Search Documents

By Mark Malamphy

MOST igneous rocks, and particularly those of the basic type, con-tain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anom-alies observed during the course of geophysical surveys by the mag-netic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemis-phere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This conven-tion facilitates comparison with anomalies in the north.

Jan 1, 1936

Lawrence Addicks, Perth Amboy, N. J. (communication to the Secretary*): The excellent series of photo-micrographs given in this paper shows clearly the relation between micro-structure and cuprous oxide in refined copper. The authors suggest that this method of examillation might be substituted for the " button " method now used to control the refining of cop

Jan 1, 1904

By John C. F. Randolph

(Read at the Amenia Meeting, October, 1877.) Tits establishment being now in full working order, it has seemed of considerable professional interest to collect together, in a concise form, the various points as to its plan, method of dressing, and equipment. The data contained in this paper have been largely drawn from the able paper of E. Kutscher, constructing engineer. of the works, contained in the Zeitschrift fur Berg-Hütten-und Salinenuesen im Preussischen Staate, 1873, supplemented by some personal memoranda made while the works were under construction and by memoranda on the works appearing in various German technical papers from their completion up to date. This is probably the largest dressing works in the world devoted to the beneficiation of argentiferous lead ores, and it is doubtful if any establishment for the concentration of mineral of any description can compare with it in size. As showing the final practice adopted in an old and very conservative mining region, in which the concentration of ores has been a matter of constant practice and experiment for a very long period, these works are of peculiar interest. The fact that the Clausthal ores strongly resemble a very large and abundant class of ores found in the United States has always attracted the attention of American mining engineers and mine owners to the methods employed in dressing and smelting them. The study of their methods of concentration of ores has, however, always been full of difficulty,

Jan 1, 1878

For the year ending February, 1920 PRESIDENT HORACE V. WINCHELL MINNEAPOLIS, MINN. PAST PRESIDENTS PHILIP N. MOORE ST. Louis,. Mo. SIDNEY J. JENNINGS NEW YORK, N. Y. FIRST VICE-PRESIDENT A. R. LEDOUX NEW YORK, N. Y. TREASURER GEORGE D. BARRON NEW YORK, N. Y. SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 9, 1919

AMONG the features that make Inspiration of outstanding A interest, particularly to the engineer, is the fact that at various times it has used, as a major method of production, three more or less distinct methods of mining and three distinct methods of treating its ores. The following chronology is of interest : Major Mining Methods: 1915-194 7 Underground block-caving, exclusively 1948-1952 Underground block-caving and opencut mining 1953-1954 Underground block-caving, opencut mining, and "glory-hole caved-block transfer" mining 1955 on Opencut mining and "glory-hole caved-block transfer" mining. Major Ore Treatment Methods: 1915-1925 Flotation concentration exclusively 1926-1930 Flotation concentration and ferric sulphate leaching 1931-1955 Ferric sulphate leaching (the so-called "Dual Process" was used for eleven months in 1937 when demand for copper was phenomenal; and the "leach-float" process was used for 24 months in 1942-44 as an expedient to help meet war demands for copper). 1956 on "Dual Process" combining a sulphuric acid leach followed by fine grinding and flotation of the residue from the leaching vats.

Jan 1, 1957

By Eric L. Christiansen

A dynamic simulation model for the iron blast furnace has been developed which predicts flow rates, compositions, and temperatures of the top gas, slag, and hot metal exit streams as a function of time from specification of the time-dependent tuyere inputs and raw material charges. As a matter of convenience, a previously developed steady- state model is employed to fix furnace-dependent parameters. It also provides initial conditions for the internal states of the furnace for subsequent dynamic solution of the simultaneous differential equations which describe the local rates of chemical reaction, heat transfer, and mass transfer in the stack, bosh, combustion zone, and hearth of the furnace. The dynamic model was tested by a demonstration of its ability to relax to steady-state representations of the time-averaged data from two separate industrial blast furnaces and of its ability to follow eight days of time-dependent operating data for one of them. Simulated responses to step changes in tuyere input and burden variables have been shown to be of the correct magnitude and duration. Although complex functions of many variables, a proper description of these responses is needed for the development of optimization and control strategies . The model correctly predicts the non-minimum-phase type dynamic response observed in real furnaces in which the output variables proceed through local minima or maxima, often including inverse responses (i.e., opposite signs from their final steady-state values ) .

