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By Dr. O’Neil Thomas J., Donald W. Gentry

It was a western truism that more money was made from selling mines than from buying them, just as it was accepted that many a good mine had been spoiled by working it. from R. E. White, "The Mining Town," Alta California August 18,1873 INTRODUCTION One of the most important aspects of mineral enterprises of US corporations is the influence of the depletion allowance on cash flow. This allowance permits mineral producers to claim sizable federal income tax deductions not available to other industries, and these deductions significantly increase cash flows in mining. In the past several years the minerals depletion allowance has come under increasingly heavy fire from many sectors as a tax loophole that deprives the federal government of large amounts of revenue. One estimate of the loss of tax dollars in 1968 was $2.25 billion due to depletion deductions and intangible expenses in the oil industry. Largely on the basis of such arguments, the Tax Reform Act of 1969 reduced percentage depletion rates for a number of minerals, and the Tax Reduction Act of 1975 totally eliminated statutory depletion for most oil and gas. In regard to percentage depletion for hard minerals, the federal government has estimated its resulting loss of revenue at $1.75 billion for 1980. The TEFRA legislation of 1982 further reduced the statutory depletion allowance available to iron ore, coal, and lignite beginning in 1984. Thus, it is clear that minerals engineers and managers should have a thorough knowledge of the origin, evolution, justification, and computational procedures relating to the depletion allowance. ORIGIN AND EVOLUTION OF THE DEPLETION ALLOWANCE

Jan 1, 1984

By Charles D. Walcott

The following acts of the Directors are reported for the information of members At a meeting held June 20, 1907, Dr. Charles D. Walcott, Director of the U. S. Geological Survey, Washington, D. C., having been recommended by unanimous vote of the Council, was unanimously elected an Honorary Member of the American Institute of Mining Engineers, in recognition of his personal services to American geology, and of his generous co-operation with this Institute, to the Transactions of which he has not only himself made valuable contributions, but has also encouraged the preparation of such contributions by the members of the U. S. Geological Survey under his charge, his liberal policy in this respect having gone so far as to permit the preliminary publication by the Institute of important results reached by the geologists of that Survey, even before their final and full publication as public documents. This wise and generous course has not only brought the U. S. Geological Survey into intimate and sympathetic relations with the mining industry of the world, but has also enriched the Transactions of the Institute, especially in the department of the science of ore-deposits, with many valuable papers. At a meeting held Jan. 14, 1908, Mr. Charles Kirchhoff was unanimously re-elected a Trustee of the United Engineering Society, to serve for a second term of three years. At a meeting held Feb. 18, 1908, directly after the adjournment of the annual meeting of the Institute, the following officers were elected for the ensuing year: President, James Gayley: Vice-President, James Douglas; Secretary, R. W. Raymond; Treasurer, Frank Lyman.

Mar 1, 1908

By Paul Averitt

In spite of recent trends in the United States toward construction of steam generating plants near mine mouths, and toward use of high-voltage direct current for long-distance transmission of electricity, coal in substantial amounts is being transported over relatively long distances to serve specific needs. As coal is a low-cost bulk commodity which is more suitable for use near the point of origin, some of these long hauls are of considerable interest because they show what can be done under the pressure for more and more coal to support industrial and economic growth. Japan has an Insatiable Appetite for Coal Perhaps the longest U.S. coal journey begins in the east Appalachian Basin of southern Pennsylvania, eastern West Virginia, and southwestern Virginia. High-quality coking coal mined in these areas is shipped by rail to Baltimore, Md., and to Hampton Roads, Va., where the coal is reloaded on freighters for shipment primarily to western Europe and Japan. In 1967, shipments of coal to western Europe totaled 19 million tons, and shipments to Japan totaled 12 million tons. Japan also imports coal from Australia, the U.S.S.R., Canada, Poland, the People's Republic of China, and to a lesser ex- tent from several other countries. In an effort to solve long-term needs, Japanese steel interests have contracted for the purchase from the Kaiser Steel Corp. of 51 million long tons of coking coal over the period 1970 to 1985. The coal will come from the Kaiser Steel Corp. mine near Fernie, British Columbia. This arrangement will reduce Japan's future dependence on Appalachian Basin coal.

