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By M. Cohen, C. Wagner, J. E. Reynolds

If the total volume of a diffusion couple changes during the diffusion, the measurement of distance becomes ambiguous. Use of distance parameters as suggested by Hartley and Crank is discussed. For small concentration differences, the standard form of Fick's second law is retained with conventional length units and the in- terdiffusion coefficient D. It is shown how D can be calculated from experiments involving large concentration differences and analyzed in terms of distance parameters. 'The merits of incremental diffusion couples involving small concentration differences are emphasized. THE conventional form of Fick's second law for one-dimensional diffusion of component B in a binary solution of A and B is where c, is the concentration of component B; x, the distance; t, the time; and D, the interdiffusion coefficient which may depend on ca. Hartley and Crank' have pointed out that Eq. 1 applies only if the total volume of the diffusion couple does not change during the diffusion process; otherwise, the definition of x becomes ambiguous. No change in total volume takes place if the specific volume of the solution is a linear function of the weight fraction Wb, or if the molar volume is a linear function of the mol fraction N. In some alloys, however, these relationships do not hold, and then it is necessary to introduce a modified measure of distance, 4 in order to retain the general form of Eq. 1. The application of Hartley and Crank's suggestions to diffusion in alloys has been discussed by Wagner.' Relation Between Measure of Distance and Units of Concentration The definition of [ depends on the choice of units for the concentration c,, as follows: 1—If the concentration ca is measured as the weight fraction W, (or weight percent), [ = 5, has to be defined so that equal increments of contain equal increments of mass m of the solution, e.g., dm = pSdx = Sdw [2] where p is the local density of the solution, and S is the cross-sectional area in sq cm which is taken to be constant in this problem of one-dimensional diffusion." * da Silva and Mehla have demonstrated the constancy of the cross-sectional area in the usual type of diffusion couple. However, experiments involving diffusion into thin wires4, 5 may exhibit changes in cross-sectional area, and therefore are excluded from the present treatment. Thus and the unit of is gram per sq cm instead of cm. 2—If the concentration c, is the mol fraction N, must be defined so that equal increments of contain equal numbers of mols of solution, e.g., dn= (S/V)dx= Sd [41 where V is the local molar volume of the solution. Thus dt, = dx/V [51 and the unit of is mols per sq cm. 3—If, as may be advisable in the case of interstitial solutions, the concentration C is measured in terms of the molar ratio of components B and A (c,, = Y, = nH/nA, where n and nl are numbers of mols of B and A), = Y has to be defined so that equal increments of contain equal numbers of mols of A, e.g., dnA= (NAS/V)dx = Sdf [6]

Jan 1, 1954

By C. D. Demond

In reverberatory smelting, fuel is the chief item of expense, as it commonly is in processes using large percentages of it. Hence the most suitable supply is eagerly sought; that is, the supply which, in the end, yields the greatest net profit. The better grades are not infrequently bought, even at an advanced price, because they are apt to be decidedly more economical. High price, of itself, however, is no merit, for freight is generally the largest part of the cost of fuel, and the nearby supply may yield as high efficiency as that from a greater distance. If a poorer grade is reasonably good, and if its cost is low enough to more than offset the decreased technical efficiency, it is of course the more suitable. Any smelting operation depends for both efficiency and economy on raising the furnace atmosphere considerably above the "critical" temperature; that is, above the temperature at which smelting is completed. If this temperature is not exceeded, smelting stops, no matter how much coal is burned; and the real value of a fuel depends on the number of degrees that the temperature is continuously kept above this point. For example, if one fuel maintains 2,500" F. and another only 2,100 F., while the "critical" temperature is 2,000" F., the first is worth at least five times as much as the second, although the increase above atmospheric temperature is only one-fifth more in one case than in the other. This "margin of temperature" above the smelting point is much more significant than the total number of heat units developed from the fuel. The case is parallel to that of water flowing from a pipe. The reservoir may contain a billion gallons of water; but, even though the fluid has come to the nozzle, not a drop will run out, where it can be of practical use, unless the level in the reservoir is higher than the nozzle; and the speed and volume of flow depend on how much higher the level is in the reservoir than at this point. If the temperature in a furnace is not above the critical level there will be no slag to flow over the skimming plate, even though there are enough heat units to bring an unlimited quantity of charge up to the point of slag formation; and just as the value of a water supply for the purpose of putting out a fire depends largely on the effective head, so the difficulties of furnace management

