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By E. W. Parker

THE anthracite region, from which there is produced annually about 80,000,000 tons, or approximately 15 per cent. of the total coal supply of the United States, has a combined area of a little less than 500 sq. mi. The total area occupied by the bituminous fields (including the sub-bituminous and lignite fields) is in the neighborhood of 400,000 sq. mi., so that 15 per cent. of the total output comes from this small area of only a little more than 0.1 per cent. of the coal-producing territory. of the United States. The productive anthracite area is divided into a series of basins or troughs, roughly parallel, extending. in a northeast-southwest direction through the. Counties

Jan 1, 1921

By Robert J. Anderson

DURing the past 5 years no subject has aroused more interest or received more attention among mill operators than flotation. One reason for this is, undoubtedly, the remarkable success of the process in Australia where that country has risen to the position of furnishing one-fifth of the world's supply of zinc. The plant of the Butte & Superior Copper Co., designed by James M. Hyde in 1912, was the first important large flotation plant in this country; other installations have been made since then with considerable frequency, particularly so in the last 2 years. Without going into complete detail, it may be safely said that although flotation is a highly successful commercial process, it is more or less on an empirical basis. Upon scanning the literature, it is found that the flotation investigations have, in the main, dealt with a solution of the problems which accrue to practise; until recently no attempt was made to remove the difficulties in the way of the formulation of a consistent and harmonious theory. Of late this phase of the work has been receiving considerable attention, particularly by the United States Bureau of Mines at its Salt Lake City station, by the Mellon Institute at Pittsburgh, by the General Engineering Co. at Salt Lake City, by many of the mining schools, and private individuals almost ad infinitum. There is, at present, an enormous amount of laboratory work being carried on in flotation research, and probably the time is not far away when a generally acceptable explanation of flotation phenomena can be set forth. However, at this time, it seems as though the current technology is befogged with a superabundance of contradictory evidence; this confusion can only be dispelled as time proceeds and the knowledge of the subject becomes more complete. Many phenomena are supposed to contribute to the flotation of minerals, whether in whole or in part is a mooted question. I shall only sketch roughly the present tendency of ideas and make no reference to the first early and crude notions which have little value other than histori-

Jan 1, 1917

By J. H. Wernick

IN a study of the rate of decomposition of ½ -in. cubes of limestone, dolomitic limestone, and dolomite in a sweeping nitrogen atmosphere, Joseph, Beatty, and Bitsianesl found that the zone of calcination advanced at substantially a constant rate at a given temperature. The purpose of this paper is to show that their data indicate at least two processes occurring when the above carbonates decompose. It is suggested that there are two processes occurring temperature range and the other the limiting process over another temperature range. The data of Joseph and co-workers have been extended by use of the Arrhenius equation, Eq. 1, a relation beween the velocity constant k of a reaction and the absolute temperature T.

Jan 7, 1954

By C. L. HUNTZINGER

THE mine here described is in the Witbank district, a coal area of the Transvaal, about 100 miles north- east of Johannesburg. and is owned by the Witbank Colliery, Ltd. The plant has a capacity of 4000 tons per eight hours, and prepares five sizes of coal. The coal seam lies at a depth of about 200 ft. below the surface, and is reached by an inclined shaft sunk at an angle of 18° with the horizontal. Although the thickness of the coal seam varies from 10 to 14 ft. or more, only about a 7-ft. bench is mined. Mining is by the hord and pillar system. Bords are driven 18 ft. wide, with pillars measuring 18 ft. square. The mine is laid out into four sections, each sewed by a main haulage way from the shaft. Arc-wall machines are used for cutting the coal. but all loading is done by hand. Native labor is employed under the supervision of white miners, who do the required blasting. The workings are practically free from gas and water, and very little timber is needed.