Jan 1, 1984

For the year ending February, 1919 PRESIDENT SIDNEY J. JENNINGS NEW YORK, N. Y. PAST PRESIDENTS L. D. RICKETTS NEW YORK, N. Y. PHILIP N. MOORE ST. Louis, MO. FIRST VICE-PRESIDENT C. W. GOODALE BUTTE, MONT. TREASURER GEORGE C. STONE, NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER W. RAYMOND, NEW YORK, N. Y. SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 4, 1918

By H. L. Riley, B. W. Gandrud

As far as the present writers know, this system of flotation has not been used elsewhere in this country, but in the last couple of years it has been introduced, with minor variations, at one plant in England and one in Wales. The system has been described and discussed in a number of publications. The following is quoted from an abstract of the latest of these," a paper presented at an International Conference on Industrial Combustion in 1952. On the basis of experience to date with the commercial plants, it is believed that the kerosene-flotation process incorporates all the necessary elements to make it greatly superior to anything else now available for treating of fines in wet processes of coal preparation. Additional study and investigation are still needed, however, to determine if certain phases of the process can be improved to such an extent as to make it generally satisfactory and acceptable to the industry. Further improvements will be needed with respect to the capacities of the flotation cells and the reagent consumption.

Nov 1, 1955

By John C. F. Randolph

This establishment being now in full working order, it has seemed of considerable professional interest to collect together, in a concise form, the various points as to its plan, method of dressing, and equipment. The data contained in this paper have been largely drawn from the able paper of E. Kutscher, constrnoting engineer of the works, contained in the Zeitschrift fur Berg-HÜtten-und Salinenwesen im Preussischen Staate, 1873, supplemented by some personal memoranda made while the works were under construction and by memoranda on the works appearing in various German technical papers from their completion up to date. This is probably the largest dressing works in the world devoted to the beneficiation of argentiferous lead ores, and it is doubtful if any establishment for the concentration of mineral of any description can compare with it in size. As showing the final practice adopted in an old and very conservative mining region, in which the concentration of ores has been a matter of constant practice and experiment for a very long period, these works are of peculiar interest. The fact that the Clausthal ores strongly resemble a very large and abundant class of ores found in the United States has always attracted the attention of American mining engineers and mine owners to the methods employed in dressing and smelting them. The study of their methods of concentration of ores has, however, always been full of difficulty,

Jan 1, 1879

By F. T. Davis

The annual review of mineral dressing was the subject of considerable discussion at the MBD meeting in New York last February. Because the amount of material now being published is so imposing, it was generally agreed that reviewers should try only to cite the items of importance. In order to conserve even more space, it was agreed to omit bibliographies. In reading these reviews, and those of the past two or three years, one is impressed by the advances in materials handling, the enlargement and the advances in automation of unit process equipment. Although there has been development of a variety of new concentration principles in flotation, magnetic separation, et al., the design of these principles into new plants has not been widespread. The probable reason is that the plants being built today are so large and costly that few are able to face the risk of any significant degree of experimentation. There are exceptions to this; for example, some of the chemical processes, but these are usually because there was no conventional process available. This situation should change in time as the ores amenable to our conventional methods become depleted.