Jan 1, 1915

By J. F. Shirley, H. K. Burke

In January, 1964, three years of laboratory and pilot plant test work reached its culmination. The San Manuel Div. of the Magma Copper Co. switched its molybdenite extraction circuit from the sodium hypochlorite-ferrocyanide process to the new process described in this paper. The San Manuel Div. Concentrator of the Magma Copper Co. is located near San Manuel, Ariz., approximately 45 miles northeast of Tucson. The concentrator treats approximately 35,000 tons of ore per day containing about 0.85% copper and 0.025% molybdenite. The San Manuel ore body is a disseminated copper deposit in quartz monzonite and quartz monzonite porphyry. The primary copper mineral is chalcopyrite; minor amounts of chalcocite, bornite and covellite are also present in varying degrees. Pyrite makes up somewhat more than half the sulfide content of the rock. The molybdenite is nearly always found on fracture faces or associated with quartz veinlets.' On January 9, 1964, the sodium hypochlorite-ferrocyanide process that had been used for molybdenite recovery was replaced by the following process: 1) A conditioning step with hydrogen peroxide, sulfuric acid, sodium cyanide and zinc sulfate. 2) A two stage rougher flotation step with stove oil and sodium ferrocyanide. 3) One cleaning step with sodium ferrocyanide. 4) One cleaning step with sodium hypochlorite and potassium ferricyanide. 5) Four cleaning steps with an anti-foam Exfoam 636 and potassium ferricyanide. COPPER CONCENTRATOR Since molybdenite recovery is closely allied with previous steps in the operation, the copper concentrator will be briefly described first. The ore is ground to approximately 5% plus 65-mesh and 65% minus 200-mesh in a two-step grinding circuit consisting of rod mills in open circuit and ball mills in closed circuit with rake classifiers. A straight forward rougher circuit producing only one concentrate is used. The rougher concentrate is combined with the discharge from the regrind ball mills and is then cycloned, with the overflow going directly to the cleaner circuit and the underflow going to the regrind mills. The feed to the cleaner circuit is approximately 90% to 94% minus 325 mesh. The cleaner circuit consists of two stages in which the tailing from the final cleaner stage is returned to the primary cleaner and the primary cleaner tailing is returned to the rod mill discharge at the head of the circuit. Approximately 0.013 lb of the allyl ester of amyl xanthate (S-3302) per ton of ore is added to the rod mills and approximately 0.006 lb of sodium isopropyl xanthate (2-11) per ton of ore is stage added down the rougher banks. The frother used is methyl iso-butyl carbinol (MIBC) and it is added at various points in the grinding and the rougher flotation circuits. Lime is added to the ball mills and/or to the rod mills to maintain the desired pH in the rougher flotation. The rougher flotation has been operated at various pH levels between 10.5 and 11.5. Fuel oil is added in the regrind mills at a loading of approximately 0.01 lb per ton of ore. Factors Which Directly Affect Molybdenite Recovery: It has been found at San Manuel that, to obtain maximum molybdenite recovery, an oily type flotation collector must be added in the grinding circuit. When molybdenite is crystallized in the characteristic platy form, which appears to be the case almost all of the time at San Manuel, its surface has a greater tendency to adhere to oils than water. 2 Of the several oily type collectors available on the market, the allyl ester of amyl xanthate seems to be the best molybdenite promoter. The floatability of San Manuel's molybdenite does not appear to be affected, at least up to a pH of 11.5, by lime. It has been reported that at several plant operations high lime alkaline circuits have adversely affected the molybdenite recovery.3,4 It has been found through microscopic studies that the bulk of the chalcopyrite will float before the molybdenite in both the rougher and cleaner circuits. It is necessary to add fuel oil to the regrind mills to enhance the

Jan 1, 1965

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,' but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation' and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a'c' and c'b are equal to a'b cos +, and a'b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m'c' and c'b are projected as lengths from point a, rather than from point a'. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889

Jan 1, 1923

MINING METHODS. JAY A. CARPENTER, Chairman P. B. BUCKY, Vice-Chairman CLYDE E. WEED, Vice-Chairman ROY A. HARDY, Secretary Alluvial Mining CLINTON BERNARD O. B. PERRY NORMAN CLEAVELAND C. M. ROMANOWITZ R. B. EARL! NO J. B. STAPLER BENERE H. GRANT CHARLES THURMAN Open-Cut Mining Iron A. D. CHISHOLM P. G. HARRISON G. E. DIEHL EARL E. RUNNER G. E. LEVEQOE

