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By J. E. Hilliard

Various methods are given for estimating the number per unit volume and average size of convex particles from measurements on a projection through a slice of the structure. The determination of the size distribution is considered specifically for spherical particles. The results are applicable to any type of transmission microscopy and also to the correction of measurements made by reflected light on semitransparent materials. WITH the advent of electron transmission microscopy, the metallurgist is confronted with the problem of relating a projected image to the three-dimensional properties of the structure. This paper deals with the estimation of the number per unit volume and size of particles dispersed in a matrix. The case of convex particles will first be treated (the results will be applicable as approximations to particles of more general shape) and then spherical particles will be considered specifically. The latter represent a special case frequently encountered in practice and one which is also amenable to a calculation of the effect of overlap on the observed particle-size distribution. Although the present treatment was prompted by the needs of the electron microscopist, the results are applicable to transmission studies with any type of radiation. In addition, they can be used in the analysis of semitransparent materials by reflected light, the depth of light penetration corresponding to the thickness of the slice or section used in the transmission studies. 1) CONVEX PARTICLES 1.1) General Expression for N,. We will suppose that a "center" (such as the center of mass) is assigned to each particle. The convention used for defining the center is immaterial providing it does not depend on the orientation or location of the particle. Consider a slice through the structure having a pair of parallel faces a distance t apart. It will be assumed that the slice is randomly located with respect to its perpendicular distance from some fixed point, but it is not necessary to assume that its orientation is random. Our problem is to deduce the relationship between the number of par- ticle images seen on an orthogonal projection through the slice with the number, Nv, of particles per unit volume in the original structure.* *Symbols are listed in the Table. The expected number of particles with centers lying within the slice is Nvt per unit area. In addition, there will be elements in the slice contributed by particles whose centers lie without. The number of such elements will be the same as the number of intersections occurring on a two-dimensional plane through the structure; namely N~K, where K is the mean distance, Fig. 1, between tangent planes to a particle averaged over all particles, i.e., Where Ni is the number of particles of class i having the same shape and size, and pi (4, 8) is the probability that an i particle will have a given orientation with respect to the slice. If the particles are randomly oriented, then K is independent of the orientation of the slice and equal to the mean cali-per diameter. The total number of particle elements in the slice is therefore Nv(t + K) per unit area, but fewer will be seen as separate images on the projection plane because of overlap. If MA is the number of elements "lost" by overlap, the number of images per unit area will be NA = Nv(t + K) -MA 121 MA is a function of the slice thickness and must vanish at t = 0. As t increases, NA at first increases, reaches a maximum, and thereafter decreases as the overlap term MA becomes predomi-

Jan 1, 1962

By Glenn Keep

THIS paper is not an announcement of the successful conclusion of the Cerro de Pasco Copper Corporation's pacos-pyrite problems, but merely a description of the commercial-scale, intermittent-roasting operations conducted by the writer, J. H. Lucas and others of the staff. It was prepared by request, for presentation at the February meeting of the Institute. The results obtained in Peru confirm the 1-ton-a-day experiments completed about three years ago at Kearny, N. J. by C. C. Gordon and Mr. Lucas, where it was first demonstrated that a mixture of about 80 per cent. pacos ore with 10 per cent. pyrite ore and 10 per cent. salt could be roasted intermittently in a small 1-ton-a-day Holt-Dern furnace without extraneous fuel, producing porous calcine that could be leached rapidly. Mr. Keep and his staff, by successfully introducing improvements in the construction of the commercial furnace and in their handling of material, have established beyond doubt a low cost for roasting. The other steps in the process of treating pacos and pyrite ores have not as yet been demonstrated as sufficiently conclusive to warrant their acceptance for a permanent plant.

