ottawa, Canada. BUNYAN, F. W Chem., Southern Pacific Railway Co., Sacramento, Cal. BURNETT, ARCHIBALD Supt., Swansea Lease Inc., Swansea, Ariz. BURTON, GEORGE E., Resident Geol., Empire Gas & Fuel Co., Varsity Shop Bldg., Norman, Okla.

Jan 8, 1918

By Paul Tyler

THE extensive employment of nonmetallic minerals antedates the use of metals, but only within the last two decades has the production of nonmetals begun actually to keep pace with the complicated activities which characterize the so-called Machine Age. The economic changes ushered in by the Industrial Revolution were reflected first in an increased demand for metals and for fuels. In the modern sense, therefore, the nonmetallic mineral industries are new and afford new opportunities for engineer and economist alike. A certain amount of caution is indicated, therefore, before attempting to apply ready-made formulas to the problems of these industries. Economics is not an exact science. In the field of production technology where the number of variables is fairly well known, the principles of economics are readily applicable, but as the student proceeds through the province of marketing into the unexplored regions of psychology and sociology he must distinguish carefully between scientific reasoning and purely metaphysical speculation, even when the latter masquerades as economics. The present paper attempts to prove no preconceived theorems and is designed primarily to stimulate careful thinking on sundry neglected phases of these industries. An attempt is made to differentiate the general problems into single aspects which afford promise of being comprehended separately; also, some fundamental statistical data are presented, but merely to indicate a method of scientific approach applicable to more intensive studies.

Jan 1, 1933

By AIME AIME

A SYMPOSIUM on current. conditions in Mexico, particularly in the oil and mining industries, was a most successful feature of the May meeting of the New York Section of the A.I.M.E. Heath Steele, vice-president of The American Metal Co.. Ltd., with an intimate knowledge of Mexico gave the principal address, and asked that his analysis of the present situation he regarded neither as an endorsement of Mexico's policy nor as the criticism of a disgruntled operator. To explain the .attitude of the great mass of the Mexican people towards recent developments, he first described briefly the political, social, and religious beliefs and customs of tile Mexican Indian. In spite of their contact with foreigners these beliefs and customs have remained unchanged throughout many generations. The old communal spirit and the idea of common ownership of the land still persist especially in the rural districts and villages; the old custom of a council for local self-government is reflected in the present-day labor committee. Mr. Steele discussed in order land oil, and mines.

Jan 1, 1938

By T. Nakao

Fujiwara quarry had been operated by the glory-hole benchcut mining system, but as it became difficult to meet expanding demand with this system, a central-shaft mobile crushing plant (MCP) system was introduced in 1979. This MCP is equipped with a hydraulic walking system manufactured for the first time in Japan. Central-shaft mining is now the common mining method of Japanese limestone quarries. With this method, crushing facilities are usually installed at the bottom of the shaft. But at the Fujiwara quarry, MCP was adopted and installed on the quarry surface. Many MCPs are operated in foreign countries, but few examples exist in Japan. Normally, Japanese limestone deposits lie in high mountain, obviously making it inconvenient for MCPs to walk in and around the quarry. This difficulty, however, was overcome, and the MCP has operated satisfactorily and efficiently for two years since its installation. To overcome difficulties in the central-shaft MCP mining system, two mining methods are employed: the slice-down method and the block-cut method.

