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By E. T. Turkdogan, M. L. Pearce

The rates of sulfurization and desulfurization of calcium aluminate, silicate, and ferrite melts by CO + CO2 + SO2 mixtures at 1550°C are reported. It is shown that for melts 10 to 15 mm deep transport of sulfide ions within the melt controls the rate of sulfur transfer. The rate data from shallow melts, i.e., 1 to 4 mm deep, have been analyzed on the basis of a diffusion or a reaction controlled process and indications are that the both processes may play a part in controlling the rate of sulfur reaction. The rates of desulfurization of silicate XVEACTION equilibria between metals, metal oxides, and gases have received considerable attention in recent years. However, the understanding of and aluminate melts increase with increasing PCO2/PCO ratio in the gas stream, the effect being most marked for aluminate melts. The sulfide equilibrium data obtained from the present work are shown to be in accord with the results of previous studies. It is shown that carbon dioxide has a measurable solubility in silicate, aluminate, and ferrite melts. Consideration is given to the partial equilibria which control the directions and the rates of reactions occurring simultaneously in complex heterogeneous systems. the kinetics of heterogeneous reactions, particularly those occurring at elevated temperatures has not been improved appreciably. Almost all the metallurgical reactions occur in heterogeneous systems involving two or more phases. Although in many authoritative text books and original Papers the basic principles concerning the kinetics of heterogeneous reactions are clearly underlined, they are seldom used to the best advantage in kinetic studies, particularly those involving the metallurgical reac-

Jan 1, 1963

By E. van Walsum

Tunneling methods through rock have, since the successful development of explosives, relied almost solely on blasting. Over the last ten years, rock-tunneling machines (moles) have been developed and some major projects have been carried out successfully with the use of such machines, which rely on the destruction of rock by mechanical means rather than blasting. Various other basically new methods are presently under study, such as the use of laser beams, water jets, etc. For practical purposes, there are presently only two methods commercially available: 1) blasting or 2) tunneling by mole. A contractor would choose at present either one method or the other. Both methods have their advantages and disadvantages (Fig. 1). The thought has occurred that the next practical development in rock- tunneling technology might be a combination of the best features of the mole technique and those of the blasting technique. A preliminary evaluation of this approach indicated that there is definitely a good potential for fruitful developments along these lines. My purpose is to place on record some of the thinking and some of the ideas which were developed along these lines and to point out certain areas where development efforts are required. In trying to find an improved tunneling technique, we looked in particular for the following qualities: 1) safety, 2) continuity, 3) uniformity, 4) automation, and 5) flexibility. TUNNELING BY BLASTING Conventional tunneling by means of blasting proceeds generally in recurring sequences of events: 1) drilling, 2) loading, 3) firing, 4) mucking-out, and supplementary operations (such as scaling and lining). These four operations (drilling, loading, firing, mucking) proceed one after another.

