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By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By M. E. Wadsworth, P. H. Yu, C. K. Hansen

A study of the rate of dissc5lution of chalcopyrite (CuFeS2) in acidic solutions under oxygen overpressures was carried out by measuring the rate of formation of cupric ions in solution. Effects of temperature, oxygen partial pressure, surface area, and concentration of sulfuric acid were evaluated. A sized batch of chalcopyrite was leached in the temperature range of 125° to 175°C and in the pressure range of 75 to 400 psi of oxygen. In 0.5 N H2SO4 all products of reaction went into solution except for trace amounts of elemental sulfur. The dissolution of chalcopyrite followed linear kinetics and was essentially independent of hydrogen ion concentration for H2S04 concentrations between 0.2 and 0.5 N. The oxygen dependence indicated adsorption approaching limiting values with increasing oxygen pressure. The linear mechanism was explained in terms of steady-state adsorption of oxygen at the chalcopyrite surface followed by a surface reaction. The enthalpy of activation for adsorption of oxygen was found to be approximately 33 kcal per mole. An activation enthalpy of approximately 9 kcal per mole was observed for the surface reaction. Charge transfer reactions are not rate controlling in the process.

Jan 1, 1973

By J. S. Rinehart, W. C. Maurer

The mechanics of impact crater formation in rock, particularly sandstone, has been sutdied, the velocity range being approximately that normally associated with oilwell gun perforators. The bullets were small steel spheres having diameters of 3/16, 9/32 and 7/16 in; impact velocities ranged from 300 to 7,000 ft/sec. The craters have two distinct parts — a cylindrical hole (or burrow) with a diameter the same as that of the impacting sphere, and a wide-angle cup comprising most of the volume of the crater. The burrow is fornred as material in front of the projectile is crushed and pushed aside, forming a cylindrical hole surrounded by a high-density zone. The clip forms as fractures are initiated in front of the projectile and propagate along logarithmic spirals, approximaling maximum shear trajectories, to the free surface of the rock. A most significant observation (made for the first time) was that, below the base of the cup in one type of sandstone, there are a group of similar fractures, not extending to the surface, which are spaced uniformly a few millimeters apart. Each fracture follows roughly the contour of the base of the cup and appears to require a certain threshold impulse to initiate it. These fractures comprise a relatively high fraction of the total, newly exposed surface area. The volume of the material removed by crushing varies as the first power of the impact velocity and the volume removed by fracturing, as the second power of the impact velocity. Penetration varies linearly with the impact velocity and is inversely proportional to the specific acoustic resistance of the target material, the proportionality constant being dependent upon the shape of the projectile. INTRODUCTION Yield of oil from a producing well is frequently enhanced by firing bullets and shaped charges through the well casing into the oil-bearing rock, forming craters and fractures from which oil can flow more readily. The purpose of this investigation has been to develop a better understanding of the mechanics of impact crater formation in rock, particularly sandstone, the velocity range being approximately that normally associated with oilwell gun perforators. FORCES OPERATIVE DURING IMPACT When a projectile moving at considerable velocity strikes a- massive target such as oil-bearing sandstone, intense and complex transient stress situations develop within both the projectile and the rock or sandstone against which it is striking. Usually the struck rock fails, the missile or projectile penetrating into the rock to some depth where it comes to rest or is forcibly ejected from its burrow by expansion of a plug of target material compressed in front of it. When the impact velocity is very high, the projectile itself may fail, breaking apart or becoming distorted; this situation is not considered here, the discussion being limited to nondeforming projectiles. Many experimental studies'.' have been carried out to determine the nature of the mechanics of crater formation and the salient features of the forces coming into play, some of the earliest studies being the French Army experiments performed at Metz between 1835 and 1845.' The stratagem in most instances has been to make a post-mortem examination of the crater, measuring volume and depth of penetration and deducing force relationships from these observations rather than performing the more difficult (usually almost impossible) feat of measuring stresses during penetration. In many materials, the force acting during penetration of the projectile is found to be the sum of two components—(1) a constant force, independent of the velocity, representing some inherent strength of the target material; and (2) a component, proportional to the square of the velocity, representing inertial forces. For such materials, the average force per unit area acting on the projectile at any instant while it is in motion and being decelerated may be written F/A = a + bv2 . . . (1) where v is the velocity of the projectile at that instant, A is the cross-sectional area of the penetrating projectile taken normal to its trajectory, and a and b are constants which are dependent upon the target material and the shape of the projectile. It follows that the total penetration s is given by .........(2) where v, is the velocity of the projectile when it just strikes the target. Values of a and b for spherical projectiles impacting in a loose sand-gravel mixture and compacted earth were obtained in the Metz experiments. For sand-gravel, a and b are 620 psi and 0.0115 (psi) (ft/sec)', respectively; and for compacted earthworks, a and b are 432 psi and 0.0008 (psi) (ft/sec)'. Figs 1 and 2

