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By A. C. Heath, E. H. Dix

The importance of aluminum-silicon alloys in thc light alloy field is now generally recognized. Where silicon was once considered detrimental to the properties of aluminum, useful alloys now contain as much as 13 per cent. Furthermore, silicon is present as an impurity in aluminum of even the purest grades. Iron is another important impurity in aluminum and likc silicon is found in small quantities in the purest aluminum available today. The manner of occurrence of iron and silicon in commercially pure aluminum and many of its alloys exerts a very pronounced influence upon their properties. The effect of large quantities of iron in aluminum-silicon alloys is so detrimental that it has been found necessary to limit the allowable maximum percentage to as low a figure as is consistent with quantity production and satisfactory physical properties. The intimate relation existing between iron and silicon in aluminurn and alurninum alloys makes necessary a more complete knowledge of this ternary system. This paper is divided into two principal parts, dealing respectively with aluminum-silicon solubility equilibria and the constitution of aluminum-iron-silicon alloys. Part I.—Aluminum-silicon Alloys The early work on this system was largely confined to determining the general form of thc diagram and in this respect the results are in good agreement. Briefly, alulninunl and silicon form a simple eutectifcrous series without compounds. Until recently the solid solubility of silicon in aluminum had not been accurately determined. Ipraenkell (1908) stated that aluminum will retain 0.5 per cent. silicon in solid solu-t'ion. Rosenhain, Archbutt and Hanson2 gave the maximum solubility as about 1.50 per cent. and added that "this solubility docs not appear

By M. G. Corson

UNTIL recently, the characteristics of cast copper have seldom been studied and such study as has been made has been inadequate. The prevailing idea seems to be that since pure copper is infrequently used in the cast state, there is no reason for trying to establish precise data regarding the properties of the metal in that condition. On the other hand, wrought copper either in the shape of sheets or wire rarely fails in service, except as a result of the action of reducing gases at the annealing temperatures, so there is little incentive to study the properties of the cast shapes -cakes, bars, ingots and billets-for the sake of tracing the causes of failures of the wrought metal to the cast stock. However, about a decade ago, wirebars of American origin often cracked badly while being hot-rolled in mills in Germany. This led to four investigations: by E. Seidl and E. Schiebold,1 by P. Siebe,2 by 0. Bauer and G. Sachs,3 and by G. Welter.4 These authors came to the conclusion that failures in hot-rolling were due essentially to the presence of a' wide zone of columnar crystals between the thin layer of fine crystals near the surfaces of the bars and the large but more nearly: equiaxed grains of the central core. This macrostructural defect was explained in turn by the probable upward deviation in the temperature of the metal while it was being poured into the molds of the casting machine. More recently, cast shapes of copper were investigated by N. P. Allen5 and by C. Blazey.6 Allen examined vertically cast wirebars and horizontally cast wedge cakes of electrolytic tough-pitch copper, but only for the distribution of densities; i.e., porosity. Blazey was interested mainly in the mechanism of the variations in electrical conductivity due to cold-work and anneal, but gave introductively an account of the composition and average densities of the tough-pitch horizontally cast wirebars used. As far as the present writer can tell, no investigation was undertaken for the sake of presenting a picture of the distribution of mechanical characteristics in the wirebars of copper, tough-pitch or otherwise.

Jan 1, 1938

By Cyril Smith

SEVERAL investigators, mainly concerned with the mechanical proper-ties of the alloys, have studied the so-called aluminum bronzes after various quenching and reheating treatments. Of these works, perhaps the most complete is that of Bouldoires,1 who studied changes of length, electrical conductivity, thermoelectric force, hardness and micro-structure oh tempering quenched alloys containing 5 to 20 per cent of aluminum, although the work of Carpenter and Edwards,2 Curry,3 Greenwood,4 Braesco,5 Matsuda;6,7 Grard8 and others has added much to our knowledge of the changes occurring during tempering. The so-called acicular ß decomposes on tempering at temperatures between 350° C. and the eutectoid, giving rise to a Widmanstätten structure of a needles in a matrix of d or fine a + d, associated with an increase in hardness and almost complete loss of ductility. Matsuda, studied the' eutectoid transformation by means of dilatation and electrical "conductivity measurements during cooling at different rates. He found that on cooling at the rate of 10° C. per minute there was a decrease in electrical resistance and in length instead of the usual increase which occurred with slow rates of cooling. On tempering the rapidly cooled samples, the increase commenced at about 400° C. and at 520° C. the resistance and length had reached the equilibrium values. These peculiarities he accounted for as being due to a transitional phase ß' being formed, ß having an electrical resistance and volume less than either ß or a + d.

