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By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Carl Wagner

AT elevated temperatures. most metals react with oxygen, sulphur, or halogen rather rapidly, although a coherent layer of the reaction product is formed and separates the two reactants from each other. The reaction proceeds, since one of the reactants or both dissolve and diffuse across the reaction product. In many cases the rate is diffusion-controlled as is indicated by the validity of the parabolic rate law of Tammann&apos; and Pilling and Bed-worth. wott and Gurney&apos; have suggested that diffusion processes also play an important part in the case of reduction reactions. This is confirmed by observations reported below. In general, however, the rate of reduction reactions is determined not exclusively by diffusion processes. Reduction of Silver Sulphide Above 179°C silver reacts with liquid sulphur very rapidly. Since the volume of silver sulphide is much greater than that of the equivalent amount of silver, a coherent layer of silver sulphide is formed in accordance with a rule established by Pilling and Bedworth.&apos; According to Wagner&apos;,&apos;&apos; silver ions and electrons migrate from the Ag-Ag,S interface across the silver sulphide layer to the Ag,S-S interface where the following chemical reaction takes place: 2 Ag +2 e + S Ag,S If silver sulphide is reduced by means of hydrogen, the equivalent volume of the reaction product, silver, is less than that of the initial substance. Accordingly, no coherent layer of silver is formed. Instead, fine filaments of silver grow from the silver sulphide surface into the ambient gas. This phenomenon has been investigated by many authors, especially by Kohlschiitter," who has also reviewed previous literature. Kohlschiitter has interpreted the observed phenomena by migration of "silver" dissolved in silver sulphide. According to Wagner,&apos; silver ions and electrons are the migrating particles. The sequence of consecutive steps involved in the reduction of silver sulphide is shown in Fig. 1. Every- where at the silver sulphide surface, hydrogen reacts with sulphur so that excess silver ions and electrons are formed, which migrate at random until they are captured by a nucleus of metallic silver. If such a nucleus lies on the surface and material is furnished only from the base, the original nucleus is pushed outward and thus a filament grows. Removal of sulphur and formation of metallic silver may also take place at different points when silver sulphide is reduced by copper. The reaction is usually formulated as: AgL,S + 2 Cu = Cu.S + 2 Ag but the actual reaction products are silver and a solid solution of the two sulphides. Primarily, excess silver and electrons dissolved in silver sulphide are formed. After a certain degree of supersaturation has been reached, nuclei of metallic silver may form. If, however, a silver foil is in contact with the silver-sulphide phase, as is shown in Fig. 2, silver ions and electrons will migrate to the Ag,S-Ag interface where they are captured. To confirm this scheme, a composite sample, with the geometry shown in Fig. 2, was made by pressing silver sulphide tablets 0.6 cm in diam and 0.4 cm high together with a copper cylinder and a silver foil in crucibles of iron, which does not react appreciably with silver sulphide at 400°C. After heating for 3 to 7 hr at 400°C. the specimens were cut normal to the phase boundaries. It was found that the thickness of the silver foil had increased from 0.01 cm as initial value to a maximum value of 0.06 cm. In the interior of the silver sulphide tablets only traces of metallic silver were observed. These observations show clearly that silver ions and electrons may migrate over distances of several millimeters before they form metallic silver. Reduction of Cuprous Sulphide by Iron The behavior of cuprous sulphide is very similar to that of silver sulphide, since the lattices of the high temperature modifications are identical, but in Cu.S there is a variable deficit rather than an excess of metal. To investigate the displacement of copper by iron, cuprous sulphide powder covered by a copper foil was pressed in iron crucibles and heated up to 800 °C for 3 to 7 hr. The thickness of the copper foil increased from an initial value of 0.005 cm to a nlaximum value of 0.029 cm. In the interior of the

Jan 1, 1953

By Bernard Moore

THE last few decades have witnessed the introduction of many new nonmetallic mineral products and changes in the use of many of those already well known. Among these is diatomite, formerly employed as a mild abrasive and, at one time, as the absorbent material in dynamite. Now nearly 100,000 tons a year are mined and milled into such things as filter aids, cement admixtures, insulants, fillers, absorbents, cosmetics, cleansers, etc. Pumice, commonly regarded as only an abrasive, is now also employed as an insulant, as light-weight aggregate and as a concrete admixture. With increasing use of insulants, light-weight aggregates, and acoustic stuccos and plasters in the building trades, both these mate-rials should find increased application. Very large deposits occur in eastern Oregon and have been studied by the U. S. Geological Survey in cooperation with the Oregon State Mining Board.

