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By Everett Parker

THIS paper describes the methods used to determine the rates of payment for contract work and the plan of contract supervision in the Elm Orlu mine. A discussion of the theory of wages and the eternal question-what is a just wage-are beyond the scope of this article. In the fall of 1920 the Elm Orlu was the largest mine in Butte using the day's pay system of payment for stoping operations. High labor and supply costs and a falling market for the product of the mine made economic mining difficult. The mining method had been changed from the square set stoping to timbered rilling to eliminate most of the shoveling. There was no opportunity to reduce the cost of supplies other than more rigid economy in their use. It was recognized, however, that the labor efficiency was low and that the reduction in costs depended on increasing the output per man. While in general, the low man efficiency was a resultant of the high wages paid and the shortage of men during the war and subsequent period of inflation, it was felt that the contract and bonus system used in the other mines was the main factor in that the most capable and energetic men had been attracted to those mines where more than average skill and dili-gence were recognized by more than average pay.

Jan 1, 1927

By R. D. Brown

This paper profiles Canada’s current economic, tax, and political environment with respect to its mining industry. Problems that must be overcome if the industry is to attain its full growth potential and are highlighted, some suggestions reflecting the opinion of many in the industry are given. Tables provide some detail on the current Canadian mining tax system, province by province, as well as for the Yukon and Northwest Territories, plus some relevant economic trends.

Jan 1, 1985

By Michel Daghert, Michel David

In the exploitation of large porphyry type deposits where a cut-off has to be applied and where "internal waste" exists, planning people ask the geologist for the estimated grade of small blocks. Comparison with actual production figures and blast hole assays shows that any kind of weighted average of neighboring DDH (diamond drill hole) samples provides an excessingly smooth picture of reality, resulting most of the time in overevaluation of tons of ore. Solutions based on examination of Past production data exist14 but it would be necessary to have a solution which can be applied before production starts as the preceeding problem also results in an overestimation of the total reserves, often by as much as 20%, thus changing the mine life accordingly and destroying any "optimum planning" which could have been done. The proposed alternative is to forecast the grade distribution of small blocks in a larger block, sufficiently well documented. Several Possible ways to estimate these distributions are reviewed and emphasis is placed on recently developed methods (source G. Matheron) where the coefficients of the orthogonal polynomial series expansion of the distribution of any size of block are directly estimated by kriging. The efficiency of the technique is tested on a level of the Cyprus Pima open pit where the predicted recovery is compared to actual production figures.

Jan 1, 1980

By G. C. Weaver, G. T. Harley

Beds or lenses of potash and magnesium salts are found in a thick salt section (Salado) overlain by Rustler Red Beds in several members of which water is present and from one of which the rehery process water used by International is obtained. Most of the holes drilled are less than 1000 ft. deep, but some wildcat holes have exceeded 3- ft. cable or rotary tools are used to drill down to the salt. when samples of water are desired the cable rig is used, but when this is not necessary, and where caving material is present, the rotary rig has an advantage. The rotary rig has a further advantage in that only one machine is required to drill and core the entire hole, whereas the cable rig must be moved off to make way for the core drill. Casing is placed in the upper section of the hole as required to shut off water, and a 5 3/16 in. string is set in the top of the salt before coring starts. With the rotary rig drilling is often carried to the salt with no casing, as drilling mud seals off caving ground and water-bearing strata, and a string of 4-in. line pipe or 4-in. flush-joint casing is landed on top of salt. Several types of gasoline-powered core rigs have been used in the field and all recover a 2 1/2-in. core. More recently the Sullivan Model 37 rotary rig has been tried, and a Sullivan Model N has been adapted to use a rotary bit in the upper section. Core is recovered in 20 ft. sections with a double-tube core barrel, and the bit used is a bottom-discharge type set with diamonds. The drilling fluid must be a saturated brine to prevent solution and etching of the minerals present. Blowouts are apt to Occur from nitrogen gas trapped under the several polybalite beds, and some have been strong enough to blow the tools out of the hole. Core recovery is practically loo per cent. All holes are plugged after drilling, with cement through the salt section and opposite each water horizon* and mud through the remainder of the hole. Cores are carefully logged and preserved, and in sections containing potash and magnesium minerals they are quartered and analyzed. The correlation of Ore beds between drill holes is briefly described. Introduction Beds Or lenses of potash and magnesium salts are found at varying depths in a thick deposit of salt (Salado formation) in what is known as the Permian Basin, in southeast New Mexico and West Texas. The Salado formation is Composed chiefly of common salt (halite) with numerous beds of anhydrite, polyhalite, and the soluble potash minerals carnallite, sylvite and langbeinite. Many other minerals are present in small amounts but their Presence has no bearing On the coring technique. Before starting to core the salt section it is necessary to penetrate 300 to 600 ft. of unconformably overlying Permian sediments (Rustler formation) which are composed of red and gray clay, sand, anhydrite, dolomitic limestone and occasional lenses of salt. The upper part of the formation is predominantly anhydrite, and the lower part predominantly clastic. A thin bed of dolomitic limestone, known