Jan 1, 1942

By G. F. Tagg

Earth-resistivity measurements are often of service in obtaining information regarding geological formations, particularly when applied to structural problems. In such problems the masses of the various bodies are large, and have a corresponding effect on the average resistivity of the soil. Much work has been done using such measurements, but in general the method of interpretation employed is empirical. Since certain simple cases can be investigated mathematically, it appears to be quite sound to endeavor to apply the mathematical solutions to the practical results, in order to deduce from the latter such unknown quantities as depth. This paper deals with such a method of interpretation for the simple case of a single horizontal stratum. In the method described by Wennerl for measuring earth resistivity, four stake electrodes are driven into the earth in a straight line as shown in Fig. 1. A current I amperes is passed between the two outer stakes and the potential difference V volts between the two inner stakes is measured. Then if a is the electrode separation, the specific resistance of the soil, which is assumed to be homogeneous, is given by the formula P = 2?v/1 [1] v or if v/1 is called a resistance R ohms, p = 2?aR [2] If a is in inches, p will be in ohms per inch cube, or ohm-inches, and if a is in centimeters, p will be in ohms per centimeter cube or ohm-centimeters. As stated above, this formula is true only if the earth is homogeneous, and when this is not the case an application of one of these formulas

Jan 1, 1934

By C. R. Fast

In order to evaluate the ability of a Hydrafrac treatment to effect a sustained increase in well production, data were accumulated on the first 65 wells in 26 fields treated by Stano-lind. Since these data were obtained from such a large number of fields, it is felt that individual well or reservoir characteristics do not affect the overall picture, as might be the case if the study were made in one field or one group of wells in a field. These data are tabulated in Table I and plotted on Figs. 1 and 2. An analysis of Fig. 1 shows that at the end of six months, 75 per cent, or 45, of 60 wells on which data were available showed a sustained production increase. At the end of two years, data were available on 25 wells. Of these, 15 wells, or 60 per cent, showed a sustained production increase. At the end of three years, 55 per cent, or 10, of 18 wells had a production rate greater at that time than before Hydrafrac treatment. The lack of information on additional wells at the end of the third year is primarily a result of the small number of treatments conducted in the early stages of field application

Jan 1, 1952

By J. S. Owens, R. W. Marsden, J. W. Emanuelson, R. F. Werner, N. E. Walker

The iron ores of the Mesabi Range occur in a 340 to 750-foot thick, Precambrian cherty iron formation termed "taconite." For about 65 years, extensive natural iron ore bodies were mined, and the ores either shipped as a direct ore or processed by gravity methods to a shipping grade iron ore. Since 1956, magnetite taconite ores, occurring in magnetite-rich horizons in the Biwabik iron formation, have been commercially concentrated and agglomerated. The transition from natural ores to concentrating-grade ores is progressing rapidly so that, in the near future, a major percentage of the iron ore shipped from the Mesabi Range will be as iron ore pellets produced from taconite. Natural iron ores of the Mesabi Range occur in the Biwabik formation as trough ore bodies in elongated channels and as irregular and tabular deposits in fractured areas associated with faults and folds. Ore bodies range in size from a few thousand tons to hundreds of millions of tons and may occur in any part of the iron formation. In some areas of strong ore development, ore was formed from the hanging-wall argillite to the footwall quartzite. The natural ores and beneficiating-grade natural crude ores were formed by the oxidation of the iron minerals, magnetite, greenalite, stilpnomelane, minnesotaite, and siderite, to hematite and goethite and by the removal of much of the silica in the cherty quartz and in the associated silicates by leaching. The ores are believed to have formed by the oxidizing and leaching action of surface waters. Magnetite taconite ores occur as stratigraphic zones in the Biwabik formation where it contains sufficient magnetite to be concentrated profitably, by magnetic methods, to give a magnetite concentrate that is agglomerated into a high quality product. Unoxidized taconite has an extensive distribution away from and between channels of oxidation and leaching but only a part of the unoxidized taconite is of ore grade. Two general types of magnetite taconite ore occur: ( 1) magnetite taconite of the Main Mesabi Range, generally west of Mesaba, which is composed of magnetite associated with cherty quartz, greenalite, stilpnomelane, minnesotaite, and carbonates and (2) magnetite taconite of the Eastern Mesabi, generally east of Mesaba, composed of magnetite associated with quartz, cummingtonite, actinolite, ferrohypersthene, hedenbergite, fayalite, hornblende, pyroxene, garnet, and biotite. The Mesabi taconite is a metasediment derived from an iron- and silica-rich chemical sediment that has been regionally metamorphosed and, on the eastern end, additionally metamorphosed by the Duluth Gabbro Complex.