Jan 1, 1934

By Jack Washburn, E. R. Parker

Kinking in zinc single-crystal tension specimens was observed under conditions of low stress and high temperature. Kinking is discussed in relation to other plastic bending phenomena on the basis of dislocation theory. Experiments on the stress-induced motion of small angle boundaries are reported. KINKING was first reported by Orowan1 as a new deformation mechanism. He observed the phenomenon in cadmium single crystals loaded in compression. Glide lamellae in a local region of the rod were observed to snap over suddenly to a tilted position, resulting in a sudden shortening of the specimen. Between the tilted portion and the rest of the crystal there were fairly sharp boundaries, with the slip plane assuming approximately mirror image positions on opposite sides of these boundaries. Orowan considered the boundaries to be regions where dislocations had concentrated. Hess and Barrett&apos; observed the formation of kinks in critically oriented zinc compression specimens. It was found that the sudden snapping over of the tilted region was not an essential part of the kinking phenomenon but rather was associated with the method of loading. Kinking was explained on the basis of the accepted mechanisms of slip and flexural glide. It was also suggested that a kink can be considered as a special type of deformation band. During a recent investigation of the effect of surface condition on creep of zinc single crystals," a similar phenomenon was observed in crystals which were loaded in tension. The specimens were 0.4 in. diam cylindrical rods with a free length of 4 in. between end connections. All of the crystals were tested at a constant load. adjusted to give an extension rate of approximately 0.05 pct per hr. Kinking, as shown in Fig. 1, occurred in some of the tests performed at temperatures above 200°C. Kinking was observed in specimens varying widely in initial orientation, scattering about a 45" angle between the slip plane and the specimen axis. The condition leading to kinking in tension appeared to be non-uniform distribution of flow along the gage length combined with the restraint imposed by the tensile load. At low temperatures and fast strain rates, the distribution of strain throughout the midsection of tension specimens was generally quite uniform; therefore, bend planes developed only near the ends as described by Miller.4 However, at high temperatures under creep conditions it was difficult to obtain specimens in which the distribution of flow was uniform. Some of the factors which may have caused differences in flow stress along the length of the crystals are: Nonuniform distribution of impurities, accidents of growth (lineage structure), slight bending or other damage during handling, surface conditions, and strain-aging characteristics due to dissolved nitrogen." Plastic flow, once started in a local region, often continued to a relatively large strain before other parts of the gage length became active. Under these conditions a series of kinks, such as those in Fig. 1, were produced. Fig. 2 illustrates how a nonuniform distribution of slip produces bending moments which- are responsible for kink formation. If no plastic bending were to occur while the rod extended by pure slip in two separate sections of the rod, it would assume a shape such as that in Fig. 2a. A specimen having this shape and being subjected to a tension load would have concentrations of stress at the concave surfaces C and lower than average stress would exist at the convex surfaces D. Therefore a bending moment is superimposed on the average stress in the regions between C and D. The positions of potential bend planes under these conditions are shown as dotted lines. Actually no such shape as Fig. 2a develops because plastic bending in the region C-D occurs simultaneously with pure slip in the intervening regions. The observed structure of a tension kink is indicated by Fig. 2b. Perhaps the best approach to an understanding of kinking as well as other related plastic bending phenomena, such as the bend planes discussed by Miller,&apos; cell formation studied by Wood et al.,6 and polygonization,7 is consideration of the dislocation model of a bent lattice. Current theories of the slip process postulate generation or multiplication of dislocations at certain lattice imperfections. The mechanism proposed by Frank and Read8 results in continuous generation of concentric dislocation loops which spread out

Jan 1, 1953

THE subcommittee on Coal Mining, since its appointment, has been engaged in collecting data about subsidences in coal mines in this country, and it now feels that almost all of the available data about occurrences of this sort in bituminous mines has been collected. As most of the bituminous seams are nearly level, the records obtained give the problem in its simplest form, without complications due to the pitch of the seam. Similar data is being compiled for the anthracite regions and it is hoped that this will be ready for the 1927 meeting. Copies of the questionnaire, Appendix A, were mailed to all of the coal operators&apos; associations, to most of the large operating companies and to many engineers, with the request that any data on the subject be returned to the committee, or that advice of any subsidences known be given. The replies to most of the questionnaires were general only, although some specific cases were given. Many of the companies were unable to reply to all questions, as they lacked the necessary data, but in nearly every case where accurate data was available, it was cheerfully furnished, and any additional information requested was secured. All specific cases of subsidence were followed up by correspondence, and in several cases by personal inspection. Figs. 1 to 31 were made from the information furnished. Table 1 gives measurements of elevations taken in one case at intervals from October, 1913, to May, 1918. With one exception, where the evidence cannot yet be released on account of a lawsuit, it is believed that the cases submitted with this report include practically all that have happened in bituminous coal mining in this country of which actual measurements were secured. Some of these have already been published in the excellent report by Young and Stoek,1 and some instances have been secured from other publications. In collecting these data, the subcommittee had the Engineering Societies Library extend the bibliography given in the bulletin mentioned above to date. This list is given in Appendix B.