By C. W. Davis

THE name fuller's earth, which was derived from its early use in "fulling" or removing grease from woolen goods, is a term that is generally considered to designate mineral matter, containing hydrous aluminum silicates of the clay group, which has a high capacity for removing colors from oils, whether of animal, vegetable, or mineral origin. Fuller's earths are usually dried and may be "tempered" by heating or may be treated with water or reagents to improve their efficiency. For our purpose the term "acid-treated earths" will include those products from the partial decomposition of mineral water by acid which are equal to or more efficient than an untreated fuller's earth from Quincy, Fla., when used in bleaching mineral oil by the "contact" process. In general, the contact process for treating oils consists of heating and agitating a mixture of oil and finely divided adsorbent, the latter being subsequently removed by filtration. The term "adsorbent" is used because, although there has been a great deal of controversy over the mechanism of removal of impurities from oils by mineral matter, there is no doubt that adsorption, which involves the surface of the solid, plays a major part.1 The properties that make fuller's earth useful in the treatment of petroleum products by "percolation" and in the purification of edible oils by the contact process have long been studied, but the comparatively recent adaptation of the contact process to the bleaching of petroleum products has made desirable the further investigation of fuller's earth and other adsorbent earths.

Jan 1, 1929

By R. B. Gavert, David J. Mack

ROOM- and elevated-temperature compression tests were made on the binary 3/2 electron compounds AuZn, CuAu, AgZn, AgMg, AuCd, and NiA1. These compounds possess either the B2 CsC1-type ordered structure or the A2 bee disordered structure represented commonly as ß and ß on equilibrium phase diagrams. In testing at room temperature, cylindrical specimens 0.508 cm by 0.330 cm diam were seated directly on an instron compression load cell (CF 0 to 10,000 lb). At elevated temperatures, testing included a special apparatus with a furnace heat source and a protective atmosphere.' The specimens were strained at a rate of 1 pet per min. The compounds were prepared from 99.99 pet or better high-purity elements. Vacuum and/or argon cover gas was used throughout the mixing, melting, and specimen drawing processes. The generally equi-axed specimen grains varied in size from 0.5 to 1.5 mm for the five different compounds. The stress-strain curves in compression showed

Jan 1, 1968

By AIME AIME

THE 122d meeting of the Institute was held in the Lake. Superior Copper and Iron Country Aug. 20 to Sept. 3, 1920 with an approximate registration of 1100 members and guests. This is the 'first visit of, the Institute to this vicinity since 1904 although previously it held meetings there every six or, seven years. 'The eastern party assembled at Buffalo and sailed on the S. S. "Tionesta ". on Friday morning, Aug. 20, arriving at Houghton, Mich., Monday, Aug. 23. En route stops were made at Detroit, where sightseeing auto trips were taken, and at Mackinac Island, where a short stop permitted a visit to the picturesque and historic Fort Mackinac.