Jan 1, 1968

By Gerhard Derge, Harold Markus

The first paper1 of this series described a technique of careful surface preparation by means of which reproducible results may be obtained from potential measurements of the behavior of tin in carbonate solutions with a pH range from 8.4 to 11.2. It then went on to establish the behavior of pure tin electrodes under these conditions and showed that the metal remains active at all times, though the steady potential attained after several hours decreases from 1.12† volts at a pH of 12.6 to 0.6 volts at a pH of 8.4. This behavior may serve as a norm with which all other data can be compared. In the second paper,2 small amounts of other anions were added to the carbonate solutions and the conclusion was reached that the common impurities encountered in alkaline materials packaged in tin do not increase corrosion. In fact, in some cases these anions may actually promote the formation of protective films. The present paper rounds out this survey by presenting data on the influence of cations added to the carbonate solutions, as well as the effect of alloy additions to the tin. In many cases the potential data are supplemented with weight-loss measurements. Information is also presented on the effects of some additional anions, the influence of gases above the electrolyte, the behavior of high-purity tin, and the effect of atmospheric oxidation on the corrosion resistance of the above-named alloys. Analysis of the entire body of data discloses some general rules applicable to corrosion in carbonate solutions. The experimental methods used are the same as those previously described. Experimental Data Cations.—The carbonates of the cations K+, Li+, NH4+, which are soluble, were studied in the same way as the anions, by adding 0.01 mol of the metal carbonate to one liter of 0.1 M sodium carbonate solution, pH 11.2, or to 0.1 M sodium bicarbonate, pH 8.4. The other metallic carbonates are only slightly soluble, of the order of 10-3 mols per liter or less, and the sodium carbonate solutions were saturated by adding excess reagent several days before the experiment, shaking frequently, and filtering just before use. The chemicals were c.p. grade in each case except the indium salt. This salt was prepared by solution of the metal in hydrochloric acid and precipitation by addition of Na2CO3. These cations may be divided into two classes, according to their effect on the potential behavior of the tin: (I) normal, (2) passive. To offer a basis of comparison, curves I of Figs. I and 2 are given to illustrate the behavior of tin in carbonate solutions saturated with CaCO3. These curves are the

Jan 1, 1941

By Harold Markus, Gerhard Derge

The first paper1 of this series described a technique of careful surface preparation by means of which reproducible results may be obtained from potential measurements of the behavior of tin in carbonate solutions with a pH range from 8.4 to 11.2. It then went on to establish the behavior of pure tin electrodes under these conditions and showed that the metal remains active at all times, though the steady potential attained after several hours decreases from 1.12† volts at a pH of 12.6 to 0.6 volts at a pH of 8.4. This behavior may serve as a norm with which all other data can be compared. In the second paper,2 small amounts of other anions were added to the carbonate solutions and the conclusion was reached that the common impurities encountered in alkaline materials packaged in tin do not increase corrosion. In fact, in some cases these anions may actually promote the formation of protective films. The present paper rounds out this survey by presenting data on the influence of cations added to the carbonate solutions, as well as the effect of alloy additions to the tin. In many cases the potential data are supplemented with weight-loss measurements. Information is also presented on the effects of some additional anions, the influence of gases above the electrolyte, the behavior of high-purity tin, and the effect of atmospheric oxidation on the corrosion resistance of the above-named alloys. Analysis of the entire body of data discloses some general rules applicable to corrosion in carbonate solutions. The experimental methods used are the same as those previously described. Experimental Data Cations.—The carbonates of the cations K+, Li+, NH4+, which are soluble, were studied in the same way as the anions, by adding 0.01 mol of the metal carbonate to one liter of 0.1 M sodium carbonate solution, pH 11.2, or to 0.1 M sodium bicarbonate, pH 8.4. The other metallic carbonates are only slightly soluble, of the order of 10-3 mols per liter or less, and the sodium carbonate solutions were saturated by adding excess reagent several days before the experiment, shaking frequently, and filtering just before use. The chemicals were c.p. grade in each case except the indium salt. This salt was prepared by solution of the metal in hydrochloric acid and precipitation by addition of Na2CO3. These cations may be divided into two classes, according to their effect on the potential behavior of the tin: (I) normal, (2) passive. To offer a basis of comparison, curves I of Figs. I and 2 are given to illustrate the behavior of tin in carbonate solutions saturated with CaCO3. These curves are the

