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Jan 8, 1950

By Mark C. Malamphy

During colonial times, Brazil was famous for the richness of her alluvial gold deposits. Paul Ferrand has estimated that the gold produced during the period from 1700 to 1820 was the equivalent of some 64 million pounds sterling. Since that time, most of the more prolific alluvial deposits have been exhausted. A few gold mines are still functioning, notably the Morro Velho mine, which is one of the deepest mines in the world. Today, the gold production of Brazil is insignificant when compared with world figures, but there are still many gold-bearing regions and it is probable that in at least some of them profitable returns would result from an exploitation program taking advantage of all the most modern innovations in gold mining and ore treatment on a large scale. In order to demonstrate the value of some of these abandoned prospects and stir up interest in increasing the national gold production, the government has stimulated research. Experimental plants have been and are being established in various places, and tests on large quantities of ores are being carried out on a semicommercial basis. The Geological Survey of the State of Minas Geraes is very active in this line and the Federal Institution is also showing an increased interest in the matter. One of the lesser known gold-bearing regions of Brazil is in the vicinity of Lavras, in the State of Rio Grande do Sul. Gold was first reported from this region in the early part of the nineteenth century. In 1811, D. João VI sent an experienced prospector from Minas Geraes to investigate the validity of the reports. According to the reports of Baron Eschwege, he succeeded in extracting some 30,000 Oitavos (about 105 kg.) during the first few years, but the production costs exceeded the value of the gold obtained.

Jan 1, 1934

By Robert Glass Cleland

IN SPITE of its widely ramified interests in manufacturing, mines, lumber, railroads, and real estate, Phelps, Dodge & Co. remained primarily interested in exporting and importing, in buying and selling, and William E. Dodge, the directing-partner, consistently styled himself a merchant. After 1849 the profits of the company mounted steadily for seven years until they approached the half-million mark, but in 1857 another severe panic ended the long period of national prosperity that had begun some fifteen years before. Extravagance, indebtedness, and inflation again took their costly toll; or, as the New York Herald of June 27,1857, declared: Governmental spoliations, public defaulters, paper bubbles of all descriptions, a general scramble for western lands and town and city sites, millions of dollars, made or borrowed, expended in fine houses and gaudy furniture; hundreds of thousands in the silly rivalries of fashionable parvenues, in silks, laces, diamonds and every variety of costly frippery are.only a few among the many crying evils of the day. The worst of all these evils is the moral pestilence of luxurious exemption from honest labor, which is infecting all classes of society. The country merchant is becoming a city stock-

Jan 1, 1952

By C. H. Ferguson

The fact that little if anything has appeared in the technical press or in the Transactions of the Institute on the subject of roll shells proper, used in various grinding appliances…

Jan 1, 1915

By H. M. Roche

MAGNETITE is the important iron ore of New Jersey although bog ore, limonite and red hematite were mined in sizable quantity early in the state's min-ing history. The deposits of mag-netite are found in the Highland area in the northern part of the state. These ores outcrop a broad belt 20 miles wide, extending in a northeasterly direction from Phil-lipsburg, on the Delaware River, to Greenwood Lake, at the southern boundary of the state of New York, a distance of 60 miles. The area in which the magnetite is found (see map, Fig. 1) contains 1200 square miles and the center of the area is at Dover, 40 miles west of New York City. In the general area are found 18 parallel ranges or lines of ore deposits. These ranges may be re-garded as mineralized zones in which occur orebodies that are rich enough in magnetite to war-rant mining. Usually a number of the orebodies lie one above the other in the same plane, all dipping and pitching in the same direction. Within the ranges, there may be several parallel orebodies of work-able size. The average strike of the orebodies is N.41° 30' E., with an average dip of 55° southeast and an average pitch of 15 ° to the northeast. Orebodies suitable for mining range from 6 to 100 ft. wide, as measured from foot wall to hanging wall. Their heights, as measured on the dip and normal to the long axis of the orebody, vary from 200 to 3,000 ft. The length along the pitch has never been determined by mining, al-though several of the orebodies have been worked to lengths of 10,000 ft. The grade of the ore as mined today varies from 30 to 60 per cent iron, and the gangue min-erals are chiefly silica, alumina, magnesia, lime and phosphorus.

