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By W. H. Yarroll

This paper presents a general discussion of the utility of the statistical technique known as multiple correlation, and gives three specific examples of its application. The first demonstrates the most simple form, or straight-line, multiple correlation. The other two demonstrate multiple correlation analysis in best-fitting third-degree parabolas. With the increasing availability of digital computers, the method becomes entirely feasible where heretofore its use was impractical. The advantages of the method are discussed, and curves are presented which were developed by computerizing the regression equations developed in the examples. The method described in this paper is for use with complex systems, and the examples given are complex metallurgical systems. This subject falls under the general classification of cybernetics, which is defined' as "the science of control and communication, in the animal and the machine." Machine, in this case, can include chemical and physical processes which take place within machines and processing equipment of all kinds. The classical approach to scientific investigation has been the construction of simple models and the changing of variables one at a time. This method is wholly inadequate for obtaining useful information from the complex systems of modern technology including many of our flotation and hydrometallurgical processes. Cybernetics offers the method by which complex systems which have been implemented as an art in the past can now be analyzed with all the discipline of a science. Mathematical techniques for achieving multiple correlation analysis have decided advantages over some of the other statistical methods.2-4 Multiple correlation does not require a series of experiments that have been rigidly planned as do many of the other statistical methods. For this reason, it can be used effectively for interpretation of information from op- erating plants, where planned experiments are impractical, as well as for laboratory experiments. First-degree multiple correlation has been used for many years, and was useful, but limited to linear or nearly linear relationships. The technique described in this paper provides a method for analyzing systems which may be non-linear. This particular technique is multiple correlation analysis in best-fitting third-degree parabolas. It is quite possible that lack of reference to the technique has been due to the overwhelming mass of computations it requires even for relatively simple problems. With the advent of computers, however, its use has become entirely feasible. For the benefit of those who may not be familiar with the subject, it might be well to pause at this point to discuss multiple correlation analysis — what it is and what it achieves. To go back to the old familiar fitting of a set of points with a best-fitting straight line by the least squares procedure, it is conceded that this a good method where there is only one independent variable influencing the dependent variable under consideration, and providing that the relationship is linear. In most fields of investigation, however, there are usually a number of factors exerting important influence, and they frequently bear relationships with the dependent variable other than straight line. Under these conditions, it is easy to see how misleading a simple correlation study might be. Multiple correlation can be used for any number of variables. Within the experience of the writer, this technique has been used to establish regression equations for determination of carbon rate, burden permeability, and production rate on iron blast furnaces, production rate on open hearth steel furnaces, life of molds for steel ingots, rolled steel tensile strength and various defects in rolled products, the performance of ore dressing equipment, and optimization of extractive metallurgical process variables. The discovery of mathematical correlation does not prove, per se, true cause-and-effect relationship, but simply establishes a hypothesis. If the regression equation can be used to make successful predictions of what will happen with future arrays of independent variables, then one can feel reasonably assured that true cause-and-effect relationships have been discovered.

