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By A. W. Schlechten, A. H. Larson

Equilibrium H2S/H2 ratios were determined as functions of temperature (500o to 900°C) and composition in a hydrogen-circulation apparatus. Within the composition range studied there exists a two-phase region of "Zr3S4" and "ZrS2". The upper composition limit of this two-phase region is hounded by a disulfide phase and is practically constant over the temperature range investigated. The lower composition limit of this two-phase region is bounded a "Zr3S4 " phase and varies appreciably with tem- perature. The upper composition limit of the homogeneous region of the disulfide phase is not definitely determined, but it appears to he bounded by the stoichiometric composition of ZrS2. The lower composition limit of the homogeneous region of the Zr3S4 phase could not he determined due to the extremely low values of the equilibrium H2S/H2 ratios. Various thermodynamic quantities are evaluated from the data. PUBLISHED free-energy data for the Zr-S system are practically nonexistent. Strotzer, Biltz, and Meisel1 measured the sulfur pressures for the reaction 2ZrS2(s) + S2(g) = ZrS3(s) in the temperature range 783" to 874°C. The average heat of reaction calculated from the temperature dependence of the sulfur pressure is -47 keal. It should be noted, however, that according to these investigators, the two-phase region as determined by sulfur pressure constancy under isothermal conditions extended from approximately ZrS2, 3 to ZrS2.7. From consideration of X-ray data they concluded that the homogeneous regions of the disulfide and trisulfide phases are ZrS1.8-2.0 and ZrS2.8-3.2, respectively. Hahn and coworkers2 have made a structure study of the zirconium sulfide phases. They summarized the zirconium sulfide phases as follows: the compounds ZrS3 and ZrS2 with narrow homogeneous regions, a "Zr3S4" phase with a homogeneous region roughly within the limits of ZrSl.5 and ZrSo.9, the compounds ZrS and Zr4S3, and a "Zr3S2" phase with a homogeneous region within the limits ZrSo.8 and ZrSo.5. It is noted that the compounds ZrS and Zr4S3 are only formed in the gaseous state through sublimation of a phase which has the approximate composition of the compound. This paper describes the determination of the stability of the zirconium sulfide phases by a hydrogen-reduction method in which hydrogen is circulated over the heated sulfide until equilibrium is attained. The resulting H2S-H2 mixture is then analyzed. Partial molar free energies, enthalpies,

Jan 1, 1964

Jan 1, 1880

A regular general meeting of the Canadian Mining Institute will be held in Vancouver, B. C., on Nov. 26-28. The Council extends a cordial invitation to all members of the American Institute of Mining and Metallurgical Engineers to attend.

Jan 11, 1919

By R. E. J. Putman

Introduction Self-tuning regulators are a class of controllers built around the concepts of sampled data theory, and are especially suitable for implementation in a digital microprocessor or minicomputer control system. The algorithms used are distinctly different from those based upon analog control techniques and include automatic adjustment features which permit them to adapt to unmeasured changes (in, for example, ore grindability) or process nonlinearities (as exhibited by cyclone classifiers). They are also designed to handle transport lags in a simple manner, for example, anticipating the effects of a variable recycle rate on particle size distribution. The advent of distributed control systems will encourage the exploration of these techniques in the minerals processing industries, and particularly for improving the control of comminution circuits, which are especially energy intensive. This paper outlines some current work in progress on this topic. Background Those engaged in the practice of process control have long had two philosophical problems for which solutions have been actively sought - what is optimal control and how can we attain it in some heuristic fashion automatically. The basic analog controller can be represented by the differential equation: [V = Ko + K1 f y • dt + K2 dt(1)] where: v and y are the instantaneous values of output and error respectively and K0, K1, and K2 are tuning constants. The empirical rules for establishing the values of K0, K1, and K2, which provide stability, have evolved from the initial suggestions of Ziegler and Nichols(9) in 1942 and have served their purpose well. However, later analyses demonstrated that there are in fact many combinations of the values of K0, K1, and K2 which, besides being stable, behave better or worse in relation to other process control criteria; some examples are duration of error, amplitude of a damped response, magnitude or rate of movement of control valve or adjustment of speed regulator, etc. The definition of optimality had broadened. In 1964, Kalman(4) published his classic paper which tried to resolve these problems. He defined a

Jan 1, 1982

By C. G. Palagi, S. S. Stillar

The C. E. Weed concentrator treats 51,000 tons per day of 0.5% to 0.7% copper ore received from the Berkeley Pit, the Continental East Pit and the Butte underground mines. Improved operating techniques and conversion from semi-autogenous secondary grinding to ball milling have increased tonnage from an original design of 42,000 tpd. Separate treatment of sands and slimes, with recovery of soluble copper from the slimes, has increased total copper recovery. Concentrator tailings are pumped 600 vertical feet and 20,000 horizontal feet for disposal.

