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By H. A. Wilhelm, P. Chiotti, G. A. Tracy

A summary of analytical, X-ray, thermal, and metallographic data obtained in the study of the Mg-U system is presented. No intermetallic compounds are formed by these two elements, and their mutual solubility is limited at temperatures up to 1255°C. The compositions of the liquids which coexist at 1135°C under a pressure of 3 atm are 0.14*0.05 wt pet U in magnesium, and 0.004 wt pet Mg in uranium. The solubility of uranium in magnesium decreases to 0.0510.03 wt pet at 675OC, and to about 0.0005 wt pet at 650°C. Due to the reactivity of both uranium and magnesium toward crucible materials, the choice of a suitable crucible presented a problem. Crucibles made from high purity magnesia to which 10 wt pet MgF2 was added to reduce porosity proved to be satisfactory. Some observations made with the use of other crucibles are given. THIS investigation was made to establish the phase diagram for the Mg-U system. Ahmann,' formerly of the Ames Laboratory, did some work on the system. He used several methods in an attempt to prepare Mg-U alloys. One of the methods involved the reduction of UF, with a large excess of magnesium. In these experiments, the magnesium wet the surface of the uranium, but there was no evidence for compound formation. The maximum solubility of magnesium in uranium was indicated to be 0.01 wt pet. In another set of experiments, uranium chips as well as uranium powder were heated in contact with molten magnesium in a graphite crucible for periods of time up to 48 hr. A reaction layer was found at the Mg-U interface in several instances. X-ray analysis of the layer material showed the presence of UC and some additional unidentified lines which were interpreted as indicating the possibility of an intermetallic compound of uranium and magnesium. These studies indicated the maximum content of magnesium in uranium to be 0.043 wt pet. One sample of magnesium which had been heated at 1025°C in contact with excess uranium was found by chemical analysis to contain 0.275 wt pet U. Rules, based on empirical or semi theoretical considerations, which attempt to predict the alloying behavior of metals have been presented in the literature. Although these rules are not infallible, they nevertheless serve as useful guides. Using them, several generalizations can be made concerning the Mg-U system. According to Hume-Rothery's' atomic

Jan 1, 1957

By J. G. McCullough

The paper is a general description of the U.S. lead and zinc industries as they are now compared to ten years ago and the effect of recent world-wide developments. Topics of interest concerning lead are the present and potential growth of the lead-acid battery business, the potential hazards of having one outlet for a major proportion of production, the expanding U.S. secondary lead production, the hardships of stringent hygiene and environmental regulations and the future supply and demand outlook. The present poor condition of the U.S. zinc industry caused by an oversupply of zinc metal - mostly in Europe - is discussed and also the shifting markets influenced by the automotive programs to reduce the weight of cars and the continuing high mine production due to the mixture of metals contained in the massive sulphide deposits which contain a major portion of the zinc metal reserves. This is all tempered by technical advances in die casting and the emphasis on the protecting of steel with zinc to prolong its useful life. New U.S. mine and smelter production facilities will be restrained due to lower cost foreign zinc from better grade ore deposits and the insistence by Governments for refining capacity to be constructed in the country that the ore is mined.

Jan 1, 1977

By Philip W. Simmons

THE Colorado Plateau uranium province is in a mining boom rivaling the most colorful days of the early West. The application of scientific skills and the use of modern and novel mechanical equipment, however, is unique. No metal has ever received such concentrated effort from geologists and mining engineers. Moreover, no other metal has had the variety of tools available for finding and mining ores. Radiation detection equipment, bull- dozers, truck-mounted wagon and core drills, jeeps, airplanes, helicopters, tractor loaders, self -propelled 3-wheeled dump cars, front-end loaders and fleets of modern trucks are some of the present-day tools of the uranium prospector and miner. Because uranium is so vital to our national defense, the Atomic Energy Commission has offered many incentives for its mining. Through a series of circulars, the AEC has established base price schedules and various incentive payments. The incentive payments for acceptable ores from domestic mines are: (1) a guaranteed base price of $3.50 per Ib for ores assaying 0.20 pct U3O8 and more; (2) premiums based on grades above 0.20 pct U3O8 as for example, ores assaying above 0.50 pct U3O8 receive $1.00 per lb premium; (3) a development allowance of 506 per Ib of U3O8 contained in ores assaying over 0.10 pct U3O8 (4) an ore haulage allowance of 64 a ton mile for a maximum of 100 miles; and (5) an initial production bonus which may amount to as much as $35,000 in addition to all other payments. The producers have been guaranteed this policy until Feb. 28, 1957. The other four will continue until April 1962.