Jan 1, 1933

By H. J. Rose, J. J. S. Sebastian

When coal is stored under ordinary conditions, progressive changes take place in its chemical and physical properties. These changes are largely caused by the reaction of atmospheric oxygen with the coal substance. Although this "oxidation" or "weathering" occurs slowly in the case of high-rank coals, it is nevertheless a matter of considerable importance, since even a small amount of oxidation may affect the value of coal for carbonization purposes. Coal storage is a necessity at all carbonizing plants. In normal times there are about 5,000,000 tons in storage at by-product coke ovens and gas retorts in the United States, as compared with an annual throughput of about 75,000,000 tons. In other words, the average coal reserve at such plants is slightly less than one month's supply. However, owing to the cost of storage and recovery, coal is usually left in stockpile for as long a time as the management thinks advisable. Storage for six to eight months is common practice and is, in fact, a necessity at certain plants which obtain their coal by water routes that are closed during winter months. Modern by-product coke ovens operate continuously, and they are not cooled down from the time that they arc put into operation until they are shut down for rebuilding—perhaps 20 years later. This continuous operation is imposed by silica-brick construction and high operating temperatures. It is therefore obvious that coke plants must at all times maintain an adequate supply of stored coal, in order to prevent a failure in supply from any cause whatever. Thus when strikes or other emergencies threaten, abnormally large coal stocks are accumulated and held at coke and gas plants. Many of these plants have been forced, at some time or other, to use coal that has been stored for several years. Such coal may fail to coke at all, or it may produce a dirty appearing, weak coke of reduced value. The yields of salable by-products may also be distinctly lowered. However, it must not be assumed that slight oxidation or heat effects are always injurious. Certain high-volatile coals produce a stronger, blockier

Jan 1, 1930

By Charles L. Thomas

A novel, highly sensitive, and reproducible nzetlzod for the determination of hydrogen in solid materials is presented. The procedure requires equilibration of the specimen with hydrogen gas, rapid quenching, and hot vacuum extraction of the dissolved gas with subse-quent quantitative analysis by mass spectroscopy. Good linearity is obtained for the Arrl~enius plots of the investigated metals. The advantages in the use of this method over that of Sieverts aye discussed. The solubility data for copper are in reasonable agveewzent with a considerable number of other inuestigations, wllile those fov silver are considerably lower than previously reported. The first known solubility data for gold are presented. Solubility equations and heats of MUCH of the data which are available on the solubility of hydrogen in various metals and alloys have been obtained by the classical Sieverts method.' The method involves the measurement of a decrease in pressure of a gas in a calibrated system, and the calculated contraction in volume is attributed to the solubility of the gas in the metal sample. The procedure requires several corrections, such as the solubility of the gas in the container walls and the diffusion of the gas through these walls, as noted by Steacie and .Johnson2 and others. In addition, errors may be incurred due to reactions between metal surface impurities, such as oxides, and the saturating gas. The precise calibration of the measuring system where large thermal gradients exist can present additional difficulties. Also, accurate volumetric measurements of small quantities of gas are difficult. Many of the objections to the Sieverts method were overcome on solid materials by Ransley and ~eufeld,~ who first saturated the metal with hydrogen and performed a subsequent extraction and measurement of the gas by chemical means. Eichenauer and pebler4 and Eichenauer, Kiinzig, and pebler5 measured the diffusion coefficient and solubility by following the degasification of a sample as a function of a rate of increase in pressure in a previously evacuated system. Here again, however, the procedure involves many of the corrections of the Sie-verts method. The present investigation deals with the solubility of hydrogen in solid copper, silver, and gold by a technique which eliminates many of the aforementioned corrections and possible errors. This procedure requires equilibration of the specimen with gas, rapid quenching, and hot vacuum extraction of the dissolved gas with subsequent quantitative analysis by mass spectroscopy. EXPERIMENTAL Two completely separate systems were employed to accomplish first, the equilibrium saturation of the sample and second, the extraction of the dissolved gas. Saturation Apparatus. The saturation apparatus, illustrated in Fig. l, consisted of a vertically mounted quartz tube with a three-way valve for vacuum or hydrogen near the top and an outlet near the bottom leading to a butyl phthalate seal. The bottom end of the tube was terminated with a joint accommodating an O-ring sealed "Asco Stirring Gland" (The Emil Greiner Co.). This gland facilitated movement of the thermocouple without introduction of air into the system. The upper portion of the tube (above the furnace) was water-jacketed. A Welsh 1405-B mechanical pump provided the necessary system evacu-

