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The Institute maintains a dual relationship with students: (1) an individual relationship with a Student Associate; and (2) a relationship with local organizations of students, known as Affiliated Student Societies or Student Chapters. 1. The conditions of Student Associateship are set forth in Section 9, Article I, of the Bylaws of the Institute (see page 64 and following pages). During 1934, sundry amendments were made for the purpose of improving the student relationship. Postgraduate students are now eligible; and associateship can be maintained, with the payment of the regular dues of $2 per year, for 18 months following graduation in June. With his regular dues, each Student Associate is entitled to receive during the year his choice of MINING AND METALLURGY, METALS TECHNOLOGY, MINING TECHNOLOGY, PETROLEUM TECHNOLOGY, or two "classes" of Technical

Jan 1, 1943

COUNCIL OF SECTION DELEGATES Nicholas A D'Arcy, Jr, Chairman (Southern California Section) Charles Chapman, Vice-Chairman (Florida Section) Ben H Parker, Secretary (Colorado Section) Frontier Refining Co Boston Bldg Denver 2, Colorado

Jan 1, 1956

By George Otis Smith

A YEAR ago, ,at the Institute's dinner, I closed my A remarks with the words: "The scientist devotes his life to the advancement of learning; the engineer gives his to the advancement of living." May 1 begin tonight where I left off then and speak first of the distinction between science and engineering? This difference is a difference both in purpose and in method: it is the sharp contrast between theory and practice; it marks the broad gap between dream and attainment. Sometimes it happens that the investigator is also the builder and applies what he discovers, yet the distinction between science and engineering serves to point out the broad dependence of the engineer upon his brother the scientist. You remember .the old - saying that "where there is no vision the people perish" translate this into modern experience and we may say that "where there is no science, the engineer fails."

Jan 1, 1929

By H. F. Yancey, O. L. Furse

Although usually coal is screened with punched plate screens having round-hole perforations, there has been an increasing use of wire-cloth screens with square apertures, especially at pneumatic coal-cleaning plants and at other plants that use vibrating screens. It is therefore desirable to establish a relationship between round-hole and square-hole screens for use not only in experimental investigations of coal-preparation problems, but also for use in commercial operations. This need is apparent whenever it is necessary to substitute wire cloth for punched plate and still retain the familiar trade-size product. Although similar work probably has been done by industrial organizations concerned with the screen sizing of coal, the only recorded study of the subject other than the one described herein of which the authors are aware is that of Roesler,1 who screen-sized two samples of limestone and two of zinc concentrates crushed to pass 1/2 in. with a set of square and round-hole screens and found the ratio to be 1:1.23. Procedure In the course of a study of various methods for determining the friability of coal,2 it was necessary to screen-size the products of a series of friability tests of three different coals with both round-hole and square-hole screens. The coals used were from the Roslyn No. 3 and the Bayne mines in Washington and the Rolapp mine in Utah. Twenty 25-lb. samples of each of these three coals at 3 to 2 1/2 in. round-hole size were dropped from a height of 10 ft. to a concrete floor, and then screened with

Jan 1, 1934

By George Boulter

Draglines 8.2-1 Introduction. The nature and characteristics of rock and rock derivatives forming the crust of the earth vary so greatly from place to place that it is impossible to use the same numerical factors to show the, productive ability of excavating equipment on different jobs or projects. Factors for each project must be developed individually and applied as the conditions and requirements dictate. TYPES' OF DRAGLINES. Types of draglines are differentiated by the propelling method used and are generally divided into four classes, as follows: 1. Wagon mounted 3. Crawler mounted 2. Truck mounted 4. Walking Figure 8.2-1 shows a truck-mounted dragline. This type is considered to be the most mobile unit. In order to increase stability over the side, outriggers are installed as part of the truck chassis. This feature is not shown in .this figure. Figure 8.2-2 shows a crawler-mounted dragline. The long, wide crawlers are used to increase the stability and reduce the bearing pressure of this unit. These features allow for use of these units on surfaces too soft for the wagon- or truck-mounted types. Figure 8.2-3 shows a walking-type dragline. The large diameter tub and the well-supported boom through the gantry gives high stability for rugged works over a long life. BASIC PARTS OF A DRAGLINE. The basic parts of a dragline are illustrated in Fig. 8.2-4. A deck layout is shown in Fig. 8.2-5 with the main components named. OPERATION OF A DRAGLINE. Following is a description of the steps and controls present in a typical cycle of operation of a large dragline having independent hoist and drag motors. Starting the cycle with positioning the bucket on the ground under the point of the boom, the next step is

