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By William C. Marshall, Frank G. Norris

The term "total operation" is meant to include problems that cannot be answered from the standpoint of either the blast furnace or the open hearth separately but must be studied by considering the interrelations of these two processes. There are other ways of expressing this idea, such as reference to the blast furnace and the open hearth as an integrated process or by emphasizing the interrelation and interaction of the two processes. Much progress has been made in metallurgy and other fields by breaking complicated processes and reactions into simpler parts and studying each of these intensively. This intensive study frequently is done under the controlled conditions of the laboratory experiment. The entire process is understood better by this specialized study of each of its parts. This procedure is so satisfactory that an understanding of unit operations is a fundamental requirement of chemical engineering. Much discussion of the open-hearth process is in terms of one heat or one furnace. By this is meant that the conclusions apply to one furnace, wherever it may be. Furnaces seldom occur singly; they are located in groups and these groups are located in steel plants having characteristic blast-furnace equipment. Problems that are affected by the number of furnaces operating, by the number of blast furnaces in the plant and by the fact that the open- hearth shop is dependent on the bla furnace capacity rather than on its o needs for the amount of iron available among those which, in contrast to "u operations," we have chosen to call "to operations." Many of these problems, such as cha ing delays and the general mechani problem of material handling, are familiar that merely to define " total op ations" brings them to mind. These pr lems are of such importance that alrea they have received careful thought 2 study and probably will merit furt study. As will be shown later, these mechan problems are so intimately related metallurgical problems of total operati that the effect of certain changes cannot ascribed with certainty to either a mech ical or a metallurgical cause entirely. Although the problems coming under general term of "railroading" are inclu in the problems of total operations, ' others are selected for the discussion of paper, One of these is strictly a problem composition; the other is strictly a prob of tonnage production. The problem of phosphorus is pres whenever basic open-hearth slag is used the blast-furnace burden. This practice not secured universal acceptance chi because of difference in preference for h manganese or low-manganese pig iron hjgh-manganese (2.00 per cent) iron is to made, open-hearth slag as a source manganese is usually cheaper than m

Jan 1, 1943

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By Hans Lundberg

IN ORDER to comprehend the help and information that may be expected from electrical prospecting, it is necessary to have at least a general knowledge of the methods and principles involved in preparing and interpreting results obtained in the field. Electrical prospecting is rather complicated, both in theory and practice, and in order to make a brief description clear to the practical mining man it has been necessary to idealize and generalize the problems, at the risk of having such simplification criticized by the theoretical man. This simplification must not be misinterpreted as showing a lack of theoretical knowledge. FIG. 1.-FLOW OF CURRENT IN AND AROUND A CONDUCTING BODY. For its operation, electrical prospecting mainly depends on the fact that most metallic ores conduct an electric current much more readily than barren rocks. If an electric current flows through a block of ground within which a body of chalcopyrite is enclosed in country rock of schist, the current will find less resistance to its passage through the chalcopyrite than through the schist, even though the passage through the latter be much shorter. This is because the longer path through the chalcopyrite offers less resistance, owing to the superior electrical conductivity of the chalcopyrite (Fig. 1).

Jan 1, 1928

By L. Segle, R. Resnick

NUMEROUS experiments in the past few years have proven that void formation occurs quite generally in the diffusion zone of bimetal specimens1-4 The phenomenon has been explained in terms of the accumulation of lattice vacancies resulting from unequal diffusion of the constituents and their eventual precipitation as holes.= Attention has recently been directed to the fact that voids also form within homogeneous metals during high-temperature creep.' The idea has been put forward that these voids form by the condensation of excess lattice vacancies generated by intersecting dislocations.".' If the precipitation of lattice vacancies from solution is treated as a nucleation and growth process, the predicted vacancy concentration for homogeneous nucleation of voids at an observable rate is 100 to 1000 times the normal thermal equilibrium concentration. It appears that voids actually form during diffusion at vacancy supersaturations which are much lower than this8 According to the calculations of Machlin,' the same must be true for voids formed in homogeneous metals during creep, if these are considered to arise from the precipitation of lattice vacancies. Therefore, if the vacancy mechanism is valid, it seems that the holes which form in diffusion and creep specimens are heterogeneously nucleated by imperfections or impurities in the metal. Irregularities in the frequency and distribution of voids in diffusion couples bear out this explanation.' , It is not known at the present time what the nuclei are on which vacancies condense. Various investigators have speculated that they could be certain dislocation configurations, already existing voids produced during solidification or working, gas pockets, or inclusions in the metal. Relatedly, the precise value of the degree of vacancy supersatura-tion for void nucleation is still uncertain. An initial attempt to estimate this value from diffusion data, made by Balluffi, indicated that voids form in diffusion couples at vacancy concentrations which may