Jan 1, 1920

By T. K. Redden

Protective coatings based on the formation of a surface coating of nickel aluminide (NiAl) were applied to the nickel-base superalloys IN 100, SEL 15, and U-700. Coated specimens were exposed to an oxidizing environment at temperatures between 1600 and 2200 F for times up to 1000 hr. The oxidation resistance and stability of the coating were evaluated by weight gain measurements, metallographic examination, and X-ray diffraction study of surface oxides and coating. The composition of the coating and diffusion zone was determined by electron microprobe traverse of samples before and after high-temperature exposure. Intermediate phases formed in the coating and diffusion zone were identified by X-ray diffraction in situ and after electrolytic extraction. The outer coating was found to consist of the inter-metallic compound, NiAl, while the diffusion zone contained MC, M23C6 or M6C carbides, and a phase in a matrix of NiAl + Nidl. Oxidation resulted in formation of an A1203 n'ch scale containing some Tz02. Depletion of aluminum during oxidation resulted in degradation of the outer coating to Ni3Al and the nickel alloy matrix. Diffusion of aluminum into the base metal was found to be slight and did not influence coating life significantly. The o formed in the diffusion zone during coating decomposed during elevated-temperature exposure to form stable carbide phases characteristic of the base metal. Diffusion zone phase changes were found to have no effect on the life of the aluminide coating in the oxidizing envzron?nent. THE oxidation resistance of many high-strength nickel-base superalloys is inadequate for extended exposure at temperatures above about 1600°F. In addition, some applications for these materials require that they be exposed to environments containing sulfur compounds and sodium salts which can cause surface attalk known as sulfidation or hot corrosion. In order to provide the necessary corrosion resistance to the high-strength alloys, protective coatings based on an aluminizing process have been developed. These processes, usually based on a pack cementation technique, result in the formation of a NiAl-rich outer coating layer either during the coating process or by a subsequent diffusion treatment. The performance of the aluminide coatings is affected by interactions between the coating layer and the base metal both during the coating process and during subsequent exposure at elevated temperatures. Knowledge of these interactions is required to guide the development of coatings capable of longer life and improved reliability. Goward et al.' recently reported the metallurgical factors which influence coating per- formance on MAR-M200. The present work is concerned with correlating the interactions and performance of coating compositions on several representative materials. EXPERIMENTAL PROCEDURES Materials. Three cast nickel-base superalloys which are used for turbine buckets in air-breathing engines were studied: IN 100, U-700, and SEL 15. Their chemical compositions are given in Table I. The alloys were vacuum-induction-melted and cast to slabs approximately 0.3 in. thick from which rectangular specimens 0.25 by 0.5 by 1 in. were machined. Coating Procedures. The machined specimens were coated by CODEP processes which were developed at the author's laboratory. These are based on pack cementation in various media to deposit either aluminum or aluminum in combination with titanium. The coating process which deposits only aluminum is designated CODEP-C, while the CODEP-D process deposits titanium in combination with aluminum. The CODEP-D process was applied only to IN 100. Both CODEP processes are applied at 1950" or 2000°F for 4 hr without need for a subsequent diffusion treatment. An outer coating about 1 mil in thickness is produced by these processes. Test Procedures. Coated specimens were exposed to static oxidation for periods ranging from 24 to 1000 hr at temperatures of 1600" to 2200°F. Terminal weight gain measurements and visual examination were used to evaluate oxidation resistance. including oxide spalling and coating failure. Both as-coated and exposed specimens of each alloy were studied by metallographic examination, electron microprobe analysis (EMA), and X-ray diffraction analysis either of the exposed surfaces or of phases extracted from the coating and diffusion zone. RESULTS As-Coated Condition. The microstructures of as-coated conditions were generally similar, irrespective of base materials or the particular coating process. They are typified by IN 100 coated by CODEP-D as shown in Fig. 1. The predominately single-phase outer layer, area A, Fig. 1, was identified by X-ray diffraction as the intermetallic compound NiA1. The NiAl zone extended inward to the original base metal interface. The diffusion zone, area B, Fig. 1, included carbide phases, a lamellar phase oriented perpendicular to the base metal surface, and a matrix phase consisting of a mixture of NiAl and Ni3Al. The phases in the diffusion zone were electrolytically extracted using a 10 pct HCl in methanol solution at approximately 1.3 amp per sq cm. The extracted phases were found to be M6C, MC, or M=C6 carbides and o as shown in Table I1 for each of the alloys. The d spacings from a typical diffraction pattern are