Jan 1, 1929

SHELBY M. HARRISON,* New York, N. Y. (written discussion ?).¬Your secretary requested a brief description of the Russell Sage Foundation, in order that members of the Institute, if they should desire to avail themselves of it, would know what type of service is offered to them through our institution. The foundation was established in 1907 by the gift of Mrs. Russell Sage of $10,000,000 as a capital fund, the income of which is to be spent for the improvement of social and living conditions in the United States. One of the lines of activity which the foundation has felt would lead toward this end is the development and promotion of community surveys; and because the scope and methods followed in these surveys are very similar to the scope and method of much of the institution's work in general, an idea of its main activities can perhaps be given best by describing one of our surveys. Incidentally, it may be pointed out that antecedent to the survey stand at least two important facts: first, the recognition. that communities are active, not static forces, that they develop, that changes in. material and human relationships occur continuously, and that with them come new social and civic problems which must, in many cases, be diagnosed and prescribed for anew; and second, the reality of scientific advances along lines which make possible at least some measure of solution of the problems. Evidences of these changes are abundant; many of them are found in the rapid growth of cities in the last few decades. Villages in agricultural districts, places where everybody knew everybody else, where the pulpit had been long the chief or only influence molding public opinion, where the air was unclouded by the smoke from factory stacks, where the water supply was not affected by pollution, where sunlight and building

Jan 5, 1918

By S. Arthur Krom

(New York Meeting, February, 1912.) THE James diagonal-plane slimer is specially adapted to handle the finest slimes, but it will also handle sands as coarse as 40-mesh. The saving efficiency of this machine is due to the original construction of the deck, and to the rapid reciprocating movement imparted to it by the head-motion. The deck consists of a plurality of connected planes, having a certain fixed ratio of inclination one to another. These planes intersect each other diagonally to the stroke-line of the table and are arranged so as to give the pulp on the table a double treatment. This double concentration performed by the diagonal-plane deck produces cleaner concentrates and tailings than those obtained by the operation of two separate machines. The action of the diagonal planes settles, combines, and holds all the concentrates in one compact mass, sharply defined from the gangue, and easily cut away without loss. Many slime-concentrating machines distribute the feed-pulp for a distance of 4 or 5 ft. only, and upon a very limited settling-surface. This results in a thick, heavy deposit, from which it is impossible to stratify the values and wash, away the gangue, the resulting products being dirty concentrates, and tailings carrying high values. The diagonal-plane slimer distributes the feed-pulp for a distance of 10 ft., and upon a settling-surface having an area of 40 sq. ft.; in other words, it spreads the pulp thinly on the table, which allows the metallic values to settle through the gangue quickly, forming a bottom stratum from which the thinly-distributed overlying stratum. of gangue is easily brushed away by the feed-water without disturbing the underlying concentrates. Referring to Fig. 1, plane A is the main settling-section, of the table. The feed pulp flows gently down this plane and is

Jun 1, 1912

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970

By Richard Borg

The partial molal free energy of Cd in each of the four intermediate phases, Cd3 Cu, Cd8 Cu5, Cd3Cu4, and CdCu2 is determined using the Knudsen vapor pressure technique. Measurements are made also within the two-phase regions, and thus the variation in FCd is now known across the entire phase diagram. The absolute values are all less the 2.0 kcal and increase regularly with increasing Cd concentration. The small absolute value of the free energy precludes the possibility of obtaining highly accurate values; nevertheless, the results are compatible with those previously reported for the liquid phase. Additional results are reported concerning the lattice parameters of the 6, E, and b phases. THE elements Cu and Cd combine to form four intermediate phases which are designated* and E and which include respectively the following inter metallic compounds: CdCu2, Cd3Cu4, Cd3 Cu5, and Cd3 Cu. The extent of each phase with respect to temperature and composition is shown in Fig. 1 which is the equilibrium diagram drawn according to Hansen.1 All four phases are brittle, and most probably are true intermetallic compounds. Only the crystal structure of the 6 phase has been thoroughly investigated.2,3 The structure is cubic and isotypic with y brass. The structure of Cd3 Cu has not been previously reported, It is hexagonal with a = 8.11 and c = 8.76 0.02Å and the structure is presently being determined.* The compounds Cd3 Cu4 and CdCu, have been each previously the subject of a single investigation. Cd3Cu, is presumed to be cubic4 with the space group Fd3m, whereas CdCu2 is hexagonal2 with the C14-type structure. Cu2 Cd is found by X-ray analysis to be hexagonat with lattice parameters a = 5.00A and c = 16.17Å. The material appears to be pure Cu2Cd as all reflections could be indexed on the basis of the single hexagonal structure. These values disagree with those of Kripyakevich and coworkers5 who report a = 4.96Å and c = 7.98Å. Their investi-

