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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

REGULATIONS (proposed) for the location, drill-ing, casing, protection, operation, plugging and filling, and abandonment of natural gas and petroleum wells; having for their objectives. the protec-tion of life and property by prevention of intrusions of oil and gas into workable coal beds, and the conserva-tion of oil and gas resources in territory not underlain with workable coal beds. ARTICLE I Definitions Section 1.-For the purpose of these regulations (proposed), definitions are as follows: Well.-A bore-hole drilled for the purpose of developing natural gas or petroleum, or a bore-hole producing natural gas or petroleum. Well Operator.-Any person, persons, firm, partnership, corporation, company or association that proposes to, or does drill, operate, or abandon a well as herein defined. Coal Operator.-Any person, persons, firm, partnership, corporation, company or association that proposes to, or does operate, a coal mine in territory known or reputed to be underlain with oil or gas-bearing strata. State Mining Department.-The duly constituted authorities of a state having jurisdiction over coal-mining operations. Plat.-A map, drawing, or print made in accordance with the pro-visions of these regulations (proposed). Casing.-The pipe greater than 3 in. in diameter commonly used in wells drilled for natural gas and petroleum. Oil and Gas.-Synonyms, respectively, for petroleum and natural gas. Cement.-Hydraulic cement properly nixed with water only. Workable Coal Bed.-A coal bed in which, in the united judgment of the coal operator, the well operator and the State Mining Department, protection for life or property will be required when wells are drilled through it.

Jan 7, 1927

By Thomas MacFarlane

IN smelting copper, lead, and silver ores, it is scarcely possible in every case to make analyses of the various parcels of ore, with the view of combining these and the fluxes so accurately as to yield, in the furnace, slags of exactly the most favorable composition. This is even more difficult with ores which require previous calcination, or with mattes which have been roasted in heaps. Even in cases where the greatest pains have been taken and the most elaborate calculations made beforehand, it frequently happens that variations in the working of the furnace interfere with the result so much desired. Generally, the practical metallurgist must be content with ascertaining the average composition of his ores and fluxes, making a calculation once for all as to the most advantageous mixture, and leaving slight changes in its composition to be taken care of as it is passing through the furnace. The various products then afford him the best material whereon to base his judgment as to the manner in which his smelting mixture is working. Of course the character of the slag is one of his chief guides, but it is not always possible from its outward characters alone to form a correct judgment as to its composition. Neither would it be possible or practicable to apply chemical analysis for this purpose, as it would be impossible to wait for its results while working a furnace. Abich was, I believe, the first to point out the relation existing between the composition of volcanic rocks and their densities, and to show that, the latter being ascertained, very correct conclusions

Jan 1, 1880

By Thomas MacFarlane

In smelting copper, lead, and silver ores, it is scarcely possible in every case to make analyses of the various parcels of ore, with the view of combining these and the fluxes so accurately as to yield, in the furnace, slags of exactly the most favorable composition. This is even more difficult with ores which require previous calcination, or with mattes which have been roasted in heaps. Even in cases where the greatest pains have been taken and the most elaborate calculations made beforehand, it frequently happens that variations in the working of the furnace interfere with the result so much desired. Generally, the practical metallurgist must be content with ascertaining the average composition of his ores and fluxes, making a calculation once for all as to the most advantageous mixture, and leaving slight changes in its composition to be taken care of as it is passing through the furnace. The various products then afford him the best material whereon to base his judgment as to the manner in which his smelting mixture is working. Of course the character of the slag is one of his chief guides, but it is not always possible from its outward characters alone to form a correct judgment as to its composition. Neither would it be possible or practicable to apply chemical analysis for this purpose, as it would be impossible to wait for its results while working a furnace. Abich was, I believe, the first to point out the relation existing between the composition of volcanic rocks and their densities, and to show that, the latter being ascertained, very correct conclusions

Jan 1, 1880

THE gold medal of the Mining and Metallurgical Society of America was presented, on Jan. 10, 1922, to Charles Warren Goodale, "for signal services in furthering the welfare and safety of workers in the mining and metallurigical industries of America." The presentation was made by Dr. J. E. Spurr, presi-dent of the Society for the year 1921, at the annual meeting held in New York City. Dr. Van H. Manning, formerly director of the U. S. Bureau of Mines, made the first address. Toward the close of his brief speech, he said, "It has happily been suggested, ?Let us balance our praise of war heroes by pausing to honor a hero of peace.' We have with us tonight a man who has been a leader and inspirer of thousands of his contemporaries. . . . His zeal in the great work of increasing the safety of men engaged in mining and metallurgical operations has become an obsession with him. . . . That lie has been success-ful is evidenced by the great work, of which I have personal and intimate knowledge, done by him in con-nection with the Anaconda Copper Mining Co. and its subsidiaries." Dr. J. F. Kemp gave a brief sketch of Mr. Goodale's career, in the course of which he said, in speaking of .the consolidation of the Boston and Montana, the Anaconda, and smaller companies, "at the same time electric current was introduced for haulage in the mines and on the surface for the running of air compressors and the hoisting of the cage. . . . We can see that there was great danger to the miner and that safety first became a very important feature of the work. . . .

