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By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By Susanne Pignolet, Richard D. Hagni

Ore microscopy has been applied to the complex cobalt-nickel- copper-lead-zinc ores from the Madison Mine in the Fredericktown subdistrict of the Southeast Missouri Lead District to predict potential beneficiation problems. It has been found that in some portions of the ore deposit, textures are present which may result in metal losses. In ores from the Bonneterre Transition Zone the intimate association of siegenite with chalcopyrite may result in cobalt and nickel losses to the copper concentrate and nickel contamination of the copper matte at the smelter. In ores from high stratigraphic horizons, this association is relatively uncommon, and siegenite is commonly associated with bravoite. This latter association will increase the the recovery of cobalt and nickel in the siegenite concentrate. However some cobalt and nickel will be lost to the tails as bravoite-pyrite particles due to the intimate intergrowth of these minerals. Other textures which may result in beneficiation problems include the intimate intergrowth of chalcopyrite and galena and the occurrence of sphalerite as inclusions in galena.

Jan 1, 1984

By James J. Halbouty, Michel T. Halbouty

Drilling activity in the South Texas area, which includes the South Corpus Christi and Laredo districts, showed a marked decline during 1941 from that of the preceding year. The rate of new discoveries, however, 'compared favorably with exploratory results of 1940 because of the many new productive sands opened in existing fields. South Texas completions for 1941 were about 12.3 per cent below the 1940 figure, compared with an increase of approximately 5.5 per cent in the total number of completions in the United States during 1941 over the 1940 total. During the year, 1452 wells were drilled in this area; of these, 1205 were drilled in or as extensions to the proven fields, and 247 were rank wildcats drilled in search of new producing pools. The comparable 1940 figures were: 1320 field or extension wells and 336 rank wildcats, a total of 1656 completions. This represents a decline in 1941 of approximately 8.7 per cent in proven-area wells, and of about 26.5 per cent in rank wildcats. It must be stressed that wells that were considered rank wildcats at the beginning of operations, but which opened production later classified as additions to existing fields, are not regarded as rank wildcats in this and previous annual reports on this same area. These wells are classified as semiwildcats (Table 2). There were 13 new oil or distillate fields and 4 new gas areas opened during the year, as listed in the next column. This listing represents a decline of 32 per cent from the 25 new areas found during the previous year, and to a great extent can be attributed to the 26.5 per cent decline in wildcatting. The rate of new discoveries based on the 247 wildcats was 14.5 to I, which compares somewhat unfavorably with the 13.4 to I ratio obtained in 1940 (Table 5). Dry wildcats totaled 230. The proof of the prolific character of the South Texas area as a source of petroleum reservoirs is to be found in the fact that of the 1205 field or extension (semiwildcat) wells completed during the past year 61 opened production from new sands or found crude in formerly distillate-producing sands. The 1940 total of 1320 such wells accounted for 50 horizons that provided either new production or crude in distillate sands, and in this respect the 1941 rate of discovery shows to greater advantage, the ratios for new sands being 19.7 to I for 1941 and 26.4 to I for 1940. The 1205 field or semiwildcat wells completed in 1941 resulted in 926 oil or dis-

