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I. THE ENERGY CRISIS STILL EXISTS A. ALTHOUGH IMMEDIATE SHORTAGE IS NOW ALLEVIATED BY: 1. Increased imports through lifting of Arabian embargo; a. Imports were 6.5 million bpd during the week ended January 17, or 1.3 million bpd higher than last year. b. 1.7 million bpd higher than March '74. 2. Decreased demand resulting from higher prices and conservation. a. January 1975 demand was 17.9 million bpd, 0.1 million bpd lower than January 1973 and … b. 2.0 million bpd, or 10% under originally projected demands for January 1975. c. Gasoline (excluding tax) went up 59% from 27d/gal in August 1973 to 43c/gal in September 1974. d. Gasoline demand for January 1975 was 6.3 million bpd, 0.1 million bpd higher than 1973 but 0.7 million bpd ( 10% ) under projected demand. 3. Increased crude and major product inventories. a. January 17, 1975 crude and major product inventory was 794 million bbl, 99 million bbl higher than the same date in 1973. b. 105 million bbl increase since April 12, compared to only 38 million bbl increase during the same period in 1973.

Jan 5, 1975

By K. S. Seljesater

Since the development of dispersion-hardenable lead-antimony alloys' in the laboratories of the Western Electric Co., Inc., studies have been made of the effect of various third constituents on these alloys.2 This paper covers a study of the effect of small amounts of arsenic. This element is important since it occurs as an impurity in many commercial antimonial leads and the results obtained are particularly interesting as indicating a class of addition agents which exert a stabilizing effect on dispersion-hardened alloys. Experimental In order to study the effect of increasing amounts of arsenic, a series of alloys were made up containing 1 per cent. antimony, and arsenic varying from 0. to 0.10 per cent., the balance Doe Run lead (99.997 per cent. lead). The alloys were cast into bars 1 1/2 in. wide by 3/4 in. thick and cold-rolled to about 1/8 in- thickness. Three samples of each composition were annealed 1 hr. at 225" C. and quenched in water. One set was aged at room temperature, one at 50" C., and the third at 100" C., the

Jan 1, 1929

By K. S. Seljesater

Since the development of dispersion-hardenable lead-antimony alloys' in the laboratories of the Western Electric Co., Inc., studies have been made of the effect of various third constituents on these alloys.2 This paper covers a study of the effect of small amounts of arsenic. This element is important since it occurs as an impurity in many commercial antimonial leads and the results obtained are particularly interesting as indicating a class of addition agents which exert a stabilizing effect on dispersion-hardened alloys. Experimental In order to study the effect of increasing amounts of arsenic, a series of alloys were made up containing 1 per cent. antimony, and arsenic varying from 0. to 0.10 per cent., the balance Doe Run lead (99.997 per cent. lead). The alloys were cast into bars 1 1/2 in. wide by 3/4 in. thick and cold-rolled to about 1/8 in- thickness. Three samples of each composition were annealed 1 hr. at 225" C. and quenched in water. One set was aged at room temperature, one at 50" C., and the third at 100" C., the

