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By FRANKM. SEIBERT, G. G. Oberfell, GEORGEA. BURRELL

The Bureau of Mines is conducting a series of investigations with the common aim of minimizing the losses that occur in the mining and treatment of mineral substances. The results of the investi- gations are being published in reports of the bureau. This report treats of a method of preventing some of the waste of the natural gas incidental to oil mining. This method, the condensation of gasoline from natural gas, offers to the oil operator and others a profitable means of utilizing some of the oil-well gas now being wasted. The most desired constituent of crude oil is obtained, the production of oil is not hindered, and the gas, after the extraction of gasoline, can be returned to the leased area to drive pumps or into pipe lines for uses to which natural gas is ordinarily put, usually with its fuel value lessened only in slight degree. Publications already issued briefly discuss the subject. In this report the work is treated in greater detail, and the results of many additional tests are shown.

Jan 1, 1915

By P. F. Allen

WITH capacity of 51,000 tpd, the Morenci concentrator produces approximately 49,000 tons of tailing for final deposition. Disposal involves distribution of thickened tailing to dams in such a manner that solids can be used for dam construction and water can be impounded for reclamation. During early operation, although tonnage treated was lower, it was necessary to use orthodox disposal practices in the areas available for tailing. Trestles mounted on a series of dams, constructed of borrow material, carried the pipelines from which tailing were spigoted behind the dams. When adequate disposal areas were finally established, it became desirable to look for more efficient methods. The idea of placing the distribution pipe or manifold directly on the crest of the dam was advanced in 1945. After a period of testing, that procedure in modified form replaced the older trestle arrangement. Marked economies resulted, and time required to prepare dams for succeeding storage cycles was greatly reduced. The tailing disposal area for the Morenci concentrator lies south and southwest of the concentrator building. Ample storage space is available. A wide valley contains three sharply defined ravines lying on an average slope of 4 pct. The more central of these ravines, and the largest of the three, is known as Morenci canyon, which provides substantially more tailing storage area than the other two. Stargo canyon lies to the west; the other is appropriately named East canyon. Total area of the tailing disposal site is nearly 31/4 sq miles, or about 2000 acres. The storage area in use was somewhat more than 850 acres at the end of 1954, or 16 acres per 1000 tons of tailing to be stored daily. At the present time none of the east side dams are in regular use but they are available in emergency. There are five dams on the west side (in Morenci and Stargo canyons) as well as two auxiliary dams adjacent to No. 4 West and No. 5 West. This has made it possible to concentrate men and equipment in a smaller area with consequent savings in both manpower and machinery. Tailing Thickening: Tailing from the flotation process reaches the thickeners with a solid content of about 18 pct. The launder carrying this pulp is subdivided at a central point into seven launders carrying a proportional share to each of seven tailing thickeners, which are located in Morenci canyon close to the concentrator. Five of these thickeners are 300 ft diam and two are 325 ft diam. Thickeners are of the peripheral traction type and rakes travel at the rate of one revolution in 37 to 39 min. The entire installation provides 500,000 sq ft of settling area, or approximately 101/2 sq ft per ton of tailing to be thickened daily.

Jan 1, 1957

By Maurice Deul

This bulletin summarizes the work conducted under the Bureau of Mines methane control research program during the years 1964 to 1979. This research effort was directed toward improving existing methods and developing alternative methods of reducing the explosion hazard during mining. The research was performed in three general areas: (1) basic factors that control the emission of methane into coal mines, (2) methane control during mining, and (3) methane drainage in advance of mining. Topics discussed in this bulletin include the magnitude of the methane problem; the equipment and instruments developed; the geological, chemical and physical parameters that control the movement of methane in coalbeds; the direct method of determining gas content; the estimates of gas content from adsorption data; and methane drainage, through shafts, through horizontal boreholes, through vertical boreholes, or through slant holes. Improvements in ventilation, control of methane in gob areas, and water infusion are also discussed, as is the potential use of coalbed methane as a supplement to natural gas supplies. This bulletin provides a comprehensive source of information on the accomplishments of the Bureau's methane control research program, on the technology developed, and on the direction of further research.

Jan 1, 1986

By M. Kanefsky

Two channel polarity coincidence and polarity difference statistics are analyzed. The signal, common to both channels, consists of sinusoidal bursts where the exact frequency of the signal is nearly known, but other parameters such as amplitude, phase, and pulse starting time are unknown. The noise inputs are dependent, narrow band, Markov processes. It is shown that the performance depends not only on the signal uncertainties, but on the precise shape of the cross-correlation functions between the noise in-puts. By using two polairty difference statistics in addition to the polarity coincidence statistic, it is shown that the decrease in performance, as well as the cost of hard limiting due to correlated inputs, can be made small.