Jan 1, 1968

By Frederick Laist

Introduction IN a leaching process, having obtained the copper in solution, the choice of the precipitation method is influenced y the following factors: 1. Availability of precipitant. 2. Adaptability to the leaching process. 3. Final product desired. 4. Regeneration of leaching solutions. 5. Fouling of solutions. There are three general classes of precipitation methods: 1. The use of iron, scrap or sponge. 2. Electrolytic deposition. 3. The use of some gas or reagent y which the copper is obtained, usually in the form of an intermediate precipitate which requires further treatment. For example, the precipitation of the copper as Cu2Cl2 from chloride solutions, with SO2 gas. The use of iron is adapted to almost any process. It has the great advantage of extreme simplicity, and the recovery of the copper and any values present in a highly concentrated, easily treatable form. The disadvantages are the cost in isolated places, the uncertainty of the scrap-iron market, and the fouling of the leaching solutions. The latter is a serious factor, When a reagent such as salt is used in them, which makes necessary their re-use. Where applicable, electrolytic deposition is very attractive. The copper is obtained in a form directly marketable, there is a regeneration of acid amid no fouling of solutions. Unfortunately, chloride solutions do not lend themselves to electrolysis. An entirely satisfactory anode material has not yet been discovered, although magnetite, apart from being rather brittle, seems to answer the requirements fairly Well.

Jan 7, 1914

By R. Schuhmann, O. W. Moles

at temperatures of 1150°, 1250°, and 1350°C for liquid copper sulphides ranging in composition from saturation with Cu to about 21.5 pct S. From the experimental data, activities of Cu, S, and Cu2S in the melts were calculated. Also, the results furnish a new determination of the location of the curve showing the compositions of Cu-saturoted sulphide melts in the CU-S constitution diagram. THE "white metal" made as an intermediate L product in converting copper matte to blister copper is a matte approximating Cu2S in composition. It has long been known that liquid Cu-S mattes can exist at a given temperature over an appreciable composition range, with S:Cu ratios ranging up from a lower limit corresponding to equilibrium of the matte with a liquid Cu phase. The Cu-saturated matte has somewhat less S than Cu2S, although previous measurements of the compositions of Cu-saturated mattes are not in good agreement.'" As the S:Cu ratio approaches and slightly exceeds that for Cu2S, the partial pressure of sulphur gas over the liquid matte rapidly approaches atmospheric pressure,5 so that Cu-S melts with much more S than Cu2S can be made and handled only in pressure apparatus. Accordingly, the liquid copper sulphides of interest in copper smelting and readily studied experimentally fall in a relatively narrow composi- tion range about Cu2S. The freezing points of Cu-S mattes show a maximum of 1129°C near the composition Cu, dropping to 1105oC for Cu-saturated mattes having less S and dropping under 1100°C for higher S mattes.' Estimates of the sulphur pressure and other thermodynamic properties of liquid Cu,S were made by Kelley; based on extrapolations from equilibrium measurements on solid Cu,S. More recently, Cox and coworkers' studied equilibria in the reaction: Cu,S + H, e 2Cu + H,S over the temperature range 700" to 1250°C. They measured equilibrium H2S:H2 ratios presumably with both the sulphide and the metal phase present, so that their data above the melting point of Cu,S should measure the S pressure of Cu-saturated sulphide melts. The sulphur pressures of liquid copper sulphides of several S:Cu ratios at their freezing points can be estimated from data given by Posnjak, Allen, and Merwin." However, beyond these few data, no systematic study seems to have been made of the relations of sulphur pressure and other chemical properties of liquid copper sulphides to composition and temperature. The measurements of the sulphur pressures of liquid copper sulphides reported in this paper represent a first step in the quantitative study of the chemistry of mattes. Similar work is planned on