Jan 1, 1929

By A. W. Adamson

A model for transport processes in liquid mixtures is discussed which supposes that the elementary act involves a position exchange between two species and that the exchange is so confined by the solvent cage as to occur nearly isosterically. The rate-determining step, thus, is likened to a bi-molecular reaction and is so treated, using absolute rate theory. The cage model has been applied to diffusion, thermal diffusion, sedimentation and viscosity, but only the first and last of these phenomena are emphasized in the present paper. The model leads to semi-empirical relationships between the absolute value for a digusion coefficient and the activation energy for diffusion, between mutual and self-diffusion coefficients and for the variation of the viscosity of a binary mixture with composition. These are discussed in relation to experimental data for various systems, including hydrocarbon mixtures. It is shown that the proposed viscosity equation and seven other commonly used ones all may be regarded as special cases of a single general relationship; a brief critical analysis is made of the basis of selection of one or the other for data fitting or interpolation. INTRODUCTION AND GENERAL THEORY The present paper covers a brief discussion of a cage model for transport processes in liquid mixtures and how this model may be useful in treating the diffusional behavior and the viscosity of such systems. Since diffusion requires the more detailed treatment, it will be taken up first, and the model then applied to viscosity. There are two types of diffusion coefficients that may be measured experimentally, apart from thermal diffusion quantities. The first is the mutual or binary diffusion coefficient, D which may be defined in terms of Fick's first law. This states that the permeation, or flux P, is proportional to the concentration gradient. In the usual experiment, P is measured relative to a frame of reference fixed with respect to the medium (e.g., the diaphragm in a diffusion cell); as a consequence, the same value of D is obtained regardless of whether P and C refer to Component 1 or to Component 2; i.e., there is only one independent mutual diffusion coefficient for a binary system. In addition to D there will be various self-diffusion coefficients. defined in terms of the gradient in labelled species i and its permeation in an otherwise uniform medium. The thermodynamic approach to mutual diffusion supposes that the actual driving force is the gradient of the chemical potential, i.e., that In the case of a dilute solution of solute, Eqs. 1 and 3 lead to the Einstein equation, If the solution is ideal and the friction coefficient is taken to be then the familiar Stokes- Einstein equation results. Mutual and self-diffusion coefficients can not be related on general thermodynamic grounds; it is necessary to invoke some additional assumptions, i.e., a model; several such have been proposed. Hartley and Crank' supposed the existence of separate, intrinsic diffusion coefficients (Dl and D2) for each component, essentially corresponding to the two self-diffusion coefficients. The two flows can not be independent, however, but must be coupled through the usual restriction that there be no net volume flow. For an ideal solution. one then obtains' Glasstone, et al' treated diffusion in terms of absolute rate theory, but their approach otherwise resembled the previously mentioned one in that each species was considered to move with respect to the general medium in a manner determined by its individual jump distance and specific rate constant. For other than dilute solutions, a coupling of flows leading to an equation such as Eq. 6 would again be present. However, as required by Eq. 6, one does expect that the self-diffusion coefficient for the solute and the mutual-diffusion coefficient for the system become identical at infinite dilution. Lamm4 recognized that there should be three distinctive interactions in a two-component system-1-1, 1-2 and 2-2 — and, therefore, proposed three rather than two fundamental friction coefficients. Mutual diffusion resulted from 1-2 interactions only, and self-diffusion resulted from 1-2 plus either 1-1 or 2-2 interactions. Again, a collective coupling between all motions was imposed to meet the condition of no net volume flow. Laity' has shown how to convert the Onsager equations to a form very similar to Lamm's. Cage Model For Diffusion Work in this laboratory on diffusion in aqueous sucrose solutions made it apparent that three, rather than two, interactions were indeed needed," but considera-

By Archer Wheeler

Introduction. THERE are two general methods in use for the production of metallic copper from matte which are worthy of consideration : (1) the Welsh blister process, and (2) the converter process.1 As practically all of the copper produced to-day is made in converters, we will give a brief outline of that process before proceeding with the special subject of this paper. Matte may be roughly defined as a mixture of the sulphides of copper, iron, nickel, silver, etc. In the converter process this is blown up to metallic copper in a modified type of Bessemer converter. The conversion of matte consists mainly in, (1) the removal of sulphur in the form of SO2, and (2) the slagging of the iron. With this brief statement we come to the two subdivisions of the process of converting mattes: Converting with acid linings. Converting with basic linings.

Jan 12, 1913

By I. E. Rosenzweig

THE problem considered in this paper is as follows: An arbitrary horizontally stratified area is given. The electrical properties of this area are characterized by a function p(z) (Fig. 1), which shows the relationship between resistivity p of thes oil and the depth z. For such general case the apparent resistivity p* will be computed, by FIG. 1.-GRAPH OF FUNCTION p(z) FIG. 2.-GRAPH OF p(Z) FOR n HOMO-GENEOUS LAYERS. earth-resistivity measurements carried out by any given configuration of electrodes. General solutions of this problem appear to be very important for interpretation of field results of resistivity measurements, concerning structural investigations. Such solutions have been given by many authors for the special case of a finite number of homogeneous layers (Fig. 2)1-4 as well as for the more general case of continuously rang-ing resistivities. 5-8

Jan 1, 1939

By Philip D. Wilson

WHEN the United Nations win the war and the decision has been made to control future armament in the Axis countries, plans for the extent and operation of such control must have been prepared, to be ready to put into immediate execution. Such control to be effective must be premised upon complete military occupation of the two countries for a substantial period, with an arrangement at the end of such occupation for continued supervision of these industries into an indefinite future.