Jan 1, 1969

By executive order of the President, dated June 25, 1918, the investigation of matters relating to gas warfare, which had been initiated by the Director of the U. S. Bureau of Mines early in 1917, and had been continuously maintained and improved since, that time, was transferred to the recently created Division of Gas Warfare of the War Department. On the occasion of this transfer, both the President and the Secretary of War took occasion to speak most highly of the efficient service that had been rendered by the Bureau of Mines. It gives us great pleasure to reproduce here a letter from the President and from the Secretary of War, bearing on this subject and also to append a brief review of the work of the Bureau of Mines, prepared by its Director, Mr. Van H. Manning. The White House, Washington. June 26, 1918. MY DEAR MR. MANNING: I have had before me for some days the-question presented by the Secretary of War involving the transfer of the chemical section established by you at the American University from the Bureau of Mines to the newly organized Division-of Gas Warfare in which the War Department is now concentrating all the various facilities for offensive and defensive gas operations. I am satisfied that a more efficient organization can he effected by having these various activities under one direction and control, and my hesitation about acting in the matter has grown only out of a reluctance to take away from the Bureau of Mines a piece of work which thus far it has so effectively performed. The Secretary of War has assured me of his own recognition of the splendid work you have been able to do, and I am taking the liberty of enclosing a letter which I have received from him, in order that you may-see how fully the War Department recognizes the value of the services. I am to-day signing the order directing the transfer. I want, however, to express to you my own-appreciation of the fine and helpful piece of work which you-have-done, and to. say that this sort of team work by the bureaus outside of the direct war-making agency is one of the cheering and gratifying evidences of the way our official forces are inspired by the presence of a great national task. Cordially yours, Dr. Van. H. Manning, WOODROW WILSON. Chief, Bureau of Mines, Department of the Interior. War Department, Washington, June 25, 1918. MY DEAR MR. PRESIDENT: In connection with the proposed transfer of the chemical section at. American University from the Bureau of Mines to the newly constituted and consolidated Gas Service of the War Department, which you are considering, I am specially concerned to have you know how much the War Department appreciates the splendid services which have been rendered to the country and to the Army by the Department of the Interior, and especially by the Bureau of Mines under the direction of Dr. Manning. In the early days of preparation and organization, Dr. Manning's contact with scientific men throughout the country was indispensably valuable. He was able to summon from the universities and the technical laboratories of the country men of the highest quality and to inspire them with enthusiastic zeal in attacking new and difficult problems which had to be solved with the utmost speed. I do not see how the work could have been better done than he did it, and the present suggestion that the section now pass under the direction and control of the War Department grows out of the fact that the whole subject of gas warfare has assumed a fresh pressure and intensity, and the director of it must have the widest control so as to be able to use the resources at his command in the most effective way possible. The proposal does not involve the disruption of the fine group of scientific men Dr. Manning has brought together, but merely their transfer to General Sibert's direction. Respectfully yours, NEWTON D. BAKER.

Jan 9, 1918

By Bennett Bates

A PAPER presented in South Africa' during 1925 by H. A. White gave a formula to express the efficiency of classification. The formula was originally developed by H. W. Newton of The Dorr Co. The derivation of this formula is as follows: Where E = Over-all efficiency of classifier Eu = Efficiency with respect to sand discharge Eo = Efficiency with respect to overflow I = Tons feed to classifier (input) 0 = Tons overflow U = Tons sands (underflow) i = Fraction of oversize in classifier feed o = Fraction of oversize in overflow u = Fraction of oversize in sands

Jan 5, 1927

By J. L. Craig, C. L. Edwards, M. D. Harper, J. M. Ray

The Los Alamos National Laboratory executed 19 intermediate scale cratering experiments in oil shale at the Colony Mine in Garfield County, Colorado. These experiments have led to a better under- standing of fracture characteristics and fragmentation of & - oil shale by use of a conventional high explosive. Geologic site characterization included detailed mapping, coring, and sample analyses. Site-specific geology was observed to be a major influence on the resulting crater geometry. The joint patterns at the experimental site frequently defined the final crater symmetry. Secondary influences included vugs, lithology changes, and grade fluctuations in the local stratigraphy. Most experiments, in both the rib and floor, were conducted to obtain data to investigate the fragmentation results within the craters. The rubble was screened for fragment- size distributions. Geologic features in proximity to the explosive charge had minimal effect on the rubble due to the overpowering effect of the detonation. However, these same features became more influential on the fracture and rubble characteristics with greater distances from the shothole. Postshot cores revealed a direct relationship between the grade of the oil shale and its susceptibility to fracturing. The Colony Mine experiments have demonstrated the significant role of geology in high explosive/oil shale interaction. It is probable that this role will have to be considered for larger applications to blast patterns and potential problems in retort stability in the future of oil shale development.

