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By Eric R. Jette, A. G. H. Anderson

During the period from 1910 to 1920, there was a lively interest in the subject of grain growth and many papers were published, followed by interesting discussions. Questions dealing with the fundamentals of grain growth—why and how it occurs—were treated in papers by Howe,' .Jeffries,² Sauveur,² Chappell,4 Beilby,5 Mathewson and Phillips,6 Mc Adam,7 Carpenter and Elam,8 Stead and Carpenter,9 Ruder,l0 as well as others. Since that decade, much indeed has been done regarding the practical control of grain size, and it is now possible to order material having a size sperified in the American Society for Testing Materials classification. Also, one hears the term "spliced boundaries" used in connection with certain tungsten lamp filamentsl1 wherein it is important to prevent "sagging" between consecutive turns of the helix.12 This practical use of a certain knowledge as to the things that influence or even control grain growth should not be taken as an indication that the subject has been thoroughly explored and that nothing more can be learned from fundamental studies. It is with this thought in mind that a report of some observations and experiments on abnormal grain growth is believed justified. Abnormal grain growth is met with in heat-treating high-carbon steels in the austenitic range,'? in the hardening treatments of high-speed steels,14'15 and in the low-temperature annealing of strained low-carbon steels as in sheet and wire material. Entirely aside from these instances of exaggerated grain growth, which some might consider as freakish, it is thought that abnormal growth is simply a case where the growth forces and the forces tending to prevent growth are almost, but not quite, evenly balanced. Information relative to grain-growth characteristics in general may be obtained from a study of abnormal growth conditions, which may be looked upon as vantage points. Reflection will show at once that if growth forces are great in comparison to inertia or resistance to growth, many crystals start to grow and, for that reason, none becomes very large, whereas if inertia is

Jan 1, 1938

By Albert H. Fay, William B. Plank

In practically all rock-excavation problem there is need for a careful study of the rock structure, its fault, cleavage or bedding planes, and even the texture of the rock itself. These studies should form the bases upon which an excavation method is selected and they should be carefully considered in predicting the amount and extent of the excavation. The need for such studies was forcibly illustrated in the problems involved in a cut made in 1929, along and underneath a 200-ft. high rock projection for a State highway near the City of Easton, Pennsylvania. The rock mass was badly faulted and also contained a number of cleavage planes at approximately right angles to the fault planes. Much of this structure was visible and could have been studied and analyzed before the work was begun. The State had rigid specifications as to finished grade and slope of cut, which apparently were made without reference to the geologic structure. The contractor complied with the specifications, under the close inspection of the State engineers. A tunnel blast was placed in the base of the cliff, with the result that 65 per cent more rock was broken than was intended by the specifications. About four years after the blast, the writers of this paper studied the circumstances surrounding the operation, to determine the cause of this excess excavation. Scope of Work The section of the roadway involved was about 200 ft. long and on a 6' curve. It was necessary to relocate points on the curve, from which all faults and cleavage planes were located and measured by the use of transit and clinometer. A plan (Fig. 1) showing the blasting tunnel, the roadway, and traces of the faults and cleavage planes on the level of the roadway, was prepared; also 13 cross-sections at varying intervals, showing the original face of the hill and the face after the blast. The original and final profiles of the rock face, taken from the plans of the State engineers, are shown in Figs. 2, 3 and 4.

