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By L. D. Keller

The application of hydraulic concentration to large scale operations has been effectively accomplished by the use of the SiphonSizer. Operation has been simple, automatic and essentially trouble free. The use of the primary desliming SiphonSizer on magnetic taconites has shown an improvement in grade of concentrate and an increase in recovery over conventional hydroseparators. Magnetic concentrates have been further deslimed and upgraded in SiphonSizers by floating a coarse middling product away from the heavier concentrate. The application of the Siphon-sizer to closed circuit grinding has met with only partial success to date. Hydraulic concentration of minerals has been practiced for a good many years. Until recently, however, the practice has been limited to equipment using a multiplicity of small pockets and relatively low tonnages and flows. The adaptation of the SiphonSizer to the concentration and classification of magnetite has changed this concept. Some fifty commercial units varying in size from a 16-ft diam circular unit to a 25x100-ft rectangular unit are currently in operation on magnetic taconites. Additional units up to 38 ft diam are under construction. Depending upon the application in the flowsheet, upgrading varies from 0.75% to 14% Fe in a single stage. To those not familiar with taconite processing, the importance of the struggle to remove economically as much silica as possible may not be fully appreciated. Perhaps some figures pertaining to transportation costs will underscore this important process. If the silica content of the concentrate from a 10,000,000 ton per year plant could be reduced by I%, a savings in boat freight, at $2.00 per ton, would amount to $200,000 annually! THE SlPHONSlZER The SiphonSizer, as illustrated in Figs. lA, 1B and 2, is a hydraulic classifier in which the hydraulic water is distributed uniformly across the bottom of the vessel by means of a system of headers (1 and 2), jet pipes (3), and nozzles (4). The depth of the teeter bed is automatically maintained by the siphon-float assembly. The feed is introduced through a feed well (5) and separated into two fractions by the effects of rising water and the density of the teetered bed. The magnetite fraction is discharged by the siphon (12) while the fine slime and light middling overflow a peripheral weir (9) to the overflow launder (6). The bed depth is controlled automatically by float valves (7), which are responsive to changes in the height of clear water supported in the superelevation tubes (8) by the density of the teetered bed. On top of the float (7) is a needle valve (10) which permits

Jan 1, 1963

By W. D. Johnston, T. P. Thayer

THE minerals that collectively are known as chromite form an isomorphous series of the general formula (Mg,Fe) 0. (Cr,Al,Fe) 203. So wide is the range in chemical composition in this group that chrome ore consisting entirely of the mineral chromite may range from less than 30 pct to more than 60 pct Cr203. The most comprehensive published data on the chemical com- position of chromite are by Stevens,62 who made complete analyses of 52 samples of chromite concentrate from many localities in North, Cen- [ ] tral, and South America. These samples were mechanically purified to remove associated silicates and might be regarded as the cleanest chromite that could be obtained by any mechanical milling process. Fig 1 shows the predominant zone of isomorphism, within the triangular prism of composition defined by the mineralogical end members of the series, wherein his analyzed samples fell.

Jan 1, 1949

By Benjamin Smith Lyman

THE importance of topography to geology is so commonly underrated as to deserve to be pointed out again and again. The relation of topography to the different branches of geology may be seen best by a glance at them all. Geology is well understood to consist of the observation of facts about rocks as materials of the earth (geognosy), and the explanation of those facts (geognosy). The facts to observe are : I. GEOMETRICAL, as (1) structure, including the dip and strike at different points, the size, shape, and position of basins and saddles; (2) vertical section, that is, the thickness of rock groups and of their parts ; (3) horizontal or geographical position. 11. PHYSICAL, such as texture, whether sedimentary or crystalline ; and, if crystalline, whether granitic, porphyritic, amygdaloidal, globular, or concretionary ; whether compact or granular; coarse or fine; pervious or impervious; hard or soft; firm or tender; with cleavage or without ; massive or thin ; the microscopic structure ; also whether magnetic or not ; soluble or insoluble ; fusible or infusible ; and the constituent minerals. 111. CHEMICAL that is, the composition of the rocks and of their minerals and their affinities. IV. PALAENTOLOGICAL, as what kind of fossils are in the rocks,

