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By Kai Wang, Chao Xu, Qiang Fu, Tong Yang, Chunyu Zhao, Wei Zhao

The stress of a coal seam is an important factor that affects the permeability of the coal seam and then affects the coalbed methane (CBM) drainage. In China, adjacent coal seam mining is an important method to reduce stress, which increases the permeability of the coal seam. However, in the process of mining adjacent coal seams, many coal pillars remain, which causes stress concentrations and results in a decrease in permeability. Therefore, it is important to study the influence of coal pillars on the stress of adjacent layers and its distribution and evolution in the floor rock. This paper took the Shendong Baode Coal Mine as a case study and investigated the influence of the coal pillar on the stress and permeability of coal seam #11. The results show that under a coal pillar, the relationship between the vertical stress of different floor depths and the width of the coal pillar can be divided into a negative correlation zone, transition zone, and positive correlation zone. The change in the coal pillar width does not affect the pressure relief range or the degree of pressure relief in the adjacent coal seams below the goaf. The field measurements show that after the mining of panel #81,505, the permeability coefficient of coal seam #11 under the goaf increased from 0.1434 to 26.3545 m2/( MPa2*d), increasing 182.7 times, and the drainage mixing volume of boreholes #1 and #2 increased from 1.24 to 1.52 m3/ min. While the permeability coefficient of coal seam #11 from 12.5 m in the coal pillar has only increased by 2.6 times, the drainage volume of boreholes #3 and #4 did not change significantly.

Nov 19, 2022

By Read T. A

PART 1The quantity of dust present and the methods used for suppression of dust in metalliferous mines has, in recent years, received considerable attention from mining engmeers in various parts of the world. Shortly after the publication of the General Report of the Miners' Phthisis Prevention Committee, South Africa, in 1916, the officers of the Broken Hill South Limited started investigations into the conditions of the dustiness of the air in the underground workings. As the methods used are not generally known in Australia, the writers are of the opinion that the present is an opportune time to place them before members of the Institute. A large amount of the subject matter of this paper has been drawn from the 1916 and 1919 reports of the Miners' Phthisis Prevention Committee, South Africa, the paper of Mr. Innes published in "The Chemical, Metallurgical and Mining Society of South Mrica"; also various articles appearing in the Journal of Industrial Hygiene, and the American Journal of Public Health. A great deal of research work into the cause, prevention and estimation of mine dust has been made by the Miners' Phthisis Prevention Committee of South Africa, and officials of the United States Bureau of Mines. The writers considered it advisable to begin the investigation at the South Mine with apparatus and methods developed by the South African Committee.Through the Australian agent of the Cape Explosives Company, inquiries were made preliminary to procuring the necessary apparatus for the determination of dust, from South Africa. The writers then learned that the older gravimetric method used by the Phthisis Prevention Committee was likely to be superseded by the konimeter...

Jan 1, 1922

By K. J. Shoop

Coal-fired power plants in the U. S. produce approximately 20 million metric tons of Hue-gas desulfurization sludge every year. The sludge mainly consists of calcium sulfite and calcium sulfate. This can be converted to synthetic gypsum, which in principle could be a marketable commodity. However, many Hue-gas scrubbers produce sludges that do not meet the quality requirements of the gypsum industry, and so their sludges must be landfilled as a waste. If a suitable method can be developed for removing certain objectionable impurities from the sludge, it will then be possible to market the material instead of landfilling it. A sludge from a natural-oxidation scrubber was characterized, and the main contaminant was found to be calcium carbonate from unreacted limestone. Based on the particle size and the characteristics of the material, froth flotation was considered as a method for purifying the material. Since no flotation studies have ever been carried out to separate calcium carbonate particles from calcium sulfite or calcium sulfate particles, it was first necessary to select a suitable collecting reagent. Based on Zeta-potential studies, the most suitable reagent was found to be an octadecylamine-octadecylguanidine complex. Results are presented for flotation of calcium carbonate from scrubber sludge using this reagent, in a reverse-flotation process. The best results were obtained when the sludge was first pre-cleaned using a water-only cyclone to remove unfloatable coarse limestone, followed by froth flotation to remove fine limestone.