Jan 2, 1926

By A. M. Gaudin, J. G. Morrow

FLOTATION requires the existence of a definite contact angle. This contact angle, the surface tension of the solution, and adsorption at the solid-fluid interface are quantitatively related. Adsorption of dodecylammonium acetate on hematite was measured for a wide range of concentrations of reagent in solution. Similar measurements for quartz have already been made. Contact angle measurements were then made on polished surfaces of hematite and of quartz immersed in aqueous dodecylammonium acetate solutions, and a functional relationship was sought between adsorption density at the mineral-solution interface and the contact angle. Finally, the surface tension of the aqueous amine acetate solutions was measured. These data were combined to give an evaluation of the work of adhesion for the three-phase system. Specular hematite was crushed and then ground dry in a laboratory porcelain mill, with flint pebbles, to pass a 200-mesh screen. The ground product was sized in a Haultain infrasizer, and one of the granular sizes (cone No. 3) was used in all adsorption tests. A hand magnet was used to remove magnetite and abraded iron. Quartz was removed in a Frantz isodynamic magnetic separator. The purified hematite was leached in aqua regia, washed with distilled water until the washings appeared free of electrolyte by conductance measurement, dried in a low-temperature oven, and stored in a pyrex container. The specific surface of the closely sized hematite was determined by the krypton gas adsorption method.&apos; Three measurements gave an average value of 1350 sq cm per g. Chemical analysis showed Fe -69.37 pct, insol = 0.72 pct. The quartz used in the flotation tests had been prepared by Chang" for an earlier investigation. Demineralized distilled water was used for all test solutions. Dissolved salt content was of the order of 0.03 ppm, expressed in terms of sodium chloride, as estimated from conductance measurements. Dodecylammonium acetate was obtained from Armour & CO. in two forms, the unmarked compound and a preparation marked by carbon 14 in the hydrocarbon chain of the aminium ion. Specific activity of the active salt was 0.134 millicurie per g. The important physico-chemical constants for the primary amine salt have been reviewed by de Bruyn. The calculated effect of hydrolysis of amine salt on pH of aqueous solutions and the effect of pH on the distribution ratio of the alkylammonium ion to free amine are of particular interest. All other chemicals used in this investigation were of analytical reagent grade. A column method&apos; was used for adsorption work. Attainment of equilibrium distribution in the adsorption column depends on the solid-solution contact time, hence upon the volume of solution passed. It was assumed that contact time required for equilibrium would be a maximum for the lowest reagent concentrations. On this premise it was demonstrated experimentally that the passage of 500 ml of solution through the mineral bed was adequate. An aliquot (1 to 5 cc) of the solution to be analyzed was transferred to a small pyrex cup and allowed to evaporate to dryness at room temperature; 4 or 5 mg of unmarked amine acetate were added to the dried sample and the cup and its contents were transferred to the combustion system for analysis. Evaporation at room temperature must be emphasized, as even slightly elevated temperatures result in loss of reagent. A laboratory model G Beckman pH meter equipped with a glass electrode was used to measure pH of amine acetate solutions. The technique of internal gas counting of radioactive carbon dioxide in a Geiger-Muller counter was used. Developed originally by Brown and Miller,- his method was adapted to the analysis of carbon-14 marked flotation reagents by Chang, de Bruyn, and Bloecher. nalytica1 method and procedures have been described in detail by Bloecher.&apos; Contact angles were measured by the captive-bubble technique." The mineral specimens were carefully selected to avoid cracks and inclusions of other minerals. All specimens were mounted in plastic and polished to produce a smooth surface. The final polishing and contact-angle measuring

Jan 1, 1955

CHARLES F: WILLIS,* Bisbee, Ariz. (written discussion?).-An employment department operated only with the object of relieving the foremen from hiring and for the purpose of centralizing record keeping is not likely to be entirely successful, and is doing but a small part of the good that practice has shown is possible; although it was .probably a desire to save time and to conduct the business more conveniently that led many mining companies to centralize their employment department. The ultimate object, however, is the reduction of labor turnover, by obtaining men better qualified to fill the positions to which they are assigned, by following up their work and providing for transfer to other departments or for promotion, if advisable, by reducing the number of quits for inconsequential reasons, and by supervising such laying-off as is necessary in such a way that the permanent force is not upset. It provides a stability &apos;of employment, free from favoritism and paternalism, probably the best form of employment insurance that we can have. The value of the employment department is in direct proportion to the breadth of its supervisor, his ability to estimate and place men, his sympathy in dealing with their petty troubles, and his analysis of quits and the reasons therefor. There is probably no better index of the soundness of the industrial relationship between the employee and the employer than the reasons why men quit; an intelligent, unbiased analysis of these reasons tells where corrective measures are necessary. In nine cases out of ten the reasons are small grievances, easily corrected, and are things usually overlooked by mine officials.