Jan 10, 1969

By H. M. Morse

Mississippi, during the year 1941, experienced the greatest diversity of oil activity since the beginning of oil interest in the state—core tests for exploration, core tests for sulphur, continued drilling at Tinsley for production, and wildcatting, which brought to light two new oil fields and two new salt domes. There were 45 wildcat wells drilled in 1941, which showed greater results and findings geologically than the 85 drilled in 1940. Tinsley Oil Field (Yazoo County).—The Tinsley oil field, with its boundaries fairly well defined now, is 8 miles long and 3 miles wide at its widest point. During the past year 213 producing wells were completed, which brought the total number of producers in the field by the end of 1941 to 325 wells. Seven producing sands have been logged, with a total average thickness of 30 ft. of oil sand. The producing formations are the Selma, Eutaw and Tuscaloosa. The average total depth of the wells is 5012 ft. The average gravity of the oil is 35.4°. Production for 1941 was approximately 15,500,000 bbl. of oil. Vaughan-Pickens Oil Field (Yazoo County).—At the end of 1941 only three wells were Producing in this field, the fourth having been abandoned. The total production for the field for the year was approximately 250,000 bbl. of oil. The producing sand is the Wilburn, in the Eutaw formation. Cary Field (Sharkey County).—The British American Oil Producing Co. completed, on Sept. I, 1941, its F. B. Houston No. A-I well, sec. 23, T. 11 N., R. 7 W. It is

Jan 1, 1942

Shooting Soot from Stacks In the DuPont magazine of June, 1916, S. R. Russell describes a method of cleaning large smoke or kiln stacks which he calls "simple,. economical- slid-most efficient" and-which- he -says can- be used in either-lined or unlined stacks, brick or steel, without fear of injury to the stack or lining. He gives the following specific directions: "The gun can be made out of air old piece of shafting about 4 in. in diameter and 14 to 16 in. long. Bore a hole 1 ¾ in. in diameter and 10 in. long in the center of the piece. Then bore a small horizontal hole ¼ in. in diameter through the piece-to the bottom of the center bore. This hole serves as a touch hole for inserting the fuse. "The-whole thing can be mounted on a pedestal about 6 in. in diameter so that it will stand in an upright position. "The -method of operation is as follows: Pour some FFF Blasting Powder into the mouth of the cannon to about 2 in. from the top. Tamp to the collar with dry clay. , A short piece of fuse is inserted in the touch hole and in contact with the main powder charge. Open the flue door at the bottom of the stack, set the cannon on the bottom and in the center of the stack, light the fuse and close the flue door. "The explosion shakes and loosens the soot adhering to the sides, causing it to fall to the bottom. It can' then be removed through the flue opening.

Jan 9, 1916

By H. M. Morse

Mississippi, during the year 1941, experienced the greatest diversity of oil activity since the beginning of oil interest in the state—core tests for exploration, core tests for sulphur, continued drilling at Tinsley for production, and wildcatting, which brought to light two new oil fields and two new salt domes. There were 45 wildcat wells drilled in 1941, which showed greater results and findings geologically than the 85 drilled in 1940. Tinsley Oil Field (Yazoo County).—The Tinsley oil field, with its boundaries fairly well defined now, is 8 miles long and 3 miles wide at its widest point. During the past year 213 producing wells were completed, which brought the total number of producers in the field by the end of 1941 to 325 wells. Seven producing sands have been logged, with a total average thickness of 30 ft. of oil sand. The producing formations are the Selma, Eutaw and Tuscaloosa. The average total depth of the wells is 5012 ft. The average gravity of the oil is 35.4°. Production for 1941 was approximately 15,500,000 bbl. of oil. Vaughan-Pickens Oil Field (Yazoo County).—At the end of 1941 only three wells were Producing in this field, the fourth having been abandoned. The total production for the field for the year was approximately 250,000 bbl. of oil. The producing sand is the Wilburn, in the Eutaw formation. Cary Field (Sharkey County).—The British American Oil Producing Co. completed, on Sept. I, 1941, its F. B. Houston No. A-I well, sec. 23, T. 11 N., R. 7 W. It is