Jan 1, 1948

By G. C. Weaver, G. T. Harley

Beds or lenses of potash and magnesium salts are found in a thick salt section (Salado) overlain by Rustler Red Beds in several members of which water is present and from one of which the rehery process water used by International is obtained. Most of the holes drilled are less than 1000 ft. deep, but some wildcat holes have exceeded 3- ft. cable or rotary tools are used to drill down to the salt. when samples of water are desired the cable rig is used, but when this is not necessary, and where caving material is present, the rotary rig has an advantage. The rotary rig has a further advantage in that only one machine is required to drill and core the entire hole, whereas the cable rig must be moved off to make way for the core drill. Casing is placed in the upper section of the hole as required to shut off water, and a 5 3/16 in. string is set in the top of the salt before coring starts. With the rotary rig drilling is often carried to the salt with no casing, as drilling mud seals off caving ground and water-bearing strata, and a string of 4-in. line pipe or 4-in. flush-joint casing is landed on top of salt. Several types of gasoline-powered core rigs have been used in the field and all recover a 2 1/2-in. core. More recently the Sullivan Model 37 rotary rig has been tried, and a Sullivan Model N has been adapted to use a rotary bit in the upper section. Core is recovered in 20 ft. sections with a double-tube core barrel, and the bit used is a bottom-discharge type set with diamonds. The drilling fluid must be a saturated brine to prevent solution and etching of the minerals present. Blowouts are apt to Occur from nitrogen gas trapped under the several polybalite beds, and some have been strong enough to blow the tools out of the hole. Core recovery is practically loo per cent. All holes are plugged after drilling, with cement through the salt section and opposite each water horizon* and mud through the remainder of the hole. Cores are carefully logged and preserved, and in sections containing potash and magnesium minerals they are quartered and analyzed. The correlation of Ore beds between drill holes is briefly described. Introduction Beds Or lenses of potash and magnesium salts are found at varying depths in a thick deposit of salt (Salado formation) in what is known as the Permian Basin, in southeast New Mexico and West Texas. The Salado formation is Composed chiefly of common salt (halite) with numerous beds of anhydrite, polyhalite, and the soluble potash minerals carnallite, sylvite and langbeinite. Many other minerals are present in small amounts but their Presence has no bearing On the coring technique. Before starting to core the salt section it is necessary to penetrate 300 to 600 ft. of unconformably overlying Permian sediments (Rustler formation) which are composed of red and gray clay, sand, anhydrite, dolomitic limestone and occasional lenses of salt. The upper part of the formation is predominantly anhydrite, and the lower part predominantly clastic. A thin bed of dolomitic limestone, known

Jan 1, 1948

By John D. Kalasky, Stephen Krickovic

Adequate ventilation in coal mines depends upon good face control, as well as upon a well designed and properly controlled overall ventilation system. The fundamentals of effective bleeding for provision of good ventilation and control and removal of methane are described. The various mine pillaring systems for which it is both easy and difficult to provide effective bleeder systems are detailed. Bleeders in conjunction with longwall mining are also discussed.