Jan 1, 1983

By Benjamin Gi ldersleeve

Uniquely colored, thin-bedded quartzite is quarried between Crossville and Crab Orchard in Cumberland County, Tenn. It is produced in all sizes up to the limits of transportation from beds usually ranging in thickness from less than 1/2 in. to 6 in. The stone is very resistant to wear and weathering and is marketed throughout the country for many different purposes in exterior and interior construction. The annual production exceeds 36,000 tons, valued at nearly $1,000,000.

Jan 1, 1950

C. Edward Stafford, Chester, Pa.:—Doring all my business life, I have been engaged in the manufacture of Bessemer and open-hearth steels, but, during my long connection with the Shoenberger Steel Co. of Pittsburg, I had some experience in the manufacture of high-grade puddled iron for horseshoes, and in making, by Dr. Otto Wuth's process, extremely pure, low-phosphorus puddled blooms (analyzing from 0.005 to 0.01 per cent. of phosphorus and sulphur), which were melted with low-phosphorus pig-iron in acid open-hearth furnaces, to make extra locomotive fire-box steel. I have also seen the Danks puddlers in operation at different times and places, notably where they were most successful, at the Otis Steel Works, Cleveland, Ohio; then under the management of our friend, Mr. S. T. Wellman. These Danks blooms were made solely for open-hearth melting-stock, to which they were well adapted. (The unavoidable presence of bits of ore-fix imbedded in the mass of the metal always prevents the profitable manufacture of merchant iron from Danks' blooms.) With the experience just described, I was to some degree in position to value fairly the means, methods and results of Mr. Roe's mechanical puddling from the metallurgical or technical and economic points of view, when given an opportunity by Mr. Roe to see his puddling-furnace or machine in operation in Pottstown, Pa. Briefly, the furnace, with water-cooled bottom, is rectangular in plan, about 20 by 8 ft. in the clear, suspended by trunnions at the middle of the long sides, at a height of 17 or 18 ft. above the general level. The oscillation (65" each way from the vertical) is accomplished by geared segments (attached to the downward-projecting side or trunnion-plates) with which engage pinions driven by a reversing engine. The whole section

Jan 1, 1906

The following list comprises the names of those persons who became members during the period May 10, 1919, to June 10, 1919. ALAYZA, CARLOS Box 850, Lima, Peru, S. A. BALLARD, P. A Surveyor, Midwest Refin. Co., Custer, So. Dakota. BARNEBL, A. J., JR.... Mech. Eng., The Dorr Co., 101 Park Ave., New York, N. Y. BILLINGS, GOODSELL Platteville, Wis. BRONSON, C. B., Mech. & Met. Engr., New York Central Lines, Room 1520, Grand Central Terminal, New York, N. Y. BUNCE, E. H Met., The New. Jersey Zinc Co., Palmerton, Pa. CHARLTON, D. E. A., Editorial Staff, Engrg. & Mm. Journals 10th Ave. & 36th St., New York, N. Y. DAVIS, JOHN N., Supt. of Mills, Engels Copper Min. Co., Engelmine, Plumas Co., Cal. DUKES, GLENN H., Chief Engr., The Sunday Creek Coal Co.,1001 Outlook Bldg., Columbus, Ohio. ERICKSON, ARTHUR .... Engr., United Smelt., Refin. & Min. Co., Mldvale, Utah. FLYNN, A. E Supt., Rand Consolidated Mines, Ltd., Goudreau, Ont., Canada. HIBBARD, WALTER R 63 Ashley St., Bridgeport, Conn. HOBSBAWN, I. BERKWOOD, Cons. Tech. Chem., Messrs. Gibbs. & Co., Valparaiso, Chile, S. A.