Jan 1, 1952

By J. B. Cohen, M. B. Beaver, R. J. Black

RECENT investigations have shown that face-centered cubic metals may deform by twinning. Blewitt, et al' found that at 4.2"K the mode of def~rmation of single crystals of copper changed at large strains and markings formed on (111) planes. Later they- emonstrated by X-ray diffraction and metallography that the markings were twins and showed that favorably oriented single crystals of copper deformed by twinning at 78°K. They also observed twinning in silver and gold deformed at 4.2 and 78°K. Wagner3 obtained evidence for twinning from the peak shape of diffraction lines of silver cold-worked at 78°K, but twins small enough to cause such effects are not likely to be detected metal-lographically. In the work reported here lamellar structures were observed in deformed silver-gold alloys. They appeared to be mechanical twins, but metallography could not establish this conclusively. Their tendency to form depended on strain rate, temperature and composition. Specimens of silver-gold alloys (0 to 83 wt pct Au) were deformed plastically. One set was worked by hammering under liquid nitrogen, at room temperature and at intermediate temperatures. Another set was compressed slowly in liquid nitrogen to the same reductions as those produced by hammering. Tensile specimens (0.015 x 0.120 x 1.5 in.) of various compositions and approximately equal grain size (0.011 to 0.016 cm) were tested at -195°C and at room temperature. In microsections of all specimens deformed by hammering at —195°C thin lamellae appeared, Fig. 1. They were aligned in definite directions in each grain. In some grains they had two orientations. Where lamellae intersected, a displacement was apparent. Near the center of the left margin of Fig. 1 shear has taken place beyond the fully developed intersecting lamella. Many lamellae resembled Neumann bands in alpha iron. They were parallel to one side of triangular etch pits in the matrix (as in Figs. 1 and 2). The individual lamellae were narrow and had little substructure. This suggested that they did not result from concentrated local slip. The shape of etch pits within the lamellae differed from that of pits in the matrix, as can be seen in Fig. 2; this indicated a difference in orientation. Specimens slowly deformed at —195°C contained regions in which the lamellae were clustered. In these specimens some lamellae were bent and presumably had formed before the termination of the deformation. Structures of greater width than the lamellae were also seen.4 More lamellar structures formed on impact than during slow compression to a given reduction. This was true of all compositions. The structures became less abundant with increasing temperature of deformation. None was observed after extension to fracture at room temperature, but they could be pro-

Jan 1, 1959

By Kung-Lee Wang, Brian W. Mackenzie, Warren E. Morrison, DeVerle P. Harris, George F. Sharrard

The term "mineral economics" is applied to a wide range of activities in the mineral industries. Earlier chapters have described the application of economic concepts to the mineral industries-supply, demand, conservation, tariffs, etc. The solution of mineral economics problems is often assisted by the application of quantitative methods. The purpose of this chapter is to describe a number of quantitative methods-econometric, operations research, and management science techniques-which find application in the analysis of mineral economics problems. These methods include input-output analysis, trend analysis, forecasting techniques, simulation, multivariate statistical analysis, mathematical programming, and market research techniques. The purpose of this introductory section is to provide a mineral economics framework for the application of these methods. Mineral economics is a subdivision of economics that is justified by a sufficient number of economic problems in the mineral industry requiring special experience and an unusual combination of skills. These problems are concerned with the conversion of minerals as geologic resources to minerals as economic goods. The mineral conversion process is outlined in Fig. 8.A.1. The physical occurrence of mineral deposits in nature and the market demand for mineral products in the economy provide the basic stimuli. The conversion process embodies a number of sequential stages-exploration, the development of mineral deposits, and mineral processing facilities and, consequently, productive activity to supply market demand. Changes in demand and the depletion of deposits illustrate the dynamics of the process. Mineral economics applies economic con-