By V. J. Sikora, W. J. McGuire

Several years ago, we used an electric analogue computer to study the effect of vertical fractures on the productivity of wells in expanding fluid-drive reservoirs. The results of this work were used both as a guide to research and as a basis for the design of actual fracturing operations. In 1958, Dyes, Kemp and Caudle' published portions of the data from this study. The results were released in 1959 to service companies for use in fracturing guides. The purpose of this note is to discuss the experimental conditions and assumptions which were made to derive the information which is already partially a matter of public record. ASSUMPTIONS This study applies to fractures which extend in a vertical plane symmetrically from the well. For simplicity, we chose to study the case of a well in a square drainage area with its fractures extending toward two of its nearest neighbors. We have assumed no migration of fluid across the boundary of this area. The quadrant shown in Fig. 1 models this system. We made the usual assumptions that the reservoir is homogeneous and isotropic, that the fluid is homogeneous and that production is effected by fluid-expansion drive. We also assumed that the fracture extends from top to bottom of the reservoir. Of more practical interest is our assumption that the fracture does not change the size of the drainage area. This premise is appropriate if all the wells in the reservoir are fractured in the same way. But where a single well is fractured, its drainage area may be enlarged at the expense of its neighbors. This could be of economic importance. The assumption that the fracture will not extend beyond the established drainage area of the well also limits the application of the results. Such long frac- tures will yield benefits in excess of those predicted here. When we assume homogeneity, we disregard the frequently observed zone of damage in the vicinity of the well. Where damage is severe, the benefits resulting from by-passing it will far exceed those predicted by this study. All comparisons were made of systems producing in the semi-steady state. By this we mean that equal volumes contributed equally to flow (pressure was dropping at a uniform rate throughout the system) when the rate of flow was observed. EXPERIMENTAL SET-UP We used the pool unit of an electric analyzer' in this study. The squase drainage system of a well was rep-

By J. K. Gustafson

Since prehistoric times, gold has been sought for its beauty and its unusual physical and chemical properties. Early in the dawn of civilization it became the ultimate unit of value, and for at least 6000 years it has been used to barter for other commodities. It has been prospected for, treasured and made into works of art and personal adornment. From time to time, it has even been the object of conquest. Because of its predominant role as a basis for money in recent centuries, economists have come to think of gold solely in these terms. Gold, however, has physical and chemical properties that make it one of the most useful metals in the modern world. It is the most ductile metal known. An ounce of it can be drawn into a continuous wire over 35 miles long. It is also so malleable that an ounce of it can be beaten into films 0.00001 in. thick covering 68 sq ft of surface. It has a density of 19.3 and is so heavy that 1 cu ft of it weighs more than half a ton. Gold is nonmagnetic and has a high electric conductivity that is only slightly less than that of silver and copper. Gold is so inert to all the chemicals found in nature that gold coins and jewelry buried beneath the soil or at the bottom of the sea for thousands of years appear to be as bright and perfect as when they were first immersed. Finally, gold has an extremely high reflectivity of both light and infrared rays.

Jan 1, 1971

By WILLETT G. MILLERS

GENERAL RECEPTION COMMITTEE.-Willett G. Miller, Chairman; F. G. B. Alan, Hon. Frank Cochrane, Eugene Coste, Thomas W. Gibson, Cyril W. Knight, J. C. Murray, 0. N. Scott, Alan Sullivan, J. B. Tyrrell, J. W. Wells, A. B. Willis. COBALT RECEPTION COMMITTEE.-Arthur A. Cole, Chairman; Will. Ask with, R. W. Brigstocke, Robt. Bryce, Fred Coombs, M. I. Culbert, I. R. Drummond, J. W. Evans, A. Ferland, F. N. Flynn, E. L. Fraleck, S. R. Heakes, Joseph Houston, D. L. Jemmett, I. R. Jones, Major Leckie, Capt. Jack Leckie, R. W. Leonard, W. H. Linney, Alexander Longwell, Frank Loring, Murdock McLeod, John Martin, D. B. Rochester, W. E. Running. COBALT RECEPTION COMMITTEE (Ladies).-Mrs. A. A. Cole, Mrs. A. Edwards, Mrs. R. Jennings, Mrs. S. H. Logan, Mrs. A. Longwell, Mrs. H. F. Marsh, Mrs. J. Smith. SUDBURY LOCAL COMMITTEE.-Mayor L. O'Connor, Chairman; S. Fournier, Secretary; A. H. Beath, W. J. Bell, F. B. Bennett, D. M. Brodie, J. S. Buchanan, F. C. Busby, Wm. Chalmers, R. Dorsett, W. A. Evans, John Frawley, J. S. Gill, A. B. Gordon, J. G. Henry, T. N. Kilpatrick, Major Leckie, Chas. McCrea, John McLeod, Wm. McVittie, R. Martin, R. S. Mitchell, J. H. Morin, J. A. Orr, James Purvis (President Board of Trade), C. R. Reid, Major Smith, W. W. Stull, J. F. Templeton, S. E. Wright. The first session, held in the Banquet Hall of the King Edward Hotel, was called to order Tuesday, July 23, 1907, at 2.30 p.m., President John Hays Hammond presiding. Prof. Willett G. Miller, chairman of the General Committee, introduced Alderman J. J. Graham, who, in behalf of the City of Toronto, extended a hearty welcome to the members and guests of the Institute. To this welcome, President Hammond replied in a few well-chosen and hearty remarks. In the hall in which the session was held there was exhibited a fine, full-length, life-size portrait of Dr. Rossiter W. Raymond, in 1871 Vice-President and acting President, in 1872, 1873 and 1874 the elected President, in 1876 and 1877 Vice-President, in 1883, by appointment of the Council, and for the last 24 years by annual election, Secretary, of the Institute. Dr. James Douglas, of New York, N. Y., on behalf of numer-