Jan 1, 1937

By R. B. Basham, C. W. Macune

Very small anomalies in oil well temperatures are detected and measured by recording the difference in temperature existing between two thermally sensitive elements which are Spaced several feet apart on a small diameter carrier and lowered into the bore hole. The elements operate in a balanced electrical circuit, sending only a reference signal to the surface as long as normal gradient temperatures are encountered. When either element enters a temperature disturbance, the circuit is unbalanced and produces large recorder deflections for minute anomalies. The system is highly sensitive to small changes in thermal gradients caused by gas or fluid movements and to the boundaries between beds of different thermal conductivities. Typical logs show successful applications of the process to locating gas and water leaks in casing, gas entry. and gas-oil contact. INTRODUCTION Temperature measurements in oil wells have been made for many years in the search for additional sub-surface data. It has been generally agreed that many conditions in the bore hole cause temperature anomalies which, if located and measured, could yield useful information. But it has been recognized also that many of the irregularities, such as those produced by small water and gas leaks in casing, might be very small and therefore difficult to detect with certainty.' Although tem-perature measurements have been made which show anomalies of less than one degree deviation from normal gradient temperatures, the results are usually uncertain and unconvincing. The general practice, therefore. has been to apply temperature surveys only to well conditions known to produce appreciable disturbances, such as large gas movements and cement hydration. The recent demand for additional data has focused attention on the problem of making dependable temperature measurements in the many instances when anomalies are small but none the less significant. It was for the purpose of detecting these minute irregularities in bore hole temperature that the program described in the following text was undertaken. It is emphasized that this presentation is not offered as a complete study, for the process is still partially experimental. But it is believed that the results obtained thus far will be of interest to the industry and will indicate some of the system's potential usefulness. DIFFERENTIAL MEASUREMENT The chief value of differential measurement lies in the fact that a difference between two factors can be measured with a scale of values best suited to that difference, a scale that might be cumbersome or impractical if applied to the factors themselves. When it is known that all factors will be nearly equal in value, and therefore the differences consistently small, it is possible to select a scale which will permit very accurate measurement of the differences. This advantage is in contrast to the difficulty of measuring small increments of a single variable, where the increment must be measured by a large scale which is suitable for measuring the entire factor. Gradient temperatures are usually measured under this latter condition where temperature measuring apparatus must have a scale extending over the range of expected temperatures, say 50' to 25O°F, and it becomes almost impossible to detect small irregularities of less than one degree. The use of large strip chart recorders and divided multiple ranges tend to amplify the small anomaly and make it more pronounced. But the instability of instruments, both

Jan 1, 1952

By D. C. Hilty, W. Crafts

Determination of the solubility of oxygen in iron containing silicon, or manganese, or both, has confirmed the earlier work on silicon, shown that manganese is more effective than expected, and has demonstrated that the combination of silicon and manganese is a much stronger deoxidizer than might have been inferred from their individual effects. SILICON and manganese are of primary impor-tance in the deoxidation of steel, and a study has been made at the Union Carbide and Carbon Research Laboratories, Inc. of the solubility of oxygen in iron in the presence of silicon and manganese, singly and in combination, as a basis for more effective control of inclusion formation. The investigation was carried out with the same equipment and experimental procedure that were used in the determination of the oxygen solubility of iron containing aluminum'. The heats were melted in a rotating crucible furnace under an argon atmosphere. Bath temperatures were controlled by platinum/platinum +10 pct rhodium thermocouples to attain equilibrium at 1550°, 1600°, and 1650°C, so that oxygen solubility isotherms were determined directly without requiring calculation from a temperature coefficient. A detailed description of the furnace and procedure is given in the paper on aluminum deoxidation1. Oxygen solubility in the presence of more than 0.10 pct silicon was found to approximate earlier determinations closely, but some deviation was observed at lower silicon contents. Manganese appeared to be more effective than had been anticipated. The combination of silicon and manganese lowered the solubility for oxygen markedy as compared with either silicon or manganese alone. Although the solubility for oxygen in the presence of both silicon and manganese represents only a part of the information needed to control inclusion formation, it suggests a partial explanation of the benefits of this combination that have been observed in practice. Manganese and Oxygen in Liquid Iron: The study of oxygen in iron in the presence of manganese was carried out in magnesia crucibles of the type furnished commercially for laboratory induction furnaces. Alumina crucibles were unsatisfactory, because the work on the aluminum-oxygen equilibria in iron' had shown that merely melting iron in an alumina crucible limited the solubility of oxygen to a level considerably below that anticipated for moderate concentrations of manganese. Silica crucibles appeared unsuitable because of the dangers of excessive fluxing by the melt. Moreover, as will be shown later, melting iron in a silica crucible also limits the oxygen content below that in equilibrium with

