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By Eugene McAuliffe

NO physical impairment can be more serious than the partial or complete loss of sight. With reasonably good eyesight, a person is equipped to care for life and I limb, provided a rational measure of t caution is manifested. When the sight of one eye is lost or badly impaired, one-half of this God-given asset is gone, and extreme care must be taken to prevent the tragedy of total darkness that closes out the beauty of sky, field and mountain, the faces of relatives and friends, and either removes entirely or in part one's capacity to produce and earn. During 1933, The Union Pacific Coal Co., operating ten coal mines in Wyoming, decided to undertake a visual survey of all of its mine operating officials and employees. Although the cost of workmen's compensation paid because of eye injuries was material, the management was more deeply concerned with the social loss and the suffering resulting from the many eye injuries. As every element of coal production cost must be scrutinized, accurate data on all accidents, with the workmen's compensation paid therefor, are carried forward monthly. The number of accidents to eyesight and the resultant compensation paid are shown in Table 1 for nine calendar years:

Jan 1, 1934

By W. C. McClain

In the design of underground excavations, rock mechanics considerations are nearly always based on an elastic behavior of rock. Most rocks do exhibit a certain amount of elasticity, and the application of principles and concepts of elasticity to rock mechanics problems has been largely responsible for progress in the field over the past 10 or 15 years. No doubt the theory of elasticity will remain the most useful analytical tool available for both the design of underground openings and the interpretation of phenomenological data.

Jan 1, 1967

By Irwin Roman, Thomas C. Serman

It has been known for many years that when a wire is moved in a magnetic field, an electromotive force is developed which is proportional to the rate at which the wire is moved in a direction perpendicular to the magnetic intensity and to the magnetic intensity itself. If the ends of the wire are connected to a current indicator, the current behaves exactly as though the source of electromotive force were a galvanic cell. If a wire is wound circularly and rotated uniformly around a diameter not parallel to the intensity, the current flowing through the wire will be alternating of sinusoidal shape. If, instead of a single loop, there are several turns wound in a short helix, the electromotive force developed will be approximately proportional to the number of turns, the area of the helix and to the speed of rotation. The maximum electromotive force will be developed when the axis of rotation is perpendicular to the field; if this is not so, only the component of the intensity that is perpendicular to the axis of rotation is effective. This is the principle of the usual earth inductor. With a few turns of wire and comparatively slow rotation, it is possible to produce a considerable deflection of a galvanometer. If two similar coils are rotated together at two different points for which the magnetic field intensities perpendicular to the axes of rotation are different, the electromotive forces developed will each depend on its corresponding intensity and be a measure of that intensity. If the intensities are sufficiently different so that the electromotive forces may be compared, the two intensities may be compared. This is the principle

Jan 1, 1934

By L. C. Brown, E. B. Hawbolt

The formation of grain boundary precipitates has been studied in Ag-5.64 wt pcl Al alloys at 688°C. Large-grain specinzerzs were used and the boundary misorientation measured by X-ray diffraction. At low-angle grain boundrrries Primary sideplates form. u)hile abore a 17-deg misorientation lenticular precipitates predominate. Growth of the lenticular precipitates was studied on individual grain boundaries using a statistical technique. The thickening and lengthening rates appeared to be independent of &apos;pain boundary misorientation, indicating that grain boundary diffusion was not significant in this system. The precipitates grew urith constant shape, with both the length and thickness increasing parabolically with time. The parabolic lengthening rates were unexpected since previous theory and experimerztal results had indicated linear growth. By approximating the shape of the precipitate to that of an oblate spheroid grouling with constant shape an equivalent diffusion coefficienl was calculated. The zlalue obtained was in good agreement with nleasurements obtained fron, diffusiorz couples. IF a single-phase alloy is heated or cooled to a temperature such that the phase becomes supersaturated, there is a tendency for a second phase to precipitate from it in order to remove the supersaturation. Precipitation takes place initially on grain boundaries due to preferred heterogeneous nucleation, but subsequently Widmans kitten plates may form in the grain interiors if the grain size and supersaturation are sufficient. The type of grain boundary precipitate formed depends on the nature of the boundary. Aaronson1 and clark2 have shown that grain boundary misorientation can be characterized by the simple parameter R, where and X, Y, and Z represent the minimum rotations about three orthogonal axes required to bring the two lattices forming the grain boundary into coincidence. The maximum value for R is 60 deg. In using this parameter the orientation of the grain boundary itself is, of course, neglected. However it was found in both Fe-si3 and A1-Ag2 that the precipitate shape depended only on the parameter R. Clark found that the vast majority of precipitates formed were allo-triomorphs— lens-shaped precipitates that grew along the grain boundaries. At low-angle boundaries, however, (R < 15 deg) Widmanstatten sideplates nucleated at the grain boundaries and grew into the adjacent grains. It has been reported that the rate of growth of grain boundary precipitates is controlled by diffusion within the supersaturated phase.&apos; The theories which have been developed for growth rates have assumed the diffusion coefficient constant over the composition range of the supersaturated phase. This is a fairly good approximation if the composition range involved is not large. Thickening rates have been calculated using the theory developed by Zener4 and by Frank5 for the growth of planar precipitates. A parabolic growth law

