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By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By R. C. Patterson

IN view of the circumstance that very few important changes have been made within the last 15 or 20 years in the equipment of rod and wire mills, the description of a new process introduced by Grenville Mellen, of Llewellyn Park, N. J., to take the place of the present laborious system of producing rods of lead, zinc, brass, copper, aluminum, etc., may be interesting to members of the Institute. This new process consists in the production of cast rods at one operation in a small continuous casting machine. The hot liquid metal is transferred from the melting crucibles directly into an endless chain of mold blocks in the machine, where solidification takes place, and the rod comes out continuously in a solid form at one end as long as the molten metal is supplied. The operation of these mold blocks so as to produce a solid rod of uniform structure constitutes an important part of Mr. Mellen's invention. The machine (Figs. 1 and 2), 12 ft. in height over all, 2 by 3 ft. in horizontal- cross-sectional area, and 6,000 11). in weight, has a framework of cast iron, holding in position two endless chains of mold blocks, which are made in sections and join in center alignment. The mold orifice is made up of these mold sections, into which the liquid metal flows. The molding chains are composed of steel blocks, grooved on one face to form the molding cavity, and linked together with flexible joints. Each block is carried on four rollers which guide the chain around the end sprockets and carry it in its course through the machine. The accuracy of alignment requisite to the production of a perfect rod in the mold groove formed by these sections is secured by careful machine work, and by building the four ways, down which the alignment takes place, so that two of the sides are fixed permanently, while the opposite sides are held to their position by spring pressure. The guides carrying the molds, while in casting position, are water-cooled square tubes.

Jan 5, 1915

By R. H. Eckhouse, M. R. Geer, H. F. Yancey, C. L. Allyn

Four coals were treated in the Humphreys spiral concentrator, and the products were examined by float-and-sink and screen-sizing tests to determine fundamental performance characteristics. The efficiency of the separation between coal and impurity was shown to be influenced greatly by particle size.

Jan 10, 1950

Jan 1, 1938

By H. B. Pulsifer

ABOUT 15 varieties, or modifications, of the best magnesium available were prepared and subjected to etching tests, then examined for microstructure. Of the 30-odd etching reagents that were tried, nearly half, mostly ammonium salts, etched the metal satisfactorily. The surfacing and etching of magnesium is shown to be a very simple and quick operation. The density and hardness of magnesium were determined. The most interesting new observations relate to the finding of the hexagonal etch figures, the crystal laminations, and the fact that the metal is plastic, cold, when restrained or quickly deformed. Under slowly applied pressure cold metal deforms slightly, then shears to fracture without plastic flow. The chief structural features of magnesium are presented in two reduced photographs and 30 photomicrographs. MATERIALS TESTED There are only two sources in the United States from which new metal can be procured: the American Magnesium Corpn. and the Dow Chemical Co. No pronounced structural or property differences in the metals from these two companies were disclosed by the work of this investigation. The following materials were obtained from the manufacturers: 1. Massive crystals of distilled metal (American Magnesium Corpn.). 2. Rods of hot-extruded metal, ½ -in. squares and 5/8-in. rounds (American Magnesium Corpn.). 3. Sheet magnesium, 0.005-in. thick (American Magnesium Corpn.). 4. Cast stick metal, 1 3/8-in. dia. (Dow Chemical Co.). 5. Magnesium-aluminum alloy, hot-rolled plate, ½ in. thick (American Magnesium Corpn.). From these materials, were prepared: 6. Sections from a furnace-cooled ingot made from distilled crystal. 7. Cold-strained pieces from (6), (4) and (2). 8. Pieces cold-squeezed to fracture from (6), (4) and (2). 9. Hammer-struck pieces from (6), (4) and (2). 10. Steam-hammer struck pieces from (6), (4) and (2). 11. Sections from furnace-cooled ingot of the magnesium-aluminum alloy.

