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By J. R. Shouldice

"IntroductionREEFS of Silurian age are recognized in southwestern Ontario, both in outcrop and from subsurface information. This paper deals with the so-called 'pinnacle' reefs which are known only in the subsurface. For the purpose of this paper, the pinnacle reefs are arbitrarily defined as those structures having a height of over 250 feet and a length of less than two miles. This definition eliminates numerous mounds and other broader, more subdued, structures of less certain origin, found in subsurface beds.The term 'pinnacle reef' is perhaps unfortunate, but it is in common usage in Ontario and is used elsewhere for different types of reefs. A new name is justified by the unusual environment and structure of the Ontario reefs, but it is unlikely that any other term would gain acceptance. Rather than propose a new term which would be ignored or result in further confusion and misuse, the name 'pinnacle', as defined above, is used in this paper.Pinnacle reefs have been found over a fairly large part of southwestern Ontario. The known reefs of this type parallel the southeast edge of lake Huron and •follow the strike of the structure contours which circle the Michigan basin (see Figure 1). In total, twenty-five such reefs have been discovered in southwestern Ontario."

Jan 1, 1955

By Ottokar Hofmann

In tank-lixiviation, the extraction of the silver from chloridized ore by solutions of hyposulphite salts is performed by filtration. The ore-particles are kept stationary, while the solvent moves down through the mass of ore. The quickness of extraction, other conditions alike, is in direct proportion to the rapidity of the movement of the solvent through the ore. The solution, if left in contact with the ore without moving, displays but very little solving energy. If the filtration is interrupted for ten or twelve hours, and thus solution and ore are left in complete contact for that length of time, it mill be found that, when filtration is started again, the outflowing solution is but very little more saturated with silver than it was at the time of interruption, and that the ten or twelve hours were almost a perfect loss in the total time of extraction. Notwithstanding the long contact, the solution had not become saturated with silver chloride to its full solving capacity. A rapid movement of the solvent through the ore is essential to a quick extraction. This fact is well known ; and the endeavor of leachers has been to hasten extraction by increasing the rate of filtration. Siphons, vacuumpumps and other devices have been used with more or less success; but none of them have given full satisfaction. I have found that, if chloridized ore is brought into rapid contact with a proper volume of moving sodium hyposulphite solution, the silver chloride contained in the ore dissolves almost instantly, and that it is rather the volume of the solvent than its concentrated state which produces this effect. Such favorable conditions cannot be attained in tanks. The rapidity with which a certain volume of the solvent can be brought into contact with the ore-particles is limited by the speed with which the solution descends through the ore; and thus the leaching-time in tanks cannot be shortened beyond the limit set by the filteringcapacity of the ore. In a trough, however, these favorable conditions can be attained by gradually introducing the ore into the moving stream of the solvent. The ore can thus be brought into

