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By G. R. Speich

A cellular precipitation reaction in which cells consisting of an Ni3Ti (DO24) phase and austenite are formed has been studied in an austenitic Fe-30 Ni-6 Ti alloy. The variation of the growth rate and interlamellar spacing of the Ni3Ti cells with temperature has been determined m the range 400" to 975°C; the interlamellar spacing is proportional to the degree of undercooling; the growth rate can be expressed by an equation of the form G = K?T)2 exp(-Q/RT). The habit of the Ni3Ti lamellae is (001)Ni3Ti (111)y;[010]Ni3T2 [010]y. An almost perfectly coherent interface is formed between Ni3Ti lamellae with this orientation rela -tionship and the intervening austenite. This first Ni3Ti cellular product is subsequently consumed by a second cellular reaction of much coarser spacing. CELLULAR precipitation reactions have been studied in copper-base,1,2 Au-Ni,3 pb-sn,4 and iron-base ferritic5,6 solid solutions, and this mode of precipitation has been treated theoretically by smith," Turnbull,8,9 cahn,10 and more recently by bohm.11 In the case of substitutional austenitic iron-base alloys little or no data are available, Cellular precipitation reactions are well known in austenitic nickel-base alloys12,13 but usually these reactions do not proceed to completion because of general precipitation occurring in the matrix, and they have not been studied in detail. Precipitation from an austenitic Fe-30 Ni-6 Ti alloy was studied as part of a larger investigation of the mechanisms of precipitation from substitutional iron-base alloys. This alloy, austenitic at high temperatures, decomposes at lower temperatures by a double cellular precipitation reaction. The first decomposition product consists of alternate lamellae of an Ni3Ti(DO24) phase and austenite. The reaction proceeds to completion, consuming all of the original austenite. This first cellular product is subsequently consumed by a second cellular reaction of much coarser spacing. The first cellular reaction was studied in detail by light and electron microscopy, hardness measurements, and by X-ray and electron diffraction. Interlamellar spacings and growth rates were measured during isothermal aging in the range 400" to 975°C. The orientation relationship between the Ni3Ti and austenite lamellae was determined and indicates that an almost perfectly coherent interface exists between the two phases. This first Ni3Ti cellular reaction is of particular interest because it occurs over such a wide temperature interval. This allows cellular growth rates and interlamellar spacing data to be obtained for much larger degrees of undercooling than reported hitherto. MATERIALS AND EXPERIMENTAL PROCEDURE The Fe-30 Ni-6 Ti alloy was prepared from electrolytic iron, Mond nickel shot, and sponge-purity titanium* by vacuum melting in a zirconia crucible

Jan 1, 1963

By S. F. Radtke

The properties and characteristics of lead and zinc have made these metals useful to man in many ways since the days of antiquity. Despite their long history of use, however, these metals have proved to be extremely resilient and responsive to modern needs. New alloys and compounds continue to be developed, adding to the growth of these metals. Consumption data is given for 1969 and compared with one and two decades ago. Trends in major markets also are cited and explained. Uses for lead and zinc which have come into prominence within the past few years are described and explained, with emphasis on the role played by the industry's cooperative research program. Current efforts in the research phase are discussed, with details given on major efforts for both metals, including new alloys, process developments, applications research, finishes, coating, paints and pigments, batteries and fundamental research. A forecast is given of promising new areas and a projection made on a longer term of new applications that may emerge from current research.