Jan 1, 1976

By M. M. Rao, P. G. Winchell, R. J. Russell

A detailed analysis has been used to correlate the avalable thermodynami c da In on iron-ric11 Fe-Ni (41loys in the body-centered a, and the face-centered y phases. The inp ut injovrt~ation required by the a am lysis consists of tile heat of the a, to y transformation at 1123°K, the heat of mixing of y at 1123°K, tile specific heats of both a, and y (decomposed into Debye, electronic, and magnelic contributions), and the positional and magnetic entropies of both a, and y. PYLrrzary oirt.bul of the analysis is the free energy of each phase as a Junction of temperature and composition. FOr Fe-Ni alloys the adjustment of twenty-one parunletevs allows the accurate reproduction of enthalpy data for both phases, the heat of mixing- for y, the a/y equilibrinm compositions in the Fe-Ni phase diagram, and the usually accepted enthalpy and entropy of a and y iron. Also obtaitzed are fuirly accurate reproductions of electronic specific heat coefficients predicted from electron- to-atom ratio interpolations and To temperatuves eslimanted from transformation studies. Also considered in the calculation are the elastic constants, Curie temperatures, saturation magnlelizalion values, and indications of short- range order. The measnred activity coefficient of iron in anstetnite could not be accurately matched. The major source of uncertainty in the model is thought to be the magnetic contribution to the entropy of austenite. Calcrclations were extended to Fe-ni-C alloys using available carbon-acliuity data. The free energy of transformation from martensile to r at fixed composition was obtained as a function of nickel and carbon contetzt, and binary thetal-carbon phase diagrams Were estimaled as a function of nickel contenl. We needed thermodynamic information for Fe-Ni and Fe-Ni-C alloys at temperatures between 400" and 800°K in order to interpret the results of several phase-transformation studies. The most recent theoretical analysis of the thermodynamics of Fe-Nialloysl was based on a lumped-parameter, regular-solution model and used the Fe-Ni phase diagram available at that time.' Because significant difficulties were encountered in attempting to extend this analysis to Fe-Ni-C alloys, and because more experimental data has become available recently, we decided to attempt a new correlation. The analysis used here allows the extrapolation of measured and calculated thermodynamic values to lower temperatures and the extension of the thermodynamic analysis to Fe-Ni-C alloys. The structure of this correlation consists of expressions containing a total of twenty-one adjustable parameters. The forms of these expressions are discussed in the next section; however, a less formal summary is presented now to provide a physical overview of the model and to indicate its connections to prior work. Primary input information for this correlation is described below. The measured values of the specific heat of iron3 and its analysis475 and theoretical estimates of the specific heat of y* iron at low tempera- loys at 1123°K has been measured by solution calori-metry.7 The enthalpies of both a, and y have been measured most recently by Scheil and Saftig,B who used a dry-ice calorimeter. These data are used to formulate expressions for the heat of mixing of y and the heat of transformation of a, to y both at 1123°K. The a and y solubility limits in the Fe-Ni phase diagram have been redetermined recently9 by methods which assure a close approach to equilibrium. The a to y transformation can occur without change in nickel content or free energy at a temperature called TO; TO temperatures for various nickel contents have been estimated from transformation studies. The computed free-energy functions are adjusted by means of the parameters to fit both the phase diagram and the TO temperatures. Primary emphasis is placed on the phase diagram fit. Iron activities have been measured in Fe-Ni austenite10 between 973" and 1173°K. These activity data, which cannot be fitted accurately with our model, indicate that iron is substantially ideal in iron-rich austenite. Secondary, but helpful, information for the present correlation is provided by neutron diffraction and saturation magnetization measurements on both body-centered and face-centered Fe-Ni alloys."-'3 These results were interpreted11 in terms of composition-insensitive, localized magnetic moments on both iron

Jan 1, 1968

By Howard H. Fields

Any mining engineer with a desire to operate independently, with some financial backing, and with no fear of heavy responsibility and long hours, should be able to make a comfortable living in Mexico. Barring a few inconveniences such as a lack of satisfactory liability or accident insurance, the difficulty of obtaining repair parts or vehicles, and the length of time required to receive returns from shipments, the operation of small mine is not at all difficult. It is, in fact, a little easier to find a good prospect in Mexico than in the U.S.

Jan 1, 1950

By Donald Barton

THE theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A = K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America; most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec.2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. In most cases, it is very nearly, but not quite, perpendicular to the earth's surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth's surface it commonly is very nearly, but not quite, a straight line.