Jan 1, 1931

By Ellsworth Daggett

Jan 1, 1879

By K. Mukai, M. Ishihara

This report is a brief discussion of the impurity levels both in primary aluminum and super-purily alnminim in connection with raw materials and proc-essing methods. Particularly, truce amounls of im-purities were analyzed by introducing nittss-speclro-gruphy and nenlron-aclivalian analysis techniques. Vanadium and gallium content in primary aluminum metal corresponded to theor amounls in anode coke. but the nickel content in primary aluminum was hide-pendent oj its amount in the anode cake. Sulfur in the anode colic might result in an increase of the iron content in the molten metal in the reduction cell. The content of sodium and calcium increased with increasing bath ratio. In the holding furnacc sodium content decreased rapidly, and nonmetallic inclusions merit separated front the mollen metal. Three-layer elctrolysis was effectire in eliminating many impuri-ties with the exception of copper, aluminum oxide. aluminum nitride, and some rare-earth elements. THE amount of impurities and nonmetallic inclusions in aluminum metal depends on impurities in the raw materials and various production processes. This paper presents an investigation of the behavior of impurities and nonmetallic inclusions in aluminum during the electrolysis process, the period in the holding furnace, and the process of three-layer electrolysis. Chemical analysis and emission spectrometric analysis have generally been used as methods to determine small amounts of impurities in both primary aluminum and super-purity aluminum; however. mass spectrography and neutron-activation analysis have been recently introduced into this field, and trace amounts of impurities can accurately be determined by these latter methods. EXPERIMENTAL WORK Common impurities were determined by means of absorptiometric. polarographic, flame-photometric. and emission-spectrometric methods. However, in the determination of trace amounts of impurities and non-metallic inclusions, the following methods were applied. In the analyses of trace impurities by mass-spec- trographic analysis, samples were exposed in the vacuum spark of double-focus ing Mattauch-Herzog type mass spectrograph (Japan Electron Optics Laboratory, Ltd.). Ilford Q2 photographic plates were used as ion detectors. Fe was used as the internal standard, and the atomic concentration of each element was calculated by the following expression and converted into the weight concentration: where E, and Ei are the exposures (coulomb) when isotopes of the internal standard and impurity elements (on which the estimate is based) show the same density, X is the percent (atomic) concentration of the standard, IF and Ii are the percent abundances of the isotopes of the standard the impurity elements (on which the estimate is based), and Ms and hfi are the mass of the isotopes of the standard and impurity elements (on which the estimate is based). The coefficient of variation in this method is about 40 pct in the range of 0.1 to 1 ppm. In neutron-activation analysis, irradiations were done in the nuclear reactors TRIGA-I1 (neutron flux: 4.7 x 10 11 n per sq cm per sec; Rikkyo University) or JRR-2 (neutron flux: 2 x 1013 n per sq cm per sec: Japan Atomic Energy Research Institute). After the chemical separation, a NaI (3 by 3 in.) scintillator connected to a 256-channel y-ray spectrometer (R.C.L.) was used for counting and recording various activated impurities. The coefficient of variation in this method is about 20 pct. In the analyses of nonmetallic inclusions, aluminum-oxide determination was carried out according to Fischer's method, 3 as follows. A slice of sample was cut off and the surface was cleaned. It was dissolved in bromine-methanol. The solution was filtered and the residue was washed. The residue was fused with potassium bisulfate flux. Then it was dissolved in weak acid, and oxine solution was added. The aluminum oxinate was extracted with benzene. Finally, aluminum was determined absorptio-metrically. Aluminum nitride determination was carried out as follows. A slice of sample was cut off and the surface was cleaned. It was put in the distillation apparatus and decomposed with sodium hydroxide solution. The solution was distilled. Then ammonia was absorbed and

Jan 1, 1967

By R. J. Grissom

PHOSPHATE deposits have been worked in many countries of central and south central Tennessee, but only ht ebrown rock deposits of Maury and Giles Counties will be discussed at any length in this articles, as all of the major opeations are now located there. They are: Mt. Pleasant District-Federal Chemical Co., Hoover and Mason Phosphae Co., International Minerals and Chemical Corp. (Maury and Giles Counties), Virginia-Carolina Chemical Corp. (formerly Charleston Mining Co.), and Victor Chemical Co. Columbia District-Armour Fertilizer Works and Monsanto Chemical Co. In the near future, the well-known, extensive deposits of blue rock in Lewis and Hickman Counties,also the brown rock in Hickman, Willamson, Summer and Davidson Counties, will again come into production. Certain physical peculiarities of the Tenessee deposit have played an important part in the design and use of mining and milling equipment.