Jan 1, 1942

By E. M. Baroody

MUCH information on intermetallic diffusion has been obtained in experiments in which two volumes, initially at different uniform concentrations, are maintained in contact at an interface which is plane, or nearly so. Concentration-distance curves are obtained after suitable times, and analyzed on the basis of a one-dimensional form of Fick's law In early work the linear equation to which Eq. 1 reduces when D is independent of concentration was used. However, when the initial concentrations c, and c, are appreciably different this simplification is often unjustified, and the suggestion by Matanol in 1933 of a way of avoiding it was welcomed. Matano's paper was based on work done as early as 1882 by Boltzmann.2,3 In 1938 Rhines and Meh14 reported an extensive investigation of systems in which the diffusion coefficient depends strongly on concentration, and included a detailed description of the Matano-Boltz-mann method. To a large degree, this description represents the formal method as it is understood and applied today, most later discussions having emphasized thermodynamic and mechanistic aspects of diffusion. Exceptions are the comments of R. V. Churchill, contained in a paper by Ham, Parke and Herzig,5 and the papers by Hall8 and by Kirkaldy.7 More discussion appears necessary since some aspects of the problem remain obscure. Better computational procedures are also needed. The common method, involving graphical determination of slopes and areas, is inconvenient and makes the estimation of errors difficult. Background of the Matano-Boltzmann Method Eq. 1 is to be considered along with initial and boundary conditions. Take the origin of x at the

Jan 1, 1958

R. W. Balluffi (Atomic Energy Div., Sylvania Electric Products Inc., Bayside, N. Y.)—Since porosity is known to form in the copper side of Cu-Ni couples during diffusion24,25 it is of importance to consider this factor in interpreting the large variations of chemical diffusivity with copper concentration reported for this system. The presence of porosity may affect the measurement of D in two ways: 1—density changes in the couple invalidate the usual solutions of the diffusion equation, and 2—the pores may act as short-circuiting paths when transport through the vapor or along internal surfaces is appreciable or else as open circuits when these effects are small. The error produced by the first effect may be estimated by a graphical analysis. Fig. 8 shows the porosity generated in the copper side of the Kirkendall interface of a pure nickel vs pure copper couple after diffusion for 350 hr at 1040°C in hydrogen. In Fig. 9 the actual diffusion curve which would be obtained by the usual slicing technique is shown as a solid line drawn to the same scale (from the data of da Silva and Mehl"). The amounts of porosity (obtained by lineal analysis) and of nickel are graphically represented by the hatched areas. The standard solutions of the diffusion equation are valid only when all volume elements of unit length and unit cross section contain equal numbers of atoms." It is possible to correct the experimental curve to satisfy this condition by shrinking the couple in the direction of diffusion in such a way as to eliminate the porosity.* The corrected diffusion curve obtained after