Jan 1, 1968

By H. D. Strain

Potash is a generic term used to describe a number of compounds containing the element potassium (K), which is one of the three major plant nutrients. Potash content of these compounds is commonly expressed as percentage potassium oxide (K20), and the market value of the products is usually dependent on contained K20. Most of the potash produced (approximately 95%) is used in agriculture as fertilizer. Potash products today are shipped by producing countries all over the world to meet the need for increased food production. WORLD POTASH RESERVES Apparent world potash reserves are shown in Table 15.2B.1 and total some 96 billion mt of recoverable potassium oxide. The Canadian reserves account for approximately one-half the known world reserves. The reserves shown represent the potassium oxide content of a variety of potash-bearing ores. The major ore is sylvinite (a mechanical mixture of KC1 and NaCl) from which KC1 or sylvite is recovered (63.2% K20 equivalent). Other ores, such as langbeinite (potassium, magnesium sulfate-22.7% K20) and carnallite (potassuim magnesuim chloride-17.0% K20) are also mined in various parts of the world, mainly for the potassium content. Theoretically, potassium is available in almost unlimited qualities from brines and saline waters. To date, the cost of recovery from salt brines has been greater than the costs by mining operations, but new technology could make brines and seawater an increasingly important source. POTASH PRODUCTION Potash production dates back to the 1860s in Germany, which was the only recorded producing country until 1912. By 1912 Germany was producing approximately 1 million tpy of K2O equivalent. Production began in France in 1913 and in the United States in 1915. World potash production and consumption are shown in Table 15.2B.2 for the years 1950-51 through 1967-68. In 1967 and 1968 the major potash-pro¬ducing countries in order of importance were those listed in Table 15.2B.3. By 1972 Canadian production had outstripped U.S. production. WORLD CONSUMPTION World consumption of potash for the years 1950-51 through 1967-68 is shown in Table 15.2B.2. Table 15.2B.4 shows total world consumption of potassium materials in 1967-68 by country. More than 70% of the world&apos;s potash is

Jan 1, 1976

By John Hall

THE Fremont test for measuring the energy consumed in breaking a notched bar of steel is not so well known in this country as it deserves to be. The test specimen used in this test is about 3/8 by 1/4 by about 1 1/4 in., notched with a hack saw on the lower side to cause the piece to break at a fixed point. A weight of 10 kg. falling 4 m., and provided with a knife or chisel which strikes the specimen, breaks the test piece by impact. The residual force in the falling weight after it has broken the specimen is recorded by a suitable device, and the difference between the total energy and the residual energy of the weight (in kilogrammeters) is the force consumed in breaking the specimen. An experience of several years with the Fremont testing machine has shown its great value in readily detecting brittleness not revealed by tensile testing or slow bending testing. I this paper it is proposed to discuss (1) the supersensitiveness of the test as applied to cast steel and (2) its value in revealing the effect of heat treatment under certain conditions. .