Jan 1, 1888

By C. F. Allen, G. B. Walker

K. F. TROMP*—In dealing with the question of the most suitable kind of solid media for heavy density suspension processes Walker and Allen point out that the particle size of the solid media should not be taken too fine, as the viscosity increases with the area of the solid media and a low viscosity is essential lor high tonnage and accurate separation. A coarser particle size of the solid media will, in their opinion, of necessity give rise to a differential density in the bath (higher gravity at the bottom of the bath than at the top) but they advocate acceptance of the differential density rather than a higher viscosity. Though I fully agree with the choice the authors have made, I cannot subscribe to their view that only by accepting a differential density in the bath a coarse particle size of the solid media can be used. There certainly is another alternative: stronger agitation. Applying sufficiently strong vertical currents, a uniform gravity can be obtained quite well in a suspension of a coarse solid media. Of course, this is not a very attractive solution, for it means a degradation of the true gravity separation and a step backwards to hydraulic classification, which makes the washing dependent on size and shape of the particles. However, to a greater or lesser extent, this is what actually takes place in all the heavy density suspension processes relying on a uniform gravity in the bath. The so-called "stable" suspension processes make no exception. They all "stabilize" their suspensions by introducing or creating vertical currents, be it upwards or downwards or both, be it by hydraulic or by mechanical means. In fact, there is no such thing as a "stable" suspension in gravity separation, as the very reason for the use of suspensions in this field is the property that the solid media is able to settle and so facilitate the recovery. I have been enlarging on this point because the characteristics of the various processes can only be well understood and viewed from the same angle (from Bar-voys up to Chance) when the fact is recognized that mechanical or hydraulic agitation is a condition sine qua non for obtaining a uniform density from top to bottom in a suspension. Is a Cone-slraped Vessel Essenlial? Of the two alternatives for getting a low viscosity Walker and Allen have preferred correctly the sacrifice of uniform gravity in the bath instead of increasing further their vertical current arid agitation. The resulting differential density of the bath brings the problem of bow to prevent accumulation of intermediate gravity products in the bath, an accumulation which, if not prevented, would ultimately plug their cone. According to the authors an open-top cone combined with a downdraft current of the bath liquid would he the only suitable way to cope with such suspensions and they assume as a fact that "in any vessel other than a cone, such a differential density could not be tolerated." My experience is quilt: different. In my process, which has been in successful operation for more than a decade, differ-ential density of the suspension is applied ranging from values below 0.1 up to differentials above 0.5, according to the prevailing requirements of the individual plant. In this process, which is charac-terized by the use of horizontal currents in a suspension of differential density, the form of the vessel is of secondary importance and different types are in operation. It so happens that none of these are in the, form of a cone. The fact that 24 washboxes on my process have been installed and 12 others are under construction may constitute sufficient proof against the opinion that only a cone-shaped separator would be suited for differential density separation. Horizontal Currents in Differentia1 Den-sity Sepparation I myself have some doubts as to the suitability of a cone with downdraft for dealing with differential density (or, for that matter, any other washbox relying on vertical currents for removing the intermediate gravity products). It ap-pears to me that it is restricted to feed of small size only and even then with watch-fulness. If we take, for example, a piece of 2 in., the draft necessary to pull such a piece down to a zone wherein the den-sity of the suspension is, say, 0.03 higher, is quite considerable. For a suspension of, say, 1.6 sp gr the downdraft will have to be in the region of 3 in. per second. Unfortunately. most of the differential in density is in the part immediately below the reach of the top current which transports the floats. Consequently, we need the downdraft where we like it least: in the upper part of the cone. This entails the risk that light float particles are carried away with the downward current. This current of, say again, 3 in. per second would carry particles up to 1.3 sp gr and 3/8 in. size into the 1.6 gravity zone. This is prohibitive. It is also prohibitive because a downdraft of 3 in. per second in the upper part of the cone would require a tremendous circulation of medium. IIalf way up a 20 ft diam cone, a downdraft of 3 in. per second would correspond with 8500 gpm. With the downward current following the way of least resistance, the strength of the downdraft will not be exactly the same at different places of a cross area. If, as I anticipate, the center of the cone is favored, the strength of the downdraft will fall below the critical value near the

Jan 1, 1950

By M. Gensamer

IT has been suggested by a number of people that it would be worth while for some one to attempt to summarize or condense the proceedings of this symposium. This task has fallen to me as organizer and co-chairman. Its difficulty will be appreciated by anyone who attempts to read the whole proceedings. It is therefore with trepidation that I offer the following digest. In recent years there has been a renewal of interest in America on this subject of the cohesive strength of materials, and a growing appreciation of the need for a better theory of cohesion failure. The theories of elastic action and plastic action are well developed, particularly the former. The theory of plastic action is still in the course of development, but it is well along. Plastic action is terminated by cohesion failure and what is needed is a theory that will tell us when to expect the cohesion failure. In the past it has generally been assumed that cohesion failure will occur when a critical value of the maximum tensile stress has been reached. Many experiments have shown that this is not strictly true, and this symposium concerns itself with the failures of this simple hypothesis, and with the efforts that have been made to devise a more satisfactory theory. The most active contributor in recent years to knowledge in this field is Dr. McAdam, and he was asked to open the symposium with a summary or condensation of his papers and views. Undoubtedly it is presumptuous to attempt a still greater condensation, but perhaps it will be useful, because even his contribution to this symposium contains no summary, no concise statement of just what his contribution has bees. Dr. McAdam makes two main points. The first is that the cohesive strength is not a single valued quantity, but that it is a function of all three principal stresses and hence must be represented diagrammatically by a surface in a three-dimensional figure. Dr. McAdam has attempted so to delineate the cohesion limit, basing his