Jan 1, 1954

By G. R. Speich, S. A. Kulin

R. C. Shnay (Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada)-—The authors are to be congratulated on an interesting and informative paper. However, several questions arise when the isothermal formation of martensite .is considered in relation to the formation of bainite at temperatures near the M, point. The reactions in an alloy and in a plain carbon steel would appear to be comparable; and in the course of a recent investigation of the austenite-bainite transformation in a plain carbon steel,Ia the writer has obtained data at temperatures above and below the M, point. These data are in some respects similar to those of the authors and a comparison would seem justified. The steel used in this investigation had the nominal composition: C, 0.80 pct; Mn, 0.20; and Si, 0.20. The course of the transformation was followed by the use of a magnetic balance. The magnetic moment of the specimen as determined by this instrument is directly proportional to the percentage of the total volume of the specimen which has transformed to bainite. ~lf specimens were austenitized at 1850°F for 4 hr, quenched to the transformation temperature, and quickly transferred to the magnetic balance. Readings were taken at regular intervals until the transformation had stopped. A typical transformation curve is shown in Fig. 9. The preliminary curve preceding the S-shaped curve was found at all temperatures above the M, to around 600°F. Both the extent of this preliminary curve and the time interval between it and the S-shaped curve were found to decrease with increasing temperature as was suggested by Davenport and Bain.14 Therefore,

Jan 1, 1953

E. R. Rice, Wickenburg, Ariz. (communication to the Secretary*):—While this paper is primarily intended as a discussion of Mr. Riter's, I think it will be best to indicate my criticism by describing my own field-methods. It has been my experience that, for ordinary work, the regular transit-book is to be preferred to the card-system for recording notes. This is specially true when computations in the field are required, for it is then necessary to have at hand the total latitudes, departures, ancl elevations. Moreover, the transit-book is easier to carry and manipulate in wet or cramped places, and is not as liable to damage as the loose leaf or card. I use a regular transit-book in the field, and then copy my notes, sketches, etc., in an o5ce-book, entering also the latitudes, departures, and other reductions. These values are then copied into the field-book, securing a duplicate record, in case either book should be lost or mislaid. In the field-book, the notes are entered on the left-hand, and the sketches and remarks on the right-hand page. The next two pages are left blank for the latitudes, departures, bearings, reduced distances, etc. Of course, the notes for the different parts of the mine are entered in the field-book in the order in which they are surveyed; but in the they are entered systematically. It has been my experience that the system of keeping notes used by a surveyor, is particularly adapted to the needs and temperament of the individual. Otherwise, he would not be

Jan 1, 1912

E. A. HOLBROOK,*Urbana, Ill.-To those who have followed the development of powdered coal two questions often occur. First, as to the moisture in the coal. In Illinois we recognize that the bituminous coals contain about 12 to 15 per cent. of what we call "contained moisture," that is, the moisture is present in the coal although this may appear absolutely dry and dusty. In addition, the surface moisture may be present in any amount. I would like to ask what is the relative effect of these two forms of moisture upon the work of pulverizing. Does Mr. Collins refer to the contained moisture or to the surface moisture in estimating the degree to which the coal must be dried? H. R. COLLINS.-In the lignite coals, of which this country possesses a great deal and is beginning to develop them to considerable extent, the "contained" or "combined" moisture does not .trouble us; we have no difficulty in reducing lignites to a high degree of fineness. But when dealing with bituminous, sub-bituminous, or semi-bituminous, we, prefer to reduce the combined moisture as well as the hydroscopic moisture as far as possible. We have recently put into operation, at a plant, furnaces and boilers consuming the lignite from northern New Mexico, which contains between 4 and 5 per cent. moisture as we pulverize and burn it. The evaporating efficiencies under the boilers have been so remarkable that we wish to check the results half a dozen times before quoting them. We have also just started two boilers at the Garfield smelter, and have obtained the same high efficiencies.