Jan 1, 1985

By J. H. Carpenter

LMENITE, rutile, zircon, and other heavy minerals are found in small amounts in the sand that covers most of Florida. Small enriched deposits occur on the beaches and coastal dunes. One beach deposit east of Jacksonville was worked during World War I and another near Vero Beach during World War 11. Both ceased operation when the resumption of imports reduced prices. Early in World War II reduction of rutile imports made a domestic source of the mineral necessary to maintain the expansion of armaments. Explorations made near Jacksonville discovered a relatively large body of low-grade ore about 10 miles inland from the beaches. A plant installed by Rutile Mining Co. of Florida using both flotation and tables encountered difficulties because of low plant capacity and organic slimes in the ore. In 1944 Humphreys Gold Corp. solved the problem of concentrating the low-grade ore by using the newly developed Humphreys spiral concentrator and by mining with a hydraulic dredge. This combination of low cost mining and concentration permitted the plant to continue operation in competition with foreign ores when imports were resumed following the war. The success of the Jacksonville operation renewed interest in Florida as a source of titanium. An extensive survey of the state was made by E. I. du Pont de Nemours and Co., Inc., under the direction of J. L. Gillson in 1945 to 1946. Sampling was carried on by drive pipe drilling to depths of 20 to 25 ft. Encouraging values were discovered near the location of the present Trail Ridge mine, 50 miles southwest of Jacksonville, near the town of Starke. The United States Bureau of Mines was interested in exploring for heavy minerals in Florida, and on the recommendation of both the state geologist of Florida and of Du Pont geologists, drilled deeper where marginal indications were found on Trail Ridge. In 1947 it was discovered that sufficiently higher values occurred at depth to make the deposit commercial. The orebody at Trail Ridge is a long sand deposit averaging about 1 mile in width and 35 ft in depth. It is approximately 1 1/2 miles wide at the north end of the portion now being worked, tapering to a blunt point 3 miles to the south. The ore reaches a maximum depth of 65 ft near the center and feathers out into barren sand at the edges. The ground surface is relatively flat and is covered with vegetation including pine, scrub oak, palmetto, and occasionally in swampy areas, cypress. The remain of a dense woody growth underlies and marks the bottom of the Ore 'One. It is difficult to drill through this layer, but in some cases where it is less than 5 ft thick it has been possible to drive through the wood. Sand lying below is coarser than that in the ore zone and contains no values. The wood layer consists of unconsolidated carbonized fragments of branches and other forest trash associated with a considerable amount of ar-

Jan 1, 1954

By James E. York

The honor so fairly earned and so incompletely and tardily paid to Henry Cort, the inventor of the puddling-furnace and the rolling-mill, has been fully set forth by Mr. Charles H. Morgan,' and needs no further emphasis here. In view of the importance of the rolling-mill in the treat ment of iron and steel, the paucity of information concerning it is surprising. With the exception of a book, written about 35 years ago, by Peter Ritter von Tunner, an Honorary Member of this Institute, and of desultory articles on simple sections, which have appeared in technical journals, I know of no publication attempting to treat this subject, although volumes have been written on the scientific theory and technical manipulations involved in other branches of the iron- and steel-industry. This strange anomaly may be due to the fact that roll-turning cannot be called a scientific business. It does not ordinarily come within the range of an educated engineer; yet it cannot be performed by an ordinary mechanic. It demands some of the qualifications of an engineer, in designing, and those of a mechanic, in execution. The men who have followeci this trade have controlled the training of their successors. In many cases the technical knowledge required has

Jan 1, 1907

By Albert Sauveur

The instrument about to be described meets so perfectly the special needs of the metal microscopist that there eeeme to be little doubt but its merits must be readily appreciated by those who have had any experience in the microscopical examination of metals. The Microscope-Stand.—The microscope-stand proper, Fig. 1, consists of a microscope-tube, provided with both coarse and fine adjustments of the best construction, and with a draw-tube, rigidly mounted on a bar supported at both ends on substantial and firm cast-iron legs. The height between the table and the under side of the supporting bar is 5 in. and the distance between the supporting legs 12 inches. This arrangement affords free space below the objective for the examination of large epecimens of metals, such as full rail-sections, without detracting in the least from the value of the

Jan 1, 1912

By George Gardner

THE application of wet cleaning processes for the beneficiation of bituminous coal has created in some localities a problem in the recovery and disposal of fine solids in the washery water. The maximum allowable concentration of these solids in the washery circuit that is consistent with satisfactory operation of the cleaning units remains a controversial point. It has, however, been generally recognized for a number of years that some degree of control should be exerted over the concentration of such material. Early methods of control involved intermittent or continuous dis-charge of a portion of the plant slurry into near-by streams or settling ponds, and this persisted even after the adoption of settling tanks or cones. The practice is not always economical, for two reasons: first, because of the waste of coal, and, second, because it is sometimes difficult and expensive to obtain an adequate supply of water. The latter condi-tion often is aggravated by chemical treatment of the make-up water that is necessary to prevent excessive corrosion of plant equipment. The modern approach to this problem has been the adoption of continuous thickening devices. However, because such equipment occupies consid-erable plant space and is somewhat expensive to construct, the practice of loading these thickeners beyond their rated capacity is widespread, there-fore often the performance of such units is not altogether satisfactory. In recent years, European washeries have increased the rate of settling of the fine coal from the slurry by the addition of specially pre-pared starch solutions. These reagents cause flocculation of the solid particles and thereby increase the rate of sedimentation.