Jan 1, 1974

By Y. C. Liu

IN the study of the rolling recrystallization of face-centered-cubic metals, a most unusual observation is the frequent occurrence of a sharp re-crystallization texture of cube orientation. Although the general conditions under which this texture occurs are known,2,3 its origin is still not well understood. Based on the observed relationship between the {110}<112> deformation texture and the (113}<211> recrystallization texture, regardless of the effect of alloying elements2,4,5 or the symmetry of the deformation texture,&apos; there is a strong indication that a specific component of the deformation texture is related to a specific component of the recrystallization texture. Using the rotational reorien-tation relationship as a means of correlating the deformation and recrystallization textures, it was proposed that the deformation component which related the cube texture has {358)<523> indices."&apos; The investigation reported here was undertaken to seek experimental evidence for the validity of this proposition. Experimental Procedure Two copper single crystals having an initial orientation within 2" of (358) [523] indices were prepared in the manner described in Ref. 5. The purity of the copper was between 99.94 and 99.97 pct. The original dimensions of the crystals were as follows: specimen A, 0.465 in. thickness, 0.844 in. width, and 0.955 in. length; specimen B, 0.535 in. thickness, 1.120 in. width, and 1.36 in. length: Rolling was done on a laboratory rolling mill according to the following schedule: 0.010 in. per pass to 50 pct reduction in thickness, 0.005 in. per pass to 70 pct reduction inthickness, 0.002 in. per pass to 85 pct reduction in

Jan 1, 1958

By W. P. Blake

The mining district and the town of Tombstone are situated in Cochise County, Arizona Territory, at the northwest end of the Mule Pass range of mountains, in longitude 110°, and latitude about 31 40&apos; N,, upon the right bank of the San Pedro River, from which the town is distant 9 miles east.. It is also 24 miles south of Benson station on the Southern Pacific Railroad of Arizona, and about 40 miles north of the Mexican line. Its altitude above the sen is 4600 feet. The Dragoon Mountains rise across a valley to the northeast, and the Huachuca Range similarly upon the southwest. The country is open, without timber, and the surface, where the mines are opened, is in general gently rolling, and accessible to wagons by. natural roads. The first locations were made in the pear 1878 by the Scheffelin brothers and Richard Gird, the latter being well known among the pioneers of Arizona as a surveyor and miner, who contributed largely to our knowledge of the geography of the Territory in early days,

Jan 1, 1882

Earth Sciences: The standard of living of the world&apos;s people depends upon human initiative, investigation, and know-how in exploiting the earth&apos;s resources. The Earth Sciences-geology, mineralogy, geophysics and geochemistry, meteorology, geography-are basic sciences dealing with those problems concerning the origin, constitution, and utilization of the earth&apos;s materials. The development of these fields in one department provides the greatest opportunity for direct contact and stimulus for scientists and teachers working in related fields. In the Earth Sciences, geology and mineralogy are obviously closely related. As rocks are the materials of which the earth is made, so in turn minerals are the constituents of the rocks. Conversely, a study of earth structures and the interplay of physical and chemical forces in the earth is necessary in order to understand the origin and source of minerals. Building on the basic core of knowledge of earth processes, earth structures, and earth history, the geologist will continue to push out the frontiers of stratigraphy, structural geology, pale-biology and petrology with growing insight into principles that control surface and subsurface rock conditions. As the field of geology has advanced, several lines of specialization have developed. The economic geologist

Jan 1, 1950

By Harrison Schmitt

THE definitions of the terms commonly used in connection with metamorphism at elevated temperature near igneous contacts are re-examined. As the study of tactite zones associated with igneous contacts progresses, more and more emphasis is put on the localization of the ore by structural forms. The generally early age of the silicates and late age of the sulphides is well established. Postsilicate structural deformation is likely to localize ore bodies. The silicates are often replaced by the ore minerals. We may not be far from proving that the elements involved in the formation of silicate aureoles are merely normal "volcanic" emanations, that silica, lime, magnesia, and alumina and probably soda and potash are likely to undergo local transfers only. The work of Newhouse suggests the agents of the formation of sulphides in deposits of various classifications are the volcanic emanations.