Jan 1, 1976

By A. P. Boller

In the victories of peace as well as of war, the science of engineering has played a prominent, if, indeed, not the leading part. While it might be interesting, and food for profitable thought, to trace the development of engineering from early times in its bearings upon the social betterment of mankind, it will be sufficient on the present occasion to suggest a few thoughts that it is hoped will aid the unprofessional listener to an appreciative consideration of the subject-matter laid down for to-day's discussion, and possibly lead the professional brother to a higher conception of the profession to which he belongs. Since the advent of the railway era, it is difficult to grasp the sequence of historic events that have led to the wondrous derelopment of mechanical science, making possible the civilization that is our daily boast, and opening up a vista of future intellectual and moral advancement among the nations of the earth, 'before which the imagination becomes hopelessly lost. Even now, looking back over a period of only half a century, we often fail to realize the vast change in the relations of individuals and nations to each other., brought about by the results of those mechanical discoveries which, having made the whole world kin, exercise a resistless levelling influence that bears fruit politically in the spread of republican ideas, and morally in the elevation of the individual through the facilities given to the dissemination of Christian ideas and general intelligence. In this view, it seems almost like a work of supererogation for a body of representative men of one department of that science to which the whole world owe. so much, to meet here at the centre of our national life to plead not only for a practical recognition of the national importance of the work to which their lives are devoted, but also for national aid, on a scale beyond that of private effort, to the end that mechanical science may be carried to a higher plane than ever yet attained, each step on the way being of material benefit to every man, woman, and child in the community. Possibly this is strong language, but none too strong when we consider that the work for which we plead is one affecting not only vast scientific and commercial interests, but also human life, to a degree little ap

Jan 1, 1882

By W. E. D. Stokes

WHEN history is written, the year of the blitzkrieg will go down as giving aviation its greatest impetus. No perceptible drop in military business, even with cessation of hostilities abroad, seems likely. The combined air force of the U. S. Army and Navy on July 1 was approximately 5000 planes, as against 50,000 planes currently discussed as necessary. Observers at the fronts are giving designers and metallurgists back home some realistic ideas to shoot at. As conventional runways reveal the location of airports to enemy raiders, operating bases are now masked. Difficult, often muddy and rough landing strips, requiring strong landing gears and exacting take-off and maintenance characteristics, are the specifications of war. This is "old stuff" to numerous mining operators in mountainous jungle areas where gradients up to 8 per cent are in more or less common use in such mountain landing fields. Although airplane building is not readily adaptable to assembly-line methods, a trend towards mass productions is now in evidence. Incidentally, a U.S. Army "Curtiss P-40" requires about 10,000 man hours of work to complete and is tied together with 75,000 rivets. During the past year a number of aircraft factories adopted the "shot-

Jan 1, 1941

By Alan Morris

In a previous paper1 the results of cutting tests on free-cutting brass rod were reported. Investigation was made of the effects of variation in lead content, microstructure and cold drawing. The author's reply to the discussion of that paper includes a study of the directional cutting properties of drawn and annealed rod. The present paper records the results of tests made on series of samples in which the tin, iron and copper contents have been varied. The apparatus used and method of testing are described in detail in the previous paper. The machine is of the pendulum-operated milling type used and described by Airey and Oxford.2 Angular readings of the height to which the pendulum rises after falling from a fixed position, both when a cut is made and when the pendulum swings freely, give the basis for calculation of the energy consumed in making a cut. Careful weighing of the sample before and after cutting gives a measure of the amount of metal removed. The results are expressed in footpoiinds per cubic inch of metal removed, and have been called "unit cutting energy." In the course of the discussion of the author's earlier paper, W. B. Price reported large-scale tests involving some 50,000 lb. of material. These tests indicated that the addition of as much as 0.6 per cent of iron and 0.25 per cent of tin had apparently no adverse effect on the highspeed cutting characteristics of the rod. The rod also contained a small amount of nickel. The test results reported here tend to confirm his observations. Effect of Variation in Tin Content The castings for this series were made 2 by 1 by 9 in. and were processed as follows: 1. Castings were annealed at 500" C. for 7 hr. 2. Cold-rolled to 0.700 in.