Jan 1, 1958

By R. Frenkel, O. D. Sherby, J. E. Dorn, J. Nadeau

A method is shown for the study of the creep rate dependence of metals on the applied stress under the condition of constant structure. The method was applied to pure aluminum and to dilute solid solution alloys of magnesium, copper, germanium, zinc, and silver in aluminum. A linear relationship was found to exist between the true stress and the logarithm of the creep rate. ALTHOUGH extensive creep data are now avail-Aable, the fundamentals of the creep phenomena are as yet only vaguely understood. Many attempts have been made to formulate theories for creep. Eut their agreement with fact has been disappointing. It appears that merely pyramiding more of the same type of data that is now available will not provide the essential aid toward formulating a better understanding of the complicated process of creep. Perhaps attempts to construct better models for the mechanism of creep might have to be tentatively abandoned until new types of definitive creep data are uncovered. The question therefore arises regarding what type of data might be needed to provide the essential knowledge for formulating better and more realistic theories of creep. Perhaps one source of the failure to uncover an adequate theory arises from the fact that practically all theories for creep and nearly all analyses of experimental data on creep disregard the well-known fact that the structure of metals changes during creep. For example, it is customary in evaluating the effect of stress on the creep rate to correlate the secondary creep rate with the applied stress. But, as has been demonstrated recently,' the structures obtained during secondary creep tend to exhibit deformation banding at high stresses and polygoniza- tion at the lower stresses. Consequently the stress-secondary creep rate relationships found in this way are not fundamental, inasmuch as they reveal not only the effect of stress but also the effect of differences in structure on the secondary creep rates. It is the purpose of the study reported here to isolate the effect of stress alone on the creep rate in an attempt to provide new data for possible formulation of a better theory of creep. In addition an attempt will also be made to ascertain how structure, temperature, and alloying might affect the stress-creep rate relationship. The procedure that was adopted was simple: A specimen was precrept at a given engineering stress U, (initial engineering stress during creep under constant load, namely the load divided by the initial area of the specimen) and temperature T to a selected engineering strain, e (engineering strain, namely, the instantaneous gage length minus the initial gage length divided by the initial gage length), at which time the true stress was reduced to some lower value of the true stress, ^ (the true instantaneous stress, namely, the load divided by the instantaneous area). The instantaneous true creep rate, i, (the true strain rate; with E, the true strain, namely, the natural logarithm of the instantaneous over the initial gage length) following reduction of the true stress to U, was then determined. Second, third, etc., tests were conducted under identical conditions except the stress was reduced to yet lower values, us, u,, yielding yet lower instantaneous creep rates, ;, and i,. Inasmuch as the precreep conditions were identical in each series of tests, the instantaneous structures obtained immediately after reducing the stress were presumed to be identical.