Jan 1, 1962

By Sir Robert Hadfield

LAST year this Institute was good enough to accept some remarks by the writer regarding sound steel, entitled Plant for Hadfield Method of Producing Sound Steel Ingots, being a continuation of a research in which for some time the writer has been engaged, and full particulars of which were submitted in papers entitled A New Method of Revealing Segregation in Steel Ingots, and Method of Producing Sound Ingots, read before the Iron and Steel Institute in October, 1912. These papers gave rise to a very interesting discussion, both in England and America. This question is one of vital importance, as unless sound steel in the form of ingots is first obtained, sound steel in the finished forms of rail billets, rails, bars, sheets, and other forms cannot be expected. The working stresses demanded by modern conditions are so great, each year they probably approach nearer to the limit of safety, that without doubt those who produce steel will be compelled to pay the attention which this subject deserves. Moreover, the problem is not an insuperable one, as shown by the writer in the papers above referred to. In view of the information which has already been presented in these papers, it is not now necessary to go into details of the system advocated by the writer, except to repeat that the ingots and steel now referred to were produced by employing in the first place sound fluid steel, free from blowholes, this being poured into ordinary ingot molds, provided with the necessary feeding heads, the insulating slag medium, also charcoal and air blast or other suitable form of applying heat to the head portion of the ingot. Tile upper or head portion of the ingot is kept fluid by the intense heat generated by the air blast and charcoal, so that such fluid steel passes into the body of the ingot below the head, thus feeding and avoiding the shrinkage or piping which would otherwise occur. The result is the production of a sound steel ingot, free from blowholes, segregation and piping, and in which the waste portion, usually termed the discard, is but little over 7 or 8 per cent.

Jan 4, 1914

Jan 1, 1915

By E. C. Harder

CERTAIN typical characteristics of bauxites, ores of aluminum permit their classification into a number of categories, each of which has special features that enable grouping within it deposits from widely scattered bauxite fields. There may be local variations in conditions that have introduced differences of lesser importance between similar deposits in different fields, resulting perhaps from the influence of factors other than those that have produced the distinguishing features of each of the different groups, but in general the similarity between the deposits in each group is sufficiently striking to make the grouping indicated of interest. Several factors and conditions enter into the decomposition process that results in the development of bauxites and laterites and affects their character. The principal conditions favoring optimum bauxitization are: (1) pres- ence of rocks with easily soluble minerals yielding residues rich in alumina; (2) effective rock porosity, enabling easy access and free circulation of water; (3) normal to abundant rainfall alternating with dry periods; (4) vegetation, including bacteria, advantageously distributed; (5) available sources of appropriate solution and precipitation agencies; (6) a tropical or at least a warm climate; (7) low to moderate topographic relief, allowing free movement of the water table but a minimum of erosion; and (8) long quiet periods in earth history. Assuming that all of these factors are operating to a greater or less degree, it seems that the one that affects most the physical character of the resulting bauxite or laterite deposits is the chemical and mineralogical composition of the rocks that by their decay yield the bauxite deposits. This factor is used in the classification followed in this paper. In the process of weathering of ordinary silicate and carbonate rocks of the earth&apos;s crust, whether of igneous or sedimentary origin, it is the minerals of the alkalies that yield most readily to attack. The alkaline earth compounds also offer no great resistance, particularly the carbonates. Thus, among the rock-forming elements, those producing the most insoluble compounds are aluminum, iron, and silicon, together with certain ones of less importance, such as titanium, manganese, and phosphorus. In normal weathering processes such as prevail in temperate regions, the common minerals of rock decay are

Jan 1, 1952

By Theodore Simons

I. INTRODUCTION PERMISSION to present this paper at the February, 1915, meeting of the Montana Section of the American Institute of Mining Engineers was liberally granted by W. A. Clark, Jr., President and General Manager of the Timber Butte Milling Co., and by the representative of the Minerals Separation Co. For the many courtesies shown the writer on his visits to the mill and for information supplied, he is indebted to all the officers of these companies, especially to W. N. Rossberg, W. D. Mangam, Hamilton Cooke, Jr., T. M. Owen, T. C. Wilson, R. McGillivary, L. L. Quigley, C. Bartzen and others. The writer takes this opportunity to herewith express to them his appreciation and sincere thanks.