Jan 1, 1970

By G. H. Kesler, C. E. Dryden, J. H. Oxley

Rates of heat- and mass-transfer from rods to recirculating air were determined within a one-quarter-scale model of a metals deposition bulb. The dependence of local and averaged rates of transfer upon outlet geometry, number of rods, position upon a rod, and airflow rate was established for flow patterns created by radial and tangential air inlets. The results are given a qualitative interpretation in terms of rates and distribution of metal deposition in a prototype deposition bulb. IT is well known that a number of metals can be prepared from volatile compounds containing them by causing dissociation of their compounds to occur at heated surfaces. Examples of such metals include silicon, titanium, zirconium, and aluminum, which can be prepared from their halides. While the ability to prepare high-purity metals by this technique is of importance in itself, the rate of deposition of metal also is important in considering the commercial potential of such a process. If the over-all process of deposition is broken down into separate steps of transport of materials to and from the heated deposition surface and establishment of chemical equilibrium at the surface, as was described in a recent paper,1 then since surface temperatures are usually high and surface equilibrium is attained very rapidly, the rate-controlling step can be considered as either that of transport of reactants to the surface or of transport of products other than deposited metal away from the surface. These two transport steps are related through the reaction stoichiometry. It can be shown1 that the rate and distribution of metal in such a transport-controlled process are determined by the over-all and local mass-transfer coefficients in conjunction with the equilibrium conversions at the hot surfaces. The rate relationship is: w = [KA(y a-y s)] B.E where the bracketed group is the rate of arrival of the reactant at the surface of area A as determined by the mole fraction driving force (y a - y s) and the convective transport constant K. The factor B is the weight fraction of metal in the reactant, and E is the equilibrium fractional conversion to metal. Numerical values of y, and y, are fixed by the vapor composition and the equilibrium compositim of reactant at the surface; and E can be determined by thermodynamic calculations or by experiment. However, values for the convective coefficient K are available generally only for systems of simple geometry, such as cross-flow past a rod or sphere or parallel flow past a flat plate or through a tube. Often it is necessary to work with systems of more complex geometry and in which the vapor flow may not be uniform or exactly parallel or perpendicular to the surface. It is possible, of course, to establish working correlations for these more complex systems by direct experiment; but the experiments usually are costly in both time and money. To circumvent this objection and to aid in arriving at an understanding of the relationships and interactions of the process variables, it is helpful to construct a model of the flow system in which air, water, or other convenient fluids can be substituted for the process vapors and with which mass-transfer measurements or analogous he at-transfer measurements can be made upon a simulated deposition surface. By this means, a large number of measurements can be made in a reasonable time, and the correlation of these results can be applied to the prototype system. Examples of the application of these techniques are to be found in the literature (e.g., Ref. 2). It is the purpose of this paper to illustrate these techniques by description of a model study which was done at Battelle Memorial Institute. The work to be described was of a preliminary nature; the investigation subsequently was extended to develop quantitative relationships among the significant dimensionless transport, geometric, and flow parameters. This more detailed study will be the subject of a future paper.

Jan 1, 1962

By R. M. Hudson

A study has been made of the decarburization of low-carbon sheet steels at temperatures from 1100" to 1475°F in mixtures containing hydrogen, nitrogen, water vapor, and in some instances carbon monoxide. Decarburization occurs principally by the reaction C (in steel) + H20 = CO + H2 and follows a first-order rate law. The decarburization rate appreciably increases with an increase in temperature up to about 1325°F, but the increase in rate is small with fur- Use of a dry hydrogen atmosphere results in a relatively slow decarburization of steel and use of a wet hydrogen atmosphere results in relatively rapid decarburization. It is now generally recognized' that the reaction C (in steel) + H2O = H2 + CO [l] accounts for most of the decarburization that occurs in wet hydrogen-containing atmospheres. The present article is concerned with the decarburization of low-carbon sheet steel in H2-N2 atmospheres ther increase in temperature. The limiting rate of decarburization can be predicted from a knowledge of the solid solubility and diffusivity of carbon and this rate is approached as the water-vapor content of an atmosphere is increased. Hydrogen contents above about 8 pct are beneficial only in that they permit higher levels of water vapor to be used without oxidation of the steel. A buildup of CO in the atmosphere lowers the rate of decarburization. containing various amounts of water vapor and carbon monoxide. The effectiveness of these atmospheres and the influence of temperature on decarburization rate will be considered. EXPERIMENTAL WORK The chemical compositions of the three steels used in decarburization-rate studies are listed in Table I. Steel A was a commercially hot-rolled rimmed steel that was cold-reduced at the Laboratory to furnish specimens 0.025, 0.041, and 0.059 in. thick. Most of the experiments in which this steel was used were made on the 0.041-in.-thick material. Steel B and Steel C were cut from 0.010-in.-thick commercially cold-reduced coils that were