Jan 1, 1970

By M. D. Hassialis

THE claim is made in a number of patents1,2,3,4 that some compounds of the class known as aryl sulphides have collector properties. One of these patents generalizes the claim to include all aryl sulphides, whose generic formula is R-S¬R[=]-R’ (where x = r,2, . . . ), with the restriction that if the aromatic radicals R, R' contain substituent groups these groups may not contain nitrogen or oxygen. Moses, Hess, and Perkins cite as evidence for their claims the results of flotation tests on Anaconda and Miami copper ores using Biphenyl sulphide, ditolyl disulphide and dinapthyl disulphide as collectors. The use of alkyl sulphides as collectors has also been reported5 with the conclusion that the alkyl sulphides are better collectors than the corresponding aryl sulphides. The experimental work cited appears to confirm this contention. In order to test these claims with respect to diphenyl sulphide, a sample, purchased from the Eastman Kodak Co., was tested against Anaconda ore. The procedure followed was that of Moses, Hess, and Perkins. A sample of ore weighing 500 grams was placed in a laboratory ball mill. To this was added 220 grams of water, 0.06 grams of commercial diphenyl sulphide (1/4 lb. per ton of ore), and 0.8 grams of lime (3 lb. per ton of ore). The material was ground until 93 per cent passed a 65mesh screen. This pulp was diluted to 16 per cent solids. A sample of the diluted pulp was placed in a Minerals Separation type of laboratory flotation cell. After a 2-min. agitation period, pine oil was added and the froth collected for a period of 15 min. This test recovered 68 per cent of the copper, with a ratio of concentration of 6.8: 1. The tailing assay was 0.3 per cent Cu. Moses, Hess and Perkins attained a recovery of 75 per cent, with a ratio concentration of 12: 1. Although these results do not compare too well with those of Moses, Hess and Perkins, subsequent tests showed an improvement, as judged by vanning of the tails. It is concluded, therefore, that the patent results are confirmed. CONTACT-ANGLE TESTS In order to study the response of the various minerals, found in Anaconda ore, to commercial diphenyl sulphide, some contact-angle tests were made. Polished particles of bornite, chalcocite, chalcopyrite, pyrite and quartz were conditioned for 15 min. in a suspension of diphenyl sulphide in water. The concentration of this suspension was 0.284 grams per liter, this being the concentration of this reagent in the ball mill. The conditioned particles were rinsed with water (not rubbed with filter paper or boiled linen) and then tested against an air bubble in the bubble machine, with the following results: born-

Jan 1, 1943

[ARIZONA Established July 10, 1915 CHARLES R. KUZELL, Chairman GILBERT C. DAVIS, First Vice-Chairman ALBERT MENDELSOHN, Second Vice-Chairman MORRIS G. FOWLER, Secretary-Treasurer Phelps Dodge Corporation, Douglas, Ariz. LYLE M. BARKER P. D. I. HONEYMAN A. T. BARR H. M. LAVENDER T. G. CHAPMAN WALTER C. LAWSON GEORGE M. COLVOCORESSES W. H. LOERPABEL EDWIN H. CRABTREE, JR. CARL F. MILLS WALTER I. GARMS P. M. MOSIER WESLEY P. Goss J. A. RICHARDS 11. C. HENRIE JOSEPH A. WILCOX C. F. WILLIS]

Jan 1, 1946

By Herbert Dumont

Since 1947 Preussag AG Metal1 has used a process for fuming zinc- and lead-containing dump slags and residues from vertical retorts in a half-shaft furnace at their Hüttenwerk Harz at Oker. Contrary to the classic shaft furnace, only one side of the half-shaft furnace is fitted with tuyeres. The opposite side is a bricked slope. The upper shaft section is piped. There zinc vapor and combustion gases are burned by sucked-in air. Gases and fume enter a boiler located on the rear length of the furnace via a piped fire bridge. The gases are then cooled in an air preheater prior to dedusting in a bag filter. The furnace is charged with briquettes of metal-bearing materials, coal and pitch. The leaded zinc oxide fume is comparatively rich in both lead and zinc. The copper in the feed is recovered in low-copper matte. The slag can be discarded. The Oker plant comprises 13 furnaces of 2.9 to 4.9 m length in the tuyere area. Two other plants in Italy and Spain are processing zinc leach residues by this technique. Fuming of zinc-lead-oxide ores as well as partially roasted sulfide- zinc-lead-copper bulk concentrates will be possible.

