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ZAY JEFFRIES (communication to the Secretary*).-Having seen Mr. Ruder's micrographs of electrolytic iron, I am of the opinion that the tentative explanation offered verbally is correct. Mr. Ruder has informed me that both of the samples were cooled in the furnace. The structures as shown in Figs. Band C resulted from the last cooling through the temperature range near 900° C. Assuming that the rate of cooling through this range was the same in both cases, the differences in struc-ture of the gamma iron in the two samples must have ]:)]-ought about, in some way, the variations in grain size and grain shape shown in Mr. Ruder's micrographs. Even though there is practically no temperature gradient in muffle-furnace treatment during the "soaking" period, during both heating and cooling, there is a temperature gradient. Fig. B should normally have been fine-grained prior to the last cooling, due to the comparatively low maximum temperature to which it was heated (1,000° C.). On cooling through the allotropic change point at 900°, these small gamma grains, iii conjunction with the temperature gradient, should form an ideal condition for germination. Germinant grains should form near the surface of the sample (the-colder portions) and the small gamma grains would be progressively absorbed as they changed into non-gamma iron. The elongated grains in Fig. B, converging toward the axis of the piece of iron, indicate that germinant grains first formed near tine surface and advanced their boundaries toward the interior of the sample. The gamma grains in Fig. C, however, should have been large, prior to the last cooling, due to time high temperature treatment (1,250 to 1,300° C.). In other words, to use one of Prof. Howe's expressions, the crystalline organization should be very complete and the change from gamma to non-gamma iron on cooling would take place reluctantly. This resistance to change from gamma to non-gamma iron would probably be greater in the interior of the large grains than at their boundaries. Non-gamma iron centers or nuclei would probably form at a great many places, at the grain boundaries, thus masking the influence, to a large

Jan 6, 1917

By J. C. Platt

I DESIRE to call the attention of the Institute to what is believed to be a new improvement in 'the construction of journal-bearings, having for its object the reduction of original cost as well as cost of renewals. In an ordinary railroad car we find the space between the top of the axle and the top of the box is filled with a "brass," weighing from seven to ten pounds. Of this amount of metal a comparatively small portion is subjected to the wear which it is intended to meet. The balance is, practically, a filling material, which from habit has long been constructed of the same metal. The Defreest bearing is made of three parts, namely, a malleableiron back, a bronze bearing-piece, and between them a filling-piece of sheet lead. The bronze takes the wear of the axle, the iron fills up the space and acts as a backing to the bronze, and the lead, being soft, adapts itself to the inequalities in the surfaces of the iron and bronze castings, thus insuring a uniform bearing on all points, and making it unnecessary to bore out the iron or turn off the bronze to bring them to a perfect contact at all points. These three parts are joined together by two soft brass rivets, with counter-sunk heads, to prevent separation in handling. A groove is cast in the iron, and a corresponding rib on the bronze, to prevent the latter from turning with the axle when in place. In renewals it is ordinarily necessary simply to drive out the rivets and renew the bronze and lead. The iron part is not subjected to much wear and should last for years. It is evident that the first cost of these journals, and also the cost of renewals, must be much less than the old form. This difference amounts, at the present price of materials, to $9.60 for an eight¬wheel car, in first cost, and $4.72 for renewals. These bearings have been in use, and found to do what is claimed for them.

Jan 1, 1880

By Henry Howe

1. Introduction.-This paper is based in large part on the examination of two rings, shown in section in Fig. 4 to 15, cut from an eroded 14-in. (35.56-cm.) gun, liner, and containing, according to Booth, Garrett, & Blair: Carbon, 0.380 per cent.; manganese, 0.655 per cent.; nickel, 2.810 per cent.; vanadium, 0; chromium, a few hundredths of 1 per cent.; tungsten, 0; molybdenum, 0. These rings were received from Admiral Joseph Strauss, then Chief of Ordnance, U. S. Navy, through the kindness of Mr. Hudson Maxim, Chairman of the Committee on Ordnance and Explosives,, of the U. S. Naval Consulting Board.