Jan 7, 1913

By Walter L. Maxson, Fred C. Bond

THIS paper is a continuation of two earlier papers, l, 2 and presents new data on the grindability of various ores and other materials-the results of several years of intermittent research work on the nature of grinding and interpretation of test results. It is divided into five parts: 1. The tabulated results of several hundred grindability tests on a wide variety of ores. 2. A method of correcting screen analyses and calculating from them the surface and other properties. 3. A description of a new method of measuring the "surface energy" of an ore by pendulum impact tests. 4. Test results. 5. A general discussion of the test results and their application to grinding problems. 1. GRINDABILITY OF VARIOUS ORES This part is a continuation of the paper listed as reference No. 1. The method of testing is described in detail in that paper. The sample to be tested is crushed to all through 6 mesh in rolls set at x6-in. opening in closed circuit with a screen. Of this sample 700 C.C. is ground dry in a laboratory ball mill under constant conditions of mill speed and ball charge in closed circuit with a screen of the desired size at 250 per cent circulating load. The mill is cylindrical, 12 by 12 in., and rotates at 70 r.p.m. It contains a charge of 285 iron balls weighing 20,125 grams and ranging from 1 ½ to ¾ in. in diameter. Each test is continued for a sufficient number of periods to establish equilibrium at 250 per cent circulating load, or until the composition of the circulating load is constant for successive periods. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the results are expressed as the net production in grams of screen undersize per revolution of the mill. This is designated as the

Jan 1, 1938

By Robert J. White

Strong&apos;s equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong&apos; published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong&apos;s paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By J. W. Koger, R. E. Hurnrnel

QUENCHED, bcc p brass, P1, transforms to a mar-tensitic phase, when it is cooled below room temperature.&apos; This transformation can be followed using resistance measurements since the resistivity of the martensitic phase is considerably larger than that of the parent phase, Fig. 1.&apos; phillips3 first reported that, when Cu-Zn alloys containing between 37.0 and 39.0 wt pct Zn were quenched from the 0 region to room temperature, variable amounts of a phase could be observed depending on the mode of quenching. If the quench occurs very rapidly, the a phase forms by a "massive transformation". The resultant phase has the same composition as the high-temperature P phase from which it was formed. If the quench is less severe, the alloy is retained largely in the p form; however, some a is formed by precipitation. In this case, a contains more copper than the high-temperature 0 phase from which it has formed. The a phase most probably does not undergo a transformation in the temperature range where p transforms to low-temperature martensite. This can be deduced from the Eesistivity-temperature relation which is linear in this temperature range, Fig. 2. The stable a phase which is present along with R. E. HUMMEL is Assistant Professor, Department of Metallurgical and Materials Engineering, University of Florida, Gainesville, Fla. J. W. KOGER, Junior Member AIME, formerly with University of Florida, is now with Oak Ridge National Laboratory, Oak Ridge, Tenn. Manuscript submitted December 13, 1967. IMD.

Jan 1, 1969

By Robert M. Dreyer

During the past two decades, synthetic abrasives have taken over successively greater percentages of the high-grade abrasive market, so that now, with the exception of natural diamonds (discussed in section 3.15.4C of this chapter), the importance of natural high-grade abrasives is negligible. The predominance of synthetic abrasives is indicated in Table 15.4A.1. This shows that the 1968 value of domestically produced synthetic abrasives (excluding synthetic diamonds) was over $80 million, whereas the value of garnet, the largest domestically produced, natural high-grade abrasive, was less -than $2 million. The major synthetic abrasives (other than synthetic diamonds) are: alumina, silicon carbide, boron carbide, tungsten carbide, and metallic oxides, including various iron oxides. A major advantage of synthetic abrasives is that the size and shape of grain can be closely controlled during manufacture. Although Table 15.4A.1 gives the average price of synthetic abrasives, such averages are of somewhat limited value. This is because the actual price varies within wide limits, depending on composition, hardness, size, and shape of grain. In 1968 the approximate total consumption of abrasives in the United States was valued at about $200 million, of which about two-fifths was in the form of synthetic abrasives (other than diamonds), one-third in synthetic diamonds, and the remainder in natural diamonds. Natural abrasive products, such as silica sand, tripoli, and pumice, are important in the low-cost abrasive field. Of the low-cost abrasives, silica sand continues to be the most important, with domestic production of about 300,000 tons at a value of $1.8 million (see Table 15.4A.1). In general, the lower the sales price of the abrasive product, the more limited is the market which can be served from a given production center. Each abrasive has applications for which it is especially useful, but there is a continual struggle among abrasive suppliers to induce substitution of one product for another. Such substitution can be stimulated by changes in method of preparation affecting hardness, shape, and size of grain.