Jan 1, 1942

By James J. Halbouty, Michel T. Halbouty

Drilling activity in the South Texas area, which includes the South Corpus Christi and Laredo districts, showed a marked decline during 1941 from that of the preceding year. The rate of new discoveries, however, 'compared favorably with exploratory results of 1940 because of the many new productive sands opened in existing fields. South Texas completions for 1941 were about 12.3 per cent below the 1940 figure, compared with an increase of approximately 5.5 per cent in the total number of completions in the United States during 1941 over the 1940 total. During the year, 1452 wells were drilled in this area; of these, 1205 were drilled in or as extensions to the proven fields, and 247 were rank wildcats drilled in search of new producing pools. The comparable 1940 figures were: 1320 field or extension wells and 336 rank wildcats, a total of 1656 completions. This represents a decline in 1941 of approximately 8.7 per cent in proven-area wells, and of about 26.5 per cent in rank wildcats. It must be stressed that wells that were considered rank wildcats at the beginning of operations, but which opened production later classified as additions to existing fields, are not regarded as rank wildcats in this and previous annual reports on this same area. These wells are classified as semiwildcats (Table 2). There were 13 new oil or distillate fields and 4 new gas areas opened during the year, as listed in the next column. This listing represents a decline of 32 per cent from the 25 new areas found during the previous year, and to a great extent can be attributed to the 26.5 per cent decline in wildcatting. The rate of new discoveries based on the 247 wildcats was 14.5 to I, which compares somewhat unfavorably with the 13.4 to I ratio obtained in 1940 (Table 5). Dry wildcats totaled 230. The proof of the prolific character of the South Texas area as a source of petroleum reservoirs is to be found in the fact that of the 1205 field or extension (semiwildcat) wells completed during the past year 61 opened production from new sands or found crude in formerly distillate-producing sands. The 1940 total of 1320 such wells accounted for 50 horizons that provided either new production or crude in distillate sands, and in this respect the 1941 rate of discovery shows to greater advantage, the ratios for new sands being 19.7 to I for 1941 and 26.4 to I for 1940. The 1205 field or semiwildcat wells completed in 1941 resulted in 926 oil or dis-

Jan 1, 1942

By A. C. Watts

For several years, a mine in Colorado experienced considerable trouble from small fires caused by the blasting of coal. Although a well-known make of permissible powder was used, it was first thought that the powder ignited gas that might be present and that this, in turn, set fire to line brattices or to the coal. Experiments were, therefore, conducted with another make of powder, but the results convinced the superintendent of the mine, Robt. Williams, Jr., that the fires were not caused by the powder but by the high-voltage electric current used for detonating the shots. The mine "makes" gas very freely, giving off from three-fourths to one million cubic feet of methane every 24 hours. The coal is a good grade bituminous of a very free burning quality. Electric shot-firing from the outside, after all men and animals were outside, had been practiced for a number of years. The shooting circuit was connected with the main power circuit at the mouth of each entry. Shooting circuit switches were mounted in boxes, which were kept locked with the handle of the switch, in open position, showing through the bottom of the box. The door of the box could not be shut and locked when the shooting switch was closed. At the entrance to each room, or working place, a small switch, called the miner's switch, was placed on the shooting line. It was the duty of the miner, when entering his place at the beginning of the shift, to see that this switch was open and that it was kept open until he left the placc at the end of the shift to go out of the mine. Grounded return was used for main power lines. The current was 500 volts, direct current, with 100 to 300 amp. The nearest working face was 9600 ft, from the shot-firers' switch outside the mine and the most remote working face was 2½ miles. The various working faces were scattered over a wide area between these two points. A description of the main power line would be valueless; the conductors were of sufficient size, the drop in voltage being not more than

Jan 1, 1927

By R. H. Moore

The data for diffusion in dilute binary alloys with the Solvents Ag, Cu, Ni, Fe. Al. and Pb hare been correlated as a function of atomic volume. Linear equations of the form: Q = b - a log V are obtained with constants "a" and "b" ciuirac-teristic of each solvent metal. In most cases. 3-d In recent years measurements of diffusion coefficients in solid binary alloys. using small concentrations of radioactive isotopes. have resulted in accumulation of highly reproducible data. Such and 4-d transition elements correlate on separate straight lines from those which serve to correlate the non/ransition elements. The data for the uon-transilion elements diffusing in silver and copper liave been fitted by least-squares analysis. It is concluded that the size and charge effects which determine the magnitude of the activation energy for diffusion are a function of atomic volume. systems represent the simplest possible examples of chemical diffusion since solute interaction effects can be neglected and Kirkendall-like phenomena do not occur. Generally it is found that thc diffusion rate of the solute is within an order of magnitude of the diffusion rate of the solvent. The differences have been attributed to the effect of size and to electrostatic interactions between the solute and solvent atoms.