Jan 1, 1928

By F. C. Sturges

FOR some time mining engineers have been interested in the possibility of using small diameter shafts, sunk by core drilling, as aids to ventilation and as emergency escapeways. The possibilities are interesting to contemplate, but new methods involve unknowns, and interest tends to remain passive until these unknowns are solved. Recently we have completed two 36-in. diam. core drilled shafts, and wish to make the data on these available to the industry. Both shafts were drilled for the McLain Fire Brick Co., one at its Buckeye mine and the other at its Colonial mine. Both mines are in the fireclay underlying the Lower Kittanning coal. Both mines have been in operation for a number of years [ ] and have required expensive maintenance work on return airways. It was decided that considerable savings could be effected by short-circuiting the air to the surface through small shafts. It was also realized that these holes, located near the present workings, would be of added value as emergency escapeways. Originally, 48-in. diam. shafts were considered, but actual computations showed 36-in. diam. shafts were more than ample at both mines. The shaft at the Buckeye mine is 240 ft deep, and that at the Colonial mine 258 ft deep. Both holes were started in the lower part of the Conemaugh formation and penetrated Conemaugh and Allegheny strata. The holes were started through the unconsolidated materials overlying bedrock by constructing a concrete collar with a wall thickness of 8 in. Then the shafts were drilled by the shot-core drill method. An annular groove was cut in the rock by the abrading action of chilled steel shot run under the shoe of the core barrel. The drilling was done in stages, the core barrel drilling the groove for a certain distance depending on conditions encountered, and then the cores broken off and taken out in sections. The core barrel had a 36-in. o.d. and the finished diameter of the shaft measured almost 37 in. The major questions that could not be answered until the completion of the first shaft were, (I) how much ground water would be encountered, how would it hinder the drilling, and how difficult would it be to seal off, and, (2) how would the walls of the hole stand up. The holes of course could be cased or lined, but that is considerable added expense in any shaft.

Jan 1, 1947

By J. Kostuik, M. J. de Bastiani

Located in the Elliot Lake mining district of Canada, the Denison mine lies between Sudbury to the east and Sault Ste. Marie to the west. This area is overlain by Huronian sediments filling a basin in the Keewatin basement complex. Subsequent folding of these sediments developed a synclinal structure, known locally as the Quirke Lake Trough, which forms the northern portion of the now famous big Z structure, the geological trademark of this region. Plunging to the west and extending nine miles from the granite outcropping in the north to the Keewatin lava contact to the south, the syncline has dips of 10° to 45° on the north limb and 10° to 20° on the south limb.

Jan 12, 1960

By C. P. Proctor, E. D. Hummer, J. A. Younkins

COMPARATIVELY little has been published relating practical experience with the control of the solid content of washery water systems that must be "closed." A "closed" system is one that for some reason may not be cleaned by the emission of any effluent of high solid content to be replaced by clean water in order to hold the solid content of the waste water within reasonable bounds for efficient washing. It is the purpose of this paper to describe practical experience with such a water system and to present data that it is hoped may be of some use to those who are faced with a similar problem. The washery clarification system described comprises three thickeners and three filters, and although it is admitted that each of the fields of water settling and thickening and filtration offers a wide scope for investigation, the authors are not attempting to present the answers to these problems but to set down the results of some experience along these lines, making no claims as to the ultimate solution of the problems in hand. The subject of water clarification has vast ramifications; for example, the science of flocculation as applied to water settling and filtering opens up fields of wide possibilities of which as yet little is known. A comparatively recent entry into the field of water treatment, which may offer possibilities of practical application, is the use of "wetting" agents such as "Aerosol." GENERAL ARRANGEMENT OF WATER SYSTEM So that the reader may obtain a comprehensive picture of the factors concerned in the control of a closed water system, it is necessary to give a brief description of the washing plant that is serviced by the water system to be described in the following pages. As we are not primarily concerned with the washing plant in detail, only a brief description of the flow of coal as it relates to the water system will be given here. For a more detailed account of this type of washer, the reader is referred to earlier papers.1.2 The washer, which handles 0 to 4-in. raw coal (750 tons per hour) is an American Rheolaveur plant of two complements; the coarse coal or sealed discharge plant and the fine coal or free discharge plant. The sealed discharge plant (Fig. r) consists of twin 48-in. primary launders, each having two washing boxes, supplemented by one 32-in. rewash launder, which also has two washing boxes. "Push" water for washing and conveying coal in these launders is supplied from a constant-head tank under pressure head of 10 ½ ft. at the point of introduction at the feed end of the launder. This tank also supplies water for upward or vertical currents used in the Rheolaveur or washing boxes. Each box discharges into a sealed boot elevator (Fig. I).