Jan 1, 1955

By H. W. Krotzer

ADOPTION on a commercial scale of electrolytic deposition of metals brought with it the problem of providing an acid-proof cell or tank. Where the electrolyte contained only a dilute solution of sul-furic acid, wooden, tanks with lead linings were gen-erally adopted. There were cases, however, where a lead lining was impractical as a result of the presence of nitric acid in the electrolyte or because of the method of handling the current for deposition. purposes. Wherever lead was unsuitable for this work, asphaltic mastic was used in its place. This material, in addi-tion to possessing acid-proof qualities and being an insulator for electrical current, is also cheaper than lead. The only reason that prevented the common adoption of mastic for all work of this type was that it was still an unknown, unproved. material; while lead, although more costly, could be relied on. There are several electrolytic tank-houses equipped with acid-proof mastic linings now in operation. The first large one was the series tank-house of the Balti-more Copper Co., where the mastic used was composed of natural asphalts and a silica aggregate. These lin¬ings are now seventeen years old and still in service. The next large plant was that of the Chile Exploration Co., at Chuquicamata, Chile, ,and it is with this that this article deals. Another plant of more recent date is that of the Nichols. Copper Co., Laurel Hill, L. I., and specifications for the new electrolytic tank-house of the Union Miniere du Haut Katanga call for mastic lining. It is also being tried out on a smaller scale or for experimental purposes by many of the larger metal-lurgical companies. Thus while mastic linings were adopted originally to meet operating conditions that prohibited the use of lead, they are now in a position to compete successfully with the standard lead linings that are in general use. The Chile Exploration Co. plant, with a total area of over a million square feet, giving satisfactory ser-vice under the most adverse climatic and metallurgical conditions can be truly called the pioneer in this work. ,This article will deal with the development of the acid-proof mastic linings in Chuquicamata from the original experiments begun in 1912 up to and including the final successful installation that has now been in service for a number of years.

Jan 4, 1927

By R. H. Olds, B. H. Sage

The formation volume and volume of the liquid phase of oil and gas obtained from four fields in the San Joaquin Valley have been investigated at pressures, temperature, and gas-oil ratios comparable to those encountered in underground reservoirs. All the fields covered in this investigation yielded a product of a gas-oil ratio in excess of 5000 cu ft per barrel and the gravity of the tank oil for the four fields in question varied between 52° and 63' API. The results of the investigation, together with analytical data concerning the composition of the oil and gas, are submitted in tabular form. Rough correlations of the formation volume as a function of pressure, temperature, and gas-oil ratio and of the retrograde dew-point pressure as a function of gas-oil ratio, temperature, and gravity of tank oil are presented. It was not found feasible to correlate simply the formation volume of the liquid phase as a function of the applicable variable. It is desired to emphasize that these correlations are considered applicable only to the range of conditions covered in this investigation and for systems of similar nature and composition. Introduction Information concerning the physical properties of mixtures of oil and gas from particular fields have often been employed in predicting the situations obtaining in underground reservoirs. One of the earlier studies of this nature was the work of Beecher and Parkhurst,1 while a more recent study of the Dominguez Field2 presented detailed volumetric data in the two-phase as well as in the single-phase regions. Although these studies were confined to individual fields, their results proved of value in application to other fields. It has recently been shown 3,4 that it is possible in the region of low gas-oil ratios* to correlate the volumetric behavior of naturally occurring hydrocarbon mixtures from a single geographical area with sufficient accuracy to be of industrial value. For this reason it is considered of interest to submit information concerning the volumetric behavior of oil and gas mixtures from four different fields in the San Joaquin Valley and, in combination with similar published data5 concerning mixtures of oil and gas from the Paloma field in the same area, to show rough correlations between the composition and the behavior of materials from these fields. This effort seems particularly worth while since all of the