Jan 1, 1968

By A. D. K. Laird, C. A. Johnson

Drag coefficients for a cylinder being towed through water at constant velocity and also at constant linear acceleration were measured. Drag coefficients for constant velocity towing showed reasonable agreement with previous results. The drag coefficients found for constant acceleration showed little correlation with either the magnitude of the acceleration or the value of the modulus AD/V2 and tended to be slightly lower than those for constant velocity. INTRODUCTION For the design of offshore structures, wave forces acting on immersed cylinders are of importance. Several investigations have been made of these forces and of how they can be predicted from wave theories. A paper by Crooke' summarizes much of the work already done. More recent research by the Wave Research Laboratory at the University of California, Berkeley, has added much to the body of data collected under ocean wave conditions, but has not found a reliable method of force prediction from basic theories of wave motion. The present investigation is part of a long-range program to collect data with which to test current and future theories and correlations. The immediate objective was to measure drag forces on a circular cylinder subjected to linear accelerations over the range of Reynolds numbers between l04 and 105 where the drag coefficient was a constant for constant velocities. In particular, the effect of constant acceleration from rest and from uniform motion was to be investigated. The effect of acceleration may be evaluated in terms of drag coefficients. A useful resistance coefficient, C, is defined by the equation for total drag force, D, exerted by the fluid on the cylinder. DT =CSp V2/2.........(1) The coefficient C may be plotted as a function of the parameter AD/V2. Here D is the diameter and S is the projected area of the cylinder. The acceleration and velocity are A and V. The mass density of the fluid is p. An alternate drag coefficient, C, corresponds to the total force of the fluid opposing the motion minus the virtual mass force. This drag coefficient, arising from the velocity of the fluid, may be compared with that for the same cylinder in uniform motion. The similarities and differences between this coefficient as calculated for accelerated and for steady motion are of interest in the inverse process of predicting drag forces on cylinders under arbitrary conditions. One serious difficulty in this method is the specification of the virtual mass which depends also on the flow picture about the cylinder.1 EXPERIMENTAL EQUIPMENT The experiment was performed in the combination wave and towing tank at the Engineering Field Station of the University of California. The tank is 200 ft long, 8 ft wide, and 6 ft deep. The tow carriage is externally propelled by a cable, and the velocity of the carriage is maintained essentially constant by means of an am-plidyne. For the purpose of the present investigation, the speed control of the amplidyne was modified by inserting a linear speed control rheostat, which was rotated at a constant speed by a small d-c motor equipped with a slip-clutch. Accelerations which were constant over a reasonable length of time were thus produced. The magnitude of the acceleration depended upon the speed of the d-c motor and the limiting speed of the carriage. Data were obtained for a range of accelerations of 2 to 10 ft/sec,2 and a range of velocities of 2 to 15 ft/sec. An accelerometer (Statham Type C-2-350) with a range of ±2g was attached to the carriage and connected to a Brush analyzer and penmotor. A continuous coil of wire with 10 turns/ft wound around a fixed wooden form extending for a distance of 40 ft along the length of the tank was connected by an electrical contact mounted on the carriage to a Brush analyzer and penmotor, to give the time-position history for each run. The test cylinder was machined from solid aluminum alloy, 17-ST. to a diameter of 1.250 in., and could be

Jan 1, 1957

DEVELOPMENT of a chemical process for the extraction of pure metals from mill concentrates or metal scrap has progressed beyond the pilot plant stage and may prove an important adjunct to present smelting and refining methods if initial commercial operations prove economically successful. Developed by the Chemical Construction Corp., the new process involves the treatment of oxide and sulphide ore concentrates by chemical methods, instead of the usual smelting and refining techniques. Several of the many applications are now scheduled for commercial use. Refiners using the new process will prepare ore concentrates by standard flotation methods, introduce the concentrate as a slurry into an autoclave along with water and an acid or ammonia. From the resulting leach solution, recovery of individual metals is made by use of suitable reducing agents. By varying conditions during treatment, different metals in the ore are produced separately as pure powders, which may be pressed into forms ready to market, or in the case of copper, extruded as rods or pipe. The reagents are generally recovered. By manipulating the variables during reduction, selective separation of nickel, and/or cobalt, and/or copper can be made simultaneously. The separation is a continuous operation. Low metal prices are not immediately in view because of the tremendous demand at this time. However, reduced metallurgical treatment costs will allow economical mining of orebodies with lower metal content, permitting increased production to meet demand. Although the practical horizon for use of the new process appears to be limitless, one factor may enter into its employment. Just how low grade a concentrate can be economically used is unknown. In addition, for present practical considerations, only metal below zinc in the electromotive series may be processed. Each commercial application requires specific technique adaptation and pilot-plant data for engineering design. A nickel-cobalt-copper process has been researched and piloted in collaboration with Sherritt Gordon Mines, Ltd., for the firm's Lynn Lake properties. In addition, processes were tailored for cobalt concentrates of Howe Sound Mining Co., and National Lead Co., in view of the urgent need for this specific metal. Major General William N. Porter, president of Chemical Construction, says of the new process, "piloting experience has shown that production cost, from ore concentrates to pure metals should be considerably below current costs." Other savings may be realized by cutting transportation and personnel costs, and by reducing the time lag between mining and pure metal from months to a matter of hours. First commercial use of the process will start sometime this summer. Chemico is slated to finish building a $2.5 million cobalt refinery for Howe Sound Mining near Salt Lake City. The plant is expected to raise world cobalt production by 40 pct. The plant will process 35 tons of 20 pct cobalt concentrates from Howe Sound's Blackbird mine near Cobalt, Idaho, daily. Yearly production is expected to reach 2000 tons of pure metal, about one half of U. S. consumption in 1950. Steps in the Howe Sound application of the process are: 1. Acid oxidation leach. 2. Filtration (residues thrown away are insoluble compounds-gangue, iron, arsenic). 3. Cementation (for Cu removal because Cu content is too low for recovery). 4. Reduction from ammoniacal solution. 5. Separation of Co and Ni as mixed metals (95 pct Co and 5 pct Ni). 6. Recovery of ammonium sulphate. Under construction at the Fredericktown, Mo., mine of National Lead is a $5 million refinery sched- [ ]