Jan 1, 1928

CONTENTS PAGE THOENEN, J. R.-Limestone Production as a Mining Problem. Discussed by Oliver Bowles, J. T. Singewald, S. R. Russell 1 GRIGGS, C. C.-Engineering in Limestone Production. Discussed by W. C. Phalen, John Rice, Samuel M. Shallcross, Oliver Bowles, Nathan C. Rockwood, George Milliron 2 WILDER, FRANK A.-Rotary Calciners for Gypsum. Discussed by L. K. Arm-strong 9 PORTER, JOHN J.-Manufacturing Problems of Cement Industry. Discussed by Samuel M. Shallcross 9 KIRKHAM, VIRGIL R. D.-Phosphate Deposits of Idaho and Their Relation to the World Supply. Discussed by F. A. Wilder, S. L. Willis, G. R. Mansfield, R. W. Stone, L. K. Armstrong 9 Limestone Production as a Mining Problem Discussion of the paper of J. R. THOENEN, presented at the New York Meeting, February, 1925, and issued, as Paper 1417-H, with MINING AND METALLURGY, February, 1925. OLIVER BOWLES, New Brunswick, N. J.-I am so thoroughly convinced of the growing importance of underground work in the production of limestone that I had the author make a detailed study of limestone mining for the Bureau of Mines and prepare a report on the principles of limestone mining. Many limestone operators, long accustomed to open¬pit work, are being forced to mining. About 6 months ago I thought there were twenty-five or thirty underground limestone operations in the United States but the author has been finding new ones until his list now runs nearer sixty. Some of these are very extensive; one at least has 4 ½ miles of underground workings. There is an ever-expanding field for the engineer in the operation of limestone mines and quarries. Some of the larger companies realize the need of skilled engineering advice, but many of the companies regard the engineer as an unnecessary expense. Although almost every metal mine, even those handling only a few hundred tons of ore per month, employs a mining engineer, many limestone operations ten times as large employ no mining engineers. Few mining engineers are at all familiar

Jan 6, 1925

[Appalachian Petroleum Section: James M. Kimbrough, chairman; John H. Adair, first vice-chairman; Walter L. Diddle, second vice-chairman; Byron M. Finch, secretary-treasurer. Balcones Section: Robert V. West, chairman; Frank W. Jessen, first vice-chairman; Zane V. Morgan, second vice-chairman; Brantley G. Myers, secretary-treasurer. Meets 4th Wed., Petroleum Club (San Antonio) or Terrace Dining Room (Austin) Billings Petroleum Section: Charles B. Evans, chairman; L. M. Lyon, first vice-chairman; Gordon E. Lansford, second vice-chairman; Fred. A. Haddenhorst, secretary-treasurer. Meets 3rd Tues., Billings Petroleum Club. California Coastal Section: Robert L. Richardson, chairman; David K. Hayward, first vice-chairman; W. Jackson Bransford, secretary; William N. Harwell, treasurer. Meets 3rd Thurs., Pierport Inn, Ventura. Caracas Petroleum Section: Edwin A. Moo re, chairman;. Jose Cirigliano, vice-chairman; Frank B. Davis, secretary; Robert N. Powers, treasurer. Meets 2nd Tues., Caracas Theater Club.]

Jan 1, 1961

By AIME AIME

WILBER JUDSON is one of that fairly large group of mining engineers that graduated at an Eastern college, worked his way up in various jobs in the West and in the Latin-American countries, and finally came to New York as an administrative officer of a large mining company. Since coming to New York he has been a loyal friend and counselor of the A.I.M.E., and is now serving a second term as one of its Directors, his first term covering the period 1935-1938. Mr. Judson was born in the capital city of Michigan on July 26, 1880. Probably it was his roving spirit rather than professorial urging that was responsible for the fact that four colleges were responsible for his education: Northwestern, University of Michigan, Harvard (S.B., 1901), and the Michigan College of Mines (graduate study). In his first ten years of professional work he might have been found serving as mine foreman at Catamarca in the Argentine, as superintendent of the Inter Ocean mine at Sunshine, Colo.. as foreman for the Cerro Prieto, Magdalena, Sonora, as superintendent of the Hudson Iron Co. in New York, or as manager of the Dolores mine in Chihuahua for the Mines Co. of America, or in Spain, or in Panama.