Jan 1, 1947

By R. H. Olds, B. H. Sage

The formation volume and volume of the liquid phase of oil and gas obtained from four fields in the San Joaquin Valley have been investigated at pressures, temperature, and gas-oil ratios comparable to those encountered in underground reservoirs. All the fields covered in this investigation yielded a product of a gas-oil ratio in excess of 5000 cu ft per barrel and the gravity of the tank oil for the four fields in question varied between 52° and 63' API. The results of the investigation, together with analytical data concerning the composition of the oil and gas, are submitted in tabular form. Rough correlations of the formation volume as a function of pressure, temperature, and gas-oil ratio and of the retrograde dew-point pressure as a function of gas-oil ratio, temperature, and gravity of tank oil are presented. It was not found feasible to correlate simply the formation volume of the liquid phase as a function of the applicable variable. It is desired to emphasize that these correlations are considered applicable only to the range of conditions covered in this investigation and for systems of similar nature and composition. Introduction Information concerning the physical properties of mixtures of oil and gas from particular fields have often been employed in predicting the situations obtaining in underground reservoirs. One of the earlier studies of this nature was the work of Beecher and Parkhurst,1 while a more recent study of the Dominguez Field2 presented detailed volumetric data in the two-phase as well as in the single-phase regions. Although these studies were confined to individual fields, their results proved of value in application to other fields. It has recently been shown 3,4 that it is possible in the region of low gas-oil ratios* to correlate the volumetric behavior of naturally occurring hydrocarbon mixtures from a single geographical area with sufficient accuracy to be of industrial value. For this reason it is considered of interest to submit information concerning the volumetric behavior of oil and gas mixtures from four different fields in the San Joaquin Valley and, in combination with similar published data5 concerning mixtures of oil and gas from the Paloma field in the same area, to show rough correlations between the composition and the behavior of materials from these fields. This effort seems particularly worth while since all of the

Jan 1, 1947

By Edwin Hopkins

The year of 1924, in Venezuela, has been one of especial interest. The figures for production marketed are not so impressive, but to the well-informed followers of the development, the ease with which this production has been obtained and with which it apparently can be increased at will merits most careful consideration. For several years, the oil world, especially in the financial centers, has been closely following the slow unfolding. of the' Venezuelan developments, which has been, and still is, one of the great pioneering achievements in the history of oil exploitation. Venezuela, from the first days of its recognition by geologists and financiers as a great future source of oil, has been a field for the enterprising vision of the larger capital groups. The laws of the country have been drafted with almost an inspired foresightedness that has favored the exploitation of the resources along constructive lines, which' has eliminated the irrational promotion schemes that accompany many of the oil developments in the United States. Developments have been exclusively in the hands of strong financial groups, who have followed a conservative policy with respect to the dissemination of detailed information concerning the geological findings and detailed production data. Within the last year, however, the rapid expansion of the production phase of the developments has been on such an important scale and has involved such a large and rapidly increasing personnel, that further restraint with respect to information of a general informative' nature can serve no useful purpose. Certainly, from the volume of references to Venezuelan oil affairs, which are now of almost weekly occurrence in the oil trade journals, the public must appreciate the fact that in Venezuela, and in the Maracaibo district in particular, a new oil region of the first magnitude is about to emerge from comparative obscurity and occupy a commanding position on the stage of world oil affairs.

Jan 3, 1925

By Otis M. Clarke

The Eufaula bauxite-kaolin district in southeastern Alabama is an important source of raw material for the refractory industries in the United States. At the present time, five companies are mining and processing bauxite and kaolin from this district and a sixth company is holding substantial reserves. Mining operations are expanding, but finding new ore reserves is a major problem. The Geological Survey of Alabama sponsored geologic research in the Eufaula district to: (1) investigate the

Jan 1, 1973

New Device Eliminates Blasting in Coal A non-explosive device developed by duPont utilizes the high pressure of a gas generated inside a steel tube which is inserted in a hole drilled in a coal seam to break down the face of coal. Chemical reaction is started by an electric current which produces heat to initiate the action. The same heat destroys the starter wire as soon as electric current is no longer needed. The tube containing the chemical is closed at the outer end by a plug with electrical connections, and at the other with a disk that is ruptured by the compressed gases formed. When the gas has been liberated in sufficient quantities to create a desired pressure the disk breaks and the released gas breaks down the coal face. The new device is called a Chemechol.