Jan 1, 1981

By M. F. Dunn

During a mine fire or other emergency, it may be desirable to reverse the airflow in order to provide an escapeway or to isolate a fire. Also, in colder areas, the airflow may be reversed to prevent ice buildup. When reversing main mine fans, the mine operator usually does not know what operating characteristics of flow and pressure to expect. Laboratory and field tests of vane axial main mine fans in the 7- to 9-ft diameter size range were conducted to establish forward and reverse performance characteristics under controlled conditions and at typical mine installations. The data obtained suggest that reverse performance characteristics are dependent upon the blade angle and the hub to tip ratio. There is also evidence that reverse performance can be predicted for a family of blade angles and a given hub to tip ratio. Generally, quantity of air is 30 to 65% less in reverse than when operating in the normal forward mode.

Jan 1, 1983

By John Wilson

"The Rietveld numerical method was used to calculate the relative abundances of phases in both synthetic binary mixtures and synthetic and natural ores, using X-ray diffraction data. The results were compared with those of image analysis and a chemical method. The ranges of the relative errors were estimated. The Rietveld method is found to be acceptable for determining the abundances of major and minor phases and the amorphous component of partially crystalline samples. In complex mixtures, where there are several trace phases (~<2 wt%) present, the technique becomes less accurate. It is most useful as an alternative technique to image analysis when sample preparation is problematic or sample particle sizes are sub-micron. It is a manual method which requires user input during the fitting process, but is both simpler and faster than image analysis due to the reduced set up time and sample preparation required. It is now implemented at CANMET as a technique for quantitative analysis.INTRODUCTIONUntil recently, the Applied Mineralogy group at CANMET used only image analysis and chemical techniques to determine phase quantities. An effort to develop quantitative X-ray diffraction (XRD) has been on-going for several years. Initially, the reference intensity ratio (RIR) method with external standards was tried with some success (Szymanski and Petruk, 1989). The main difficulty with this technique was finding adequate standard material for each phase present in the sample. This shortcoming made the method ultimately impractical, given the wide variety of materials which come to the laboratory for analysis.The Rietveld refinement method of quantitative XRD (Hill et al 1993, Mumme et al 1996), in contrast, requires no standards and requires minimal sample preparation and therefore a more rapid turnaround compared to image analysis. The Rietveld method also has advantages over image analysis in that it can identify and quantify polymorphs, ultra fine materials and many types of hydroxide products. As well, it is useful for analyzing materials such as bauxite or talc, which do not polish well enough for making mounts of the quality required for image analysis. To quantify amorphous material and phases which are present in amounts below the detection limit of XRD, the addition of a standard material is still required. However, in such cases only one standard is needed, which is alumina."

Jan 1, 2003

By G. Couture, J. -F. Dubé, F. Letarte-Lavoie

"The Xstrata Nickel Raglan concentrator, located in Quebec’s Nunavik region, has been in operation since 1997. Originally designed to process 800,000 tonnes per year of high-grade nickel ore, the plant’s current capacity is 1.3 million tonnes per year due to various optimization projects. In 2011 and 2012, the Metallurgical group, with assistance from BBA, updated and optimized the variables affecting SAG throughput in order to optimize process stability while maintaining maximum plant throughput. This project consisted of reviewing the control strategy and completely updating the pre-existing Fuzzy Logic controller. This paper describes the successful update of the controller including a complete revision of control rules, a new process control strategy and the integration of new process variables, most notably mill rotational speed. It will also show how this new approach has provided a simple and robust way of delivering both an increase in throughput while reducing process variability.INTRODUCTIONThe Xstrata Nickel Raglan Mine concentrator is located in Northern Quebec along the 62th parallel. It has been in operation since 1997 and was originally designed to treat 800,000 tonnes of ore annually. The Raglan Agreement held with the Makivik Corporation and the Inuit communities limits the annual tonnage of ore that can be processed at 1.32 million tonnes.The ore is processed in a 24 foot variable speed, semi-autogenous grinding mill (SAG). The conversion from Autogenous Grinding (AG) to SAG was completed in 2006. Before the ore is processed by the SAG, its size is analyzed by a Wipfrag camera that provides a granulometry estimate. A cone crusher reduces the SAG’s discharge screen’s oversize material. A 14 foot diameter ball mill ensures final grinding before the flotation stage.Many control strategies were used at the SAG over the past few years. Fuzzy Logic was first used in 2007 in order to control tonnage feed to the SAG. This first version only measured the value of the variables without taking into account their rate of change. Revisions were made over the course of the last few years to improve controller performance. Other variables were added such as slurry density and crusher Closed Side Setting (CSS). The previous revision of the Fuzzy Logic was done in 2009 with a review of the rules only."