Jan 1, 1965

By R. A. Pallanch

Probably one of the most perplexing problems with which a mill operator contends is the proper evaluation of his mill results. True, he accurately determines his recoveries of metals and grades of products monthly, weekly, and often daily. These figures do not of themselves directly translate to mill economics. When one figure is unusually good there may be an offsetting circumstance. The advantage of high lead or zinc concentrate grade may be offset by poorer recovery; high lead recovery may be offset by poorer zinc recovery, or vice versa; and so on. Besides, grades or recoveries may not of themselves mean more than a reflection of the grade and character of the ore during the period under study. What the operator sorely needs is some one measuring stick that tells him when he has achieved his greatest return, regardless of grades or recoveries—for if he knows his methods and practices are yielding the optimum return he need no longer concern himself with the assays of products and tailings, or the corresponding distribution of metal values. At first blush it would appear that the obvious answer to this is the actual money return to the mill. Paradoxical as it may seem, however, money return does not make a dependable yardstick any more than do grades and recoveries, as ore condi- tions would vary enough to bring about greater money return during periods when the actual metallurgical work is not as good. The mill operator, of course, should always aim for the greatest return on the ore, once it is in the mill bins, with proper attention always to mill treatment cost. The need of a proper yardstick becomes more imperative with the increasing complexity of the problem. In the case of a simple, single-product operation on a fairly uniform ore, in which only one metal is of significant importance, the need is not great, as grade and recovery pretty well tell their own story. At the other extreme is the operation that makes three or four separate marketable products from a complex mixture of heterogeneous ores that vary tremendously in individual metal contents and ratios, degree of oxidation, and other characteristics, and in which gold, silver, copper, lead and zinc are all significant values. Economic Recovery The first attempt at obtaining a proper single yardstick for a fairly complex ore with which I am familiar is the use of the ''Economic Recovery" term at the lead-zinc flotation mill of the Sunnyside Mining and Milling Co., Eureka, Colorado. This method had been applied there early in Sunnyside flotation-mill history (not later than 1920) and credit for the innovation I believe belongs to Messrs. Kuryla and Marquand. The term "Economic Re-

Jan 1, 1949

CHARLES CATLETT, Staunton, Va. (communication to the Secretary*). -I hesitate to discuss in general terms a paper such as Mr. Wysor's, which bears evidence of so much careful and detailed investigation, yet it is the broad possibilities which his paper presents that are really attractive and his cautious conservatism may make us unappreciative of these possibilities. Mr. Wysor calls attention to the fact that the iron-ore mixture which he uses, carrying 0.28 per cent. of potash, is probably above the average. No doubt this is true, but on the other hand it may be very much less than the mixture at some blast furnaces or very much less than would be the case with special mixtures bearing the question of potash in mind. Unfortunately, iron ores are not ordinarily examined for potash, and with the ordinary analyst there is opportunity for very considerable error in the determination. The 10th Census gives 270 complete analyses of iron ore, on the accuracy of which we may rely. Of these, there are 21, or 8 per cent., that carry more potash than Mr. Wysor's mixture; 14 of these carry approximately twice as much, or more; eight carry approximately three times as much, or more; three carry approximately five times as much; one carries over seven times as much. It may be worth while to take some of the ores that are known to be high in potash and consider the possibilities in the light of Mr. Wysor's investigations.

Jan 5, 1917

By Luther Wagoner

For a number of years I have, at odd times, tried to perfect a method of assay sufficiently delicate to find and estimate minute quantities of gold and silver. The object in view was to examine rocks remote from veins or mineral areas, in order to test the probability of the lateral-secretion theory. Having succeeded in measuring approximately the amount of gold and silver contained in one cubic centimeter of sea-water, I present a detailed account of the method employed, with some of the results obtained. General Method of Assay. The use of purified lead without other flux, blowpipe methods, extraction by cyanide, and measurement of the beads by the microscope. Purged Lead. The method of testing is by cupellation. On a properly prepared cupel, it is easy to cupel and find a bead of 0.002 mm. diameter. Such a bead of silver weighs about 1 part of a milligramme. A bead 0.02 mm. in diameter weighs about 1/24,000 mg., and a close approximation can be made to its weight. It is desirable that the lead used in the assay should be low in silver so as to avoid large correction, but as the parted