Jan 1, 1941

By D. S. Sanders

IN the four mills of the Cerro de Pasco Copper Corp. in Peru, some 3000 tons of complex sulphide ores are treated daily, with four kinds of concentrates produced: copper, lead, zinc, and pyrite, each containing values in silver, gold, bismuth, and some other metals. Copper occurs in the various ores as chalcopyrite, enargite, tetrahedrite, tenantite, bournonite, and chalcocite; lead as galena; and zinc as sphalerite and marmatite. Small amounts of silver and tungsten minerals are also present. The gangue consist mainly of shale, quartzite, calcite, rhodochrosite, pyrite, and pyrrhotite. In general the values are freed with a relatively coarse grind, about 70 prr cent minus 200 mesh being the finest to which the pulps are ground. In Morococha and Casapalca however. sphalerite particles much finer than this contain inclusions of chalcopyrit r. At Cerro de Pasco the silver and gold are present in all sizes of the ground pyrite.

Jan 1, 1945

By J. Greenspan

The anisotropy of fracture and slip, that is, the brittleness and ductility of the beryllium single crystal, is characteristic also of po1ycrystalline beryllium in which the grains are oriented in a preferred manner. Beryllium with grain orientations resulting from hot working either unidirectionally or bidirectionally is ductile or brittle in directions given by the anisotropy and orientation of the grains. Textures developed from various hot-working sequences are given, and tensile results are correlated with textures. Not only texture, but fine grain size is necessary for obtaining high tensile elongation. Ultimate tensile strength and elongation are both correlated with grain diameter. Of particular interest is the case in which unusually high tensile elongations of 30 to 40 pct are obtained when basal planes are oriented to carry THE beryllium crystal (of nominal purity) is probably unique among metals with respect to its unusually acute anisotropy of slip and fracture. While extensive slip can occur on the system (1010) [ll20] starting at about 19,000 psi, the (0001) plane is particularly vulnerable to fracture at 4500 psi or less. Fracture occurs also on the (11zo) plane at about 26,000 psi.1"3 Further, there seems to be no other slip System which contributes significantly to

Jan 1, 1960

By B. E. Field

Cobalt is a silvery white metal with a slight bluish cast. It strongly resembles nickel in its appearance and properties, notably its resistance to corrosion, although its alloys with other metals differ decidedly in their properties from those of nickel. The name "cobalt" was derived from the German Kobold, meaning goblin, and this came to be applied to the cobalt minerals which, although they resembled ores, did not readily yield metal when smelted by the primitive processes available in the Middle Ages. Cobalt minerals were used as pigments by potters and glass workers before the Christian era. Cobalt blue glass was found in the tombs of the Egyptians and in the ruins of Troy, and many colors used by the ancient Greeks and Romans contained cobalt. The ancients were entirely unaware that the colors they used were caused by cobalt and the metal itself was not isolated until about the middle of the eighteenth century, by Brandt, although the preparation of cobalt compounds had been carried on in a small way ever since the opening of the silver-cobalt deposits at Schneeberg, Germany, in 1470.

Jan 1, 1935

By Clinton H. Crane

IN October, 1925, J. R. Finlay delivered an address entitled, "The Future Price of Lead." Lead was then selling at 8.85c. and Mr. Finlay and most of the rest of us were concerned about the shortage. Now, a little more than six years after, lead is selling for 3.55c., and nobody is worrying about the difficulty of getting plenty of it. For 1931 the U. S. G. S. reports United States produc¬tion as 390,000 tons of recoverable lead in ore. Our estimate is slightly higher than this; nearer 400,000 tons. This is the smallest production since 1911 and 1912, but in spite of this, stocks for the year-have increased nearly 50,000 tons. Our estimate for the production outside the United States is 1,120,000 tons, or more than double the production of either 1920 or 1921, and 30 per cent more than in 1913. Stocks abroad probably have not increased more than stocks in the United States. In other words, foreign consumption is double what it was in 1.920-21, whereas domestic consumption is substantially less. It looks as if Mr. Krueger, president of the Swedish match trust, was right when he said that "This country had better stop worrying about Europe and think a little bit more about its own affairs."