Jan 1, 1951

By Jerry H. Service, F. L. Partlo

The following investigation was undertaken to develop a method for determining with reasonable accuracy the depth of overburdens of 100 ft. or less. Seismic methods seemed to offer good possibilities. The problem differed from that of the familiar salt-dome location in that the depth of overburden to be determined is much less than is encountered in oil prospecting. This means that a much shorter time interval must be measured with accuracy. Refraction methods seem at present to offer greater possibilities than reflection. The air sound persists for from 0.1 to 0.5 sec., because of echoes, and seismic reflections coming during this time are difficult to detect. A seismometer sensitive to vertical vibrations only offers possibilities and has been used here with some success. It is hoped that the application of this type of seismometer to reflection shooting in this region may be investigated still further. The apparatus used consisted of a carbon-button seismometer followed by a three-stage, transformer-coupled, vacuum-tube amplifier and a General Radio string oscillograph. Time marks are provided by a 1000-cycle, 600-r.p.m., synchronous motor provided with five spokes which intercept the light to the camera at 1/50 sec. intervals. This motor is driven by a two-stage vacuum-tube amplifier of 3 watt output, actuated by a tuning fork. The power supply for the seismometer amplifier is one 2-volt storage and one 45-volt B battery. The motor amplifier is powered by a 6-volt storage battery and 6 to 225-volt, 15-watt motor generator. The temperature-frequency characteristics of the tuning fork have been determined and for ordinary working temperatures the error in time that would be introduced is less than M millisecond for time intervals up to 100 milliseconds. The impact is produced by a sledge blow for surface distances less than 100 ft. and dynamite for greater distances. Two steel balls with wires attached form an electric circuit through a 1-ft. piece of railroad rail upon which they rest. When the rail is struck by the sledge the balls rebound, opening the circuit and indicating the time of impact by a break in the oscillograph record line as at A, Fig. 3. When dynamite

Jan 1, 1934

By Albert Sauveur

AT the New York meeting of the Institute, February, 1914, Professor Hopkinson and Sir Robert Hadfield presented an important paper entitled Research with Regard to the Non-Magnetic and Magnetic Conditions of Manganese Steel.1 Any contribution on manganese steel by its discoverer necessarily carries with it much weight and is entitled to serious and close consideration. The momentous discovery of that alloy by Sir Robert Hadfield some 30 years ago was the signal for great activity in the field of alloy steels; and the remarkable results obtained in the last two decades probably constitute the most important modern advance in the metallurgy of steel. The authors of the paper referred to above are unable to reconcile with the allotropic theory the interesting results obtained by them in heat treating manganese steel. When they speak of the allotropic theory, however, I understand that they have more especially in mind the existence of beta iron. It is not my understanding that they question the occurrence of iron in the two allotropic varieties known as gamma and alpha. If I am wrong, I trust they will correct me. A careful consideration of the experimental results reported and discussed by the authors leads me to believe that on the contrary they can be very satisfactorily explained in terms of allotropy and that, in the light of our present knowledge, they cannot be accounted for in any other way. The physical properties of non-magnetic manganese steel described by the authors are those pertaining to iron-carbon alloys in which iron is present in the gamma condition, or, in other words, to austenite. The metal is then characterized by great tenacity and ductility and low elastic limit, while its hardness, mineralogically speaking, is not excessive, but of a special kind termed "tough hardness" by the authors. Even when subjected to the restraining influence of a large amount of manganese and of considerable carbon, however, relatively rapid cooling

Jan 9, 1914

By R. A. Sharma, F. D. Richardson

Manganese oxide acitivities and sulfide capacities have been measured at 1650°C in mixtures of MnO + A1203 and MnO + SiO2 - Al2O3. Sulfide capacities have also been measured at 165O0C for melts of MnO + SiO2, MgO + SiO2, MgO + SiO2 + Al2O3, MgO + MnO + SiO2, and SiO2 + Al2O3 and for crystalline CaO. The activity coefficients of the sulfides of manganese and magnesium have been derived where possible. It looks as though the activity coefficients of sulfides are greatest at compositions where the free energies of formation of the silicate mixtures have their maximum negative values. The amphoteric nature of alumina is reflected in the results for the binaries and ternaries in which it is present with silica. The limiting solubility of CaS in CaO at 1650°C is 6.3 x 10-4 mole fraction. THE activities of manganese oxide have been measured in a variety of silicate and aluminate melts by use of the equilibrium (MnO)slag = [Mn]pt .½O2 [l] and the experimental techniques described previously.' Sulfide capacities (CS = wt pct S (PO2/PS2)½) have also been determined in a series of melts, by use of an established method2 which exploits the equilibrium (O°) + ½S2 = (S") . ½O2 [2] If CS and the activity of a metal oxide are known in a melt, the activity coefficient of the metal sulfide can be calculated by use of the equilibrium constant K, for the pure phase reaction MO i ½S2 = MS + ½O2 [3] The activity coefficient of the sulfide is then given by the equation