Jan 2, 1922

By Albert H. Chester

DURING the summer of 1875 I visited some of the iron mines of Houghton County, Mich., and was quite interested to observe the progress made there within a. few years. Working in open pits is gradually giving place to underground work in most of the mines where this system is practicable. In some cases, as in the Lake Superior Mine, the body of ore is so irregular, and the deposit so liable at any time to be pinched out, or nearly so, that it has been found impractical, if not impossible, to lay out any plan for systematic underground work. But in many other mines the deposit is so regular in character, that the work can be laid out in shafts at regu¬lar intervals, and a series of 60 feet levels. The Michigammi Mine, opened in 1872, and first worked in 1873, is arranged on this plan, though some quarrying is still done. But the men are being put at overhead stoping as fast as it can be got ready for them, and before long it will all be worked in this way. The New York Mine is undergoing a similar change to the pillar system, and several others have either been changed, or it is about to be done. My principal object in visiting this region was to obtain samples from some of the important mines, so as to be able to answer the question : "What is the average percentage of iron in the Lake Superior ores?" Most iron furnaces work on mixtures of ore, so that it is impossible to tell, from their records, just the percentage in each one.

Jan 1, 1876

Problems discussed and research opportunities identified during the workshop in the major areas of 1) flocculation, 2) flotation, 3) leaching and magnetic separation are summarized below. I. FLOCCULATION Problems Practical problems caused by unintentional flocculation or dispersion were described in the papers that dealt with iron ore processing, selective flocculation, fine coal processing, phosphate processing and potash processing. Ideas generated during the discussions ranged from the very practical suggestion that a conscious effort be made to transfer knowhow from the experienced clay industry to the metals and fuels-from-slimes industry. . . , to the familiar appeals for omnipotent theoretical developments. There was surprising recurrence of some questions in many contexts. Recurring questions are emphasized here rather than commodity-specific problems because their answers would serve a wider clientele usage. There is indeed no objection and some advantage to commodity-specific research, however, provided the proposed project is planned with full cognizance of transferable knowledge in other commodities, and of the possible usefulness of these results in other areas. Research Needs Most of the questions or research opportunities can be classified into three groups: a) water chemistry, b) dewatering, and c) flocculation theory. Other classifications are possible and probably useful. In each group there is a clear need for outwardly esoteric theoretical research a clear application of that work to current practical problems. Higher priority should be given to proposals for theoretical research which explicitly show the expected ultimate usefulness of the result. Likewise, proposals for applied research should demonstrate cognizance of applicable theory. Both of these types of projects could profit from collaboration among industrial, university and government personnel.

Jan 1, 1979

By C. E. Beecher

THE application of gas or air under pressure to obtain more oil from a sand which has been practically exhausted by ordinary production methods has been practiced to a limited extent for many years. Until recently such methods were confined to the Eastern fields, principally those of Ohio and West Virginia, where in many cases the production obtained after applying pressure for a few years was nearly equal to the total production prior to that time which had been obtained by the usual production methods.' As early as 1917, J. 0. Lewis1 called attention to this method of increasing the recovery of oil and cited the phenomenal results obtained by H. E. Smith, I. L. Dunn and 0. C. Dunn, who pioneered the application of air or gas pressure recovery methods. With this information available it would appear that other oil-producing sections of the country have been extremely slow to realize the advantages of repressuring. However, after a few successful projects in the Mid-Continent area, the oil producers appreciated the value of this method for obtaining further and profitable production from their practically exhausted leases and are now making extensive use of it. In general, it has been the practice to apply pressure to the sands when production has declined to a small yield per well. The purpose of this paper is to discuss some of the advantages which may be expected from returning gas under pressure to the oil sands during the early stages of development, before the rock pressure has been dissipated and the gas exhausted, and to stimulate discussion of this subject on which comparatively little actual field data are available.