Jan 1, 1932

Callow, John M. Notes on Flotation. Discussed by R. H. Richards, Joseph W. Richards, Leonard Waldo, George Van Arsdale. 881 Horwood, E. J. Broken Hill Underground Mining Methods. Discussed by Albert R. Ledoux, W. L. Saunders 885 Lindgren, Waldemar, and Ross, Clyde P. The Iron Deposits of Daiquiri, Cuba. Discussed by Waldemar Lindgren, Max Roesler, Benjamin B. Lawrence, Louis C. Graton, Harrison Souder, Charles P. Berkey, Alfred C. Lane, John D. Irving. 886 Powers, Sidney and Lane, Alfred C. Magmatic Differentiation in Effusive Rocks. Discussed by N. L. Bowen, Alfred C. Lane, Sidney Powers 893 Tolman, C. F. Observations on Certain Types of Chalcocite and Their Characteristic Etch Patterns. Discussed by Louis C. Graton, Alfred C. Lane, Joseph T. Singewald, Jr., Charles P. Berkey, E. Posnjak, E. T. Allen, H. F. Merwin, C. F. Tolman, Jr. 895 Warren, H. M., Biesecker, A. S., and Powell, E. J. Tests on Various Motor-Driven Equipment Used in the Preparation of Anthracite Coal. Discussed by R. V. Morris, William Kent. H. M. Warren. K. A. Pauly 901

Jan 5, 1916

By Walter S. Weeks

THE process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case 1 If compressed air is allowed to expand to the atmospheric pressure through an orifice in an sir line that is supplied by a running compressor, no cooling results except the negligible one due to the Joule-Thompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. Cv Specific heat of air at constant volume, B.t.u. per lb. per deg. F. Cp Specific heat at constant pressure, B.t.u. per lb. per deg. F. T1 Absolute temperature of air in pipe, deg. F. T3 Absolute temperature of air outside after expansion and mixing and coming to rest. J Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

By Walter S. Weeks

The process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case I If compressed air is allowed to expand to the atmospheric pressure through an orifice in an air line that is supplied by a running compressor, no cooling results except the negligible one due to the JouleThompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. C, Specific heat of air at constant volume, B.t.u. per lb. per deg. F. C, Specific heat at constant pressure, B.t.u. per lb, per deg. F. T1 Absolute temperature of air in pipe, deg. F. T8 Absolute temperature of air outside after expansion and mixing and coming to rest. j Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

F A. THOMSON, president of the Montana School of Mines, gave an interesting talk on mining schools of the past, present and his ideas of the future before a recent meeting of the Montana Section of the A. I. M. E. He covered the history .of the various mining schools and com- pared the three main types of schools; those attached to or forming part of an endowed college or university such, for example, as' the Columbia School of Mines, the Mining Department of the Massachusetts Institute of Technology and the Mining Department of Stanford University. These resemble in a general way the second class, those attached to the state universities and colleges. The schools of this general type have had varied success.

Jan 1, 1928

By L. Kovisars, F. Buttazzoni

The current demand for copper in the western world exceeds 7 million tonnes annually. The growth in demand is expected to average 2.6% annually to a level exceeding 11 million tonnes in 2000. Copper mine production is currently about 6 million tonnes annually; the annual net addition to mine output in the future will have to average about 190,000 tonnes of contained copper. The industrial nations of Europe and the western Pacific are heavily dependent on copper imports. Currently these import needs are supplied by Canada, Africa and Pacific producers. The increased demand for copper in the future is expected to further weight the trade balance to the Pacific suppliers. An evaluation of undeveloped deposits allows the ranking of these deposits based on total cost of production, including provision for plant and infra- structure investment as well as political/social/ economic risk. Peru, Canada, and the Southwest Pacific are expected to significantly increase exports. The United States will develop deposits to replace depleted mines, maintaining mine production at a level approximately equal to current output, with a consequent increase in copper imports. Chile is expected to become the world's leading copper producer, as well as expanding it's position as the leading exporter.

Jan 1, 1982