Jan 11, 1918

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

R. V. Norris, Wilkes-Barre, Pa. (communication to the Secretary*):—Mr. Stow's paper presents a series of arguments, numbered from 1 to 18, concerning the relative merits of four systems of colliery-ventilation, designated by the author as " plain pressure-ventilation," " plain exhaust-ventilation," " obstructed pressure-ventilation," and " obstructed exhaust-ventilation." These arguments are subsequently compared by means of tables, in which an arbitrary numerical value is assigned to each, and which consequently serve no other purpose than that of showing his opinions and predilections, as indicated by his assignment of the said numerical values. In addition to this general summary, Mr. Stow intimates his preference for a fifth method of colliery-ventilation—namely, what he calls " alternating pressure-ventilation," which consists in the running of the fan at "pressure " during working-hours, and as an " exhaust" between shifts—a system which he proposes as, perhaps, new, yet which he thinks deserves recognition " as a standard form." This proposed " standard form " is not to be found in practice ; and I think it would be impracticable in gaseous mines of large extent, for the following reasons: 1. It takes considerable time to reverse the air-current in a large mine; and the reversal would involve a period of complete stoppage of ventilation, long enough to permit serious accumulations of gas. 2. In shaft- and slope-mines, at least, it is hardly practicable to have " every man out of the mine" during the night, and certainly impracticable to avoid keeping mules and horses inside. 3. The doors necessary to divide and direct the air-current are properly hung to open against the air-pressure; and, unless

Jan 1, 1910

By William P. Blake

The salt-beds at Salton, on the line of the Southern Pacific railway, in San Diego county, California, have been successfully worked for many years by the corporation known as the East Liverpool Salt Co., and the salt has been largely used upon the Pacific coast generally and in the interior. But the industry has lately been destroyed by the overflow from the Colorado river. The salt is dissolved, and the waves of the Salton sea now roll 50 ft. above the site of this once thriving and growing business. The salt-bed was evidently the residual accumulation from the waters of an ancient lake, which I have named Cahuilla, from the name by which a large part of the valley—the home of the Cahuilla tribe of Indians—is known. The deposit covered a comparatively small area in the lowest part of the valley, 280 R. or more below the sea-level. This depressed area is now generally known as the Colorado desert, but has a soil of wonderful fertility wherever water can be had on its surface. The deserted beaches, and the water-lines, only a few feet above tide-level, upon the rocks of the bordering mountains, as well as a great abundance of shells in the soil, all bear decisive testimony to the former occupation of the valley by water. The depression is topographically the northern end of the Gulf of California, from which it is now separated by the delta of the Colorado river, extending practically from the mouth of the Gila river across the valley to the coast mountains on the

Jan 1, 1908

First Session BRASS Wednesday, A.M., Nov. 29 Co-Chairmen: CARTER S. COLE, Staff Engineer, A.S.T.M. E. A. ANDERSON, Chief of Metals Section, Research Div., New Jersey Zinc Co. (of Pa.) Second Session BRASS Wednesday, P.M., Nov. 29 Co-Chairmen: D. K. CRAMPTON, Director of Research, Chase Brass and Copper Co., Inc. A. W. TRACY, Metallurgist, The American Brass Co. Dinner and Technical Session Wednesday Evening, Nov. 29 Toastmaster: N. L. MOCHEL, Manager Metallurgical Engineering, Westinghouse Electric Corp. Talk on "How Do Things Look Today and For the Future" RALPH KELLY, President, Baldwin Locomotive Works Technical Paper on Stress-Corrosion Cracking E. H. Dix, JR., Assistant Director of Research and Chief Metallurgist, Aluminum Company of America Third Session BRASS Thursday, A.M., Nov. 30 Co-Chairmen: W. B. PRICE, Director of Research, Scovill Manufacturing Co. A. L. JAMIESON, Associate Metallurgist, Frankford Arsenal First Session LIGHT METALS Thursday, P.M., Nov. 30 Co-Chairmen: L. L. WYMAN, Metallurgist, General Electric Co. M. A. HUNTER, Professor of Metallurgical Engineering and Head, Dept. of Metallurgical Engineering, Rensselaer Polytechnic Institute Second Session LIGHT METALS Thursday Evening, Nov. 30 Co-Chairmen: R. T. WOOD, Chief Metallurgist, American Magnesium Corp. J. D. HANAWALT, Director, Metallurgical Dept., Dow Chemical Co. First Session STEEL Friday A.M., Dec. I Co-Chairmen: H. S. RAWDON, Chief, Division of Metallurgy, National Bureau of Standards A. L. FEILD, Director of Research, Rustless Iron and Steel Corp. First Session MISCELLANEOUS METALS Friday P.M., Dec. I Co-Chairmen: E. A. ANDERSON, Chief of Metals Section, Research Div., New Jersey Zinc Co. (of Pa.) CARTER S. COLE, Staff Engineer, A.S.T.M.