Jan 1, 1944

By M. Gensamer

It has been suggested by a number of people that it would be worth while for some one to attempt to summarize or condense the proceedings of this symposium. This task has fallen to me as organizer and co-chairman. Its difficulty will be appreciated by anyone who attempts to read the whole proceedings. It is therefore with trepidation that I offer the following digest. In recent years there has been a renewal of interest in America on this subject of the cohesive strength of materials, and a growing appreciation of the need for a better theory of cohesion failure. The theories of elastic action and plastic action are well developed, particularly the former. The theory of plastic action is still in the course of development, but it is well along. Plastic action is terminated by cohesion failure and what is needed is a theory that will tell us when to expect the cohesion failure. In the past it has generally been assumed that cohesion failure will occur when a critical value of the maximum tensile stress has been reached. Many experiments have shown that this is not strictly true, and this symposium concerns itself with the failures of this simple hypothesis, and with the efforts that have been made to devise a more satisfactory theory. The most active contributor in recent years to knowledge in this field is Dr. McAdam, and he was asked to open the symposium with a summary or condensation of his papers and views. Undoubtedly it is presumptuous to attempt a still greater condensation, but perhaps it will be useful, because even his contribution to this symposium contains no summary, no concise statement of just what his contribution has been. Dr. McAdam makes two main points The first is that the cohesive strength is not a single valued quantity, but that it is a function of all three principal stresses and hence must be represented diagrammati-cally by a surface in a three-dimensional figure, Dr. McAdam has attempted so to delineate the cohesion limit, basing his

Jan 1, 1945

By Huan-Qiang Zhang, Gang-Hai Huang, Yu-Yong Jiao, Fei Zheng, Zhang. Xiu-Li

An efficient and accurate three-dimensional (3-D) contact detection algorithm is of vital importance in large-scale computing of discontinuous deformation analysis. The contact detection algorithm takes up a large proportion of the whole calculation time because of the increasing calculation number in three-dimensional case. For block systems which consist of convex polyhedrons, the efficiency and accuracy of the contact detection algorithm is a great challenge. The presented contact detection algorithm in discontinuous deformation analysis (DDA) method is carried out in three phases: the global neighbour searching, the local contact type searching and the contact transferring. A contact detection algorithm for 3-D DDA is presented with some improvements on the three phases. A grid-based global neighbour searching algorithm is used to eliminate unnecessary neighbour blocks to the exact number. The local contact type searching includes two steps. In the first step, the common plane method is used to determine the contact type between convex polyhedrons. In the second step, the contact pairs detected by the common plane method are divided into four basic types. In the third phase, the four contact types are transferred into two basic contact types, vertex-to-face contact type and edge-to-edge contact type, which are managed in a uniform procedure. Three verification examples are calculated, the results show that the proposed algorithm based on the three contact detection phases is robust and efficient.

Jan 1, 2015

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.l Part II gives an account of the practical elaboration of the instrument, together with some description of measurements performed. I. Principle of Using Astatized Pendulums1 In order to reduce the trouble and waste of time attending the use of ordinary pendulums in measuring the force of gravity, various instruments of another type have been suggested for relative determinations, as a rule arranged in such a way that the attraction of the earth on a certain body or mass of fluid is balanced by elastic force from a spring or a shut-in mass of gas. A change in the force of gravity is then made manifest as a change in the position of equilibrium of the body, in that the deformation of the spring (or compression of the gas) is changed. With such instruments there are, however, great difficulties in keeping the elastic force constant or its variation known with sufficient exactitude, because of elastic after-working, influence of temperature, and so on. The author suggests for relative determinations of gravity another type of instrument, in which two directional forces (control coefficients) rather than two forces are compared with one another. By "directional force" or "control coefficient" is meant that quantity in a rotatable system that, multiplied by the angle of deflection, indicates the moment counteracting the deflection. In this way it will be possible greatly to reduce the influence of the elastic after-working, which in instruments with spring devices acts so disturbingly. The instrument is made with a rotatable system arranged in such a way that the total control coefficient acting upon it, is composed

Jan 1, 1940

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.l Part II gives an account of the practical elaboration of the instrument, together with some description of measurements performed. I. Principle of Using Astatized Pendulums1 In order to reduce the trouble and waste of time attending the use of ordinary pendulums in measuring the force of gravity, various instruments of another type have been suggested for relative determinations, as a rule arranged in such a way that the attraction of the earth on a certain body or mass of fluid is balanced by elastic force from a spring or a shut-in mass of gas. A change in the force of gravity is then made manifest as a change in the position of equilibrium of the body, in that the deformation of the spring (or compression of the gas) is changed. With such instruments there are, however, great difficulties in keeping the elastic force constant or its variation known with sufficient exactitude, because of elastic after-working, influence of temperature, and so on. The author suggests for relative determinations of gravity another type of instrument, in which two directional forces (control coefficients) rather than two forces are compared with one another. By "directional force" or "control coefficient" is meant that quantity in a rotatable system that, multiplied by the angle of deflection, indicates the moment counteracting the deflection. In this way it will be possible greatly to reduce the influence of the elastic after-working, which in instruments with spring devices acts so disturbingly. The instrument is made with a rotatable system arranged in such a way that the total control coefficient acting upon it, is composed