Jan 1, 1902

By T. M. Daulton, Chester F. Lee

The Atlin Mining District is in the northwest corner of the Province of British Columbia. Ruby Creek, where the operation to be described is situated, is 17 miles east of the town of Atlin and about 18 miles south of the south line of Yukon Territory (Fig. 1). Gold was discovered in the district in January, 1898, and the production to date from placer mines has been $4,518,000, according to the reports of the Minister of Mines for the province. Geology The essential points in the regional geology are given in the following paragraphs. Long erosion produced a plane-like surface slightly above sea level with a few peaks and ridges.' A gradual uplift followed and erosion increased, the streams cut deeper, the cuts so made being afterward increased by glaciation. The ice straightened and planed the slopes of the main valleys and widened and lowered their floors, in some cases flooring the valleys with silt, sand, gravel, and clay. As the glaciers rapidly retreated, lakes were formed. As to the origin of the gold, J. C. Gwillim says? "The Surprise granite has been carried northward toward Gladys Lake and Teslin, and the granite of the great plateau on the Taku trail was found in blocks on the opposite range across Hurricane River 10 miles north of its original position. Otherwise there is little evidence of far removed material, the boulders of the lake shore and creek beds being of local appearance. This appears to strengthen the opinion that the placer gold had its origin within the drainage basins where it is now found." In the gold-bearing creeks of the Atlin district there are two "runs"

Jan 1, 1917

By A. W. Schlechten

The proposition is advanced that edutcation specifically for exlractive metallurgy is desirable not because the course content is cmique but rather as a means of indoctrinating the student with a backgrocmd that will give him an interest and pride in the profession. Factors that have caused the decline in enrollment in metallurgical engineering courses emphasizing extractive processes are being overcome. There is a need to distinguish between the sciences of metallurgy and the engineering applications to avoid confusion both in and out of the profession. AS a first step in preparing the 1967 EMD Lecture I searched the literature to determine what my predecessors had done hoping thereby to gain some clues for my own performance. The Transactions of the Metallurgical Society show that the first EMD Lec- turer in 1959 was Dr. W. J. Kroll, known chiefly today for his pioneering work on the production of titanium and zirconium, but equally respected by an earlier generation for his contributions to lead refining. He has been followed by a series of well-known and competent metallurgists all possessing specialized knowledge that has served as a basis for their lectures. The EMD Lectures have in general been a review of the development of a certain aspect of the extractive metallurgical industry or a preview of a particular area of science or technology that has applications in extractive metallurgy. The usual format is to describe developments of the past, summarize the present state of knowledge, and make predictions for the future. There has been great variation in the relative amount of time devoted to these three subdivisions, the past, the present, and the future. For example, Professor Gaudin, the 1961 EMD Lecturer, in speaking of Separation Engineering on the Moon, did not have too many examples of past practice and so had to emphasize the future. It is cheering to observe that all of these authorities were optimistic in their predictions. Despite the fact that four of the previous EMD Lecturers have been educators, Professors Gaudin, Pidgeon, Schuhmann, and Kellogg, none of them discussed the subject of education for extractive metallurgists. I might say parenthetically that lecturers in other divisions, such as B. M. Larsen, J. B. Austin, F. D. Richardson, John Chipman, and R. F. Mehl, have commented with concern on the present state of training for extractive metallurgy. What can you say that is new about extractive metallurgy education? Certainly nothing new can be said about the educational process itself. Professional educators do have new approaches to teaching and learn-

Jan 1, 1968

By John Wellington Finch

In August, 1927, the writer examined certain copper deposits in New Mexico1 which occur in beds of sandstones and shale, and in connection therewith reviewed the literature upon deposits of this type. Such deposits are known and have been reported upon at various points in Texas, Oklahoma, Arizona, Colorado, Wyoming and Utah, but in New Mexico they have been given more development than elsewhere and apparently occur there more conspicuously than in the other states. Some 25 years ago the writer examined deposits of similar origin in northern Arizona and more recently other deposits in western and southwestern Colorado, and these examinations have led him to realize how widely scattered are the deposits and how generally noncommercial they are. On superficial development, to one without a comprehension of their geologic nature, they are alluring on account of occasional small amounts of high-grade ore and much misplaced capital has been expended upon them. This paper, therefore, aims to present briefly certain theories of genesis, some details of which may possibly be new, and to lead up to practical conclusions which may be useful to other geologists and engineers. A bibliography of the more important literature upon such deposits is given below.2 Coffin's Bulletin upon the Radium, Uranium and Vanadium Deposits of Colorado, published in 1921, is a particularly clear discussion. The most comprehensive recent statement is Butler's.