Jan 1, 1944

By R. Maddin, C. H. Mathewson, W. R. Hibbard

According to conventional crystal mechanics, a face-centered cubic single crystal slips on the system {111} <110> which receives the highest shear stress in terms of the stated orientation of the stress axis of the crystal.l However, in brass, the slip process is never as simple as this conventional analysis indicates. There is always a second cooperating plane which contains the same slip direction as the primary plane.2&apos;3 There is still another cooperating slip system commonly called the conjugate system3 previously observed to function with considerable lag only after the rotation due to the action of the first plane had produced a symmetrical condition of equal shear stress on the two systems. In the 1943 Campbell Lecture,4 a slip mechanism was outlined in which the {111) planes moved step-wise in two adjacent <112> directions integrating into the <110> slip direction. "... the slipping process would be visualized as a succession of steps 30" to the right and left of the resultant, microscopically observed, slip direction; a first step setting up the twinned configuration in the single spacing involved and an ensuing slip returning the atoms to the untwinned configuration while completing a fully integrated <110> movement."4 This process is shown diagrammatically in Fig 1 which shows two close packed layers of atoms at a slip site. A movement of the full circles through the "valleys" into the adjacent sites would produce a twin configuration with respect to the open circles. The term, "twin fault," seems most appropriate to define this faulted condition of the lattice. Annealing twins in face-centered cubic metals may arise from preformed nucleii which could be described as twin faults produced by the first movement of this two stage slip process. However, it is clear that this kind of slip does not take place so as to embrace a measurable number of adjacent planes because careful X ray examination has not conclusively shown the existence of ponderable twin lamellae (as in the case of Neumann bands in the body-centered ferrite). In view of the imponderable character of these hypothetical twin faults, the search for evidence of their existence seems restricted to indirect methods. The most obvious experimental technique serving this purpose is the determination by micrographic and X ray methods of the alignment of the composition planes of annealing twins with the former slip planes in axially strained and recrystallized single crystals. In previous attempts of this sort not all of the annealing twins could be traced to slip planes known to be operative in the conventional sense and hence evidence appeared negative or inconclusive. With the discovery of additional slip systems2&apos;3 operating in conjunction with&apos; the major system of highest resolved shear stress in axially strained brass it became apparent that the simple technique outlined above might be re-employed with more gratifying results. If, on annealing single crystals of alpha brass previously strained in tension, twins are found with their composition planes parallel to all three operative slip planes and with no participation of the fourth plane there is good evidence in favor of the existence of twin faults and of the two stage slip process. Experimental Procedure and Resuits Single crystals of alpha brass of the 70-30 composition were grown by solidification from the molten state.

Jan 1, 1950

By P. W. Bridgman

Flow and fracture are admittedly complicated phenomena of which we are yet only partially masters. There is not even nni-.persal agreement as to the details of the language best adapted merely to describe the phenomena, to say nothing of any theory. Certain points of view, however, are widely held, and there are certain general expectations as to what sort of procedures will prove permissible. A complete description of any situation involving fracture would demand a complete history of all the variables in the control of the experimenter. The experimenter endeavors so to choose his independent variables that they are adequate to determine completely the situation in the sense that when an experiment is repeated on the same initial material and with the independent variables running through the same sequence, all the other measurable properties of the system will also run through the same course. It is, I think, the universal conviction that when we are dealing with phenomena of flow and fracture, the most important of the necessary variables are the external forces acting on the various parts of the body; when the force history repeats, with certain obvious restrictions such as that temperature must be constant and non-mechanical forces, such as magnetic field, must be small enough to be ineffective, then the history of all measurable properties will repeat; in particular the alteration of geometrical shape due to flow will run through the same course, and when fracture comes, the character of the fracture will be reproduced. Complete mastery of merely the descriptive aspects of flow and fracture would demand the ability to predict the entire course of flow and complete characterization of the final fracture for every possible combination of forces, varying in time in all possible ways, when applied to bodies of all possible shapes. This full situation is obviously of prohibitive complexity. The first stage in reduction to manageable simplicity is to resolve the total situation into the sum of contributions made by small elements. Our thesis is that if each of the elements is adequately characterized, the behavior of the whole system is fixed. The element is usually taken of a simple geometrical shape, suggested by the mathematics best adapted to the particular situation. The forces acting across the faces of the elements are ultimately determined by the forces acting across the free faces of the whole system. The detailed process of finding the precise forces on the faces of all the elements in terms of the external forces involves the use of a special mathematical invention, the stress, a constructional quantity consisting of six components. The stress at any point in the body is determined by both the external force system and by the physical properties of the body at all points; quite different stresses prevail at the interior of bodies of the same shape under the same external forces in the elastic and plastic ranges. The forces on the faces of any element are, however, uniquely determined by the stress system at the element. Our fundamental thesis