Jan 1, 1952

By F. W. Jessen, R. W. Durie

The dissolution of salt in the development of salt cavities is controlled by free-convection boundary layer flow along the salt surfaces. It is the purpose of this paper to expand upon results published previously, and primarily to illustrate the influence of surface features on the boundary layer and hence the dissolution process in the development of underground salt cavities. General dissolution equations are presented that apply to a surface inclined to the vertical. A salt surface inclined so as to be overlain by water is dissolved by boundary layer flow, while an inverted surface is dissolved by a combination of boundary layer and cellular flow. Detailed investigation of the boundary layer was limited to laminar free-convection flow. Truly laminar free-convection boundary layer flow may be encountered only in laboratory solution cavities, but the boundary layer will control dissolution even where cavity dimensions are such that free-convection turbulence will occur. The factors found to significantly affect the laminar boundary layer will affect dissolution with a turbulent boundary layer. INTRODUCTION Underground salt cavities have been used extensively for the storage of LPG products, and the use of these cavities is expanding each year. The increasing requirements for such cavities suggest the need for a better understanding of the mechanisms involved, for the purpose of the control of cavity geometry and the most effective use of the injected water. A previous paper outlined a quantitative approach to the determination of salt dissolution rates in the laminar free-convection dissolution of salt. It is the purpose of this paper to expand upon the results previously published and to point out significant factors in the application of these results to the dissolution of field cavities. The dissolution of salt in laboratory scale cavities is controlled by the free-convection boundary layer, which is the region of flow along the salt surface caused by the difference in buoyancy forces resulting from the salt dissolution. The transfer of salt into solution at the salt face causes an increase in salinity, and hence a greater density, in the water at the salt surface. The region of higher density tends to fall through the lighter, less saline water and a flowing boundary layer is the result. The water remains stationary at the contact with the salt surface,l so the resulting velocity profile is such that the influence of gravity is opposed by a viscous shear force at the salt surface. For salt to be transferred into solution from a solid surface to a boundary layer of fluid, it must diffuse through a stationary film of water at the salt contact. According to Fick's first law, the rate of mass transfer by diffusion is the product of the diffusion coefficient and the concentration gradient, with diffusion transfer in the direction of decreasing salinity. Once the salt has passed into the boundary layer, it will be transferred by a combination of molecular diffusion and convection. The convection transfer will in turn affect the rate of dissolution by influencing the gradient of the salt concentration at the surface. In the previous investigation by the authors to determine the basic mechanism of the salt dissolution process, an equation was developed that agreed very well with the experimental rates of free-convection salt dissolution from a smooth vertical surface. The technique was taken from the work of Eckert2 in the analogous heat transfer system and will be referred to as the integral method. The rate of salt transfer from a vertical section of height H was found to be:

Jan 1, 1965

By W. S. Gatley, F. C. Appl

This paper presents a combined analytical and experimental study of chisel penetration vs time during chisel impact on rock, a problem of fundamental importance in improving the performance of roller-cone bits or percussion drilling toots. For a given force-time relationship between chisel and rock, the problem of determining the penetration (displacement) vs time of the chisel is formidable. This is so because the rock is a nonlinear system with distributed mass and distributed damping (friction, dissipation of energy due to rupture, etc.). Since the literature does not contain adaptable solutions, the rock behavior to impact was simulated approximately by an "equivalent" lumped system, that is, an "equivalent" mass, spring, dashpot system. With this assumption, an analytical solution was found for chisel penetration vs time due to a sinusoidal load between chisel and rock. From this solution were found curves, in terms of dimension-less variables, for the maximum depth of penetration vs the frequency of the sinusoidal loading and for the energy transfer vs frequency. The results of this analysis were used to predict the penetration rate of rotary rock bits us rotary speed. The curve indicated that an optimum speed exists. To verify this analysis, an experimental apparatus was constructed and used to apply a sinusoidal pulse to a chisel penetrating a rock specimen under atmospheric conditions. Strain gauges were mounted on the chisel shank and a velocity transducer was mounted between the chisel and the rock surface. The velocity was integrated electrically and picked up simultaneously with the strain gauge signal on an oscilloscope. Permanent records were made photographically to provide simultaneous records of force us time and penetration us time. In comparing the experimental results for limestone and dolomite with the theoretical results, good agreement was found in the frequency range of the experiments. Unfortunately, the inertia effect (peak penetration) indicated by the theory occurs at a frequency much higher than could be obtained experimentally with the apparatus constructed. A "rate-of-loading" effect is indicated theoretically, but has not yet been verified experimentally. INTRODUCTION The process of drilling with percussion tools or rotary rock bits is basically related to the transient response of rock to surface impact. Each time a bit tooth contacts the rock, high stresses are developed which result in penetration and rock removal. As the tooth moves on, stresses are relieved and a new cycle begins as the next tooth contacts the rock. Thus the drilling process, which consists of an endless succession of these cycles, can be studied in terms of a single cycle. It is apparent, therefore, that the study of single-chisel impact on rock is fundamentally important in improving the performance of roller-cone and percussive-type drills. Previous studies in this area have been conducted by Simon1 and Hartman2 by means of drop tests. In these tests a chisel was attached to a weight and allowed to fall, due to the force of gravity, so that the chisel was driven into a rock specimen upon impact. Strain gauges were attached to the chisel shank and the resulting force-vs-time curves were recorded photographically from an oscilloscope screen. The depth of penetration and crater dimensions were also measured. These tests have provided much valuable information but, as mentioned by the investigators, have not provided complete information on the effect of "rate of loading'! This is partly due to the fact that the chisel motion during drop tests is not a controlled motion which can be varied in form and frequency. Therefore, it seemed that additional information could be obtained by studying chisel impact under conditions where both the motion and the frequency of loading could be controlled. This paper presents a combined analytical and exper-