Jan 1, 1937

By J. E. Tobey, David R. Mitchell, J. H. Kerrick

DETAILED knowledge of purchase specifications established by coal consumers is essential to the successful design and operation of a coal-preparation plant. ANTHRACITE Specifications should be considered by both the consumer and the producer as guide posts outlining a certain path for both to follow. Plants differ, therefore specifications must differ to meet the varied requirements. Specifications are not of themselves a "cure all" or an assurance of complete satisfaction in fuel utilization. Specifications should not be regarded as a license to engage in an orgy of buying any and all coals that may happen to fall within their limits. This would lead to the-indiscriminate mixing of coals which may vary in their burning characteristics. Different coals of equal grade tend to be individualistic in their burning characteristics. Rather, specifications should be used to help simplify coal selection, to reduce the actual number of coals used over a given period; in other words, to have a stabilizing influence on coal or customer turnover. In the final analysis, the use of too many coals per year in a plant is costly to both the consumer and the producer. Too many sources usually result in higher operating and maintenance costs for the consumer and higher sales costs for the producer. Finally, the statement included in the report accompanying the comprehensive Coal Selection Charts prepared by the Coal Committee of the National Association of Purchasing Agents, and released in 1938, is significant. This Committee worked diligently for a period of 15 years seeking to find a scientific and reliable method for selecting coals. The two following paragraphs are quoted from its report: More important is the fact that no ready-made classification or set of specifications can possibly replace the judgment and resourcefulness of an experienced combustion engineer, or fuel technologist, nor the usual need for full scale plant tests under the exact conditions of use before a final decision is made . . .

Jan 1, 1943

By M. Schmellenkamp

By comparing two longwall operations, one begun in 1956 and the other in 1960, the author is able to demonstrate the increases in production and performance made possible by longwall mining. These achievements have been brought about by continuous development of longwall mining equipment and associated roof supports. Because of this progress, longwall mining is able to provide, under proper conditions, high production per man-shift, remarkable cost savings, dependable roof control, safe working conditions and truly continuous production. It may seem odd that the title of this paper is not simply "Longwall Mining" but instead "Progress in Longwall Mining." However, the word "Progress" definitely has its place in longwall mining. If it had not been for progress in the development of longwall mining equipment and roof supports, the longwall mining method would not be able to compete in production and performance with modem coal mining machines. The longwall mining method was practiced at the beginning of the century and there were several successful operations in coal fields in Illinois. In those early days of longwall mining, the coal was undercut by hand 2 to 2.5 ft at the bottom of the seam and packwalls were built in the gob to support the roof. The roof eventually subsided and the weight of the subsiding roof was used to ride the face and break the undercut coal. Utilizing natural weight to soften the coal face is still practiced in modern longwall mining; however, the packwalling method has been replaced by the caving method and the roof is now supported by yielding steel roof supports and forepoling steel headers. The purpose of these yielding-type roof supports is to provide a safe working area for the crew along the entire longwall face, to permit continuous mechanical mining across the prop free face, and to provide a strong resistance for the roof by forming an even breaking line at the gob for the roof to cave. Roof supports and associated forepoling headers should be kept as close as possible to the face in order to prevent a caving between face and supports, especially under friable roof. This means that the coal should be extracted in small slices, allowing only a narrow roof area to be exposed and unsupported. The coal planer with its relatively high cutting velocity of 75 ft per min provides such an extraction of coal and has proved its high performance under difficult mining conditions. Since 1951, several longwall faces in southem West Virginia and Pennsylvania which have been equipped with the coal planer and friction-type manual roof supports have been successfully operated. Compared to today's longwall mining, these longwall faces required such a large crew, primarily to handle the roof supports, that the actual high production per shift was charged with too high a labor cost, thereby decreasing the tons per man. Yet, even then the longwall faces outperformed the conventional mining system under the same conditions. In order to demonstrate the progress that has been made in the development of longwall mining, a comparison will be made between a longwall face in Arkansas which was installed in 1956 and a modemized longwall face started in 1960 in southern West Virginia. LONGWALL MINING IN 1956 The 320-ft longwall face was developed in a 32-in. thick coal seam near Greenwood, Ark. The method of mining the 320-ft coal block was the advancing system in which three entries on either side of the face were driven ahead of the advancing longwall face. The face was equipped with a coal planer and a Panzer conveyor; timbering was done with wooden timbers and cribs. The roof supports were set without any pattern. The crew to operate the planer and to handle the roof supports (timbers and cribs) consisted of 15 men per shift. During a period of approximately eight monthsof single shift operating time, the average tonnage produced in this relatively low seam amounted to about 263 tons of clean coal per shift. To show the development in the coal plow from then until now, it should be pointed out that the standard plow was used in this operation. The plow was equipped with rigid bottom bits which could not be adjusted if the plow started to climb, thereby leaving bottom coal to be recovered by pick hammers end causing delays in production. The height of the plow