Jan 1, 1998

By Lyman Moore

This Bureau of Mines report describes 2nd evaluates iron ore resources in California and Nevada and analyzes the California and Japanese iron ore markets in which these resources will be used. The competitive position of California-Nevada ores, in these markets, was estimated by comparing regional iron ore prices, production costs, and transportation costs with those of foreign suppliers. Resources were determined to be sufficient to produce the equivalent of 585 million tons of 64-percent iron pellets at a price of less than $15 per ton delivered at California ports. Much higher tonnage could be produced at higher prices. Iron ore requirement of the California iron and steel industry will increase to an estimated 15.9 million tons by the year 2000. A study of the iron ore production potential of California-Nevada deposits and of out-of- State sources indicated that this ore requirement can be supplied most economically by California-Nevada ores. Iron ore import requirements of the Japanese iron and steel industry will increase to an estimated 150.0 million tons by the year 2000. A study of price trends in this market indicated that very little California-Nevada iron ore will be sold in Japan after 1973 when existing sales contracts expire. Iron ore-exports might be economically possible if ore could be transported from California to Japan at ballast rates as backhaul on existing petroleum shipping.

Jan 1, 1971

By P. J. Cook

Comminution is one of the fundamentals of mineral processing, requiring large expenditures to be made on capital equipment, installation, power and maintenance. The trend toward lower grades and higher operating costs, mean mining operations are becoming increasingly marginal. The challenge is to improve and more importantly, utilize crushing and milling technologies that provide for reduced capital and operating costs whilst providing increased unit efficiencies. The Svedala Barmac Autogenous Crushing Mill presents such an opportunity by providing many of the cost savings and production increases required by its ability to produce a finer mill feed size and realize reduced energy consumption. This paper briefly describes the operation of the Svedala Barmac Autogenous Crushing Mill and reviews its benefits towards improving the efficiency of crushing and milling operations.

Jan 1, 1999

By R. F. Waters

Laboratory-scale selective volatilization methods developed by the Bureau of Mines to recover germanium and gallium concentrates from coal fly ash and phosphorus furnace flue dust are summarized. In the better experiments between 85 and 98 percent of the germanium was recovered as the lower oxide and as sulfides, and between 75 and 97 percent of the gallium was recovered as the lower oxide and as the trichloride. Grades of the condensates were inconsistent and varied between a few tenths of a percent and 8 percent, depending on the method used. In the primary extractions of germanium alone the degree of enrichment surpassed 100 to 1, and for gallium the best ratio was 30 to 1. Upgrading of condensates by vaporization retreatment and by leaching and precipitation is discussed. An appreciable degree of mechanical preconcentration by attrition scrubbing and elutriation was possible on two fly ash samples.

Jan 1, 1967

By Raja V. Ramani, Robert L. Frantz

"The House/Senate Joint Conference Committee has instructed the Bureau of Mines to have the Advisory Committee on Mining and Mineral Resources Research review on an annual and simultaneous basis each generic mineral technology research center (GMTC). In order to accomplish that review promptly and uniformly, committee members have revised and approved an in-depth questionnaire. That document formed the basis of their review. The information provided by that questionnaire was an important factor in their recommendations concerning the future direction of the program; a presentation was made at the last National Plan Update.The comprehensive nature of the questionnaire and the scope of the information contained therein make it an excellent retrospective of the Center. Having a clear vision of where the Center has been and knowing where it is now will help guide it into the future. It is felt that such a detailed view of the Center's facilities and research program will be of value to Center personnel and Advisory Committee members.Each aspect of the questionnaire has been examined, answered in detail, and documented throughly. With the completed questionnaire as a guide, this volume examines the research program, Center personnel presently active on GMTC projects, number of graduate degrees granted with GMTC support, GMTC publications, degree of individual interaction, technology transfer, the reference center, GMTC equipment and facilities, and any envisioned plans for future research. It is hoped that this volume will serve as a review of the years 1984-1988, the first four years of the Center's operation."