Sep 1, 1907

By L. W. Pommier, F. B. Brien, A. K. Bhasin

In the field of mineral processing, although many operations are applied to suspensions of ore particles in fluids, there is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. Previously proposed equations, based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids, are exam ined in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. As more knowledge is acquired in regard to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow predictions of conditions to achieve optimum results for engineering purposes. In the field of minerals processing, many operations are applied to suspensions of ore particles in fluids. The differential movement of solids of various sizes and densities in suspensions is of utmost importance to gravity concentration, wet classification, flotation, hydrometallurgy, and pipeline transport of solids. The subject is also of importance to other branches of engineering; for example, those involved with soil mechanics, ceramic slips, and oil-well drilling fluids. There is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The problems encountered in the direct application of the well-known Stokes and Newton's Laws to non-Newtonian systems have been examined in a previous paper.' Equations were proposed based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids. This present paper examines these equations in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. It is thought that, as more knowledge is acquired as to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow prediction of conditions to achieve optimum results for engineering purposes. The purpose of this paper is to make an initial assessment of the nature and magnitude of pertinent suspension variables. In order to avoid too voluminous a document, the examination of kinetics and mechanisms will be omitted at this time. THEORY A Newtonian fluid is defined as a fluid in which the stress is proportional to the rate of strain, 2 i.e.: H = viscosity; see Table I. for list of symbols The following equations are conventionally used to assess the motion of spherical particles moving under laminar and turbulent flow conditions through Newtonian fluids: When these relationships are applied in practice to suspensions, the liquid density is substituted by a composite suspension density, and viscosity is usually taken as that of the suspending liquid or an approximated "apparent viscosity." However, suspensions are non-Newtonian in character3 and thus, more than one viscosity parameter is required to describe their behavior. A number of models have been proposed for non-Newtonian fluids;2,4 among these the simplest is the Ostwaldde Waele or power-law model for incompressible fluids which for one dimensional flow may be reduced to:

Jan 1, 1970

By J. V. W. REYNDERS

NOT only is your toastmaster silver-tongued in his references 'to myself, but he is also quite in the habit of "saying it in silver." I have analyzed with some care his statistics of the world's silver production, which have been distributed here along with the menu, although frankly from the point of view of most of us, the distribution rather than the production of silver is of immediate concern. Unlike the performers by whom we have been entertained between courses, the rest of us on the program will have to do without costume or musical accompaniment, which as my friend Rains can testify puts an artist under severe strain. I am entitled by right of office and of precedent to receive your attention for ten minutes. The Governor, who appears on the program as a speaker; however, has asked me for five minutes of my time, and Senator Thomas has insinuated that he would appreciate one-half of the remainder, wherefore, I must ask your close attention to the very brief remarks that I am able to make under such restricted circumstances. To begin with, I want you to believe that I am approaching the task set by your toastmaster with misgivings. In looking over the Institute records relating to the Salt Lake City meeting of 1914 for some precedent as to what I ought to say, I found but one reference-and that of the following indefinite char¬acter-" and Friday night there was a hilarious banquet to 350 members and guests."

