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By William G. Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the nonhomogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of deforming beyond the limit of purely elastic strains, a plasticity theory is required. The purpose of this chapter is to present a plasticity theory for anisotropic rocks and soils. The proposed theory is based on the work of Hill in anisotropic metal plasticity and represents an extension of his work so as to include anisotropic geologic materials. The point of departure from metal plasticity theory begins with the inclusion of the normal stresses as linear terms in the yield condition, which plays a central role in plasticity. Once the yield condition is established, the plastic strain increments are obtained immediately through the principle of normality. For practical applications, some simplification of the three-dimensional theory is re-

Jan 1, 1972

By G. B. Sazuyer

DEVELOPMENTS respecting beryllium during the past year have been sufficient to center attention on it as likely to be the most important of any of the chemical elements that have recently found a place for themselves in technical industry. This importance is only potential, however, largely because adequate supplies of beryllium ore will be necessary. The beryllium industry will be only as great as the mines which support it. To find and develop large mines will be the problem. Chief of the immediate commercial developments in the United States is beryllium-copper and its espousal by Anaconda and Riverside even at present high prices. According to the pamphlets of these companies, it ap¬pears that beryllium is to copper nearly what carbon is to iron. When one considers that the tensile strength of pure copper is about 33,000 lb. per sq. in., but that the addition of 1.5 to 2.5 per cent of beryllium produces a heat-treatable alloy with a maximum tensile strength of 220,000 lb. or over, the analogy to carbon and iron is made strikingly, clear. Striking among the properties of beryllium-copper is its resistance to fatigue, claimed to be equal or superior to that of spring steel. It needs little imagination to foresee a great industry for this alloy alone.

Jan 1, 1934

SINCE the adoption by the U. S. Bureau of Standards several years ago of specifications for standard 100- and 200-mesh sieves, frequent requests have been received that this Bureau test and certify sieves of other sizes than these. With a view to the adoption of a series of standard testing sieves which might be of use to all industries making fineness tests, this Bureau for .two years has been studying the question of such a standard screen scale. Various scales that have been proposed were considered, and information was sought of representative firms in the various industries interested as to their requirements. Manufacturers of sieves have also been consulted as to the desirability of different screen scales and the practicability of their manufacture. As a result of this study of the question, a conference was called at the Bureau of Standards, Apr. 20, 1916, of representatives of various committees of the American Society for Testing Materials, American Society of Civil Engineers, American Institute of Mining Engineers, American Foundrymen's Association,. [Mining and Metallurgical Society of America, American Water Works Association, American Institute of Metals and the American Spice Trade Association; also representatives of the Committee of Revision of the U. S. Pharmacopoeia, the U. S. Geological Survey, the U. S. Bureau of Mines, the U. S. Office of Public Roads and Rural Engineering, the U. S. Office of Grain Standardization and the U. S. Bureau of Standards; also representatives of a number of private firms engaged in industries in which sieves are used, such as the glass, the drug milling, the abrasive, the asphalt, the mining, the spice, the chemical, and the graphite industries; also representatives of the firms in this country manufacturing wire cloth and sieves. This Conference, after considering the various screen scales either proposed or now in use, adopted as a Standard Screen Scale that given in Table 1, and recommends that it be adopted generally by scientific,

Jan 6, 1917

By R. H. Sweetser

THERE are SO many conditions affecting blast-furnace results that it is hard to get satisfactory comparative data on the working of two furnaces, and much more difficult to get comparable results from the use of two entirely different fuels. The several advantages of charcoal over coke as a blast-furnace fuel have doubtless been apparent to many managers; but probably the conditions for comparative tests of the two were never so favorable as during the year 1905, at the works of the Algoma Steel Co., Sault Ste. Marie, Ontario, which comprise two modern blast-furnaces, well equipped, though of comparatively small capacity. For four consecutive months one of these furnaces was run with charcoal and the other with coke. Then the charcoal-furnace ran for a while with part charcoal and part coke; and, still later, with coke only. The ore-mixtures were about the same in the two furnaces, and, of course, all the climatic conditions were identical. The dimensions of the two furnaces, and their work with the different fuels, are given in Table I.