Jan 2, 1967

By Zay Jeffries

It has been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat arid cooling, either rapidly or slowly with nearly pure iron, but slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point,, which is near 700" C. The present paper will not consider these old and well known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, In 1886, reports that both working steel and heat treatment of steel in the blue-heat range arc highly injurious. Recently, however, some metallurgists believe that the straiglltening of warped steel forgings at a blue heat produces a beneficial effect on the metal2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes in Iron and Steel below the Thermal Critical Range, which has the following personnel: K. R. -Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F. C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood. This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 1, 1922

By Zay Jeffries

It has been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat arid cooling, either rapidly or slowly with nearly pure iron, but slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point,, which is near 700" C. The present paper will not consider these old and well known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, In 1886, reports that both working steel and heat treatment of steel in the blue-heat range arc highly injurious. Recently, however, some metallurgists believe that the straiglltening of warped steel forgings at a blue heat produces a beneficial effect on the metal2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes in Iron and Steel below the Thermal Critical Range, which has the following personnel: K. R. -Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F. C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood. This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 1, 1922

By L. O. Millard

Stockpiles in the minerals industries serve a wide variety of purposes. Usually they are for surge between stages of processing, for a dependable plant feed in anticipation of delays, or to provide for single or double shift mining in conjunction with round-the-clock milling. Often surge piles are necessary to insure a uniform feed to continuous process equipment where the material is received as an intermittent or variable flow. Extensive use is made of stockpiling for the primary purpose of blending. The significant fact about all stockpiling of bulk materials is that storing and reclaiming are two separate and distinct operations and they may present widely different problems in the selection of methods and tools.

Jan 10, 1959

By L. R. Plitt, M. K. Kim

The collecting properties of the fatty acid type collectors for barite were studied using zeta potential measurements, infrared spectroscopy, and Hallimond tube flotation tests. Based upon the experimental results, an adsorption model has been formulated which emphasizes the predominant role of the hydrocarbon chain in collector adsorption.

Jan 1, 1975

By A. F. Witt, A. M. Gaudin, A. K. Biswas

Finite contact angles in the rutile-water-organic liquid system are traceable to contamination or are due to addition of a surface-active agent. Finite contact angles are invariably accompanied by hysteresis.1-7 Besides surfactant concentration and pH, the nature of the organic liquid is found to be a factor influencing the magnitude of contact angle hysteresis. In a recent paper the authors have reviewed principles and applications of measurement methods for contact angles and their hysteresis.22 In this paper, these methods are applied to a system consisting of rutile, an organic liquid (benzene, decane, or dode-cane) and water. Surfactant (dodecylamine hydro-chloride) was used at various concentrations and various pH values. MATERIALS A synthetic rutile crystal supplied by the Linde Co. was used. It is a cylinder 1/2 in. diam, with faces cut perpendicular to the c-axis. The crystal is stated to be alumina-free and to be 99.9% pure. Rutile is a high surface energy solid, its calculated average field strength being 2.7 x 105 e.s.u.,9 its dielectric constant10 is 114. The zero point of charge of rutile was measured11 and found to be at pH 6.0. The atomic distances and bond angles of the tetragonal crystal of rutile have been precisely determined.l2 The organic liquids were specially purified. Reagent grade benzene was repeatedly shaken with concentrated sulfuric acid to remove thiophene, then neutralized with sodium hydroxide solution, rinsed with distilled water, dried overnight over anhydrous calcium chloride and filtered. The refractive index of this chemically purified benzene was 1.4977 (at 25°C) - very close to that of pure benzene (n25 1.4979).13 Both n-decane and n-dodecane were washed with aqueous sodium hydroxide, concentrated sulfuric acid (repeatedly, until the acid layer was colorless) and again with alkali, to free the organic hydrocarbon from fatty acids and unsaturated hydrocarbons. The organic phases were subsequently washed with distilled water and dried over anhydrous sodium sulfate. The filtered hydrocarbons were then distilled under vacuum (9-10 mm pressure). Decane, thus purified, showed traces of unsaturated and of carboxylic compounds. On gas chromatographic analysis the purified n-dodecane showed the presence of two impurities. However, the relative retention times of these components did not change substantially when measured on a polar or a nonpolar column. This indicates that the compounds were probably in the same polarity class, i.e. the components were nonpolar like dodecane. Conductivity water has always been one of the liquids. Conductivity of the water used was 10-6 ohm-' cm". Dodecyl ammonium chloride was prepared from pure amine (supplied by Armour and Co., Chicago), by Li in the MIT Mineral Engineering Laboratory.14 The critical micelle concentration at 25°C is known, 0.0138 mol per liter15 or 3.06 gpl. All our experiments have been done at concentrations lower than the critical micelle concentration. The glass vessels, glass drop holder and the rutile crystal were all cleaned with hot chromic acid followed by distilled water, concentrated hydrochloric acid, and again distilled water, and conductivity water. During the experiments, a nitrogen atmosphere was maintained. For this purpose, commercially purified nitrogen was further purified by passing it over hot copper wire at 450°C, then through columns of acidic chromous chloride solution, concentrated alkali solution and distilled water. APPARATUS AND METHODS Hysteresis was produced by the "captive drop" or constant volume drop method as well as by the "expanding-contracting drop" or variable volume drop method. The image of the drop while it is expanding, contracting or moving is projected on a screen and photographed. The developed film is projected through an enlarger and the contact angles measured with a protractor.