Jan 1, 1968

By J. A. Herbst, K. Rajamani, Y. C. Lo

In spite of potential theoretical and economic advantages of large-diameter ball mills, many manufacturers elect not to build them owing to what is perceived as an excessively large design risk. This is because traditional predictions for mill scaleup to large diameters are not always accurate. Alternative methods of analysis and scale-up are required. Recent studies have shown that detailed population balance models which account for important grinding subprocesses (grinding kinetics, material transport, and classification) are capable of predicting the performance of small- and intermediate-diameter mills (up to 4.3 m, or 14 ft) from small-scale batch tests. These same models are used in the current study to predict the performance of a "borderline "large ball mill (4.7 x 5.5 m, or 15 x 18 ft) at Asarco's Sacaton operation, a ball mill (5 x 5.8 m, or 16.4 x 19 ft) at Kennecott's Chino operation, and one of the world's largest ball mills (5.5 x 6.4 m, or 18 x 21 ft) at Cities Service Pinto Valley operation. Model parameters required for scale-up have been estimated in a 380-mm-diam (15-in.-diam) batch mill. Predictions are compared with the results of detailed plant sampling in the three plants. For the Sacaton and Chino operations, the error of the predictions was found to be less than 2.5%, while the corresponding error for the Pinto Valley operation was less than 2.7%. It is concluded that proper representation of the major subprocesses of grinding in the model equations is the key to achieving accurate scale-up. Of special importance is the need to account for the size distribution of the grinding media and the influence of the size distribution environment in the mill on grinding kinetics.

Jan 1, 1986

By J. E. Hanlon, J. D. Wolf

The relaxation peaks observed in plastically deformed materials at low temperatures have been reviewed by sack1 and Niblett and wilks. 2 In particular, the dislocation-relaxation in columbium has received considerable study.3-6 The present work deals with the lower-temperature dislocation-relaxation peak (referred to by Chambers and Schultz as the a peak) in columbium and Cb-5 pct Zr. The columbium and Cb-5 pct Zr specimens were machined to 3/8-in.-diam by 7-in.-long rods from bars hot-extruded at 1200°C. The internal friction and resonant frequency of the samples were measured in torsion at kilocycle frequencies at a maximum strain amplitude of -10-6. The interstitial content of both materials was approximately 70 ppm N and 200 ppm 0. The dislocation-re laxation peaks were measured in the hot-extruded state and after successive anneals. Fig. 1 is a compilation of the data. The resonant frequencies for the columbium and Cb-5 pct Zr samples were, respectively, 5.5 and 6.5 kc. Other workers have noted that the dislocation-relaxation peaks in columbium are not characteristic of a single relaxation time. As can be seen in Fig. 1, the zirconium addition further broadens the spectrum of relaxation times. The magnitude of the modulus defect as computed from resonant-frequency data also reflects this extension. The occurrence of the low-temperature a peak at a position 20°K higher in Cb-5 pct Zr as compared to pure columbium, in the hot-swaged state, suggests a decrease in the average dislocation mobility for the alloy. The authors do not feel that these data are sufficient to permit an interpretation in terms of any detailed models.

