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By Charles Hardy

?POWDER METALLURGY? is the production of semiformed or fully formed metal products by compressing metal powders. It had its beginnings in the fabrication of tungsten and molybdenum bars and wire by compression, sintering, and swaging. Powder metallurgy, although still in its infancy with other metals, has shown remarkable progress in recent years. Production of Metal Powders-The first step in any powder-metallurgy process is the production of metal particles of suitable shape and size. Mechanical processes for producing metal powders, as by crushing, stamping, or grinding, are usually not suitable, as the resulting particles may cause laminations and decreased strength in the finished articles. The principal metal powders now in use on a large scale are produced by electrolysis or by reduction of metal oxides by gases.

Jan 1, 1936

Q: It is May 1961 at Bill Wrather's Washington house. Bill, think back to your first job after college. Wrather: Perhaps I ought to go back a little bit further than my first job. I entered the University of Chicago with the idea of studying law. My intention was to take a 4-yr liberal arts course and superimpose a law degree on that. But during my undergraduate work I fell under the influence of R. D. Salsbury. He decided I had some talent as a geologist and influenced me to take a geological course. Nevertheless, I did not give up the idea of law. While in school I took a spell of typhoid fever and almost died. The doctor recommended outdoor exercise, so a geological job seemed logical. W. H. Emmons was a graduate student in the University and he interceded with Dr. Hayes of the USGS. I went on the payroll as assistant packer at $60 a month. I had one of the most glorious summers I ever spent in my life. That fall and the following year I took law courses and became thoroughly convinced that I was cut out for a geologist rather than a lawyer. I finished up my law work in 1908 while waiting for a job with Bill Emmons, who was doing a careful study of Goldfield and Tonopah.

Jan 4, 1964

By E. F. Koppe

The Upper Freeport coal in the Freeport and New Kensington quadrangles, Pennsylvania, varies from a bony streak to a thick coal deposit often exceeding ninety inches, the "Double" or "Thick Freeport". Distinctive basal partings, a central bone layer, and a canneloid top bench may be present. The appearance of a sandstone roof, sandstone rolls, and bony coal at the top of the main coal bench can be anticipated in thin Freeport areas when basal partings are absent. When the two basal partings are present, a shale roof is normal. These effects are correlated with the original topography upon which the coal was deposited. The original depositional high areas tend to coincide with present structural highs. Preliminary data indicate that coal quality, in part, is affected by the deposi-tional setting. In "high" areas, a tendency exists for the main coal bench to contain higher percentages of fusain and mineral matter. Within limits, some-what higher ash fusion temperatures appear to correlate with paleotopographic highs. As a result of these findings, critical examination of the paleotopography and related sediments is indicated in other areas and other coals. The Upper Freeport coal is quite variable both in thickness and composition in the Freeport and New Kensington quadrangles of Pennsylvania (Figure 1). The coal horizon in these quadrangles is marked either by a thin carbonaceous shale bed or by a single bed containing a variable number of partings (binders). The complex coal zone known locally as the "Double" or "Thick Freeport" contains the Upper Freeport Coal Bed at the base; but in addition, it has an overlying bone layer and an upper coal bed occasionally capped with a canneloid layer. The "Thick Freeport" often exceeds 90 inches in thickness, whereas the normal Upper Freeport coal usually varies between 34 and 50 inches.