Jan 4, 1954

By John J. Cioston

THE steadily rising flood of gold production from all parts of the world has created an avalanche of rumors regarding the stability of the present price of this metal. Markets have been unsettled from Johannesburg to London from New York and Toronto to Melbourne, despite repeated denials from, American and British authorities of any immediate intention to alter the price. Various economists and financial writers have blossomed forth with predictions that the price would be set at the old level of $20.67 per oz.; some have even been so brash as to state That a price of $15 would be necessary to bring production within control. These effusions, based entirely upon monetary theories and with no regard to production costs, serve to confuse rather than clarify the situation.

Jan 1, 1937

By ERNEST A. HERSAY

ACCURATE ore-sizing with screens is drawing attention to certain details that now, more than ever before, require attention. There are many tests that must be preceded by careful sizing. The assayer often could profit by a more careful selection of screens. In milling, more attention is given the slimes produced. Cement-manufacturers are pulverizing and screening finer than they formerly did, and others are reducing materials to fine sizes at high cost, with screens used to govern the fine¬ness of the pulverized product. Fine screens are expensive, easily injured by mis-use, are carried in stock sparingly by most dealers, and are handled often by those who know little about them except their designated number. More attention, on the whole, needs be given the actual size of the mesh-openings, and less emphasis placed upon any custom or conventionality in numbering. An effort to classify wire screens, in this respect, leads at once into computations, where one is confronted with details of sizes and standards, of different wires, different gauges, and different customs. There is always uncertainty about the exact working-size of a screen until one gives the matter special attention, and devotes more time to it than its simplicity seems to demand. To know only the number is not sufficient for all uses. Often, in sets, superfluous sizes are used; and sizes are omitted that are of critical importance. In wire screens, the use of different standard sizes of wire makes important differences in dimensions that must be taken into account. The dealer usually grades screens by the number of openings per linear dimensions, regardless of the size of the openings or of the wire. Certain 100-mesh screens in use are found, by measurement, to he actually coarser than others of 90-mesh, a result which is due, of course, to the use of larger

May 1, 1906

By Frank Milliken

IN September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1007 to 1019. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was dissemi-nated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was prob-ably less than 6o per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a com-plete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof com-prised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. 1, which gives percentages of tonnage and copper content.

Jan 1, 1940

By Theodore Nagel

Fuel-oil, natural gas and coke oven gas, producing the higher temperatures of open-hearth current practice, have been gradually displacing producer gas the lowest cost fuel for open hearth operations. The lower temperatures of combusts on products from producer gas is caused by nitrogen dilution. Practical Application of Combustion Thermochemistry One pound of carbon burned to CO produces 3,960 B.T.U. and one pound of carbon burned to C02 produces 14,140 B.T.U. The second unit of oxygen uniting with gasified carbon (CO) produces (14,140 - 3,960) 10,180 B.T.U. which is (10,180 - 3,960) 6,220 B.T.U. more heat than produced by the first unit of oxygen forming CO by uniting with solid carbon. A review of the relative combustion heating values of commercial gaseous fuels reveals CO requires a minimum of air for combustion and because of minimum nitrogen dilution and the high thermal release from CO higher temperature combustion products are produced from CO than from natural gas or from coke-oven gas under similar combustion conditions. Inert nitrogen diluent lowers the calorific value of fuel gas and its diluting effect is cumulative in lowering the temperature of the products of total combustion. It is not only logical but practical in partial combustion, converting bituminous coal to gas, to generate the gas with reduced nitrogen dilution.