Jan 5, 1908

By M. F. McCarty, R. S. Olson

New organic flocculants of high-molecular weight are replacing lime, glue, and starch in liquid-solid separation. Of these synthetic materials, poly-acrylamides are outstanding. Polyacrylamides form a class of compounds varying widely in composition and activity. Separan 2610, one of the first of these flocculants' released to the mining industry in 1954, is described' as a high-molecular weight polymer of acrylamide with or without a copolymer material and with some replacement of amide by carboxylic groups. MECHANISM OF FLOCCULATION In practice, flocculation makes solids settle faster and filter better. But two opposing factors control it. The random motion that causes particles to collide favors Van der Waals' forces, which hold the particles together. The effect of zeta potential opposes this contact, and particles are mutually repelled. Flocculation can be achieved by reducing the magnitude of the zeta potential; this is the mechanism of flocculation by lime addition. The way in which polyacrylamides accomplish flocculation is not fully understood, but the action is undoubtedly comp1ex and probably varies considerably depending on the system. To begin with, the active groups of these compounds have an extremely high affinity for solid surfaces, probably by hydrogen bonding." Initially some active groups of the molecule attach themselves to the solids with a large portion of the molecule extending into the solution. Two particles can become tied together by long flocculant molecules in the following ways—by bonding between the active groups of two flocculant molecules on different particles, or by an extended molecule from one particle attaching itself directly to the surface of the other particles." These flocculant bridges prevent the particles from moving apart through random motion, but when such motion moves them together other active groups on the flocculant bridge bond to the solids, holding them in the closer position. This process is repeated until the particles are close together. Although bridging is probably a major flocculation mechanism, it is not the only phenomenon involved. Relatively neutral acrylamide flocculants reduce the magnitude of the zeta potential by increasing the viscosity of solution in the immediate vicinity of the solid surface which contains the mobile counter ions of the double layer. In other words, it moves the shear surface which bounds the zeta potential out into the solution containing counter ions which tend to neutralize the zeta potential. This effect is probably more pronounced during the initial adsorption period, before the flocculant molecules are pulled close to the solid. In some cases the slight charge of the polyacry-lamide molecule tends to neutralize a zeta potential. However, this is not a primary flocculation mechanism, as evidenced by the fact that the polyacrylamides will flocculate solids with either positive or negative zeta potential. Adsorption of polyacrylamide flocculants by a solid is substantially an irreversible reaction. Since the flocculant molecule is attached to the particle surface by many active groups of high bonding strength, desorption would require the simultaneous breaking of many bonds—an unlikely occurrence. UNIQUE PROPERTIES The irreversible adsorption of certain polyacrylamides, the flocculant's high affinity for solid surfaces and its rapid adsorption make it effective, but these unique properties require special techniques to achieve maximum flocculation. If flocculants of this type are added to a pulp as a relatively concentrated solution, the solids in the

Jan 1, 1960

By Richmond Bennett

Airborne geochemistry became a reality with the advent of a high-sensitivity air¬borne gamma ray spectrometer with large volume NAI(Tl) crystal detectors. The high-sensitivity spectrometer measures small variations in the concentration of potassium (as Ks°), thorium (as Tl308) and uranium (as Bi.214) along the flight lines in the area surveyed. Hydrothermal dispersion patterns are indicated by anomalous measured values of the concentrations of potassium, thorium, uranium, or their ratios. In two recent Australian survey areas, copper mineralization was located along favorable structures within hydrothermal dispersion patterns delineated by airborne geochemical surveys. In metamorphic terrane where there had been po¬tassium metasomatism, the hydrothermal dispersion patterns were indicated by high potassium/uranium ratios (K40/Bi). In a sedimentary environment that had been intruded by a stock, the path of hydrothermal fluids was indicated by uranium (Bi214), thorium (TV'), and uranium/ thorium (Bi214/Tl208) ratios.