Jan 1, 1945

By John J. Dran

The elaborate analytical techniques for risk analysis used by the large mining companies in conjunction with the valuation of mineral reserve sites are totally inappropriate for the small miner. The small miner does not possess the financial and technical resources which are available to the large companies for such risk analysis. Even if these resources were available to him, the relatively small size of his investment would not justify a huge expenditure for risk analysis. What is required by the small miner is an improvement over the single point estimates provided by the valuation techniques that he currently uses. Such improvement should provide an indication of the extent to which the true value (known only after the fact) might differ from his estimated value of the mineral reserve site. In addition, a rough indication of the chance of occurrence of various differences between the true and estimated values would be helpful to him. These improvements must be obtained at low cost to be useful to the small miner. Such improvements would have to be based on a simple system requiring very few additional estimates by the miner. The small miner is not accustomed to dealing with sophisticated risk analysis techniques. Hence, any complex, time-consuming approach would be doomed to disuse or possible misuse. A simple, uncomplicated approach requiring a minimum of additional estimates by the miner can be based on a system devised by Frederick S. Hillier Although Hillier&apos;s method can be applied to various mineral reserve valuation methods used by the small miner, this note is specifically oriented to the discounted cash flow model. The basic discounted cash flow (DCF) approach provides a single point estimate of value and introduces the concept of risk (i.e. the possibility that the annual cash flows may differ from their estimated values and thus lead to an incorrect investment value) through the use of a risk-adjusted discount rate. This approach simply lowers the present value estimate with increases in the discount rate (i.e. increases in the risk assessment). The single point estimate still remains. Although the lower value estimate makes it less likely that the risky investment will be deemed profitable and undertaken, it provides no indication of risk that is suitable for examination and analysis. In addition to the "best guess" estimate of annual net cash flows required in the DCF model, application of the Hillier risk analysis model requires that the miner

Jan 1, 1976

By E. W. Lithgow, E. G. Williams, R. R. Holbrook, B. R. Wilson

The mineralogy and geochemistry of Pennsylvanian shales and underclays were studied to determine their suitability for lightweight aggregate and refractory ladle brick. Eighty percent of the variation in bloating of shales and clays was explained by the variation of Si02, A1203, and fluxes (Fe203, MgO, CaO, Na20, and K20); 60% by variation in quartz, kaolinite, illite, and chlorite. The best bloating was exhibited by marine shales, whereas freshwater shales and underclays experienced little or no expansion. Regional paleogeographic maps o f Pottsville and Allegheny shales permit bloating to be geographically predicted. It was found that clays meeting the specifications for refractory ladle bricks were obtained from underclays having over 34.5% mica, over 40% kaolinite and less than 15% quartz. Underclays of this composition are confined to the lower Allegheney outcropping along the near-margins of the coal basin. The best clay is that underlying the Lower Kittanning coal. Porosity of the first fired brick was found to be inversely correlated with reheat expansion.

Jan 1, 1975

By E. M. Norris

THE Western phosphate deposits extend over a large area in the Rocky Mountain region, comprising portions of south central Montana, southeastern Idaho, northeastern Utah, and southwestern Wyoming. A limited acreage of these deposits passed into private ownership prior to Dec. 9, 1908, at which time 7000 sq. mi. of land in these phosphate fields was withdrawn from public entry by direction of the Secretary of the Interior. Under the Act of Feb. 25, 1920 (41 Stat. 437) title to all phosphate lands in the public domain was reserved to the United States with provisions for leasing portions to citizens, corporations, states, etc. The above act, in effect, created by law a Western phosphate reserve of approximately 2,269,055 acres.