Jan 1, 1936

By Theodore Nagel

Fuel-oil, natural gas and coke oven gas, producing the higher temperatures of open-hearth current practice, have been gradually displacing producer gas the lowest cost fuel for open hearth operations. The lower temperatures of combustion products from producer gas is caused by nitrogen dilution. Practical Application of Combustion Thermochemistry One pound of carbon burned to CO produces 3,960 B.T.U. and one pound of carbon burned to C02 produces 14,140 B.T.U. The second unit of oxygen uniting-with gasified car-bon (-CO) produces (14,140 - 3,960) 10,180 B.T.U. which is;(10,180 - 3,960) 6,220 B.T.U. more heat than produced by the first, unit of oxygen forming CO by uniting with solid carbon. A review of the relative combustion heating values of commercial gaseous fuels reveals CO requires a minimum of air for combustion, and because of minimum nitrogen dilution and the high thermal release from CO higher temperature combustion products are produced from CO than from natural gas or from coke-oven gas under similar combustion conditions. Inert nitrogen diluent lowers the calorific value of fuel gas and its diluting effect is cumulative in lowering the temperature of the products of total, combustion. It is not only logical but, practical in partial combustion, converting bituminous coal to gas, to generate the gas, with reduced nitrogen dilution.

Jan 1, 1936

THIS chapter and the one following deal with the heat quantities involved in open-hearth steelmaking, including the thermal efficiency of the furnace as a generator of high-temperature heat, the heat storage in the steel and slag produced and in the furnace walls, and the heats of the various chemical reactions involved in combustion, in the formation of slag, and the refining of steel. The fundamental laws to be considered are the simplification of the first two ' laws of thermodynamics as applied to problems involving sensible and potential (or latent) heat only 1. Heat input equals heat outflow plus storage. 2. Heat may be transferred only from a hotter body to a colder one. The first of these laws relates to the various heat quantities or the "heat balance" of the process. No one has as yet made an open-hearth heat balance that came out almost exactly balanced, and we assume that the cause lies in the difficulties of accurate temperature and flow-rate measurements at the high temperatures involved and the inherent complexities of flow distribution, air leakage, etc., present in any real, open-hearth furnace system. Some idea of the magnitude of the heat quantities involved can be obtained- by a brief, crude outline of the heat balance of a 90-ton heat of steel. We will assume a 60 to 70 per cent hot-metal charge in a fairly fast working and only moderately efficient furnace, burning fuel oil, with a fuel consumption of around 4 million B.t.u. per net ton. of ingots produced. The time from start of charge to tap is 9 hr. During this period, the oil burned represents 360 million B.t.u., and the sensible heat in the preheated air at the port ends is 117 million B.t.u. so that the total heat input at the ports is 477 million B.t.u. Heat stored in the steel and slag at the end of the heat, plus the various amounts absorbed by certain bath reactions, amounts to a total of 195 million B.t.u., but 120 million of this is supplied by the heat in the hot metal and by various heat--evolving reactions in the bath, so that only 75 million B.t.u. need be supplied to the bath by the flame.

Jan 1, 1944

By P. Chiotti, G. R. Kilp

IN the study of zinc-zirconium1 and zinc-uranium2 systems, vapor-pressure measurements were made in order to establish the equilibrium phase diagrams for a pressure of 1 atm. In each of these systems, only zinc has an appreciable vapor pressure over the temperature range investigated. The zinc pressure was measured over a sufficiently wide temperature and composition range to permit calculation of the standard free energy, enthalpy, and entropy of formation for the compounds ZrZn, ZrZn2, ZrZn3, ZrZn6, ZrZn14 , and U2Zn17. In these calculations the compounds were treated as line compounds. Although the exact composition range was not determined, metallographic and thermal data indicate that the solubility range for these compounds is small. It is to be noted that the compound initially reported to correspond to the formula UZn9, 2 has been shown by the crystal structure work of Makarov and vinogradov3 to correspond to the formula U2Zn17,. The crystal structure is similar to that for the compounds Th2M17, investigated by Florio,4 et al; here M represents iron, cobalt, or nickel. Therefore, thermodynamic calculations are based on the formpla U2Zn17 EXPERIMENTAL The dew-point method employed to measure the vapor pressure of zinc over uranium-zinc alloys has been described previously.2 The same procedure and apparatus were used in measuring the zinc pressure over zinc-zirconium alloys. In the case of alloys in the two-phase region consisting of a zirconium and the compound ZrZn, the Knudsen effusion method was employed to obtain a few values in the temperature range 600" to 560°C. In most cases, tantalum crucibles were used to contain the zirconium alloys. THERMODYNAMIC PROPERTIES OFU2Zn17 A least-squares treatment of the vapor-pressure data obtained for 35 and 65 wt pct U alloys in the temperature range 650° to 940°C gave lOg10PAtm = 7,713/T + 6.33 Here, as in following equations, T represents degrees kelvin and P represents the zinc vapor pressure in atmospheres. The probable errors for the two constants were calculated to be 60.68 and 0.0563, respectively. This relation represents the equilibrium dissociation pressure for the reaction U2Zn17 (s) - 2U(s) + 17Zn(v) The solubility of zinc in solid uranium is negligible and the only additional information required to calculate the free energy of formation of U2Zn17 is the free energy of vaporization of pure zinc. K. K. Kelley5 gives the relations, AF°= 30,902 + 6.03Tlog T + 0.275 X 10-3T2 - 45.03T