Jan 1, 1942

By E. L. Jr. Spain

This study was undertaken primarily to determine the reasons for certain varia-tions in the soundness of gravel aggregate taken from a number of widely separated points on the Tennessee River. Under laboratory tests, concrete made with these various aggregates it some cases exhibited marked differences in specific gravity, crushing strength and durability. Gravel was studied in detail from Chattanooga to the mouth of the river and to a lesser extent from Chattanooga to Knoxville. The causes of variation were determined, and variational curves were constructed, which accurately predict the composition of aggregate at any point on the river and therefore its relative suitability for use in concrete. The aggregate at any point is suited for making sound concrete; the variance of suitability is due to varying percentages of sandstone and weathered material, which are less sound than other constituents.

Jan 1, 1937

A list of publications of the United States Bureau of Mines, complete from its establishment to the end of June, 1931, may be had upon request. In addition a monthly leaflet of new publications is issued and is sent to those on the mailing list of the Bureau. Publications are separated into three main divisions: 1. Sales Publications.-Those for which a charge is made. Any orders or remittances in payment for sales publications should be sent directly to the Superintendent of Documents, Government Printing Office, Washington, D. C., and not to the Bureau of Mines. Sales publications are classified into (1) Bulletins, (2) Technical Papers, (3) Economic Papers, (4) statistical reports of the mineral resources of the United States, (5) Monographs, (6) Handbooks, and (7) Schedules. Bulletins and Technical Papers present the results of scientific and technical investigations. Economic Papers are analytical studies of production statistics, sources, resources, .distribution, and industrial flow of mineral commodities. The Annual Report, entitled "Mineral Resources of the United States," includes chapters, published separately, on the production and consumption of metals and of nonmetallic minerals. Monographs give detailed results of extensive cooperative investigations of special

Jan 1, 1933

By Rudolph Gahl

RUDOLF GAIL, Miami, Ariz.-Since I wrote the paper on flotation which is in your hands, important developments have taken place, and, for this reason, I will try in a few words to bring it nearer up to date as far as the Inspiration plant is concerned. You, may have noticed that in the Inspiration concentrator, flotation is not solely relied upon for the recovery of the coarser material, but that flotation tailings are split into a sand and a slime product on drag classifiers. The sand product is treated on tables which thus supplement the work of the flotation machines. Extensive tests have shown, us that, if we wanted to, we could leave out these tables and substitute additional flotation machines, as they will make fully as good, if not a better recovery than tables on the deslimed feed, but the treatment would be more expensive, especially in view of the fact that oils are required which cost more than those which we are now using in our main flotation plant. We have, however, decided to apply flotation treatment to our table middlings. I would also like to add a few words regarding the treatment of oxidized copper ores. Although our experience shows that the addition of hydrogen sulphide and other soluble sulphides effects a very good recovery of copper carbonates with certain ores, we have not been able to prove that we could use it advantageously for the ore mixture which we are treating in our concentrator, and for this reason, have looked toward leaching for extracting the carbonate and silicate copper that we are losing now. Experiments in this direction are going on and are giving very encouraging results. It may interest you to hear that we intend to use limestone for the precipitation of the copper which goes into solution, as electrolytic precipitation seems to be out of the question on account of the diluteness of the resulting solutions, and precipitation by iron was rightly objected to on account of the unavoidable contamination of the water supply. We feel very hopeful about the success of our limestone precipitation which, if it holds what it seems to promise, will develop into a novel feature of copper metallurgy.