Jan 1, 1942

By George B. Langford

ON THE QUESTION of postwar controls there are today three schools of though ; some advocate state control of everything the socialists ; second are those who advocate the removal of all governmental control over industry - the freedom of enterprise ideal ; and third are those who advocate a middle course - sufficient control to stabilize economic and industrial life, and to prevent violent fluctuations such as we saw in the interwar years. I advocate this third course. I firmly believe un free enterprise, but not in freedom of enterprise, or laissez faire, and there is a great and significant difference between these two.

Jan 1, 1944

By AIME AIME

SECOND only to the February Annual Meeting of the Institute are the Regional and Divisional meetings held in the fall of each year. Six such gatherings are scheduled in the next the months, with something likely to interest every member of the Institute. A brief résumé of the programs follows. Regional Meeting Vancouver T HE regional meeting of the Institute will be held at Vancouver, Sept. 13 to 20, in conjunction with the annual western meeting of the Canadian Institute of Mining and Metallurgy. The pro gram appeared on page 350 of MINING AND METALLURGY for July and-proof of careful preparation-a month later re- quires no correction and little elaboration. On the technical side there are few changes. A new item on the Wednesday morning program is the paper, "Investigation of Residential-type Stokers," by H. F. Yancey, supervising engineer, Northwest Experiment Station. U. S. Bureau of Mines, Seattle. As to entertainment the meeting is taking on some most pleasurable aspects. Two notable excursions have been arranged.

Jan 1, 1937

By KENNETH CROPPER

USUALLY we forget about the things which move along smoothly. There are no causes for worry when there are no troubles. But when troubles arise we must put forth some thought and effort to alleviate them. No one "worries about his automobile until it begins to knock, develop flat tires, or refuses to start. However, when these ailments become apparent we get wide awake on the spot, and do our best to repair the car. So we find ourselves now. The old bus seems to hit all the ditches. There is rough ground on all sides and none of us is able to do anything toward improvement. A state of pessimism stares us in the face, and there is sufficient cause for it. With lead at 3.75 cents, copper about 8 cents, zinc under 4 cents, -and silver about 26 cents, one has a reason for grief. When we think of the 5000 or less men employed in Utah mines and smelters in 1931, as compared with about 12,000 in 1929, the calamity seems even worse. In view of the present economic crisis we cannot even think of new men getting a job.

Jan 1, 1931

[Separates of all the Technical Publications published in 1929 are available at lnstitute headquarters. All the papers are on file in public, university and technical libraries, and when so indicated in the list, may be found in the Transactions.] Metal Mining Technical Pdbli- Title Author Meeting Trans. cation . Volume No. and Page* 182-A-23 The Royal Commission on Mining Henry Louis New York Subsidence Feb., 1929 183-A-24 Cycles in Metal Production D. F. Hewett Nen. York T29, 65, 95 Feb., 1929 199-A-25 Ventilation at the United Verde Oscar A. Glaeser New York T29,- 114. Mine Feb., 1929 206-A-26 Air Conditioning In Deep Mines R. W. Waterfill New York T29. 99, 112 Feb., 1929 245-A-27 Bumps in No. 2 Mine, Springhill, Walter Herd New York Nova Scotia (with discussion) Feb., 1929 257-A-28 Misfires: Their Causes, Prevention New York and Treatment on Occurrence Feb., 1929 Misfires in Anthracite Coa1 T. D. Thomas Mines (With Discussion) Misfires in Bituminous Coal W. H. Forbes Mines (With Discussion) Misfires in Non-metallic Mining A. W. Worthington (Limestone) (With Discussion) Milling and Concentration 195-B-15 A Study of Differential Flotation C. R. Ince New York Feb., 1929 196-B-16 Elements of Operation of the Arthur F. Taggart New York Pneumatic Table H. L. Lechmereoertel Feb., 1929 202-B-18 Silver-bearing Minerals of Some A; W. Habn New York T29, 325 Ores from Tintic Mining District Feb., 1929 204-B-17 Experiments with Flotation Re- A. F. Taggart New York agents T. C. Taylor Feb., 1929 C. R. Ince 208-B-20 Cyanide Regeneration or Recov- C. W. Lawr Sun Francisco ety as Practiced by the Com- Oct., 1929 pania Beneficiadora de Pachuca, Mexico 214-B-19 Calculations in Ore Dressing W. Luyken New York E. Bierbraer Feb., 1929 217-B-21 Differential Grinding Applied to Leon M. Banks San Francisco Tailing Retreatment George A. Johnson Oct., 1929 224-B-22 Reducing and Oxidizing Agents Research Staff San Francisco and Lime Consumption in Flo- of United Verde Oct., 1929 tation Pulp Copper Co. 247-B-23 Copper Sulfate as Flotation Acti- 0. C. Ralaton San Francisco vator for Sphalerite 0. R. King Oct., 1929 F. X. Tartaron