Jan 1, 1928

By M. A. Torcaso, P. Raimondi

The distribution of the oil phase in Berea sandstone resulting from increasing and decreasing the water saturation by imbibition was investigated Three types of distribution were recognized: trapped, normal and lagging. The amount of oil in each of these distributions was determined as a function of saturation by carrying out a miscible displacement in the oil phase under steady-state conditions of saturation. These conditions were maintained by flowing water and oil simultaneously in given ratios and by using a displacing solvent having essentially the same density and viscosity as the oil. A correlation shows the amount of trapped oil at any saturation to be directly proportional to the conventional residual oil saturation Sor The factor of proportionality is related to the fractional permeability to the water phase. Part of the oil which was not trapped was displaced in a piston-like manner (normal part) and part was eluted gradually (lagging part). The observed phenomena are more than of mere academic importance. Oil which is trapped may well provide the fuel essential for forward combustion and thus be beneficial. On the contrary, in tertiary recovery operations, it is this trapped oil which seems to make current techniques uneconomic. INTRODUCTION A typical oilfield may initially contain connate water and oil. After a period of primary production water often enters the field either from surrounding aquifers or from surface injection. During primary production evolution and establishment of a free gas saturation usually occurs. The effect and importance of this third phase is fully recognized. However, this investigation is limited to a two-phase system, one wetting phase (water) and one non-wetting phase (oil). The increase in water content of a water-wet system is termed imbibition. In a relative permeability-saturation diagram such as the one shown in Fig. 1, the initial conditions of the field would be represented by a point below a water saturation of about 35 per cent, i.e., where the imbibition and the drainage curves to the non-wetting phase nearly coincide. When water enters the field the relative permeability to oil decreases along the imbibition curve. At watered-out conditions the relative permeability to the oil becomes zero. At this point a considerable amount of oil. called residual oil, (about 35 per cent in Fig. 1) remains unrecovered. Any attempt to produce this oil will require that its saturation be increased. In Fig. 1 this would mean retracing the imbibition curve upwards. In addition, processes like alcohol and fire flooding, which can be employed at any stage of production, involve the complete displacement of connate water and an increase, or imbibition. of water saturation ahead of the displacing front. Thus, in several types of oil production it is the imbibition-relative permeability curve which rules the flow behavior. For this reason a knowledge of the distribution of the non-wetting phase, as obtained through imbibition, whether "coming down" or "going up" on the imbibition curve, is important.

Jan 1, 1965

By H. I. Smith

THE recently developed potash industry in southeastern New Mexico, though based on a relatively new discovery, marks the latest and perhaps culminating phase of the effort to obtain a domestic source of potash that began with the leaching of wood ashes more than 300 years ago. In the search for mineral potash in America, the Geological Survey has played a conspicuous part and has paved the way for much of the private activity that now bids fair to free the nation of foreign domina¬tion in supplying the nation's potash requirements. HISTORICAL REVIEW A pamphlet published by Thomas Stephen in 1758 pictures the industry in its early struggling condition.1 Just before the Civil War, a deposit of mineral potash had been found in Germany and its value as a fertilizer had been discovered. On this account and because the supply of wood ashes had decreased, the Ameri-can potash industry gradually lost its importance. During the next 50 years, with European potash available with little effort and with satisfactory substitutes on the market for the manufacture of soap, the interest of the American people in American potash declined. In 1910 this interest was suddenly revived by the abrogation of American potash contracts in Europe. Congress passed an act, approved by President Taft March 4, 1911, providing for "researches with a view to determining geological conditions favorable to the presence of deposits of potash salts." Appropriations were made to the Geological Survey and the Bureau of Soils to carry out the provisions of this act. The work of the Survey was directed toward the finding of commercial bodies of natural soluble potash salts; the Bureau of Soils was more concerned with the processes of extracting potash from industrial wastes and organic sources. Private agencies also became interested in the program. The Geological Survey has continued its search throughout the ensuing period of more than 20 years and has studied many types of deposits in many parts of the country.