Jan 1, 1965

By William A. Johnson

THE mathematical analysis of diffusion curves in solid metals is Carried out ordinarily by analogy with the flow of heat in a continuous medium and no account is taken of the fact that the materials involved are composed of discrete particles that move discrete distances at irregular intervals. It is possible to treat the problem on the basis of simple assumed atomic mechanisms, in which case, because of the small scale of the elementary process compared to the gross effects observed experimentally, the two procedures lead to the same expression for the variation of concentration with distance. Thus, for engineering purposes, the usual methods are quite satisfactory. If, on the other hand, our purpose is to go beyond the mere collection of data, however desirable this may be, it is necessary to recognize and understand the factors that are of fundamental importance. One factor that has not hitherto been considered when dealing with solid metals is the difference in atomic weights of the isotopes of a single metal. While all the atoms of a given element are alike chemically, their weights may vary by a small but significant amount, and atoms of different weights may have different diffusion rates. With gases this variation in isotopic weight produces a change in the rate of diffusion by a factor inversely proportional to the square root of mass. While, except for the lightest gases, this is not a large effect, it is, for example, sufficient to permit a considerable concentration of one isotope at the expense of others. If metals exhibit a similar phenomenon, some modification of the analysis of the diffusion process will be required, since the different isotopes of a given metal will have different probabilities of moving and the heat-flow analogy will contain a fundamental error. This situation cannot be rectified by using a diffusion coefficient based on the average probability of moving, and it can be shown that even when the diffusion coefficient is independent of composition, the diffusion curve will not agree with the simple theory except in the rare cases where only one isotope exists; e.g., gold. If, however, the mass effect in the solid state were no larger than in the gaseous, the errors arising therefrom in the analysis of ordinary diffusion curves would be quite negligible. Nevertheless, our desire to obtain all possible information concerning the details of the diffusion process, and the possibility of diffusion in the solid state as a means for separating isotopes are cogent reasons for undertaking an experimental study to determine whether isotopes of different masses diffuse at different rates. EXPERIMENTAL PROCEDURE If isotopes of different masses diffuse at different rates, the ratio of the concentration of one relative to another will vary with the distance from the diffusion inter-

Jan 1, 1946

By Charles R. Keyes

PAGE. I Introduction,........674 11. Occurrence............ 676 III. Geology of Death Valley BoRate-Region,....677 1. Surface.Relief ......677 2. Geologic Formations,....680 3. Geotectonics,..684 IV. FURnace Canyon Deposits..686 1. General Features..686 2. Geologic Structure..688 3. Ores.....690 4. Typical Section ...691 V. Lost Valley Deposits...693 VI. Mojave Desert Deposits..693 1. Distribution....693 2. Geologic Structure ........694 3. Ores............ 696 VII. Santa Clara Valley Deposits .699 1. Distribution....699 2. Geologic Structure..700 3. Ores.....700 VIII. Ventura County Deposits..701 IX. Geologic Occurrence of Borax .701 1. Original Sources...701 2. Solfataric Borax...702 3. Lacustrine Borax...703 4. Marsh Borax....703 5. Terranal Borax...704 X. Chemistry of Natural Borates.... 705 1. General Considerations.....705 2. Composition of Saline Waters...706 3. Solubility of Components....707 4. Time-Element in Water.Concentrations . 707 5. Effect of Temperature.....708 6. Effect of Pressure......709 XI. Occurrence of Other Commercial Salines,.... 709 I. Introduction. A complete transforrnation has taken place in the borax industry during the year 1908. A most remarkable factor in