Jan 1, 1967

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Ti-Mn alloys were studied in order to determine the factors affecting the mechanical properties of &stabilized titanium alloys. The principal compositional factors have been found to be solid-solution strengthening, the martensitic transformation, and instability of the P phase. Structural factors, such as grain size and shape, were found to have more influence on ductility and toughness than on strength. THE alloys of titanium with the &stabilizing elements offer the chief hope for developing useful heat treatments. Conversely, the heat-treatment response possible with the p-stabilizing elements causes difficulties such as weld embrittlement and thermal instability during service at elevated temperature. Therefore, it is of considerable technical importance to understand the factors that govern the heat-treatment responses in these alloys, so as to be able to soften the alloys if they are embrittled by an adventitious heat treatment, to render them stable in service, or to harden them while maintaining adequate ductility and toughness. The Ti-Mn system is a good example with which to demonstrate the factors that govern strength and heat-treatment response in. a P-stabilized system. The region of the a-j3 transformation, after the work of Maykuth, Ogden, and Jaffee,' is shown in Fig. 1. The a solubilities are low. This means that, in the two-phase a-p field, partition of manganese between the two phases occurs practically only to the P phase. The solid-solution effects are therefore chiefly the result of solution in the ,8 phase. The eutectoid occurs at 20 pct Mn and 550°C, and proceeds very sluggishly. It can be ignored in heat treatments in hypo-eutectoid alloys, except for long-time storage at low temperatures below the eutectoid temperature. Even here, there is some question that diffusion proceeds far enough to involve eutectoid decomposition. Three compositional factors bear on the mechanical properties and structure of titanium a-P alloys. These are: 1—solid-solution strengthening, 2—mar-tensite transformation, and 3—P instability. Combined with the purely structural factors of grain size and shape, these govern the properties of the alloys. Perhaps the most important factor is solid-solution strengthening. The facts that manganese dissolves in a titanium to a maximum of only 0.5 pct and most of the manganese partitions to the p phase dominate the structure and properties of the a-/3 alloys. Because of the overwhelming preference of manganese for the ,3 phase, the P phase is harder and the a phase is softer. The relative amounts of both phases may be modified by heat treatment in the a-P field as application of the lever rule in the two-phase field clearly shows. A critical temperature in the Ti-Mn diagram is 800°C. This is the P transus temperature of the 6.4 pct Mn alloy, which has the lowest manganese content which will form all retained-P phase on quenching to room temperature. Any quench performed from below 800°C will produce a structure consisting of only a, a plus retained P, or retained p, for alloys of the compositions used in this work. For alloys containing less than 6.4 pct Mn, any quench from above 800°C will always result in structures

Jan 1, 1955

Occasionally it is interesting, and sometimes useful, to review the past for early references to our industry, and to learn of the trials and travail passed through before it arrived where it now is - and the results of such a review follow. Some time ago one of our modern playwrights and poets, Arthur Guiterman, turned to coal, with the following result : Afar in the Carboniferous time I grew in Paleozoical slime, A lepidodendron with boughs on my stem And lepidostrobusea grew out of them. My roots in the mud of the ages I spread And up to the heavens I vaunted my head, I throve in the heat of tropical sun, And now I am coal at two dollars a ton.

Jan 1, 1935

By F. Clerf

BLAST-FURNACE practice in France is determined more or less by the character of the ores used. Some French ores are siliceous and others are calcareous, therefore by proper burdening a self-fluxing mix can be used. This is not always clone, as, for instance, at the Caen furnaces of the Société Métallurgique de Normandie, where the Soumont ore of Normandy is used, which is a carbonate. This ore is crushed and calcined at the mines, yielding a product that is porous and well sized for blast-furnace consumption. The lines of the Caen furnaces are given in Fig. 1. Originally these furnaces had 16 tuyeres; six are plucked and these tuyeres are set in the lower part of the bosh. Operating data on these furnaces are given in Table 1.

