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By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By Sidney A. Swensrud

The writer has been interested for some time in trying to appraise our industry's prospects for gasoline consumption over the next half dozen years or so. Anyone who has even approached the problem knows the intimate relationship to it of the number of automobiles in use— by automobiles I mean both passenger cars and trucks. Probably at least 90 per cent of our gasoline is used in automotive vehicles. Some recent estimates secured from the Department of Commerce show the following breakdown: Per Cent Passenger cars............................................ 60.0 Trucks................................................... 27.4 Busses................................................... 2.9 Taxicabs................................................. 2.2 Subtotal............................................... 92.5 Aviation, motor boats and railroads......................... 0.5 Agricultural: farm tractors, etc.............................. 3.3 Balance (manufacturing, government use, construction, etc.)... 3.7 100.0 Up to the beginning of the depression there was, of course, a constant annual increase in the number of automobiles in use, for each year the industry added to the total inventory or ''population" more new units than were being scrapped, as may be seen in Fig. 1. Few of us in the oil industry needed to give much attention to the detailed figures, although the automobile industry seemed to interest itself in all sorts of calculations of replacement demand vs. new car demand, the average life of the car, the number scrapped, and the like. Probably many people in the oil industry, as well as outside it, were surprised at the way in which automobile registrations and gasoline consumption held up during the early years of the depression. Nor were they greatly perturbed when, as in the last two years, both registrations and consumption began to fall somewhat. That was natural enough; it

Jan 1, 1933

By Jerome F. Kuzmick

Many investigations have been made on the effect of the variables of pressure, sintering temperature and sintering time on the physical and microstructural charactcristics of metal-powder compacts. Severa1 such investigations have indicatcd that pressure is the least important of these three factors in an attempt to secure a dense. strong compact by a simple coltl-pressing and sintering procedure. However, it was felt that a further study of the effect of pressure on pressed and sintered metal powder compacts might prove interesting, for the following reasons: In work done in the past on the effect of pressure, temperature. arid time, the, metal-powder compacts were subjected to long sintering periods, and temperatures right up to the melting point of the metal were applied. It was thought that pressure might exert a more profound effect under short-time simtering and within narrower ranges of temperature. such as normally would be applied in large-scale production of metal-powder parts. 2. It was hoped that something further might be learned of the nature of the bond in pressed and sintered metal-powder compacts. 3. It was thought that interesting infor mation concerning the work-hardening effect of pressure on the crystal structure. of sintered metal-powder compacts would be obtained. Procedure Rectangular bars, 2 by 1/2 by 1/4 in. were molded from the following metal powders: Atomizcd till powder, 325-mesh Atomized aluminum powder, 325-mesh Reduced copper powder, 100-mesh Electrolytic iron powder, 100-mesh Atomized 70-30 brass powder, l00-mesh The, till powder was molded at various pressures up to 40 tolls per sq. in. This was the maximum, because at higher molding pressures there was considerable extrusion of tin into the die wall, jamming the die plungers. The tin specimens were not -in tered, as this phase of the work was- done merely to see how much a very sold metal could be compressed. The aluminum powder was compressed at various pressures up to 50 lons per sq in. Higher pressures could not be used because of extrusion into the die wall The compacts were sintered one hour at 000 in pure dry hydrogen. The copper powder was molded at vari-ous pressures up to 96 tons per sq. in. One set was sintered at 750°C., another at 050 C. for one hour in pure dry hydrogen. The electrolytic iron powder was molded at various pressures up to 00 tons per sq. in. and sintered, one set at Soo°C and one set at 1300°C for one hour in pure dry hydrogen. Extra 325-mesh specimens were also prepared to study the effect of reduced particle size on grain structure. The brass powder was molded at various pressures up to 96 tolls per sq. in. and silltered for one hour. one set at 65o°C. and one set at 800°C, in pure dry hydrogeu.

Jan 1, 1945

By Miroslaw Hajdasinski

Estimation of the economic effectiveness of industrial development projects including mining ones is generally made on the basis of the discrete model of the value changes in time, although the character of these changes is similar to the continuous model. In this paper an attempt has been undertaken to investigate the problem of the value equivalence of both models exemplified by a construction of an underground coal mine. An effort has been made to determine the errors which for different estimation criteria appear in result of the application of the discrete model. Theoretical considerations have been supplemented with practical conclusions.