Jan 1, 1976

John M. Cairns, in an interesting letter dated June. 19, 1918, tells us of his experiences in Italy. He says, "It may interest you to know I came out to Italy after being on the Afghan frontier of Indian Baluchistan, in August last year, and for some time was posted at Turin as Railway Transport officer. At that time Turin was in the toils of the riots which were the forerunners and preliminaries which led up to the great Italian retreat (Capretto). Since then I have been all over Italy from (deleted by the censor) in Transportation intelligence, and now have just been transferred to the Directorate of Requisitions and Hirings, which now permits great opportunities of going nearly all over Italy (deleted by the censor). My address is L. of C. Branch, D. R. & H., A. P. 0. L/1, I. E. F.

Jan 9, 1918

By Takeyasu Ito, Mayumi Someno, Kazuhiro Goto

SINCE the pioneering work by Kiukkola and Wagner,1 many experiments have been reported on solid electrochemistry at elevated temperatures. However, the studies have been confined to experiments under isothermal conditions. One may conceive many situations under nonisothermal conditions. With two different temperatures T1, and T2 at the two electrodes, the electromotive force, E of a Galvanic cell will be expressed by the following equation under a steady state heat transfer in solid electrolytes of zirconia-lime and thoria-lime. E = ^ $ l&-dGO2+a(T2-Ti) [1] where tO2- is the transference number of oxygen ions in the electrolyte, Go, is the chemical potential of oxygen, and a is the coefficient of the thermoelec-tromotive force due to the temperature difference. The objective of the present study was to evaluate the coefficient of the thermoelectromotive force for zirconia-lime and thoria-lime under isobaric condition. The physical meaning of this coefficient is out of the scope of the present communication. The experimental cell assembly is schematically shown in Fig. 1. The zirconia-lime electrolyte tube and thoria-lime electrolyte tube were 8.0 mm OD and 5.0 ID, from commercial sources with chemical analyses of 94.8 wt pct ZrO2, 3.85 pct CaO, 0.83 pct SiO2, 0.25 pct TiO2, and 0.05 pct Fe2O3; and 95.0 pct ThO2, 4.0 pct CaO and rare earth metal oxides, respectively. The specific gravity was 5.5 g per cu cm for zirconia-lime and 9.8 g per cu cm for thoria-lime. Original powder size before shaping and sintering the tube was several microns for both electrolytes. The distance separating the two electrodes was 4.0 or 5.0 cm. Platinum wire of 0.5 mm diam was used for the electrodes. The temperature gradient was controlled by heating one electrode with a small heating coil of nichrome wire. The temperatures at the two electrodes were measured with two calibrated Pt-13 pct Rh:Pt thermocouples, directly contacting the two platinum electrodes. The atmosphere was either air or pure oxygen. The partial pressure of oxygen in air was considered equal at the vicinities of the two electrodes, with negligibly small thermal segregation in the gas phase. The difference of the chemical potential of oxygen was controlled only by the temperature difference at the two electrodes and not by the oxygen pressure difference. The temperature ranges were 600" to 1200°C for zirconia-lime and 850" to 1200°C for thoria-lime electrolytes. Fig. 2 shows the relation of the measured electromotive force and the difference of the oxygen chemical potential at the two electrodes for zirconia-lime and thoria-lime electrolytes. The electromotive forces in the figure were measured by a *0.05 mv potentiometer. The chemical potential difference was calculated by the following equations.&apos;