Jan 2, 1918

By Michael J. Messel

W. P. MOULD*—Has consideration been given to the problem of retreating the 4,000,000 ton tailings pile to recover the very considerable amount of asbestos fiber that was lost over the years due to insufficient operation and poor recoveries? Also, what was known about the possible content of chromite and the sulphides of nickel and cobalt? M. J. MESSEL (author's reply)—Consideration was given to the problem but nothing concrete has been done up to this time. W. P. MOULD—I am certain the tail- ings contain a very considerable quantity of fiber, not all of which is in the shortest lengths, because in the milling of talc rock from a neighboring location having a common origin with the asbestos bearing serpentine source of the tailings pile, a concentrate carrying 15 pct Ni and Co in complex sulphides and constituting about 4/10 of 1 pct of the talc rock was recovered. In the belief that the tailings also contained an appreciable content of chromite (then in demand, 1937) it was suggested to the management of the asbestos company that a truck load of the current tailings be sent to the flotation plant of the talc company where it would be put over the concentrating tables in an effort to discover the presence and roughly the percentages of chromite, nickel, and cobalt. Preparations for the test were woefully inadequate and the test was completely snarled up by the surprisingly large quantity of asbestos fiber from 1 in. long down to very short fiber, all of which matted up and plugged launders and pumps with disastrous effects and practically the total loss of the sample. If anything was indicaded by the test, it was that a wet process for milling asbestos was worthy of very serious consideration. M. J. MESSEL—A wet milling process for tailings retreatment only, is at present under study at our plant. One asbestos mining company in Canada has constructed a fairly large test plant for this purpose, but as yet no definite results have been obtained other than in a small test unit plant which were in some respects quite encouraging.

Jan 1, 1950

[NORTH AMERICA UNITED STATES Alabama BIRMINGHAM BURROWS, WILLIAM C. CORD, RICHARD H. COSTON, OTIS D. JR. FAIRHOPE RUFFLES, WILLIAM R. HUNTSVILLE WAGGONER, JERRY B. MOBILE PETROUTSON, PETER C. SELMA JONES, JAMES J. JR. UNIVERSITY CUDWORTH, JAMES R. JONES, WALTER B. RICHARDS, EDWARD F.]

Jan 1, 1961

CHARLES F. WILLIS,* Bisbee, Ariz.-(written discussion?).-The consensus of the discussion of the paper of Dr. Lanza indicates that the physical examination, while it is probably a good thing, is fought by the workingman, and that, because of this fact, it has been proved unsuccessful. The physical examination standing alone is worth but little, and could easily be made a subject both of ridicule and dissension unless the company having such examination shows its own good faith in promoting a thoroughly better health program. It is easily seen why a workman would resent his employer expecting him to be physically fit, if at the same time the employer provides un-healthful, unsanitary, working conditions, or if the town in which the employees are expected to live is dirty and unkempt. One mocks the other. The employer cannot say, "You must remain healthy so that I can get by with unhealthy conditions." But if working- conditions are as good as can be obtained to keep men well, the employer can ask his men to be in a healthy condition. A State examination and standard would have many difficulties, owing to the fact that a man would pass or would not pass the standard set, thus eliminating the discretion on the part of the employer in placing men whose physical condition might well permit working in one place and not another. Any physical examination that is run for the purpose of eliminating the physically unfit is unjust, both to the worker and to the nation as a whole; a State examination would make a distinct dividing line, whereas examination by the employer is conducted with a vision of the positions available. The workman's opposition to the physical examination comes from the fact that he has been taught to believe that it is an interference in his personal affairs, that he can be clean or dirty as he chooses, that he can he healthy or unhealthy, and that it is nobody's business but his own. The war has taught us, however, that the individual is no longer the unit and that all such propositions must be based on the greatest good for the greatest number.

Jan 6, 1919

By F. R. Hensel

THE demand for clean steel is increasing daily. New processes of refining steel are being developed in order to remove all nonmetallic inclusions as completely as possible, as it is the general opinion that. inclusions affect the dynamic properties of steel and iron to such an extent as to justify great expense for their removal. It is surprising to note at the same time the commercial development of a new process for making artificial wrought iron. By this process slag and steel are thoroughly mixed, the amount of nonmetallic inclusions usually exceeding 2 per cent in weight. The contradiction in these two efforts is obvious and is responsible for the investigation reported in this paper. H. W. Gillett also has recently emphasized the need for further research on wrought iron.1