Jan 1, 1933

By M. S. King

A series of cross-hole acoustic measurements have been performed in a columnar-jointed basaltic rock mass around an underground opening mined by the drill-and-blast method. The purposes of the test program were: to evaluate the rock mass characteristics around the opening; to determine the zone of blast damage; and to evaluate seismic methods for anomaly detection ahead of mining in this type of rock. The cross-hole measurements were made between four 76-mm diameter horizon- tal boreholes diamond-drilled 12 m into a wall of the underground opening. Repetitive pulses of compressional (P) and shear (S) waves of frequencies in the range 3 kHz-100 kHz were propagated from a transmitter sonde through the rock mass to a receiver sonde, both of which were clamped hydraulically to the borehole wall. After amplification the received P- and S-wave signals were digitized at the surface by a digital oscilloscope and stored on floppy discs. The results indicate considerable reductions in P- and S-wave velocities at distances less than 2 m from the face. Clearly these low values are associated with blast damage. Beyond 2 m, the velocities in a vertical direction indicate almost constant values. The velocities in the horizontal direction beyond 2 m appeared erratic, but showed a general tendency to increase as a function of distance from the face. Their maximum values remained, however, still lower in value than the corresponding velocities in the vertical direction. Near the face, the differences in velocities were considerably greater: with horizontal velocities considerably lower in value than those vertical. Results of the spectral analyses of the received signals indicated that Q-values were strongly influenced by the vertically- oriented sets of joints. Only for waves travelling in the vertical direction was the effect observed of the blast-damaged zone immediately around the opening. The acoustic data obtained are clearly indicative of an anisotropic jointed rock mass, with a greater intensity of jointing for travel paths in the horizontal than the vertical direction. The vertical, columnar joints are probably less tightly closed than those oriented in the horizontal plane.

Jan 1, 1984

By R. S. Busk

Niels Engel (University of Alabama, University, Ala.)— In this paper it was pointed out that the electron-gas and energy-band theory accounts for the fact that the lattice parameters exhibit a sudden change when the electron concentration (number of bonding electrons per atom) exceeds a certain number around two. This statement is said to support and prove the electron-gas theory. But this theory is not able to account for a series of experimental data. Also several expectations, deduced from this theory, are not found to exist. In Figs. 6 and 7 the energy bands of the second and third periods are given as they must be assumed in order to account for the electrical properties of the elements in these periods. In Figs. 6 and 7 the electron-gas and energy-band theory is compared with the electron-oscillator hypothesis in accounting for the properties of the elements in the second and third periods. Fig. 6 shows the second period, The energy-bands are overlapping and separated to be in agreement with the electrical conductivity of the elements. The oscillator hypothesis explains conductivity due to electron vacancies. In graphite there is a closed s-shell in every other atom and two vacancies in the others. Conductivity is therefore only maintained by migration of s-electrons in graphite. In boron there are no s-electrons. The diatomic molecules of nitrogen and oxygen and the paramagnetism of oxygen can be accounted for by a similar behavior as the s-electrons of the bonding electrons. But this explanation will deviate too much for the purpose of this discussion. Fig. 7 shows the third period. In the energy-band picture about two s-electrons are assumed in magnesium and aluminum, but only one s-electron is assumed in silicon. The diamond lattice is assumed to be controlled by a sp3 hybrid. However the electron distribution develops ideally according to the oscillator hypothesis. Only sodium, magnesium, and aluminum exhibit electron vacancies and conductivity. To account for the insulator properties in Si, P, and S in the third period it must be assumed that the four last added p-electrons must be taken up in bands containing only one electron per band.' (Compare the electron band picture in Hume-Rothery.' Hume-Rothery does not consider the insulator properties of the nonmetals.) In the second period already the first p-electron must have entered a single electron band. Based on the energy-band picture in Figs. 6 and 7, the following questions must be asked: 1—Is it consistent with the energy-band idea that electrons of the same kind (p-electrons) can be divided into separated bands? 2—Is it consistent with the energy band idea that single electron bands can exist? 3—Why are the first two p-electrons (in boron and diamond) separated into two single electron bands in the second period, but overlapping in the third period (aluminum)? 4—Why are s-electrons and d-electrons taken up in continuous overlapping bands, while p-electrons are divided into single electron bands? 5—Why do the peaks and valleys (y and w and further x and z) of the energy band below four electrons per atom not show up in the electrical conductivity of alloys? For example consider the Li-Mg system or the alloys between Mg and three electron metals where the mentioned discontinuity in the lattice parameter is found. 6—Why does the beginning of the p-electron band (x) not show up in the lattice constants similar to the filling up of the s-electron band (z) ? In magnesium alloys the electron-gas theory postulates the first Brillouin zone to be filled at about two electrons per atom. This is claimed to explain the sudden change in lattice spacing and c/a values of several magnesium alloys when the electron concentration exceeds a few percentage points over two electrans per atom. This was emphasized in the paper by Busk. If the electron-gas energy-band theory is correct a sudden change in electrical conductivity and possibly other properties .should be expected when the same electron-concentration or temperature is exceeded. A sudden change in lattice spacing or other properties should also be expected when the filling degree is such that p-electrons are introduced into the p-band, for example at x in Figs. 6 and 7. Such phenomena are at found by experiment. and If the number of electrons should vary with the energy level depending on the average number of bonding electrons per atom, the electrical conductivity should be expected to vary in accordance with the energy band layout (Figs. 6 and 7) caused by different numbers of conducting electrons at different filling up degrees. Nothing indicating such a behavior is observed. In addition to these discrepancies between the electron-gas and energy-band theory and measured data, the theory violates the principles developed along with the Bohr theory of atomic structure. According to these principles a filled shell is saturated and therefore unable to form bonds. Therefore two S-electrons per atom should form a closed or saturated shell, which has been pointed out as accounting for the inability of helium to form bonds. Beryllium, magnesium, or calcium atoms with two s-electrons should be expected to form inert atoms with properties almost like the helium atoms. Several other inconsistencies and disagreements with measured data of the energy-band theory can be mentioned. Some of these are discussed with reference to other papers. 8 Because the electron-gas and energy-band theory seems to fail on several points, I have developed another theory which can account for all the phenomena the electron-gas theory is able to account for. This new theory is further able to account for things which are impossible to explain by the electron-gas theory at the present state.