Jan 1, 1970

By R. M. Caves

High-purity dense tungsten coating is obtained by means of a modified de Boer-van Arkel iodide process using tungsten bromides. The all-glass reaction system is pumped, baked, and sealed (pinched-off) at about 10-7 mm Hg pressure. The bromides then formed in situ are decomposed, depositing tungsten on heated tungsten surfaces. Heating of the specimen is done inductively in a novel arrangement that avoids electrodes of glass-to-metal seals. The tungsten, deposited at specimen temperatures from 2000° to 2800°F and bulb (halide) temperatures of 225" to 725°F, was adherent and uniform, and ranged in thickness to 1/8-in. REFRACTORY metals are of interest at NASA for use in hypersonic aircraft, in rocket engines, and in other thrust devices where very high temperatures are encountered. Tungsten, with a melting point about 6100° F, is potentially very useful for some of these applications. Considerable research on tungsten and its alloys is currently being conducted at the NASA Lewis Research Center. In this tungsten research program, there is need for a method of depositing high-purity, nonporous tungsten coatirlgs. Metallurgical bonding of the coating both to itself and to the substrate is required. In addition, it is necessary to be able to deposit thin, uniform coatings on substrates of a variety of shapes and sizes for laboratory test purposes. A survey of the methods previously used for depositing tungsten coatings indicated that none would likely meet these requirements for high purity, good uniformity, and high density except thermal decomposition of the halides. The method for coating that was selected for investigation was the thermal decomposition of tungsten bromide. This is a variation of the van Arkel and de Boer iodide process established years ago and recently reviewed.1,2 This process is applicable to the transition metals in general. More recently, the application and techniques were extended with chlorine3 and fluorine,4 and included the coating of tungsten. This is believed to be the first report on the use of the bromide for tungsten coating. Bromine was chosen over the other halogens because it promised a lower temperature for tungsten

Jan 1, 1962

By R. S. Handy

DOES hand-sorting of mill feed pay? The fact that the practice is so general would seem to indicate that there must be good reasons for following it; yet, to my mind, the advantage in many cases is doubtful enough to invite a thorough discussion of the subject, in an effort to determine under what conditions hand-sorting does pay. A typical sorting plant in the Coeur d&apos;Alene district handles about 800 tons of mine-run ore per day. The material is run over a grizzly with about 4-in. opening; the oversize is crushed to about 4-in. size and joins the undersize, and the whole product is washed and screened on trommels with about 1 ½ -in. openings. The oversize from these trommels is spread on a belt and the waste and first-class ore are sorted out by hand, the residue being further crushed, and passes, together with the trommel undersize, into the mill feed bins. About 50 tons of shipping ore and 150 tons of waste are sorted out per day, leaving about 600 tons of mill feed. To sort out this material requires 20 ore sorters and five bosses and repairmen. The normal cost of hand-sorting is about 16 c. per ton of run-of-mine ore, or 65 c. per ton of material sorted out. I believe that straight crushing and milling of the run-of-mine ore, in this case, is not only cheaper, but is metallurgically moree canonical and efficient than hand-sorting followed by milling of the residue. At one of the Bunker Hill rock-houses, 1250 tons of run-of-mine ore are reduced to pass 30-mm., or about 1 ¼ -in. opening in six hours, requiring five men. The equipment and the power consumed are not greatly different from that required in a sorting plant of the same capacity, and the normal cost of thus preparing the feed for milling is under 3 c. per ton of mine product. The relative cheapness of this method as against hand-sorting is thus clearly established, the saving being about 13 c. per ton. If there is any virtue in hand-sorting, then, it must lie in the metallurgical results achieved.

Jan 4, 1918

By George Wolff

To THE average person, the purport of the items and figures on the balance sheet of a mining company are hazy and the real financial condition of the company is cloaked in obscurity. It is also likely that the satisfaction of the stockholder in his investment, as well as the determination of the prospective investor, rests more on the reputation of the company, his confidence in the management, the stated earnings per share and the dividends paid, than on a comprehension of the information contained in the balance sheet. The balance sheet of any company at best can only closely approximate the true financial condition as of a given date. Any item of asset, except cash, can probably be altered if another&apos;s viewpoint is applied. It is difficult and expensive to drill and explore an orebody to determine the entire tonnage of ore therein. Those inherent difficulties render it practically impossible to prepare an absolutely correct balance sheet of a mining company. It is possible, however, to present the facts of a mining company more intelligently and comprehensively than is usually done. With this in mind, a balance sheet of an imaginary mining company is submitted, with supporting schedules. The same fundamental principles hold true whether we consider a large or a small company. Less complexity is involved in dealing with the affairs of a smaller company. Therefore, for this purpose, the assumed company operates but two mines and a smelting plant. It has been deemed advisable to introduce the features of the operation of a mine acquired prior to March 1, 1913 and one after that date. The presentation therefore is concerned in one mine with the appraisement as of March 1, 1913 and in the other with the appraisement by reason of discovery. A consequential factor pertains to dividends paid from depletion reserves and therefore free of surtax to the stockholders. While supporting schedules, when necessary, give details of certain items on the balance sheet, it seems desirable to give further explanations with respect to some of them. This seems to be important because some mining companies do not treat the items as indicated on the statements submitted.