Jan 1, 1939

By S. P. Barber, G. W. Cutting, V. Alesse, M. Ciriachi

Just what is happening in the preparation and mineral separation stages are questions frequently asked about most processing plants. It is unusual to find the answers readily available in the operating metallurgical data. Knowledge is nominally available from metallurgical balances about the head ore grade, grade and recovery of the concentrates, and the plant tailings. However, the mechanisms which control grade recovery and losses are seldom monitored in such a way as to permit specific analysis: Thus, when questions about the effectiveness of the process are asked, the answers are based frequently upon intuitive professional judgments and local expertise. Detailed investigations of process functions are extensive in terms of manpower, time, and interference with production. An investigation method in which process operating conditions could be provided in a cost effective manner would assist in local process assessment and control. Such a collection of process operating data is defined as a process audit and the development of the necessary techniques forms the subject of this paper. A typical application to a lead-zinc concentrator highlights both the manner of implementing a process and the plant data made available for local use.

Jan 1, 1980

It is claimed that the first mining of copper by Americans in Arizona was done at Ajo, near the Mexican border, in 1854,* a year after this region had been added to the United States, under the terms of the Gadsden purchase. A group of adventurers, organized at Los Angeles under the name of the Arizona Mining & Trading Company, came, to the district. This party of prospectors consisted of 20 men, led by Major B. Allen, J. D. Wilson, and William Blanding. † They went first to Yuma, where the party divided, some of them going southward into Mexico while the remainder took the trail to Tinaja Alta, where they heard of the copper deposits of Ajo, which is 85 miles southeast from Yuma.‡ They found attractive outcrops of copper ore, and set to work energetically, but their operations suffered many interruptions, because that part of the country was still controlled by the Mexicans, who were uncertain about the exact position of the new international boundary. The Mexicans tried to expel them, but they held their ground. The first shipment of ore, consisting of native copper and cuprite, came from what is now the western end of of the New Cornelia workings; it was hauled in ox-carts to San Diego, 400 miles across the desert. § Later shipments were hauled to Yuma and floated on barges down the Colorado river to the Gulf of California, whence the ore was loaded on

Jan 1, 1932

By H. T. Kennedy

The fact that intrusion of water into oil wells can be prevented by treating the sand adjacent to the well seems to have been only recently recognized. Swan1 mentions the process of solidifying naphthalene in strata. R. Van A. Mills2 recommends the use of materials such as sodium silicate and sodium carbonate, which react with oil-field water to form solid plugging agents. When a well is drilled in a new field the oil sands are found essentially devoid of water (Fig. 1). Unless a completely impermeable break exists over wide areas in the field, no water is found above the lower limit of the oil zone and no oil is found below the upper limit of the water zone. After considerable oil has been taken from the well, however, it is almost universal experience that water intrusion occurs. This intrusion may be of two kinds. The water may follow a path parallel to the bedding planes of the producing formation through loose streaks in the pay sand, as shown in Fig. 2, or the water level of the field may rise and enter the well by coning (Fig. 3). Water entering from the side is called "edge water," and that coming in from the bottom is called "bottom water.'' Effectiveness of any method for shutting off water depends not only on the effective treatment of the sand adjacent to the well but on

Jan 1, 1936

By H. T. Kennedy

The fact that intrusion of water into oil wells can be prevented by treating the sand adjacent to the well seems to have been only recently recognized. Swan1 mentions the process of solidifying naphthalene in strata. R. Van A. Mills2 recommends the use of materials such as sodium silicate and sodium carbonate, which react with oil-field water to form solid plugging agents. When a well is drilled in a new field the oil sands are found essentially devoid of water (Fig. 1). Unless a completely impermeable break exists over wide areas in the field, no water is found above the lower limit of the oil zone and no oil is found below the upper limit of the water zone. After considerable oil has been taken from the well, however, it is almost universal experience that water intrusion occurs. This intrusion may be of two kinds. The water may follow a path parallel to the bedding planes of the producing formation through loose streaks in the pay sand, as shown in Fig. 2, or the water level of the field may rise and enter the well by coning (Fig. 3). Water entering from the side is called "edge water," and that coming in from the bottom is called "bottom water.'' Effectiveness of any method for shutting off water depends not only on the effective treatment of the sand adjacent to the well but on