Jan 1, 1963

By Edward L. Estabrook

This paper gives a brief account of the geologic and production problems encountered in the Grass Creek oil field, the methods used in their solution, and the beneficial results obtained from the work. The author wishes to acknowledge the assistance received from J. H. Pearson and Miss Ninettta A. Davis in the collection of the data and the preparation of the cross-sections. Permission for its publication was given by the officials of the Midwest Refining Co. and the Ohio Oil Co. The Grass Creek oil field is located in Ts. 98-99 W., R. 46 N., Hot Springs County, Wyo. The productive area includes about 2 1/2 mi. (4 km.) on the apex of a great anticlinal fold occupying more than 150 sq. mi. Fig. 1 shows the structural contours of the field. Oil was dicovered in the field in June, 1914; development proceeded rapidly and production rose to a maximum in 1918. The marketed production has been approximately as follows: Barrels Barrels 1915.................... 94,073.5 1918................... 2,946,774.27 1916................... 1,404,183.97 1919................... 2,000,584.84 1917.................... 2,780,697.51 1920................... 1,485,080.94 About 350 wells, 800 to 1500 ft. (243 to 457 m.) deep, have been drilled to reach the upper oil sands; two companies, the Ohio Oil Co. and the Midwest Refining Co., operate the entire field. The principal producing sands in the field are members of the Frontier Formation, a series of sands and shales occuring in the upper portion of the Colorado Group of the Upper Cretaceous seriee. These Frontier, or "Wall Creek" sands are also productive in the Salt Creek, Big Muddy, and Elk Basin fields and, therefore, are much the most important reservoirs of light oil in Wyoming. At Grass Creek, the sands in the Formation are more numerous than in the other fields and much less uniform in thickness and character. Usually, eight distinct beds are encountered and in some wells twelve sands have been reported. The formation above

Jan 1, 1923

By Edward L. Estabrook

This paper gives a brief account of the geologic and production problems encountered in the Grass Creek oil field, the methods used in their solution, and the beneficial results obtained from the work. The author wishes to acknowledge the assistance received from J. H. Pearson and Miss Ninettta A. Davis in the collection of the data and the preparation of the cross-sections. Permission for its publication was given by the officials of the Midwest Refining Co. and the Ohio Oil Co. The Grass Creek oil field is located in Ts. 98-99 W., R. 46 N., Hot Springs County, Wyo. The productive area includes about 2 1/2 mi. (4 km.) on the apex of a great anticlinal fold occupying more than 150 sq. mi. Fig. 1 shows the structural contours of the field. Oil was dicovered in the field in June, 1914; development proceeded rapidly and production rose to a maximum in 1918. The marketed production has been approximately as follows: Barrels Barrels 1915.................... 94,073.5 1918................... 2,946,774.27 1916................... 1,404,183.97 1919................... 2,000,584.84 1917.................... 2,780,697.51 1920................... 1,485,080.94 About 350 wells, 800 to 1500 ft. (243 to 457 m.) deep, have been drilled to reach the upper oil sands; two companies, the Ohio Oil Co. and the Midwest Refining Co., operate the entire field. The principal producing sands in the field are members of the Frontier Formation, a series of sands and shales occuring in the upper portion of the Colorado Group of the Upper Cretaceous seriee. These Frontier, or "Wall Creek" sands are also productive in the Salt Creek, Big Muddy, and Elk Basin fields and, therefore, are much the most important reservoirs of light oil in Wyoming. At Grass Creek, the sands in the Formation are more numerous than in the other fields and much less uniform in thickness and character. Usually, eight distinct beds are encountered and in some wells twelve sands have been reported. The formation above