Jan 1, 1937

By C. S. Matthews, M. Prats, R. I. Jewett, J. D. Baker

By mathematical analysis it was found that injectivity history of a uniform five-spot pattern can be calculated by rather simple formulas. These calculated injectivities were found to agree rather well with injec-tivities measured in a potentiometric analog. With this as a basis, a simple method was finally developed which allows prediction not only of rate of injection but also of rate and kind of production at the production well, for a uniform five-spot. Using this method formulas for the eflective injectivity and production behavior of a waterflooded reservoir having a wide range in permeability can be calculated by considering that the reservoir consists of several layers, each having a uniform but different permeability. Rather good agreement is shown by a comparison of the observed production history of a field in the Illinois basin and that calculated by the methods just described. INTRODUCTION The importance of being able to predict the injection rates for a water flood is well known, for upon injection rate depends the life of the flood, the size of pumping and treating facilities, and the rate of oil recovery. One method of determining rates of injection is through a pilot flood. However, it appears that even if a pilot flood is resorted to, a theoretical method for calculating injection rate will be valuable in extending field results to times after inter- ference and to locations of other five-spots. It is also important to be able to predict the production history of a flood. Such prediction must generally be done by theoretical means, since in general a small pilot flood will not furnish much quantitative information in this regard because of the distortion after oil-bank interference. Methods for predicting the behavior of five-spot water floods have been proposed by Yuster and Cal-houn' and by Hurst.? However, these methods do not consider the effect of the mobility of the different fluids in the reservoir. Other investigators3,4,5,6 have determined the effect of the water-to-oil mobility ratio on the production history by means of different experimental techniques. Most of the published work applies to homogeneous sand bodies, does not provide information for determining the injection requirements of a flood, and seldom considers the rate of build-up of the oil bank as it fills up the partially depleted reservoir.* The present work was undertaken because of the lack of predictive method which takes into account mobility ratio and the rate of buildup of oil bank resulting from the void space in a partially depleted reservoir. As water is injected into the reservoir, which contains oil, water, and gas in macroscopically homogeneous saturation, it forms several banks ahead of the injection well. In each bank or region there is assumed to be only one mobile phase—water in the water bank, oil in the oil bank and gas in the gas region. The saturation in each region and a plan view of the banks are shown in Figs. 1 and 4, respectively. FACTORS AFFECTING INJECTION AND PRODUCTION RATES Results in this report are determined as functions of the three parameters, F, M, and M, , and of a fourth parameter, r,/L** which relates the size of the well to the flood spacing. The parameter F is the displacement factor defined by Hurst in Ref. 2. It determines the rate of build-up of oil bank as it fills up the partially depleted reservoir. When gravity effects are neglected, the four parameters just given are sufficient to describe the waterflood behavior for horizontal and homogeneous reservoirs having incompressible liquids. Definition of InjectIvity The dinlensionless injectivity (or injection rate) used in this report is defined by

By C. E. Lawall

WHEN this study was started very little information was available, regarding the physical characteristics of West Virginia coals. This was particularly true of friability and of crushing strengths of the coals. Some work had been done on specific gravity studies but the available information applied to only a few coals. In practically all coal-classification systems thus far proposed, the predominating factors of classifications are largely based on the chemical characteristics of the coal. Recently some investigators have pointed out that a classification based on chemical and physical properties of coal might serve to place coals in their proper group better than classification systems based on chemical properties alone. One of the aims of this study was to obtain some data on the physical properties of coal which might help to properly classify West Virginia coals.

Jan 1, 1932

By F. W. Schroeder

AT the annual meeting of the Institute 2 years ago, a paper,1 " Requirements of Refractories for Open Hearths," was presented by F. W. Davis and G. A. Bole of the U. S. Bureau of Mines. In a brief foreword, D. A. Lyon stated that the paper was not to report the results obtained but rather to present an outline to serve as a basis for discussion. The essential parts of an open-hearth furnace were described and the conditions under which they operate. Some constructive discussion followed the reading of the paper. One of the first fellowship investigations undertaken by the Bureau of Mines in 1924 under the cooperative agreement with Carnegie Institute of Technology, through the Metallurgical Advisory Board, was to determine service conditions of open-hearth refractories. The present paper gives the results of this work which was done in the Pittsburgh district and was in charge of the authors. Material contributions in the form of data were contributed by E. N. Bauer, J. W. Campbell, G. H. Pfeiffer and A. Grodner, Carnegie Institute of Technology research fellows. The study covered 18 mos.

Jan 7, 1926

By William Fink

NICKEL is used as an alloying element in several complex commercial aluminum alloys, among which are found some very interesting proper-ties, such as relatively high strength at elevated temperatures, relatively low coefficient of expansion, the absence of permanent growth, ability to take a good polish, and a bright, pleasing as-cast surface. For that reason the aluminum-nickel system was included in the list of binary aluminum systems that are being studied as a preparation for the investigation of more complex commercial alloys. This paper is the fifteenth of a series from the Research Laboratories of the Aluminum Company of America reporting the results of investiga-tions of equilibrium relations in aluminum-base alloys of high purity. The aluminum-nickel equilibrium diagram from 0 to 18 per cent nickel was determined, using the purest material available.