Jan 1, 1977

By R. Costantini

A. Brebner (Chairman, Dept. of Civil Engineering, Queen's University, Kingston, Ont., Canada) — Under the heading of friction losses, the author, in Eq. 10, gives the relationship

Jan 1, 1962

Jan 1, 1968

Jan 1, 1943

Jan 1, 1943

By W. T. Bishop, G. A. Crowe

While the literature in the United States on general polarographic technique is extensive, very little appears to be directly applicable to the analysis of flotation tailings. For this reason, it seemed worth while to present a few polarographic methods of ore analysis that have been in constant use in the laboratories of the Hercules Experiment Station for the past few years. At the time of our initial investigation of the polarographic method, there was little or no mention of its specific application to flotation tailings. It was therefore necessary for us to establish suitable conditions for the analysis of our flotation tailings and to consider possible interfering constituents. The polarograph, or dropping mercury electrode, method was discovered in 1925 by J. Heyrovsky and M. Shikata,1 of the Charles University, Prague. This method has since received extensive development and the literature contains many articles on the use of the polarograph for the quantitative determination of metals as well as anions, oxygen in solution, and reducible organic compounds. Kolthoff and Lingane,² by the publication of their book, "Polarography," in 1941 did much to advance the knowledge and use of the polarograph. In chapter 25 of that book, methods for the polarographic analysis of brass, steel and iron products, alloys, and zinc ore are given. Aluminum,³ cadmium,³,4 cobalt,4 cop-per,³-9 gold,10 iron,3,11 lead,³,l2,l³ molybdenum,14 nickel,4,8,9 tin," and zinc³,4,5,7 in ores have been analyzed by the polarograph. However, most of the work on tailing samples has been published in Russian journals and translations are not yet readily available. In this paper we will describe the method that was developed and used in our laboratory for the determination of copper, zinc, and lead in flotation tailings. Principle OF the Method The polarograph is an instrument for applying a potential to a mercury pool and a dropping mercury electrode separated by a solution, and for measuring the resultant electrical current. The procedure is essentially a small-scale electrolysis, in which the voltage required to reduce or oxidize the material identifies it qualitatively and the current measures the concentration quantitatively. Different constituents in a sample may often be determined simultaneously provided they reduce at sufficiently different voltages. An example is the determination of copper and zinc in the same solution. The reduction potentials are quite far apart, as shown in Fig. I. The polarographic method is particularly useful in the range of concentration between those normally determined by spectographic and chemical methods. In

Jan 1, 1947

By G. A. Crowe, W. T. Bishop

While the literature in the United States on general polarographic technique is extensive, very little appears to be directly applicable to the analysis of flotation tailings. For this reason, it seemed worth while to present a few polarographic methods of ore analysis that have been in constant use in the laboratories of the Hercules Experiment Station for the past few years. At the time of our initial investigation of the polarographic method, there was little or no mention of its specific application to flotation tailings. It was therefore necessary for us to establish suitable conditions for the analysis of our flotation tailings and to consider possible interfering constituents. The polarograph, or dropping mercury electrode, method was discovered in 1925 by J. Heyrovsky and M. Shikata,1 of the Charles University, Prague. This method has since received extensive development and the literature contains many articles on the use of the polarograph for the quantitative determination of metals as well as anions, oxygen in solution, and reducible organic compounds. Kolthoff and Lingane,² by the publication of their book, "Polarography," in 1941 did much to advance the knowledge and use of the polarograph. In chapter 25 of that book, methods for the polarographic analysis of brass, steel and iron products, alloys, and zinc ore are given. Aluminum,³ cadmium,³,4 cobalt,4 cop-per,³-9 gold,10 iron,3,11 lead,³,l2,l³ molybdenum,14 nickel,4,8,9 tin," and zinc³,4,5,7 in ores have been analyzed by the polarograph. However, most of the work on tailing samples has been published in Russian journals and translations are not yet readily available. In this paper we will describe the method that was developed and used in our laboratory for the determination of copper, zinc, and lead in flotation tailings. Principle OF the Method The polarograph is an instrument for applying a potential to a mercury pool and a dropping mercury electrode separated by a solution, and for measuring the resultant electrical current. The procedure is essentially a small-scale electrolysis, in which the voltage required to reduce or oxidize the material identifies it qualitatively and the current measures the concentration quantitatively. Different constituents in a sample may often be determined simultaneously provided they reduce at sufficiently different voltages. An example is the determination of copper and zinc in the same solution. The reduction potentials are quite far apart, as shown in Fig. I. The polarographic method is particularly useful in the range of concentration between those normally determined by spectographic and chemical methods. In

Jan 1, 1947

Frank Firmstone, Easton, Pa. (communication to tlie Secretary*) :—Mr. Dilworth's formulas hnd tables are of course correct, and the extillction will occur as calculated, provided the nioney periodically set aside for sinking-fund be really invested and the interest compounded as assumed in the calculation. Actually, in alrilost all cases, such funds are used " in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must he made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varyillg and continually increasing one until the date of extinction. On many accounts it scems more natural and conveniellt to make the extinction by a fixed periodical charge under the legal rule for partial payments,