Jan 6, 1919

By E. G. Bailey

The bituminous coal industry faces a real problem, if it desires to retain the position in the power-generation field to which it is economi-cally entitled. More power is probably produced today for electrical energy, for steam-driven and steam-heating industries and processes, for transportation by rail, water, highway and air, collectively, than ever before, and yet the total bituminous coal production has decreased about 38 per cent, from 575,000,000 tons in 1926 to 357,500,000 tons in 1934. It is not the intention of the writer to recommend coal as a fuel for automobiles and airplanes, but rather to point to these forms of transpor-tation as being responsible in a very measurable degree for reducing the coal consumed by railroads. Petroleum products may still further reduce consumption of locomotive fuel through the extension of the use of Diesel-driven trains. Oil-burning steam-driven locomotives are replacing coal in some places, where railroads operating high-speed pas-senger trains are willing, temporarily at least, to pay a premium for the fuel, that is low in ash and produces less smoke and practically no cinders. In the navy and ocean-going passenger ships, oil is so firmly estab-lished, and has such definite advantages over coal as formerly fired, in steaming radius, in ease of bunkering, cleanliness, and reduction in firing labor, that very outstanding developments in the handling and burning of coal will be required in order to replace oil. For freighters on the Great Lakes, coal is the logical fuel, but there is great and immediate need of radical improvements in its use, else that market also may be lessened. It is not within the scope of this paper to discuss in detail bitumi-nous coal for either locomotive or marine use, but, rather, generation of power in stationary plants, consisting of electrical generating stations and that very large group of miscellaneous industrial plants, such as paper, rubber, textile, steel and other industries that use electrical, mechanical, and steam power, derived from either hydro or some form of fuel.

Jan 1, 1935

The paragraphs quoted, regarding Mr. Hoover&apos;s appointment as chairman of the newly organized food board of the United States, are taken from the editorial page, of the New York Times for April 13: ?The country is fortunate in commanding the services of Herbert C. Hoover as Chairman of the newly established Food Board. This is n, problem of first importance. Few realize the extent to which American food stuffs will enter into the decision of the war, and it is doubtful if it has occurred to many minds as yet that we shall have to deny ourselves what we have regarded as necessaries in order to keep our European allies supplied. " Mr. Hoover is one of the leading mining engineers of the country. At the outbreak of the war he put his private affairs aside to become the head of the American Commission for Relief in Belgium. He has had an experience that perhaps no other man has ever had, covering the raising of money and the purchase and distribution of supplies on a large scale; He has been brought into close relations with the neutrals and the belligerents on both sides. By them all he is recognized is one of the best executives brought to the fore by the mar. Mr. Hoover is in a position now to place abilities and experience at the service of his country. He will come back with comparative data that will enable him to measure resources and deficiencies accurately. This appointment gives renewed assurance of our Government&apos;s grasp of the problems of war and its resolve to apply, business principles to their solution."

Jan 5, 1917

By K. E. Beu

IN the measurement of retained austenite concentrations in steels using the integrated intensity method,1 Averbach has pointed out" that the absorption factor A(0) for a flat sample making a glancing angle 4 with the incident X-ray beam can be combined with his constant factor R to obtain our constant factor" G provided that "1—There is no preferred orientation in the sample, and 2—The geometric requirements [for the sample, film, and X-ray beam] have been met precisely."&apos; If A(0) can be combined with R to give G according to the equation G = R . A(0) [14] then the possibility for making non-compensating errors in the austenite determination has been eliminated. This has been described previously in a technical note." Because of the brevity of the previous note,3 it was impossible to emphasize the fact that the two conditions on preferred orientation and geometry can be easily met experimentally, contrary to Aver-bach&apos;s statement that: ". . . the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2 [the theoretical equation for A(0)]."" he way in which these two conditions can be met experimentally will be discussed briefly to help clear up this point. In addition to these two conditions, other factors such as sample shape, homogeneity, and grain size which also affect A will be included in this discussion. A (0) depends on sample shape. The theoretical function for A was derived originally for a flat surface.&apos; In general we have found that a flat sample surface is readily obtainable." If such a surface can * The effect of surfaces which are not flat on the measurement of retained austenite will be discussed later. be obtained, it has the following advantages: 1—it is easily reproducible from sample to sample, 2—it is the form required for metallurgical examination —this type of examination being frequently desirable for this work, and 3—it is an efficient shape for diffraction purposes. Perhaps the most important of these features is that a flat sample surface is easily reproducible; hence, this requirement on the repro-ducibility of A from sample to sample is met for all such samples. Fig. 1—Schematic diagram of the quartz crystal monochromator diffraction unit. The centerline of the main beam is at 6&apos; to the target face. The tangent to the crystal face is at 16.8&apos; to the moin beam. The centerline of the monochromatic beam is at 33.6 to the main beam. The sample surface can be rotated in its own plane. The angle of the sample surface and the monochromatic beam can be adjusted by rotating about the vertical axis, The film holder can also be rotated about B so that the film can be exposed over the desired angular range. For Fe K, X = 1.932A. 1011 planes of quartz have d = 3.35A. A(0) depends on homogeneity and grain size. If the sample is badly segregated or the grain size is large, the effect of micro-absorption and primary extinction1. &apos; must be considered. It has been shown, however, that for most plain carbon or low alloy hardened steels, neither micro-absorption nor primary extinction effects are present.&apos; A (0) depends on camera geometry. For a given angle 0, A remains theoretically constant from a geometrical viewpoint only if the following factors are kept constant: 1—the angle of inclination .+ of the sample to the X-ray beam, and 2—the centering of the sample with respect to the film cylinder. These are mechanical problems which can be solved readily if the facilities of a good machine shop are available. The arrangement used to insure that the angle 4 remains constant and the centering of the sample is reproducible is indicated schematically in Fig. 1. The sample is clamped against a thin plate with a hole in it by means of a spring-loaded pres-