Jan 1, 1933

By Newell G. Alford

Forecasts of future timber consumption in soft-coal mining are handicapped by the lack of adequate experience records for estimating properly the timber requirements of the industry. Data were obtained from plants where records are kept or from operators who collected the information and to these were added composite figures for the continental United States in 1905 and 19191 and for central and western Pennsylvania and for Illinois in 1922.2 The result, representing slightly over 928,000,000 net tons, is shown in Table 1. Some of the companies furnishing data were unable to segregate the timber into classes of use but for those who did, Table 2 shows the board feet of posts and cross ban used per ton of coal mined and the percentage of the total timber consumed that was used in roof support. The wide variation in amounts of timber per ton of coal mined is the result of

Jan 1, 1924

By B. W. Howlett, M. B. Bever, Somnath Misra

The heats of Formation of the compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 and the heats of solution of tellurium and selenium in liquid bismuth have been measured in a liquid metal solution calorimeter. The heat capacities near the melting point, the heats of fusion, and the melting points of the two tellurides have been measured in a constant temperature gradient calorimeter. The thermo-dynamic quantities are interpreted in relation to the stability of the compounds and the nature of the solid-liquid transition. THE selenides and tellurides of several elements of Group VB of the periodic system are of interest because of their electronic properties. The compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 are semi- conductors; they also have gained prominence in the fields of thermoelectricity and photoconductivity. However, little is known about their thermody-namic properties. As part of a research program on the thermo-dynamic properties of intermetallic compounds, the heats of formation of the compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 were measured in a liquid metal solution calorimeter. The heat capacities near the melting point, the heats of fusion, and the melting points of the two tellurides were measured in a constant temperature gradient calorimeter. The results, in addition to their intrinsic interest as thermodynamic quantities, contribute to an understanding of the stability of the compounds and the nature of the solid-liquid transition. 1) EXPERIMENTAL 1.1) Materials. Samples of the compounds SbzSe3 and Bi2Se3 were prepared by melting the elements in stoichiometric proportions in evacuated Vycor capsules followed by quenchinn in water. They- were then annealed in vacuum for 12 hr at 550°C. A sample of Sb2Te3, consisting mainly of one large grain, supplied by the Lincoln Laboratory,

Jan 1, 1964

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

By J. T. Burwell

The crystal orientation in silicon iron that has been given a particular treatment described by Goss,l has been studied by Goss, by Bozorth2 and by Sixtus,3 but their results do not agree and are almost entirely qualitative. The following pages give a description of the orientation of the crystals in the material as determined by means of X-rays and expressed graphically in a pole figure. The treatment consists of hot-rolling the material into strip and then giving it two cycles of cold reduction followed by recrystallization. This produces remarkably good properties in the rolling direction, the product having a maximum permeability in this direction of more than 25,000 and a permeability at 16,000 Gauss of more than 2200. It is now generally agreed that Goss's original conclusion1 that the crystals in the final product are randomly oriented was incorrect, since Bozorth2 and Sixtus,3 using different methods, have shown that there is a decided preference in orientation. Those writers, however, expressed their results only in terms of one or more ideal orientations with deviations therefrom. X-ray Data A strip of the material containing 3.1 per cent Si, prepared by Goss,† 1.2 by 0.0125 in., was etched rapidly in warm dilute hydrochloric acid until it was 0.005 in. thick, in order to eliminate the effect of the two surface layers. The specimen was then mounted in an integrating camera similar to one described in the literature.4 The purpose of this camera is to translate the specimen during exposure, so that a statistically large number of grains contribute to the pattern photographed. The camera also allows the plane of the specimen to make various angles with the X-ray beam. An area 5 by 1.2 in. was scanned by a beam of unfiltered radiation from a molybdenum target tube operating at 37 kv., and the measurements were made principally on the peak of the white radiation. X-ray photographs were taken at intervals of 15" in a plane