Jan 7, 1919

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By F. C. NINNIS

AT THE Belmont mill, the pregnant solution is de¬livered to a 30 by 10-ft. tank, from which it is pumped to three Merrill clarifying presses of the sluice-bar type, whence it flows through the meter to the precipitation supply tank. ?The solution for precipitation is pumped by a 10 by 10-in. Aldrich triplex pump and delivered through a 6-in. line to the forty-eight triangular frame Merrill presses at the head of the mill. Zinc dust is fed in at the pump suction and the solution precipitated to 0.01 to 0.02 oz. silver. The solution flowing from the presses is tested at 1-hr. intervals with sodium sulfide. All solution is precipitated to the same value; 4J tons of solution are precipitated for each ton of ore treated and the presses are cleaned every 15 days. The product from the presses' is dumped into steel cars having steam-jacketed bottoms, in which they are dried until the moisture content is between 15 and 17 per cent. when 8. per cent. of soda and .3 per cent. of borax are added and the contents thoroughly mixed. In the case of special clean-ups, the precipitate is tested and the flux is added to meet the requirements.

Jan 1, 1921

By B. C. Craft

The outstanding event of the year 1932 in this area was the intensive drilling activity in the Zwolle field of Sabine Parish, Louisiana. More new development work was undertaken and completed than during the previous year. This was due in part to the increased price of oil and in a Includes 19 parishes: Beauregard, Bienville, Bossier, Caddo, Caldwell, Catn-houla, Claiborne, Concordia, DeSoto, Grant, Lincoln, Morehouse, Natchitoches, Ouachita, Red River, Richland, Sabine, Union, Webster. B H. K. Shearer: Oil and Gas Development in South Arkansas, North Louisiana and Mississippi in 1931. Trans. A. I. M. E. (1932) 98, 159. a Includes 14 counties: Ashley, Columbia, Dallas, Drew, Hot Springs, Lincoln, LnFayette, Little River, Miller, Ouachita, Pike, Sevier, Scott and Union. * H. K. Shearer: Oil and Gas Development in South Arkansas, North Louisiana and Mississippi in 1931. Trans. A. I. M. E. (1932) 98, 159. part to the fact that production is below local market demands. Exploration during 1932 resulted in the discovery of a new oil field and a new gas

Jan 1, 1933

By W. H. Adams

Shortly after becoming one of the van-guard of mine-developers in the State of Virginia, during the year 1883, I called the attention of the Institute to certain deposits of pyrites, which have been largely worked since. In all cases these deposits are covered with iron-ore (limonite), extending 40, 50 or 60 feet from surface to water-level. The several classes of brown iron-ores are found almost continuously along a prominent ridge of mineral-bearing slates, which can be traced from the James river northeasterly to the North Anna, the Rappahannock and the Potomac rivers, crossing the counties of Louisa, Spottsylvania and Stafford. Outcrops are plainly discoverable from end to end of this belt, also, in places, to the right and left of it, and at intervals there are evidences of workings, some of them for known purposes and others of unknown age and meaning. These old workings have an interest aside from the minerals they may contain or may have yielded. I have been engaged during the past five years in the collection of facts concerning them, which might determine definitely the site of those iron-furnaces, placed by tradition within reach of " the towne called Germanna," which were the first ever built in this State or on this continent. The events which led to the establishment of this important industry are sufficiently narrated in a paper written by Mr. R. A. Brock, Secretary of the Virginia Historical Society, and printed in the Proceedings of the National Museum, 1885, page 77, from which I quote the following : " To Virginia, the first of the English settlements in America, belongs the honor of inaugurating within her limits, as a colony, that most important industry, iron manufacture. "The London Company contemplated a variety of manufacturing enterprises from the very beginning of its authority; prominent among them was that of iron. In 1610 Sir Thomas Gates testified before the council of the Company at London, that in Virginia ' there were divers minerals, especially iron-oare,' lying upon the