Jan 1, 1945

By C. Goldberg, R. H. Wynne

WHEN using an optical goniometer to determine crystal orientation' it is advantageous to use a preferential etchant so that the etch pits have plane faces which are parallel to crystallographic planes, all of which are of the same "form." "Westinghouse Silver Etch" (WAg), a preferential etch for germanium, is made up as follows: 40 ml of 49.7 pct hydrofluoric acid, 20 ml of 70.7 pct nitric acid, and 40 ml of distilled water containing 2.0 g of silver nitrate. Examination of metallographs of WAg etched surfaces (Fig. 1, for example) indicates that, regardless of crystal orientation, the faces of the etch pits are (111) surfaces. Optical goniometer examination of these WAg etched surfaces also indicates that the faces of the etch pits are (111) surfaces, i.e., all bright reflections are from (111) planes. When using an optical goniometer of the type described by Barrett,' not only (111) reflections from a WAg etched germanium surface but also other reflections of lower intensity will be observed. These latter reflections can cause confusion. We have used an optical goniometer made from a war surplus astrocompass and a galvanometer lamp. The reflections are observed by using the goniometer in a darkened room and letting the reflected light be in- cident upon a piece of white paper. The resulting decrease of goniometer sensitivity enables (111) reflections only to be observed. This in turn permits the crystal orientation to be determined in a matter of minutes, since only two measurements are necessary. The authors wish to acknowledge the help received from R. E. Davis who assisted in making the metallographs and aided the authors in the interpretation of the metallographs.

Jan 1, 1954

The Fifth Annual National Exposition of Chemical Industries will be held in Chicago at the Coliseum and First Regiment Armory during the week of Sept. 22. It was decided to hold the exposition in Chicago, this year, for two reasons: The U. S. Army commandeered the Grand Central Palace Exposition Building in New York, immediately on the close of the last exposition and converted it into a receiving hospital, the use for which is now, happily, nearly ceased; and it was thought that the Exposition would succeed in bringing about a greater development of chemical industries in the Chicago district and the adjoining states. The Advisory Committee of the Exposition consists of: Charles H. Herty, Chairman, Editor Journal of Industrial and Engineering Chemistry; Raymond F. Bacon, Director, Mellon Institute; L. H. Baekeland, Member Naval Consulting Board; W. D. Bancroft, President, American Electrochemical Society; Henry B. Faber, Industrial Filtration Corpn.; Ellwood Hendrick, President, The Chemists' Club; Bernard C. Hesse, Chemist, General Chemical Co.; A. D. Little, President, Arthur D. Little Inc.; Wm. H. Nichols, President, American Chemical Society; R. P. Perry, Vice-president, The Barrett Co.; H. C. Parmelee, Editor Chemical &; Metallurgical Engineering, G. W. Thompson, President, American Institute of Chemical Engineers; T. B. Wagner, Vice-president, U. S. Food Products Corpn.; M. C. Whitaker, President, U. S. Industrial Chemical Co.; and Charles F. Roth and Fred W. Payne. There is also added a special Chicago committee consisting of L. V. Redman, W. D. Richardson, A. V. H. Mory, Carl S. Minor, F. W. Willard, and Wm. Hoskins; the managers, as in the past, are Charles F. Roth and Fred W. Payne.