Jan 1, 1964

By Calvin Bjorne, John Keeley

In the face of a highly competitive iron ore market, the Cleveland-Cliffs Iron Co. developed a process now being practiced at the company's Republic mine in Michigan's Upper Peninsula. By this process, a specular hematite crude ore is being beneficiated to produce a high iron-low silica concentrate with a suitable size structure for the production of a high quality pellet. This process involves crushing, primary grinding and primary flotation, followed by regrinding, heating and refloating the primary flotation concentrate. The ores consist predominantly of specular hematite with relatively minor amounts of magnetite and martite in a recrystallized chert gangue. A wide variety of silicates have been identified, particularly in association with intrusives of various description. The more abundant of these are sericite, talc, grunerite and chlorite with some carbonates, primarily calcite.

Jan 6, 1964

By E. W. Davis

The mixing of fine ores with fuel and burning under induced draft is called sintering in iron-ore practice and either sintering or roasting in copper and lead metallurgy. The first development of sintering was the Huntington-Heberlein process, in which fine sulfide ores mixed with fuel were charged into a pot and burned under the action of an upcast current of air introduced at the bottom of the pot. Modern development has resulted in two types of machine; the continuous Dwight-Lloyd machine, which consists of heat-resisting grates and a moving beltlike type of hearth constructed of metal, in which air is drawn downward through the bed, and the stationary Greenawalt batch process, which operates in the same manner as the Dwight-Lloyd except that the hearth is stationary. The recent rapid increase in the use of sintering has been the result of two great advances in metallurgical process—flotation and the treatment of flue dust. The Dwight-Lloyd machine is used in many plants for agglomerating flotation concentrates and at the same time reducing the sulfur content to furnace requirements and it has become standard practice to treat iron blast-furnace flue dust by either the Greenawalt or Dwight-Lloyd machine, so that it can be recharged into the furnace. The mining of low-grade magnetite iron deposits and their beneficiat-ing by grinding and magnetic separation resulted in a fine concentrate extremely detrimental to blast-furnace practice. These concentrates are sintered and made into ideal material for blast-furnace use. Incidentally, coke savings of about 400 lb. per ton of pig are reported. Sintering at Evergreen Plant The application to limonitic iron ores is the most recent development of the sintering process. The first plant in the Lake Superior region was erected by the Minnesota Sintering Co., a subsidiary of the Evergreen Mining Co., at Ironton, Minn., in 1924. This plant was designed to treat Cuyuna Range iron and manganiferous ores containing low silica, high moisture and a structure objectionable because of a large proportion