Jan 1, 1936

By D. N. Seidrnan

In the present note we present thermal-analysis data for the liquidus curve from 0 to 76 at. pct Se and for the selenium-rich monotectic reaction in the Pb-Se system. We have previously reported that no expey-imental eviderzce was found for a lead-rich monotectic reaction, at -860°C with a monotectic composition of -20.5 at. pct Se, as found by Nozato and Igaki.&apos; Our additional data substantiated this earlier finding and extended the composition range studied. The alloys were prepared from semiconductor -grade lead and selenium purchased from the American Smelting and Refining Co. Both elements were 99.999+ wt pct pure as determined by the supplier. The impurities for lead were Fe (1 ppm) and Cu & ppm) while for selenium the impurities were Cu (< 1 ppm), As (< 1 ppm), Te (1 ppm), and C1 (<1 ppm). The general procedures used for thermal analysis were those specified by the National Bureau of Standards. A Pt/Pt-10 pct Rh thermocouple calibrated against the freezing points of zinc and copper purchased from the National Bureau of Standards and antimony (99.985 pct pure) purchased from A. D. Mackay, New York, was used for all the thermal analysis. The thermocouple electromotive force was measured with a Rubicon Type B potentiometer used in conjunction with a galvanometer with a sensitivity of 0.5 pV (mm) -&apos;. The absolute accuracy of this thermal-analysis system was *0.5"C. One-hundred-gram alloys of the desired composition were sealed in quartz crucibles, with a central thermocouple well, at a pressure of less than 10"1 Torr. The alloys were initially heated well above the liquidus curve and shaken vigorously to insure homogeneity. Cooling curves were then taken by the direct method at cooling rates ranging from -0.5" to 1.5"C (min)-&apos;. The phase diagram from 0 to 76 at. pct Se as determined by direct thermal analysis is shown in Fig. l.* An extrapolation of the selenium-rich portion of the liquidus curve to the monotectic reaction isotherm (678.3"C) gave a value of 76.1 at. pct Se for the monotectic composition. A tabulation of all the thermal-analysis data is given in Table I. As we previously reported no experimental evidence was found Fig. l—The partial Pb-Se phase diagram from 0 to 76 at. pct Se as determined by direct thermal analysis. For the sake of clarity the points for the 49.00 and 49.16 at. pct Se alloys were not drawn on this phase diagram, see Table I. for the lead-rich monotectic reaction found by Nozato and Igaki.&apos; This result was further substantiated by the fact that none of twelve lead-rich alloys, see Table I, examined for this monotectic reaction exhibited a thermal arrest in the temperature range (849" to 863°C) cited by Nozato and Igaki for the lead-rich monotectic reaction. Hence, our results tend to support the earlier qualitative work of ~elabon&apos; and Friedrich and ~eroux" in the 0 to 50 at. pct portion of the phase diagram, though the selenium-rich monotectic composition and reaction isotherm temperature were in agreement with the approximate values (75 at. pct Se and 672" to 680°C) given by Nozato and ~~aki. &apos;

Jan 1, 1967

By B. S. Taylor, J. D. Fraser, W. L. Chen

Steam coal quality is less stringent than metallurgical coal quality. Steam coal is prepared either by cleaning a full-size range of raw coal or cleaning coarse coal only, leaving the fine coal raw. The latter scheme is more cost competitive. It is particularly applicable to US eastern soft coal where low ash coal is concentrated in fine sizes. For raw coal size separation the Rotating Probability Screen, developed by the British Coal Board, may be used for easy change of raw coal separating size, and to avoid screen deck plugging when handling wet and clayey raw coals.

Jan 1, 1985

By William B. Phillips

The concentration of natural magnetites has been carried on in this country for several years, and more or less information has been collected on the subject. Various inventors, availing themselves of the magnetism which is inherent in such ores, have devised machines for separating the impurities from the ore by means of the electric current; and a greater or less degree of success has rewarded their painstaking and persevering efforts. We are now fairly in position to judge of the value of the process as applied to such material. It is not my purpose to speak of this matter further than may be required by the emergencies of the case. I shall assume that most engineers and metallurgical chemists are already acquainted with what has been done at the Chateaugay mines, at Mineville, at the Benson mines, at the Weldon and Ogdensburgh mines, and at Cranberry; although, at this latter place, there has not been so much done as we could wish. I shall not now speak of the various types of separators. From the time of William Fullarton, to whom was granted an English patent, in 1792, for separating iron-ore by the application of magnetic attraction, down to the present time, a great. many devices have been suggested, and a great many patents taken out for this purpose; but it is not necessary now to enter upon a discussion of their merits. Perhaps, at some future meeting of the Institute, after we shall have experimented further with some of the machines on the market, there may be an opportunity to contribute something to the current knowledge of the efficiency and economy of separating-machines. In this paper I propose to give, as briefly as possible, the results already reached in converting a non-magnetic ore into magnetic ore, and then concentrating it over a magnetic separator of the alternate-polarity type. I am aware of the work