Jan 1, 1963

By Clarence Carleton Semple

At a number of mines in eastern Nicaragua, 3.5- or 5-ft. Huntington mills are used for grinding gold-ore after a pre-liminary breaking in jaw-crushers. The smaller mills are made sectional to facilitate transportation to the more difficultly accessible mines. The capacity of the smaller mills is about 20 or 25 per cent. that of the larger, but in proportion to the quantity of ore ground they require more power and are subject to greater wear. The notes herein given are from records of the performance of the larger mills at one of the mines, but, in general, apply to the smaller mills also. The Nature of the Ore. The ore occurred as a series of flat veins in a' highly-decomposed rock, probably alaskite. The primary mineralizatioll comprised pyrite, pyrrhotite, marcasite, chalcopyrite, and quartz; the oxidation-products of which were chiefly hydrated iron oxide or limonite, chrysocolla, azurite, and malachite. The kaolinization of the feldspar of the country resulted in the admixture of a great quantity of clay with the oxidized ore. The quartz was sandy, imbedded in the clay; and probably the greater part represented the residue from the crushed rock in the fissures after leaching, and kaolinization of the feldspar. There was little vein-quartz in the unaltered primary sulphide ore. Only the oxidized ore was mined for the gold that it contained in amouiits that averaged $4 per ton. No specks of gold mere ever seen in the ore, and the gold obtained by panning was always exceedingly fine. The amalgamation-bullion was about 800 fine in gold and from 60 to 80 in silver. The ore delivered at the mill contained from 5 to 15 per cent. of moisture; during the rainy season the quantity was much greater. The moisture and clay made the ore so sticky that it had to be raked over steeply-inclined grizzlies; it hung in the ore-bins,

Jan 1, 1912

By Hiro Minagawa

Japan's contact with the mining industry of British Columbia began as far back as 1952 with the first shipment of iron ore from the Texada mine. Five years later, the Big Three steel mills of Japan-that is, Nihon Kokan Kaisha, together with Yawata and Fuji Steel Mills-dispatched a coal survey mission to inspect coal mines in British Columbia. This resulted in 100,000 tons of coking coal being initially imported by Japan from western Canada in 1959. Also in 1959, Yawata, Fuji, NKK, Kawasaki and Sumitomo sent an iron ore survey group to Alaska and Canada. During the preceding year, Nippon Mining Company and Sumitomo Metal Mining Company initiated a project whereby they would assist in the development of Cowichan Copper on Vancouver Island. As a net result of this activity Japanese mining groups, who had heretofore concentrated on Southeast Asia and South America, finally turned their eyes toward Canada. It was in the fall of 1960 that the government of Japan, in order to keep pace with Japan's rapid economic development, announced a long-range economic plan whereby her gross national income would be doubled by 1970. This had the effect of further propelling Japan's desire to develop sources of raw material supplies abroad. With the development of Craigmont Mines and the signing of a long-term contract to export copper concentrates to Japan, and with the Sumitomo group's extending financial assistance to develop Bethlehem Copper, Canada itself began to realize that Japan was indeed a very important market for British Columbia. A number of surveys to develop mines in British Columbia was begun with an eye on Japan as the major market, and the activity has continued to this day.

