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* George M. Humphrey, president of the M. A. Hanna Co. and of the Iron Ore Co. of Canada, has announced arrangements for financing the development of the Labrador-Quebec iron ore deposits in the total amount of $200 million. Plans call for immediately beginning the construction of mining, railroad, and handling facilities, and contemplate the start of ore shipments in 1955 which will reach 10 million tons a year shortly thereafter. Total drilled and proven ore now exceeds 400 million tons of high grade open-pit ore with prospects for large additional tonnages. Capital structure of the company authorizes up to $125 million of first mortgage bonds, $40 million of income debentures and $60 million of common stock.

Jan 12, 1950

Kaiser Sees Bright Future for Jamaica Kaiser Aluminum Co. has a big stake in the British West Indies, the Island of Jamaica in particular. There, Kaiser is busy developing one of the most promising bauxite finds in recent years. The $12 million operation was officially opened in February. Facilities have a rating of an annual capacity of 2 million tons and will supply Kaiser plants with ore for years. The ore comes across the Gulf of Mexico, up the Mississippi to stockpiles at Baton Rouge. The stockpile at Baton Rouge would throw many an old river boat skipper for a loss. Where no mountain once existed now stands a man-made bluff of bauxite, known as Bauxite Peak.

Jan 6, 1953

By D. O. Rausch

The economic relationship between steepening slopes and decreasing waste removal requirements ahead of ore mining is one of the most important factors in the design of open-pit mines. The steepness and stability of the pit slopes often spells the difference between ore and waste profit or loss in low cost open-pit operations. Unfortunately, the technology necessary for designing stable rock slopes is still in the early stages of development. Past and current pit-design methods have been, and still are, empirical, with rock slopes frequently made too steep or too shallow. As such, large expenditures are often made for correcting slopes after failures occur, or for unnecessarily removing more waste material than required.

Jan 6, 1965

By D. W. Fuerstenau

A detailed study of the residence time distribution in an industrial balling circuit is presented. Using fired recycle pellets as a tracer impulse in each experiment, material was found to pass through the drum under plug flow conditions with a mean residence time of about 20 seconds. The time for a single pass through the entire circuit is about 60 seconds. Approximately three passes are required for fresh feed to report as product. Segregation of the tracer pellets in the system, according to their diameter, was observed and reasons for this are suggested. These results should be of potential use in the modeling and control of ball balling circuits in the iron ore industry.