By W. B. Mather

Of the 61 dikes examined some yielded cassiterite, tantalite, and beryl; eight contained spodumene; and six carried amblygonite. Two mines stockpiled spodumene as a byproduct. Only zoned pegmatite dikes carried lithium minerals. GEOLOGICAL studies have revealed the occurrence of hundreds of pegmatite dikes in northeast Brazil, Fig. I, in the three states of Rio Grande do Norte, Paraiba, and Ceara. Heretofore data have not been available on the possible production of lithium minerals from these areas, and in March, April, and May 1953 the author undertook a reconnaissance survey covering a cross-section of the pegmatite~. Sixty-one pegmatites were examined. The pegmatites of Rio Grande do Norte and Paraiba are located in an arid region (Seratao), and except in the most southerly portion there is a minimum of vegetation and overburden. The region is easily prospected and relatively accessible by jeep or truck. The pegmatites examined in Ceara are in an area of lush vegetation along the flanks of the Jaqueribe River valley. It is therefore more difficult to prospect, and the dirt roads, as a means of access, leave much to be desired. For all practical purposes rail transportation, except in Ceara, is not available. The rocks of the area are composed of Pre-Cambrian schist, gneiss, quartzite, and marbles. They have been intruded by granites, monzonites, and diorites and cut by quartz veins and pegmatites. Pre-Cretaceous erosion reduced the area to a peneplain upon which Cretaceous or younger sandstones were deposited. Recent erosion has left only a few remnants of these younger rocks. In most of the Rio Grande do Norte-Paraiba area the pegmatites were more resistant to erosion than the enclosing schists and therefore stand out in relief. This is not true in the rolling country of Ceara, where the pegmatites lack topographic expression. With regard to structure and lithology, the pegmatite~ of northeast Brazil are divided into two types, uniform and zoned. Of the 61 examined, 19 belong to the uniform and 42 to the zoned type. Uniform pegmatites are normally long, narrow, and tabular, with sharp contacts. They are composed of an intimate mixture of feldspar (microcline or ortho-clase), mica (biotite, phlogopite, or muscovite), and quartz. The grain size5 varies from fine at the contact to coarser in the interior. They are not considered a commercial source of pegmatite minerals, although efforts have been made to produce green beryl of gem variety. This type of dike is often abundant in schists and gneisses close to granite intrusives. The productive dikes — lenticular, pod-shaped, or irregular in outline, with sharp contacts — are of the zoned variety. Zone contacts are gradational, except for those with the quartz core. Zones re identified as follows, see also Fig. 3. Border Zone: This outer zone, in contact with the country rock, is composed chiefly of fine-grained muscovite and biotite, with lesser quantities of finegrained microline and quartz. It is the narrowest zone, usually measurable in inches. Wall Zone: Lying between the border and intermediate zones, the wall zone is composed of medium-grained feldspar (often microcline), muscovite, and quartz. Usually it is the widest zone. Widths of 50 ft were noted. Intermediate Zone: Lying between the wall zone and core, the intermediate zone is composed principally of coarse-grained microcline (occasionally with some orthoclase and albite). It may also carry minor amounts of coarse-grained quartz and fine to medium-grained mica. The width varies from less than 3 ft to more than 30 ft. Core: The center of the dike is composed almost entirely of massive quartz, occasionally with minor amounts of fine-grained muscovite. The width reaches 30 ft. Lithium and other minerals of potential economic value are found in the following zones:

Jan 1, 1955

By James H. Boettcher, W. Durand Eppler

INTRODUCTION In the second quarter of 1979, Rapid Mining Co., Inc. ("Rapid") inquired whether Crocker National Bank ("CNB") would provide $4 million in term loan financing to help ("Dry Creek") acquire the outstanding shares of the Dry Creek Coal Company ("Dry Creek") in West Virginia. Prior to approaching CNB, Rapid had sought financing with the assistance of a financial advisor from a number of commercial banks without success. A summary of the initial terms requested by Rapid is shown in Table 1 compared with the actual terms on which the transaction closed. It is not difficult to note that the two sets of terms differ significantly. This is often the case when financing requests based on the expectations and vision of a mine developer are juxtaposed with more pragmatic requirements of a commercial bank. The "art" and fund of structuring financing plans for mining ventures (highly leveraged acquisitions or grass roots) comes in working with mine developers to arrive at a final financial structure that meets their objectives and constraints as well as those of the bank or other financial institutions providing much of the financing. Beginning with the terms requested by Rapid and ending with the terms that closed the transaction, this article briefly describes the process we went through with Rapid Mining. The Seller and Buyer The Dry Creek Coal Company was established in 1961, after its owner acquired the coal leases from Republic Steel. Republic has mined the primary coal seam from 1948-1961. Dry Creek was owned as a subchapter S corporation (i.e., for federal income tax purposes, income is taxed at the shareholder level) and had been run on a low key basis. Since the company had virtually no debt and limited cash needs, the owner produced primarily when rail cars were available and income was required. Output was therefore erratic as is shown in the top of Table II, but the result was a profitable little company with an attractive free cash position. Because the owner wished to retire and enjoy his wealth in a more readily spendable form, he had put the mine, with stated recoverable reserves of approximately 13 million tons, up for sale. In contrast, Rapid Coal's investors consisted of a number of investors of disparate financial situations. They had agreed upon a primary objective of income maximization and planned an annual production rate of 120,000 TPA which they and the current owner believed realizable. The Formulation of a Financing Structure Figure 1 presents a simplified overview of the sequence of steps taken in the financing process which lasted approximately three months from start to finish. Since banks see many requests for funding and considerble time is required to follow up on each, an important step was determining, after a brief review of the materials provided to us, whether the basic "eonomic entity" was viable. In this case, the size and quality of the reserves, the inherent operating cost characteristics, the sales arrangements, the management/labor situation and Rapid's principles all appeared to be sound enough to warrant investing the time necessary to do a thorough analysis of the project. Once this decision was made, the evaluation and analytic process shown in Figure 2 was initiated. The first and most fundamental concern of any banker is whether the loan will be paid back as scheduled from the cash flow generated by the project. The amount of debt relative to the owner's equity is of course crucial in such a determination. Before the debt/equity issue was addressed, however, a number of more qualitative factors had to be studied and if