Jan 12, 1963

THE preceding chapter has recorded the initiation of mineral industry education during the period 1890-1910 in numerous institutions that had not previously offered it. It should also be emphasized that in many institutions where instruction had begun before 1890, as recorded in earlier chapters, but had not yet become firmly established, this period was one of marked growth and development. This was not universally true, however, for at the Universities of Pennsylvania, Michigan, Illinois, Wisconsin, Washington (St. Louis), Iowa, Vanderbilt and Tennessee, and at the Polytechnic College of Pennsylvania, mineral industry instruction was being dropped during this period, instead of gaining in strength. It is necessary to emphasize this, because writers on the subject have not infrequently attempted to make a much too simple correlation between mineral discovery or production and the intensity of student interest in mineral industry curricula. It would naturally be true that periods of large mineral production would, in general, coincide with cycles of business prosperity, and the latter are conducive to starting new ventures, educational as well as business. It should be equally evident that opportunities for business and professional success might, in such periods, appear to increase at a more rapid rate in industries other than mineral, or in the utilization of minerals rather than in their production. The author has not been able to perceive any simple and clear relation between interest in mineral industry education and mineral discovery, production, and utilization, or general business prosperity. On the contrary, the more the problem is studied the more complex the factors involved in it appear to be. In a later chapter an attempt will be made to analyze them in more detail

Jan 1, 1941

By James M. Link

The design and construction of cross-country pipelines for fluids such as crude oil appears relatively simple compared to the complex problems encountered in slurry systems. Considerable effort has been expended in hydraulic research laboratories in an attempt to improve the understanding of slurry behavior. This effort has been rewarded with considerable success and is best illustrated by the large number of slurry systems now planned or under construction. However, slurry transport in pipelines is still, in many instances, more of an art than a science. In order to minimize the risk factors in the construction and operation of large scale slurry systems, studies are frequently conducted in pilot scale test loops such as the one at the Colorado School of Mines Research Institute. The pilot scale projects are designed to provide the basic engineering data necessary to design slurry transport pipeline systems. Usually three slurry solid concentrations are pumped at various line velocities and optimum slurry densities and velocities are determined. Critical velocities, friction head losses, power requirements, and so forth, are also determined from measurements and calculations. Wear tests are also strongly recommended and anticipated pipe wear rates in inches per million tons of solids reported.

Jan 11, 1972

By T. Sterry Hunt

THE geognostical relations of the metals and their ores present many problems of great interest, alike for the geologist, the chemist, and the mining engineer. The association with certain rock-formations of characteristic mineral species may help to guide the geologist in the identification of geological horizons, and throw light on the chemical activities which have been especially manifested in certain periods; while it is clear that such relations, if established, must be of great utility to the miner, and especially to the explorer of new regions. In inquiries of this kind, however, it is only by careful observations over wide areas, and by the collocation of a great number of facts, that anything like a safe basis for induction can be attained. The effects of hasty and imperfect generalizations in this field have already in many instances been felt to the prejudice of scientific progress. I come before you to-night, therefore, not to lay down any laws or general principles, but to call your attention to certain facts, many of them doubtless known to you, which have forced themselves on my attention, with regard to the associations of various metallic ores and other useful minerals with different series of stratified rocks, and to ask you to aid the progress of this branch of geognostical inquiry. Your observations in the various regions to which you may be called by your professional duties will enable you to determine how far these associations are mere coincidences, and how far they are chemical and geological constants. The associations here to be noticed concern only those mineral species which occur, either distributed through the strata in such a manner as to show that they are contemporaneous deposits, or occupy rifts or gash-veins in these strata, and may be supposed to have been