Jan 1, 1923

By F. W. Jessen, C. A. Johnson

The effect of treatment with ferrochrome lignosul-fonate on both sodium and calcium bentonites has been examined. In the early stages of treatment it appears that some base exchange of iron and chromium for sodium may occur with the sodium bentonite. Such exchange appears specific for exchange of sodium ions when the calcium ion concentration represents 40-5.5 per cent of the total exchangeable cations, and when additions of lignosulfonate are less than 1 lb per bbl. Adsorption appears entirely physical above 1 lb per bbl treatment level for all concentrations of calcium studied. Gel strength and plastic viscosity of both calcium and sodium bentonite systems were reduced with treatments of ferrochrome lignosulfonate up to 2 Ib per bbl, the greatest reduction occurring within a range of calcium concentration of 40-5.5 per cent of the total exchange capacity of the clay. INTRODUCTION The problem of control of viscosity and gel strength of drilling fluids by the action of thinners or dispersants has been studied by many investigators.1-7 In addition, much work has been done on formation of gel structure in clay suspensions. However, gel formation and structure still are incompletely understood, and the use of the various dispersing chemicals is based, to a large extent, on data almost entirely empirical in nature. In recent years the lignosulfonates have become increasingly important in the treatment and control of drilling fluids. More specifically, ferrochrome lignosulfonate has found rather wide acceptance, particularly in calcium systems.5-7 Lignosulfonates are refined lignin products made from spent sulfite liquor from which the fermentable sugars have been removed.15 The exact structure of lignin is not known; however, it is believed to be a phenolic propane type polymer which may exist as a branched chain or cross linked structure. The molecular weights of lignosulfonates probably range from 300 to 100,000 or more.15 A better understanding of the mechanism of adsorption of dispersants is essential before improvement and development of characteristics of drilling fluids and drilling fluid control is possible. This investigation was undertaken to determine the action of ferrochrome lignosulfonate on sodium and calcium montmOrillonite' LABORATORY INVESTIGATION A Stormer viscosimeter and Fann V-G meter were used to measure viscosity and gel strength. A Zeiss spectrophotometer was used for analysis of Fe and Cr and the flame attachment was employed in the analysis of Na, Ca and Mg. A General Electric X-ray diffraction unit utilizing Copper Ka radiation and a Ni-filter was utilized in the X-ray studies. PROCEDURE Two systems were studied. Predominately sodium clay, obtained from Wyoming, and a predominately calcium clay from Texas were used. These particular samples were chosen because of the extensive work of characterization completed by Mungan. Ionic base exchange capacity determined by flame photometry and total exchange capacity by the Kjehldahl method were obtained experimentally. A 7-per cent suspension of the sodium clay and a 20-per cent suspension of the calcium clay in distilled water were prepared by mixing with a high-speed mixer. The suspensions were allowed to stand for two weeks for complete hydration. Calcium chloride was added to portions of the sodium and calcium cla suspensions to obtain suspensions varying in Ca++ concentration as shown in Table I. A series of treatments was run with 500-ml portions of the original suspensions using a ferrochrome lignosulfonate. Treatment was carried out in the same way with each of the suspensions of varying Ca concentration. Viscosity and gel strength were measured and a filtrate obtained at each treatment level. Ten ml of filtrate were diluted to 50 ml, and aliquot portions of the 50 ml were taken for the Na, Ca, and Mg analysis by the flame photometer. The pH of these filtrates ranged from 7 to 7.3. Standard

Established as a Division September 27, 1949 LeRoy Scharon, Chairman C. M. Cooley, Secretary 29 West 39th Street New York 18, N Y