Jan 1, 1972

By D. R. Irving

Prior to this time, ample supplies of high grade mineral fillers, such as clay, have been available close to consuming centers. Now depletion of these accessible deposits, coupled with other factors such as increasing demand due to population expansion and standard of living rise, has made development of upgrading techniques attractive to producers. Various investigations being carried out by the U.S. Bureau of Mines are described. Factors making the development of improved methods for upgrading clays attractive to producers include: depletion of accessible deposits of high-grade clays, rising transportation and labor costs, more exacting specifications, and increased demand resulting from an expanding population and a constantly rising standard of living. Industry recognizes the need for upgrading presently unusable materials and has cooperated with the U.S. Bureau of Mines by providing samples from submarginal deposits and by evaluating the products that USBM upgrades. Following are some examples of recent clay beneficiation work by the Bureau. FIRE CLAY BENEFICIATION At the Rolla Metallurgical Center, Rolla, Mo., the Bureau is conducting research to develop technically and economically feasible mineral-dressing methods to remove quartz, pyrite, and other impurities from submarginal fire clays. The research has been spurred by the growing shortage of high-grade bur-ley, flint, and plastic clays in the Missouri fire-clay district resulting from increased consumption and the low rate of discovery of new deposits of adequate quality. There apparently is ample tonnage of submarginal flint and plastic clays to maintain the industry for many years if such material can be upgraded to commercial quality. Samples have been submitted to USBM by several major producers of refractories, including A. P. Green Fire Brick Co.; Harbison-Walker Refractories Co.; Mexico Refractories Div., Kaiser Aluminum and Chemical Corp.; and Wellsville Fire Brick Co. Research on some samples has been completed and still is in progress on others. The Bureau has found that specimens containing quartz or pyrite in grains coarser than the accompanying clay generally can be upgraded either with a gravity table or hydraulic cyclone. The improvement in quality is notable not only in chemical analysis but in an increase in pyrometric cone equivalent (PCE) of one or more cones. As an example, consider the results attained on a sandy flint—a fine-grained mixture of kaolin and halloysite with quartz and minor quantities of iron and manganese oxides. Chemical analysis was: 35.4 pct alumina (A12O3) and 47.8 pct silica (SiO2). The sample contained 9.2 pct free silica as quartz. The PCE was 33. The sample was crushed to -10-mesh, blunged with water, and then stage-ground to -48-mesh. The ground sample was tabled to yield a clay fraction containing 37.6 pct A12O3, and 45.3 pct SiO2 of which 2.4 pct was free silica. The PCE was 34. Recovery of alumina by this process was 73.6 pct. Concentration of the same clay in the hydraulic cyclone was even more effective in respect to quartz removal. The clay fraction analyzed 38.6 pct A12O3, 45.0 pct SiO2 of which 0.5 pct was free silica as quartz, and had a PCE of 34. Recovery of alumina was 71.9 pct. The hydraulic cyclone was also effective in reducing the pyrite content of a plastic clay which likewise was a mixture of kaolin and halloysite, plus some pyrite, quartz, and carbonaceous material. It analyzed 30.6 pct Al2O3, 52.3 pct SiO2, 2.3 pct Fe2O3, and 0.76 pct S. The sample was blunged and screened through 10-mesh to remove some coarse pyrite, then ground to -65-mesh and cycloned to remove most of the remainder. The final product recovered 81.8 pct of the alumina at a grade of 32.3 pct A12O3, 50.9 pct SiO2, 1.4 pct Fe2O3, and 0.1 pct S. The PCE was 32-1/2, compared with a PCE of 31-1/2 for the crude clay. The fine beneficiated clays, of course, must be pelletized and dried or fired to meet commercial acceptance. This operation has already been solved by industry. Little progress has been made on two remaining problems. One is that of fine-grained impurities, not separable by table or cyclone. Flotation is being investigated to solve this. Although fine pyrite is readily rejected, a satisfactory quartz-clay separation has not been attained. The second problem, a stubborn one, is that of alkali. Samples containing as much as 5 pct potas-

Jan 1, 1961

By H. M. Howe

It is a grave objection to the present system (or rather lack of system) of mineralogical nomenclature that, in the very great majority of cases, the name of a mineral gives no hint of its chemical composition, one might almost say no suggestion, however faint, of anything connected with it or characteristic of it, chemical, physical, historical, geographical, geological, or lithological. In becoming acquainted with a mineral, in addition to learning its composition and important characteristics, one must also learn a name wholly unconnected with any of them. It has occurred to me that a system might be devised in which the name of each mineral should express at least an approximation to its ultimate composition. It is far easier to learn the names of most minerals than their compositions. Most of us are familiar with the names and appearance of many minerals, especially among the silicates, of whose compositions we have but a rough notion. It would be the aim of such a system to enable us, in making the one slight effort of learning the name of a mineral, by that same effort and involuntarily to learn its composition, which now requires an additional and a much greater effort. I have worked out a system designed to meet this requirement, and its description occupies the remainder of this article. Doubtless there are many devices on which could be based other systems fulfilling the requirement above set forth better than that about to be described does, and at the same time furnishing names