Jan 1, 1970

By J. D. Verhoeven

In the past 15 years a considerable amount of experimental and theoretical work has been done concerning the onset of convection in liquids as a result of interm1 density gradients. This work, which has been doue in many different fields, is reviewed here and extended slightly to give a rrlore quantitative understanding to the probletrz of conzection in liquid metal dlffusion experinletzts. In liquid metal systems the capillary reservoir technique is currently used, almost exclusively, to measure diffusion coefficients. In this technique it is necessary that the liquid be stagnant in order to avoid mixing by means of convection currents. Convective mixing may result from: 1) convection produced as a result of the initial immersion of the capillary; 2) convection produced in the region of the capillary mouth as the result of the stirring frequency used to avoid solute buildup in the reservoir near the capillary mouth; 3) convection produced during solidification as a result of the volume change; and 4) convection produced as a result of local density differences within the liquid in the capillary. The first three types of convection have been discussed elsewhere1-a and are only mentioned for completeness here. This work is concerned only with the fourth type of convection. Local density differences will arise within the liquid as a result of either a temperature gradient or a concentration gradient. It is usually, but not always, recognized by those employing the capillary reservoir technique that the top of the capillary should be kept slightly hotter than the bottom and that the light element should be made to migrate downward in order to avoid convection. In the past 15 years a considerable amount of work, both theoretical and experimental, has been done in a number of different fields which bear on this problem. This work is reviewed here and extended slightly in an effort to give a more quantitative understanding of the convective motion produced in vertical capillaries by local density differences. The Stokes-Navier equations for an incompressible fluid of constant viscosity in a gravitational field may be written as: %L + (v?)v = - ?£ + Wv - g£ [1] where F is the velocity, t the time, P the pressure, p the density, v the kinematic viscosity, g the gravitational acceleration, and k a unit vector in the vertical direction. A successful diffusion experiment requires the liquid to be motionless, and under this condition Eq. [I] becomes: where a is the thermal expansion coefficient [a =-(l/po)(dp/d)], a' is a solute expansion coefficient [a' = -(l/po)(dp/d)], and the solute is taken as that component which makes a' a positive number. Combining with Eq. [3] the following restriction is obtained: Since there is no fixed relation between VT and VC in a binary diffusion experiment, Eq. [5] shows that the condition of fluid motionlessness requires both the temperature gradient and the concentration gradient to be vertically directed. Given this condition of a density gradient in the vertical direction only, it is obvious that, as this vertical density gradient increases from negative to positive values, the motionless liquid will eventually become unstable and convective movement will begin. The classical treatment of this type of instability problem was given by aleih' in 1916 for the case of a thin fluid film of infinite horizontal extent; and a very comprehensive text has recently been written on the subject by handrasekhar.' It is found that convective motion does not begin until a dimensionless number involving the density gradient exceeds a certain critical value. This dimensionless number is generally referred to as the Rayleigh number, R, and it is equal to the product of the Prandtl and Grashof numbers. For the sake of clarity a distinction will be made between two types of free convection produced by internal density gradients. In the first case a density gradient is present in the vertical direction only, and, since the convection begins only after a critical gradient is attained, this case will be called threshold convection. In the second case a horizontal density gradient is present and in this case a finite convection velocity is produced by a finite density gradient so that it will be termed thresholdless convection. Some experimentalists have performed diffusion experiments using capillaries which were placed in a horizontal or inclined position in order to avoid convection. These positions do put the small capillary dimension in the vertical direction and, consequently, they would be less prone to threshold convection than the vertical position. However, if the diffusion process produced a density variation, as it usually does, it would not be theoretically possible to avoid thresh-

Jan 1, 1969

By R. S. Shoemaker, F. W. McQuiston

EMPEROR GOLD MINES Vatukoula, Fiji 1974 Operating Data to July 1 ORE DESCRIPTION: Ore bodies occur in basalt and associated ash beds overlain by andesite tuffs and sediments. The basalt in much of the ore mined is weathered with alteration of olivine to serpentine and iron oxides, and augite to chorite. The most important host minerals for gold are the tellurides sylvanite and hessite. Next in importance the sulphide s, pyrite, marcasite and arseno-pyrite. A small amount of free gold also occurs. Chalcopyrite, sphalerite, tetrahedrite, bornite, galena and native tellurium are present in small quantities. TYPE OF MINE: Underground and open pit ORE HAULAGE TO MILL: 3.5 ton bottom dump skips from underground. 7 ton trucks from open pit. CAPACITY IN TONS/24 HRS: 1345 short tons ASSAY HEADS (1973): 0.232 oz Au per ton, 0.357 oz Te per ton PRODUCTS: Gold Bullion (400 oz bars) Metallic Tellurium (1 2 lb bars ) RECOVERIES: AU 86.2% Te 88.0% ORE GRINDABILITY: 9.25 Kwh/T TOTAL POWER: 25.7 Kwh/T WATER: Pumped 112 mile to a 318, 000 gallon head tank. Consumption: 2 140 gal per ton, no reclaimed water used. TAILINGS: Pumped 2 /3 mile through 8" pipe. Uphill sections are steel. Downhill sections are fibro asbestos.