Jan 1, 1910

By Gerhard Derge

METALLURGISTS have used borax as a fluxing agent traditionally, but until recently elemental boron has played an insignificant role as an alloying element. Neither the metal nor its compounds have been regarded as important metallurgical materials and there is a surprising lack of knowledge concerning their metallurgical behavior. The new applications to steelmaking of both boron and borates, which arose in part from wartime incentives and restrictions, have been seriously handicapped by this lack of data. For example, rasorite, a naturally occurring sodium borate, has been shown to be an effective substitute for aluminum as a ladle deoxidizer in rimming steels.1 Likewise, the effectiveness of boron as an alloying agent has been demonstrated, 2,3 giving deep hardening when used in restricted amounts. The exploitation of both of these uses has been retarded by the difficulty of attaining suitable metallurgical control. Recognizing that the most important information required was a knowledge of the equilibrium between boron and oxygen dissolved in liquid iron, Gurry4 calculated this relation from the best thermal data available. However, estimates of the entropy of melting of boron, the activity coefficient of boron in liquid iron and the activity coefficient of B203 in slag were involved, and experimental work on this problem was obviously desirable. The experiments to be described were planned to establish the boron-oxygen relations in liquid iron and to demonstrate at the same time the ferroborate slag compositions in equilibrium with various amounts of oxygen in liquid iron. Accordingly, slags containing varying proportions of iron and boron oxides were held in contact with molten iron, and samples of both slag and metal were analyzed. The limitations upon the accuracy of the data will be considered, but in a practical sense the oxygen levels that can be attained in iron by iron borate slags, and the amounts of boron in iron at these oxygen levels were established. EXPERIMENTAL PROCEDURE No entirely suitable refractory was found for the mixtures of iron oxide and boron oxide used as slags. Crucibles of silica, magnesia, Ramix, beryllia, and zirconia were all tried unsuccessfully. The most satisfactory method discovered for handling them was the rotating-crucible technique, which creates a parabolic crucible of liquid iron 5,6 Even this was not entirely successful, for at steelmaking temperatures (1600°C.) the slags had such a low surface tension that they crept up to the refractory and slowly dissolved it. These difficulties made it impossible to maintain a constant slag composition for an unlimited period of time. However, by using the rotating

Jan 1, 1946

By B. S. Butler

AN understanding of mineralizing solutions and how they carry and deposit metals is of prime importance to students of ore deposits. Lindgren states: "The whole problem surely is very complicated. One difficulty is that we know so little about the stability field of ore minerals."1 Lindgren further states: It is believed that they [the solutions] were in small part oxidized to sulphates, for instance, but in large part they were composed of hydrogen sulphide, alkaline sulphides and various halogen compounds. Doubtless, however, free carbon dioxide was present. Becker's view of the double sulphides as important constituents of the solutions probably holds good. In the fourth edition of Mineral Deposits2 Lindgren had changed his views somewhat: From the work of Day, Allen, Shepard, and others, it would seem probable that many of the volcanic gases are acid when given off but are in unstable equilibrium, and could not have preserved this acid character after having been long in contact with the surrounding rocks. It is believed that they were in small part oxidized to sulphates, for instance, but in larger part they were composed of hydrogen sulphides, alkaline sulphide, and various halogen compounds. Doubtless, however, free carbon dioxide was present. Becker's view of double alkaline sulphides as important constituents of the solution probably holds good. The writer wonders if progress would not result from an attack on the problem in steps, the steps to contribute to the attack on the whole. The initial step would deal with the simpler bodies of supposed magmatic (hydrothermal) origin, that is, those composed essentially of silicates, oxides, sulfates, and sulfides. The following discussion attempts to develop one step of a method that was proposed on a more comprehensive scale in 1929 by the writer and W. S. Burbank.3 The accompanying partial table (Table I) of the electromotive series is from a table distributed by Merck & Co. Inc., manufacturing chemists, prepared in turn from Fundamental Chemistry.& The electromotive arrangement brings together elements that in hypogene ore deposits occur: 1) in oxygen combination only; 2) in combination with sulfur as well as with oxygen; and 3) as sulfides, arsenides etc., and as native metals, see Table 11. The writer clearly recognizes that he is not qualified to discuss the formation of ore deposits as a chemical problem, but he feel that some of the relations that are met by the geologist can well be stated with the hope that the chemical explanation will be forthcoming. By consideration of a group including mainly the elements oxygen, hydrogen, sulfur and iron, complications are avoided, especially with elements of the lower electromotive group. The results can only contribute to the solution of the problem, not to the completion of it. The pH and Eh of the solutions and also temperature probably determine what minerals form. The mineral groups that contain elements high in the electromotive series are alumino-silicates, titanites, simple silicates, spinels, oxides, carbonates and sulfates, in all of which the elements are combined with oxygen. These groups are also recognized as the general order of temperature at which the minerals start to form, see Table 11. At low temperature are sulfides, arsenides, antimonides, sulfo-salts, and native metals, in all of which the elements are characteristically not combined with oxygen. The intermediate temperature group contains elements that form both oxygen compounds and sulfur compounds.