Jan 10, 1916

Dr. Wadsworth's discussion of leaching is straightforward and certainly points out some of the critical areas in regards to the fundamental aspects of leaching. I will address myself to the more practical aspects of leaching. As a couple of general comments, very fine particles are often dealt with only when necessary. In many processing applications the sands and slimes are separated with the sand portion being treated by common metallurgical techniques and the slime portion being treated essentially by any technology that will recover some of the values. Ore treatment techniques such as leach/precipitate/float (LPF) have been used in the copper industry to take advantage of leachable copper preferentially reporting to the fine fraction. The second advantage, of course, is the improved metallurgy associated with the treatment of the sand fraction. Cases can be made for sand/slime separations in the aluminum and uranium industry where most of the value reports to the slime fraction and the sand fraction is rejected In the agitated leach systems, fine particles are often the most readily attacked and leached. In dump, vat and in-situ leaching, fine particles cause considerable problems. The fines will tend to restrict the solution flow from portions of the leach feed. This either causes a significantly reduced solution flow or, more probably, the solution will channel, by-passing much of the ore. In either case the result is a decreased metal recovery from ore. The fine particles of principal concern are clays of a flat plate-like shape which can very effectively compact, swell and cause a decreased solution flow. Discrete silica grains or sulfide grains due to their shape, even though they may be very fine, will not cause nearly the problems clays and secondary precipitates can cause.

Jan 1, 1979

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, graduate Columbia School of Mines, age 35, married, best of health, dependable, desires position as manager or scout for reliable interests. Experience covers responsible positions incident to the mining and milling of gold-silver, copper, lead, and zinc ores, and the examination of base and rare-metal deposits in United States and Mexico. Salary $3600. Available April 1. No. 453. Member, mining engineer, technical training, age 32, assayer, engineer and superintendent of porphyry copper development, churn drilling and shaft sinking. Examination of prospects and development of gold prospects. Considerable flotation experience. No. 454. Young Columbia graduate, conscientious worker, with experience in inorganic analysis, surveying, draughting, and wit. post-graduate training in geology, desires position wt. prospects. Minimum salary considered, $130 in U. S. and $150 in Mexico. At present employed. Draft exempt. No. 455.

Jan 5, 1918

A MINING institute open to all men interested in any branch of the mining industry will be held at the Col-lege of Mines, University of Washington, Seattle, during the week beginning March 5. Prospectors, miners, mine owners, persons interested in metallurgy, investors in min-ing enterprises, and the public generally are invited to at-tend. This institute will take the place of the Winter Min-ing Session which originated at Seattle in 1897 and con-tinued for twenty-eight years. The complete new equip-ment of the Mines Laboratory will be used to give demon-strations of new machines and processes of mining, ore dressing, and metallurgy. This year the ceramic industry, including cement and branches of clay working of special Importance in the Northwest, will be included in the insti-tute. All instruction will be given by specialists. Prominent technical men and managers will give lectures on their special subjects. Among the speakers engaged are G. T. Jackson, formerly superintendent of the Alaska-Gas-tineau and the Chichagof mines, who will speak on the mining of large bodies of low-grade ore; R. F. McElvenny, superintendent of the Tacoma Smelter, on the nature of contracts that a smelter can offer to mines and prospects; M. D. Leehey, mining lawyer, on some popular errors re-garding the mining law; H. H. Townsend, on the explora-tion and purchase of prospects by operating companies; J. L. McAllen, on quartz mining in the Willow Creek dis-trict, Alaska; F. Powell, on gold dredging. In the evenings, lectures illustrated by stereopticon views and moving pic-tures will be given. The week will close with an excursion o mines and plants.