Jan 1, 1985

By Robert E. Brand, Strathmore R. B. Cooke

For a study of the bonding that occurs in magnetite pellets during oxidation, cubes of magnetite, hematite, and quartz were prepared, each with one surface polished and nearly optically plane. These faces were fired together under pressure and at various temperatures to determine whether bonding would occur. Sections of surfaces that bonded were examined microscopically. An attempt was made to measure the strength effected by this treatment. EARLIER work1,2 has shown that the strength developed by fired magnetite pellets containing silica or silicates is due to three separate effects. Two of these are associated with the formation of slag in the interior of each pellet at temperatures above 1000°C, where the atmosphere is substantially though temporarily neutral. The third is independent of the silica content and is responsible for the development of a hard shell around the pellet during the initial stages of firing, a condition which permits the pellet to assume the increasing load of the overlying burden and prevents extrusion of the slagged and semi-liquid interior. Pellets made from hematite concentrates do not show these effects unless specific additives are incorporated, and it is these differences in behavior which in large part account for the difficulty in producing satisfactory pellets from such concentrates. Elsewhere it has been stated that "the most important factor responsible for the development of strength in fired magnetite pellets containing no additive is the oxidation of magnetite to hematite and the subsequent recrystallization and grain growth of this constituent."' The object of the investigation reported in the present paper was to study in detail the mechanism described above and to evaluate its contribution to the strength of the fired pellet compared with other possible mechanisms, excluding slag bonding. This was effected by placing together polished faces of two cubes prepared from specific minerals and then heating them under constant pressure at different temperatures both in air and in nitrogen. The materials used were magnetite, hematite, and quartz. The magnetite was coarsely crystalline material from western Montana, the hematite was Itabira ore from Brazil, and the quartz was of optical grade but of unknown origin. A high-grade Lebanon (Pennsylvania) magnetite concentrate was used to prepare briquets for the investigation of bonding strength. Analyses of the iron oxide materials are given in Table I. The specimens for furnace treatment were prepared with a carborundum cut-off wheel, which cut the minerals into cubes approximating % in. along each edge. Care was taken to make the sides as parallel as possible. The edges of the faces to be polished were beveled, and the cubes were mounted in brass rings with sealing wax, this being essential to prevent the specimens from rocking during polishing. To prevent excessive friction, the wax was recessed so that only the brass ring and the face of each specimen would be in contact with the polishing lap. Each specimen was then ground with No. 600 carborundum to produce a level surface before polishing. The Graton-Vanderwilt process was not used for polishing because of the long time required by this method, but several other methods were tried. Cloth laps using levigated alumina or chromium oxide did not produce the desired polish. Satisfactory results were obtained by means of a pitch lap: which was used for all the mineral cubes, with levigated alumina as the polishing medium. The lap was operated in a machine similar to those used in the preparation of single optical surfaces. It was run at low speeds and moderate pressures, and polishing was stopped occasionally to prevent overheating of the lap. A good polish with flat surfaces could be obtained in about 5 min. After polishing the sealing wax was removed either in hot water or in a solvent such as turpentine.

Jan 1, 1955

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