Jan 1, 1961

By P. A. Beck

ACCORDING to a recent hypothesis of Sully,' xY. binary CT phases are characterized by 1.7 bonding 3d electrons per atom, which completely fill the first Brillouin zone. This hypothesis appears to imply that there are no empty 3d orbitals in the u phase, and that, correspondingly, this phase must be dia-magnetic, or at most weakly paramagnetic. On the other hand, Bowen and Hoar' reported that a u phase extracted electrolytically from an alloy steel became ferromagnetic when cooled to about —113°C. In view of the fundamental interest of the problem from the point of view of the electron structure of the u phase, it seemed worthwhile to study the magnetic properties of massive u phase specimens of various known compositions. Sigma specimens of the following compositions were tested: 1—40 atomic pct Fe, 40 atomic pct Cr, and 20 atomic pct Mo 2—35 atomic pct Fe, 35 atomic pct Cr, and 30 atomic pct Mo 3—48.7 atomic pct Fe, 50.2 atomic pct Cr, and 1.1 atomic pct W 4—40.7 atomic pct Co and 59.3 atomic pct Cr All specimens were found to be strongly paramagnetic at room temperature, particularly alloy No. 1. At liquid nitrogen temperature, alloy No. 1 be- came ferromagnetic; the other u alloys remained paramagnetic. Even though apparently not all u alloys become ferromagnetic at liquid nitrogen temperature, in view of their strong paramagnetism it is probable that the electron structure proposed by Sully is not correct. Similar qualitative studies were made with the p, P, and 8 phases." A p phase specimen of 57.2 atomic pct Co and 42.8 atomic pct Mo; a P specimen of 19.9 atomic pct Cr, 37.8 atomic pct Ni, and 42.3 atomic pct Mo; and a 8 specimen of 50.4 atomic pct Ni and 49.6 atomic pct Mo were tested at room temperature, and all were found to be paramagnetic, although considerably weaker than the u phase specimens described above. A test at liquid nitrogen temperature gave similar results for all specimens; none became ferromagnetic. Thanks are due to D. K. Das for preparing several of the alloys and to Pol Duwez of California Institute of Technology for kindly loaning four specimens of cr alloys. References 1 A. H. Sully: The Sigma Phase in Binary Alloys of the Transition Elements. Journal Inst. Metals (1951) 80, p. 173. - K. W. J. Bowen and T. P. Hoar: Low Temperature Ferromagnetism of Sigma Phase in an Alloy Steel. Research (1950) 3, p. 484. 3 S. Rideout, W. D. Manly, E. L. Kamen, B. S. Lement, and P. A. Beck: Intermediate Phases in Ternary Alloy Systems of Transition Elements. Trans. AIME (1951) 191, p. 872; Journal of Metals (October 1951).

Jan 1, 1953

By Winston W. Spencer

ALTHOUGH by far the largest A consumer of platinum metals in the world, the United States until recently has been in- significant as a producer. Writing in the "Minerals Yearbook" for 1939, H. W. Davis states that 1938 probably marked the beginning of an- other period of transition in the world production of the platinum metals. In that year, he says, their production in the United States jumped to 49,380 oz., or fourth in the rank of world output. In the ten-year period 1925 to 1934 United States output ,averaged only 8300 oz. Practically all of this sudden in- crease in production is attributable to the introduction of mechanized equipment at the placer deposits in the Goodnews Bay district of Alaska. This district adjoins the Bering Sea and Kuskokwim Bay (accented on the first syllable), and is approximately 120 miles south of the mouth of the Kuskokwim River. The nearest village and post office is Platinum, which lies about eleven miles north- east of the Goodnews Bay Mining Company's camp. A good gravel road connects the mine camp and the village.