Jan 1, 1947

OF what use is the federation to me and why should I support it?" is a question that has been asked by many members of the constituent societies of the F. A. E. S. during the last year; a question that is asked because the speakers do not realize what the Federated is doing or what is the field of its activities. "What is it doing for the profession and for mankind?" would be a more appropriate question, the answer to which is found in the closing chapter of Prof. Cassius J. Keyser&apos;s "Mathematical Philosophy."&apos; The chapter is entitled "Science and Engineering." Professor Keyser writes from the layman&apos;s point of view. He is looking at the profession and at engineers from the outside. We have in his thoughts the oppor-tunity that Burns sought when he wrote "Oh wad some power the giftie gie us to see oursels as ithers see us." With the permission of the author and the publisher, we quote the following paragraphs: A layman, viewing a profession from the outside, seeking thus to ascertain its proper relations to the common weal, may bring to the task a certain freedom, which, were he a member of the profession, he might have lost. "Men trained in a profession," said Prof. David Swing, "come by degrees into the profession&apos;s channel, and flow only in one direction, and always between the same banks. The master of a learned profession at last becomes its slave. He who follows faithfully any calling wears at last a soul of that call-ing&apos;s shape. You remember the death scene of the poor old schoolmaster. He had assembled the boys and girls in the winter mornings and had dismissed them winter evenings after sundown, and had done this for fifty long years. One winter morning he did not appear. Death had struck his old and feeble pulse; but, dying, his mind followed its beautiful but narrow river-bed, and his last words were: It is growing dark-the school is dismissed-let the .girls pass out first."&apos; I shall not be so much concerned with the present status of the science as with its potency and promise. Of individual engineers the ideals may be high or low, worthy or unworthy; but of engineering itself the ideal is great and mighty. It is of that ideal that I intend to speak.

Jan 9, 1922

By H. I. Young

INASMUCH as there has been a great deal of activity in this district recently, a paper of this kind should treat of all the various phases of mining, namely, prospecting, developing and operating. PROSPECTING Where ore is found it a depth of 100 ft. (30 m.) or more, the prospect work is done by churn drilling. Several makes of churn drills are used in this work, both steam- and gasoline-driven machines being used. The drilling is usually started with a 6-in. bit, and the size of the bit is reduced, if necessary, as the hole is advanced. It is general practice to drill from 100 to 400-ft. holes, but this is governed entirely by the location and formation of the ground. In drilling sheet ground, close spacing of drill holes is unnecessary, but in narrow orebodies, the holes are spaced from 15 to 50 ft. (4.6 to 15 m.) apart. Ten years ago, very few assays were kept of the drilling, but during recent years records have been kept very accurately, showing the location, elevation, assays, and also the vertical section of the hole. After the orebody is reached, cuttings are taken every 2 or 3 ft. (0.6 to 0.9 m.) samples being sometimes taken by pouring the water off the cuttings and taking a portion of the coarse material for assay. It has been found, however, that very often the sludge material poured off with the water contains high mineral values. To overcome this, cuttings from each 2 or 3 ft. are put in a container and after the water is evaporated, sample for assay is taken by means of Jones samplers. Permanent records of cuttings showing various formations are kept in glass jars or glued on large cards. Drilling at present is costing from $1.25 to $1.50 per foot. In pre-war times, the drilling costs ran from 75c to $1 per foot.