Jan 1, 1985

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969

By D. E. Coates, G. R. Purdy, S. V. Subramanian

The morphological stability of the planar solid-liquid interface in dilute ternary alloys, undergoing steady-state unidirectional solidification, is analyzed in terms of both the constitutional supercooling principle and the perturbation methods recently developed by Mullins and Sekerka. First, various steady-state solutions for the two solute distributions ahead of a planar interface are examined. The nature of the solutions depends on the size and concentration dependence of the off-diagonal diffusion coefficients. W~thin the framework of the constitutional supercooling principle, a cumulative contribution to instability frorn the two solutes is found to exist in the absence of diffusional interaction. It is shown that the latter can produce a further enhancement of instability or can have a stabilizing influence, depending on the form of the liquidus surface and on the sign of the solute-solute interaction. A perturbation analysis, which ignores diffusional interaction, verifies the cumulative influence of lhe solute fields and demonstrates that the Mullins-Sekerka stability criterion for binary systems (with capillarity accounted for) can be readily extended for application to ternary systems. SOME time ago, Tiller et al.' calculated the solute concentration distribution ahead of the planar solid-liquid interface of binary alloys undergoing steady-state unidirectional solidification. An earlier qualitative proposal that the transition from planar to nonplanar growth morphologies is associated solely with the onset of constitutional supercooling in the liquid layer ahead of the moving interface2 was used in conjunction with this calculation to put the now well-known constitutional supercooling (C-S) stability criterion into quantitative terms. Mullins and Sekerka,3 in a recent and very elegant analysis, established a more complete criterion (hereafter referred to as the M-S criterion). Interfacial stability was investigated by determining the time derivative of the amplitude of a sinusoidal perturbation of infinitesimal amplitude which had been introduced into the originally planar shape of the moving interface. Of particular importance is the fact that capillarity was included in the boundary conditions of their calculation. The purpose of the present paper is to extend all of this earlier work on dilute binary systems for application to dilute ternary alloy solidification. The analysis is divided into three sections. In the first the two solute distributions ahead of a moving planar interface are considered. Mathematical solutions are de- termined for situations in which: a) diffusional interaction is negligible, 6) diffusional interaction must be considered but circumstances permit use of constant diffusion coefficients, and c) the concentration dependence of off-diagonal diffusion coefficients can be described by first-order dilute solution approximations. In the next section, a stability criterion analogous to the C-S criterion is developed and the influence of diffusional interaction on interface stability is analyzed. Finally, the perturbation formalism of Mullins and Sekerka, with capillarity included in the boundary conditions, is extended for analysis of ternary systems in which diffusional interaction is negligible. The study of interface stability in binary systems usually commences with the assumption that the equilibrium distribution coefficient and the slope of the liquidus line are constant at values corresponding to infinite dilution. Similar assumptions have not been introduced into the present treatment; that is, we do not assume planar solidus and liquidus surfaces joined by tie lines which yield constant distribution coefficients. The latter involves the assumption of no ther-modynamic interaction between solute species in both the solid and liquid. We consider a ternary phase diagram for which the solidus and liquidus surfaces are, in general, nonplanar and of course pass through the corresponding binary solidus and liquidus lines. These lines are not assumed to have constant slope. In the dilute regions we are concerned with, the following assumptions are made: i) The solidus and liquidus surfaces are of a form such that both the solidus and liquidus temperatures are monotonically varying functions of each solute concentration. ii) The tie lines are such that the equilibrium distribution coefficient of a given solute is greater than unity for every point on the solidus (or liquidus) surface or it is less than unity for every point. STEADY-STATE SOLUTE DISTRIBUTIONS IN THE LIQUID As will be demonstrated in the next section, a knowledge of the steady-state solute profiles is not a necessary prerequisite for the formulation of a ternary C-S stability criterion. However, in that details, such as the complete description of the equilibrium liquidus temperature profile, require an evaluation of the solute distributions, the overall treatment is enhanced if these distributions are determined. Consider a ternary system (solvent plus solutes 1 and 2) for which a planar solid-liquid interface is in unidirectional motion at constant velocity V. At this stage it is unnecessary to limit ourselves to dilute solutions. For a stationary frame of reference the generalized forms of Fick's equations are:

Jan 1, 1969

REPORT OF PRESIDENT C. F. RAND FOR THE YEAR 1917 The noteworthy occurrences during 1917 were the creation of Engineering Council; the completion of the addition to the Engineering Societies Building. and the occupation by the American Society of Civil engineers of the space thus provided for it; the addition of 67,000 vol-

Jan 3, 1918

By H. R. MacMichael

THE rate, at which zinc ore can be sintered varies widely, depending on the characteristics- of the ore. A coarse table concentrate already roasted to a very, low sulfur content may sinter at the rate of-8.6 tons per hour per 100 sq.ft., of wind-box area. At the other extreme is a finely ground flotation, concentrate, with considerable sulfur remaining in the ore as delivered to the sinter plant, for which corresponding rate may be only 3.8 tons per hour, or 44 per cent of the first rate. A usual, size-of sinter machine in zinc plants is one with wind-box 3.5 by 33 ft., making 115.5 sq. ft. of area, and using a 100-hp. fan. Such a machine with the coarse concentrate described would produce 10 tons of sinter per hour; and with the fine, flotation concentrate would produce only 4.4 tons per hour. Ore of the latter class is -sintered at the plant of the Mexican Zinc Co. (subsidiary of the American Smelting & Refining Co.) at Rosita, Mexico. ; Consequently, an unusually large sintering capacity per ton of ore to be treated is required, and provision was made for treatment of 9000 tons concentrates per month, preroasted to. 5 to 9 per. cent sulfur. For this duty three of the usual 33-ft., 100-hp. sintering machines would have been needed.. Considering the auxiliary equipment. necessary for proportioning, handling, and mixing charge, as well as means for disposition of the sinter, a three-unit plant becomes-very complicated, especially if the capacity should be doubled later. After much study it was decided to build a single sintering unit of ample capacity for the work, the plant thus being much simpler and cheaper in construction as well as in operation (Figs. 1 and 2). The sintering machine was built with a wind-box 5.25 by 60 ft. (315 sq. ft.) and provided with a 300-hp. fan.