Jan 6, 1919

By Alan Stanley

R. T. Hukki (Finland Institute of Technology, Helsinki, Finland)—In the analysis of mill products containing minerals of appreciable difference in specific gravity the well-known principle of the method described by Stanley is applied in a number of ways for a variety of problems. The use of Le Chatelier bottle as explained in the paper may be a dependable and sufficiently accurate way, although no information is given as to the reproducibility of the specific gravity determinations. In the case of MacIntyre ore the method is applied for three separate products produced apparently without reagents and relatively free of fine slimes. Should it be applied for flotation products carrying a substantial amount of slimes, difficulties should be anticipated in the process of eliminating air inclusions from the sample. The difficulties mentioned above may be overcome by the use of a volumeter, an instrument designed for specific gravity determinations of finely divided solids in dry state. This instrument, see Fig. 4, is manufactured by F. Süffert-Bürner A. G. in Basel, Switzerland. Its operation is based on the law of Boyle and Mariotte. With the use of the volumeter, the specific gravities of test samples having a total volume of about 30 cm are easily reproducible within ±2 units in the second decimal of the specific gravity figure, and even better than that with utmost care. This accuracy is sufficient for ordinary operational control. How closely the specific gravity determinations follow the respective chemical assays depends primarily on the nature of the sample itself. In this respect no specific gravity instrument can give better results than those justified by the consistency of mineral distribution in samples analyzed.

Jan 1, 1954

INTRODUCTION AND SCOPE This chapter is intended as a brief review of the mathematics of compound interest and of the meaning of time equivalent money. In order to make valid economic evaluations of various investment alternatives, it is important that they be analyzed on an equivalent basis, taking into account the time value of money. Compound interest has been said to be one of the eighth wonders of the world. Certainly compound interest is a fact of life in today's economy. Whenever we deal with money over time-investments, earnings, savings, loans, etc.-we are immediately confronted with the principles and effects of compound interest. In such an environment it is necessary to be able to determine time value equivalence of various sums of money received or paid at different dates. It follows that all future payments or series of payments that would repay a present sum with interest at a stated rate can be said to be equivalent with each other. Equivalence, then, is a function of the interest rate. MATHEMATICS OF COMPOUND INTEREST FACTORS In order to develop mathematical formulas for various time value equivalence of compound interest we will use symbol designations: P is Present or principal sum of money; usually refers to value at time zero. F is a single sum of money at some designated future date. R is The amount of each payment in a uniform series of equal payments made at the end of each period. n is Number of interest compounding periods (may represent annual, semiannual, quarterly, or even daily periods). i is the period compound interest rate. Figure 20-1 illustrates the increase of princi-

Jan 1, 1980

By J. Chipman, J. B. Gero, T. B. Winkler

IN the basic open hearth process the reaction of manganese in the bath with iron oxide in the slag attains a condition very closely approximating true equilibrium, and the distribution of manganese between slag and metal during the refining period is determined by the factors which control this equilibrium condition. For this reason a number of investigators have studied this reaction both in the laboratory and under various conditions of furnace operation. The principle reaction and its equilibrium constant are: FeO (in slag) + Mn = MnO (in slag) + Fe (liq.) [1] (MnO) .= (FeO),[%Mn] The symbols in parentheses represent activities of the two oxides in the slag which, in the simple slags consisting almost wholly of the two oxides, may be assumed equal to the respective mol fractions. The symbol (FeO)r is used to denote the total iron oxide computed as FeO; or it is the sum of the mol fraction of FeO plus twice that of Fe2O3. Early attempts to obtain laboratory data on this reaction suffered from failure to appreciate the great speed of the reaction. When slag and metal are cooled slowly together, the equilibrium shifts with temperature and the final compositions correspond to equilibrium at the freezing point rather than at bath temperature. The early work of Oberhoffer and Schenck¹ and of Tammann and Oelsen² apparently suffered from this source of error. In most of the other published laboratory investigationsa. '.' this error was not present but other uncertainties have existed, notably dependence upon optical temperature measurements and exposure to atmospheric oxidation.

Jan 1, 1951