Jan 10, 1951

By C. F. Jackson

THE work of, the Mining Methods Committee is now well under way. Following discussions previous to and during the February meeting, an Outline for Papers on Mining Methods was prepared, and over a thousand copies have now been distributed to committee men, to section secretaries and to members who have indicated any interest in the subject. The objective of the committee is to prepare a symposium on mining methods which will be of real practical value to the operator and engineer in the solution of every-day mining problems. It is planned to cover the entire field of mining in such a way that the different branches of mining, such as coal and ore (iron, copper, lead, zinc and precious metal) can benefit from the experience of the others at points where they have problems in common.. It is realized fully that each of these branches of mining possesses its own peculiar problems, but at the same time, there are prob-lems in connection with each, where the experience in others should be of value. The committee proposes to proceed along the following lines: 1. To present a general classification of mining methods, showing their inter-relationship, and at the same time .provide a common language for the discussion of mining methods and a nomenclature that will have the same meaning wherever used. A com-plete set of illustrations will accompany the classi-fication to make clear the terminology adopted and to show graphically the inter-relationship of methods. 2. To show the relationship between the physical characteristic of the deposit, the economic consider-ations and the. mining method., It is not proposed to treat this subject as a mere academic problem, but to secure reports from every mining company of impor-tance in this country, which will show what methods or modifications and combinations of methods have actually been applied and the physical conditions and economic considerations which have led to the adoption of these methods in each case. The Mining Methods Committee has drawn up an Outline for Papers on Mining Methods to be distributed among mining engineers and operators, giving in detail the information desired. This outline is the result of several months of careful thought and is a composite of the suggestions of many engineers and mining company officials from all parts of the United States.

Jan 7, 1922

By C. O. Lee, Z. W. Bartlett, R. H. Feierabend

The Grand Isle sulfur mine is located in the Gulf of Mexico, approximately seven miles off the coast of Grand Isle, Jefferson Parish, La. The deposit is on acreage covered by oil, gas, and mineral leases originally issued in favor of Humble Oil & Refining Co. by the State of Louisiana which were continued, maintained, and redesignated by the U.S. Department of the Interior after passage of the Outer continental Shelf Lands Act. The sulfur deposit was discovered in 1949 when Humble Oil & Refining Co. penetrated more than 200 ft of sulfur-bearing limestone in a zone between 1813 and 2075 ft below sea level. In 1954, Humble drilled ten more sulfur prospect holes, eight of which encountered sulfur ore.

Jan 6, 1960

By William J. Potter

The current financial environment differs markedly from past commodity price expansions, which have benefited the mining industry. Deregulation, financial innovation, and the globalization of capital markets in the 1980s have altered financing and investing patterns. Investment bankers and smart money within the industry have recognized the alterations and trends that facilitate fee revenue and profitable growth. This paper profiles transactions exemplifying change and documents financing techniques or instruments that have developed during the past half decade, emphasizing equity in the global marketplace.

Jan 1, 1990

By V. Lessels, W. A. Hamilton

White Pine Copper Co. is a wholly owned subsidiary of the Copper Range Co. The property of White Pine is about 5 miles south of Lake Superior in Carp Lake Township, Ontonagon County, Mich. The new town of White Pine, adjacent to the company plant, is 18 miles south and west of the town of Ontonagon, and about 55 miles north and east of Ironwood, Mich. A diamond drilling program begun in 1937 to develop the orebody was carried on until 1950. During this period a test shaft, known as the Schacht shaft, was sunk on the orebody and approximately 8000 ft of development drift were driven. In an effort to solve the ore beneficiation problems, considerable metallurgical test work was done on ore extracted through the mine development. This work was conducted in a small pilot plant located in the mill of the Copper Range Co. at Freda, Mich.

May 1, 1956

HOWARD N. EAVENSON, Chairman C. T. HAYDEN, Vice-chairman, Bituminous Coal Production CHARLES DORRANC~ Vice-chairman, Anthracite Coal Production HOWARD P. ZELLW, Vice-chairman, Evaluation of Coal for Coke Making W. H. F'LTLWEILER, Vice- Chairman Gas and Its Manufacture 3. B. MORROW, Vice chairman, Coal Preparation