Jan 1, 1892

By R. F. Shurtz

R. Duval (Mining Engineer, Ancien eleve de PEcole Polytechnique, Paris, France) I do not agree with the Eq. 3, reading: m =1/100- [(0.214x30.4) + (0.7B6 x0.00)] =6.5pct CaO If 0.214 and0.786 were proportions by weight, the equation would represent the well known mixtures law of the conventional arithmetics and 6. 5 pct CaO would be the correct average content. But it is not the case as the author states: "In samples consisting of single grains of mineral, those grains must, as already mentioned, be either of dolomite or magnesite. Since 78.6 pct of the deposit consists of magnesite and 21.4 pct of dolomite (excluding for present purpose the presence of other minerals), for any single grains picked at random the probability will be 0.214 that is it dolomite and0.786 that is it magnesite. In 1000 such samples the expected numbers of dolomite and mapesite grains will be 214 and 786 respectively." 0.214 and 0.786 would be proportions by weigbt under the necessary condition that all grains of dole mite and magnesite should have an identical weight. Obviously it is not the case, as the specific gravities are not the same for mapesite and dolomite and the volumes of the grains are different. Furthermore, because of these differences the conditions for a random sampling are not fulfilled and we are not authorized to state that the probabilities are, respectively, 0.214 and 0.786. The author however makes a simple application of Eq. 1: M = 1/n— ? fi x i . n Should we deduce that this relation is wrohg? Not at all, but when applying Eq. 1 you must not overlook what it actually. means. Eq. 1 gives a definition of the arithmetic mean of a total of n observed values Xi and nothing else. But the average conteht of a deposit has not the same significance. It is the ratio between the weight of concerned mineral in the deposit and the total weight of the deposit. As from 1000 particles the 214 of dolomite and the 786 of magnesite have not the same weight, the two definitions do not concur, and when applying Eq. 1 the result is an arithmetic mean of figures which has no connection with what is named average contentof a deposit. The situation is similar to the calculation of an average velocity. If a car travels a first mile over at 30 miles per hr and a second mile over at 60 miles per hr, when applying formula 1 you find as average velocity for the 2 miles: 30+60 ------- - 45 miles per hour. Many people calculate in this way and they do not realize that a mistake is involved. In fact the definition of he average velocity for the 2 miles is the quotient of the distance of 2 miles by the time (in hours) necessary for 2 miles travel, i.e.: 2 ---------- = 40 miles per hr. 1 + 1 30 60 In other words, the average volocity wanted is not the arithmetic but the harmonic average of the two velocities. The above mentioned bias in the calculation of the average contents of deposits is frequent, even in the assessments made by experienced engineers and is independant of what is named the sampling error. In order to supress the bias and to be able to use Eq. 1, you must apply a correction. An example on the subject can be found in an article by Duval et al. in the January 1955 issue of the ''Annales des Mines" (French), page 19. R. F. Schurtz (Author's Reply) Mr. Duval's position is quite correct. The proportions shown for dolomite and magnesite., respectively, of 0.214 and 0.786 are, in fact, proportions by weight uncorrected for specific gravity. In our day to day operation of producing magnesite from these mines at a very substantial rate, we do not normally make corrections for the difference between the specific gravity of dolomite and that of magnesite. If these corrections are made in Eq. 3 as shown in my article, then the numbers of grains turn out to be in proportions of 0.226 dolomite and 0.774 mapesite instead of the values actually shown in the equation. For the purposes of our work, and in view of the inherently low accuracy of the data, this correction was not deemed worthwhile making.

Jan 1, 1961

By Francis A Thomson

Montana Bureau of Mines and Geology, Montana School of Mines, Butte, Mont Francis A Thomson, President. The Bureau of Mines and Geology was formerly known as the Bureau of Mines and Metallurgy. A list of publications will be sent upon request¬ A series of six Bulletins and five Memoirs liave been issued by tlie Bureau, as well as several miscellaneous contributions Where the price is not indicated in tlie following selected list of those publications which are now available, the publications are presumably distributed gratis: Bulletin 3, Mechanical ore sampling in Montana, by H B Pulsifer (1920); 6, Geology and ore deposits of Bannack and Argenta, Montana, by P. J Slienon, 50 cents, Memoir 1, The Kevin-Sunburst and otlier oil and gas fields of the Sweetgrass Arcli, by E S Perry (1929), 2, Natural gas in Montana, by E S Perry (in preparation), 4, Tlie geologic structures of western Montana, by C H Clapp and others (in preparation), 5, Placer mining possibilities in Montana, by O A Dingman (1932).

Jan 1, 1933

By Evan Evans

WITH the expiration on April 30, 1941, of the agreement between the anthracite operators and the United Mine Workers of America, a new agreement was entered into, providing for a general wage increase of 7 1/2 per cent effective May 1, to be brought to a total of 10 per cent on Oct. 1. Contract rates were increased from the rates established under the agreement of September 1923, and hourly rates were raised above the agreement of May 1936 as modified from the eight-to seven-hour day in May 1937. The new rates are to be in force for the duration of the agreement, ending April 30, 1943.

Jan 1, 1942