Jan 1, 1975

By A. G. Metcalfe, A. Siede

The hardening of annealed copper during fatigue testing appears to be independent of the applied stress and to occur largely within the first 4000 cycles. Copper hardened by fatigue is more resistant to annealing than copper hardened by static means, and softens by a multistage process. Creep studies at 300°C show that copper hardened by fatigue also has greater resistance to creep than statically hardened copper. Some theoretical explanations are discussed. RECENT interest in the behavior of metals subjected to fatigue stems from observations of phenomena which could not be explained by current theories of the structure of metals. In 1953 Bullen et al.l showed that the hardening caused by fatigue at low stresses did not cause severe bending of the lattice as did hardening by static methods. This was later confirmed by Wood, 'and Broom and Ham.3 Clarebrough et al4 showed that as the stress level used in fatigue hardening was increased, bending of the lattice was introduced, eventually approaching that of metals deformed by conventional cold-working methods. The type of hardening introduced by fatigue has other interesting characteristics. Kemsley5 showed that copper fractured by fatigue at low stresses resisted annealing as compared to copper hardened an equal amount by static means. The work of Clarebrough etal, shows that the manner of energy release during annealing differs for fatigue-hardened and statically hardened metal in both magnitude and temperature range of release. In addition to hardening of the lattice, fatigue has been shown to cause softening in materials previously hardened by static methods,5 and also in age-hardened alloys.7 The superposition of a small fatigue stress on the static loading of high-temperature alloys has been shown to increase their resistance to creep.' The present work was an attempt to determine the relationship between fatigue hardening, resistance to annealing, and the creep properties of pure copper. EXPERIMENTAL PROGRAM The program described here was designed to answer three questions: 1) Can stress-cycle combinations well below the failure values give significant increases in hardness? 2) Does hardening, under different stress-cycle combinations, give increase resistance to annealing? And if so— 3) Does superior resistance to annealing confer superior creep properties over statically hardened material? Three-quarter hard OFHC copper was annealed in vacuo at 550°C for 1 hr to produce a strain-free material having a fine grain size and uniform hardness. (The standard deviation of the mean hardness of the annealed samples was less than + 1.9 Dpn). Annealing was performed after machining the fatigue specimens so as to avoid work-hardened surfaces. Jigs were used to avoid distortion. The fatigue properties of the annealed copper were determined using an accurately aligned Baldwin-Sonntag SF1-U machine operating at 1800 cycles per min. This limited the minimum number of cycles which could be examined to about 4000 stress reversals. Since failure resulted in specimen damage, hardness increase with number of cycles was measured by testing specimens fatigued to different fractions of the failure values. The results are shown in Fig. 1, and are superimposed on the S-N curve of the copper in Fig. 2. The resistance to annealing of fatigue-hardened material was compared to that of material hardened by uniaxial tensile straining. Specimens hardened to equal values by both methods were progressively annealed for 1 hr at temperature in vacuo. After each annealing treatment the hardness was measured using a Leitz Durimet hardness tester with a 500-g load. At least five tests were made for each hardness determination. The standard deviation for individual specimens varied from 0.26 to 1.48 hardness points. The results are shown in Figs. 3 to 5. The discontinuous nature of the annealing process has been brought out by drawing idealized curves through the data points. This can be justified by the consistency of the results as well as by general agreement with results of Kemsley.5 The creep resistance of fatigue-hardened and