Jan 1, 1957

By L. Hartsell Cash

INTRODUCTION Created in 1944 to help rebuild those economies, principally in Europe, which were seriously damaged or destroyed during the Second World War, the World Bank--or to use its correct name, the International Bank for Reconstruction and Development-began its operational phase by making a loan to the Government of France to accomplish two tasks: (i) to import coal for space heating purposes; and (ii) to buy new machinery and equipment to help rehabilitate its coal mines. Once the thrust of reconstruction in postwar Europe was largely accomplished, the World Bank Group (for today the World Bank has three separate lending windows) turned to mobilizing funds to improve living standards in developing countries, which remains its primary goal today. Over this period of time, the World Bank Group has continued to assist the world mining industry in various ways and, since 1955 the World Bank Group has financed mining or mineral processing projects with loans/credits totalling $1.5 billion. The World Bank Group consists of two institutions--the World Bank itself and the International Finance Corporation (IFC), which was founded as a separate institution in 1956 and three separate lending windows--the World Bank, the International Development Association (IDA), and IFC. The World Bank loans are provided at commercially-related interest rates but have grace periods usually of up to 3 to 5 years and repayment periods ranging from around 15 to 20 years. Since the World Bank raises its operating funds on the international capital markets in varying currencies and in varying interest rates, it relends a basket of currencies at floating interest rates which are fixed every six months to reflect the Bank's own borrowing cost. At the present time, the interest rate is just below 10% per year and in addition, a one-time front-end fee of 1/4 of 1% is charged. Also, a commitment fee of 3/4% per year is charged on the undisbursed amount of the loan itself. For loans to industrial and mining projects, it is normal to charge an additional guarantee fee of 1 to 1.5% in addition to the annual interest rate. This guarantee fee is payable to the government of the country in which the project is carried out since, by its charter, the World Bank is required to have the guarantee of the host government for each loan made in a specific country. By far the greatest source of lending funds within the World Bank Group is that of the World Bank itself and for the fiscal year ending June 30, 1984, the World Bank approved loans totalling $12 billion. The second lending window within the World Bank Group is IDA which performs the same functions as the Bank itself and has the same staff. Nevertheless, its loans (called credits) are made on much softer terms and are made to the poorest nations only. IDA funds are subscribed by the wealthier countries, usually as grants, and these are relent as credits to those countries with the lowest per capita income. IDA credits are made for 50 year periods, including 10 years of grace, to the government itself. The credits are interest free, but there is a service charge of 3/4% per year on the amount withdrawn and outstanding to defray the administrative costs of IDA. Credits approved during fiscal 1984 totalled $3.5 billion. The third lending window is IFC. While IFC is a separate corporation and operates quite separately from the World Bank and has its own staff and regulations, it works very closely with the World Bank on its overall approach to the mining sector and to a particular country. IFC's mission is essentially to supply venture capital and to stimulate development of the local private sector in capital markets as well as to promote the international flow of private capital to developing countries. Unlike the World Bank and IDA, the IFC does not lend directly to governments

Jan 1, 1985

By John N. Hobstetter

IT is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spontaneous diffusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow,' Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Becker1 in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r. beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration, The increase in free energy per mole accompanying the formation of a nucleus which is just stable, ?fe, is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. THE NATURE OF THE NUCLEUS It is necessary to have rather detailed knowledge of the nature of a nucleus if ?Fe is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown3

Jan 1, 1948

Discussion of the paper of C. W. WASHBURNE, presented at the Pittsburgh meeting, October, 1914, and printed in Bulletin No. 93,. September, 1914, pp. 2365 to 2378. ROSWELL H. JOHNSON, Pittsburgh, Pa.-It seems to me rather important to bear in mind one thing which is sometimes lost sight of, that the marine sedimentary rocks are laid down in water. We have to start with an initial charge of water. That being so, and the surface tension between the water and the -oil being as slight as it is, as referred to by Mr. Washburne,. the phenomena of capillarity are bound to be most important as between the liquid surface and the gas surface. So far as the liquid-gas surface is concerned, capillarity, in my opinion, is of the utmost importance, and it seems to me this paper of Mr. Washburne's is of great value to us for that reason. Starting out as we have, with our attention concentrated upon gravitational sorting, we have had to wait for the discussion of movement furnished by Munn, and this discussion of capillarity by Washburne, for a more balanced view of the situation. It seems to me that in the accumulation of oil and gas we have a problem of the interworking of gravitational sorting, capillarity, viscosity, immiscibility, and movement. All five things seem to me to be important. I would have expected Mr. Washburne to have given a fuller treatment of the relation of movement to capillarity. In my own experiments I find that gravitation and capillarity alone seem remarkably impotent when everything is at rest, but if I furnish a little movement, gravitation and capillarity step in and accomplish a great many results that one would not expect. Take a horizontal tube and fill a portion at the middle with an ordinary sand saturated with oil, and then put water and sand in each end, and the tube may remain at rest a very long time without that oil distributing itself along the top of the tube. But with a little motion that oil will gradually work up to the upper side. So gravitation and capillarity alone are rather impotent unless they get this element of movement. It would not be necessary to have very extensive movement, but some degree of movement is essential. Now if natural gas, in addition to the method of origin by the action of bacteria on organic matter in mud, may also arise by pressure at great depth, as the overburden is added, a great deal of motion may result. I think more motion is produced in this way than by the descent of meteoric waters.