Jan 6, 1915

By Fred C. Bond

AN improved method of measuring the surface area of a comminution product down to any desired particle size has been developed. The method is largely graphical, and requires relatively little calculation. It can be used with materials containing large amounts of clay, or excess fines of any kind. The surface area S is expressed in terms of square meters per100 c.c. of solids. This expression is based upon volume rather than weight, and is considered to be more suitable for crushing and grinding problems, where the machines ordinarily are operated under constant volume conditions. It has the advantage that surface areas of different materials can be compared directly, even though their specific gravities may be unknown. The "specific surface" of a material, or the number of square centimeters of surface area per gram, is equal to 100S divided by the specific gravity. Particle diameters are expressed in microns, K being the diameter of the largest particle present and L the grind limit, or lower size limit of the particles formed directly by grinding. The value of K does not always coincide exactly with the diameters of the largest particles retained on the coarsest testing sieve, since the largest particles formed in crushing and grinding are often slabby, or have other irregular shapes. L has been chosen as 0.700 microns, or number 27.5 in the size number series,1 for reasons to be explained later. S is the total surface area of all particles larger than L microns in diameter. When a homogeneous comminution product is separated into fractions whose diameters bear a constant geometrical relationship [p] to each other, and the log per cent weight retained upon each size and passing the next larger size is plotted against the log diameter, a straight line results, which is called the distribution line, and which has a slope in called the distribution modulus. The distribution line can be extended to any desired limiting size, and the total surface area of all particles larger than that size can be calculated. The equation of the distribution line is w = Cxm [I] where w is the per cent weight retained on each successive sieve; x is the particle diameter; and C is the per cent weight retained on an opening of unit diameter.2 Theoretically, the distribution line can be extended to include infinitely small particles. When it is so extended, and the assumption is made that no fine particles are present other than those accounted for by the equation; the log per cent cumulative weight passing any series of sizes, plotted against the log diameter passed, will result in a straight line lying parallel to and above the plotted distribution line.

Jan 1, 1941

By Tommy Wilson

OIL well drilling fluids have become a vital part of the drilling industry during the past 25 years. From chance usage of drilling mud at the fabulous Splindletop field in 1901, drilling fluid control has become an extremely technical and exacting science. Drilling for oil today involves exploration at depths ranging to 21,000 ft, nearly 4 miles. Geological formations encountered at these depths offer a tremendous challenge to the production, research, and service facilities of any drilling mud company.

Jan 5, 1954

By Howland Bancroft

AMERICAN investment in foreign mining interests today faces its greatest task. U. S. dollars must make possible the. steady procurement of the minerals our defense effort consumes in huge quantities. The two most vital factors involved in foreign procurement are time and the continued good will of the nations from which minerals are purchased. The Point IV program was formulated to care for the second item, but it has failed to do the job. Its lack of success has not been from intent or from basic failure in formula. Foreign Investment, Four Eras Foreign mineral development, in so far as participation by private capital from the United States is concerned, may be divided into four main chronological categories: First: The period prior to the first World War when people, capital and products moved with relative freedom across international boundaries, and London was the recognized mining seat of the world. By the end of 1919 the United States direct investments abroad amounted to $3.9 billion of which some $900 million were in mining and smelting and $600 million in petroleum. Investment climate throughout most of the world was excellent. Second: The period between the end of World War I, when the international economy had been shaken from its foundations, and the beginning of the great depression of the 1930&apos;s, which still further disrupted the world economy. By that time the world mining center had moved across the sea and the United States direct investments abroad had increased to $7.7 billion of which mining and smelting accounted for $1.2 billion and petroleum for $1.1 billion. Investment climate was good in most parts of the world. Third: The period of the depression of the 1930&apos;s and the beginning of World War II during which foreign trade was still further disorganized and the international economy collapsed. Nazi barter agreements were initiated in many parts of the world, and Soviet propaganda commenced to make its, influence felt in many countries. During this period United States direct investments abroad decreased to $7.3 billion. Mining and smelting investments during the same period decreased some $200 million, though direct investments in foreign petroleum areas increased an equal amount. Investment climate became less and less hospitable in all parts of the world affected by economic nationalism. Fourth: The period since the beginning of World War II during which total direct investments abroad increased from $7.3 to $13.7 billion. Of this sum, at the beginning of 1950 investment in foreign mining and smelting is reported to have been $1.2 billion-back to where it was in 1929, and in petroleum to have reached $3.7 billion. Investment climate remained favorable in the countries respecting contractual obligations and fair in their treatment of invested capital. [ ] As noted above, the relative freedom of passage across international boundaries by people, capital and products ended with World War I and the situation remains unchanged in a greater part of the world. While this same war upset international economy, the depression of the 1930&apos;s caused the collapse of world trade, and exports from all countries fell to an alarmingly low figure. Some countries almost ceased to export. Chile, for example, reported a drop of 88 pct in exports. Countries with