Jan 1, 1925

By E. C. Olsen

This paper describes the unusual hazardous conditions encountered in mining thick, inclined coal beds under heavy cover in Carbon County, Utah. This description includes heavy roof conditions, sloughing ribs, steep pitches, and severe bouncing experience. Emphasis is placed on the top bench system of mining and development in the top half of a 16-ft seam, under the roof rock, which is bolted, and the recovery of the bottom coal on retreat; success of bolted roof and ribs; and shuttle car haulage on pitches up to 25%. The use of protective cages for operators of face equipment, the guarding of belt conveyor systems to prevent injury associated with deliberate entry, and the positive lockout of electrical equipment is described and illustrated. Most coal mining areas of the Western United States are characterized either by thick beds, steep pitches or heavy cover. Individually, each of these may present inherent safety hazards that in- fluence mining. When all are met at one location, the combined effect is to make the safe operation of the mining property a challenge to management. These combined conditions are met in the coal mines of the Columbia-Geneva Steel Div. of the United States Steel Corp., in southeastern Utah. This coal bed measures up to 16 ft in thickness, the pitch is as much as 25% and mining is under a cover approaching 3000 ft. The Sunnyside coal bed is found in the Book Cliff Mountains, a great escarpment extending from west of Castle Gate, Utah, some 180 miles to Grand Junction, Colo. West of Green River, Utah, the Book Cliffs swing sharply to the north because of the domelike uplift of the San Rafael Swell to the southwest. It is in this northerly extension of the Book Cliffs that the Sunnyside coal in the Blackhawk Formation of the Mesa Verde Group, Upper Cretaceous Age is found. The strata are transected by numerous faults with from a few inches to as much as a hundred feet of displacement. All of these faults have had some effect on the mining operation, either in roof control or, in the case of major faulting, the pattern of mine development. MINING PRACTICES Mining has generally been confined to the Lower Sunnyside Seam which measures from 7 to 16 ft in

Jan 1, 1963

By John R. Eckel

A Iaboratory drilling rig has been devised and placed in operation which permits the application of hydrostatic, terrastatic, and formation pore pressures to a rock sample for drilling under controlled conditions. Calibrated rests of this equipment in-dicate qualitative agreerment with field results on the effect of weight on bit, rotary speed, and rate of circ~~lation on drilling rate. Tests under pressure, using water and air as the drilling fluids, indicate that when drilling saturated limestone samples, a pressure differential between hydrostatic and formation pressure is the only pressure which affects drilling rate. A differential in either direction causes a reduction in rate, but the same diflerential from the wellbore into the formation causes the greater reduction. Also, in lime.stone, air favorably affected drilling rote only when compared to water at high hydrostatic pressurre, all other conditions remaining constant. Large increases in drilling rate with air could be obtained in the laboratory only while drilling a shale, which offered a limited permeability to nitrogen and which could be drilled with a differential from the formation into the wellbore. In general, the magnitude of the changes due to the pressure effect were small compared to changes in drilling rate obtainable by changing either bit weight or rotary speed. INTRODUCTION In the course of Humble's drilling research program, the desirability of investigating several factors which lend themselves to laboratory rather than field study became obvious. Principal reasons for this are the expense involved in field studies and the difficulty of exercising the required degree of control. Of primary importance are investigations of the effect of fluid pressure on rock rate, the effect of pressure on rock drillability, and a study of the fundamental mechanics of rock failure and chip generation. Several years ago some work in the laboratory on the effect of mud properties on drilling rate was re- ported to the API', but the completion of this work and the investigation of the other variables affecting drilling rate required equipment somewhat more elaborate than that used on these earlier tests. This equipment has been assembled to form Humble's Drilling Engineering laboratory. To date only the effect of pressure on rock drillability while using water and air has been investigated, and this work is not yet complete. Facilities are available to investigate the effect of fluid properties on rate of penetration, and information is being assembled on a current basis on the mechanics of drilling. The sequence of presentation in this progress report is somewhat different from that in which the data were obtained since the order of ex-

Jan 1, 1967

By James M. Link

Slurry transport of industrial minerals has proven to be practical, economical, and efficient. Industrial minerals currently being pumped for long distances include cement, clay, phosphate, sand, and various waste product from industrial mineral processing operations. This paper will touch upon the basic theory of hydraulic transport of solids and then consider the economic and engineering considerations upon which construction and operation of such a line would be based. Where possible, actual cost data will be presented.