Jan 1, 1944

By F. E. Bedale

STUDY of several severe mine explosions that occurred during the winter of 1907 led to the belief that coal dust was a definite explosion hazard. The Consolidation Coal Co. was a pioneer in the early work to' eliminate this hazard and to combat the dangers incident to poor ventilation and the presence of methane. Maintenance of high humidity throughout the mines was one of the first measures adopted, later to be superseded by rock-dusting. In the twenty years from 1907 on, many safety measures were developed and adopted, and several prizes were won, though the practice was crude by present-day standards. But in 1927, the company went to work in earnest, and organized a Department of Safety with adequate personnel and with authority to enforce all approved rules for the prevention of accidents and the preservation of company property. All plans for new construction work, changes in mining systems, and proposals for the purchase of new mining equipment had to receive the approval of this Department. A set of operating- and safety standards was written to govern the activities of all employees, and physical examinations for them were required.

Jan 1, 1938

By V. F. Leferrer

A new process for the treatment of silver crusts from desilverization of lead has been developed by Societe de Penarroya. The zinc contained in the crusts is recuperated by vacuum distillation at low temperature. The use of special retort crucibles is avoided. AT Noyelles-Godault the Parkes process (zinc addition to a silver-bearing lead melt) is used to desilverize lead bullion from the blast furnace. The crust which rises to the surface of the bath is removed and pressed by a well-known process in a press of the Howard type. The pressed crust, called zinc crust or silver crust, contains 10 pct Ag, 30 pct Zn, and 60 pct Pb. It is melted under a salt bed in a small, narrow, and deep kettle heated only in its upper part. A liquid concentrated alloy is obtained which is called T.A.C. in France (triple alliage concentr6) analyzing approximately 25 pct Ag, 65 pct Zn, 8 to 10 pct Pb, and 1 to 1.5 pct Cu. This T.A.C. is a real metallic alloy, completely deoxidized, and can be stored indefinitely. The process used at Noyelles-Godault consists in distilling this alloy in a tight furnace, under low vacuum and at low temperature, so that only the zinc distills and is condensed into liquid form. The residual silver-bearing lead is almost entirely free from zinc and oxidized dross. The vacuum dezincing equipment, see Figs. 1 and 2, consists of: 1) A furnace, constituted of a casing of steel plate lined with refractory bricks, heated internally by means of graphite resistors. The temperature of the furnace is measured by a thermocouple device and controlled by an automatic temperature regulator which acts upon the flow of the current passing through the resistors. Two doors, numbered 1 and 2 in Fig. 2, are provided for, one for charging the T.A.C., the other for tapping the high silver-bearing lead. 2) A condenser, and an ordinary room lined with good heat conductor refractory material. This condenser is provided with a graphite resistor which serves to bring to temperature when starting the furnace. A thermocouple records the temperature of the zinc melt and controls the temperature in the furnace, that is, the flow of current through the resistors, by means of the above mentioned regulator, so that the distillation rate in the furnace does not exceed that of the condensation. The condenser is connected to the vacuum pump by a filter. The whole equipment should, of course, be fluid-tight. The operation is carried out under a vacuum of about 10 mm Hg.