Jan 1, 1940

Discussion of the paper of K. Huessener, (Trans., vol. 53, pp. 402 to 4333, and of the papers of Linn Bradley, H. D. EGbert and W. W. Strong, pp. 303, 319. R. J. WysoR, So. Bethlehem, Pa. (communication to the Secretary*). —At our plant (Bethlehem Steel Co.), we have had several Bradshaw burners under course of construction and erection for some time, but up to the present we have not had opportunity to put them in service. I regret that I can not take part in the discussion with some actual results from these burners. Mr. Huessener properly emphasizes the importance of obtaining the highest combustion temperature practicable in boiler practice, which demands a near approach to perfect combustion conditions. The ideal burner is the one which, while meeting the various mechanical requirements, fulfills the above condition under a wide range of gas pressure. The question as to the relative value of hot raw gas and cold washed gas for boiler use is a very interesting one. I think that in the past the importance of low temperature of washed gas sometimes has been overemphasized. Mr. Huessener has pointed out that so far as temperature is concerned, no advantage accrues in washing gas below 100" F. In many plants, there is a notable operating economy in using furnace cooling water, which is appreciably warmer than the supply water. However, in a given type of washer, other conditions being constant, the lower the exit gas temperature the lower will be the dust content; this is equivalent to saying that the more washing water is used, other conditions being constant, the lower will be the dust content of the exit gas. For each type of washer there is a certain desired average temperature difference between inlet water and exit gas, concomitant with known average dust and moisture contents, and with economical operation. With the present tendency toward smaller stove checkers, it is generally agreed that gas for stove use should be cleaned to a dust content of 0.20 grain or less. The method employed and extent of gas cleaning are clearly problems for individual furnace plants. As a general proposition, wet washing is decidedly more attractive for furnaces smelting soft, fine Lake ores than for those reducing chiefly hard, lumpy ores, such as the foreign and domestic magnetites. In the former case the average moisture content of the gas is probably 35 grains per cubic foot, the dust content is relatively high and the top temperature relatively low. In our plant, the ore mixtures consist almost exclusively of hard magnetites. The average dust content of the gas leaving the dust catcher will average only about 2 grains and the moisture about 12 grains per cubic foot, corresponding to saturation at about 83" F. The temperature is fully 100" F. higher

Jan 1, 1917

By Kadri Dagdelen

Production scheduling of an open pit mine is one of the most important steps in open pit mine planning. The production schedule of a mine defines the distribution of cash flows and as a result directly influences the net present value and overall economic feasibility of a project. It is becoming more and more critical to obtain an exploitation schedule of a deposit such that highest possible returns are achieved from a project. As the mining industry mines lower and lower grade ores, production scheduling is becoming a key item which can make or break a project. Although the need to plan and operate a mine with an optimum production schedule has been obvious for some time, the methods used to obtain such a schedule have not been. There is not a single, mathematically proven, optimum mine production scheduling algorithm which is widely accepted and used today. In an attempt to determine a production schedule which is optimum, a new algorithm was developed. This algorithm, in theory, is based on the lagrangian concepts of mathematics and in practice is based on the parameterization concept of mining. This paper describes the fundamentals of this newly developed algorithm.

Jan 1, 1986

By Richard L. Unger

Equipment is the primary cause of injury in 11% of all mining accidents and a secondary cause in another 10%. Purchasers should select new equipment carefully to ensure that the machine incorporates good ergonomic design criteria that maximize the safety of their mine workers. One potential problem area is the workstation-the control center of the machine. Safety problems often occur when the workstation provides insufficient clearance or visibility to the operator or has controls that are difficult to reach. This is especially true for underground mines, where confined space is an issue. In reclined or stooped postures, operators will have less strength and agility and often experience reduced visibility. We have conducted and published much research in Human Factors design of mining machine workstations. This information is currently being compiled into a series of Human Factors design recommendation reports. The reposts dl cover many topics, including workstation layout, control design, seating, and visibility. Each topic has a list of basic or first principles of design. Understanding these principles is the key to designing or purchasing a workstation that is both safe and efficient. Following is a sampling of these main topics and first principles.