Jan 1, 1884

By Frank D. Hoyt

BY far the most conspicuous of the Pennsylvania slate districts is that extending from the New Jersey line at the Delaware Water Gap westward almost to the Schuylkill River. This covers parts of three counties in east-central Pennsylvania: Northampton, Lehigh, and Berks. The most important development, both in geographic size and product importance, is in Lehigh and Northampton counties. The greater part of the region is underlain by only one formation-the Martinsburg, consisting of slates, clay slates, and sandy shales, all of the Ordovician period. The slate-bearing Martinsburg formation is underlain by Cambro-Ordovician limestones. Immediately overlying the Martinsburg formation is the Tuscarora quartzite of the Silurian period. The Martinsburg formation itself is divided into three distinct divisions, termed simply: the upper, the middle, and the lower members. Commercial slate has been extracted from all of these members, but the formation of greatest importance is the upper member, representing 2600 ft of the total formation thickness of nearly 11,000 ft. The upper member is commonly referred to as the "soft slate" and consists of three facies: 1) beds of blue-gray, very sandy, almost quartzitic slate, in many places, approximately a medium-coarse sand- stone with calcareous cement; 2) blue-gray sericitic slat-the dominant rock type of this member-with occasional chloritic beds; and 3) dark gray or virtually black, highly carbonaceous beds, referred to locally as "ribbons."

Jan 8, 1958

By Asheim, Harald A.

Parameter estimates affect both the optimum field development decisions and the economic result. A general methodology for assessment of the effects of parameter uncertainty in offshore development decision situations is proposed, and used to analyze aspects of the initial development situation for the Statfjord field.

Jan 1, 1982

By Arthur Hockman, Howard W. Jaffe, Howard F. Carl

THE problem of establishing practical techniques for evaluating natural corundum ores arose from the desire to improve the existing purchase specifications for crystal corundum procured by the Federal Government for stockpiling. Such purchase specifications had been developed for a large number of products, including minerals and ores considered to be critical and strategic because of the country's dependence on foreign sources of supply. It will be apparent to anyone considering the subject of purchase specifications that the determination of whether or not a submittal meets the specifications is a prime consideration. Consequently satisfactory specifications for minerals should not only incorporate physical, chemical, and mineralogical requirements that are practical but should also establish the means by which both buyer and seller can be assured that materials meet stated requirements.

Jan 4, 1954

By AIME AIME

THE MODEL LAW previously referred to', in these columns several times, prepared by Engineering Council, to be o ered in any state where legislation is introduced for licensing engineers, is given in abstract below. , Mining engineers throughout the country should watch legislation of this sort and see that the draft prepared by Engineering Council is in the hands of any state legislative committee which proposes to frame a licensing law. So far as this office is informed, the mining engineers are a unit against licensing, but if we must be licensed the most innocuous law that has been submitted is the draft prepared by Engineering Council. ABSTRACT OF MODEL LAW -FOR REGISTRATION OF PROFESSIONAL ENGINEERS, ARCHITECTS, AND LAND SURVEYORS

Jan 1, 1920

By Whitmell J. Smithwick, Charles E. Dandois

The first operating unit of the ring or annular shaft kiln as developed by Mr. Karl Beckenbach of West Germany was rated 185 tpd and was installed in 1962. Today, there are approximately 84 units in operation in Western Europe and Japan. Twenty-one additional units are under construction or on order. Sizes range from approximately 100-330 tpd, however, units of over 500 tons are in the design stage. The ring shaft kiln is a single vertical cylinder to which are attached the required service platforms, combustion chambers, injectors and distribution piping (Fig. 1). Auxiliaries such as recuperator, exhaust fan and dust collector are mounted on the appropriate service platform. The charging pan, feed conveyor, etc., are mounted at the kiln top and at the bottom of the kiln is the silo with a vibrator type discharger. Mounted separately is the required blower for injector air and fan for internal cooling.

Jan 4, 1973

By Betty L. Gibbs

A company must have an organized approach to effectively sort through the profusion of available software and hardware and find the programs and equipment which fit defined needs. The selection process must build a complete compatible system which includes hardware and software. The methodology presented in this paper helps identify some of the more important considerations. The steps needed for an organized approach to software/hardware selection are: •All involved staff should contribute to an assessment of current computer capabilities and projection of future needs. •Alternatives are analyzed to determine what software and hardware is available and how selections may possibly be merged into the existing computer system. The evaluation process focuses on details of program capability and hardware compatibility. Analysis must be done to determine how closely individual programs fit the established requirements. The final decision is often a balance of needs between program capabilities and hardware availability. Any programs selected must be able to run on existing and newly purchased hardware. Any additional hardware selected must be capable of meshing with the available computer system.