Jan 1, 1954

By N. J. Grant, D. S. Bloom

N recent reports, Sully&apos; and Beck and coworkers&apos; I have advanced hypotheses concerning the formation of the phase. Both of these hypotheses are based on Pauling&apos;s theories of the electronic configuration of the elements of the first transition group. Sully considered that the number of electrons which can be absorbed in filling electron "holes" is the factor which determines whether or not the structure can form. Beck suggested that the presence of a certain concentration of electron "holes" is the controlling value. It can be shown that a similar criterion can be developed without making reference to Pauling&apos;s theories. Table I shows the elements of the first transition group and the incidence of the a structure in the binary systems of these elements according to the data presently available. Also appended is the number of electrons considered to exist in the 3d-4s levels of these elements. If the atomic percentages for the phase are listed as shown in Table 11, and if the number of electrons in the 3d-4s levels per atom is calculated for the a boundary values, the results are as shown in the last column. It can be seen that the numerical values are all in the vicinity of 7 electrons per atom. This is true also for the ternary Cr-Mo-Ni IT phase, which occurs in a system in which none of the binary compositions are known to develop the phase. In the Fe-Mo binary, the high temperature a phase, which occurs at a composition of 50 atomic pct of each element, also yields a ,;1 e of 7 electrons per atom. From inspection of Tables I and 11, it develops that any series of sequential numbers which is assigned to the elements under consideration will result in the numbers pertaining to a compositions grouping themselves around one specific number. It does not follow, however, that this random number necessarily has physical significance. Such a point has already been discussed by Hume-Rothery." One interesting point develops from this study, however, and that is the position of manganese with reference to the other elements and to the phase. In the system used here, the formation of phase is associated approximately with the value of 7 electrons per atom, which is also the number of electrons per atom that manganese has. Manganese, it will be recalled, exists in three different crystal forms, none of which are the usual, simpler metallic forms; on the other hand, elements just to the left of manganese (in Table I) generally have lower coordination-number structures (body-centered cubic) than do elements to the right of manganese (face-centered cubic). The contribution to a complex crystal structure by the interalloying of elements from opposite sides of manganese is significant in that the a phase is formed in binary systems including one element from each side of manganese, with manganese capable of participating with both sides. It is indeed an interesting coincidence that manganese, with 7 electrons per atom, solidifies in complex crystal forms, and that when alloys of the transition elements are made which have seven 3d-4s electrons per atom, they, too, tend to assume a complex crystal form. From the above, it might be deduced that the study of the a phase might be advanced by a critical examination of the element manganese and how its structure is affected by small additions of elements which change the 3d-4s electrons per atom number. The role of atom size would also be of interest in formation. References &apos; A. H. Sully: The Sigma Phase in Binary Alloys of the Transition Elements. Journal Inst. Metals (1951) 80, Part 4, p. 173. 2 S. Rideout, W. D. Manly, E. L. Kamen, B. S. Lement, and P. A. Beck: Intermediate Phases in Ternary Alloy Systems of Transition Elements. Trans. AIME (1951) 191, p. 872; Journal of Metals (October 1951). "W. Hume-Rothery, H. M. Irving, and R. J. P. Williams: The Valencies of the Transition Elements in the Metallic State. Proc. Royal Soc. (September 1951) 208A. p. 431.