Jan 4, 1915

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

Trans. Pamphlet Volume Number Title Author Meeting and Page* 1033 Relation of Air Presaure to Drilling H. W. Seamon New York 66, 743. 766 Speeds of Hammer Drills . Feb. 1921 1034 Time Factor in Depletion of Mines J. W. Roberts New York 66, 711 Feb., 1921 1035 Calculation of Ore Tonnage and Grade J. E. Harding New York 66, 117, 122 from Drill-hole Samples Feb., 1921 1038 Diacuasion of Papers Presented in 1920 1041 Run-off and Mine Drainage H. N. Eavenson New York 66. 624. 630 Feb.. 1921 1043 The Health of the Underground Worker A. J. Lanza New York Feb, 1921 1045 Dust-ventilation Studies in Metal D. Harrington New York 66, 272, 288 Mines Feb., 1921 1046 Discussion of Papers Presented at New York Meeting, 1921 1072 Breakage and Heat Treatment of Rock- B. F. Tillson New York 66. 758 drill Steel Feb., 1921 1073 Discussion of Papers Presented at New York Meeting, 1921 1076-M Analysis of Some Drill-ateel Teats F. B. Foley New York 66,789 Feb.. 1921 1077-M Application of Magnetic Analysis to C. W. Burrows New York 66, -796 Rock Drills Feb., 1921 1078-M Heat Treatment of Rock-drill Steel G. H. Gilman New York 66.779 Feb., 1921 1080 What is the Ideal Drill Steel? F. H. kingdon New York 66, 807 Feb.. 1921 1081 Rock Drill-Steels, etc. W. T. Ober New York 66,814 Feb.. 1921 1082-C Underground Mine Development, Its J. B. Dilworth Wilkes-Barre 66,715, 761 Definition and Valuation Sent.. 1921 1081 Drill Steel from Hollow Ingots P. A. E. Armstrong New York 66,809 Feb., 1921 1068 Authors' Replies to Recent Discussion 1092 Heat Treatment of Rock Drill Steel A.E.Perkins New York 66,811 Feb., 1921 1096-M Octagonal Ventilation Shaft of Davis- J. L. Bruce Wilkes-Barre 66. 252, 608 Daly Copper Co. Sept., 1921 1100-C Determination of Electrical Equip- G. Bright Wilkes-Barre 66,580,606 ment for a Mine Hoist Sept., 1921