Jan 1, 1932

By Alan Morris

Brass rod for use in automatic screw machines is one of the major products of the brass mills. A large tonnage is consumed each year in the manufacture of an endless variety of finished articles and parts for assembly into other products. The machines that do this work have been developed to a high degree of efficiency, and their manufacturers are still striving for higher production speeds. This development has brought with it a demand for brass rod to meet the increasingly difficult machining conditions. This paper is a report of the results of tests undertaken in an effort to obtain a measure of the effects of such variables as lead content, microstructure and cold work on the machinability of brass rod. It is realized that the term "machinability" has never been well defined. Power, finish and tool life all should have a place in such a definition. In practice it is sometimes found necessary to sacrifice some of these in order to obtain a rod that will not tend to throw up a burr, or will give a burr which is easily tumbled off. Again a specially stiff rod may be necessary because of long overhang from the chuck or a rod of special characteristics is needed to take a given broaching operation without chattering. It is only through an understanding of the effect of basic mill operations on the machinability of the rod that such problems as these may be solved most economically. It is hoped that this paper, together with the discussion it may evoke, will prove to be a basis for such an understanding. Testing Apparatus The testing apparatus used was of the single-tooth milling cutter type, in all respects sirnilar to that first used and described by Airey and Oxford1 and again by Boston. The machine used in the present test is shown in Fig. 1. It is an ordinary milling machine in which a heavy pendulum has been substituted for the pulley on the arbor. If the pendulum is raised

Jan 1, 1932

By Benjamin Petkof

The mineral mica, which has been known to man since ancient times, has played an impor¬tant role in the development of our modern industry. In the latter part of the 19th century sheet mica began finding use as a dielectric insulating material in the newly developing electrical industry. Later, when modern elec¬tronics began to develop, it became a vital insulating and dielectric material for use in electronic equipment. Both the electrical and electronic industries were greatly dependent on some form of natural mica. The manufacture of electric motors of varying sizes, electronic tubes, and other electronic items was dependent on an adequate supply of sheet mica. During World War II this material was so vital to national defense that special efforts were made to mine it in the United States as well as to obtain it from overseas mica-producing areas. However, advancing technology has successfully begun the progressive development of man-made mica-based and non-mica-based materials that can replace mica for many uses. In addition, developing technology has dictated changes that have made sheet mica unnecessary for some uses. As the demand for sheet mica declined, the demand for scrap and flake mica has continued to increase. In fact, today the domestic production and use of scrap and flake mica far outshadows the necessity for good¬quality sheet mica in this country. Historically the United States has always been dependent on foreign sources of material for good-quality sheet mica and imports practically its entire requirement. In the case of scrap and flake mica, the United States is the dominant world producer and consumer. End Uses Sheet mica (Chowdhury, 1941; Rajgarhia, 1951; Skow, 1962) is available in many com¬mercial forms, but these forms can be broadly classified into manufactured and unmanufac¬tured mica. Manufactured mica consists of mica that has been shaped, punched, or other¬wise processed into some form, suitable for a particular end use. Unmanufactured mica con¬sists of partially hand-trimmed or processed material that has not been prepared for any particular end use. Unmanufactured mica is broken into two commercial classes consisting of sheet mica and scrap and flake mica. These classes of mica differ greatly in their ultimate end uses and marketed forms. Sheet muscovite mica can be classified by color, degree of prep¬aration of the crude material, thickness, size, visual appearance, and electrical quality. In addition, phlogopite mica is also classified by its thermal stability. Scrap and flake mica consist of mine, trimming shop, and factory scrap that occurs as remnants from mining, processing, and manufacturing operations, and small particle size mica that is available from the beneficiation of pegmatites, clays, schists, or other mica-rich host rock. The end uses for sheet mica vary so greatly from those of scrap and flake mica that it is necessary to discuss them separately. Sheet Mica Sheet mica consists of relatively flat sheets of material which have been mined as naturally occurring books or runs of mica. These sheets are hand-trimmed to remove any imperfections and are punched or stamped into specified shapes for industrial use. Sheet mica can be further processed and is described or specified as block, film, or splittings based on thickness. Block mica is not less than 0.007 in. thick with a minimum usable cross-sectional area of 1 sq in. Film mica is split from the better quali¬ties of block mica to specified thickness groups ranging from 0.0012 to 0.004 in. Splittings are sheets of mica with a maximum thickness of 0.0012 in. and a minimum usable area of 0.75 in. Other small sized, lower quality block mica