Jan 1, 1953

By Takahide Wakamatsu, Yoshiaki Numata, Charn Hoon Park

INTRODUCTION A technique is needed to apply the flotation method successfully to apply the flotation method successfully to low grade and complex ore bearing hard-to-float oxide minerals. Thus it is necessary to find a new selective, powerful collector or to develop a new flotation process. Some attempts to use two or more kinds of collectors combined in flotation have been made but the principle of the reaction between the collectors used and the surface of mineral as well as the effect of combined collectors on flotation has not yet been fully understood. As part of the study on the improvement of selective collection in flotation, we have been investigating the flotation of minerals using two kinds of organic reagents, one of which is a conventional collector. We found xanthates were able to adsorb even onto the surface of oxide mineral, with the help of another organic reagent, e.g. a chelate compound (1). Furthermore, a notable effect of combined reagents such as the xanthate-amino acid combination (2) was found on the reagent adsorption phenomena and the collection phenomena, depending on the combination of reagents. The present study was carried out to clarify the effects of adding two kinds of collectors to the collection of mineral in flotation in the following two cases: (1) joint use of xanthate and di-alkyl dithiophosphate for galena collection and (2) joint use of a cationic collector with xanthate for scheelite collection.

Jan 1, 1980

By Harry A. Lipsitt, Attwell M. Adair

A number of papers have appeared in the past several years concerning the nature of the fatigue limit. The hypotheses presented in those papers fall into three groups. Some authors attribute the fatigue limit to the distribution of interstitials prior to testing (static group). Others consider the fatigue limit to be due to dislocation-interstitial reactions during testing (dynamic group). Still other propose that the fatigue limit results from a characteristic peculiar to the iron (bee) lattice (inherent group). This communication is an attempt to digest the salient features of each of the hypotheses, discuss them, and present some constructive criticism. It is shown that each of the extant ideas has some merit, and that each of the mechanisms thus far proposed is necessary, but individually insufficient, to provide the desired level of understanding of the fatigue-limit behavior of metals. Static Group. The data of Oates and wilson1 on finegrained (=0.022 mm diam) low-carbon steel indicate that the fatigue limit exists in the absence of sufficient plastic deformation for any dynamic strain-aging mechanism to be operative. Specimens tested just below the fatigue limit showed yield-point behavior typical for unstrained material when removed from the fatigue machine and tested in tension. These results led them to the conclusion that initial dislocation locking controls the fatigue limit in this material, which has a yield stress higher than the fatigue-limit stress. Prestraining this material just prior to fatigue testing would be expected to lower the fatigue-limit stress; this they observed experimentally. Yoshikawa and sugeno2 are of the opinion that the sharp fatigue limit in fine-grained iron is caused by