Jan 1, 1961

By A. U. Seybolt, R. E. Honnemon

THE purpose of this communication is to present activity data of nickel in the Ni-A1 binary system that was obtained for oxidation studies in this system. This data has been calculated from previous aluminum activity data at 1000°C1,2 by two types of Gibbs-Duhem integrations. These results should be of particular current interest to oxidation studies of aluminide coated nickel-base superalloys3 as well as other problems. The aluminum activity of Steiner and Komarek1 is plotted in Fig. 1 as a function of composition in Ni-A1 alloys at 1000°C. The dashed parts of the aluminum curves represent our approximate extrapolations from the directly measured regions. In the terminal solution regions (a and L phases) standard parabolic solution functions of the following form are assumed: where i is the component subscript, Ki is a constant at a fixed temperature, and xi is the atom fraction. The resultant nickel activity curve at 1000° C from the Gibbs-Duhem integration4 of the aluminum data is shown in Fig. 1. The solubility ranges of the phases present in the Ni-A1 binary at 1000°C are also denoted at the bottom of Fig. 1. Corresponding values of the nickel activity, aNi and yNi, are listed in Table I at useful compositional intervals. including phase boundary values. The aNi and yNi data listed in Table I are subject to the uncertainties present in the experimental aluminum activity data1 and to deviations from parabolic solution behavior in the terminal solutions. The errors introduced into aNi and yNi due to the parabolic solution assumption are expected to be relatively small (<20 pct of the values given) in all the phases except the liquid phase. Some deviation from parabolic solution behavior in the liquid phase is indicated

Jan 1, 1970

By J. J. Jakosky

THE method of electrical mapping of oil structures to be described possesses certain limitations, as well as certain definite advantages. It, in common with other geophysical methods, is not a panacea for the solution of all subsurface geological problems. It operates on differences in electrical conductivity of the geological strata, whereas the other most-used methods operate on (1) differences in magnetic properties, (2) differences in gravimetric properties, or (3) differences in seismic properties. This modification of the resistivity method is therefore able to obtain subsurface information under conditions not favorable to the other methods mentioned. Where the other methods have been employed with ambiguous results it may act as a complementary method.

Jan 1, 1936

By P. Nicholls

THOUGH the burning of fuels extends far back into antiquity, and though fuel beds are the most common and widely distributed example of chemical actions and engineering practice, there has been little attempt to group fuel beds by types or to define the principles associated with them. This paper does not profess to cover completely the subject of fuel beds. It suggests some of the over-all principles of the two more com-mon types. No new investigational data are included, but the deduc-tions are largely based on a recent publication of the U.S. Bureau of Mines1. DEFINITION OF TYPES There are three primary types of fuel beds: (1) Underfeed, in which the fuel and the air move in the same direction; (2) overfeed, in which the fuel and the air move in opposite directions; (3) crossfeed, in .which the fuel and the air move at right angles to each other. The principle that fixes the type is the relation between directions of the flow of fuel and of air. Fig. 1 shows the three types diagrammatically. All other types are compounded of these three in a simple or more or less complex manner. It does not follow that these three type designations are limited to the methods used in representing them in Fig. 1; they may be turned in any direction, and as long as the relative directions of the fuel and air are the same the type is not changed. For example, A as shown resembles a pot-type stoker, but the air and fuel can move downward as in the so-called smokeless heating boiler furnace. Also, C can be placed hori-zontal, as in chain-grate stokers. For this reason, the terms used to designate the three types are not all that could be desired; more logical ones could be coined, but those used probably are satisfactory until the discussion of fuel-bed types becomes more common.

Jan 1, 1935

By Kefton H. Teague

This paper deals with the practical application of the Dutch State Mines cyclone separator for fine-coal cleaning. The more important operating variables are discussed, and results of a number of continuous-scale tests on various fine coals with a 6-in. cyclone separator are given. Descriptions of the Cyanamid Pilot Plant and the 50 tph Cyclone Separator Plant at the Emma Washery in Holland are included.