Jan 1, 1975

By H. R. Green, D. M. Lamb, A. D. Taylor

The design of slurry launders has usually been based on strictly empirical concepts. An examination of the most common procedures reveals that they do not account for many of the variables that are recognized as significant for slurry transport. These may include flow rate, volume concentration of solids, solids specific gravity, solids size distribution, particle shape, launder geometry, and roughness of the wetted surface. It was decided to develop a design procedure, which would accomplish two things: First: Take into consideration most of the known significant variables and systematize the procedure to assure consistent results. Second: Provide a rational basis for examining and utilizing operating data to refine and improve the system. To accomplish this, it was necessary to develop a basic design concept. This concept has been developed through a complex development history, and yet still appears workable and technically sound. That concept may be outlined as follows: First: The solids transport velocity is the fundamental basis for slurry launder design. Second: The stream configuration, hence the launder size, is integrated with the solids transport velocity so that the actual stream velocity exceeds the solids transport velocity. Third: The launder slope is that which will achieve the

Jan 1, 1979

By D. O. Ehrenburg

DURING the earlier period of electrical prospecting, the search for orebodies was by far the most important application of this method of geophysical prospecting. In the past few years, however, increasing attention has been paid to the possibilities of this method in the investigation of subsurface structures. Not only have fault zones been located, but attempts have been made to determine the depth to certain strata and thus contouring on some bed which proves to be a good "electrical marker." Many workers have published the results of field tests showing how their particular interpretations have agreed with the actual field conditions, but very few have stated their method of interpretation. Weaver, Hummel and Stefanesco and Schlumberger1 have given a more theoretical discussion of the resistivity methods. Hummel and Stefanesco and Schlumberger have published mathematical solutions for the flow of electricity in a medium involving four layers. In this paper the authors present a solution for the flow of electricity in a medium of any number of horizontal strata. By means of this solution, curves showing the relationship between the apparent resistivity and the electrode spacing can be computed for ideal cases.

Jan 1, 1931

By Frederick F. Frick

SPONGE iron as produced at Anaconda is a fine, -35 mesh, impure product, about 50 pct metallic iron, obtained from the reduction of iron calcine at a temperature of 1850°F by use of coke resulting from slack coal. The metallic iron particles are bulky and spongey and precipitate copper readily and rapidly from a copper sulphate solution. Investigation of the treatment of Greater Butte Project, Kelley, ore at Anaconda early showed the desirability of using sponge iron as a precipitant for the copper in solution resulting from desliming of the ore in a dilute sulphuric acid solution. Anaconda had done considerable work on the production of sponge iron in 1914 for use as a precipitant of copper from leach solutions. Some success and considerable experilence were attained at the time. indicating that, sponge iron might be successfully made by a modification of the process used in 1914, a batch process in which an iron calcine was reduced by means of soft coke, resulting from noncoking coal, in a Bruckner-type revolving horizontal cylindrical furnace widely used 50 years ago. The coke and calcide formed the bed in the Bruckner furnace, which was rotated at about 1 rpm. The bed was brought to a temperature of about 1800°F by means of an oil flame over the surface. Although results were reasonably satisfactory, they did not warrant full development of the process at that time. A good deal of work has been done in the last 50 years on the production of sponge iron. The objective in some cases has been the production of a precipitant for copper from solution, but the bulk of the work has been done for the production of open-hearth steel furnace stock. The production of an open-hearth stock presents two problems rather than one: first, producticon of the sponge iron, and second, what is perhaps of equal difficulty and importance, conversion of the sponge iron into a form suitable for use in the open-hearth furnace. So far as is known to the writer, none of the sponge iron processes tried in the past have proved to be economically feasible. However, Anaconda had a combination of conditions appearing to justify an attempt to produce sponge iron which would serve for the leach-precipitation-float process. It was thought that the process used in 1914, if changed to a continuous one, might work out satisfactorily. The following favorable conditions at Anaconda justified the investigation: 1—A sufficient tonnage of good grade iron calcine resulting from the roasting of a pyrite concentrate in one of the acid plants, at substantially no cost. 2—Reasonably cheap natural gas. 3-—The fact that there was no need for production of a high grade product. 4— The fact that there was no need for obtaining a consistently high reduction of' the iron in calcine. A small revolving Bruckner-type furnace about 2 ft ID by 4 ft long was set up for early pilot work at the research building. This pilot furnace showed that a satisfactory product could be obtained at reasonable cost. It also indicated a marked advantage in preceding the reduction furnace with a furnace of similar size and capacity for preheating and roasting out any residual sulphur from the feed. The small furnace was operated for several months, various details of the process were worked out. and sponge iron was produced to supply a pilot LPF plant which treated 300 lb of Kelley ore pel- hr. Later a second pilot furnace 5 ft in diam and 12 ft long inside was set up at our reverberatory furnace building. This furnace confirmed the data of the small furnace and gave a basis for design of the final plant. At Anaconda a pyrite concentrate, running about 48 pct S, is recovered from copper concentrator tailings by flotation. This concentrate is roasted to sulphur of 3 pct or less at the Chamber acid plant. The iron calcine contains about 57 pct Fe and 18 pct insoluble. The iron calcine feed, as mentioned before, is re-roasted and preheated in a reroast furnace preceding the reduction furnace. Both are of the Bruckner type. The reroasted calcine is fed into the reduction furnace at 800" to 1000°F along with 30 pct slack coal. In the feed end of the furnace the volatile is burned from the slack, giving a soft coke which readily serves for reduction of the iron. Hard metallurgical coke will not serve the purpose. since it does not reduce CO readily at a temperature of 1850°F. All indications are that the actual reduction of the iron is accomplished by carbon monoxide below the surface of the bed, which is 30 in. deep at its center. Apparently there is a constant interchange: Fe²O³ + 3CO = 2Fe - 3CO², CO² + C = 2CO Actually iron oxide is reduced by CO at somewhat lower temperature than the 1850 °F used in the process. but this temperature is necessary to obtain a satisfactory rate of furnace production. The furnace atmosphere is generally reducing, and typical blue carbon monoxide flames satisfactorily cover the bed. Gas flames from four 3-in. Denver Fire Clay Inspirator burners are played directly on the bed, which is slowly cascaded by the 1 rpm of the furnace. An excess of coke is necessary to assure maintenance of good reducing conditions in the furnace bed. Part of this coke is recovered for re-use.