Jan 1, 2013

By Y. Shu, A. R. Laplante

"A laboratory Knelson Concentrator (LKC), 7.5 cm in diameter, was used to study the performance of a similar unit at plant scale, 76 cm in diameter, This paper reports on sampling and assaying procedures and problems, and discusses the performance of the plant unit.The sampling procedure was based on the extraction of large samples, 5-15 kg, and their complete processing with a LKC, to characterize size-by-size performance. The procedure yielded reliable estimates of overall gold assays, after blatant assaying errors were corrected. The plant centrifugal unit concentrate was sampled in situ, which yielded very erratic grades, with a large overall negative bias. Due to the very heterogeneous nature of the concentrate, which can be linked to flow patterns in the riffles of the unit, it is recommended that for future testwork, the concentrate be recovered separately, blended and then sampled.The plant centrifugal separator, when operated at a feed rate of 25 t/h, yielded total and free gold recoveries of 41 % and 62%, respectively. This is much lower than previously reported data, and suggest that at 25 t/h, the unit is overloaded. However, recovery did not decrease with time over a loading cycle of 2 hours, which suggests that present loading cycles, generally 1 hour, can be significantly increased. INTRODUCTIONThe study of gold gravity circuits is plagued with the statistical problem of determining the behaviour of particles occurring with a very low frequency. This problem becomes particularly acute with increasing particle size. For example, considering the average weight of a gold flake in the 840-1200 µm (20/28 mesh) to be about 5 mg (Banisi et al, 1991), a reasonably high grade feed of 10 git would require, for a relative error (standard deviation) of 10% on grade, 100 particles, that is 0.5 g of gold, or 50 kg of 840-1200 µm material (a Poisson distribution is assumed). Gy's formula, for the same data, yields a weight of 33 kg, with a shape factor of 0.1 and a size distribution factor of 0.5. Both results are comparable; to obtain the suggested weight of material, a stream containing 5% weight in the 840-1200 µm would require 1 tonne samples (of unsized material). The problem rapidly disappears with decreasing particle size. Still with Banisi et al's data, a gold flake in the 300-420 µm range averages 0.5 mg in weight; the same 10% error on grade corresponds to a weight of 5 kg. Gy's formula for the same size distribution and particle shape factors as above predicts a required mass of 1.4 kg. This would correspond to an unsized sample weight of 10 kg with 14% weight in the 300-420 µm, for example."

Jan 1, 1992

By Jerome F. Kuzmick

Condusions. From the work on aluminum powder, the following general con clusions can bc drawn: I. The physical properties of aluminum compacts, such as density. strength and ductility, increase with increasing pressure, up to the practicable pressure limits. 2. Good properties ill aluminum con pacts can be secured only by the use of high pressures, because it is neccssary to rupture the refractory oxide film on aluminum powder. 3. Considerable softening of the specimens occurs upon sintering. regardlers of the pressure used. General Conclusions 1. For relatively short-time sintering. molding pressure is a very important factor in the final physical properties of the sintered specimens. 2. The effect of pressure. is difierent for each metal, so that few general rules can be drawn that would apply to all metals. 3. In many cases, fur a particular metal powder and sintering temperature there is a critical pressure at which the best physical properties can be obtained. 4. The principles of cold work and in nealing and their effect on grain structure applied to massive metal also holds true for sintered metals. 5. Particle size, at least for electrolytic iron powder, does not have a. great effect on ultimate grain six. DISCUSSION [E. E, Schumacher presiding V.. V. Crane. *—I was particularly impressed with Dr. Kuzmick&apos;s work on tin IF not the illustration, particularly the Second one. a very good illustraition of hot preessing. in that

Jan 1, 1945

By Gilles Landry, Mohamed Ourriban, Pierre Pelletier, Ahmed Bouajila, Claude Gagnon