Aug 31, 1989

By Evvie Chockalingam

Acid mine drainage (AMD) is a perennial problem particularly in abandoned mines, occurring due to the oxidation of sulphidic mine wastes. AMD is usually characterized by high concentration of dissolved metal ions, sulphate and low pH. The efficacies of substrates such as rice husk and the bark of Eucalyptus tereticornis (Sm.) are assessed for the removal of metal ions such as iron, zinc and copper from acid mine water obtained from an abandoned copper mine. Over 99 % of Fe, 98 % of Zn and 95 % of Cu removal could be achieved from acid mine water, with a concomitant increase in the pH value by three units using rice husk as an adsorbent. With respect to tree bark as an adsor-bent, about 96 % of Fe, 75 % of Zn and 92 % of Cu could be removed from the acid mine water with an attendant increase in the pH value by two units. The free energy of adsorption of the metal ions onto rice husk and tree bark is found to be negative in both the cases, while the adsorption process is endothermic in the case of rice husk and exothermic for tree bark. The adsorption process is found to adhere to the Lagergren pseudo-first order rate equation. The reduction of sulphate con-centration in the acid mine water is achieved using a typical sulphate reducing bacteria namely De-sulfotomaculum nigrificans. Desorption experiments indicate that about 88 % of Zn, 87% of Cu and over 77 % of Fe could be recovered from rice husk and over 70 % of Fe, 82 % of Zn and 77 % of Cu could be desorbed from the metal loaded tree bark using 5 M HCl. The possible mechanisms of metal ion and sulphate removal from acid mine water using rice husk and tree bark are discussed.

Jan 1, 2014

By J-P Franzidis, E V. Manlap

Froth transportation characteristics have a significant impact on the flotation recovery especially in large flotation cells. The probability of an attached particle being recovered into the concentrate depends strongly on the location where it enters the froth phase. A mathematical model for froth transportation in industrial flotation cells was proposed (Zheng et al, 2004). The model has been tested on the experimental data obtained from testwork conducted at the Western Metals Hellyer lead/zinc concentrator. The results show that the model fits the experimental data well, especially when the froth is well developed (ie for a deep froth). The model fitting can be significantly improved by incorporating an air dispersion factor. However, the models encounter some limitation, ie inconsistent prediction at different froth heights, due to change in froth viscosity which cannot be modelled at the present time.

Jan 1, 2005

By John Loop, W. A. Gibbins, Donald D. Hogarth

"Introduction Background The Frobisher voyages of 1577 and 1578 were organized by the Cathay Company for the express purpose of finding and mining gold ore. Since publication of the Baffm expedition of Charles Francis Hallill, the location of Kodlunarn or Countess of Warwick Island, the headquarters of Frobisher's third (1578) voyage, and focal point of the largest Arctic voyage of all time, has been known to the world. Through Hall we also know the location of the Countess of Warwick Mine on Kodlunarn Island. However, the exact locations of the other mines are not known. Of the ""ore"" we know little. Pieces of the original ""black stone"", once as large as ""a half-penny loaf' have now disappeared altogether. Specimens collected at random from the repository of shipments in England and from loose rock on Kodlunarn Island were termed, respectively, ""hornblende pyroxenite"" and ""amphibolite"" and from a locale about 200 yards from Kodlunarn as (hornblende) ""pyroxenite""121. However, it is uncertain whether these specimens are representative of Kodlunarn or of the other mines, although Blackadar131 notes that, in the northern trench of Kodlunarn, biotite gneiss contains lenses and bands of amphibolite. The ""gold"" itself is even less well defined. It has long been accepted that gold was virtually absent in Frobisher's ore. The ""gold"" has been termed pyrite, biotite and both biotite and pyrite together. Even t h e word "" marquesset"" , which appears and reappears in contemporary descriptions, is nebulous and is defined as ""a stone participating in the nature of some metal, yet in so small quantity, that the metal cannot be melted from it"" (0.E.D., definition of 1616)."