Jan 1, 1950

By S. S. PRENZ

Discussion held at the sessions of the Canal Zone meeting, November, 1910. [SECRETARY&apos;S NOTE.-As a result of this discussion, an expression of opinion covering all points of unanimous agreement was adopted and signed by members of the Institute party as individuals. This statement, which was printed in the Bulletin of December, 1910, is reprinted below, as an introduction to ,the detailed report of the discussion. It should be clearly understood that it does not constitute an official declaration by the Institute, the rules of which forbid any such action. At the New Haven meeting of February, 1909, a free discussion of the plan of the canal took place, in which the critics of the present scheme had full opportunity to state their views. That discussion was continued at considerable length in the newspapers ; but the Institute was never committed to either side. In this latter instance, the situation is precisely similar. Certain members and guests of the Institute, having had the advantage of later developments and of personal inspection, have expressed the conclusions at which they have arrived on their own responsibility ; and these conclusions are published by the Institute, subject to further discussion, like any other part of its proceedings. The general statement referred to contained a promise that the full discussion, of which it was a result, would be subsequently printed ; and this promise is fulfilled, so far as practicable, in the subjoined report, concerning which I beg to offer the following explanations: 1. It is made up of the remarks of the members of our party, as subsequently written out and mailed to the Secretary. 2. In editing these contributions, I have condensed the material considerably by cutting out much repetition of opinions and phrases ; and in such excision, I, frankly confess, the authors whose communications were delayed, have been the sufferers. Nevertheless, there is a good deal of repetition left, as there must be, when so many persons had talked so much, and come to agreement upon so many points. 3. It has been found impossible to preserve in this report the actual order of the free and informal oral discussion represented. Consequently the several contributions have been arranged in alphabetical order under the names of their authors. References to "preceding speakers," etc., must therefore be construed as referring to other speakers, preceding or following.-R. W. R.] S. S. PRINZ AUGUST WILHELM, AT SEA, November 14, 1910. We, the undersigned, members and guests of the American Institute of Mining Engineers, after a visit to the Isthmus of Panama, and inspection of the work of the United States Isthmian Canal Commission, and after full discussion of our individual impressions, find ourselves in unanimous agreement as to the following conclusions:

Jan 1, 1911

By William B. Plank

IN this paper are presented the results of a complete statistical survey of the enrolment, courses and degrees, and the employment situation of recent graduates in all of the 46 institutions in the United States, including Alaska, and four of the six schools in Canada that grant degrees in mineral technology. The data were collected by the writer by means of a questionnaire in December, 1933, to which all the institutions, except one, replied. Included also are data of a similar study made by the writer in May, 1933, for the S. P. E. E. summer session of mining and metallurgical teachers at the University of Wisconsin and published in the Journal of Engineering Education for December. 1933. Some of the data of a paper of the writer&apos;s entitled, "The Trend of Mineral Engineering Student Enrolment in the United States," read at the A. I. M. E. meeting on Feb. 16. 1931, are given for comparison. Acknowledgment is made to all the administrative officers of the institutions who took the time from their busy lives to supply the in- formation asked for. Their fine cooperation has alone made possible these two surveys with a completeness of detail never before attempted

Jan 1, 1934

By AIME AIME

THE following paragraphs, constituting the concluding portion of the Annual Report of the Council for 1903, have been withheld from publication until now, in order to make them as accurate and complete as possible. They will be published in Volume XXXV. of the Transactions in their proper place at the end of the said Annual Report. Franklin Ballou was born in Pittsburg, Pa., May 29, 1845. He was the son of an old resident, Arthur Ballou, a manufacturer and wholesale dealer in vinegar. In early youth Franklin attended the Western University of Pittsburg, but left school at the age of 16 to become book-keeper for his father, upon whose retirement from business, in 1868, he associated himself with Walter C. Childs, of Pittsburg, in the manufac¬ture of furnace-grates and asbestos-cement for blast-furnaces. This firm was known as W. C. Childs & Co., and did a success¬ful business for several years. In 1869 Mr. Ballou married Miss May S. Wilson, daughter of Judge Wilson, of Lewistown, Pa. In 1876 he spent several months traveling in the West and studying the mining industry, which greatly interested him. In consequence of this journey, he wound up his business in Pittsburg and removed in 1877 to Georgetown, Colo., where for several years he conducted a sampling-works, and built up an extensive business as an agent for the sale of ores, besides engaging to some extent in mining enterprises. , It is said that he controlled at one time about one-eighth of the output of the Leadville mines. In the early 80&apos;s, he became Vice-President and General Manager of the Bimetallic Smelter at Leadville, of which Mr. David H. Moflat was the principal owner. This was practically the first successful demonstration of pyritic smelting in Colorado. Upon the sale of the works in 1897 to the American Smelting and Refining Co., Mr. Ballou retired