"This paper summarizes the work carried out to develop and implement the gold cyanidation by size class (CSC) process, a novel concept aiming to reduce cyanide consumption.First, the authors will present the methodology and results of laboratory tests conducted to evaluate the response and the expected gains for the selected ore when submitted to the CSC processing. In the second part, focus will be on the methodology behind the CSC scheme development prior to its implementation at Sleeping Giant Mine concentrator. Finally, the evaluation of the modified circuit performance (operating since July 2007) will be addressed as a reduction of cyanide consumption by more than 30% and of free NaCN in the tailings by more than 50% is confirmed.INTRODUCTIONCyanidation is the most widely used technique to extract gold from hard rock ore. Its use of oxygen as an oxidant still makes it the cheapest process available after more than a hundred years. Unfortunately, gold cyanidation is known to be a slow process that requires high consumption of cyanide. In fact, cyanidation plants are designed with very long residence times (Habashi, F., 1967). Drawbacks of long cyanidation times are, among others, loss of gold in tailings, high reagent consumption and high capital investment and maintenance costs.Responding to their members expectations for the improvement of cyanidation process, COREM undertook a challenging R&D program covering the development of alternative concepts (processes) and the understanding and solving of mass transfer, gold passivation and process water chemistry problems. One of the interesting findings of the R&D program is a patent pending process technology based on the cyanidation by size class (CSC) concept (Côté and Ourriban, 2004; Gagnon and Ourriban, 2007; Gagnon and Ourriban, 2004).The new technology was tested at the Sleeping Giant concentrator, a plant member of COREM. The existing flowsheet was modified in order to implement the CSC process in the full-scale plant. The plant has been operated using the modified CSC based process since August 2007. Laboratory testwork was conducted prior to the industrial application in order to properly design the new process scheme. The modifications included:1) Reclassification of the grinding circuit product through an hydrocyclone2) Leaching of the coarse size fraction3) Addition of the fine fraction to the coarse leaching circuit tails."

Jan 1, 2009

Numerical models play a significant role in the design of safe underground mining excavations and support systems. Advances in the capabilities of numerical modeling software, together with ever increasing computational speeds, have made it possible to investigate the very nature of the large-scale rock mass and its response to mining excavations. The improved understanding of the rock response obtained from modeling enhances our designs, resulting in greater stability and safety of the mining excavations. To help advance the state of the art in this field, the National Institute for Occupational Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers address a wide range of issues, including various numerical modeling approaches, rock mass modeling, and applications in coal and metal mines.

Jun 1, 2009

By W. M. Myers

Jet is a substance of organic origin and has been defined by the U. S. Geological Survey as a "dense black lignite, taking a good polish, and sometimes used for jewelry". Jet is characterized by the lustrous, intense black surface it displays when polished. It is due to this property that the expression "jet black" is so commonly used to imply intense blackness.

Jan 1, 1923

By Stephen H. Chung

The blasting performances identified above are considered to be the most practical ones for judging the effectiveness of a design combining explosives / rock / drill pattern. In a total blast design process, productivity relates closely to both fragmentation and heave / displacement of muck. In cast blasting, the more overburden displaced by explosives, the less blasted material there is left to be removed with mechanical equipment such as draglines or trucks. For wall protection and dilution control, estimates of the maximum extent of cracks / damage generated in situ due to blasting will help determine the location for drilling and loading perimeter blastholes.

Jan 1, 1994

By S. H. Lorain

This paper is one of a series on mining and milling method and costs being published by the United States Bureau of Mines. The Golden Messenger mine, operated by the United Gold Mines Corporation, is in the York-Confederate Gulch mining region in Luis and Clark County, Mont., 22 miles northeast of the city limits of Helena and about 1 mile north of the town of York. It is the first operation to exploit successfully the low-grade ores of the York-Confederate Gulch area. The unusual vein structure presents some mining problems that have been solved in ail interesting manner.

Jan 1, 1937

By John S. Cummings

Although there are many geologic situations which might be discussed at a session such as this, as I considered the problem, it became apparent to me that I should discuss a situation which has been of concern to me, and should be of concern to the geologic community. As a result, the questions which I will pose, and the criticisms, have not been arrived at quickly or easily, but have accumulated through time, to the point where I feel discussion is necessary. Very briefly let me say that my criticism of geologic mapping, of conclusions reached, and objectives or lack of such, results from my association with many areas where such studies have been completed, and resultingly my inability to comprehend the system of evidence or logic which supports extensive age-formational designations. The heart of the problem is that many conclusions resulting in geologic designations are based on weak or non-existent evidence, and such should be catagorized as hypotheses. Although the geologic community as a group does not approve or disapprove of such designations, it is evident that many or most of such designations attain a "status", and arc accepted as more or less valid statements. As will be shown, the amount of specific lithologic data provided in some quadrangle mapping projects is exceedingly slim. However, of concern herein is that the type of information presented at any stage is sufficient to warrant conclusions drawn. To see the magnitude of the problem, it is probably necessary to review some basic fundamentals upon which our geologic systems are established. The United States Geological Survey has defined a "formation" as the broad unit of geologic mapping consisting of a large and persistent stratum of one kind of rock. Obviously such a designation allows that a formation could be considered "time variant" in a horizontal as well as in a vertical context. However, other definitions enable a formation to mean units