Jan 9, 1917

By Anson G. Betts

A solution of lead-fluosilicate, containing an excess of fluosilicic acid, has been found to work very satisfactorily as an electrolyte for refining lead. It conducts the current well, iseasily handled and stored, non-volatile and stable under electrolysis, may be made to contain a considerable amount of dissolved lead, and is easily prepared from inexpensive materials. It possesses, however, in common with other lead electrolytes, the defect of yielding a deposit of lead lacking in solidity, which grows in crystalline branches toward the anodes, causing short circuits. But if a reducing-action (practically accomplished by the addition of gelatine or glue) be given to the solution, a perfectly solid and dense deposit is obtained, having very nearly the same structure as electrolytically-deposited copper, and a specific gravity of about 11.36—that of cast-lead. Lead-fluosilicate may be crystallized in very soluble, brilliant crystals, resembling those of lead-nitrate and containing four molecules of water of crystallization, with the formula PbSiF,,4H20. This salt dissolves at 150 C. in 28 per cent. of its weight of water, making a sirupy solution of 2.38 sp. gr. Heated to 60° C., it melts in its water of crystallization. A neutral solution of lead-fluosilicate is partially decomposed on heating, with the formation of a basic insoluble salt and free fluosilicic acid, which keeps the rest of the salt in solution. This decomposition ends when the solution contains, perhaps, 2 per cent. of free acid; and the solution may then be evaporated without further decomposition. The solutioi~s desired for refining are not liable to this decomposition, since they contain much more than 2 per cent. of free acid. The electrical conductivity depends mainly on the acidity of the solution. My first experiments were carried out without the addition of gelatine to the fluosilicate solution. The lead-deposit con-

Jan 1, 1904

By H. V. Winchell

It seems to me that uniformity of mining law in North America must of necessity start with uniformity in each country. I understand that the Provinces of Canada have the right to make their own individual laws and conditions, to prescribe the terms under which the prospector or the applicant for mineral titles may secure the same. That is not true of the states in the United States. In this country, the Federal Mining Law was made applicable to the public domain, which, at the time of the adoption of this Act in 1872, was chiefly west of the Missouri River; it is impossible to locate a mining claim in most of our eastern states. It is true, however, that there are certain holdover rights, mostly obsolete, arising from the fact that at the time of the formation of the Confederation of States, the land that belonged to each state became the property of the Federal Government. I am not quite correc-t in that, it was sometime after the adoption of our Constitution, I think it was 1778, but those rights were largely, by agreement, surrendered to the Federal Government; but it is a fact that the great acquisitions of territory in the West, with the single exception of Texas, were of domain that came into the possession of the Federal Government and our Federal Mining Law applies to that territory. No state has the right to (by legislative enactment) enlarge upon the rights given by the Federal Mining Law, governing the acquisition of mining claims in its territory, within its boundaries. Each state, however, may, and some of them do, limit somewhat the rights given to the prospector. For instance, the Federal Mining Law provides that a claim may be taken, staked upon the public domain, of 600 ft. in width and 1500 ft. in length. Some of the states, like South Dakota and Colorado, have at times said "that is an excessive amount of land for a single mining claim; we will therefore limit it to 300 ft. or 200 ft. in width." There is, therefore, not any direct and immediate need for uniformity of mining laws in the United States, such as there might possibly be if it were considered at all desirable upon the whole in Canada. The initiation of mining rights under the Federal Mining Act is the act of discovery of valuable mineral in place, referring now to the lode mining claims, but the same is true of the placer claim. It is true that the emphasis has never been laid upon the word valuable and that

Jan 1, 1920

By Daniel Houdouin

Data is frequently collected in mineral processing plants in order to evaluate operating performance or to model process units. Metal concentrations, circulating loads, products flow rates, classifiers efficiencies, flotation units recoveries, grinding mill efficiencies are typical parameters calculated from plant data. The validity of these calculations depends strongly upon the reliability of the data used for that purpose. The objective of this paper is to illustrate that flowrates, efficiencies and rate parameters of mineral processes are more reliable when calculated from balanced data rather than from raw data. Using variance-covariance matrices of balanced data produced by automatic mass balance packages (including flow rates, concentrations, percentage of solids and size analyses), variances of separator efficiencies (flotation or classification) and of mill grinding rates are derived. The variances are compared with those of variables calculated from raw data. The advantage of using balance data is illustrated with real data from flotation, grinding and classification units.