Jan 1, 1958

By W. J. West, T. D. Mueller, J. E. Warren

The authors have presented valuable information on the influence of the interfacial tension and the contact angle on the recovery efficiency of the waterdrive process. It is considered, however, that the following points deserve a closer examination. 1. As pointed out by Wyllie and Spangler1 the displacement pressure PD i.e. the pressure required to initiate the displacement of the wetting phase from the core, is a measure of the maximum pore diameter dmax. If the capillary pressure Pe as a function of the wetting

Jan 1, 1956

By E. P. Klier, Jane Jellison

The course of the transformations on cooling in a series of Cu-A1 alloys has been followed by means of thermal analysis, X-ray diffraction, and optical metallogrAphy. Specimen size was found to have a pronounced effect on the time of completion of the pearlite transformation due to modification in the unmber of nuclei. The ordeving transformation zvas observed for all cooling rates for all alloys studied, and is considered insuppvessible. At intermediate cooling' rates, a transitional struchire for 011 alloy compositions and based ox the bainite reaction was observed. The alloys of aluminum and copper possess a eu-tectoidal region at from about 9.4 to 16 pct Al. Above the critical temperature, the disordered bcc phase, 0, is stable. At subcritical temperatures, the 0 phase decomposes under equilibrium conditions into the stable phases, a and y,. At the eutectoid composition, these phases develop a lamellar pearlite structure, in appearance much like that found in steels. During rapid quenching from supercritical temperatures, the diffusion processes required for the formation of the equilibrium phases are suppressed, and the 0 transforms to an acicular martensitic phase, designated B or y' depending on the aluminum content, or to a mixture of the two. Early investigators of this system concentrated on determining the equilibrium phase diagram, ''' the structure of the equilibrium phases,3 and later the isothermal decomposition of the 0 phase at subcritical temperatures, or the decomposition of the martensite on tempering. Other work which treated the nonequilibrium transformations concentrated largely on the martensite transformations and the structure of the b and y' phases.15"17 Since the pearlite and martensite transformations in this system resemble those in steels, the one being formed by nucleation and growth of adjacent lamellae of the equilibrium phases, and the other by a diffusionless, shear-type transformation, the present study has been undertaken to investigate the structures formed on continuous cooling, with the objective of constructing cooling transformation diagrams analogous to those derived for alloy steel systems. In particular it was desired to determine whether parallels between the A1-Cu and iron-iron carbide systems on continuous cooling extended to encompass the intermediate phase, namely the bainite structures, which form by a combined martensitic-diffusion mechanism,'' but which are supersaturated with respect to the equilibrium phase upon which their crystal structure is based. To this end the transformations in representative alloys of the Cu-A1 B eutectoid system have been followed, using the methods of thermal analysis, X-ray diffraction, and optical microscopy. EXPERIMENTAL PROCEDURE Materials. The materials tested were those used by Klier and Grmko 5 in their study of the isothermal decomposition of these alloys. The alloys were melted in graphite crucibles and chill-cast into 5 by 2 by 1/4 in. ingots. The ingots were then hot-rolled to sheets 1/8, 1/16, and 1/32 in. thick. The compositions are given in Table I. Specimen Preparation. Specimens for thermal analysis were in the form of small squares approximately 1/4 in. on a side. For the 11.9 and 13.5 Al-Cu alloys, the sheet thickness was 1/16 in. and for the 10.5 A1-Cu alloy the 1/32-in. sheet was used. One lead of a chromel-alumel thermocouple was spot-welded to either face of the square with the specimen itself thus forming the hot junction of the thermocouple. Specimens for X-ray analysis were prepared as filings from martensitic sheet stock and were sealed in glass ampoules under 1/2 atm of argon. Metallographic examination of the powder specimens was carried out on a portion of the heat-treated filings mounted in lucite. All specimens were examined metallographic ally after etching