Jan 1, 1932

Part 1. Coal Part 2. Industrial Minerals

Jan 3, 1977

By W. E. Hale, G. J. S. Govett

An orientation survey was conducted over a known disseminated copper deposit and a Au-Cu vein deposit and employed geological, geophysical, and geochemical methods. Geochemical techniques proved the most effective and economical means of locating and defining areas underlain by these types of mineralization. Six additional, widely separated occurrences were also investigated and mineralization was confirmed by determination of cold-extractable copper in stream sediments. The length of anomalous drainage varies from several to 16 km and depends on the type and tenor of mineralization. Despite generally marked relief and extreme physical and chemical weathering, cold-extractable copper anomalies in soils appear to reflect closely variations in the ore mineral content of immediately underlying rocks. Threshold values vary with local geological conditions and type and grade of mineralization. Significant thresholds in stream sediments are about 65 ppm and 10 ppm for cold-extractable copper in disseminated and vein copper occurrences respectively. Similar differences are encountered in soils. This necessitates the use of a scale of threshold values at progressive stages in each exploration program. Dis-seminated copper occurrences are presently the major source of mineral production m the Philippines. Much potentially productive ground remains to be investigated and applied geochemistry appears to offer the best available approach. The Institute of Applied Geology (I.A.G.), a joint project sponsored by the University of the Philippines, the Philippine Bureau of Mines and the United Nations Development Program (Special Fund) undertook during 1965-66 a number of field projects in Northern Luzon Island (Fig. 1). These field operations were of a two-fold nature and involved both orientation and exploration. During approximately six weeks, an orientation survey, involving geological mapping, geophysical surveying and geochemical prospecting, was conducted over a partly developed, disseminated copper deposit at Santo Nino (Fig. 1). This study demonstrated the economic and technical feasibility of geochemical ptospecting, relative to the other methods tested, for the location and delineation of a typical disseminated copper occurrence characteristic of those that represent the major source of metal in the Philippines.' Geochemical techniques, similar to those tested at Santo Nino, were then applied in a second orientation study of a vein occurrence at Suyoc (Fig. 1). The results of these two orientation studies suggest that, in reconnaissance work in this region, stream sediment analyses, combined with the determination of pH in the same streams, can be used to indicate areas underlain by rock containing anomalous concentrations of copper, whether it occurs in the large tonnage, low grade, disseminated deposits or in the comparatively small tonnage, higher grade, gold vein occurrences. Furthermore, the orientation surveys demonstrate that soil sampling and analysis serve effectively to outline more closely the mineralized zones within the generally anomalous areas identified from the stream reconnaissance. To further test the methods selected from the two earlier trials, six additional, widely separated prospects were investigated. The geological and geochem-

Jan 1, 1970

Western Mining Corp. has announced plans to expand its mining operations at Kambalda, and to build a nickel refinery at Kwinana, near Perth, Western Australia. The refinery will use the ammonia-leach hydrogen reduction processes of Sherritt Gordon Mines Ltd., and it is expected that by 1970, when the expansion is scheduled for completion, Western will be the world's fourth largest nickel producer. Although estimates have not been finalized, the total cost is expected to be about $55 million. The mine and mill facilities at Kambalda, which began production in June 1967, are now producing at the rate of 11 million lb of contained nickel per year. The company estimates the sulfide ore reserves at Kambalda and St. Ives at 10.4 million tons averaging an usually high grade of 3.8% nickel, or about 790 million lb of contained nickel. In addition, silicate and oxidized ores have been located in both areas.

Jan 3, 1968

From 1917 to 1926 mining at the Climax Molybdenum Co. property was confined to the Leal and White levels at elevations of 12,145 and 11,935 ft respectively and to surface outcrops above the Leal level. At present the production is coming from the Phillipson and Storke levels at elevations of 11,465 and 11,168 ft. Until 1926 when B. S. Butler recognized the relationship existing between the orebody and a central core of fine-grained hydrothermal quartz, the orebody was believed to be tabular in form. The orebody lies within the pre-Cambrian granites and schists and another rock type designated as the Climax porphyry and surrounds a highly silicious core, the mineable portion of which varies in thickness from 250 to 400 ft.

Aug 1, 1955

By Morris Muskat

ANALYTICAL calculations have been carried out on the effect of casing perforations on the productivity of wells, and formulas have been derived for general types of perforation patterns. The numerical calculations, however, show that the resultant well productivity is essentially independent of the perforation pattern, but is determined mainly by the total perforation density. Thus, for example, for a density of three perforations per foot of casing, the well productivity will be cut to one third of that of the uncased well for a perforation radius of 1/3 in., and to approximately one half for a perforation radius of 1/4 in,, regardless of the detailed manner in which the perforations are distributed over the casing surface. The analytical theory is also extended to include wells completed with slotted liners. It is shown that the reduction in productivity due to such liners will be relatively small as compared with that due to perforated casings.