Jan 1, 1911

R. H. THURSTON, Cornell University, Ithaca, N. Y. (communication to the Secretary): The " tri-axial diagram" was, I think, first employed by me in the work of the " U. 8. Board Appointed to Test Iron, Steel and Other Metals." A model was exhibited to the American Association for the Advancement of Science, and the diagram was first published, and the model described, in a paper presented to the same society at its Nashville meeting in 1877." The problem then presented to its inventor was to find a method of planning a research involving proportions of ternary compositions in such manner that, a limited number of such compositions being tested, the results should give the law of variation in the physical properties of all possible combinations of the three elements, and the actual numerical values of such as were important to the investigator. The investigation of the binary alloys, copper and tin, copper and zinc, and tin and zinc, had been completed and satisfactorily discussed, employing the usual bi-axial diagram, of which the ordinates represented the one, and the abscissæ the other, of the characteristic properties to be studied, the composition being commonly indicated by the abscissæ. In these cases it was easy to ascertain, by the study of a limited number of compounds, the law of variation in strength, ductility, etc., with composition; but, for a long time, the ternary alloys were not attacked, because no simple and satisfactory method presented itself of securing results significant for the whole field by the investigation of a comparatively small number of alloys. The tri-axial diagram was finally hit upon as a means of representing and interpreting results, and researches were at once begun, and in due time satisfactorily completed.

Jan 1, 1899

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

By A. T. Miesch, L. B. Riley

An error occurred in the preparation of Fig. 3, p. 249, of Basic Statistical Measures Used in Geo-chemical Investigations of Colorado Plateau Uranium Deposits. This figure shows the relation of the arithmetic mean: geometric mean ratio to the geometric deviation. Curves for the cases where n, the number of samples, is 100, 10, and 5 are too high with respect to the ordinate. The error is negligible at low geometric deviations, but becomes increasingly greater wi,th higher values of geometric deviation. Arithmetric mean values in Table I1 are not effected by the errors in Fig. 3. The authors will endeavor to supply copies of the revised curves on request; write to: A. T. Miesch, Geologist, Branch of Radioactive Materials, U.S. Geological Survey, Bldg. 25, Federal Center, Denver 25, Colo.

Jan 1, 1962

By Andrew B. Crichton

The oft repeated statements of the United States Geological Survey and the Bureau of Mines that the coal reserves in the United States are sufficient for 3000 yr have given us all a sense of security hard to disturb. If we discount that statement 66 pct, which to the uninformed seems drastic, we would still have 1000 yr supply, and why should mortal man worry about the difference between 1000 and 3000 yr supply of coal. That is exactly the attitude which many who should be better informed have taken toward the problem. A recent brochure "How Strong is America," by the New York Herald Tribune, states there is "no end to coal * * The truth is staggering * * U. S. has enough coal to last 4000 years." What the statement actually means is that the calculator got as high as 4000 yr and decided it was pointless to go on. The President's ERP Committee on Natural Resources and others in high places continue to assure the country of our superabundance of coal. In the past few days the "Wall Street Journal" carried an item from Director Boyd of the Bureau of Mines saying that within a hundred years we would need to triple our annual coal production of 600,000,000 tons, making it 1,800,000,000 tons annually, and at that rate we had coal reserves sufficient for 1000 yr. In my humble opinion, we cannot now or ever produce 1,800,000,000 tons annually, because we do not have the reserves in the producing districts to do it. Past reckoning in geology may be, as in the Psalms, a thousand years are as yesterday, but the future must be considered more realistically, and " a thousand years" is really a "heck" of a long time. In most developed areas, mining engineers can count the coal reserves in terms of a hundred years or less, and in some important areas now producing large annual tonnages in much under fifty years. They think when they hear of thousands of years coal reserves, reference is made to distant fields and "the fields are always green far away." The estimates of our coal reserves upon which we are relying were made in 1907 under the direction of Marius R. Campbell, Director of the United States Geological Survey. It is apparent this work was not well done. It was necessarily based on rather meager data because of the little development and prospecting as of that date. There were mistakes in the correlation of seams, and they assumed the continuity of thick seams throughout large coal bearing areas where coal often did not exist. The overstatement of coal bearing areas in the Campbell figures are common. The 1907 survey includes all coals over 14 in. in thickness to a depth of 3000 it. The total coal reserves according to Campbell were 3157.2 billion tons. The production and mining losses that year would amount to 570 million tons and

Jan 1, 1949

R. W. Raymond, New York City: From a study of Mr. Johnson's paper, I conclude that his apparatus is simple in construction and operation, and imitates in a revolving machine the movements of hand-shoveling. It does what a man would do in removing sand from the waste-water with a perforated shovel. I am sorry to say that I fear the present condition of the brown-ore mining industry in the East, as long as

Jan 1, 1899

Jan 1, 1944

Jan 1, 1944

John Langton, New York, N. Y. (communication to the Secretary*):—In Mr. Firmstone's discussion (Trans., xli., 912) the formula he gives for the periodical payment—his equation (2)—may be simplified in form. The expression given by Mr. Firmstone is : q=S(l+ r) 1-(1+r)-(1+r) r which is a simpler form to use in calculations. Where S= principal to bc extinguished. Q = periodical payment or charge for sinking-fund, r = rate of interest per period (i. e., interest on $1 per period). n = number of payments or periods. Kent's Mechanical Enyineer's Pocket Book, under the heading Annuities, equation No. 5, gives : " The annuity which $1 will purchase for any number of ytlars n is * Received Jiily 16, 1911.

Jan 1, 1912