Jan 1, 1974

By Charles Hardy, George D. Cremer

POWDER metallurgy has been established for some time as a novel method for manufacturing a great variety of articles generally specialties that could not be made conveniently by any other method. In this category are such parts as porous hearings cutting tools of sintered carbides, and electrical contacts in which the metallic constituents do not tend to alloy in the proportions employed. The industry, however, is now at a stage where it has begun to manufacture articles that can and have been made by other methods. Thus, powder metallurgy is now preferred technique for the production of numerous machine parts characterized by high strength, accuracy of configuration, and substantial lack of porosity. Manufacture of such machine parts from metal powders has no doubt been stimulated by the war, although the trend in this direction has been apparent for several years. In any case, quantity production of high-density precision pieces by ponder metallurgy is now in full suing in the United States, and such production can and should continue to expand during and after the war.

Jan 1, 1942

By J. B. Gayle

PRESENT flotation processes depend almost entirely on the buoyant properties of air bubbles to effect separations of mineral and gangue, but there is no convenient method for measuring aeration in flotation cells. Consequently the relation between aeration and cell performance has not been definitely established. In connection with a comparative study of kerosene and froth flotation processes, a modification of the displacement method' was developed in which air escaping from the cell surface is measured with a wet-test meter. The arrangement shown in Fig. 1 is satisfactory for use with a number of cells and is not critical, except that care must be taken to use connections and tubing large enough to avoid excessive back pressures. Attempts to use smaller tubing resulted in back pressures that caused displacement of the liquid level in the receiver, so that some air was lost around the sides, an occurrence readily visible when measurements were taken with only water passing through the cell. With the arrangement shown, the manometer indicated an average reading of about 1/2-in. water pressure. No loss of air was evident. Fig. 2 presents typical data for a standard Denver sub-A 24x24-in. unit cell operated at impeller speeds from 0 to 710 rpm. Each plotted point represents the average for five readings distributed over the entire cell surface. Readings were taken with only water passing through the cell. Results of this type have been used in a study of the influence of operating variables on cell performance and in detecting inherent differences in the operating characteristics of cells of various kinds. Although the information presented in Fig. 2 resulted only with water passing through the cell, the apparatus is suitable for use during flotation of coal when various reagents are present. Possible modi- fications that might prove convenient under special circumstances include varying the size and shape of the receiver and substituting a calibrated, inverted, water-filled carboy or other gas-measuring device for the wet-test meter. If such modifications result in excessive back pressures, some form of draft should be applied at the discharge end of the measuring system.

Jan 1, 1959

Nominating Committee.-On the recommendation of the President, the Board of Directors, at their meeting on Apr. 25,1913, appointed the following Nominating, Committee to nominate officers and directors for next year: John Hays Hammond (Ex-President), Chairman. Robert H. Richards Chairman of Boston Local Section. Richard S. McCaffery, . . . . Chairman of Spokane Local Section. Chester F. Lee Chairman of Puget Sound Local Section. Frederick G. Cottrell, . . . . San Francisco, Cal. Charles W. Goodale Butte, Mont. James W. Maleolmson, . . . . Kansas City, Mo.

Jan 5, 1913

By R. W. Heins, N. Street

An investigation was made of the Rehbinder-Kuznetsov pendulum as an instrument to aid in the study of rock drillability and of the effect of surface active agents on rock drillability. The "critical weight", i.e., the pendulum weight at greatest sensitivity, was determined for several solids and it was shown that a change in surface environment changed the maximum value of the apparent hardness but not the critical weight, and the critical weight increased with increase of hardness of the solid used. Using silver halides as the solid material, and solutions of either silver nitrate or the appropriate alkali halide, it was shown that there is a hardness maximum at the zero point of charge of the particular silver halide. INTRODUCTION The development of relative hardness measurement by the method of damped oscillations, or what has been called the pendulum sclerometer, is due largely to the Russian workers P. A. Rehbinder and V. D. Kuznetsov and their co-workers.1,2 The apparent simplicity of the method has led to its use in a number of fields, particularly those where relative hardness has to be determined on a brittle solid. As will be shown, the simplicity of the method belies its complexities. THEORY OF THE PENDULUM SCLEROMETER The operation of the pendulum is quite simple. Make a sharp point such as a diamond, hardened steel or tungsten carbide, as the fulcrum of a pendulum, with the center of gravity of the system below the point of support. The attenuation of this pendulum is a function only of air friction, provided no fragmentation, breakage or other work is performed by the point. However, when the solid surface breaks or disintegrates under the point, and the latter penetrates the solid, part of the energy of oscillation is absorbed in the work of creating new surface, and the rate of attenuation increases. In the case of brittle solids, the point of the pendulum produces fragmentary particles, whereas the point produces plastic deformation in a plastic solid; but in both cases damping occurs. This pendulum damping is a function of the hardness or strength of the solid. Whereas a pendulum oscillating on a hard material attenuates primarily by air friction, in the case of a soft material, the points penetrate the surface of the solid, producing new surface, and the pendulum damps much faster. Thus the attenuation rate is a function of the hardness or strength of a material in both plastic and brittle substances. Russian workers initially used a single support for the pendulum, but this created many problems because of oscillation of the pendulum in more than one plane. A revised version used two points, or sometimes a prism as support, successfully confining oscillation to one plane. The version using two points was constructed and used throughout this investigation, making the recording of the attenuation as a function of time relatively easy. That both points should be in contact with the solid during the damping is implied. Rehbinder (c.f. Kuznetsov2) proposed that the hardness H as measured by this method could be expressed by a quantity which is inversely proportional to the relative initial rate of attenuation of amplitude. where H = hardness parameter (arbitrary units) a, = initial amplitude da/dt = rate of attenuation of amplitude with time. In the simplest case of damping with a constant logarithmic decrement, H can be regarded as a constant for the duration of the whole damped oscillation process. That is