Jan 1, 1999

By M. J. Humenick, K. Garwacka

A laboratory experimental research project was conducted to evaluate the use of chlorine for the oxidative destruction of residual ammonia that may remain in ground water after in-situ uranium solution mining operations. The work tested the idea of injecting high strength calcium hypochlorite solution into the mining zone to convert ammonia to nitrogen gas as a final cleanup process for ammonia removal from the ground water system. This paper details ammonia removal efficiency as a function of chlorine dose, reactant, and product material balances, and how the concept may be used as a final ground water restoration process.

Jan 1, 1985

By S. Shrestha

Magnesium-based alloys are of growing interest for many industrial applications due to their favourable strength-to-weight ratio and excellent castability. Mass reduction has advantages in many industrial sectors for example, in automotive, a reduction in mass improves fuel economy and can lead to more efficient mechanical systems by reducing the weight of moving parts like wheels, gears, pistons. However, the relatively poor corrosion and wear resistance limits the use of magnesium and its alloys in many potential applications. The patented Keronite® plasma electrolytic oxidation (PEO) process enables manufacturers to overcome such problems and, in its latest generation equipment has been developed to industrial realisation for high volume production. This paper presents microstructural characteristics and corrosion performance of two most widely used high pressure die-cast magnesium alloys AZ91D and AM6OB with a duplex corrosion protection coating system that comprised a thin Keronite pre-treatment followed by a subsequent automotive grade final powder coat.

Jan 1, 2006

By H. Breuer

Mineral processing is characterized by a constant adaptation to changing raw materials and market conditions. It is the link between the mined raw material and a marketable product. As a lot of high grade reserves are exploited, a steady deterioration of raw material quality can be observed. At the same time, the customers´ requirements for product purity and consistent quality increase. Indian iron ores are characteristically friable in nature that results in generation of sizeable quantity of fines (0-10mm) every year during various stages of mining and processing in the country with grade varying from 50-60% Fe(T) and are high in silica/alumina (Al2O3 5-8%). The fines generated cannot be directly used for iron making (blast furnace/DRI units) in the country due its physical and chemical properties; therefore, large portion of it gets exported or dumped. Value addition to iron ore fines through various activities such as beneficiation & palletization is the need of the hour, which will not only be economically beneficial to the mining sector in the long run but also generate value addition & employment opportunities. Incentives may be given for adopting latest technologies for direct use of fines in iron making by agglomeration of fines in the form of Pellets and Sinters, as fines forms considerable part of iron ore resources. Due to selective mining, although the iron content of the ore is high but the alumina(Al2O3) content in iron ore is also significantly high which demands for beneficiation as high alumina will create problem during iron making like higher fuel consumption, poor quality of slag produced, reduced productivity of B.F. all mineral has been engaged in hematite iron ore beneficiation with its gravity and magnetic separators since the mid-nineties. The delivery of jigs started for the upgrading of iron ore for its utilization in a Direct Reduction Plant in Australia. Since then, various other installations with jigs for lumps and fines as well as upstream separators for fines are in operation in Brazil, Australia, India and South Africa. Low grade run of mine and/or dump ores are being processed with alljig®-, allflux®- and gaustec®-WHIMS as the core equipment. The article describes the technology in use, the characteristics of various iron ores and the product qualities achieved. The data presented shows the specific advantages of jig application on iron ore upgrading due to the possible high gravity cuts and the easy and low cost operation. The allflux®- technology provides the big advantage of high capacities and a two-step process, both in a single unit. The gaustec®-wet high intensity magnetic separators offer high capacity in combination with unsurpassed process flexibility. Keywords: iron ore, gravity separation, jig, upstream classifier, wet high intensity magnetic separation (whims), pelletization, sinteringMineral processing is characterized by a constant adaptation to changing raw materials and market conditions. It is the link between the mined raw material and a marketable product. As a lot of high grade reserves are exploited, a steady deterioration of raw material quality can be observed. At the same time, the customers´ requirements for product purity and consistent quality increase. Indian iron ores are characteristically friable in nature that results in generation of sizeable quantity of fines (0-10mm) every year during various stages of mining and processing in the country with grade varying from 50-60% Fe(T) and are high in silica/alumina (Al2O3 5-8%). The fines generated cannot be directly used for iron making (blast furnace/DRI units) in the country due its physical and chemical properties; therefore, large portion of it gets exported or dumped. Value addition to iron ore fines through various activities such as beneficiation & palletization is the need of the hour, which will not only be economically beneficial to the mining sector in the long run but also generate value addition & employment opportunities. Incentives may be given for adopting latest technologies for direct use of fines in iron making by agglomeration of fines in the form of Pellets and Sinters, as fines forms considerable part of iron ore resources. Due to selective mining, although the iron content of the ore is high but the alumina(Al2O3) content in iron ore is also significantly high which demands for beneficiation as high alumina will create problem during iron making like higher fuel consumption, poor quality of slag produced, reduced productivity of B.F. all mineral has been engaged in hematite iron ore beneficiation with its gravity and magnetic separators since the mid-nineties. The delivery of jigs started for the upgrading of iron ore for its utilization in a Direct Reduction Plant in Australia. Since then, various other installations with jigs for lumps and fines as well as upstream separators for fines are in operation in Brazil, Australia, India and South Africa. Low grade run of mine and/or dump ores are being processed with alljig®-, allflux®- and gaustec®-WHIMS as the core equipment. The article describes the technology in use, the characteristics of various iron ores and the product qualities achieved. The data presented shows the specific advantages of jig application on iron ore upgrading due to the possible high gravity cuts and the easy and low cost operation. The allflux®- technology provides the big advantage of high capacities and a two-step process, both in a single unit. The gaustec®-wet high intensity magnetic separators offer high capacity in combination with unsurpassed process flexibility. Keywords: iron ore, gravity separation, jig, upstream classifier, wet high intensity magnetic separation (whims), pelletization, sintering