Jan 1, 1952

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid cobalt and a number of dilute cobalt alloys Was measured in the temperature range 1550" to 1700°C at nitrogen pressures to 1 atm. At 1600°C and 1 atm nitrogen pressure, the solubility in pure cobalt is 0.0047 wt pct [3.8 cu cm (stp) per 100 g Co]. The standard free- energy change for the solution reaction 1/2 N,(g) = gout pct in Co) is iF - 10,000 + 5.24 T cal per g atom N. The alloying elements Cv, Cu, Mo, Nb, Tu, W, and V increase the nitrogen solubility, while Al, Fe, Ni, and Si decrease the nitrogen solubility. THE solubility of nitrogen in cobalt was studied previously by Sieverts, Busch and Dodd,2 and Schenck, Frohberg, and Graf.3 Sieverts investigated the solution below the melting point of cobalt, and Busch and Dodd worked with the liquid metal; however, neither study found any solubility for nitrogen in cobalt. Schenck et al, reported a solubility of 0.005 wt pct N in cobalt at 1600°C. Seagle et al. 4 reported residual nitrogen in cobalt after electron-beam melting, although no reasons were ventured for the presence of this interstitial impurity. This investigation was undertaken to clarify these inconsistencies, and to provide additional data on atomic interactions in dilute metallic solution. EXPERIMENTAL PROCEDURE This study was well-suited to the Sieverts' method, which has not changed significantly since its introduction by Sieverts. 5 The apparatus was of the same design as that described by Humbert and Elliott, 6 with a reaction bulb similar to that reported by Weinstein and Elliott. 7 The buret was not water-jacketed, but the measured gas volumes were corrected for small changes in room temperature. The melt temperature was measured by a disappear ing-filament optical pyrometer sighted through a prism onto the melt surface. Temperature calibration was made based on a measurement of the melting point of pure cobalt taken as 1495°C. The difference between the reciprocal of the observed and the true temperatures was assumed to be a constant, neglecting the changes in emissivity with small additions of alloying elements. The total error in gas-volume measurement caused by accuracy limitations in reading the mercury level in the buret, variation in ambient temperature, and variation in melt temperature was about 0.5 cu cm. This represents approximately 10 pct of the total solubility, and is a larger relative error than in previous studies6-' because of the small nitrogen solubilities encountered in the present investigation. The source and purity of the materials used are listed in Table IA. Recrystallized alumina crucibles were used throughout the investigation. Examination of the crucibles after solidification of the melts showed no reaction or penetration. Alloying of the cobalt melt was accomplished with the dropping technique described by Humbert. 6 The investigation was started using cobalt from African Metals Corp. in shot form, but this material was not of sufficient purity and did not yield consistent solubility results. Sherritt Gordon Mines Ltd. cobalt was then used throughout the investigation. In experiments involving alloying elements which could react with oxygen dissolved in the melt, the cobalt was further refined by annealing at 1400°C in a dry-hydrogen atmosphere. This treatment, described by Woolley and Pehlke, 8 markedly reduced the oxygen content. The oxygen and nitrogen analyses of the cobalt used in this study are presented in Table IB. RESULTS Hot Volume. The hot volume was measured prior to each run and was 50 to 55 cu cm (stp) at 1600°C. It increased linearly with increasing pressure and decreasing melt temperature. Pure Cobalt. Measurements of the solubility of nitrogen in pure cobalt and the temperature coefficient of solubility are summarized in Table 11. At 1600°C and 1 atm nitrogen pressure, the solubility was found

Jan 1, 1967

By J. H. Scaff, H. C. Theurer, E. E. Schumacher

The microwave region of the radio spectrum was effectively utilized in radar designs during the recent war and it has become of increasing interest in the field of communications. Work in this field has led to an important use for silicon—that of the point contact rectifiers†1 in the frequency converter of microwave (radar or radio) receivers—and has stimulated considerable interest in the electrical properties and preparation of silicon and its alloys. Silicon is an electronic semiconductor. Its conductivity at room temperature results principally from the presence of certain impurities. While for metals an increase in impurity content increases the resistivity, for semiconductors such as silicon the opposite occurs and, in general, the addition of impurities lowers the resistivity. Silicon materials may be classified into one of two groups depending upon the manner in which the impurities contribute to electrical properties. These have been termed for convenience p-type or n-type. P-type silicon develops a very large positive thermal emf against metals, has a Hall coefficient of positive sign and a low resistance direction in point contact rectification with the silicon positive with respect to the point. N-type silicon, on the other hand, develops a negative thermal emf against metals, has a Hall coefficient of negative sign and a low resistance direction in rectification with the silicon negative with respect to the point. Impurities which produce n-type silicon are called donors inasmuch as these elements contribute to electrical conductivity by donating electrons to an unfilled energy band in the silicon. On the other hand, elements which produce p-type silicon are known as acceptors as these impurities contribute to the electrical conductivity by accepting electrons from a filled energy band permitting what is known as conductivity by "holes" in which the sign of the carriers appears to be positive. A general treatment of the mechanism of conduction in semiconductors from the viewpoint of modern band theory has been given recently by Pearson,2 by Becker, Green and Pearson,3 and by Torrey and Whitmer.4 In this investigation boron and aluminum have been found to be acceptors, and phosphorus, arsenic, and antimony to be donors in silicon. Data on the effect of boron and phosphorus on the electrical properties, when present singly and in combination, have been acquired. These data are discussed in the present paper. Raw Materials Used and Methods for Adding Seeond Constituents Silicon from two sources was used in this work and these will be referred to as A and B respectively. Silicon A is a material of high purity supplied by the Electro Metallurgical Co. It is prepared by chemical purification of "commercial" silicon obtained from the arc furnace reduction of SiO2. It contains 99.8 pct silicon, minimum, with small amounts of calcium, iron, aluminum, boron, and phosphorus as the principal impurities. This material was extensively employed in these studies as well as in the commercial preparation of rectifier materials. Silicon B is a material of high purity from the du-Pont Co. It is prepared by a pyrolytic reduction of Sicl4 and is free of analytically detectable amounts of boron and phosphorus. Its use permitted study of the effect of boron and phosphorus individually on the properties. This material contains, however, spec-troscopic traees of a number of metals, some of which affect electrical and rectification properties. Typical analyses for the two grades of silicon are given in Table 1. To make controlled additions of boron to the charge it was necessary to employ a low boron content master alloy since the quantity of boron to be added was usually only a few thousandths of one percent. The alloy containing nominally one percent boron was prepared by melting chemically pure boron with silicon A using the melting techniques for 320 g silicon