Jan 1, 1944

By N. V. Hansell

l. INTRODUCTION. THE last few years have shown an increasing interest in the subject of beneficiating iron-ores -in all iron-producing countries. In the United States, this movement has been slower than in certain parts of Europe, for the obvious reason that the abundance and relative cheapness of the Lake Superior iron ores has hindered the development of enterprises for the preparation of low-grade ores. Gradually, however, conditions have changed. The world&apos;s consumption of iron is increasing enormously. Being in 1900 about 40,000,000 tons, in 1910 ii was already 60,000000; and there is no reason to doubt that for the near future the increase in iron-consumption will continue at the same rapid rate, especially with, the development of China, certain parts of Africa, and other regions which have hardly been touched as yet by modern industrialism. It is. therefore, not surprising that apprehension is felt that the known available iron-ore resources of the world are gradually being depleted. Signs of this feeling are the recent investigation, under the direction of the U. S. Geological Survey, of the iron-ore resources of the United States, and the estimate presented to the last International Geological Congress, at Stockholm, Sweden, of the iron-ore resources of the world. These investigations have emphasized the fact that the known high-grade ore-deposits are limited in extent, and will, at a not distant future, be exhausted, compelling the iron industry to depend for raw material on the enormous deposits of low-grade ores which are distributed over almost all the world. The discovery of new deposits of high-grade ore, in countries not yet thoroughly explored, will not materially change this prospect. Of course, the part which such new deposits will play in the future cannot be forecast. The difficulty and cost of transportation will probably exclude many of them from use at the present centers of the iron industry.

May 1, 1912

By A. A. Burr, D. G. Ebeling

The effects of casting texture, grain orientation and grain size upon the performance of Alnico permanent magnets is described. Single-crystal specimens were produced by special sintering and grain coarsening techniques to study the effect of crystal orientation. In addition to texture and orientation effects, an analysis of the results indicates that the permanent magnet performance is impaired by a refinement of the grain size. AN excellent historical review of the development of Alnico permanent magnets has been prepared by Bozorth.1 The desirable permanent magnet characteristics of Fe-Ni-A1 alloys were discovered in 1932 by Mishima.2,3 The work of Ruder&apos; showed that the alloys were age-hardenable, and Betteridge5 defined the best composition and heat treatment for the magnetically isotropic alloy known as "Alnico 3." Horsburgh and Tetley0 increased the energy product by the addition of cobalt and copper, "Alnico 2," and Oliver and Sheddon7 demonstrated that cooling in a magnetic field improved the residual induction of this alloy. Jonas8,9 then disclosed the great practical benefits of heat treating an alloy of higher cobalt content in a magnetic field and the resulting alloy, "Alnico 5," has become the standard of the industry. This paper describes the fundamental aspects of a procedure which can be used to further improve the properties of these anisotropic permanent magnet alloys. A study of the casting techniques used in the production of anisotropic Alnico permanent magnets indicated that the magnetic quality was affected by the as-cast macrostructure. Improved performance was observed in magnets containing a high percentage of columnar grains whose long axes were parallel to the magnetic axis of the casting. McCaig10 studied the effect of such columnar grain structures upon the magnetostriction characteristics of similar alloys, however no data was presented showing the effects on other magnetic properties. The following paragraphs describe two experiments which were conducted to determine the effect of various grain orientations upon the energy product. Special composite molds were prepared of highly conductive and highly refractive components to remove the heat of solidification from the casting in a controlled manner. Representative macrostructures produced by these techniques are shown in Fig. 1, along with the relative volumes of favorably oriented columnar grains. The alloy, Alnico 5, has the highest permanent magnet performance of any commercial magnet material. It has the nominal weight composition of 8 pct Al, 14 pct Ni, 24 pct Co, 3 pct Cu, and 51 pct Fe. A heat of this material was cast into molds producing the type A and B grain structures shown in Fig. 1 and pairs of the resulting magnets were placed in heat-treating boats so as to eliminate any biasing effects of boat position. After a standard heat treatment the type A magnets, with 16 pct of the volume composed of favorably aligned grains, had a maximum energy value of 3,940,000 gauss-oersteds, while the type B magnets with 73 pct aligned grains averaged 5,090,000. This large im-