Jan 1, 1934

NORTH AMERICA ALASKA Anchorage.-Strandberg, H. College.-Barber, R. J. Burns, W. T. Henricksen, R. Henton, H. M. Joesting. H. R. Comet.-Albertson, F. E. Douglas.-Cahill, W. E. Carlson, L. Fairbanks.-Andregg. J. N. Coats. R. R.

Jan 1, 1938

By G. Sachs, E. J. Ripling, J. J. Lynch

It is general practice to evaluate the strength properties of a particular metal from its stress-strain (s1 — el) curve obtained by means of a conventional tension test. Such a stress-strain curve, Fig I, illustrates two important properties of a metal, its ability to strain harden, and its ability to withstand a certain limiting stress, the "fracture stress," (s), and a certain limiting strain, the "ductility" (es), before it fails by separation. These two fracturing characteristics are the coordinates of the point of fracture in Fig I. In the case of a metal which necks in a tension test, both the fracture stress and the ductility (measured in a tension test) are dependent upon (I) the shape of the neck and (2) average values of the stresses and strains over the cross-section at the moment of fracture. However, for the pur. pose of this investigation, these average quantities, rather than the actual values, may be considered for reasons of simplicity. It appears that the conclusiom also hold true if the analysis were carried out for actual values of fracture stress and ductility at the locos of failure. In this paper, the effects of straining (at room temperature) by various methods on the above metal characteristics, which were determined by subsequent tension tests will be discussed. According to Our present knowledge, any such prestrainitlg results in a stress-strain curve (in subsequent testing by tension), Fig 2, the general shape, or flow characteristics, of which can be derived from the original stress-strain curve of the unstrained metal minus a certain portion exhausted by the initial straining. This phenomenon is called strain hardening, and may be measured by the magnitude of the cut-off, or the "effective strain,'' from which the new curve must start in order to coincide in its plastic branch with the original stress-strain curve.

Jan 1, 1949

Jan 10, 1951

By Robert Glass Cleland

FROM the time of its organization down to 1917, a period of more than eighty years, Phelps, Dodge & Co. was seldom involved in what could be called a major labor difficulty. Behind this remarkable record lay both a philosophy and its practical application. The philosophy was an attitude toward society called the Golden Rule. That philosophy had been a living principle in the lives of the founders of the company, Anson Phelps, Daniel James, and William E. Dodge. Their successors, William E. Dodge, Jr., and Daniel Willis James, accepted the same philosophy. Dr. James Douglas governed his life by it. All of these men and their families had given tangible expression to that conviction in benefactions of great magnitude and variety-churches, hospitals, educational institutions, libraries, missionary undertakings, and other organizations for human betterment, such as the Young Men's and Young Women's Christian Associations, and the development of model communities about their mills and factories. According to the best standards of their generation, they had sought to improve the condition of labor,

Jan 1, 1952

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By J. L. Rodda

THE desirability of a uniformly sized abrasive for metallographic polishing has probably been recognized in a general way for a long time. Certainly all metallographers have recognized the damage that can be done to a polished surface by a piece of grit, especially if one of the softer metals, such as zinc or aluminum, is being polished. It is to be doubted, however, whether many metallographers have had any adequate idea of the particle size of the abrasives they were using or of the range of sizes encountered in any given grade of abrasive. At any rate, the descriptions of abrasives for metallographic work found in the literature are generally very meager. It was with the idea of securing an abrasive with a limited range of particle size that a study of this problem was commenced. Commercial abrasives, even when recommended for metallographic work, are made up of particles of varying sizes. One such abrasive contains some particles so fine that they remain in suspension for days and other particles so coarse that they settle at the rate of 3 in. per minute. It is evident that the coarsest particles are over 100 times the diameter of the smallest ones, or over 1,000,000 times the volume. The hopelessness of avoiding scratches under these conditions is evident. Vanderwilt1 has described a laboratory method for grading abrasives in which the elutriator is used. Le Chatelier's method, described by Goerens,2 also makes use of an elutriator. However, the elutriator is too slow for this purpose and requires too delicate a control for the range of sizes desired. The method of stirring up the abrasive in water, allowing it to settle for as given time, then drawing a measured depth off the top of the suspension, has been finally adopted as the simplest proce-dure. The largest particle in a given portion is. then determined by Stokes' law:3

Jan 1, 1931