Jan 1, 1954

By D. L. McDanels, J. W. Weeton, R. W. Jech

An investigation was conducted to determine the stress-strain behavior and tensile properties of metallic composites and to relate them to the properties of the base materials. Tungsten fibers in a copper matrix were chosen as the model sys-tem to investigate these properties. Room-temp-atzcre tensile and dynamic -modulus tests were used To meet the demand for improved structural materials, considerable effort is being directed toward the creation of composite materials. One such material under investigation is the fiber-reinforced composite, in which a ductile, relatively weak matrix is reinforced with high-strength fibers. Some work has been done on the reinforcement of metallic matrices with metallic fibers1"5 as well as with ceramic-whisker reinforcement. Summaries of much of this work have been published by Mach-lin7 and Baske~.&apos; Work done at the Lewis Research Center of NASA-" has involved the making and testing of composites composed of a fiber, tungsten, and a matrix, copper, which were insoluble in each other. An equation was presented that showed the relation between the ultimate tensile strength of the composites and the strengths and relative volume percents of the components. This relation was verified experimentally for composites containing fibers extending the full length of the specimen as well as for composites reinforced with short-length or discontinuous fibers. Since the publication of the preliminary results,9&apos;10 additional data have been obtained. This paper presents these data as well as analyses of the stress-strain behavior and the mechanics of deformation of uni-axially oriented, fiber-reinforced metallic composites, in which both components are mutually insoluble. EXPERIMENTAL PROCEDURE Composites were made with high-purity copper as the matrix and 3-, 5-, and 7-mil-diam tungsten wire as the reinforcing fiber. Some specimens were made in which the reinforcing fiber extended completely through the full length of the composite test section. The fibers were placed in ceramic to determine these properties. The composites were reinforced with either continuous or discontinuos tungsten fibers. The tensile properties and stress-strain behavior of composites reinforced with either type of reinforcement were similar, and in both cases the full strength of the fiber was utilized. tubes to insure axial orientation and infiltrated with copper at 2200°F for 1 hr. Composites were also made with short-length (3/8 in. long) 5-mil-diam tungsten fibers as discontinuous reinforcement and infiltrated under the same conditions. The reinforcing fibers in both cases were longitudinally oriented in the direction parallel to the tensile axis. Room-temperature tensile tests were conducted on the composites, stress-strain curves were obtained, and ultimate tensile strength and elongation were measured. Dynamic modulus of elasticity, based upon the resonant frequency induced in the flexural mode of vibration, was also determined for the composites and the components. A more detailed discussion of the experimental procedure employed in this investigation may be found in Ref. 11. RESULTS Room-temperature tensile tests were conducted on 3-, 5-, and 7-mil-diam tungsten wires which had been annealed for 1 hr at 2200°F and show the tensile strength of the wires to be 331,000, 327,000, and 290,000 psi, respectively. Since all the composites were infiltrated under these conditions, the strengths were considered to represent the strength of the fibers in the composites throughout this study. The average tensile strength of the annealed copper used as the matrix in this investigation was 27,800 psi. Results of room-temperature tensile tests on composites reinforced with 3-, 5-, or 7-mil-diam tungsten fibers are plotted as functions of composition in Fig. 1. These data represent previously reported datag,l0 as well as data more recently obtained. The line shown on each curve represents a prediction of tensile strength as a function of composition; the calculation of this line was explained in Refs. 9 and 10. A similar plot is presented in Fig. l(d) for composites reinforced with short-length, discontinuous 5-mil-diam tungsten fibers. Again, both the previously reported and the recent data are presented, and the line shown is identical to that shown for

Jan 1, 1965

By A. Blake Caldwell

Tyrone-a complete mining and concentrating facility built by Phelps Dodge Corp.-straddles the Continental Divide where surface water on either side flows in opposite directions although all water is taken from and returned on the northwest side of the Divide. At the outset, Tyrone was saddled with a problem of an adequate water supply, and the Gila River some 23 miles distant appeared to be the logical source. This in itself presented a major obstacle to Phelps Dodge because of the distance water had to be pumped and because of an adverse head which had to be overcome between the Gila River and the two 4-million-gal-capacity terminal water supply tanks at the mill. Having acquired water rights on the Gila River and in order to control the seasonal fluctuations in water volume, the company built the Bill Evans, off stream, earth-filled dam. This reservoir will contain 2100 acre-ft of water when full and it was constructed by the Hamilton Construction Co. for Phelps Dodge. The dam impounds fresh water for the Tyrone plant&apos;s use and four vertical turbine pumps (4500 gpm each) lift the water 275 ft from the Gila River into the reservoir. Since construction, Phelps Dodge has optioned the lake to the New Mexico State Game Commission for recreational purposes. In addition to the lake, land around the reservoir has been optioned to the State Game Commission for public use. The lake has already been stocked with trout and by next summer some keepers should be available for the taking.

Jan 12, 1969

By Robert W. Thompson, Darry A. Ferguson

In August, 1977 the United States Congress passed Public Law 95-87 which has been commonly referred to as the Surface Mining Control and Reclamation Act (or SMCRA). This title is somewhat misleading in that the act creates as many regulatory requirements for underground coal mines as for surface coal mines. How- ever, this paper will concentrate on the effects of SMCRA on designs and stability for various activities of surface coal mines, specifically those concerning "Disposal of Excess Spoil". In the past, the objective of most laws and regulations applicable to the mining industry has been to achieve goals of safety or environmental concerns for all types of mining. However, SMCRA is unique in that it sought to regulate-all-activities of coal mining from initial data gathering, exploration, mine design and facilities design to reclamation activities and design. More specific to the stability of the activities of surface coal mining, special criteria for design and construction performance standards have been promulgated for the construction and maintenance of roads, dams and embankments, coal processing waste, ex- cess spoil piles, backfilled reclamation and pit slides. The criteria for design for the previously mentioned facilities has been enumerated by regulations and in many ways restrict the use of site specific design parameters. The restrictions imposed by regulations significantly inhibit the engineer&apos;s ability to develop the best practical and economical design and in some cases may re-