Jan 1, 1960

The co-operation of the members of the Institute is earnestly sought by the Committee on Nominations, recently appointed by the Board of . Directors, in its work of formulating a ticket for officers and places falling vacant in the Board of Directors in February, 1916. The Committee must present the official ticket of nominations to the Board of Directors at its October meeting. Members are, therefore, urged to send promptly their nominations for officers and Directors in order that the Committee may have an opportunity to give them full consideration. The officers to be elected at the annual meeting in February, 1916, are: One officer, known as Director and President. Two officers, known as Director and Vice-President. Five officers, known as Director; The attention of members is called to Articles V and VII of the Constitution, and to By-Law XIII, which reads as follows: "The geographical districts to be considered by the Committee on Nominations shall he as follows, until otherwise ordered by the Board. District No. 1. New England, New York, and New Jersey, excepting New York City and district., which is provided for in the Constitution. (N. B.-New York City and district is designated District 0.) District No. 2. Pennsylvania. District No. 3. Ohio, Indiana, Illinois, Iowa, and Missouri. District No. 4. Minnesota, Wisconsin, and Michigan. District No. 5. Montana, North and South Dakota, Wyoming, Nebraska, Kansas, Washington, Oregon, Idaho, and Alaska. District No. 6. California and Nevada. District No. 7. Utah, Colorado, Arizona, and New Mexico. District No. 8. Louisiana and Texas. District No. 9. Other Southern States and District of Columbia. District No. 10. Mexico. District No. 11. Canada."

Jan 7, 1915

By C. O. Tarr, G. V. Smith, R. F. Miller

METALLURGISTS have long recognized that the Fe3C type of carbide is not a stable phase in steel and that, given sufficient time, it will decompose with formation of graphite, at least at temperatures below about 2050°F.1 This slow graphitization has never been of much concern to users of hypoeutectoid steels, for in such steels it occurs only during prolonged exposure at elevated temperature. In 1935, Kinzel and Moore2 reported complete graphitization of the carbide of a 0.1 5 per cent carbon steel that had been in senrice for about 26,000 hr. at a temperature of about 1100° to 1200°F. In discussing this paper, both Mathews and Sauveur reported graphitization of slightly hypereutectoid steels. In an extensive investigation of graphitization of high-purity iron-carbon alloys, Wells1 produced graphite at 7o0°C. (1290°F.) in an alloy containing as little as 0.13 per cent carbon, and showed that graphite may precipitate either directly from austenite or from decomposition of Fe3C, also that the rate of graphitization tends to increase with increase of temperature, at least up to a certain point, and with the presence of graphite nuclei. Jenkins, Mellor and Jenkinson,3 studying the structural changes in carbon steels ranging from 0.17 to 1.14 per cent carbon during stress-rupture tests at elevated temperature, obsenred graphite in an aluminum-killed 0.40 per cent carbon steel after fracture in 4340 hr. under a stress of 17,900 lb. per sq. in. at 840°F. and in many of the steels after stress-rupture test at 1200°F. Unstressed samples of 0.60, 0.86 and 1.14 per cent carbon steels graphitized almost completely in 360 hr. at 1200°F., while samples of 0.90 and 1.10 per cent carbon steels were somewhat graphitized, and steels containing 0.24, 0.40 and 0.57 per cent carbon showed no sign of graphite. Their results indicate that graphite precipitates the more readily the higher the carbon content, though this tendency is influenced to some extent by deoxidation practice, and that graphitization is accelerated by plastic deformation. In a recent study of the graphitization of 0.4 and 0.6 per cent carbon steel strip, made by M. A. Hughes,4 it was found that at 1200°F. graphite appeared after 72 hr. in aluminum-killed but not in silicon-killed steel, and that the rate of graphitization was increased by slow cooling from 1600°F. and by cold-working prior to annealing. In creep tests of normalized o. I 5 per cent carbon steel killed with 2.5 lb. of aluminum per ton, at the U. S. Steel Corporation laboratory at Kearny, spheroidization and some graphitization were found after 3000 hr. at 1000°F. under a stress as low as 15m lb. per sq. inch.