Jan 1, 1984

By R. W. Prouty

THE methods of sampling and ore estimating used at the Copper Queen Branch, Phelps Dodge Corpn., as applied to the Copper Queen mines at Bisbee, Ariz., fall into two divisions because of the difference in occurrence, manner of prospecting, and methods of mining: that for the underground operations and that for the Sacramento Hill steam-shovel operations. The orebodies of the Warren district may be divided into three classes: Replacements of limestone, replace-ments of porphyry, and replacements of contact breccia The first class is more or less intimately related to porphyry intrusions, although in badly fractured country this relationship may not be well shown. These orebodies are mainly oxide and carbonate ore and very irregular, both in size and outline, although usually roughly lenticular and following the bedding of the limestones. There is usually quite a sharp boundary between the ore and waste in the carbonate and oxide orebodies and sampling is not necessary to determine the limits of commercial ore. In the sulfide orebodies it is exceedingly difficult, without sampling, to deter-mine the boundary between commercial ore and the surrounding low-grade or barren pyrite. Calculations made a few years ago showed that these orebodies had an average thickness of 35 ft. As some of the ore-bodies have a thickness of from 100 to 300 ft., it can be seen that the smaller ones form a difficult problem both in prospecting and in estimating.

Jan 11, 1922

By L. B. Ticknor, M. B. Bever

An isothermal calorimeter suitable for measurements of heats of solution in liquid tin as solvent is described. Measurements of the heats of solution of gold, silver, copper, and a gold-silver alloy are reported. The heat of formation of this gold-silver alloy is also reported. HEATS of solution in liquids can be determined directly, but few such data have been published for metals as solvents. Knowledge of heats of solution is desirable because it contributes to the general understanding of energy relations in metallic solutions. Thermochemical measurements of this type also furnish answers to specific problems: For example, from the heats of solution of an alloy and of a mixture of its constituent elements in a given solvent, the heat of formation of the alloy may be found. Similarly, differences in the energy content of samples of the same metal in two different states, such as the annealed and cold worked states, may be determined. In the work reported here, gold, silver, and an alloy of gold and silver were dissolved in liquid tin at 240°C and gold, silver, and copper were dissolved in tin at 300 °C. The experiments yielded the heats of solution of these metals in tin. The heat of formation of the gold-silver alloy was also determined. The same calorimetric method is being used to measure the energy stored in metals during cold working and preliminary results have been published.&apos; Equipment and Experimental Procedure The isothermal calorimeter used in this work, Fig. 1, consisted of a Dewar flask completely immersed in a constant-temperature salt bath. A long neck provided space for thermocouple leads and a stirrer shaft and permitted the injection of solute samples. The metal bath in the calorimeter flask was stirred at about 100 rpm by a small glass impeller driven by a constant-speed motor. The shaft of the stirrer passed through a Wilson vacuum seal.2 All measurements were made under vacuum in order to eliminate temperature disturbances resulting from gas convection and to prevent the oxidation of tin. The calorimeter flask was joined by an all-glass connecting line to a gas-control system which made possible the use of a protective atmosphere of deoxidized and dried hydrogen. At the operating temperature of the calorimeter tin oxide was not reduced by hydrogen, presumably because the reaction rate was too slow. Part of the closed system was a removable side tube through which the solute sample could be introduced and in which it was held at a temperature of 0°C prior to injection into the metal bath. The salt bath containing a mixture of sodium, lithium, and potassium nitrates was similar to that described by Beattie3 and was equipped with a stir-