Sep 1, 2012

By F. D. Fox

Abandoned mill tailings deposits can be found scattered throughout the Northern Black Hills of South Dakota, indicative of past mining activities that originated during the great gold [ERRATA SHEET RESTORATION OF GOLD MILL TAILINGS, BLACK HILL, SOUTH DAKOTA 84-119 F. D. Fox Under subtitle Prospects Related to Present and Future Tailings Disposal Practices, include reference No. 12 in paragraph seven after "construction of the Grizzly Gulch tailings disposal project,"12 Reference 12 should read: Jeffries, Lawrence F. and Tczap, Andrew, "Homestake's Grizzly Gulch Tailings Disposal Project," paper presented at 1978 International Mining Show, October 11, 1978.]

Jan 1, 1984

By Dwayne D. Tannant

The Adra tunnel near Naramata BC experienced a fire in 2010 that burned timber sets within the tunnel and caused severe spalling of rock from the roof and tunnel walls. The nature of the damage is documented and efforts completed to rehabilitate and open a portion of this tunnel to the public are described. The use of shortcrete and rock bolts is a technically and economically superior support system to timber sets as well as being far more fire resistant.

Jun 1, 2012

By Ahmet Tezcan, Zeki M. Dogan, Yalçin Kaytaz

Autogenous grinding in Turkey was first applied to quartzite where the mill is grate discharge type with an internal diameter of 2.99 m, having a length of 3.20 m and a capacity of as to 11.0 tons per hour. The second autogenous grinding was applied to a copper ore at Murgul Cakmakkaya Flotation plant of (KBI) Black Sea Copper Works having three mills 26 feet in diameter and 10 feet in length in close circuit with hydrocyclones. Recently, alterations were made in grinding circust by adding pebble mills. Furthermore, rubber liners and lifter bars were introduced pebble extractor and classifier were new features in the primary mills and circulating load was reduced by 20-50 tons per hour. At the end of these charges, capacity of each mill line was increased to 48 tons per hour with a full capacity of more than 9000 tons per day. Thirdly, autogenous grinding has been executed successfully on the slags of Samsun Smelting Plant of (KBI) Black Sea Copper Works with a mill of 20 feet in diameter and 6 feet on length having pebble mill following autogenous grinding.