Jan 1, 1927

By Glenn C. Waterman

Richard Strong (Oliver Iron Mining Div., U. S. Steel Corp.)—Mr. Waterman states (p. 59, Trans., January 1954): "Core-sludge combining factors have been calculaied for any combination of core-sludge recovery on the basis of several logical assumptions: 1—The sludge sample loses reliability geometrically as sludge recovery drops. 2—The sludge sample should not be used if the percentage of sludge return is less than the percentage of core recovered. 3—A core sample should receive a weighting at least equal to the percentage of core recovery." Assumptions 1 and 2 seem justified at Chuquicamata and most geologists would agree to the validity of assumption 3. However, contrary to the statement quoted above, the core sample does not in general receive a weighting at least equal to the percentage of core recovery when the Chuquicamata methgd is used. Furthermore, the basic Chuquicamata method is identical to the Longyear or relative volume core-sludge assay combining method. Finally, the Chuquicamata method does not, in its present form, reflect true geometric loss in sludge sample reliability according to the relationship L = AR (N-1) The basic equations representing the two steps of the Chuquicamata method can be combined algebraically as follows (using the symbology of the original article except as noted): Vol A + B Assay 2 = ASA = Assay 1 Vol A VolB Core Assay [I] Vol A CA.F + ASA (100 —F) Combined grade =[21 100 Pct where F and (100 — F) are the core and adjusted sludge assay factors from Fig. 3. Substituting Eqs. 1 and 2 and collecting terms Combined grade = Vol B Vol A + B CAF (100—-F) + Assay 1 (100-F) Vol A Vol A 100 pct Eq. 3 is a unified and general statement of the Chuquicamata method. The true core factor includes not only the factor F from Fig. 3 but also the quantity VolB ------------- (100 — F), which is implicit in the value of Vol A the adjusted sludge assay. This quantity is real and positive for all values of F and core recovery less than 100. Therefore the true core factor is always less than F except when F is equal to 100. If sludge recovery is 100 pct, Eq. 3 can be further simplified as follows: Let F = percentage of core recovered. Let Vol A = Vdh (100 Pct — Pct CR) where Vdh is the total volume of the sampled interval and let Vol B = (Vdh — Vc.) Pct CR where V, is the core volume in the sampled interval at 100 pct core recovery. Then combined grade = Vo V. CA Pct CR- + Assay 1, 100 Pct — Pct CR Vdh Vdh [4] 100 Pct Eq. 4 shows that when sludge recovery is 100 pct the laboratory sludge assay receives significant weight in the Chuquicamata method, even at 100 pct core recovery. The maximum weight assigned to the laboratory sludge assay depends on drillhole size, as follows: Eq. 4, with suitable changes in symbology, is identical to Royce's formula 8,' which is a statement of the Longyear or relative volume method of combining core and sludge assays. If Mr. Waterman's assumption 3 is of paramount concern to the geologist, the Royce method (for core recoveries of 60 pct and above) or a method employing the percentage of core recovered as a core weighting factor are the only recognized methods known to the writer which achieve the desired result. A modification of the latter method embodying Mr. Waterman's assumptions 1 and 2 would result from applying the factors from Fig. 3 directly to the laboratory core and sludge assays.

Jan 1, 1956

By James D. Reilly

13.1-1. Introduction. COAL RESERVES OF THE UNITED STATES. Bituminous coal is the most abundant fossil fuel in America. With reserves of 1,660 billion tons and assumed recovery of 5070, there is more than 830 billion tons of recoverable coal--enough to assure ample supplies of energy for centuries. Looking at Fig. 13.1-1, coal is found in a majority of the states, including [ ]

Jan 1, 1968

By AIME

COAL, its acquisition and consumption, has loomed large enough in the lives of many of us at one time or another, not from a technical standpoint, perhaps, but on a utility basis, to keep the house warm and the plant going. The Chairman of the Coal Division was much like many of us in that respect until after his graduation from Northwestern in 1928. Then he went to work as geologist for the Zeigler Coal Co., investigating strip coal possibilities in western Illinois, and also did research in the microscopy of coal at the Illinois Geological Survey. His interest in coal was originated and stimulated by Gilbert H. Cady, of the Illinois Geological Survey. With his advice, and with the co-operation of M. M. Leighton, Survey chief, the results of his research work on the mineral constituents of coal at the Survey were accepted as a thesis for his doctorate which he received from Harvard in 1935. Nine days before the Christmas of 1906, Clayton Garrett Ball was born at Wauconda, Ill. His father was professor of geology at Northwestern until he retired in 1946; retirement didn't lessen his active interest in his profession; he's still teaching geology at the University of Kansas City. So it was only natural for Clayton to study at Northwestern. In 1937, following a year's connection with the Bell &

Jan 1, 1948

By J. S. FINLAY

OPERATING a "muck stick" never appealed to me. It always seemed a terrible waste of energy to "put rocks in the box" by hand-particularly when my own personal energy was involved. But during the past forty years, there have been periods-more or less extended when I was compelled, against my finer instincts, to muck or quit eating. For about the same length of time, I have devised schemes to make mucking faster and more painless. There was always something mechanically wrong with these designs-too many;" parts to wear out and need replacement, and excessive cost incidental to a complicated mechanism. The idea of a shovel unit comprised of a single, rigid assembly which would roll from a digging to dumping position solved the problem of simplicity and durability. Ingersoll-Rand's utility engine provided a splendid power plant, small enough and powerful enough for the job. In the machine finally developed, known as the Eimco-Finlay loader, roller chains are preferred to gears for power trans-

Jan 1, 1935