Jan 1, 1967

By R. V. Smith, E. J. Dewees, R. H. Williams

Before this paper was presented, the terms "f" and "v1/f in flow equations had been called "friction coefficient" and "friction factor," respectively. However, many authors have used the names for the terms interchangeably, with the result that considerable confusion has existed in the literature on flow of fluids. In an effort to establish a clear and concise terminology for these terms, the authors have designated f as "resistance coefficient" and dm as "transmission factor." Transmission factors for the flow strings of gas wells were determined by tests on wells in six fields of Oklahoma, Texas, and Louisiana. Data were collected on 14 gas wells while gas was flowing through 1 1/4, 2, 21/2, and 3-in. tubing and 51/2 and 7-in. casing. The transmission factors developed from these data were found to follow the resistance equation published by Nikuradse1 for turbulent flow in "rough" pipes with an average absolute roughness of 0.000,65 in. This average absolute roughness is believed to be representative generally of the flow strings of gas wells with the exception of those that have been exposed to corrosion or other conditions causing undue roughness. Also, use of an absolute roughness of 0.000,65 in. probably will result in transmission factors that are more representative of gas-well conditions than those in common use today, provided that the transmission factors are calculated by the methods outlined in this report. The authors believe that use of these transmission factors will permit calculation of more accurate subsurface pressures in gas wells than those in use today. Engineers use transmission factors in flow equations to compute subsurface pressures in flowing gas wells from measured wellhead pressures. These subsurface pressures are necessary for determining the productivity of gas wells from "back-pressure" tests. The methods of calculating pressures in flowing gas wells, as outlined by Rawlins and Schellhardt2 in Bureau of Mines Monograph 7, are based on the transmission factors in the well-known Weymouth formula" Natural gas engineers have realized that errors introduced by using transmission factors as given by the Weymouth formula are relatively unimportant in testing low-capacity gas wells; but they also know that such factors are important considerations in testing large-capacity wells. Accordingly, the research described in this report was undertaken to fulfill the need for more accurate means of calculating subsurface pressures in gas wells. This report is part of the Bureau's study of the flow of natural gas through pipe and commercial pipelines. Several of the conclusions regarding flow in the flow strings of gas wells were influenced by the results of the study of flow in horizontal pipelines. These instances are mentioned in the text of this report. METHODS OF COMPUTING TRANSMISSION FACTORS Methods and procedures for computing transmission factors for turbulent flow in circular pipes from test data taken on gas wells have been derived and explained in detail in a paper by Smith4. As these methods were used to calculate the transmission factors presented in this report, a summary is included. Starting with

Jan 1, 1955

By James Gardner

IN 1923, Oklahoma took second place as an oil-producing state; whereas in 1922 it was the leader. California surpassed it, in 1923, by nearly 100,000,000 bbl. In 1923, Oklahoma produced, according to statistics of The Oil & Gas Journal, 165,013,685 bbl., or an increase of approximately 10 per cent. over the preceding year; the increase in California was approximately 90 per cent. The number of wells drilled in Oklahoma and the results of the two years are contrasted in the following table from data published in a preliminary bulletin by the U. S. Geological Survey. 1922 1923 Oil wells 4,149,68%. 3,515, 60% Gas wells 571, 9 %u 587, 11% Dry holes 1,428,23% 1,731,29% Total wells 6,148 5,833 The initial production from wells drilled in Oklahoma in 1923, according to The Oil & Gas Journal, was the largest in the history of the state, being 1,277,936 bbl. It has been 32 years since oil development began in the state, last year being the largest in the amount of production. The production of the past year would have been considerably greater were it not for the shutdown order in the Burbank field and curtailment of production in the Hewitt and Tonkawa pools.

Jan 3, 1924