Jan 1, 1944

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

Reserves of Lake Superior Manganiferous Iron Ores Appendix-to paper by CARL ZAPFFE, presented at the Cleveland Meeting and issued, as Pamphlet No. 1664-C, with MINING AND METALLURGY, May, 1927. The author has made several test calculations on the basis of manganese units that are and may be involved. These are summarized here, as follows: On the basis of ore produced since 1902, the average annual requirement of manganese units would be 91,000 tons; on the basis of the production of the past 4 or 5 years, the requirement would be 145,000 tons; on the basis of the year 1925 only, the requirement would be 155,000 tons. Applying the percentage of increase for the next 20 years, as determined by the plat shown as Fig. 3, the total requirement for 20 years would be 3,254,000 to 3,572,000 tons, if one used either 145,000 tons or 155,000 tons as a starting point. We have the following interesting facts: (1) The Michigan ores contain only about one-half the manganese that the Cuyuna ore does; (2) the Cuyuna district now produces one-half the ore required; (3) the known tonnage of Cuyuna reserves is greater than the speculative reserve offered for Michigan; (4) at the present rate of production considered by tons, Michigan ores ought to be exhausted in 20 years or less while Cuyuna ores would last up to 44 years. We should now reduce the estimated reserves to a basis of manganese, units. Using the tonnages listed in Combinations 2, 3, 4 and 5, the reserves total 3,118,225 tons, 3,781,995 tons, 5,041,995 tons and 5,560,342 tons, respectively. Therefore, needing at the most 3,572,000 tons, as shown above, either Combination 3, 4 or 5 will not only suffice but will leave an excess-enough for 1 or 2 years for Combination 3, 9 or 10 years for Combination 4, and 12' to 13 years for Combination 5. This means that for Combination 5, without using tonnages obtained from beneficiating or from mixing poor ores, the reserves are ample for about 33 years.

Jan 5, 1927

By R. C. Hirschfeld, H. H. Einstein, R. W. Bruhn, R. A. Nelson

The objective of the model studies described in this paper is to determine the effect of planar discontinuities on the strength and deformability of a rock mass. A model material was used because it satisfied concurrently three requirements that available natural-rock samples did not: (1) low strength, which was desirable for minimizing the loads that had to be applied in the laboratory; (2) ease of producing test specimens with geometrically regular joint patterns; and (3) uniformity of the test specimens. The model tests were performed on specimens made from a single modeling material and tested under triaxial stress conditions with [u,=u,]. Results are presented in this paper for tests on specimens that had (1) a single joint set inclined at several angles to the major principal direction, including 0º and 90°, and (2) two joint sets that were mutually perpendicular, one set perpendicular to and one set parallel to the major principal direction. Several different joint spacings were used in each series. Future tests will include a series with two sets of joints that make oblique angles with each other and with the major principal direction. The results of model tests and tests on cores of jointed rock by several investigators (e.g., Müller and Pacher,l Moore,2 Krsmanovic and Milic,3 Hayashi,4 Rosenblad,5 Jaeger,6 and Lane and Heck 7, have contributed significantly to the design of these experiments, which are believed to be the first in which a comprehensive study has been made of the combined effects under triaxial loading of joint spacing and joint orientation (Fig. 1).

Jan 1, 1970

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

US 4,181,703-Removal of magnesium impurity from phosphate rock. Crushed screened ore containing more than 0.3% by weight of magnesium is slurried with sea water, acidified with sulfuric acid to a pH value not lower than 2 5, and filtered and washed before the neutralization point is reached. W. Wengeler, F. Wolstein, and E. Hoffman, assigned to Uhde G.m.b.H. Jan. 1, 1980 4 pp (423-167) Filed: 11-18-77 (852,918)

Jan 1, 1982

By K. L. Komarek

Based on theoretical and experimental evidence a discussion follows of the behavior of phosphorus -bearing iron ores in the R-N Direct Reduction Process and suggestions are made of methods of reducing the amount of phosphorus in the metallic end product. In ferrous metallurgy a direct reduction process is one in which iron ores are reduced to metallic iron with gaseous or solid reductants without the appearance of a liquid phase. A number of attractive features have induced several companies and government agencies to invest in the development of direct reduction processes. A summary of all direct reduction processes up to 1954 has been given by Barrett,' and Wiberg,2 and Willems3 have reviewed the most recent developments in this rapidly expanding field. Many difficulties have been encountered in direct reduction processes and the nature of these difficulties has varied from process to process. One problem common to almost all of them is the removal of phosphorus which is one of the reasons for the rather pessimistic outlook given by some government publications4'5 to direct reduction processes. In this paper an attempt is made to give a theoretical explanation of the variations in phosphorus removal observed in the R-NY Direct Reduction Process. However, many conclusions are general enough to be applicable to other processes. Most iron ores treated by the R-N process yield products lower in phosphorus than the original ore. A qualitative account of the factors has been given by Stewart, Reed, and Herasymenkoe but the erratic removal of phosphorus from some ores and the general importance of this problem make a more careful analysis of the theoretical aspects desirable. In the R-N process mixed ore or balled fines, ex-