Jan 1, 1952

By Robert Linton

M ETHODS by which Americanization is developed among the foreign workers at the mines in the United States, with particular reference to mines of the Pennsylvania coal region, were discussed in a most constructive way at the Wilkes-Barre Meeting of the Institute. Arthur Notman, of the Phelps Dodge Corpn., as chairman, guided the discussion. Americanization was defined by E. E. Bach, !chairman of the Institute&apos;s Sub-committee on Americanization, who said: "Americanization applies either to the native-born or foreign-born and is that process of assimilation which guarantees the full functioning of American citizenship. Naturalization papers merely entitle one to the privileges of citizenship."

Jan 1, 1921

By R. V. Higgins

This paper presents a computer method to obtain the shape factors and equal cell volumes of the channels for any well spacing pattern from a potentiometric model. By using this program the authors have processed the data for the seven-spot, direct line-drive and the staggered line-drive patterns. The data for the five-spot pattern had been previously processed by a noncomputer method and are included for completeness. The shape factors and volumes for the channels are presented in tables for those who want to use them to process data using their own permeability relationships and viscosities of their reservoir oils. The authors have used the data and sets of representative permeability curves to process sample calculationr of waterflood performances. The comparison of the calculated results shows that the influence of well spacing is small. The permeabilities of the reservoir rock to oil and water had a greater influence on oil recovery for a given pore-volume throughput of water than the well spacing pattern. The more water-wet the reservoir rock, the better the possibility of permeabilities which are conducive to good recovery. The viscosity of the reservoir oil also influences the recovery more than the well spacing pattern. The reduction in the percentage recovery of oil with increase in viscosity of the reservoir oils is small when oil viscosities are in the range of 0.1 to 3. Above this range the reductions in recoveries are extensive. Sample comparisons of the time required for different patterns to recover the oil are presented. Results of an example calculation are given to show the effect of the permeability profile on recovery. INTRODUCTION The effect of well spacing pattern on the recovery of oil when flooding with either gas or water has been studied by many investigators. Muskat et al.1 presented an analysis using conductivity, sweep efficiency and unit mobility to the time of breakthrough. Dyes et al.2 used experimental techniques (X-ray shadowgraphs) and different mobility ratios. They presented quantitatively the relationship between mobility and sweep efficiency at and after breakthrough. Hauber3 presented a method to predict waterflood performance for arbitrary well spacing patterns and mobility ratios. Craig et al.,4 using techniques similar to Dyes et al. to determine sweep efficiency for a five-spot pattern, added the use of relative permeability curves at breakthrough and thereafter. Douglas et al.5 sed rela- tive permeabilities and continuously changing saturations throughout the entire five-spot flood pattern. In obtaining their solutions they used finite-difierence equations. Hig-gins and Leighton6,7 also used relative permeabilities and continuously changing saturations throughout the pattern before and after breakthrough. They employed techniques that process a flood-pattern calculation on the computer in about one minute. The methods of Douglas et al. and Higgins and Leighton both checked closely the laboratory results for a wide range of mobility ratios. This paper presents some sample performances calculated by the Higgins and Leighton method that show the effect on recovery of different permeabilities and viscosities using the seven-spot, the line-drive and the staggered line-drive, as well as the fivespot flood pattern. No previous paper has presented these data using different permeability curves and continuously changing saturations throughout the flood patterns. The paper also presents (1) the results and analyses of the flood-pattern prediction, (2) the computer techniques for determining the shape factors and volumes from the potentiometric models for the foregoing flood patterns, and (3) the shape factors and volumes of the channels of the flood pattern in the event reservoir engineers may like to process waterflood calculations using their own permeability curves and reservoir oils. DESCRIPTION OF METHOD VOLUMES AND SHAPE FACTORS The use of channels taken from a potentiometric model (see Fig. 1) to aid in calculating the performances of water floods of nonlinear patterns has been thoroughly explained in the literature.0,7 Therefore, very little theory, discussion, or proof regarding this phase will be repeated in this paper. The computer method presented in this paper to calculate the volumes and the shape factors of the channels of potentiometric models employs the trapezoidal rule for the volumes and the Pythagorean theorem (the hypotenuse equals the square root of the sum of the squares of the two sides of a right triangle) for the shape factors. In calculating the volume of a channel, the area of each cell in the channel is determined and then multiplied by the thickness to obtain the volume. In determining the areas of the cells, trapezoids are constructed whose vertical sides are spaced Ax apart, as shown in Fig. 2. The length of the sides is the difference between an ordinate cut off by the top and bottom of the cell — usually equipo-tentials. The coordinates of the points along an equipo-tential or streamline are obtained by Lagrange&apos;s8 equation of interpolation for which the constants are coordinate points at the intersections. Three intersections for con-