Jan 1, 1950

By Benjamin C. Craft

A review of development in North Louisiana during 1936 centers around the Rodessa field, in Caddo Parish. Continued extension of the

Jan 1, 1937

By P. V. Brough, K. B. Gillaspie

DECISION to build a mill at the Bayard property was made in May 1942. Western-Knapp Engineering Co., of San Francisco, assisted by engineers of U. S. Smelting, handled the design and construction. Much of the milling equipment was moved from the Company's mill at Goldroad, Ariz. Wartime restrictions necessitated wood construction and paper sheathing except for structures adjacent to the Bullfrog shaft. Construction started in September 1942 and milling in March 1943. Bayard ores are processed in a single-ection mill. About half of the ore treated during the past year was hoisted through the Bullfrog shaft and the rest was trucked from other shafts. Coarse storage includes four bins, two of 120 tons each for Bullfrog ores and two of 85 to 120 tons each, served by a truck ramp. The low capacity figure refers to

Jan 1, 1948

By A. C. Stevenson

IN OUTLINING the various steps taken and the exigences met during the time of unwatering and rebuilding the burnt top equipment at the Hecla mine, the major portion of the detail is omitted and a general description of the experience only is given. All the electrical power lines were out of commission, as were the mine feeder cables. The first effort, there- fore, was to restore electrical connections. The Washington Water Power Co. immediately put a crew to work restoring the power line, it being necessary to rebuild about 4000 ft. of 66,000 volt transmission and about 2000 ft. of 2200 volt feeder. This work was rushed and power was again available at the mine sub- station about 26 hours after the fire. During the same time temporary lighting lines were strung and transformer equipment obtained, so that when electrical connection was resumed the lights were turned on and the dump well lighted that night.

Jan 1, 1924

By C. Y. Cheng

THE purpose of this note is to show that the dislocation mechanism controlling the creep of Fe-4 pet Si alloy1 may equally account for the behavior of a-Fe2 over the same temperature range. A recent study of the creep behavior of a-Fe has been made by Ishida et al.2 Their results were in agreement with the mechanism of nonconservative motion of jogged screw dislocations over the entire range of temperatures investigated, from 480° to 1045°K. However, the observed creep rate was much higher than that which could be accounted for by the above model unless the authors assumed that pipe diffusion became significant below 775°K. More recently, Cheng et al.1 inves-gated the creep of Fe-4 pet Si alloy over about the same temperature range and found that the results could be correlated fairly well with a dislocation climb mechanism as represented by Eq. [l]. Proceeding as shown previously,1 if creep is controlled by a single climb mechanism, at intermediate stresses, the shear creep rate, y, can be represented by where n and K are material constants {K is independent of the temperature but dependent on the structure, that is, K decreases during the primary stage and reaches a steady-state value over the secondary stage of creep), t is the applied shear stress, G is the shear modulus, gc is the free energy of activation for creep (usually equal to that for self-diffusion, gd), and RT has the usual meaning. By solving for y, the apparent activation energy for creep, Q which can be determined experimentally, is given by where hc is the enthalpy of activation for creep which usually is also equal to that for self-diffusion, h^. By using Eq. [2], the data in Fig. 2 of Ref. 2 can be re-plotted as shown in Fig. 1. By comparing the two figures, it is seen that the slight increase in the apparent activation for creep over Region II, as noted in Fig. 2 of Ref. 2, is due to the influence of temperature on the shear modulus rather than of the stress on the