Jan 1, 1942

By Herbert Hoover

NO ONE could fail to be gratified to receive so profound an approbation in his calling from the members of one's own profession. To have re-ceived this distinction from men, many of whom have been professional associates and friends over more than a quarter of a century, warrants a pride. and satisfac-tion that could come from no other source. It has often been said that men are really known only to their brothers in labor and in profession. The long friendship I have received from Mr. Saunders and the distinguished service that he has contributed to the mining industry add to my appre-ciation of this event. Mr. Kelley's remarks bring my mind easily to the beginning of that period of great advance in the engineering, profession of forty years ago. Three great forces contributed to the development of the profession. The first was the era of intense development of minerals, metallurgy; and transportation in our great West. It greatly stimulated invention; it made a demand for training and skill on the part of our engineers. The pressure of national development advanced our American practice beyond the rest of the world. Moreover, the skill of our engineers of that period owes a great debt to American educators. The leaders of our universities were the first of all the educators of the world to recognize that upon them rested the responsibility to provide fundamental train-ing in, the application of science to engineering under the broadening influence and cultivation of university life. They were the first to realize that engineering must be transformed into a profession in the highest sense, not only in the training and character but that the essential quality of a profession is the instillation of ethics. That implies not alone the job but the responsibility of the community for the job. Our uni-versities poured into our development a great stream of men with this background and training. A third distinction that grew in American engineering was the transformation from solely a technical profession to a profession of administrators-the business manager with technical training.

Jan 3, 1928

Jan 1, 1888

By L. F. Porter, G. J. Dienes

The effect of netltron irracliation on mart ensite transformation in the iron-nickel system was studied by means of electrical resistance and magnetic induction measuremertts. Irradiation lowers the M8 temperature of the allay, causes changes in the electrical and magnetic properties of the high-temperature phase which indicate either an accelemtion of phase separation or a clustering of nickel, and enhances strain recovery on specimens partially transformed to martensite prior to irradiation. Possible mechanisms to account for the effects; are discussed. 1 HERE is a good deal of evidence to indicate that neutron irradiation is capable of affecting phase changes in metals and alloys. While the mechanism of the effect often is not well understood, such studies hold promise of improving our understanding not only of irradiation damage but also of the phase changes involved. To date systematic and detailed investigations have been made of the influence of nuclear radiation on order-disorder transformations in the copper-gold, nickel-manganese, and copper-zinc system, and on precipitation reactions in the copper-iron, nickel-beryllium, and copper-beryllium system.' These solid-state reactions are diffusion controlled and the results can be explained largely on the basis of enhanced diffusion due to the presence of irradiation produced vacancies. Reversion of low-temperature eutectoid phases to the high-temperature phase has been observed in the fissionable uranium-molybdenum and uranium-niobium systems.2 Here it is necessary and logical to postulate a displacement spike mechanism to account for the effect. The only case of irradiation induced diffusionless transformation in metals is the allo-tropic transformation of p to a tin reported by Flee-man and Dienes. 3 They found that neutron irradiation markedly decreases the incubation time for transformation, but the mechanisnl is not well understood. Another diffusionless transformation which one might expect to be influenced by neutron irradiation is the martensite transformation. This transformation is known to be sensitive to strain, structural hardening, and the presence of imperfections.6,7 Since the transformation is diffusionless, one also

Jan 1, 1960

By Hon. Charles McCrea

MINING taxation is a subject which bears definitely upon-the welfare of the mining indus-try. Every government must have a revenue but that revenue should be raised in such a way as to hamper as little as possible legitimate enterprise or industry. A mining tax should be fair, and one which appeals to the natural sense of justice. Our present system is a tax on net- profits after all expenses are met. On profits in excess of $10,000 the Mining Tax Act takes three per cent., one-half of which goes to the Govern-ment and one-half to the municipality in which the mines are situated, to meet local needs for roads, schools, etc. On profits from one to five million dollars", the tax is five per cent.; over five million, six per cent., and so on. The first $10,000 profit is exempt. The result is that if a mine is worked at a loss, it pays no tax at all; if it makes a small profit, it pays a small tax; if profits are large, the tax increases accordingly. It is difficult to imagine a fairer or less onerous method of taxation, or one better adapted to meet fluctuating conditions from year to year as profits rise or fall. A just and fair tax should be levied on profits, never on capital. There is, one branch of the mining industry upon which is levied a higher tax than upon other branches, namely, the nickel industry. I see no good reason why any branch of the mining industry should be discrim-inated against on a profits tax basis. A mining tax should not discourage development. The present tax meets this requirement. In the early years of a mine, when it is all outgo and no income, the mine pays no tax. Not until it reaches a productive and. profitable stage does the tax take effect, and then the mine can afford to pay it. Further, a tax on profits does not operate against the opening up of low-grade deposits, or those in which the chance of success is to a certain extent speculative.