Jan 1, 1940

By E. T. Turkdogan, L. S. Darken, R. J. Fruehan

Further consideration is given to the application of the quadratic formalism to evaluate the thermodynamics of binary metallic solutions from experimental data. The use of the thermodynamic relation, in(r1/r2) dN2= 0, in the evaluation of activity data is discussed. The empirical correlations derived previously for enthalpies and entropies of solutions in Part II are shown to be predicted theoretically for a special case. The applicability of the quadratic formalism to the activity coefficients for binary organic solutions is demonstrated. DARKEN&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. In a subsequent paper (Part II) Turkdogan and Darkeen2 extended this formalism to the enthalpy and excess entropy of binary metallic solutions, and showed that the available data for the activity coefficients and heats of mixing of many solid and liquid binary metallic solutions confirm reasonable applicability of the quadratic formalism. Much variation was noted, however, in the extent of the terminal regions from one system to another, commonly from about 10 to 70 at. pct. For the present purpose, equations derived previously need be given only for one of the terminal regions, e.g. region (I), 0 < N2 < N&apos;2: where subscripts 1 and 2 indicate quantities for components 1 and 2 and superscript ° the values at infinite dilution; other terms are: N = atom fraction, y = activity coefficient, = partial molar enthalpy of solution, ?HM = molar heat of solution, ?Sx = excess partial molar entropy, ?Sx = excess molar entropy. The heat and entropy like terms (constants) el, and S12 are defined in the following expression for the temperature dependence of a12, thus a12 £12 — s12 rnl 2.303RT 2.303 R l J Using this formalism, the thermodynamics of binary systems in the terminal regions may be described over a temperature range of experisental interest in terms of eight quantities: Lº1—Lº2, ?Sx1,?Sxº2 , £12 ,£21,fiai, S12, and S21. In the previous paper, these quantities were evaluated for many solid and liquid binary solutions, and two significant correlations were observed between these thermodynamic quantities pertaining to the terminal regions, thus [10] and [11] Combining Eqs. [9], [l0], and [ll] and rearranging gives a12 -a21 = 1.382R log rº2- 0.08(?S2xº- ?S1xº) [12] Since the second term involving entropies is small and Eqs. 1101 and [ll] are empirical relations, the above equation may be simplified to a12 = 2.74 log rº2 [13] Using the values of a&apos;s and y°&apos;s compiled in Parts I and 11, a12 - a21 is plotted against log(rº2/rº1) in Fig. 1; the line drawn has a slope of 2.74. For Hg-K at 300°C, log(yº2 /yº1)= —5.10, not shown in Fig. 1, and from correlation [13], a12 - a21 = -13.97; this is to be compared with -10.76 derived from the activity data (Part II).

Jan 1, 1970

By Arthur B. Foote

Ore production from the property of the Miami Copper Co. began early in 1911. Until 1925 this ore came from the so-called high-grade orebodies, which contained a little over 2 per cent. copper. This ore was mined by the following methods: 1. Top slicing after mining the peaks by square setting, which produced 4,524,347 tons, including ore from square setting. 2. Shrinkage stoping with sublevel caving of the pillars, which produced 2,230,577 tons. 3. Undercut caving with hand tramming, which produced 15,427,672 tons. Estimating December tonnage, the total ore mined to the end of 1929 will amount to slightly more than 43,000,000 tons. The first method was described by E. G. Deane&apos; and the second by D. B. Scott,&apos; and the third, together with a general description of the mine, by J. H. Hensley, Jr.&apos; The geology of the district has been worked out by Dr. F. L. Ransome.2 The author acknowledges also the assistance of R. W. Hughes, assistant mine superintendent, E. V. Graybeal, chief mine engineer, A. J. McDermid and S. R. Burdick, engineers of Miami Copper Co., Miami, Arizona. Factors Influencing Selection of Mining Methods The mining method described herein was selected primarily with a low mining cost in view and was developed to avoid as far as possible dilution of the already very low-grade ore. In 1924, with the exhaustion of the high-grade orebodies in sight, it was decided to develop the low-grade orebody, which at that time contained 36,000,000 tons of ore assaying 1.06 per cent. copper, and had an area of 50 acres with an average thickness of 206 ft. overlain by an average thickness of 320 ft. of barren capping.

Jan 1, 1930

Jan 1, 1902

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971