Jan 1, 1929

By Richard P. Rothwell

The anthracite coals of Pennsylvania are all mined from large veins. A seam less than four feet. in thickness is generally considered as unworkable, those from which most of the coal now comes being from 8 'to 30 feet thick. The system of mining employed is, almost without exception, that known as " chamber and pillar work;" that is, the coal is taken out of chambers of from 18 to 30 feet in width, and pillars of from 12 to 20 feet are left between these to support the roof. In general, the entire thickness of the seam, even

By John F. Elliott, John P. Hager

The standard free energies of formation of the lowest stable sulfides of chromium, molybdenum, and tungsten in equilibrium with the corresponding metal hazle been determined by reacting the sulfide and metal with H2(g)/H2S(g) mixtures. The reaction is A method for estimating the standard ~nolav entropies and standard entropies of formation at 298°K of the sul-fides of refractory metals is presented. The standard free energies of formation of the lowest sulfides of the metals in group VIa of the periodic table are probably best determined with the reaction* is known with greater accuracy than is that property for any other sulfur-bearing compound or solution which might serve as a reference phase to establish the chemical potential of sulfur for the essential re- However, there still remain significant problems to the use of Reaction [I] in studying these sulfides. First, the equilibrium gas ratios (Ph2S/PH2) are very small, and with the most stable sulfides in the series the ratios tend to be at the limit of the range for precise chemical analysis (10-4); and second, the reaction rate for the formation or reduction of these sulfides appears to be relatively slow. A primary reason for the latter problem is that the gas phase near the equilibrium concentration has very little capacity for transport of sulfur. It is to be noted that the thermo-dynamic properties obtained from the experimental results by Eq. [I] apply for 1 g-atom of sulfur in the metal-saturated compound even though the exact composition of the compound has not been determined. The work reported here is a study of the standard free energies of formation of the lowest sulfides of chromium, molybdenum, and tungsten, and of copper, by Reaction [I]. In planning the experimental program, it was decided that the technique that has been used previously3"' could be used with modification and that an improved analytical method was needed for determining H2S in the gas phase. THE EXPERIMENT The once-through flow of gas was selected in preference to recirculating the gas, a) because of the low sulfur capacity of the gas, b) because of the relatively slow rate of reaction and the danger of the

Jan 1, 1968

By Robert S. Nichols

Fording Coal Limited's mine in the Rocky Mountains near Elkford, B.C. has produced 21.8 million clean tonnes of metallurgical coal from 1971 to 1980, inclusive. This production has come from several pit areas and required the removal of 149.1 million bank cubic meters of waste rock and overburden by truck-shovel and dragline operations. Waste dumps from 30m to 200m in height have been successfully constructed on natural slopes, generally between 10° and 26°. Design considerations for the dumps include foundation and soil conditions, natural slope angles and containment of weak overburden or rehandle materials. Dump control is maintained by monitoring the crest and the face of an active dump area. Crest movement is measured by extensometers locally termed "Spoil Monitors". When crest movement rates progressively increase above normal, dumping operations are temporarily relocated. Some unstable conditions and mass failures have occurred as the result of natural foundation slopes being in excess of 26°, failure of weak water saturated foundation soils or weak material being placed on the dump.

Jan 1, 1983

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By William E. Ford, Edward Salisbury Dana

The important BARITE GROUP is the only one among the anhydrous sulphates and chromates. Mascagnite. Ammonium sulphate, (NH4)2S0,. Orthorhomhic. Usrially in crusts and stalactitic forms. p = 1.523. Occurs about volcanoes, as at Etna, Vesuvlus, etc. Taylorite. 5K2SOa.(N&)ySOd. 111 small compact lumps or concretions. From the guano of the Chincha Islands. Thenardite. Anhydrous sodium sulphate, Na2S04. In orthorhombic crystals, pyrarnidal, short prismatic or tabnhr; also as twins (Fig. 384, p. 160). White, to brpwnish. 0 tically +. p = 1.477. Soluble in water. Often observed in connection with salt lates, as on the shores of Lake Balkhash, Central Asia; similarly elsewhere; also in South America in Tarapaca, Chilc. In the United States, forms extensive deposits on the Rio Verde, Aria. In Cal., at Borax Lake, San Bernardino Co. Aphthitaiite. Arranite. Glmerite. (Ii,Na)&O1. Rhombohedral; also massive, in crusts. Color white. From Vesuvius, upon lava; at DouglashaU near Weateregeln, Ger- many, in hloditc; Stassfurt, Germany; Rocalmuto, Sicily.

Jan 1, 1922