Jan 1, 1965

By J. W. Freeman, E. E. Reynolds, A. E. White

Fram a study of 63 systematic alloy modifications it was found that molybdenum, tungsten, and columbium, added individually or simultaneously, and increases in chromium cause major improvements in 1200°F rupture strengths of Cr-Ni-Co-Fe base alloys. Rupture strengths were a function of the effect of composition modifications on both the inherent creep resistance and the amount of deformation the alloy would tolerate before fracture. THIS paper describes the results of an investigation of a series of alloys with systematic variations of the chemical composition of the following basic alloy: C, 0.15: Mn, 1.7; Si, 0.5; Cr, 20.0; NI, 20.0: Co, 20.0: Mo, 3.0; W, 2.0; Cb, 1.0; N, 0.12; Fe, 32.0 pct. The 62 modifications of this alloy were produced under conditions which minimized all factors influencing properties at high temperatures except composition. Melting, fabrication, and heat treatment were carefully maintained constant. Stress-rupture properties at 1200°F were used as the primary criteria of evaluation of the alloy. The objective of the study was to obtain data for determining the fundamental role of the influence of alloying elements on properties of heat-resistant alloys at high temperatures. In addition the results should be useful in determining optimum chemical compositions, the sensitivity of properties to variations in composition, and the degree to which alloy content could be reduced while retaining worthwhile properties. It is difficult or impossible to develop correlations between properties at high temperatures and systematic variations in chemical composition from published data for wrought heat-resistant alloys developed for gas turbines.&apos; &apos; The main reason for this is the extreme dependence of the properties on conditions of treatment of the alloys." In most cases variation in final treatments between alloys so influences the properties that the influence of chemical composition is obscured. In addition it is recognized Table I. Basic Alloy and Some Modifications Used Basic AllOy, Variations in Element Pct Composition, Pct C 0.15 0.08. 0.40. 0.60 Mn 1.1 0.03,0.25.0.50,1.0,2.5 S1 0.50 1.2, 1.6 Cr 20.0 10, 30 Ni 20.0 0, 10,30 Co 20.0 0. 10, 30 MO 3.0 0. 1.2.3, 5, 7 W 2.0 0, 1, 5, 1 Cb 1.0 0.2,4,6 N 0.12 0.004, 0.08, 0.18 Fe 32.0 that variations exist between heats of the same alloy which are related to melting practice and that there is a strong possibility that conditions of hot working influence response to final treatments. The development of heat-resistant alloys has been based on the gradual accumulation of data roughly related to composition from extensive testing programs. There is every reason to believe that in most cases the optimum compositions have been achieved by this procedure in the alloys commercially available. There are, however, very little data showing the influence of systematic variations of composition free from the influence of other factors, particularly for alloys of the type investigated. Several investigators of cast alloys have demonstrated compositional effects, notably Grant,1-6 Epremian,t Guy,8 and Harder and Gow.9 Sykes10 eviewed the work on the wrought alloy Rex 78 and the systematic variations of carbon, copper, molybdenum, and cobalt leading to the development of the stronger Rex 337A alloy. From the papers by Wilson11 and Henry12 it is possible to deduce the beneficial effect of substituting cobalt for iron in 0.45 pct C-20 pct Cr-20 pct Ni-4 pct Mo-4 pct W- 4 pct Cb alloys. Wilson mentioned but did not present the extensive compositional studies involved in developing these alloys. Binder" showed optimum properties for 3, 2, and I pct, respectively, for molybdenum, tungsten, and columbium in 20 pct Cr-20 pct Ni-20 pct Co-30 pct Fe alloys for limited systematic variations of these