Jan 1, 1954

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By John Bell

Aim of Rock-Crushing Experiments THE aim of the laboratory experiments described in this paper was twofold: 1. To measure as accurately, as possible the maximum amount of crushing that can be effected by 1 hp. acting for 24 hr., by the two proposed methods for measuring the amount of crushing, namely: (a) by Rittinger's method; (b) by Stadler's method, based on Kick's law. 2. To show, if possible, that by one of these methods, the amount of crushing produced by 1 hp. in 24 hr. is a constant amount throughout a wide range in the diameter of the piece crushed, and that by the other method, the amount of crushing is a variable quantity over the same range of diameter; or else show that neither of the proposed methods for measuring the amount of crushing indicates a fixed relation between power and crushing and consequently a new method for computing this amount will have to be found to permit the establishment of a law of crushing. Experimental Methods Testing machines, calorimetric methods and commercial. types of rock-crushing machines were considered with reference to their value for measuring power used in crushing. The following electrically driven crushing machines, installed and available in the McGill Ore-dressing Laboratory and which had been used in previous rock-crushing tests, on the whole seemed especially suited to the investigation: (1) Comet "A" crusher; (2) 7 by 9-in. Dodge crusher; (3) 10 by 16-in. rolls. In later tests a 3 ½ -ft. Huntington mill was used.

Jan 2, 1917

By John W. Bell

The aim of the laboratory experiments described in this paper was twofold: 1. To measure as accurately as possible the maximum amount of crushing that can be effected by 1 hp. acting for 24 hr., by the two proposed methods for measuring the amount of crushing, namely: (a) by Rittinger's method; (b) by Stadler's method, based on Kick's law. 2. To show, if possible, that by one of these methods, the amount of crushing produced by 1 hp. in 24 hr. is a constant amount throughout a wide range in the diameter of the piece crushed, and that by the other method, the amount of crushing is a variable quantity over the same range of diameter; or else show that neither of the proposed methods for measuring the amount of crushing indicates a fixed relation between power and crushing and consequently a new method for computing this amount will have to be found to permit the establishment of a law of crushing. Experimental Methods Testing machines, calorimetric methods and commercial types of rock-crushing machines were considered with reference to their value for measuring power used in crushing. The following electrically driven crushing machines, installed and available in the McGill Ore-dressing Laboratory and which had been used in previous rock-crushing tests, on the whole seemed especially suited to the investigation: (1) Comet "A" crusher; (2) 7 by 9-in. Dodge crusher; (3) 10 by 16-in. rolls. In later tests a 3 ½-ft. Huntington mill was used.