Jan 1, 1928

By Mungo Park, C. Baring Horwood

This paper is intended, in the light of recent investigations, to call attention to some of the essential features of good practice in sampling and mine-valuation. Mine-sampling may be divided broadly into two classes: (1) development-sampling and cornputatioll of ore-reserves; and, (2) stope-sampling and estimation of stope-values. Development-Sampling. It is with development-sampling only that this paper deals— the term development being taken to mean the opening-up of a mine by cross-cuts, drives, connections, etc., preparatory to actual extraction of the ore for milling. In development-sampling the work of the sampler and the consequent estima-

Jan 1, 1909

By John McDonald

THIS report is a continuation of an earlier one with a similar title,1 to which the reader is referred for such details of procedure as do not appear here. A brief summary will be given of the objects and methods of the research at this time. It was pointed out in the previous paper that properties of magnesium alloys, as re-ported by different workers, often differ. This was thought to be due to differences in the preparation of the specimens tested. The ideal way to compare alloys would be to prepare each of them in so many ways that reasonable assurance would exist that the best properties of each alloy had been developed. The alloys would then be com-pared on the basis of these properties. The treatment actually given the alloys of these studies is necessarily a compromise with completeness. Nevertheless, enough treatments have been given so that a con-siderable degree of assurance exists that the properties obtained are representative of the alloy as such, and not merely of the manner in which it was worked and heat-treated.

Jan 1, 1940

By A. G. Paithankar, G. B. Misra

Although certain physical mechanical properties of rocks have been claimed to give an estimate of penetration rate in percussive drilling, the authors' work shows that the correlation of penetration rate with individual rock properties is Poor. The authors have developed a good correlation between penetration rate and a set of rock properties but the relation is complex. Energy per unit volume has been used as a measure of penetration rate in percussive drilling by Hustrulid and Fairhurst; however, their test setup is large wing a full size drill bit. The authors determined the minimum energy for unit volume Ev min for any rock at the optimum index angle in a simple laboratory drop tester wing a sharp microbit with a tip angle of ll0°. This Ev min has been found to correlate well with penetration rate obtained in controlled laboratory drilling in different rocks for different stages of bit wear. A comprehensive relation has been developed between penetration rate and Ev min.

Jan 1, 1981

The Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties. United Engineering Trustees, Inc. When Mr. Carnegie made his gift which made possible a home for the engineering societies, a separate corporation was organized to act as a holding company and to manage the common property. This was long known as the United Engineering Society, but the name has now been changed to one which more nearly reflects the real function of the corporation. It holds title to . the Engineering Societies Building and to various funds placed in its charge and is managed by a Board of Trustees, of which three are chosen by each of the four societies, American Institute of Mining and Metallurgical Engineers, American Society of Mechanical Engineers, American Institute of Electrical Engineers and American Society of Civil Engineers, which have equal and undivided interests in the property. The land and building cost two million dollars. During the year 1934, the Constitution and Bylaws of The United Engineering Trustees, Inc., were thoroughly revised and a better organization of its functions was affected: The Engineering Foundation and the Engineering Societies Library were made "departments" of the United Engineering Trustees. The Founders Societies share in the property which it holds, and estimated at the present time, as follows: Real estate, $1,987,793; Depreciation and Renewal Fund, $336,992. The U.E.T. has endowment funds-' amounting to $1,107,677. The A.I.M.E. trustees are W. D. B. Motter, Jr., A. L. .Queneau and Albert Roberts.

Jan 1, 1937

By N. W. Lord

There hare been made at one or two places in Ohio, during the last year or two, some irons of rather unusual phosphorus-percentages. The first of these which I had occasion to examine came from Moxahala Furnace, in Perry county. The furnace was built originally to smelt an ore found in large deposits near its furnace in the " black band" horizon. The deposit was easily exposed by simple stripping;" it was from six to eight feet thick, being a blne carbonate ore, very free from silica. This ore yielded, on analysis, from two to 3 per cent. of phosphorus, when carefully sampled. The furnace company had trusted entirely to old analyses made on "outcrop" ore, well weathered, and received all other results with indifference. The result of the first run of the furnace was an iron in large whitish-gray crystals, and so brittle that it could be pulverized in a mortar. This iron contained 4.90 per cent. phosphorus. A limited quantity only was made, which was gradually disposed of as a great ('softener" to foundries. The Moxahala Furnace was subsequently run on Lake Superior ore mainly. The second case of such iron occurred last summer at Mt. Vernon Furnace. A deposit of what was locally known as "Hallelujah" ore, was opened for the furnace. This ore was a blue carbonate, similar to the first-described. The iron made was pure tin-white in color, and showed large crystals without a trace of the grain of ordinary pig-iron. It was sopposed at the furnace to be spiegeleisen, and was sent to me to be

Jan 1, 1884

At a time when Congressional stiffening of health and safety regulations in the nation's coal mines seems all but an afterthought, when the problems confronting both mine operator and worker are being tossed about like a pigskin in an Australian- rules football match, what could be more appropriate to the times than to incorporate a discussion on these matters into the proceedings of an annual coal meeting. Integration of both technical and topical discussion provided the strength for this 28th Annual Meeting of the Central Appalachian Section of the AIME, convened at the The Greenbrier, White. Sulphur Springs. W. Va., Oct. 31-Nov. 1. Three technical sessions prepared for the occasion were served to those in attendance. First of these was held on Friday morning. Rendered excellent coverage, topics included Roof Structure Analysis at Blacksville No. I, presented by David Eyer, Christopher Coal Co.; Methane Monitors (evolution and evaluation of present day detection equipment); and Instantaneous Control Reaction to Mine Fires and Explosions, in which Elmer A. Fike illustrated the point quite vividly by showing a film on the potential of such control equipment. Indeed, the ability to snuff out a mine fire before it is allowed to spread even beyond its own igniting sparks speaks very well for itself. However, Fike hastened to point out that certain difficulties had to be overcome before these "fire watchers" could be implemented successfully in mines. These "bugs," inherent in virtually all coal mining environments, include ignition of sulfur pockets on mine facings and delivery of sparks on trolley rails, both of which may impede the accuracy of such control monitors.