Jan 1, 1905

By Frederic Dewey

(New York Meeting, February, 1913) This old and well-known method of determining, silver is, in bullion work, so far superior to the furnace-assay that it is looked upon with reverential awe by many, if not by most, users, and its-ease of execution, with proper equipment, commends it highly where much commercial bullion work on silver is required. The method is so thoroughly well known that a, description of it here may seem to be unnecessary, but many thousands of determinations are annually made by it in the U. S. Mint Service and its practice is there reduced to an art. This is necessary both for the sake of economy of time, acid because high-grade work with it requires constant practice. It is useless for a person who uses it only occasionally to expect to attain high accuracy with it, without spending more time upon a determination than is warranted in a busy commercial laboratory. It is always employed in the Mint service whenever possible, but its chief field is in the determination of silver in standard silver (ingots and coin), which is 900 fine in silver and 100 fine in copper, and I shall first briefly outline its use on this metal and then take up various points in detail, especially as related to the accuracy of the results obtained.

Jan 4, 1913

By Lawrence H. Van Vlack, Alfred S. Keh

The distribution of sulfur in iron was found to be dependent upon the time and temperature of the treatment as well as the chemical composition of the sulfide. With higher temperatures, the sulfide phase spreads more extensively between the iron grains. A complete network, however, does not form until approximately 1300°C (2372°F), ot which temperature the dihedral angle approaches zero. Silicon has little effect on this change. Aluminum, oxygen, and manganese all modify the temperature of sulfide network formation to a higher value. The microstructures which result and have significance in relation to hot-shortness are discussed. SULFIDE inclusions in steel were recognized by metallurgists before the turn of the century. Considerable attention has been paid to them, and numerous studies have been made on the working properties of steel as affected by them. It has been suggested that ho t-shortness of steel is due to the presence of an enveloping liquid sulfide film at the grain boundaries of the steel in the range of the hot-working temperatures. However, several facts have been observed in commercial steels which do not seem to be completely consistent with this explanation: 1) the frequent absence of continuous films of sulfide as observed under the microscope, 2) the absence of hot-shortness in some high sulfur and resulfurized steels, and 3) the limitation of hot-shortness to a definite temperature range. The role that manganese plays in steel to eliminate hot-shortness is well known, but the theory behind it is still under question. Moreover, the effect of de-oxidizers such as aluminum and silicon, and the effect of oxygen are still not clearly known. In this study, the effect of heat treatments and of additions of manganese, aluminum, silicon, and oxygen upon the distribution of sulfide inclusions in iron was investigated. Both the as-cast and the heat treated structures were studied, using microscopic and autoradiographic techniques. Part of the results were interpreted in terms of Smith&apos;s&apos; concept of microstructure. Review of Literature Metallurgists used to consider sulfide inclusions as suspended particles. It was Wohrman&apos; who first pointed out that sulfide inclusions are soluble in liquid iron. Many observed facts may be understood on the basis of this concept of solubility. Wohrman found that small castings contain small inclusions. and larger castings contain larger ones. Also, inclusion sizes are smaller near the chilled surface. For the same size ingot, the average inclusion size in a given heat of steel depends upon the rate of solidification. That is, with slow solidification, enough time for precipitation and agglomeration of these