Jan 1, 1918

By David P. Shoemaker, Clara B. Shoemaker

It has been shown for an important class of complex transition intermetallic compounds (a, P, R, 6, and p phases) characterized by "normal" coordination [CN12 (icosahedral), CN14, CN15, CN16/ that interatomic distances nay be calculated to a good approximation as the sum of characteristic atomic radii. Two radii, one for major ligands and one for minor ligmds, are specified for each atom, except in the case of CN12 where only a miaaor-ligand radius is specified. The same appears to be true of transition-metal phases of simpler struc-ture: Laves phases (CN12, CN16), and p-tungsten phases (CN12, CN14). In the case of known examples of the more complex phases, a simple rule is given which specifies these radii. However, only a fraction of the known examples of the simpler phases obey this rule closely. To include the latter phases the rule may be modified by considering the radii as linear functions of the weighted average of the Pauling CN12 radii of the two kinds of atonzs, with the radii weighted according to the over-all chemical composition of the alloy. With very few exceptions interatomic distances for both tlze complex and the simpler transition phases can b$ predicted with this modified rule to within 0.06A. ManY intermetallic compounds are known of composition A,By, in which A is a transition element to the left of the manganese column in the periodic table and B is a transition element in or to the right of it. Frequently the coordination numbers (CN) found in these compounds are CN12 (icosahedral), CN14, CN15, and CN16 (called "normal" coordinations by Frank and Kasperl). Well-known examples are the cubic and hexagonal Laves phases which have CN12 and CN16, and the 0-tungsten (CrsO) phases which have CN12 and CN14. In the more complicated (often ternary) phases, such as the a phase,2 the Beck phases p3 and R~, the 6 phase,5 and the p p atoms occur with CN12, CN14, CN15, and (except for a) CN16; in many cases several crystallographically independent atoms of one particular CN occur in the asymmetric unit. A large number of independent interatomic distances are found in these complicated phases, varying from 20 in the a phase to 94 in the 6 phase. These distances show a large spread; they vary, for example, from 2.358 to 3.278A in the 6 phase. In our analysis of these distances we found that in each of these compounds every atomic position can be characterized by either one or two radii. The CN12 positions are characterized by a single radius, The higher coordinated positions are characterized by two radii, namely: the CN14 positions by 4 in the direction of the twelve "5-coordinated" ligands3 (called 'minor" by Frank and Kasperl) and by r:, in the direction of the two "6-coordi-nated" ligands (called "major" by Frank and Kasper); the CN15 positions by r15 for the twelve minor and r:, for the three major ligands; the CN16 positions by rlE for the twelve minor and r:, for the four major ligands. We have expressed the experimentally determined interatomic distances in observational equations as the sums of the appropriate pairs of these characteristic radii and the value of these radii have been determined by the method of least Squares. Despite their wide range, the interatomic distances could then be predicted by the sums of these atomic radii with an average deviation in any one compound of 0.06A or less. The results are summarized in Table I. Inspection of the radii thus obtained shows that in the structures in Table I the radii (in A) are given to a first approximation by the simple relationship: Where CN is the coordination number (12, 14, 15, or 16), and A = 1 for major ligands and = 0 for minor ligands. The interaLomic distances can be predicted within about 0.1A by sums of these atomic radii. Another phase belonging in this group with CN12, 14, 15, and 16 is the y phase & B7, in which A is molybdenum or tungsten and B is iron or cobalt. Recently the M%C phase has been refinedE and the observed distances also agree well with those calculated with Eq. [I]. (In the original determination of the structure of W6FeV7 the F$(II)-W(II1) distance was erroneously given as 2.84A, but we have recalculated it fro? the published parameters and found it to b? 2.57i4, in good agreement with the value of 2.6A predicted with Eq. [I.].) Many binary transition alloys are known to crystallize with the simpler structures having "nor-