Jan 1, 1954

By C. R. Swarts

The use of compressed air or gas in oil wells for raising crude oil to the surface has, within the last year, become a dominant factor In production engineering. Previous application of this principle was largely confined to oil wells that had been pumping for a considerable length of time. In the Seminole area, the gas-air lift has been applied to wells imniediately after natural flow has ceased and in some cases while the wells were still flowing. This early application of the gas-air lift has been watchcd with intense interest by the petroleum industry, both with respect to methods of application and mechanical installations and to the effects on immediate and ultimate production. Methods of Application The Seminole pool at its inception contained sufficient gas associated with the oil to cause natural flow. As no frce gas was found in the main productive horizon, the Wilcox sand, all the gas present was dissolved in the oil, hence the natural flowing life was short, rarely lasting over 45 days. When natural flow ceased, high fluid levels were common, and as depth and crookedness of holes were obstacles to efficient pumping, the gas-air lift was used almost exclusively in raising the oil to the surface. Because of the high gravity of the oil, 41" A. P. I., and its high gasoline content, and also because of the desire to obtain production before offset wells became productive, quantity of production was the aim of the operators and a method of flow was used whereby this aim could be fulfilled. One of the outstanding features of this method consisted in flowing the wells through the annular space between the tubing and rasing. By this means a greater quantity of fluid could be handled than by flowing through the tubing of the size in ordinary use. Wells that would produce only a few hundred barrels on the pump were by this rnethod made to produce as high as 7000 bbl. on the lift. A few days or wreks of production at that rate meant a large recovery of oil. Casing of 636 in. diameter was commonly used as a production string with a 5 3/16-in. liner set on top of the oil sand. Upset tubing for irtro-

Jan 1, 1928

By A. B. Kinzel

SILICON and its metallurgical uses have been the subject of speculation since the earliest days of modern civilization. The early philosophers, Theophrastus and Pliny, believed that silica was a special form of ice, an opinion that was not seriously challenged until the seventeenth century. The first comprehensive view of the nature of silica was advanced by Lavoisier in 1787. He assumed silica to be an oxide of an unknown metal. In 1808 Berzelius produced ferrosilicon by heating silica, iron and charcoal. Probably the first produc¬tion of crystallized silicon was in 1854 when H. St. C. Deville accidentally produced the material while electrolyzing a double chloride of aluminum and sodium containing siliceous impurities. It is not strange that the early investigators should have given so much attention to silica and silicon, because of the great natural abundance of the former. Although silicon does not exist in the elemental state in nature, it has been estimated that the lithosphere contains approximately 60 per cent silica; quartz and rock crystal are found in practically every part of the world.

Jan 1, 1933

By James Aston

A PROPER consideration of this subject is not confined to the technical channels of production and metallurgy. It concerns an industry, and should cover economic aspects which are of material importance in any program of development. The discussion may logically be treated under three subdivisions, as follows: (1) manufacture, (2) characteristics related to quality of material; (3) adaptability and exploitation of product. MANUFACTURE OF WROUGHT IRON The manufacture of wrought iron is the most ancient art of the ferrous metal industry. The eighty years or less of existence of processes identi-fied with our modern "Age of Steel" is a relatively brief interval com-pared with the several thousand years associated with the production of wrought iron by man. From the primitive early methods of production, manufacture for many centuries followed the line of direct reduction. There were developments as experience was gained through the years; but man&apos;s needs for a strong, ductile, forgeable product were met by reducing the ore to metallic iron in a single-stage operation. Following the development several centuries ago of what has become our modern blast-furnace operation, manufacture of wrought iron was gradually transformed into a two-stage method of first producing cast iron and then refining this to the desired degree of forgeability; the fore-runner in principle of today&apos;s scheme of manufacture of steel. The product retained the essential characteristics of highly refined base metal with iron-silicate slag incorporation, which were associated with the material resulting from direct reduction methods. Cort&apos;s invention of the puddling process in 1784 is a landmark in wrought-iron manufacture. It consisted essentially in adapting a coal-fired reverberatory furnace to the refining operation; thus lifting the industry out of the slough of