Jan 1, 1969

By L. Adler

Analysis of a mine roof can be based on fixed-end beam behavior. The author here analyzes the effects of zero restraint at deflecting beam supports. Formulae are given for determining permissible support deflections. Analysis of a mine roof in a bedded deposit usually follows the assumption that the behavior of the roof is analogous to a beam with both ends fixed. Yet it is recognized that the end restraint itself varies with the thickness of cover, so that at shallow depth the restraint is minimum, and at great depth, maximum.' Consequently, an analysis on the basis of fixed ends or full restraint represents only one extreme in the possible range of conditions. Since the actual amount of restraint is difficult to ascertain, a more rational approach is to consider the two extreme cases of end restraint. Such situations regarding uncertainty of the restraining effects of supports are not uncommon in structural analysis, and are handled in a like manner.' Since previous studies9)4 have dealt with full restraint, this paper will analyze the effects of zero restraint at deflecting beam supports. In such a case a mine roof with several intermediate supports becomes analogous to a uniformly loaded continuous beam on simple supports, as shown in Fig. 1A. Such a structure is statically indeterminate to a degree equal to the number of intermediate supports, n. Therefore, with the three equilibrium equations, n additional equations are needed. A number of methods exist to analyze this problem, but The Theorem of Three Moments is Simplest. The continuous beam is divided at each support into a sequence of simply supported single span beams, with the unknown end moments, as appears in Fig. 1B. Continuity requires that the common ends of adjacent beams have the same slope (Fig. 1C). eiB= B(i+l)~= ei(i+l)and MiB= Mti+I)A= Mi(i+i). [1I A Glossary of all terms is given in Table I. Furthermore, if we first consider that the supports do not deflect, the slope at a support is the sum of the slopes due to each of the individual loads shown in Fig. 2, yielding:

Jan 1, 1961

By Paul Berggreen

LIST OF PUBLICATIONS In the Bibliography titles of publications are replaced by corresponding symbols in this list. American A-1. Transactions of the American Institute of Mining Engineers, New York. A-2. Journal of the New York Microscopical Society, New York. A-3. Journal of the Franklin Institute, Philadelphia, Pa. A-4. The Metallographist, Boston, Mass. A-5. The Electrochemical and Metallurgical Industry, New York. A-6. Bulletin of the American Institute of Mining Engineers, New York. A-7. The Iron Trade Review, Cleveland, Ohio. A-8. The Journal of Physical Chemistry, Ithaca, N. Y. A-9. The Physical Review, New York. A-10. Van Nostrand's Electric Engineering Magazine, New York. English E-1. Proceedings of the Institution of Mechanical Engineers, London. E-2. Journal of the Iron and Steel Institute, London. E3. Proceedings of the Institution of Civil Engineers, London. E-4. Journal of the Chemical Society of London, London. E-5. Philosophical Magazine, London. E-6. Proceedings of the Royal Society of Edinburgh, Edinburgh., E7. Carnegie Scholarship Memoirs, London. E-8. Proceedings of the Royal Society of London, London. E-9. Chemical News, London. E-10. Philosophical Transactions of the Royal Society of London,, London. E-11. Transactions of the North-East Coast Institution of Engineers and Shipbuilders, Newcastle-on-Tyne E-12. Iron, London. E-13. Nature, London. E14. English Mechanic and World of Science, London.

Jan 6, 1914

By Frederick Prime

In this second supplementary list no titles to which an * is pre fixed hare been seen by tlie compiler; and he will be most thankful to have any omiesisne or inaccuracies in the list sent to hiin to be ptiblisi~cd as a third supplement in the next volume of the actiotra. The author is indebted to Prof. J. J. Stevenson, of New Tork, Prof. P. R. Uhlcr and John 'CV. M. Lee, Esq., of Balti more, and Lloyd P. Smith, Esq., of Philadelphia, for valuable assistance. office, allkntorn iron compaxy, 30 South Third Street, Philadelphia, September 5th, 1881. Alabama. Geologiml Survcy of Alabama. report of Progress for 1879 and 1880, by Eugene A. Smith, State Geologist. Montgomery, 1881. 8vo., 158 pp., and 2 maps. California. Omit Report of Hon. T. Butler Ring, iu sopplemeut I. For Trask's Geology and Illdustrial honrecp, etc., in Supplenlvut I., read Tyson's, etc. Fremont's Menloir on Upper Califijrnia, is also published as XXXth Congress, lat Session. Senate Ms. Doc., No 148, and has a map. For Randall's Report in Supplement I, rend Report of the Special Committee in favor of a Geological Snrvey, subrn-itted by Mr. Randall, April 24th, 1861. n.d., 1851. 8cWo., 19 yp. XXXIst Congress, 1st Session, Sen. Ex. Doc., No. 47, Part 2 [Part 1 is Tyson's Report.) RejW of the Secretary of War in further compliance with the Resolution of the Senate?, calling for Colbies of