Jan 1, 1983

By L. F. Reinartz

The furnace in which rimming steel is made has an important bearing on the quality of the steel produced. Furnace.—Particularly in the manufacture of low-carbon rimming steels, it is necessary to have an efficient, easily regulated furnace, because of the relatively high finishing temperature requirements. In recent years, the most important development in design of open-hearth furnaces has been the sealing and insulation of the greater part of the furnace to prevent air infiltration and loss of heat. Efficient, straight-line valves insure proper draft. Combustion controls guarantee correct gas-air ratios. Furnaces of all sizes ranging from 20 to 200 tons have been used successfully in the manufacture of rimming steels. Metal bath is varied from 20 to 40 in. in depth without appreciable variation in quality. Charging.—A normal open-hearth charge consists of pig iron (hot or cold), scrap of miscellaneous nature, and slag-making additions, such as limestone and burnt lime. Because of local conditions, some plants find it necessary to discard the use of pig iron and use some carbonaceolis substances with varying percentages of cast iron to replace the pig iron. It is questionable whether such practice will consistently produce the quality of rimming steel required for auto stampings and other severe drawing requirements. Pig Iron.—An open-hearth furnace under proper control should melt 150 tons of low-carbon rimming steel on about 35 to 38 per cent pig-iron charge basis. In some practices, best results are obtained when the total charge contains from 0.40 to&apos; 0.50 per cent silicon. If reasonably low-

Jan 1, 1935

By L. F. Reinartz

The furnace in which rimming steel is made has an important bearing on the quality of the steel produced. Furnace.—Particularly in the manufacture of low-carbon rimming steels, it is necessary to have an efficient, easily regulated furnace, because of the relatively high finishing temperature requirements. In recent years, the most important development in design of open-hearth furnaces has been the sealing and insulation of the greater part of the furnace to prevent air infiltration and loss of heat. Efficient, straight-line valves insure proper draft. Combustion controls guarantee correct gas-air ratios. Furnaces of all sizes ranging from 20 to 200 tons have been used successfully in the manufacture of rimming steels. Metal bath is varied from 20 to 40 in. in depth without appreciable variation in quality. Charging.—A normal open-hearth charge consists of pig iron (hot or cold), scrap of miscellaneous nature, and slag-making additions, such as limestone and burnt lime. Because of local conditions, some plants find it necessary to discard the use of pig iron and use some carbonaceolis substances with varying percentages of cast iron to replace the pig iron. It is questionable whether such practice will consistently produce the quality of rimming steel required for auto stampings and other severe drawing requirements. Pig Iron.—An open-hearth furnace under proper control should melt 150 tons of low-carbon rimming steel on about 35 to 38 per cent pig-iron charge basis. In some practices, best results are obtained when the total charge contains from 0.40 to&apos; 0.50 per cent silicon. If reasonably low-

Jan 1, 1935

By C. B. Scotty, E. F. Egan

INTRODUCTION The neutron-garnma log has been used for stratigraphic correlation by the oil industry for a number of years. In the past few years, the quantitative application of the log to provide information with respect to porosity has received considerable attention. The basic concept of quantitative interpretation has been pointed out in the literature.1 It shall be the purpose of this paper to develop by empirical means a method whereby the relationship of porosity to neu. tron-gamma deflection may be predicted for various bore hole diameters. This relationship is applicable to the present commercially available neutron-gamma log run in open hole. Data available at present are insufficient to establish similar correlations for cased holes. Through the development of such a correlation, the importance of the various factors which influence the log become evident. NEUTRON-GAMMA CURVE The logging tool conisists of a source of neutrons and a means of detecting and measuring gamma rays, the detector being shielded from the direct emission from the source. The gamma rays reaching the detector have three sources of origin: (1) the natural gamma radiation emitted by the formations, (211 induced gamma radiation resulting from neutron bombardment. (3) gamma rays emitted by the source and scattered by the formation. It has been found that a neutron derived porosity correlation is best for shale-free formations. Under this condition the natural gamma ray radiation is quite low, and therefore, will be neglected in this work. The induced gamma ray radiation resulting from neutron bombardment is predominantly a function of the hydrogen atom concentration of the substance penetrated. Due to the geometry of the presently used system, the neutron-gamma curve indicates low radioactivity opposite high hydrogen concentration and high radioactivity opposite low hydrogen concentration (Figs. 1 and 2). Having a curve which measures hydrogen atom concentration, it follows that if the matrix of the formation penetrated consists only of atoms other than hydrogen, and if the fluid filling the pores is either oil or water, the curve should be an indication of porosity (both oil and water have practically the same number of hydrogen atoms per unit volume&apos;). The above criteria for a porosity (Correlation are fulfilled in clean sandztones and limestones in which the pore volume is completely filled with liquids (oil or water), but not in formations containing either free gas or shale or both. Free gas. even under pressure, contains considerably less hydrogen per unit volume than oil and water; therefore, a variation in response on the curve would be expected. Camp- bell and Winter,&apos; indicate that this difference in hydrogen concentration is sufficient to distinguish between sands containing water or oil and those containing dry gas. Shale is a mineral that contains hydrogen in its molecular structure in addition to the hydrogen which is present in the water of hydration. Thus, in formations containing variable amounts of shale, the hydrogen concentration indicated by the curve is not a direct indication of porosity. Bush and Mardock&apos; have indicated that a correction may be made by use of the gamma ray curve to provide a porosity correlation. Since the induced gamma rays are predominaiitly a function of hydrogen concentration, it would be anticipated that the fluid filled bore hole would materially influence the logs. It has been pointed out that the neutron-gamma curve response decreases with increase in hydrogen concentration, therefore, the response due to the induced gamma ray component decreases with increase in fluid filled hore hole diameter. The scattered gamma ray component of the log increases with increase in bore hole diameter. Although there is an