Jan 1, 1935

By R. H. Tien

Temperature distribution as well as position of the solidified front is solved by means of "heat balance integral", for the case of freezing a slab with time-dependent surface temperature. Numerical solutions for the cases of linear variation and exponential decay for surface temperature are given. Application also includes solidification of casting. An increased interest in the heat-transfer problem involving a change of phase has been developed in recent years. Practical problems include solidification of a casting, freezing and thawing of soil, ice formation, and others. Despite the importance of the topic, a literature search reveals relatively few solutions which may be extended to practical problems. Due to mathematical complexity, which comes from the nonlinearity of governing differential equations, exact analytical solutions which have been published are limited to a few cases with simple boundary conditions. Although numerical solutions of these problems have become available after highspeed digital computers were introduced, lack of simple and general methods of programming for computation makes this approach impractical. The case of the semi-infinite slab with constant surface temperature was solved in the 19th century. In honor of Neumann, who first found an analytical solution, this kind of problem is generally referred to as the Neumann solution. As has been shown in Fig. 1, the problem to be analyzed is the freezing of a semi-infinite region (x > 0) which is initially liquid at the melting temperature with the surface (x = 0) maintained at time-dependent temperature. This analysis can be applied to the study of many casting processes where most of the heat removal is essentially unidirectional. "Heat balance integral" which has been used by Goodman1 is employed in this analysis. The concept of "heat balance integral" is to define a quantity, d(t), called the thermal layer. Beyond this thermal layer, for all practical purposes, there is no heat transfer, and the region is at the equilibrium temperature. "Heat balance integral" is obtained by integrating the conduction equation with respect to the space variable over this thermal layer d(t). Choosing some plausible temperature distribution, usually a polynomial or a finite trigonometric series in the space variable, this integral equation becomes an ordinary differential equation, with time as the independent variable, which can be solved by classical methods. The thermal layer and "heat balance integral" are equivalent, respectively, to the boundary-layer thickness and the momentum integral in hydrodynamics. A modern account of Prandtl&apos;s concept of the boundary layer and von Karman&apos;s momentum integral may be found in Ref. 2. Although the problem considered here has been limited initially to uniform melting temperature, the present method is equally applicable to the case with arbitrary temperature distribution in the liquid. STATEMENT OF THE PROBLEM The physical situation and coordinate system used in the problem to be analyzed are shown in Fig. 1. Notations used are listed in the table of nomenclature. Let us assume a semi-infinite region extending over positive x, initially at the uniform melting temperature. At the surface x = 0, a time-dependent temperature, which has a numerical value

Jan 1, 1965

By Richard W. Lodge

Ix the crucible-method of assaying ores for silver a certain amount of litharge is essential to supply sufficient lead to collect the precious metals. The object of this paper is to point out that the use of a .large excess of litharge in the assay of some ores will give results for silver that are uneven as well as low. So far as I know, however, an excess of litharge does not affect the results obtained in the crucible-assay of ores for gold. The main reasons for using, in the crucible-assay, much more litharge than is required to give the necessary lead button are : 1, its action as a flux; 2, its action as a desulphurizer; and 3, its action as an oxidizer, especially on metals like copper and nickel, whereby they are forced into the slag as oxides and thus prevented from passing into the lead button. Hence, by the use of much litharge in the crucible-assay more-ore can often be taken than in the scorification-process, and a lead button obtained which can possibly be cupelled at once or after a single scorification. The method is specially advantageous with an ore carrying much copper or similar impurity and poor in silver, when the assayer does not wish to resort to a wet-analysis for the determination of the silver. It is well known that some ores give better results when assayed by the scorification-method, while others give better results by the crucible-method. For several years I have noticed that, when much litharge was used with certain sulphide and arsenical ores, the results were considerably lower than when the scorification-method was used. This fact was more forcibly brought out in connection with certain work carried on this year by Messrs. H. A. Frame and

Sep 1, 1907

By F. N. Pease, C. B. Dudley

Those who have worked a good deal on the chemistry of pig-irons of which the physical properties were known, cannot fail to have been struck by the remarkable want of relation between the physical properties of different samples, and the ultimate chemical composition. It is very well known among foundrymen that irons which will give say 4 inch of chill, and are, therefore, approximately the same in chemical composition, are very far apart, many times, in their physical properties. The foundryman&apos;s tests for strength are, of

Jan 1, 1886