Jan 1, 1881

"Located on Missouri River 16 miles N. E. from Helena, 67 miles from Butte and 18 miles below Canyon Ferry. River drainage area 16,000 sq. miles.DAM: Built in 1907; rebuilt of concrete in 1911. Maximum height 129.3 ft., length over all 720 ft.; elevation of crest 3621; elevation of bridge 3640; normal head 60'; normal tail water elevation 3568.5.SPILLWAY: Length over all 491 ft.; clear opening in 24 sections; 445' flashboards, 14 high to elevation 3635, which is 3.5' above Canyon Ferry normal tail . water elevation.PENSTOCKS: 5 of steel, 12 ft. diam., about 75 ft. long from canal to main turbines, and 3 40-inch diam. from canal to exciters.WHEELS: 5 main pairs, horizontal, center discharge, 48-inch bronze turbines, 225 rev., 4,000 h-p. at 60 ft. head, made by S. Morgan Smith Co., direct coupled to generators, and--3 single, horizontal, 25-inch units, direct coupled to exciters.GENERATORS: 5 W. E. & M. Co. water wheel type, revolving field, 2,800 k-w., 2,400 v., 225 r. p. m., 3 phase, 60 cycle alternators.OPERATION: The plant has a larger water storage than Canyon Ferry and can also use stored water from Canyon Ferry storage. Separate transmission lines 13 miles long connect to lines from Canyon Ferry to Butte, and the Plant operates in parallel with the Canyon Ferry plant."

Jan 1, 1913

By G. Barbery

Since the original paper, two methods have been introduced to compute the parameters of the three parameter size distribution equation: [ ] Both of them are based on graphical means, which are time-consuming and of little statistical significance. A program has been developed, using the Gauss-Newton method to compute by nonlinear regression analysis the parameters of the equation. Although the method is quite general in curve-fitting applications, it does not appear to be used in the field of size analysis, and a brief description is given. As applied here, the Gauss-Newton method involves the minimization of the least squares: [ ] where n is the number of sieves used. The second member of Eq. 2 can be approximated by a multiple Taylor's series expansion of first order about a starting value [ ] The minimization of Q (r,s,Xo) means: [ ] Putting Eq. 3 into Eq. 2 and differentiating, we obtain a system of equations which can be represented in matrix symbolism (box) The system can be solved for: [ ] and the operations repeated with new values: [ ] The starting values for r and s are taken as 1, for Xo, a value higher than the maximum sieve opening value. Applied to the data given by Herbst 5,6 for batch grinding of 7 X 9 mesh dolomite, the parameters given in Table 1 were obtained. The discussion of the significance of the residual sum of squares is a difficult subject in multiple nonlinear

Jan 1, 1972

By William B. Plank

NEVER before have so many men chosen the mineral technology field for their college training. In the college year 1936-'37, 7190 such students were enrolled in the 53 schools of the United States. My last study of the mineral technology schools of the United States and Canada was made for the year -1934-'35, and the current study, as the previous one was made for the A.I.M.E. under the auspices of the Division of Mineral Industry Education. Altogether, four studies of enrollment have been made. The first three were for successive college years beginning with 1932-'33. This present one covers a two-year period, for the purpose of these studies may he served satisfactorily if they are made biannually. The data on the schools were collected in the same way as for former studies, 'namely, by questionnaire, dated in this case Nov. 18, 1936. The figures reported are therefore comparable with those of former cars.

Jan 1, 1937