Jan 1, 1953

By W. L. Zeigler

The gravity concentrator of the Heela Mining Co. was originally constructed in 1888 by the Milwaukee Mining Co., which was operating the Gem of the Mountains mine. It was purchased by the Hecla Mining Co. in 1900, and placed in operation 2 years later. At that time the capacity was only about 200 tons a day, but many additions and changes in equipment have been made so that the present capacity is about 800 tons. One of the outstanding improvements made was the substitution of Callow flotation cells for vanners, which occurred in 1915. The recent building of a flotation plant for treating jig tailings, and the construction of a modern surface plant at the mine, following the

Jan 1, 1928

By P. N. Ivanov

The world experience shows that the tremendous potentialities of the computers and other technical means in improving management efficiency are not fully utilized. One of the causes is the tendency to solve the problems of management automation divorced from the management methods and schemes which demand continuous improvement in view of the steady progress of the social production. It may be safely affirmed that making decisions on management improvement divorced from management schemes or on both divorced from management automation problems cannot lead to success. The grave and sometimes unsuperable difficulties encountered in management automation arise from copying traditional management methods and schemes without solving the problems which exist both in management and automation fields. The system solution of management problems has unquestionable advantages and is not proposed for discussion. What is proposed to discuss is the difficulties emerging in developing a methodology of the system approach to management improvement and automation. Though aware of the fact that the questions proposed for discussion are not new, we think it advisable to briefly review them, first because they fall in the "chronically unsolvable" category, and, secondly, as it will enable us to illustrate the method of solving them in the framework of the proposed system approach.

Jan 1, 1977

By C. B. Smith, A. G. Guy

The power and convenience of tensor analysis are employed in deriving the equations that describe three-dimensional diffusion in an n-component system plus vacancies. A "Kirkendall coordinate system, &apos;&apos; defined in principle by Kirkendall markers, is used in defining the intrinsic diffusion coefficients that are of primary interest. The defining equations are then transformed to local cartesian coordinates and to fixed cartesian coordinates, the latter being convenient for experimental measurements. Finally, it is shown how the intrinsic diffusion coefficients can be calculated from the experimentally determined quantities. It is generally recognized that any treatment of the essential diffusion phenomena in metallic systems—the jumping of atoms from one lattice position to another—must be based on movement of the atoms past Kirkendall interfaces.&apos; A logical extension of this idea is the proposal that, fundamentally, diffusion must be described mathematically in terms of "Kirkendall coordinates." The basic equations thus obtained may then be transformed into other coordinate systems, when such transformation leads to simplification of either the experimental or mathematical treatment of diffusion data. Tensor analysis is clearly the appropriate mathematical tool for this purpose, since it provides methods both for determining general equations that are valid for all coordinate systems and for conveniently transforming the equations from one coordinate system to another system related to the first in some known fashion. For the present purpose three coordinate systems are used, and it is convenient to begin with a description of the relations among these three systems. FICK LAW FOR KIRKENDALL COORDINATES The reference coordinate system, and the one that is useful for most experimental measurements, is a cartesian coordinate system, xi (i = 1, 2, 3), fixed with respect to some point in the specimen, such as an end of the alloy bar undergoing diffusion. A second set of coordinates, the Kirkendall coordinate system, is one that in principle can be described by the location of inert markers (Kirkendall interfaces). A convenient mathematical relation between Kirkendall coordinates, x&apos;i, and the reference cartesian coordinates, ii, is obtained by specifying that the Kirkendall coordinate system coincide with the cartesian system at time, t = 0. After diffusion has occurred for some time, t = t, the Kirkendall coordinate system will differ from the reference system in the manner shown schematically for the one-dimensional case in Fig. 1. The third coordinate system is Darken&apos;s1 local cartesian-coordinate system, xi, which is identical with ii in orientation and units, but which moves with the point under consideration in the Kirkendall coordinate system. Even though most diffusion problems are essentially one-dimensional, there is an advantage in first carrying out the analysis of the three-dimensional problem to gain a clearer insight into the assumptions that are made in the usual one-dimen-

Jan 1, 1962