Jan 1, 1928

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By JAMES QATLEY

THE atmosphere, which plays such an important part in the manufacture of iron and steel, is the most variable element involved in its several processes; and particularly is this true of the blast-furnace process, which consumes air in large quantities. At no time since the blast-furnace became an important and widely used apparatus-even when it was operated in the most crude manner-have the variations in composition of the raw materials used been as frequent and as great as the variations in humility of the atmosphere. Important, improvements have been made in the blast furnace and its accessories, such as the hot-blast stoves, the increase in size and change in the shape of the furnace, more efficient blowing engines, the increased protection given to the bosh walls, and the careful preparation of&apos; the raw material, all of which have exerted a pronounced influence on the furnace-operations from a metallurgical standpoint. But during the past eight years little advance has been made in this direction; the fuel-consumption has not diminished, nor has there been any material increase in production. Within that period, however, there has been witnessed the greatest development in appliances for the economical handling of material. So complete has been the work in this direction, that, except in isolated cases, in this country at least., a further extension does not hold out much promise of a satisfactory return on the investment required. It seemed that, with the exception of the gas-engine, we had about reached the limit, for like a strong wall, the atmosphere, with its humility as variable to-clay as when first blown into a primitive blast-furnace, appeared to stand as a Barrier to

Jan 1, 1905

By Jack F. B. Silman

Proving up any large, open pit ore deposit by normal exploration drilling under the best of conditions is a noteworthy accomplishment. But, when adverse conditions preclude standard drilling methods, and the same end result is achieved by a relatively new and little known type of drilling, special comment is in order. Three major problems confronted exploration drilling at the Questa molybdenite mine of the Molybdenum Corporation of America-sampling, terrain and time. Surface and underground longhole drilling provided the needed solutions, thus making the greatest single contribution to an exploration and development program that was successful in proving a major, open pit molybdenum deposit.

Jan 5, 1965

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. TEMPERATURES AND UNDERGROUND WATERS Surface Temperatures.-The average surface dry-bulb temperature at Superior is 72.4°; wet-bulb, 57.4°; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the down-cast shafts; however, the variation between winter and summer causes a difference of only 2° to 3° in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.-Rock temperatures on the deeper levels of tile mine are as follows: LEVEL DEGREES LEVEL DEGREES 2000 109 3200 127 2250 112.5 3400 130 2550 116 3600 134 2800 120 3800 137 3000 124 4000 140 There appears to be no difference in rock temperature for any particu-lar horizon of the various formations or in the vein. Water encountered is always the same temperature as the rock from which it flows, and for this reason it is thought that the water is heated by the rock; not the rock by the water. The country rock apparently has been heated by the various intrusions, perhaps the vein itself, and has not yet had time to cool off. The geothermal gradient (Fig. 2) as indicated by the rock tem-peratures given above is 1 1/2 ° per 100 feet.

Jan 1, 1938

By Frank W. Osterwald

Violent, spontaneous destruction of coal faces and ribs during, what are commonly called, bumps endangers and at times destroys life and property in mines of the Book Cliffs coalfield, Carbon County, Utah. Because these mines supply much of the coking coal for the West Coast steel industries, mining is necessary, although costs are high and operating conditions are very difficult at times. As operations continue, mining will go to greater depths, and the difficulties will increase. Whether or not mining can be continued successfully depends in part on whether or not incidence of bumps can be controlled successfully. For this reason, the U.S. Geological Survey, at the request of and in cooperation with the U.S. Bureau of Mines, undertook a study of the Sunnyside No. 1 mine to determine what geologic factors were related to the incidence of bumps. This report presents the preliminary results of that study and indicates that some observable geologic features in the mine may be related directly or indirectly to bumps, and that other features may be used to infer stress distribution around workings that will aid in design of roof support measures. Coal is mined in the Sunnyside No. 1 mine from depths as great as 2500 ft by room-and-pillar methods. The surface topography is rugged with many steep cliffs and deep canyons, hence the load on the coal varies greatly within short distances. Much of the Sunnyside coal is under high stress, and while being mined, it shatters continuously&apos; and falls from the face. Continuous shattering (bumping) makes mining easy, but if the shattering is interrupted, greater stress is built up and violent bumps may result when the coal is mined.

Jan 4, 1962