Aug 1, 1996

By E. Stamboliadis

Dithiophosphates are reaction products of phosphorous pentasulfide with various organic compounds such as phenols, alcohols, mercaptans, dioalcohols, amines, and nitrides. The products with alcohols are commercially known as "aerofloats" and these are investigated in this presentation. It appears that the formation of insoluble metal dithio phosphates is responsible for their collecting properties with minerals." In this aspect they are very similar to xanthates.3 The solubility of metal dithiophosphates depends on the number of carbon atoms in the organic chain of the corresponding alcohol. An empirical mathematical model is presented here. It allows one to predict the number of carbon atoms necessary to ensure that a certain metal dithiophosphate will form at a selected pH value of the water solution. The Nature of Dithiophosphates Dithiophosphoric acid is the product of the reaction of phosphorus pentasulfide with an alcohol, as shown in the following equation: [P2S3 + 4 ROH - 2 (RO)2 PS2H + H2S (1)] where R stands for a hydrocarbon chain. The acid so produced can be neutralized by a base to produce the corresponding salt as shown in the following: [(RO), PS2H + NH- (RO)2 PS, NH,. (2)] In this aspect dithiophosphates are similar to xanthates, the only difference being the substitution of the tetravalent carbon atom in the xanthate polar group by a pentavalent phosphorus atom in the dithiophosphate group. This difference implies at least two characteristics: (1) that there are two hydrocarbon chains associated with the polar group so that an increase in the number of carbons of the single chain is expected to have a pronounced effect on the flotation properties, and (2) that the bond between the sulfur and the central atom is stronger than in the xanthate group. This probably leads to a decrease in both the polarizability of the electronic cloud of the sulfur and the interaction with cations.3 However, what is lost in the dithiophosphates by having a weak polar group can be gained by an increase in the number of carbons as will be seen later. Taking into account the size of the atoms involved in a dithiophosphate molecule, as listed in Table 1, It is possible to draw an approximate diagram of its structure as shown in [Fig. 1]. It is assumed here that the length of the single hydrocarbon chain is equal to that of the corresponding alcohol. Preparation and Purification Acid dithiophosphates can be prepared, as previously mentioned, in accordance with Eq. 1. The rate of this reaction is too slow at room temperature and can be improved by increasing the temperature to about 60° or 80°C7 or by evacuating the system. In our investigation evacuation was performed by a water aspiration pump. The dithiophosphoric acid so produced is liquid and dissolves in the alcohol. At the end of the reaction the product is filtered from the remaining P2S3; and dissolved in petroleum ether. By blowing anhydrous ammonia gas into the ether phase the ammonium salt forms as a white precipitate and can be sepa-

Jan 1, 1977

By J. A. C. Diering

All underground openings are three-dimensional, and in many cases it is not valid to analyse two-dimensional sections. This has been a problem in the past owing to the magnitude and complexity of three-dimensional stress analysis. In this paper a three-dimensional boundary element approach, using non-conforming quadratic elements, which is specifically applicable to underground excavations, is described. In addition, the philosophy of application of stress analyses is discussed. Three case histories are presented to demonstrate the practical nature of the approach as a tool in solving mining problems.

Jan 1, 1987

By Kalle Härkki

Sustainability principles in the minerals industry are now becoming more and more important from the perspective of securing a license to operate and enhancing environmental, economic and social performance. This trend is also setting new challenges for the design and operation of future concentrator plants. It is evident that ore grades are declining and ores are becoming more complex requiring new technology innovations and holistic approach for process optimization. There is a demand for more energy-efficient process technologies especially in comminution that is the major energy consuming unit operation in the process chain. Energy is not only a major source of cost but also contributes significantly to the carbon and environmental footprint. There is also an increasing awareness that more intelligent water management is required for reduction of fresh water consumption and mastering the impacts of process water recycling will cause for process performance. In association with water recycling, tailings disposal is an integral part of concentrator plant representing significant environmental and economic issues to the operation. This presentation will discuss general trends and challenges of future minerals processing plants and how innovative technology solutions and better integration of unit processes in conjunction with intelligent process control would contribute to meeting the sustainability challenges.

Jan 1, 2014

The great variety of geological conditions in French coal deposits has obliged the industry to develop different thick seam mining methods. In very steep seams in a dense deposit where stowing is necessary to avoid spontaneous combustion, surface subsidence and water problems, a rising horizontal slice method is used, the coal being hard enough and the seams regular (Lorraine). In very thick and irregular steep seams where the stowing is not necessary, a sub-level horizontal slicing is used; a third method has to be used in Dauphine.