Jan 1, 1992

By A. M. Evans

"INTRODUCTION Exploration of the Iron Mountain and Bader iron-ore deposits in Llano County and the Gamble deposit in Mason County, Texas, was begun by the Bureau of Mines in January and completed in May 1944. The deposits had been examined by A. B. Needham, district engineer of the Bureau, in November 1942. Detailed geophysical studies by the gravity method as well as with a dip needle were made by the Bureau of Economic Geology 3/ of the University of Texas and the Federal Geological Survey. 4/ACKNOWLEDGMENTSIn the program of exploration of mineral deposits, the Bureau of Mines has as its primary objective the more effective utilization of our mineral resources to the end that they make the greatest possible contribution to national security and economy., It is the policy of the Bureau to publish the facts developed by each exploration project as soon as practicable after its completion. The Mining Branch, Lowell B. Moon, chief, conducts preliminary examinations, performs the actual exploratory work, and prepares the final report. The Metallurgical Branch, R. G. Knickerbocker, chief, analyzes samples and performs beneficiation tests."

Apr 1, 1947

By Brian Koch

Michels installed 242 drilled shafts to support the piers for a new basket-handle, true-arch twin bridge across the Mississippi River from Moline, IL to Bettendorf, IA. The installation of the drilled shafts was completed with the simultaneous use of two Liebherr LB36 and one IMT 300 drill rigs. Utilizing barges, 233 drilled shafts were installed in the river. Michels crews also installed 7-ft to 10-ft permanent steel casing into the bedrock, and drilled to depths of 60 feet for each shaft. Despite working in strong currents, freezing temperatures and on rocking barges, Michels crews placed the shafts within 3 inches of plan position. Since the drilled shafts are the key piece in supporting the bridge structure, Michels provided cross-hole sonic logging to verify the integrity and strength of the concrete within the shafts and to add another level of quality control for the owner/customer. Extensive planning took place each day to ensure that tugboats, the linchpin of the project, were being efficiently utilized to shift the barges and materials daily. On any given day, Michels transported five concrete trucks by barge from shore to shaft sites to pour between 40 and 240 cubic yards of concrete. The Michels environmental team was diligent with preparing, discussing and implementing a water treatment plan that was accepted by all state and federal agencies and adhered to strict environmental regulations. Grain hopper barges were rented to control and treat the water that was used in the drilling operations. Another challenge crews ran into was the discovery of caverns when drilling into some parts of the bedrock. Michels worked with the engineer to develop a plan to construct the drilled shafts that encountered the caverns.

Jan 1, 2019

By D. Harrington

Although for many years considerable attention has been given to devising safe and efficient methods of using explosives, with some success, relatively little has been done to provide satisfactory storage facilities for them. This was known long before the present war began, but it was emphasized during the past 30 months? inspections of explosive magazines by employees of the Bureau of Mines in administration of the Federal Explosives Act of December 26, 1941. These inspections have revealed woeful in adequacy as well as definite hazards and the urgent need for obtaining better storage facilities either by remodeling old magazines or constructing ink new ones that would afford suitable protection for the contents against theft, fire, deterioration, and detonation. The purpose of this paper is to offer suggestions and to show by sketches and drawings some of the fundamental features of suitable magazines. Type of construction and available materials differ with different; localities, but the information herein contained can be applied to most magazines, whether already constructed or the construct: on of which is planned. It is hoped that this information will be helpful and will aid persons who are trying to provide suitable storage for explosives end detonators. It is also hoped that States and cities will be made aware of the unbelievable laxity practiced in storing explosives in the United States and will take some remedial action.

Jan 1, 1945

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970