Jan 1, 1983

By Sylvain J. Pirson

The number of seismograph field crews employed in the active survey of potential oil territories is still on the increase, owing to the ever pending threat of a shortage in the supply of crude oil. It is to be expected that for years to come the seismograph will be responsible for discovering many new oil fields, both in wildcat territories and in deeper formations, and that the seismographic campaign will go on unabated. Yet improvements in instrumental design, in the field and interpretative techniques, are brought about year after year, and lead to the reshooting of areas many times surveyed previously. Notwithstanding the experience gained by the past eight years of active work in reflection seismographic surveys, the results given by this method of mapping deep formations have in many instances been at variance with the information subsequently obtained by the drill. To overcome this shortcoming, geophysicists have used closer spacing of the shot points and closer control of the depth points. The method discussed here is being used actively in the Mid-Continent region and endeavors to reduce the interpretation work to a mere mechanical technique, leaving as little as possible to the opinion of the interpreter. The New Method Field Technique.—In sectionized territory where country roads are available every mile, shot points are preferably located every 1/4 mile when six detectors are available or every % mile when eight detectors are at hand. The disposition of individual spreads is represented on Fig. I; in each case a shot point is located at the section corners. Fig. 2a represents the layout of a spread between shot points, the vibration detectors being preferably equidistantly located. Normally in the 1/4-mile control, the distance between shot points is 1320 ft. and the distance between detectors 220 ft. When shooting from shot point S.P. I, detectors 1 to 6 are connected to the recording galvanometers and detector 0 (which indicates the vertical travel time of the wave corre-

Jan 1, 1940

By Sylvain J. Pirson

The number of seismograph field crews employed in the active survey of potential oil territories is still on the increase, owing to the ever pending threat of a shortage in the supply of crude oil. It is to be expected that for years to come the seismograph will be responsible for discovering many new oil fields, both in wildcat territories and in deeper formations, and that the seismographic campaign will go on unabated. Yet improvements in instrumental design, in the field and interpretative techniques, are brought about year after year, and lead to the reshooting of areas many times surveyed previously. Notwithstanding the experience gained by the past eight years of active work in reflection seismographic surveys, the results given by this method of mapping deep formations have in many instances been at variance with the information subsequently obtained by the drill. To overcome this shortcoming, geophysicists have used closer spacing of the shot points and closer control of the depth points. The method discussed here is being used actively in the Mid-Continent region and endeavors to reduce the interpretation work to a mere mechanical technique, leaving as little as possible to the opinion of the interpreter. The New Method Field Technique.—In sectionized territory where country roads are available every mile, shot points are preferably located every 1/4 mile when six detectors are available or every % mile when eight detectors are at hand. The disposition of individual spreads is represented on Fig. I; in each case a shot point is located at the section corners. Fig. 2a represents the layout of a spread between shot points, the vibration detectors being preferably equidistantly located. Normally in the 1/4-mile control, the distance between shot points is 1320 ft. and the distance between detectors 220 ft. When shooting from shot point S.P. I, detectors 1 to 6 are connected to the recording galvanometers and detector 0 (which indicates the vertical travel time of the wave corre-

Jan 1, 1940

By R. E. Reed-Hill

The shear continuity conditions under which one mechanical twin may cross another are considered. Twin intersections usually involve various types of slip deformation in addition to twinning. Because the shear of the crossing twin may be partly transmitted through the crossed twin by slip mechanisms, continuity of the twinning shear vectors is not required at a twin intersection. It is concluded that analyses based on twin intersections should not he used as an independent method for deducing twinning elements in newly observed twinning modes. WHEN one mechanical twin passes through another, a twin intersection is said to occur. In the simplest form of intersection, Fig. 1, the crossing of one twin by another is accomplished with the aid of a second-order twin induced, in the twin that is crossed, by the crossing twin. The subject of twin intersections is significant to the field of deformation studies because it has been postulated by cahn1 that twin intersections should occur only under the following continuity conditions: 1) the traces of the primary and second-order twin must be parallel to each other in the plane of the crossed twin; 2) the direction 771 and magnitude, S, of the twinning shear must be identical in the crossing and second-order twins; also, the sense of shear must be the same. If these postulates are valid they constitute a valuable tool for determining twinning elements of newly observed twinning modes in metals. In his classic paper in 1953 on the plastic deformation of a uranium, Cahn1 used these continuity conditions to deduce twinning elements for several uranium modes. However, in the same year, pratt2 showed that both of Cahn's continuity equations were violated for (1012) twin intersections in zinc. Later, Kiho and Maruyama3, 4 showed that Cahn's second postulate was violated in {301) and (101) twinning in tin and (101) twinning in bismuth. In spite of this documentation that Cahn's second postulate is often violated, several recent papers5'6 have been published which have attempted to use the condition of continuity of twinning shear vectors for the evaluation of twinning elements. The primary purpose of this paper is to call attention to the possible ambiguity inherent in applications of Cahn's postulate, and to present additional information concerning the nature of twin intersections.