Jan 1, 1963

By Carroll C. Bailey, William F. Boericke

Mine financing, or providing adequate capital for developing and bringing a mining property into production, is an essential requirement for a successful operation. Today it presents a different picture than even twenty-five years ago. The day appears to be gone when a mining property could pay its own way from grass roots to production. The country has been quite thoroughly combed for surface showings from which sufficient initial profit could be immediately garnered to pay for further development and production facilities. The four M's for success in mining-mineral, market, management, and money-are still essential; but doubled or tripled wage costs and steep advances in cost of equipment and supplies throw increased emphasis on adequate capital funds for bringing in a prospect and making it a producer. Consequently, the old picturesque, although seldom rewarding, grub- staking procedure where a single venturesome citizen might advance funds to a prospector on a fifty-fifty basis for whatever discovery he might find, has largely disappeared. Its place, to some degree, has been taken by the small syndicate of venturesome members who band together for furnishing funds to a group of prospectors for the same general purposes. Such a syndicate has a definite organization and is usually assured of sufficient initial funds, or flow of funds, to carry on work for several years. It is headed by an engineer-promoter who has had considerable field experience as well as personal knowledge of his prospecting crews. For the owner of a potential mining property who has ample capital, the problem is to determine (1) justification for the necessary investment in exploration and development, and (2) the economics of the enterprise as to size and degree of integration of the final operating entity. If the owner of such a property has little or no capital, he also faces these same basic problems but, in addition, must be able to present the findings of fact and persuade the prospective investor that the enterprise will produce

Jan 1, 1959

By A. CHESTER BEATTY

SO much has been written about African, and particularly about Northern Rhodesian, copper during the past two years that I feel safe in assuming that you are familiar with the general background of the Rhodesian picture. Therefore, I will confine myself to certain of the high lights in connection with the history, geology, development, ore reserves, and contemplated mining methods in this relatively new and highly important copper field., Unlike most of the other great orebodies of the world, the Roan Antelope mine was not discovered by the hoof of a starving prospector's faithful burro; nor even, as its name might suggest, by a well-placed kick of protest from an antelope stumbling over a malachite outcrop. Late in 1905 an English prospector named Collier, traveling in the N'Dola district, came upon some natives using a green powder for medicinal purposes. Closer examination of the powder revealed that it ' was ground-up malachite. Collier endeavored to persuade the natives to tell him where they obtained this medicine, but' for a long time without success, because of the general feeling among the natives that they did not wish to reveal the resources of their land to the white. Finally however, - he persuaded- brie 'of-the elders to at" least take 'him part way toward, the- place where the malachite was supposed to occur. The bid took him, to a point on the lower regions of the Luanshya river and there left him with the instructions that if he followed the stream up toward its.

Jan 1, 1931

By W. V. Vietti, W. A. Oberlin

Crude petroleum produced in the Texas Panhandle oil field is both an asphalt and a paraffin-base oil and is further characterized by being a high-gravity crude with an extremely high cold test,. An eight-well composite of Panhandle crude showed the following characteristics: Gravity, 36.6° A. P. I. Viscosity: 61 sec. Saybolt at 100° F. 170 sec. Saybolt at 75° F. 1560 sec. Saybolt at 50° F. (stirring) Cold Test, 60° F. Distillation Test: Per Cent. Per Cent. Gasoline........................ 28.8 Wax........................... 19.2 Kerosene........................ 4.8 Asphalt........................ 13 .0 Gas oil......................... 30.7 Sulfur1......................... 0.8 Fuel oil......................... 34.7 Subsurface Conditions The original pressure in the formation in the Panhandle field closely approximated 420 Ib. gage or 435 Ib. absolute pressure. Temperatures taken indicate that the formation temperatures do not exceed 90° F. The temperatures in Table I are typical measurements taken on one lease. * A contribrition from the research department of the Marland Refining Co. of Oklahoma and the production engineering department of the Marland Oil Co. of Texas. 1 Smith [Analysis of Panhandle and Rig Lake Crudes. U. S. Bur. Mines, Circular No. 6014 (December, 1926)] found an average sulfur content of 0.6 per cent.

Jan 1, 1928