Jan 1, 1957

By N. H. Emmons

In the United States the value of gold- and silver-ores is everywhere reckoned in ounces troy of the metal per " short ton " (2000 lbs. avoird.) of the ore. In the case of silver, which fluctuates in market value, the New York quotation on a given day must be known, in order to determine the gross value of an ore at that date. In Mexico the assay is reported &apos;in kilogrammes of silver or grammes of gold per metric ton. As everyone is aware, this is practically a percentage system, 1 kg. of silver per metric toll (1000 kg.) being 0.1 per cent., and 1 gramme of gold per metric ton, 0.0001 per cent. The notation is simple and convenient for both assayer and miner.* The Mexican government purchases at an unvarying price for silver, payable in silver, and at a fixed price for gold, payable in gold if the seller insists, but preferably in silver at about the rate of exchange between U. S. gold coin and Mesican silver coin. The value of silver is $40.915 per kilogramme in Mexican silver dollars. That of gold is $675.416 per kilogramme in gold coin. The mints do not, as a rule, issue gold dollars, as the government keeps them to pay the interest on the national debt. Almost all bullion containing a considerable percentage of gold is shipped to foreign countries (principally the United States) to be refined. The Mexican mint receives for refining and coining no bullion which is not at least .950 fine in gold and silver, separately or

Jan 1, 1902

By D. H. Trollope

In engineering in general, close agreement between theoretical predictions and structural performance is rare—this is particularly true in rock slopes. Since the complexity of natural arrangements makes exact theoretical solutions of associated structural problems almost impossible, the role of theory should be that of developing guides or markers to which observations and experience can be related. The author in this paper has outlined the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Some important practical considerations result—especially in regard to horizontal stresses—when theory is compared with full-scale experience. In the field of engineering activity, specific examples of close agreement between theoretical prediction and structural performance are rare. Particularly is this so for the case of rock slopes, where, owing to the complexity of the natural arrangements, it is quixotic to expect exact theoretical solutions to the associated structural problems. The role of theory is rather that of developing signposts or guide rails to which observations and experience can be related. It is with this in mind that the present paper has been prepared; the author&apos;s aim has been to set out briefly the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Despite the idealization of the problem, it will be seen that the theoretical conclusions are in accord with full-scale experience, particularly as far as horizontal stresses are concerned, and they point to some important practical considerations. CLASSIFICATION OF ROCK SLOPES At the risk of over-simplification, an attempt has been made to classify the problem of rock slopes into three broad categories with respect to internal stress systems. These are illustrated in Fig. 1. It is tacitly assumed in this classification that the strength of individual particles is very much greater than the interparticle strength whether the particles are the crystals of an igneous rock (Case I) or the blocks of Cases 2 and 3. The Homogeneous Monolith: This case is representative of uniform unjointed rock. Under relatively low stress conditions the internal stress system may approximate to that of an elastic body as given by Terzaghi.&apos; It is more usual, however, for overall stability, to consider the material as a rigid plastic which yields in shear when S =C + c tan 4> where S is the shear yield stress, o is the normal stress on the surface of failure, and C and d are empirical constants according to the Mohr-Coulomb criterion of failure. Sokolovsky has recently developed, for the first time, a series of mathematical solutions to problems involvinga C, mass subject to self-weight. He demonstrates that for such a case a semi-arch (Fig. 2) is stable. A corollary of this argument is that for a true C, d material a curved overhanging slope is possible and such an observation may well aid field identification of these materials. The shape of the curved slope face is however directly dependent on the C-value, and from the long-term point of view this is a most difficult value to establish with any degree of confidence. It is customary to measure C and 0 in some form of shear test—usually a triaxial compression test—on core specimens sampled from the rock, and as far as the author is aware the present case is the only one in which, as far as overall stability is concerned, such tests are

Jan 1, 1961

By G. W. Josephson

JUDGING by the progressive atmosphere prevailing in the nonmetallic mineral industries during the past year, postwar conditions were healthful though inflationary. Demand for most industrial mineral products has been exceptionally high and many new production records were attained. Severe shortages of some commodities existed, especially building materials and fertilizers. Production costs and prices increased and profitable operation was general. Under these conditions expansion programs were the order of the day. Ample funds were available to finance the purchase of good equipment; and, as wages and other operating costs were increasing, primary emphasis was placed on attaining maximum efficiency in new installations. These efforts were hampered by shortages and slow delivery of desirable equipment, so compromises in design were often necessary. However, on the whole, production practice improved.