Jan 1, 1965

By G. Sandoz, C. A. Siebert

OIL quenching of steel, in good commercial practice, is carried out using a great deal of agitation in the quenching bath. Many of the tests reported in the literature represent the results obtained on steels quenched into still oil. Scott1 describes three stages of cooling in liquid quenching baths, namely: "State `A'-Vapor Blanket Cooling-In this, the first stage, a thin stable vapor film surrounds the hot metal. Cooling is by conduction and radiation through the gaseous film and is therefore relatively slow. "Stage `B'-Vapor Transport Cooling- Termination of the `A' stage is marked by wetting of the metal surface. Vapor forms copiously in bubbles and is carried away by gravity and convection currents to condense in cooler surrounding liquid. This is the fastest stage of cooling. "Stage `C'-Liquid Cooling--The `B' stage ends as the surface temperature of the metal approaches the boiling point of the quenching liquid. Vapor no longer forms, so cooling is by conduction and convection and the temperature difference is greatly decreased. This mode of cooling is slower than that of the `B' stage." Mechanical agitation of the quenching medium will accelerate all three stages of cooling. The greatest effect, however, will be noted on stage `B' because the removal of the bubbles from the surface of the steel will not be entirely dependent upon gravity and natural convection currents. The method employed in this investigation for evaluating the oils was the end quench test. The various oils were substituted for water as the quenching liquid and hardness determinations were made at various distances from the quenched end. Most of the tests were run using a 3/8-in. orifice with a 2 ½ -in. stream height. However, to check the effect of other velocities two additional conditions were used, namely: (I) A 3/8-in. orifice and 1-in. stream height, and (2) a ½ -in. orifice and a 3 ½ -in. stream height. In all cases the samples were suspended so that the quenched end was ½ -in. above the orifice. The steel used was an NE 9450 having the following analysis: [ ] Some tests were run on an NE 8740, 3312, and a 4340 steel. The results obtained on these steels confirmed those obtained on the NE 9450 and have therefore been omitted' from this paper. The test bars were machined from 1 1/8 -in. stock to 1-in. diam by 4 in. long.

Jan 1, 1948

By AIME AIME

OUR own Institute of Metals and Iron and Steel divisions cooperated with the Iron and Steel Division of the American Society of Mechanical Engineers, the American Welding Society, and the American Society for Steel Treating in a busy week at Cleveland. The morning sessions were held at the Hotel Cleveland and the afternoon ones at the Auditorium, where the metallurgical exhibition under the auspices of the American Society for Steel Treating not only occupied the arena of the Auditorium but completely filled the huge adjacent Annex. In the intervals of sessions the members thronged the exhibits but in the evenings the local attendance was so great that if the crowds had been any larger it would have been difficult to see the exhibits. With so many firms, both producers of metals and of equipment accessory to their production and use, it would be impossible to mention them -all and unfair to single out a few, since no two individuals' judgment would coincide as to relative interest and importance. In any case an exhibit is a thing to be seen rather than described, and these were well worth seeing.

Jan 1, 1929

By R. I. Jaffee, J. G. Dunleavy, W. Hodge, H. R. Ogden

Jan 1, 1949

The Cuajone and Toquepala copper projects are located in the extreme southern area of Peru. Since 1960, Southern Peru Copper Company has operated the Toquepala open -pit mine, flotation mill, 110 smelter, townsites, power plants, and railroad. Toquepala and 10, the smelter and port location, are connected by a 110-mile-long (176 lun) railroad. Much of Toquepala's infrastructure has been used for the Cuajone project. Cuajone, at an elevation of 11,400 ft (3475 m), required five standard-guage railroad tunnels with a combined length of 17 miles (27.2 km) to connect with Toquepala so concentrates could be shipped to the no smelter. The total cost of Cuajone is estimated at $726 million for a designed annual capacity of 180,000 tons of copper, equivalent to about $4,000 per ton of installed production capacity. This relatively low cost per ton, by today's standards, has been made possible through the use of the 110-to Toquepala railroad, the ability to expand the 110 copper smelter, and other favorable factors. To mine the 468 million tons of copper sulfide or e at a grade of 1.0% copper, approximately 24 1 million tons of waste were stripped- before mining of ore to supply the new Botiflaca 45, 000 ton per day concentrator. The mining rate must exceed 300,000 tons of waste plus ore per day to maintain the 45, 0 00 tpd sulfide ore milling rate which was to be reached at the end of 1976. Waste stripping is done with 15 cu yd electric shovels and 120 -ton trucks. Ore mining is done with 8 and 9 yd shovels. A railroad connects the pit with the 60 in. by 89 in. Allis-Chalmers gyratory crusher. Side-dump railroad cars of 50.cu yd capacity dump onto a 0 16 ft 9 in. long (5. 1 m) grizzly inclined at 40º with 7 to 8 in. (178 to 203 rnrn) bar spacings. The grizzly is divided into two 22 ft 4 in. (6.8 m) wide sections and two side -dump railroad cars discharge simultaneously into the 150-ton capacity dump pocket. A Barco rock manipulator is used for breaking or removing oversize from the dump pocket. The bin receiving the grizzly undersize has a capacity of 5,000 tons, and the pocket beneath the crusher holds 900 tons. Each is equipped with an 84 in. apron feeder, which feeds a 60 in. (1.52 m) conveyor belt to the 150,000 ton coarse ore stockpile, where the ore is distributed by a 72 in. (1. 83 m) tripper conveyor. The 45, 000 live tons in the coarse ore stockpile are reclaimed by twelve 48 in. (1. 22 m) apron feeders. Maintenance on the crusher eccentric is made easy by an eccentric