Jan 1, 1930

By H. B. Goodrich

Anthony I?. Lucas died suddenly at his home in Washington, D. C., on Sept. 2, 1921. Captain Lucas, as he was known to us, was born in Dalmatia, Austria, in 1855, of Montenegrin ancestry. He was graduated as an engineer at the Polytechnic of Grate and served in the Austrian Navy as second lieutenant. In 1879, he obtained leave of absence and visited an uncle in the United States. After an extension of this leave of absence, in order to undertake an engineering engagement in the lumber district of Michigan, where he resided, he decided to become an American citizen. He was naturalized in May, 1885. His name was Luchich, but as his uncle had adopted the name of Lucas, which was more easily pronounced by Americans, from his entrance to this country, he used this Anglo-Saxon form. Without knowing this fact, upon first meeting him a person was sometimes surprised to note the rather Germanic pronunciation of the Captain. Although he subsequently revisited Austria with Mrs. Lucas, he made his permanent home at Washington, D. C. His son served with distinction in the A. E. F. during the World War. His activities in this country as a mining engineer were at first in Colorado and later in salt mining at Petit Anse and Belle Isle, La. During his salt investigations, his attention was directed toward the possibility of oil in the Gulf Coast region and in January, 1901, his well, the "Lucas Gusher," on Spindle Top, Tex., started a new era in the oil business and his reputation as discoverer made him famous throughout the world. Captain Lucas became a member of the A. I. M. E. in 1895. During 1914, 1915, 1918, and 1919, he was chairman of the Petroleum and Gas Committee of the Institute and was at all times prominent in Institute affairs. As to the personality of Captain Lucas, the lasting impression is of a courteous hospitable gentleman, genial, affable, obliging, and helpful with his advice br assistance to any colleague. He was sincere, honest, firm against all obstacles, backing his judgment with his own hard work along any course which he had determined to be correct. His value in the engineering world lies mainly in the petroleum industry. In the oil business all wild-catters are pioneers that deserve credit and gratitude upon their success. There are, however, names that particularly stand out in our history. Drake conquered such obstacles as ridicule, lack of finances, and started the oil business. In 1901, Captain Lucas had the conviction that Spindle Top, a dome rising about 12 ft. above the coastal prairie south of Beaumont, Tex., contained commercial oil. He was scoffed at by practical oil men of the East. Noted geologists

Jan 1, 1921

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors' laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris's review,' the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert's analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969

By C. E. Sims

The carbon-oxygen reaction without doubt is the basic reaction in steelmaking. It is important on several counts: In the first place, carbon is the element that distinguishes steel from iron. It is the principal element controlling properties, and its control is of prime concern. Although the principal objective of the carbon-oxygen reaction is to oxidize excess carbon, the accompanying boil should not be underrated. The mechanical agitation, stirring, and mixing resulting from the boil are so useful in the distribution of heat and in promoting uniformity of composition in the bath that, were it not a natural accompaniment of the carbon-oxygen reaction, it is probable that something would have to be invented to replace it. The open-hearth operation, for example, with the bath heated from above by radiation, would be impracticable without the carbon boil. The electric-arc furnace is somewhat less dependent on it, but every melter knows how much easier it is to gain temperature with minimum damage to refractories during the boil than with a dead bath The motor action of the induced current of the induction furnace makes the carbon boil unnecessary but even there a severe oxidation has been found useful in giving greater freedom from porosity in certain steels. The quantitative aspects of the carbon-oxygen reaction have been given considerable attention by a large number of investigators, and the principles of physical chemistry have played an important part in these studies. Physical chemistry is the science of the mechanics and mathematics of chemical reactions. It is possible to study the mechanisms of reactions in a qualitative manner writhout reference to mathematics and thus obtain valuable concepts as to the manner in which the wheels go around. When it is desired to express quantitative relations in these reactions, however, resort to mathematics is not only convenient but necessary. Mathematics may also be regarded as the shorthand language of physical chemistry. A basic relation whose description requires numerous words may be expressed very simply by a mathematical formula or equation. A good example of this is the equilibrium constant for a chemical reaction. Expressed verbally, it is: When a chemical reaction has reached a condition of equilibrium, the Product of the concentration of the reacting substances on one side of the equation, divided by the product of the concentration of the reacting substances on the other side, gives a quotient that is a constant at constant temperature For the carbon-oxygen reaction C + O ^ CO this is expressed simply as % C X % O -%co where K (from the German Konstant) is the equilibrium constant for the reaction. Although mathematics is such a necessary and useful tool, it is also a potential pitfall. Mathematics in itself is an abstract science, which is not inhibited by consideration of mechanisms or materials.

Jan 1, 1948