Jan 1, 1873

By T. Sterry Hunt

THE geognostical relations of the metals and their ores present many problems of great interest, alike for the geologist, the chemist, and the mining engineer. The association with certain rock-formations of characteristic mineral species may help to guide the geologist in the identification of geological horizons, and throw light on the chemical activities which have been especially manifested in certain periods; while it is clear that such relations, if established, must be of great utility to the miner, and especially to the explorer of new regions. In inquiries of this kind, however, it is only by careful observations over wide areas, and by the collocation of a great number of facts, that anything like a safe basis for induction can be attained. The effects of hasty and imperfect generalizations in this field have already in many instances been felt to the prejudice of scientific progress. I come before you to-night, therefore, not to lay down any laws or general principles, but to call your attention to certain facts, many of them doubtless known to you, which have forced themselves on my attention, with regard to the associations of various metallic ores and other useful minerals with different series of stratified rocks, and to ask you to aid the progress of this branch of geognostical inquiry. Your observations in the various regions to which you may be called by your professional duties will enable you to determine how far these associations are mere coincidences, and how far they are chemical and geological constants. The associations here to be noticed concern only those mineral species which occur, either distributed through the strata in such a manner as to show that they are contemporaneous deposits, or occupy rifts or gash-veins in these strata, and may be supposed to have been

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Jan 12, 1959

By Alden B. Greninger

In a recent study1 of the deformation of metastable beta copper-zinc and beta copper-tin crystals, it was established that the parallel markings that appear on the surface of these crystals after slight deformation represent lattice transformations. Stereographic analysis showed that in beta copper-tin, the poles of these markings deviated one or two degrees from poles of the form {133}. In beta copper-zinc the plane delineated by the markings corresponded to no one crystallographic plane of the matrix lattice; the marking poles deviated from 5° to 11° from poles of the form (110), and were displaced only a few degrees from (110) zones. Inasmuch as the new transition lattices produced as the result of the deformation are different for each alloy, it was thought at first that the habits of the markings might be the result of a cooperation between matrix lattice and transformed lattice. (Both matrix lattices arc body-centered cubic.) Such a cooperative effect is thought to obtain in the formation of Widmanstätten figures, for it is well known that the matrix lattice alone does not determine the habit assumed by a segregate phase. On the other hand, it is not inconceivable that the dissimilarity in marking habit might be due to differences in deformation characteristics of beta brass and beta bronze. Barrett and co-workers2 have shown that slip-line habits in pure iron are markedly different from those in high-silicon ferrite; and although it has been repeatedly demonstrated that plates of a segregate phase do not necessarily form on the slip planes of the matrix lattice, deformation characteristics may be more intimately allied with plate formation when a transformation is made to occur as a result of plastic deformation. However, there is the fact that the orientation of markings in metastable beta copper-zinc is the same whether the markings be produced by quenching, deformation, or liquid-air cooling; likewise, quenching and deformation markings in metastable beta copper-tin are oriented in the same way with respect to the beta matrix. During the course of the investigation referred to above, samples of 52:48 (stable beta) copper-zinc were deformed and examined micro-

Jan 1, 1938

By Alden B. Greninger

In a recent study1 of the deformation of metastable beta copper-zinc and beta copper-tin crystals, it was established that the parallel markings that appear on the surface of these crystals after slight deformation represent lattice transformations. Stereographic analysis showed that in beta copper-tin, the poles of these markings deviated one or two degrees from poles of the form {133}. In beta copper-zinc the plane delineated by the markings corresponded to no one crystallographic plane of the matrix lattice; the marking poles deviated from 5° to 11° from poles of the form (110), and were displaced only a few degrees from (110) zones. Inasmuch as the new transition lattices produced as the result of the deformation are different for each alloy, it was thought at first that the habits of the markings might be the result of a cooperation between matrix lattice and transformed lattice. (Both matrix lattices arc body-centered cubic.) Such a cooperative effect is thought to obtain in the formation of Widmanstätten figures, for it is well known that the matrix lattice alone does not determine the habit assumed by a segregate phase. On the other hand, it is not inconceivable that the dissimilarity in marking habit might be due to differences in deformation characteristics of beta brass and beta bronze. Barrett and co-workers2 have shown that slip-line habits in pure iron are markedly different from those in high-silicon ferrite; and although it has been repeatedly demonstrated that plates of a segregate phase do not necessarily form on the slip planes of the matrix lattice, deformation characteristics may be more intimately allied with plate formation when a transformation is made to occur as a result of plastic deformation. However, there is the fact that the orientation of markings in metastable beta copper-zinc is the same whether the markings be produced by quenching, deformation, or liquid-air cooling; likewise, quenching and deformation markings in metastable beta copper-tin are oriented in the same way with respect to the beta matrix. During the course of the investigation referred to above, samples of 52:48 (stable beta) copper-zinc were deformed and examined micro-