Jan 1, 1948

By EDWARD B. DURHAH

(San Francisco Meeting, UCtober, 1911.) THE refinery at the San Francisco Mint takes the bullion purchased by the receiving department, and carrying more than 200 parts of precious metals in 1000, or, in mint parlance; over 200 fine, and separates and refines the various metals contained therein, using electrolytic processes exclusively. Bullion containing silver is treated in cells charged with a nitric electrolyte. These cells produce fine silver and leave a residue rich in gold. The residue from the silver-cells, together with crude gold-bullion, is treated in cells having a chloride electrolyte. These produce fine gold and leave a residue containing silver chloride. The latter is reduced to the metallic state with zinc and is then treated in the silver-cells. The various waste solutions and the wash-waters, after being freed from the bulk of their precious metals, still contain copper and other metals. These are removed by scrap-iron, and are then treated in the copper-cells, having a sulphate electrolyte. These cells produce pure copper, and collect a residue containing lead, some gold and silver, and all the metals of the platinum group that were in the bullion. This residue is relatively small, and is melted into bars and stored until sufficient accumulates to warrant treating it for platinum, etc. The refinery occupies three large and three small rooms. The large ones are, a melting-room, 30 by 34 ft.; a cell-room, 39 by 46 ft.; and a wash-room, 30 by 33 ft. The small rooms are used as foreman&apos;s office, laboratory, and generator-room, respectively. The methods here described are those in use in December, 1909, when notes for the present paper were taken.

Oct 1, 1911

By A. Timur

Fluid flow properties of porous media have long been of interest in such varied disciplines as geology, geophysics, soil mechanics, and chemical, civil, and mechanical engineering. This interest has resulted in numerous models of porous media that have been proposed, tested, and found to be useful under, at best, only special circumstances. A critical review of most of these models is given by Scheidegger. 1 The application of each new tool to the study of porous media has helped to test some of the existing theories and to form new ideas based on the new parameters being measured. In the application of nuclear magnetic resonance (NMR) techniques to the study of the properties of fluids in porous media, the theoretical studies of Korringa et al.2 resulted in a model for the relaxation of spin polarization of protons in a hydrogenous fluid in a pore of a solid. Seevers3,4 verified this model, established a method for measuring the surface-to-volume-ratio distribution in a porous medium, and proposed a technique for determining specific permeability in sandstones. In the present investigation, the uses of NMR methods are extended and a simple model of porous media is developed from an analysis of pulsed NMR measurements. In this model, the pore spaces of a porous medium are divided into three groups on the basis of their surface-to-volume ratios. To evaluate predictions of the NMR model, laboratory measurements of spin-lattice relaxation time, porosity, permeability, and residual (irreducible) water saturation were conducted on more than 150 sandstone samples obtained from four oil fields in North America. Applications are discussed for estimating the volume of movable fluid, ?p, and the specific permeability, k, of sandstone samples. The former parameter, which can be considered as producible porosity, is expressed by ?p = [1 -- (Swr/100)]? , .... (1) where + is porosity in percent of bulk volume and Swr is the residual (irreducible) water saturation in percent of pore volume at a capillary pressure of 50 Psi. Fast, nondestructive laboratory methods are described for determining porosity, movable fluid, and permeability of sandstone samples from measurements with a pulsed NMR (spin-echo) apparatus. Procedures are given for adapting these methods to samples of irregular shape and small size. Theory General In the Korringa, Seevers, and Torrey2 (KST) model the observed decrease in the spin-lattice relaxation time, T1, of protons of a hydrogenous liquid contained in the pore spaces of a porous solid is attributed to an increase in the correlation time for the random motion of the water molecules and to the presence of paramagnetic centers at the liquid-solid interface. This KST model predicts the observed relaxation time of a hydrogenous liquid in a pore of a solid through

Jan 1, 1970

By AIME AIME

It is with the deepest personal sorrow, and with the regrets of the Steel Company of Canada, that I report to you the death of one of our most valued associates, the late Frank B. McKune, superintendent of the Open-Hearth Department of our company. Many of you will remember Mr. McKune for his long attendance at these meetings, for the intelligent interest he took ill them, as well as for his innovations in steel-production practices.