Jan 1, 1972

By M. L. Harris

In underground mines, coal dust explosions are prevented by the addition of rock dust sufficient to render the coal dust inert. The National Institute for Occupational Safety and Health (NIOSH) has developed a hand-held instrument that uses optical reflectance to measure the explosibility of a rock dust and coal dust mixture. This instrument is called the Coal Dust Explosibility Meter (CDEM). In this study, NIOSH personnel accompanied Mine Safety and Health Administration (MSHA) inspectors on their routine band surveys in five and three underground coal mines in MSHA District 2 (PA) and District 11 (AL), respectively. While underground, NIOSH personnel and MSHA inspectors used the CDEM to assess the explosibilities of the dust samples. The values of percent incombustible content (% IC) determined by the CDEM agreed well with those obtained later by low temperature ashing (LTA) in both MSHA and NIOSH laboratories. Further, the meter identified some samples as potentially explosible that LTA analysis had found to possess sufficient rock dust for inerting. The CDEM provides more information on the hazards in the mine. Rapid identification of areas with explosible dust mixtures using the CDEM allows for immediate intervention rather than a wait of several weeks for laboratory analysis.

Jan 1, 2008

By Lise Chénard

El presente texto señala los lineamientos del proyecto REFORMIN, así como su repercusión en la dinámica de promoción de la industria minera. REFORMIN surge en el 2001 como un proyecto bilateral entre Canadá y Bolivia, cuyo financiamiento proviene de la Agencia Canadiense de Desarrollo Internacional (ACDI). Su finalidad es apoyar al Viceministerio de Minas, facilitándole el acceso a la pericia canadiense para lograr una gestión más sana y eficaz de los recursos minerales del país. Para ello, se basa en los principios fundamentales tales como: mejora de la gestión del medioambiente minero, apoyo a la prevención y gestión de conflictos sociales en las comunidades mineras, a los mineros artesanales y a la promoción de los recursos minerales del país, -en tanto benefician al desarrollo de la industria minera en un contexto de mercado globalizado.

Apr 22, 2003

By Kenneth J. Hartman

Introduction The term kaolin is derived from kauling, a Chinese word meaning high ridge. This was the name of a hill in China where kaolin was first mined several hundred years ago (Murray, 1976). Other common names used for kaolin include clay and China Clay. Clay technically has a broader meaning and could refer to bentonite and ball clay as well as kaolin. China clay, as a descriptive term, apparently results from kaolin&apos;s origin. But it could also be due to a significant historical use in ceramic applications. The terms kaolin and clay will be used interchangeably in this analysis because of the common practice of using these terms in the paper industry. Major reasons for kaolin&apos;s wide-spread industrial usages center on kaolinite&apos;s physical features of good color, low viscosity, and inertness. Kaolin is described as a hydrous aluminum silicate with an approximate composition of 2H2O • A12O3 . 2SiO2. A new version of the product is calcined clay with modified hydration content. It is gaining widespread use. Components of any particular kaolin, in addition to alumina and silica, are viewed as impurities. The more values deposits and, hence, higher priced kaolin products are those of the highest purity. Kaolin is the most widely used mineral in paper manufacturing throughout the world. Key production centers are located in England and the US. Most of the Tatter&apos;s production is located in Georgia. The key markets for Georgia kaolin are paper markets - both paper coating and paper filling. These paper markets extend throughout the world, not just to domestic markets. In fact, export markets are second in size only to domestic paper markets for Georgia&apos;s producers of kaolin. Just as the paper markets are important for kaolin producers, kaolin is an important raw material for papermakers. Compared to the other three major pigments - titanium dioxide, calcium carbonate, and talc - kaolin&apos;s 1984 tonnage for papermaking represented 85% of the total. Even though titanium dioxide&apos;s unit value is much higher, kaolin&apos;s estimated total 1984 value still represented 51% of total dollars spent by papermakers for the four pigments. Kaolin grades- are briefly defined using particle size and brightness as principal means of classification. Likewise, grades of papers using kaolin are defined using the American Paper Institute&apos;s guidelines. From these definitions, associated kaolin grades used in particular grades of paper are reviewed. Special emphasis is placed on how qualities desired in certain papers are achieved through the use of specialized kaolin grades. World kaolin production World production statistics (Coope, 1979; Table 1) demonstrate that kaolin is produced in many areas of the world. About 60% of production is centered in the US and England (Fig. 1). Deleting Eastern Europe&apos;s produc-

Jan 4, 1987

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946