Jan 1, 1964

By J. G. Hadley

IN THE early stages of the depression the Utah Copper Co. realized that an unemployment problem would he created which demanded an intelligent and sympathetic solution. The company recognized that as many men as possible must be kept at work on a basis which would ultimately permit of the most efficient reabsorption of displaced labor. The company therefore determined to distribute available work among the greatest number of men and to that end adopted a system of rotating employees on a part-time basis. An employer requires a certain number of days' or shifts' work during the month. Obviously one employee working thirty days or shifts a month is equal to two employees each working fifteen. In principle, therefore, where two employees equally fitted to do certain work are available the work could be divided between them on an equitable basis and twice as many persons would benefit. A rotation plan on this basis was adopted by the Utah Copper, Co. on Jan. 30, 1930. Some variations of the orig¬inal plan have been made from time to time, the reasons for which will be discussed.

Jan 1, 1932

By Edward Martinez

The literature on the beneficiation of serpentine asbestos ore states that the specific gravity of the rock containing fiber and the fiber itself is the same so that specific gravity cannot be used as a basis for separation. An investigation of particles of asbestos ore ranging in size from 4 mesh to 5 in. revealed that the fiber-bearing particles generally had a lower specific gravity compared to essentially barren particles. The difference in specific gravity was sufficient to make an effective gravity separation of ore particles and reject a low grade tailings product. The results of laboratory tests are described that lead to the running of pilot plant tests with 20-ton ore samples using a heavy media separator. These tests indicated that a large amount of low grade material could be rejected from the raw ore at a coarse size. Although the process used is a wet separation, it can be added to a conventional dry asbestos mill. A gravity preconcentration would allow the mining of lower grade ore, increase the life of the mine, increase the value of the feed to the fiber recovery section, and decrease maintenance costs by removal of low grade tailings early in the flowsheet.

Jan 1, 1975

By Raymond Mancha

TO determine the optimum inside dimension of an airshaft, it is necessary to strike the proper balance between the cost of power for air friction and turbulence losses within the airshaft, on the one hand, and the cost of sinking the airshaft, on the other. An airshaft larger than necessary is extravagant because the increased amortization rate exceeds the reduction in power cost. Conversely, an airshaft smaller than is needed wastes more power than can be justified by the corresponding reduction in amortization rate. The airshaft power is a function of the air volume Q cu. ft. per min. and the air-pressure drop p in. water gauge across the airshaft. † The airshaft pressure drop is calculated by the formula: R X l X O X Q2 P= 5-2 X A3 wherein R is the air-friction coefficient for the portion of the airshaft 1 ft. deep, 0 ft. in perimeter and A sq. ft. in area, when passing an air volume of Q cu. ft. per minute. The airpower w kw. dissipated within the airshaft is computed by the formula: w= 0.746Q X P 6345 With a combined over-all unit efficiency of the fan and drive of E per cent, the air-shaft power requirements become W = 100w There are 8760 hours per year, so with energy at I cent per kilowatt-hour the annual cost per kilowatt for continuous operation is $87.60; therefore, with energy at C¢ per kw-hr. the annual airshaft power cost MI dollars per year becomes: M1 = 87.60W X C which, expressed by the component parts, becomes: M1 V 5.2X4' / XQ Z 0.746 X 100 X 87.60 X C V 60 X E ) The amortization rate a dollars per year per dollar invested includes both depreciation and interest on the investment. These in turn involve the expected useful life of the airshaft and available molletary interest rate. For the purpose of this discussion the cost of airshaft sinking is assumed to comprise a fixed move-in charge Y dollars, which covers the cost of transporting, erecting and removing the shaft-sinking equipment and is independent of the air-shaft size. Also, it is assumed that the cost of shaft lining, if any, is fixed at $X per cu. yd. of lining material and that excava-

Jan 1, 1947