Jan 1, 1938

By Samuel L. Hoyt

The present report represents that part of the work that has been done by the War Minerals Investigation, Manganese Section, of the Bureau of Mines, on the use of manganese alloys in open-hearth practice. The magnitude of the work and the number of people participating in one way or another make it difficult to acknowledge adequately the services of all who have contributed to the success of the work. It would be amiss, however, to pass to the body of the report without mentioning the hearty cooperation and willingness to assist of the various manufacturing interests. With such a sympathetic attitude toward this investigation, our work was assured of success. Inasmuch as the unhappy circumstances that rendered this investigation necessary have now passed, this report is made in the hope that the results may prove of some permanent value to the peace-time operation of our open-hearth industry. Broadly speaking, the purpose of the manganese investigation was to consider the most suitable means of utilizing our domestic supply of manganese and thus relieve, to the maximum extent possible, our shipping of the burden of importing manganese ores. It was not held that any decided shortage of manganese was imminent but rather that every legitimate means should be utilized for making our ship tonnage available to European service. While we have considerable metallic manganese in this country, it occurs largely as a low-grade mixture with iron or silica or with both. The open-hearth investigations, therefore, were carried on to determine the extent to which domestic or low-grade alloys could properly be substituted for high-grade alloys without materially impairing the steel production as to either quality or quantity. Also, it was held that such an investigation would yield valuable results to the steel industry as well as contribute, in no small way, toward directing future investigations in the same field. To the practical steel manufacturer, especially to him who felt no immediate concern about

Jan 1, 1920

By K. A. Natarajan, I. Iwasaki

The meaning and the utility of redox potential (Eh) measurements in sulfide flotation systems are examined. Since some preliminary plant Eh and laboratory flotation data were available, experiments were made to establish the pH range at which a platinum electrode might be used for such measurements without much difficulty in aerated systems. Triangular wave voltammetry was used to study the surface conditions of the electrode immersed in pyrrhotite suspensions at different pH. The measured Eh both at the plant and the laboratory is interpreted in terms of the experimental water-oxygen line.

Jan 1, 1974

By N. E. Maccallum

Almost half a century has passed since the Siemens brothers, after tedious and costly experiments, finally began the manufacture of open-hearth steel. The furnace of that time was very small, having a hearth-capacity of from 3 to 4 tons, and we can appreciate the wonderful development that has taken place in those 50 years by the knowledge that to-day furnaces of 50 times the original capacity are in operation. As the new steel process assumed importance, and furnaces began to grow in number and in size, a question arose, to which no satisfactory answer has ever been given, and that was: aWhat is the safe and economical limit of the open-hearth furnace ?" Various stopping-places have been suggested, and 20, 30, 40, and 50 tons have each been advocated, but all such arbitrary restrictions have been passed, and 60 tons would probably represent the average furnace, although in a few instances from 70 to 80 tons are regularly tapped into one ladle. The furnaces which are the subject of the present paper have gone far beyond even these limits, and since, in my opinion, they mark another step in the progress of open-hearth steel, they will be considered fairly and frankly, in order that those to whom the matter may be of interest may be able to judge and form their own conclusions. Short accounts of the work of these furnaces have appeared from time to time in various technical journals, of which the following is a brief résumé. These furnaces are the property of the Phoenix Iron Go., of Phœnixville, Pa., and their distinctive and important feature is, that they charge to twice the capacitl of one ladle, and tap simultaneously into two ladles, with a device for controlling the flow into either. In this way the capacity of the furnace is not limited, as formerly, but heats of any size within the capacity of two ladles may be charged.

Jan 1, 1913

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.