Jan 1, 1978

By John W. Tieman

Coal is a term applied to vegetable matter (trees, grasses, etc.) which was subjected to heat and pressure through geologic ages. This resulted in a change in both the physical and chemical properties. Because its chemical composition is variable, geologists classify coal as a heterogeneous mineral rather than a homogeneous mineral. Peat represents the initial, unconsolidated stage in the development of coal. This coalification continues with time and the application of temperature and pressure to lignite, subbituminous, bituminous, and anthracite toward the theoretical graphite end member. PHYSICAL PROPERTIES OF COAL The physical properties are concerned with the characteristics of coal in its natural state, or prior to its end use as a fuel. For example, the hardness and grindability of coal determine the maintenance cost for coal mining, handling, and pulverizing equipment; the specific gravity of coal and its associated minerals determines the coal preparation technique used in a cleaning plant as well as the capacity of coal bins, boats and size of cargo, and other coal storage facilities. The physical properties are, of course, dependent on the chemical constituents of coal, and all properties are interrelated. Specific Gravity The specific gravity (sp gr) of a solid is the ratio of the weight of a cubic foot of the solid to the weight of a cubic foot of water. The specific gravity of pure coal has been reported to range between 1.23 to 1.72 and increases with the change in rank from lignite to anthracite. This means that it is 1.23 to 1.72 times heavier than water.

Jan 1, 1981

By John W. Tieman

Coal is a term applied to vegetable matter (trees, grasses, etc.) which was subjected to heat and pressure through geologic ages. This resulted in a change in both the physical and chemical properties. Because its chemical composition is variable, geologists classify coal as a heterogeneous mineral rather than a homogeneous mineral. Peat represents the initial, unconsolidated stage in the development of coal. This coalification continues with time and the application of temperature and pressure to lignite, subbituminous, bituminous, and anthracite toward the theoretical graphite end member. PHYSICAL PROPERTIES OF COAL The physical properties are concerned with the characteristics of coal in its natural state, or prior to its end use as a fuel. For example, the hardness and grindability of coal determine the maintenance cost for coal mining, handling, and pulverizing equipment; the specific gravity of coal and its associated minerals determines the coal preparation technique used in a cleaning plant as well as the capacity of coal bins, boats and size of cargo, and other coal storage facilities. The physical properties are, of course, dependent on the chemical constituents of coal, and all properties are interrelated. Specific Gravity The specific gravity (sp gr) of a solid is the ratio of the weight of a cubic foot of the solid to the weight of a cubic foot of water. The specific gravity of pure coal has been reported to range between 1.23 to 1.72 and increases with the change in rank from lignite to anthracite. This means that it is 1.23 to 1.72 times heavier than water.