Jan 3, 1928

According to the June 27 issue of Business Week, Rep. Kearns (R., Pa.) introduced a bill in Congress along lines suggested by the National Society of Professional Engineers, to amend the Taft-Hartley Act to permit scientific, technical, and professional groups to discuss wages, hours, and working conditions with management-with the protection and support of the federal law. The article reports that the bill is opposed by a loosely knit group of professional and technical unions, the Engineers & Scientists of America. This group wants Taft-Hartley amended to make it an unfair labor practice for employers to discuss collective bargaining matters with professional organizations.

Jan 9, 1953

By Luther Lennox

THE purpose of this article is not to compare one type of grinding machinery with another and to conclude from a series of tests that one particular machine is superior to all others. Neither is the reader asked to tire himself with the details of many tests to prove the statements herein made. The Chilean mill stands today almost, in outcast from the milling world. It ranks with the applicant for a job who has been given a trial along with others and condemned because he was not able to perform the definite task assigned as well as the others, and was forever eliminated. The judges did not tarry long enough to try this aspirant in a field of a slightly different nature. Even though it has been condemned, the writer contends that the published records will indicate that the trials were never shifted into the field of greatest efficiency for the Chilean mill. Those of us who cling to this outcast as a fine grinder in our milling operations do not wish, naturally, to be condemned along with the machine, and yet we feel that we are classed as behind the times, at least in this phase of our milling judgment. Hence there is considerable personal feeling in our efforts. During the last few years there have been published several papers on the relative merits of the various grinding machines. In two of these articles a comparison was made between Chilean mills and cylindrical grinders. In each case the Chilean mill came out second best from about all standpoints. The outstanding feature in these comparisons would seem to be the decided attempt to keep all conditions the same, so that each machine could be judged on its merit. As Mr. David Cole states, "We are inclined to regard a direct comparison of grinders arranged side by side, and making a product that affords as nearly as possible the same screen measure, as the Supreme Court in these grinding matters." The writer agrees that this is the very best method for true comparison between machines. The results in the two detailed tests should give the relative merits of the two grinders in doing the work assigned. And they probably do. The conclusion drawn in each case was adverse to the

Jan 9, 1919

By E. P. Shea

The Anaconda Co.'s Geological Department at Butte, Mont., was started early in the Company's history because of litigation involving vein ownership and extralateral rights. The problems, some of which were resolved in courts, were many because of the large number of veins and lode locations. Defensive action was required to prove ownership and protect against illegal exploitation of the downward and extra-lateral extensions of the ore bodies. In many cases it was necessary to define the outcrop of the vein and to show that its apex was within the boundaries of the lode claim. Exhibits illustrating geology were needed to present the cases clearly, and these could be made only after careful inspection and mapping of the underground workings by competent geologists. Also, The Anaconda Co. was one of the first companies to recognize the worth of skilled mining geologists and the value of accurate records in the search for new ore. The department was organized in 1900 by H. V. Winchell who, with D. W. Brunton, worked out the methods. Reno Sales was Chief Geologist from 1906 until 1948 when he was succeeded by V. D. Perry, the present Chief Geologist. Under their direction, F. A. Linforth, M. H. Gidel, C. H. Steele, E. P. Shea, C. C. Goddard, Jr., and W. A. O'Brien enlarged the scope of the work and improved the technique.

Jan 3, 1961

Conquista, the uranium mining and milling complex owned jointly by Continental Oil Co. and Pioneer Nuclear, Inc., has begun operations in Falls City, Texas. The mill has been designed to produce 1.5 million lb of U3O, from 600,000 tpy of ore mined. Currently, the plant processes a maximum 2000 tpd of ore. Mine Planning Texas ore deposits are small and scattered in comparison to other uranium mining districts. Those to be mined at Conquista range from a few acres to more than 100 acres in size. Ore thickness ranges from a few inches to over 15 ft, and depth from less than 20 ft to more than 170 ft below ground surface. Distance from the mill ranges up to 35 mi.