Jan 10, 1923

By W. L. Hill, W. H. Armiger, S. D. Gooch

The physical properties, chemical behavior under thermal treatment, and fertilizer value of fluorine-containing pseudowavellite (hydrous calcium aluminum phosphate) that occurs as phosphate clay admixed with quartz sand in an extensive deposit near Bartow, Fla., were determined by experiments in laboratory, pilot-plant, and greenhouse. When the mineral was heated at 500°C, 80 pct of the phosphorus became citrate soluble. The heated product, however, deteriorates markedly under moist conditions such as obtain in the soil.

Jan 1, 1950

By D. V. BURR

THE ORIGINAL HUDSON RIVER TUNNEL. NOT quite forty years ago a man of uncommon character entered New York. He had several hundred thousand dollars earned by railroad building in the Nest. He was not an engineer, but he had ideas of engineering work which he was destined to prove correct.. He introduced new ways of tunneling, but his plans had only one distinguishing feature-they were simply interesting as showing how such work could be done; they added nothing to the science, have never been used since his clay, and never will be used again. Engineers of repute ridiculed his proposition ; he was an Ishmael in the profession. But if engineers looked askance at him, he certainly returned their contempt in the heartiest fashion, and had no hesitancy about expressing his views of them individually and collectively. This worked to. his disadvantage when he afterward tried to raise the means to go on with the work. He found that the opinion of engineers was respected by financiers, and that money would not flow contrary to their advice. While his conception of large constructions was distinguishingly original, much more marked was his method of demonstrating the feasibility of, his schemes. In the present clays of great undertakings it is the custom to make the other man pay for the experiments. But the man from the West had other notions of how the thing ought to be done. Having wonderful confidence in his own ability and in his perception of the task before him, he used up all his own money before seeking outside assistance. By building several hundred,, feet of tunnel he proved the correctness of his theory, and the tunnel then dug forms a part of the present tube. The result-he failed to finish the tunnel. He was blind in

Mar 1, 1908

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By Thomas O. Ziebold, Robert E. Ogilvie

Experimental analysis of diffusion samples covering the entire Cu-Ag-Au system at 725°C has been carried out. Experimental coefficients are computed at twenty-eight points in the lermary system. It is found that the direct coefficienl for copper is nearly independent of the silver, content for 1ow-silver alloys and that the cross coefficient for silver correlates with the ther-nzodynatnic properlies. This lalter observalion leads to the conclusion that the mobililies of copper and gold are nearly equal. Thermodynarmic actiuilies for Cu-Ag-Au were computed from binary data and adjusted to be consistent with neasured tie lines across the two-phase region which extends into the ternary diagram at 725°C. Application of these therknodynarnic calculaliorls to the dijftcsion data terifies the Onsager reciprocal relations to the extent that experimental uncertainlies will allow. It is jound that diffusion neav the critical point of the 1200-phase field in the isothermal section at 725°C causes the composition gradients for copper and silver to approach infinity while the direct and cross coeficients become equal. From the standpoint of experimental Procedures, it has been shown that microanalysis of ternary samples may be carried out using a simple expression for the conversion of X-ray zntensily to composilion. The accuracy of' this method has been demonstrated by the analysis of standard alloys and by the reproducibility of composition determinations using differed X-ray lines. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. When only two elements are present there is just one independent composition variable, and the diffusion profile of composition vs distance across a sample must change monotonically through all solid solutions bracketed by the terminal alloys. If two-phase regions are stable for compositions between the terminal values, these must appear as planar interfaces in the diffused sample, with the composition profile exhibiting sharp discontinuities. Adding a third element may alter this picture completely. Because of the additional degree of freedom in the composition, we may see composition profiles which do not change monotonically through solid-solution ranges, and stable, nonplanar phase interfaces. Even though two-phase regions may lie between the terminal compositions of a diffusion sample on the constitution diagram, they will not necessarily appear in the diffusion profiles. In binary diffusion only one coefficient is needed to describe the interdiffusion process. From Fick's law this coefficient relates the diffusive flux of one component to its own composition gradient. In ternary diffusion we must allow for cross interaction between the two independent species. By a linear extension of Fick's law we introduce "cross" or "off-diagonal" diffusion coefficients which relate the flux of one component to the composition gradient of the other independent constituent. Thus, we require four interdiffusion coefficients to describe the transport process in a ternary system. In its most general form,1,2 the rate equation for mass transport by isothermal diffusion in a system of s components states that the diffusive flux of component i, Ji, is a linear summation of all driving forces, Xk, each force being multiplied by an appropriate compliance coefficient:

Jan 1, 1968