Jan 1, 1981

By GLENVILTE A. COLLINS

(Presented at a Meeting of the Spokane Local Section of the Institute, Feb. 17, 1912, and accepted for publication in the Bulletin. ) WHILE I am not at the present time engaged in active mine-management, my duties permit of extensive study and examination of many mines, mills, and reduction-works in various places throughout the United States. Being much interested in efficiency-work in general, and an ardent reader of writings on this subject by Frederick W. Taylor and others, as applied to manufacturing-plants, and having served my apprenticeship from mucking to the engineering design of ore-dressing and underground plants, I hope that this paper will lead others to investigate the field more fully, to the improvement of general mine- and mill-operations, as well as the advancement, intellectually, physically, and financially, of the employee and his relations with the employer. If a man who is prepared to look closely and observe broadly starts in Canada and zig-zags from camp to camp to southern Mexico, taking time casually to inspect mines, mills, and smelters, he will be pitifully impressed by the great difference in customs, and the general waste of labor, time, and money throughout the country. He will so seldom observe a dollar's worth of results given in exchange for a dollar spent that he will form a poor opinion of operating-efficiency and management. This highly-scientific department, requiring an amount of skill and executive ability equaled in few, if any, of the professions, certainly falls short of the standard established in our greater manufacturing industries. It is easily said that this is due to the diversity of conditions in mining, milling, and smelting. But on second view it must be admitted that there is room for tremendous improvements in nearly every mining-organization. The proposal of such improvements is often met by the argument that any mine

Sep 1, 1912

By Paul T. Benson

MOST important of the various departments of a custom smelter, so far as the financial welfare of the plant and the confidence of shippers are concerned, is that responsible for correct weights, accurate moisture sampling, and the obtaining of control samples that are strictly representative of the lot of ore from which they come. Treatment rate schedules are based on the metal content of ores received, reduced to dry weight. These rates must be low enough to keep the ship- per from taking his business else- where and still must allow the smelter a profit. Assay results, likewise, must satisfy the shipper, but if they show too high a metal content for the ore they represent, the smelter will actually lose money. It is always considered, and constant checks through umpire assays prove, that laboratory results are closely correct, so the bur- den of the plant profit and loss and the satisfaction of the shipper rest squarely upon the sampling department.

Jan 1, 1936

By J. Serra, M. Turpin, R. Alberny

A new method is proposed to obtain automatically an unbiased estimate of the interdendritic spacing A. It is shown that the structure can be built by a random distribution of a rectangular basic unit. The usual definition of the interdendritic spacing yields a value 1 which, coupled with A, gives the shape of the basic rectangular unit. A study of the relationship between dendrite arm spacing and solidification rate was conducted as a part of a research program on dendritic solidification. For any comparison between theory and experiments to be meaningful, it is necessary to measure reproducible and clearly defined spacings. Fig. 1 shows clearly that even in a fairly simple structure such measurements are difficult. if we compare photos (a) and (b), we can hardly assess which one shows the larger spacing. Moreover, the quantity to be measured can be defined in several ways. On a small scale, dendrites seem to be distributed in a very regular and ordered way. However, on a larger scale, this regularity no longer exists. The usual way to measure spacings is to pick up some rows of dendrite stalks; such measurements are obviously biased since less orderly regions are not taken into account. A more objective method is to section the picture with randomly oriented straight lines and average the measured interdendritic spacings. The purpose of this paper is to show that such measurements, which can be conducted automatically, yield objective and reproducible results which are directly related to characteristic features of the dendritic structure. I) THEORETICAL ANALYSIS 1-1) Mathematical Morphology and Function of Co-variance. Matheronl and Serra2 enlarced- the definition and geometrical meaning of the notion of covariance to encompass problems in mathematical morphology. A brief review of part of their theory can be stated as follows. Let A' be an isolated particle, and let us consider a group of two scanning points h is the vector joinlng these points, h its modulus, and a its direction. Let us also define a boolean function, k(x), whose value is 1 if x lies inside the particle and 0 if it 1s outside. The total number of events in which both points are inside A' IS the covariance Ii',(h): is the measure of the intersection of A' with the particle ALh obtained by translating A' of -h Obviously K,(O) is the volume of the particle A', or its area if A' is a two-dimensional body. The average value of K,(h), when the direction of a vector h of constant modulus is rotated, is: An important property of the covariance is illustrated on Fig. 2: if the shape of a particle shows some regularity along a direction a, K,(h) generally presents a maximum. We now consider a group A, made of many particles A' distributed in space; then k(x) is taken as the realization of a stationary random f~nction.~ The volume fraction (or fraction of area if the problem is two-dimensional) occupied by A equals the average value q of k(x): meaning "average value of"). We also replace

Jan 1, 1970