Jan 12, 1969

The Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties. United Engineering Trustees, Inc. When Mr. Carnegie made. his gift which made possible a home for the engineering societies, a separate corporation was organized to act as a holding company and to manage the common property. This was long known as the United Engineering Society, but the name has now been changed to one which more nearly reflects the real function of the corporation. It holds title to the Engineering Societies Building and to various funds placed in its charge and is managed by a Board of Trustees, of which three are chosen by each of the four societies, American Institute of Mining and Metallurgical Engineers, American Society of Mechanical Engineers, American Institute of Electrical Engineers and American Society of Civil Engineers, which have equal and undivided interests in the property. The land and building cost two million dollars. During the year 1934, the Constitution and Bylaws of The United Engineering Trustees, Inc., were thoroughly revised and a better organization of its functions was effected: The Engineering Foundation and the Engineering Societies Library were made "departments" of the United Engineering Trustees. The Founders Societies share in the property which it holds, and estimated at the present time, as follows: Real estate,. $1,993,793; Depreciation and Renewal Fund, $401,000. The U.E.T. has endowment funds amounting to $1,086,893. The A.I.M.E. trustees are W. D. B. Matter, Jr., A. L. Queneau and Albert Roberts.

Jan 1, 1939

By Heinrich Ries

In another place,* the writer has called attention to the modern methods of the laboratory investigation of clay, and it is desired here simply to discuss one branch of the subject, which, though of considerable importance, has heretofore received little attention in this country, viz., the rational analysis of clay. In order, however, the better to point out the bearings and advantages of this procedure, it is necessary to refer briefly to the ultimate analysis as well. The remarks in this paper refer only to the use of clay for the manufacture of clay-products. Pure clay or kaolin-f is extremely refractory, possesses little plasticity, and usually shrinks aud warps considerably in burning. Even the smallest proportion of impurities changes these properties, so that the kaolin exhibits variations in shrinkage, plasticity, tensile strength, fusibility, and often color when burned. The majority of nearly pure kaolins consist of kaolinite (A1,O2 2SiO,, 2H20), undecomposed feldspar, and quartz. The kaolinite generally forms the finest particles of the clay and is known as the clay-substance, while the rest of the clay-particles are collectively spoken of as sand. In the ordinary or ultimate analysis, the substances generally determined are silica, alumina, ferric oxide, lime, magnesia, alkalies and water. An analysis of this type simply regards the clay as a mixture of elements or oxides, but gives no clue as to the actual condition in which these substances exist, i.e., whether as silicates, oxides or carbonates, etc., a point which it is of the highest importance to know; for the individual components of the clay influence its properties not only according

Jan 1, 1899

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

Jan 1, 1940

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

By T. S. Liu, E. A. Peretti

A LITERATURE survey of the In-Sb system, which was made before a study of the binary diagram was undertaken, revealed that the intermediate phase InSb existed and that its crystal structure is face-centered cubic of the zinc blend type. In 1929 Goldschmidt' determined the lattice constant for InSb and obtained a value of 6.452A. A more recent value, 6.461A was reported by Iandelli2 in 1941. The purity of the indium used was not very high, however. The indium used by Iandelli contained 2 pct Ge. In view of this fact it was decided to remeasure the lattice parameter using high-purity indium (99.97+ pct In) and spectrographically standardized antimony of the highest purity available (99.91 pct Sb). Specimens corresponding to the InSb composition were made by carefully weighing the ingredients on an analytical balance and heating them in vacuo in a quartz tube at 700°C. As melting losses were negligible, the alloys were not analyzed chemically, but the intended analysis was taken as being accu- rate. Powder samples were prepared by either filing or crushing of the brittle alloy, followed by screening at 325 mesh. The powders were then annealed at 400°C in evacuated capsules for about an hour. X-ray photograms were taken with a Debye and a back-reflection focusing camera, using characteristic cobalt K. radiation. Lattice parameters were calculated by Cohen's³ method. The results of a Debye pattern and of a back-reflection pattern at 25°C are given in Tables I and 11. The lattice parameter at 25 °C is 6.47602A.

Jan 1, 1952