Jan 1, 1940

By M. G. Corson

THE theory of hardening by interference with slip which has been so clearly developed by Jeffries and his co-workers requires that an alloy to be amenable to age or heat hardening should contain among its components some that will stay in solid solution at high temperatures and precipitate as a secondary phase on cooling. This secondary phase may be either a more or less pure individual element (chromium in the case of copper, anti-mony in the case of lead), or some intermetallic com-pound. Those cases of hardening which depend on the precipitation of a compound are not only the most frequent, but are also far superior in the efficiency of hardening obtained. However, the slip interference theory as stated in its most general form is not sufficient to foretell new cases of this type of hardening and also will not explain some phenomena of a more intricate nature. It is not sufficient that a secondary phase might be absorbed by the main one at high temperatures and precipitated at the lower ones. The kinetics of this precipitation and the accompanying. physical phenomena of dimensional changes play independent and highly important parts. These kinetics, while not yet sufficiently studied to he formulated in the shape of physicochemical equations, might find their expression-in a qualitative systema-tization of the phenomena of precipitation according to two different viewpoints. To begin with, we encounter the question as to the velocities of the precipitation and of the growth of the phase precipitated. To harden a metal in an efficient manner we must be able to control the precipitation on one hand and also to bring the total of the secondary phase to such a number and size of the particles pre-cipitated as, will produce a desirable hardening effect under commercially feasible conditions of. age or heat hardening. From this viewpoint six different cases may be dis-cerned.

Jan 7, 1928

By Coolbaugh, Franklin

CRUSHING of Climax mine-run ore is carried out in two plants: No. 1 plant (flowsheet in Fig. 1) has a capacity of approximately 5000 tons per day. It is used as a stand-by except when maximum production is required. No. 2 plant (Fig. 2) has a top capacity of approximately 17,000 tons per day. The No. 2 crusher is more efficient to operate on reduced tonnages regardless of the wide variation in peak capacities. The system of crushing is similar in both plants: Mine ore, of a size which can be drawn through 48 by 96-in. slusher openings underground, is dumped into the crusher bins from ten-ton mine cars and fed into 48 by 60-in. Buchanan jaw crushers by means of chutes and Ross chain feeders. The jaw crushers are set to discharge at approximately 9-in. size. Jaw crusher discharge is conveyed to 7-ft. Symons standard cone crushers where it is broken to minus-2-in. size,

Jan 1, 1946

By C. F. Jackson

THE work of, the Mining Methods Committee is now well under way. Following discussions previous to and during the February meeting, an Outline for Papers on Mining Methods was prepared, and over a thousand copies have now been distributed to committee men, to section secretaries and to members who have indicated any interest in the subject. The objective of the committee is to prepare a symposium on mining methods which will be of real practical value to the operator and engineer in the solution of every-day mining problems. It is planned to cover the entire field of mining in such a way that the different branches of mining, such as coal and ore (iron, copper, lead, zinc and precious metal) can benefit from the experience of the others at points where they have problems in common.. It is realized fully that each of these branches of mining possesses its own peculiar problems, but at the same time, there are prob-lems in connection with each, where the experience in others should be of value. The committee proposes to proceed along the following lines: 1. To present a general classification of mining methods, showing their inter-relationship, and at the same time .provide a common language for the discussion of mining methods and a nomenclature that will have the same meaning wherever used. A com-plete set of illustrations will accompany the classi-fication to make clear the terminology adopted and to show graphically the inter-relationship of methods. 2. To show the relationship between the physical characteristic of the deposit, the economic consider-ations and the. mining method., It is not proposed to treat this subject as a mere academic problem, but to secure reports from every mining company of impor-tance in this country, which will show what methods or modifications and combinations of methods have actually been applied and the physical conditions and economic considerations which have led to the adoption of these methods in each case. The Mining Methods Committee has drawn up an Outline for Papers on Mining Methods to be distributed among mining engineers and operators, giving in detail the information desired. This outline is the result of several months of careful thought and is a composite of the suggestions of many engineers and mining company officials from all parts of the United States.