Jan 1, 1976

By F. Cadena

HIWASSEE Dam, now under construction by the Tennessee Valley Authority on the Hiwassee River, a tributary of the Tennessee River, will require aggregate for approximately 800,000 cu. yd. of concrete. Near the damsite deposits of natural sand or gravel are not available and graywacke, a rock that is found in abundance, suggested itself as a likely source of manufactured aggregate. Graywacke is a metamorphosed sandstone composed principally of a mixture of quartz (65 per cent), mica (25 per cent), and feldspar (10 per cent). Other minerals are pres-ent in negligible amounts. The rock varies in different parts of the quarry from very fine to a coarse grain containing particles of about 1/4 in. maximum size, although the bulk of the deposit is medium grain. Exten-sive tests showed that graywacke would be suitable as a source of both coarse and fine aggregates. The aggregate plant available for use at Hiwassee Dam consisted of the coarse-aggregate and sand plant used on the Norris project. The coarse-aggregate plant had also been used at Chickamauga Dam. Although most of this plant equipment is now in use at Hiwassee, the present flowsheet is not only different from that at Norris and Chicka-mauga but is also unique as compared to the flowsheet of the average crushed-stone aggregate plant. It is hoped that this paper will show the importance of proper arrange-ment of equipment if the optimum in flexibility and capacity is to be attained.

Jan 1, 1939

By Javier Antoñanzas, Juan Carlos Múgica, Lourdes Yurramendi

The gasification of wastes containing an organic fraction is usually performed at low-medium temperature using different kind of catalysts. The off gas obtained is a mixture of carbon oxides, mainly carbon monoxide, and hydrogen and can be used for different energetic applications. The main problem is the production of tars in the off gas that has to be separated from the valuable gas flow and, finally, treated separately. An interesting alternative is the partial or total treatment of organics at high temperature. In this case, the off gas contains a higher content of hydrogen and elemental carbon as particulate matter. The energetic source to obtain a temperature in the range of 1,000 - 1,200 ºC is obtained by a plasma torch. In order to make de process attractive, an important issue to be considered is to commercialize the carbon obtained for different industrial applications.

Jan 1, 2008

By E. T. Turkdogan, B. B. Rice

Desulfurization of limestone during and subsequent to calcination has been investigated using U.S. Steel's Rogers City quarry-Michigan limestone cut to 25-30-mm diam spheroidal shapes. The experimental observations indicated that the sulfur present as iron pyrite in commercial limestone is oxidized partly to SO, during calcination and partly converted to sulfides (FeS, CaS) and CaSO4. If calcination is carried out under oxidizing conditions, most of the sulfur is converted to CaSO4, which can be removed from burnt lime readily in CO,-CO mixtures, the higher the CO content the faster is the rate of reaction. In the 30-mm-diam spheroids gas diffusion in the pores of limestone and burnt lime is fast relative to rates of the desulfurizing reactions. Over the temperature range investigated, e.g., 850° to 1200°C, there is internal desulfurization.

Jan 1, 1974

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method' for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By B. E. Grant

There are several exceptions from the practical operating viewpoint that might be taken with the paper. The author recommends using a "curve" in plotting safety factors of ropes and suggests that the U. S. Bureau of Mines change its present "step curve" method to the "curve" method. From an engineering theoretical point of view that is possible, but from a practical standpoint it is not possible. Rope manufacturers fabricate their ropes in diameter gradients of 1/16 in. to 1/4 in. which automatically sets up a step pattern gradient. If ropes were manufactured in the diameter gradients of 1/1000 of an inch or thereabouts, the curve method could be used. Also, from a practical standpoint, if an operator is to hoist from a depth of 4000 ft, for example, he will determine the size of the rope necessary for that depth, and it is only natural that he will have safety factor to spare at lesser depths, and in plotting this excess capacity the natural end result is a curve. The U. S. Bureau of Mines tables are set up so that the operator will know what size rope at the required safety factor he will need at his maximum depth. He is not concerned with lesser depths. W. A. Boyer (author's reply)-Mr. Grant states, "Rope manufacturers fabricate their ropes in diameter gradients of 1/16" to 1/4" which automatically sets up a step pattern gradient." There is no connection or relationship between the "size" pattern gradient and the present "factor of safety" step pattern gradient. The inherent factor of safety values for any particular size of rope with a given connected load when plotted for various depths is a curve, and with modern rope material and construction the inherent factor of safety curve is quite far removed from the present recommended factor of safety step curve. This is shown quite clearly in Figs. 3 and 4 of my paper.

Jan 11, 1954