Jan 1, 1964

By Newell Alford

THE data in this paper were collected to show both the volume and speed with which bituminous mines have indefinitely suspended operation while economic advantage in the industry has so gravely declined. The study was limited to the bituminous coal-mining states east of the Mississippi River, wherein conditions affecting production and demand are more common respectively to all of the mining districts included and represent about 95 per cent of the nation's coal mining. Data for the compilation of these statistics and for the construction of these graphs have been obtained in all cases from state mine depart-ment reports, except from those of Ohio and Virginia. In Virginia essential individual mine data were secured from an authentic source, but no individual Ohio mine information is obtainable, because all Ohio fact-gathering agencies are prohibited by law from revealing such data. In other states the facts were tabulated and later checked with the cooperation of Chief Mine Inspectors. In all, excluding Ohio, over 17,000 individual annual mine returns were examined. Special infor-mation was secured from each state mine department about suspensions in 1932. Accurate information was not available from all states about mine abandonment due to exhaustion of coal reserves, and while these were completed for several states, it has not been shown because it was not perfected for all states. However, the total observed sample was comprehensive enough to show that exhaustion accounts for a very limited part of the suspended production. Wherever mention is made of "suspended production" the largest annual output of the mine in the five years prior to suspension has been taken as the measure of its probable production had it continued to operate. A mine is not regarded in this category, as having suspended, when it merely ceases to produce. The word "suspension" is used only where there is a complete abandonment of activity for an indefinite period, as evidenced by the fact that both ventilation and pumping are discontinued.

Jan 1, 1933

By Wilbur Nelson

Little drilling has been done in Kentucky and Tennessee in 1923, with the exception of the Kettle Creek area on the Kentucky-Tennessee line. Oil prices fluctuated between $2.86 and $1.36 Per bbl. for light oil. The Kentucky production was slightly over 8,000,000 bbl., being 1,000,000 bbl. less than during 1922. Tennessee production was approximately 8500 bbl., being a decrease of 1000 bbl, over. 1922. During 1923, the first producing well was brought in, in Clay County, Tenn. Production in Tennessee will undoubtedly increase considerably in 1924, and Kentucky production will probably increase slightly. THE year 1923 has been a dull period in oil development in Kentucky and Tennessee, with the exception of the Kettle Creek area along the Tennessee-Kentucky line, in Clinton and Cumberland Counties, Kentucky, and Clay County, Tennessee. The price of oil during the year has been so low that wildcatters have shown little interest in drilling. At the beginning of the year, light oil sold for $2.31 per barrel and medium oil for $2.06 per, barrel. Prices increased to the highest point for the year in February, when light oil brought $2.86 per barrel and medium oil, $2.61. In April, prices had declined 35 c. while in May an additional decline of 25 c. went into effect. During June, prices declined 20 c. per barrel; during July, 45 c. per barrel; remained stationary during August and September, and dropped during November and December to the low price of $1.36 per barrel for light and $1.21 for medium oil. At present, an increase of 29 c. has brought the price of light oil up to $1.55, and indications are that the price will continue to increase during the coming months. It can readily be seen that during 1923 the price of oil was such as to prevent any drilling except that necessary to hold leases and to maintain production enough to take care of overhead expenses.

Jan 3, 1924

By Newell G. Alford

The data in this paper were collected to show both the volume and speed with which bituminous mines have indefinitely suspended operation while economic advantage in the industry has so gravely declined. The study was limited to the bituminous coal-mining states east of the Mississippi River, wherein conditions affecting production and demand are more common respectively to all of the mining districts included and represent about 95 per cent of the nation's coal mining. Data for the compilation of these statistics and for the construction of these graphs have been obtained in all cases from state mine department reports, except from those of Ohio and Virginia. In Virginia essential individual mine data were secured from an authentic source, but no individual Ohio mine information is obtainable, because all Ohio fact-gathering agencies are prohibited by law from revealing such data. In other states the facts were tabulated and later checked with the cooperation of Chief Mine Inspectors. In all, excluding Ohio, over 17,000 individual annual mine returns were examined. Special information was secured from each state mine department about suspensions in 1932. Accurate information was not available from all states about nine abandonment due to exhaustion of coal reserves, and while these were completed for several states, it has not been shown because it was not perfected for all states. However, the total observed sample mas comprehensive enough to show that exhaustion accounts for a very limited part of the suspended production. Wherever mention is made of '(suspended productionJ' the largest annual output of the mine in the five years prior to suspension has been taken as the measure of its probable production had it continued to operate. A mine is not regarded in this category, as having suspended, when it merely ceases to produce. The word "suspension" is used only where there is a complete abandonment of activity for an indefinite period, as evidenced by the fact that both ventilation and pumping are discontinued.

Jan 1, 1934