Jan 1, 1940

By Frank Armstrong

ALL the mining machinery of the Penn Iron Mining Co. has been operated by electric power for several years and when another shovel for stockpile loading was required the advantages of an electric shovel were naturally considered. After considerable study, serious objections suggested themselves the use of a shovel operated directly by electrical apparatus by reason of the complicated control, severe service on the motors FIG. 1.-ELECTRO-HYDRAULIC SHOVEL FIG:. 2-THE SHOVEL AS IT WAS OPERATED CINDER CONSTRUCTION. THE FIRST YEAR. and the heavy surges of current required from the line. It was finally decided to construct an electro-hydraulic shovel using water under pressure to perform all the necessary operations except that of propelling, for which a separate motor was best suited. A car body with boom, dipper handle and dipper of late design, but without any of the steam machinery, was purchased. A motor-driven centrifugal pump, a pressure tank, an air tank, a small air compressor and water cylinders with plungers, pistons and valves, were installed in place of the; steam equipment. Fig. 1 shows this shovel under construction and Fig. 2 shows it as it was operated during the first year, the summer of 1914. The large tank at the back of the car, in Fig. 1, carried air under

Jan 2, 1916

By R. J. Charles

F. C. Bond: This is an outstanding paper on comminution theory and represents a considerable advance in mathematical formulation. It clears the way for a discussion that should ultimately decide whether the work index should be considered as a parameter according to the Third Theory or as a constant. In the empirical differential equation dE = —Cdx/x [1] either Corn must be treated as a variable to satisfy known crushing and grinding conditions. The author has chosen the exponent n as the variable, with C as a constant. According to the Third Theory, in the general case n is a constant equal to 3/2, and C is a variable related to the work index Wi. If x is placed equal to P (the size in microns which 80 pct of the product passes) and F is the size 80 pct of the feed passes, then C equals 5 W1, and dE = 5 -5 Widx/x = 10 Wi 10 Wi w = vP vF which is the basic equation of the Third Theory. It is apparent that this integration involves the error of treating the parameter Wi as a constant, just as the author&apos;s treatment involves the error of integrating his variable n as a constant. These errors are probably relatively unimportant, considering the small range of the variables. When more is known about the factors contained in the work index, Eq. 1 can be revised as a partial differential equation. The Third Theory exponent of 1/2, or n = 3/2 in the Charles&apos; differential equation (Eq. l), was not chosen primarily because it is the average between the Kick and Rittinger exponents; this may be merely fortuitous, since it is illogical to define truth as the average between two errors. It was first discovered from the study of a large mass of crushing and grinding data and confirmed by laboratory testing. The general correspondence of the Third Theory equation to actual crushing and grinding results over the entire size reduction range argues strongly that a fundamental phenomenon is involved. The a posteriori theoretical explanation of the constant Third Theory exponent is that the work done in breaking rock is proportional to the length of the crack tips formed. Compressive force applied to the rock results in deformation and strain energy. When this locally exceeds the breaking strength a crack tip forms, the surrounding strain energy flows to the crack tip and extends it to split the rock, with release of the energy as heat. Under rapid impact the crack tip may form before the strain has reached equilibrium, resulting in less energy expenditure and probably a coarser product. In any case, the elastic limit of a brittle material is practically the same as its breaking strength, and the work necessary to form the crack tip is the work required to break. The crack length of a ton of broken rock cannot be measured directly. However, the particle shapes of feed and product are similar, and the crack length is considered equal to the square root of one half of the new surface area formed. It is, therefore, proportional to 1/vD, where D is the equivalent product particle diameter. This is the basis of the Third Theory equation. Many secondary factors can be imposed upon the crack length breakage. These may cause the Third Theory work index to increase or decrease somewhat as the product size becomes finer. The work index is properly a parameter rather than a constant, making it an increasingly valuable practical criterion of the work input required in crushing and grinding.

Jan 1, 1959