Jan 1, 1966

By F. Lowell Lawrance

JOHN SMITH, citizen of the U.S.A., has become so accustomed to reading that Congress has appropriated billions of dollars to pay war costs. that he no longer is impressed by relatively small figures, such as several hundred thousand or a few million, in connection with Government departments.

Jan 1, 1944

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

By Curtis Wilson

FROM the results of his investigation of the hardenable copper-nickel-silicon and copper-cobalt-silicon alloys, M. G. Corson1 explained the dispersion-hardening effect by assuming the precipitation of the inter-metallic compounds nickel silicide and cobalt silicide, and on this basis he constructed diagrams for the pseudobinary systems copper-nickel silicide and copper-cobalt silicide. A consideration of these diagrams and of the factors that exert such an important influence upon the rate of precipitation, such as degree of supersaturation, nucleus number and rate of diffusion, leads to the expectation that the rate of precipitation of the silicides on reheating the quenched solid solutions at temperatures below the alpha-phase boundary should increase continuously as the reheating temperature is raised. The present investigation shows that while this rate does increase with the reheating temperature in a general way, it does not do so continuously. Supplements to Corson's diagrams are offered, showing the discontinuities, and slight modifications in the solubility curves are suggested.

Jan 1, 1933

By P. K. Guerrero, N. Arbiter

The correlation of power consumed by a tumbling mill with the dimensions, speed, and load has been attempted by three principal methods. One of these, the torque formula, has been reviewed critically elsewhere.' This approach, while analytical, disregards the individual motion and speed of the tumbling bodies and assumes that the gross geometry of the entire load is sufficient to establish the power requirement. A more general approach, using dimensional analysis, has been applied in this laboratory by the present authors1'1, and more recently by Rose.3 This disregards the internal conditions within the mill entirely and in effect is an empirical procedure for correlating data. Finally, the complete analysis of tumbling mill dynamics as first made by Davis' attempts to develop the power requirement from individual ball and rod paths and velocities. Although Davis' result is applicable only at a single speed for a given size and load it could be useful, since his optimum speed is at the upper limits of conventional tumbling mill practice. Where power values predicted by the Davis equation were compared with actual mill requirements, they were found too low for small mills and much too high for the largest mills. This suggested that the agreement with actual intermediate range requirements might be fortuitous, and the development of the equation was examined critically. The probable source of error was found to lie in an erroneous assumption made by Davis in converting the energy of ball or rod motion to power. With the same approach, but with different assumptions, a modified equation has been obtained which predicts results that are usually consistently high. This is to be expected, since it is assumed that there is no slip between load and shell and no interference among tumbling bodies. Both these effects should account for the difference. Development of Equation: When a cylindrical shell charged with a substantial weight of rods or balls is slowly rotated about a horizontal axis, the load surface first assumes an inclination that gradually increases to a maximum. Continued rotation results in failure within the load, characterized by a sliding of the top layers down the slope and a reduction in the angle of inclination. Further rotation again increases the angle, and the cycle repeats. If the speed is increased, there is continuous load failure and build-up and a continuous stream of rods or balls descends over the upcoming mass, which moves in circular arcs. At higher speeds the up-

Jan 1, 1961