Jan 8, 1972

By M. R. Louthan

The susceptibility of titanium to stress orientation of hydride precipitates was investigated. It was determined that, when hydride precipitation occurred in titanium under an applied tensile stress of 30,000 psi, the hydrides precipitated on the titanium habit plane oriented most nearly perpendicular to the stress axis. Stress orientation of the hydride platelets occurred because the precipitation of the lower density hydride phase perpendicular to the stress axis caused expansion of the matrix in a direction that tended to relieve the applied stress. The Ti-H system has received considerable study in recent years, mainly because of concern over the effects of hydrogen on the mechanical properties of titanium. The amount of hydrogen present in commercial titanium is now quite low and should have no appreciable effect on its mechanical properties; however, many titanium applications require ex- posure to hydrogenous atmospheres under conditions in which hydrogen pickup is likely. In such cases continued exposures may cause the hydrogen content to increase to the extent that titanium hydride does precipitate as a second phase. The hydride phase has been shown 1,2 to have an adverse effect on the mechanical properties, particularly the impact properties, causing reductions in strength and ductility. BACKGROUND The behavior of titanium is often quite similar to that of zirconium and zirconium-base alloys, and the technology developed on one metal can often be applied to the other. Marshall and Louthan3,4 have shown that Zircaloy is susceptible to stress orientation* of zirconium hydride platelets, and that the platelet orientation has a pronounced effect on the mechanical properties of Zircaloy. They showed that when zirconium hydride precipitated in Zircaloy under an applied stress the hydride platelets tended to be aligned parallel to a compressive stress and perpendicular to a tensile stress. They also showed

Jan 1, 1963

By G. Thodos, R. B. Grieves

A method has been developed for the accurate calculation of the cricondentberm and cricondenbar temperatures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain any number of components including paraffins and isoparaffins, olefins, acetylenes, naphthenes and aromatics. This approach is based upon the mole fraction of the low-boiling component in the mixture and graphically presents the ratios of the cricondentherm and cricondenbar temperatures to the pseudocritical temperature as {unctions of a boiling-point parameter. The only requirements are the critical temperature, normal boiling point and the approximate vapor pressure behavior of each component. For mixtures of more than two constituents a stepwise calculation procedure is necessary where the pseudocritical temperature is based upon the critical temperature of the pure low-boiling component and upon the actual cricondentherm or cricondenbar temperature of the mixture of all the remaining higher-boiling components. From an analysis of 22 binary systems (123 compositionsl, the average deviation of calculated cricondentherm temperatures from reported values is 0.87 per cent, based on degrees Rankine; and for 10 multicomponent mixtures containing from three to six components, the average deviation is 0.98 per cent. From an analysis of 18 binary systems (104 compositions) the average deviation of calculated cricondenbar temperatures from reported values is 0. 79 per cent; and for 15 multicomponent mixtures, 1.47 per cent. Equations, derived from the graphical relationships, are presented which enable rapid calculations for both binary and multicomponent systems. INTRODUCTION With the increasing tendency towards the use of high pressure processes, the need for an accurate method of calculation of the properties of a multicomponent hydrocarbon mixture in the critical region is becoming more essential. Critical region phase relations are also significant in gas condensate reservoirs, for which a knowledge of the fluid phase boundaries and regions of retrograde condensation make it possible to evaluate optimum operating conditions. The possibility of liquefaction in the underground structure may be established, and information on the feasibility of the use of repressurizing may be determined. A typical phase diagram for a multicomponent hydrocarbon mixture is presented as Fig. 1. This figure also shows the regions of retrograde behavior encountered by following lines AB and AC. If accurate methods of calculating the temperatures and pressures at the critical, cricondentherm (maximum temperature) and cricondenbar (maximum pressure) points of multicomponent hydrocarbon mixtures of known composition were available, it would be possible to estimate closely the entire phase diagram of any mixture. Several methods have been presented in the literature for the estimation of the critical temperatures and pressures of multicomponent mixtures containing all types of hydrocarbons and including the fixed gases.4-8,21 Considering the cricondentherm and cricondenbar points, the work is more limited. Etter and Kay5 have developed rather complex equations for