Jan 1, 1952

By Herbert Hoover

This paper is in the nature of a rough preliminary report on the progress that has been made in the application of the mass spectrometer to various problems arising in the petroleum industry. A few years ago the authors considered a number of the problems that were arising in the qualitative and quantitative measurement of small amounts of hydrocarbons. The methods available of making analyses by chemical techniques appeared to leave much room for improvement. Without going into the reasons at this point, attention was turned to the possibility of employing physical instead of chemical methods of accomplish-ing the desired results. A preliminary investigation disclosed that the mass spectrometer presented a possibility of solving many problems which could not easily be accomplished by other methods. Work was begun in developing the necessary apparatus and technique. A great deal of encouragement and many valuable suggestions were received from Dr. Robert A. Millikan, Dr. W. R. Smythe, and Dr. W. N. Lacey, of the California Institute of Technology, and from Dr. E. 0. Lawrence, who recently received the Nobel Prize, of the University of California. The authors particularly wish to acknowl-edge the very great willingness of these out-standing scientists to be helpful in solving many of the problems that were involved. So far as the authors are aware, this was the first application of the mass spectrometer to commercial work. The results were considerably better than had at first been anticipated. Briefly, it is pos-sible to run a qualitative and quantitative analysis of an unknown mixture of hydro-carbon gases, with an accuracy of better than plus or minus 5 per cent of each of the various constituents. An exceedingly high degree of sensitivity has been obtained, and a relatively short time is required to com-plete an analysis. Furthermore, it is un-necessary to separate a mixture of gases into its various components in order to complete the analysis.

Jan 1, 1940

By F. M. Lewis, J. F. Meyers

In the mining and handling of sulphide ores, some degree of oxidation takes place on the sulphide surfaces, which are exposed to the atmosphere. It is, moreover, well known that the oxidation compounds formed are a factor when such ores are subsequently treated by flotation. Modern operating technique and reagents are capable of contending with this condition to a major degree, provided that the proportions of the reagents used are varied correctly. This is particularly true at the Tennessee Copper Co., where the ore treated contains pyrrhotite in addition to other sulphides. A number of soluble salts, some of which are unstable, can be formed during the oxidation of the sulphide ores. Those unstable salts, whose oxygen requirements are unsatisfied, are constantly changing to more stable forms because oxygen reacts with them during the crushing, grinding and other operations of ore preparation. We add no chemicals of any kid to the ore pulp in its preparation for flotation feed. Consequently the only compounds that are present in the flotation feed are those produced by the natural oxidation of the ore in the presence of air and water. The Tennessee Copper Co. ore is composed of from 60 to 70 per cent sulphides and from 40 to 30 per cent non-sulphide material. It is not the purpose of this paper to discuss the nature of these various oxygen-sulphur compounds nor their effect on flotation, but to describe a method for correcting the effect. Suffice it to say that we have found that the reducing sulphur and oxygen salts have a depressing action on our bulk flotation process.&apos; From long experience we find that the best means of correcting for this variation in our work is to increase or decrease the quantity of xanthate, the promoting agent, as the quantity of the reducing salts increases or decreases. It was, therefore, very desirable to provide the operators with some quick and

Jan 1, 1947

By F. M. Lewis, J. F. Meyers

In the mining and handling of sulphide ores, some degree of oxidation takes place on the sulphide surfaces, which are exposed to the atmosphere. It is, moreover, well known that the oxidation compounds formed are a factor when such ores are subsequently treated by flotation. Modern operating technique and reagents are capable of contending with this condition to a major degree, provided that the proportions of the reagents used are varied correctly. This is particularly true at the Tennessee Copper Co., where the ore treated contains pyrrhotite in addition to other sulphides. A number of soluble salts, some of which are unstable, can be formed during the oxidation of the sulphide ores. Those unstable salts, whose oxygen requirements are unsatisfied, are constantly changing to more stable forms because oxygen reacts with them during the crushing, grinding and other operations of ore preparation. We add no chemicals of any kid to the ore pulp in its preparation for flotation feed. Consequently the only compounds that are present in the flotation feed are those produced by the natural oxidation of the ore in the presence of air and water. The Tennessee Copper Co. ore is composed of from 60 to 70 per cent sulphides and from 40 to 30 per cent non-sulphide material. It is not the purpose of this paper to discuss the nature of these various oxygen-sulphur compounds nor their effect on flotation, but to describe a method for correcting the effect. Suffice it to say that we have found that the reducing sulphur and oxygen salts have a depressing action on our bulk flotation process.&apos; From long experience we find that the best means of correcting for this variation in our work is to increase or decrease the quantity of xanthate, the promoting agent, as the quantity of the reducing salts increases or decreases. It was, therefore, very desirable to provide the operators with some quick and

Jan 1, 1947