Jan 1, 1953

W. H. SHOCKLEY, Chairman, FRANK H.-PROBERT, :Vice-Chairman, T. A. RICKARD, Sec.-Treas.; 420 Market St.,. San Francisco, Cal. C. C. BRAYTON, J. F. NEWSOM. A Meeting of the San Francisco Section was held on May 7, 1917. Chairman Shockley was in the Chair. The Section was honored by the presence of President Moore and Secretary Stoughton of the Institute. C. W. Merrill introduced President Moore, who then spoke to the Section on the Aims of the Institute. He discussed the possibility of improving the standards of membership by introducing a classification of membership. The present rigid investigation of applicants was pointed out by him. He spoke of the important influence that the local Sections can exert on the Institute and of the importance of sociability and informality at the meetings. Secretary Stoughton, who was introduced by the Chairman, emphasized somewhat the same points. He mentioned the need for making the Bulletin of the Institute more, interesting than it is at present, this to be accomplished by raising the necessary funds by increased advertising. He asked for an expression of opinion on this point. He. said that the employment department of the Institute is now used extensively. At the request of Mrs. Mark L. Requa, Mr. Stoughton. announced that a San Francisco branch of the Woman&apos;s Auxiliary of the, Institute was being formed and asked that the ladies of the members&apos; families send in their names to Mrs. Requa or to the Secretary of the Institute.

Jan 10, 1917

By John J. Collins

The plight of the Japanese mining business is pitiful. Coal mines were given the highest priority for all materials they needed, yet between the end of the war and June 1948, the government was obliged to subsidize them to the extent of 22 billion yen, this being the difference between the consumer&apos;s price and the producer&apos;s price. Most of the metal mining companies have been operating at only one fifth to one third of war-time production rates, and financial losses have been terrific. The chief difficulties have been a plethora of office workers and a dearth of equipment, supplies, and miners. The principal material needs at metal mines are steel rails. cars, plates, nails, rubber hoses, and belting, to say nothing of modern core drills which are totally lacking. Until recently the great shortage was in coal; for lack of fuel the smelters and factories failed to produce the very metals and equipment now needed to operate the mines. Nation-wide shortages have created a monstrous inflation of prices throughout all the economy, currently amounting to 200 times the prewar figures. For example, the price of copper ranged from 500 to 900 yen per metric ton for many years until 1937, but in mid-1948 producers were

Jan 1, 1949

By J. O. Glanville, L. H. Haley

Ice frozen from a dilute chemical solution is mechanically weaker than ice frozen from pure water. This phenomenon is the basis of a practical method for reducing the strength of a mass of frozen coal. If a chemical additive is applied to moist coal prior to its shipment during freezing weather, the resulting frozen coal can be more easily broken than in the absence of the chemical additive. This greatly expedites the unloading and handling of coal during winter. There has been considerable research into the nature and mechanical strength of ice frozen from various solutions. In this paper, literature relating to this process as well as literature relating to the chemical treatment of coal and mineral particulates is reviewed. Some important articles are discussed and speculations made about the nature of the ice-weakening process. A laboratory evaluation of the effects of chemical additives on the mechanical strength of ice and frozen coal has been made. An apparatus designed for this purpose is described, and some results obtained with it are discussed.

Jan 1, 1983

By George C. Branner

STATE geological surveys have had an interesting development in this country. They first appeared more than a hundred years ago. The fact that they have persisted and are now an important part of most state governments indicates the basic need for state departments con-cerned with mineral problems. The number of state surveys in 1941 (43) is at an all-time high, as is the aggre¬gate appropriation for their support for the fiscal year 1940-&apos;41 ($1,600,708). The first surveys, those of North and South Carolina (see Fig. 1), made their appearance in 1820-&apos;30, but neither survived that period. During the next two decades surveys were created in twenty states, but only three survived. In fact, it was not until the decade 1900-&apos;10, when eighteen surveys were created and only five abolished, that these agencies became firmly established.

Jan 1, 1941