Jan 1, 1928

By Anson Hayes, John Chipman

THE quality of sheet and strip products made of rimming steel is closely related to the structure and chemistry of the ingots. The variation in composition throughout the ingot, as affected by segregation, is of great importance, as are also the form and distribution of the voids that result from the gases evolved. It is because of this importance that the considerable literature in this field has accumulated. No attempt is made in the present paper to compile a bibliography of the excellent work that has already been done, as this has been adequately covered in the many excellent reports on the heterogeneity of steel ingots prepared by a joint committee and published by the British Iron and Steel Institute.1 From time to time, in any field of investigation new tools and new technique are developed, which make further progress possible. In the field with which this paper is concerned, this is true. The development of the vacuum-fusion method as a means of following oxygen segregation, and a technique for obtaining the volume and composition of the gases evolved during solidification, have opened the way to obtaining data by means of which some considerable progress has been realized in developing more of the detailed mechanisms of solidification and segregation in rimming-steel ingots. GENERAL THEORY OF SEGREGATION The basic cause of segregation lies in the fact that the impurities are less soluble in solid than in liquid iron. The solid that forms from the impure liquid is more nearly pure than the liquid itself. If solidification proceeds slowly enough, or if the liquid and solid phases are maintained in contact with one another for a sufficient time, a condition of equilibrium is set up, which may be represented by a phase diagram. Portions of the

Jan 1, 1938

ALABAMA Anniston. Carrington, F. G. Ashland.-Herr, I. Auburn.-Brown, R. L. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Salmon, H. S. Schaber, C. F. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Ball, E. M. Bonnyman, J. Bowron, J. Bush, M. W. Crawford, G. G. Crockard, F. H.

Jan 1, 1917

E. T. Dumble, Houston, Texas (communication to the Sec-retary?):—In addition to the list of publications mentioned by Mr. Schorr and those by Prof. Hofman, I call attention to the following references:— Sludi sulle Lignite, by Capacci. Turin (1890). (An excellent work.) Report of Brown Coal Industry in Germany. J. Cosmo New-berry. Department of Mines, Victoria (1892).

Jan 1, 1905

By L. Burris, C. H. Stockman, I. G. Dillion

Zone melting is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Equations are presented which 1—predict the concentration profiles after successive passes of the zone and 2—give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing in the last zone length. These equations were solved numerically using an electronic computer, and the concentration profiles are presented as a function of the solute distribution coefficient and the ratio of molten zone to total bar length. ZONE MELTING is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Separation occurs if the solid freezing from a solution at any moment has a composition different from that of the liquid from which it is freezing. Solutes which lower the freezing point will tend to remain in solution and will be moved in the direction of zone travel. Solutes which raise the freezing point will preferentially freeze out, and they will be moved in a direction opposite to that of zone travel. After repeated unidirectional passage of a molten zone through a bar of material, impurities will be concentrated in the ends of the bar. A limiting concentration gradient will be reached in the bar after a large number of passes of the molten zone. Both the magnitude of this limiting concentration gradient and the rate of movement of solute in any pass depend on the zone length and on the equilibrium concentrations of solute in the liquid and solid phases. The basic theory of zone melting was thoroughly covered by Pfann.1 The purpose of this paper is to extend the theory of zone melting by presenting 1—equations which relate the concentration profiles in successive passes of the zone and 2—equations which give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing* in the last zone length concentration of a given solute in the solid to the concentration of the same solute in the liquid. Analytical methods for determining the concentration profiles after any pass have been developed by Lord2 and Reiss. The method developed by Lord does not take into account normal freezing in the last zone and also becomes very complicated when the number of passes becomes large. The method developed by Reiss enables the direct calculation of the complete concentration profiles (including that in the last zone) after any pass for values of k close to unity (0.9 < k < 1.1). Both methods are useful and provide valuable insight into the zone melting process. The equations given in this article are based on the same assumptions used by Pfann. These are: 1—uniform composition in the liquid, 2—negligible diffusion in the solid, 3—constant distribution coefficient, 4—constant length of the liquid zone (except at the ends), and 5—solubility of the solute in the melt is not exceeded at any point. Equations for Concentrations in Successive Passes For a melted zone of length 1 at the left-hand end of a bar of uniform unit cross-section, the amount of solute in the liquid is J0Cn-1(x) dx [1] where the subscript is the number of the pass. Cn-1(x) represents the concentration (expressed as weight per unit volume) obtained in the previous

Jan 1, 1956