Jan 1, 1896

By J. E. Hilliard

It is proposed that shape anisotropy in the internal structure of materials be defined by distribution functions which specify what fraction of the total line length or boundary area lies in a given direction. Methods are descriibed for determinirg these distribution functions from measurements on sections through an opaque material. New derivations, that have certain advanifages over those given previously, are Provided for well-known expressions used in estinzating the total density of lineal or areal features. INCREASING attention is being given to the quantitative description of imicrostructures in metals and other materials. This interest stems from the recognition that the structure often provides a convenient half-way point between the properties on the one hand and the processing variables on the other. Such cross correlations become increasingly desirable as materials become more complex and the demands on them more stringent. One of the principal aims in structure analysis is therefore to find parameters that are readily measurable and specific enough to be correlated with other properties of the material. Certain properties, such as magnetic and mechani cal behavior, are strongly influenced by structural anisotropies; in order to relate such properties to the structure it is obviously necessary to have means of specifying and measuring the type and degree of anisotropy. For the determination of preferred orientations in crystal structure, X-ray diffraction methods are available and are widely used, but scant attention has been given to the estimation of anisotropy in the shape of grains and particles. It is the latter problem that will be considered in this paper. It is evident that shape anisotropy can be describe in terms of preferred orientations of lineal and area elements of the structure. It will be shown that these preferred orientations can, in turn, be specified by distribution functions that define what fraction of the total line length or boundary area lies in a given direction. Methods will be given for determining the distribution functions from measurements on sections through the structure. Even when the orientation distributions are of no interest per se, they still have an important bearing on the measurement of the total line length or boundary area by means of an intercept analysis. The treatment in terms of orientation distribution functions leads to new derivations, that have certain advantages of those given previously, for the well-known expressions used in estimating the total density of lineal or areal features. The treatment is divided into two main sections. The first deals with the orientation distribution of a two-dimensional array of lineal features such as occurs in the projected image of dislocations in electron transmission microscopy. The other section treats the estimation of the distribution of lineal and areal features dispersed in three dimensions.

Jan 1, 1962

By G. H. Gilman

The campaign now being waged to improve the quality of the rock-drill bit is the natural outcome of the scientific development of the drilling machine during the past twenty years. In this development there has been a great increase of power output per unit of weight of machine. But the development of the rock drilling engine has been seriously hampered by the need of a drill bit that would withstand, without undue wear or breakage, the heavy rapid blows of the improved pneumatic hammer. This problem was difficult to solve because an increase in the weight or section of the drill-steel bar resulted in decreased cutting speed and higher operating costs of both the bit and its actuating engine. The solution, therefore, is to make the bit of steel that, for a given weight or section, will be more shock and wear resisting. In the attempt to meet these requirements, many of the drill-steel manufacturers alloyed the steel with vanadium, chromium, nickel, etc. on the assumption that such elements would improve the rock-drill bit but due to the sensitiveness of such steel to forging and heat treatment, higher cost, and lack of continuity of effort on the part of the steel manufacturer to perfect this product, but little progress has been made in the adoption of these steels and the so-called straight carbon steel is today recognized as the standard material for all rock-drill bits. The first step in improving drill-bit efficiency is the determination of the cause of breakage and wear. For this reason, in 1917, certain rock-drill manufacturers, in conjunction with some of the larger mining interests, conducted exhaustive tests in both the field and the laboratory. It was then found that, in the main, the cause of drill-steel troubles is not attributable to the duty imposed upon it by the normal operation of the drilling engine, but to improper forging and heat treating of the bit and to the subjecting of the bit to improper use. The fact that it is possible to minimize the troubles attributable to improper heat treatment of the drill steel has been demonstrated and it is recommended that such knowledge be made available by teaching those interested in the production, use, and up-keep of drill bits the principles on which success in this direction may be achieved. Unfortunately, but little attention has been given to the education of the drill smith. But a few years ago, the instructions given the man

Jan 1, 1922

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951