Jan 7, 1922

By W. O. Hotchkiss

RECOVERY and profits in the mining business do not go hand in hand. Some part of an orebody can usually be recovered at a lower cost per ton than the whole orebody or a higher proportion of it. Similarly, the total of the profits that may be made from mining an orebody is in itself not a true measure of the value of the business. The yardstick for money value should be present worth, and this is particularly so for purposes of com-parison. A simple example, well within the bounds of practicability, illustrates these points: Assume a mine to have known ore reserves of 4,000,000 tons. The ore is of uniform grade but is so situated that 1,000,000 tons could be mined more cheaply than the remainder. Present operations are on the basis of complete recovery of the ores. Output is 100,000 tons per year at a profit of $1 per ton. It is estimated that the 1,000,000 tons of readily accessible ore could be mined at the same production rate but at a profit of $2 per ton. For an output of 100,000 tons each year at a profit of $1.00 per ton, the mine will have a life of 40 years; will produce $4,000,000 of total profit, and, at Hoskold rates of 8 and 4 per cent, will have a present value of $1,104,690. If only the easy one-quarter of the ore is considered, with an output of 100,000 tons each year, at a profit of $2.00 per ton, that part of the mine will have a life of 10 years, will produce total profits of $2,000,000, and at rates of 8 and 4 per cent will have a present value of $1,224,800. . Under conditions such as these, then, one-quarter of the reserve ore promptly mined is worth some 10 per cent more than the entire reserve would be on an average basis extending over the longer period. Assume further that one-half, or 2,000,000 tons, of the reserves could be promptly mined at the same yearly rate of 100,000 tons at a profit of $1.50 per ton. Then this part of the mine would have a life of 20 years, would produce total profits of $3,000,000, and would have a present value of $1,320,630; approximately 20 per cent greater than for the whole ore-body on an average basis for the longer period.

Jan 1, 1936

By Keats, J. L.

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical charac- teristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained.

Jan 1, 1957

By G. A. Vissac

The only fine coal washer with proved automatic controls, the feldspar jig is capable of good efficiencies even at low separating gravities, handles a variety of products, and treats 150 tph and over. IN continental Europe the feldspar jig is used almost exclusively for cleaning the fine sizes of coal; it operates with an artificial bed, made up generally of pieces of feldspar or of any other hard and heavy rock with good cleavages. A primitive form of this machine requiring close supervision was used in this country years ago, but output was small. The modern machines are generally air-pulsated Baum-type jigs, with capacities up to 150 tph, and treat sizes from % in. to 0, usually previously dedusted or deslimed. These jigs are equipped with very accurate and sensitive automatic controls insuring satisfactory operation even at low separating gravity and with feeds irregular in quality and quantity. This paper will deal more particularly with coal cleaning separation, but the technical studies apply equally to all minerals. Theory of the Feldspar Jig To understand fully the operation of the feldspar jig and to appreciate its potential value, it is necessary to measure and analyze the motion of small particles of various specific gravities, falling in various media, under various conditions. As no practical formulas were available for that purpose, the writer has developed new theories and established new sets of formulas, which cannot be demonstrated here. They are applicable to all minerals and to many problems of coal or mineral concentration. These formulas do not pretend to absolute accuracy, but results, tested by comparison with experimentally recorded data, are sufficient for practical purposes, as they give definite indications of trends, relative values, and order of magnitude of the many factors involved. For pulsating motions no earlier formulas are available. In the case of continuous currents or motions, such formulas as Rittinger's, Allen's, or Stokes', over a hundred years old, apply only to special shapes and sizes of particles, involve factors and coefficients difficult to measure or appreciate, and deal only with free motions. They are of little use in solving practical problems. Units used with the formulas presented here are in the CGS system. Lateral friction and suction have been taken into account according- to methods currently used in aerodynamics, and only hindered motion is dealt with. As the feldspar jig is primarily intended to create a fluid bed condition, the mixture of fluids and solids obtained is homogeneous, and the apparent specific gravity of the separating medium is calculated accordingly. For instance, if 20 pct of the volume is coal and shale, with an average of 1.60 sp gr, in a liquid of 1.10 sp gr, the actual specific gravity of the separating fluid is 0.80 x 1.1 + 0.20 X 1.6 = 1.20. The fundamental equations are as follows: The general motion of a particle falling in a medium of specific gravity equal to u, hindered motion. is dv/dt = g/Ls [ L (s-u) - u/g v2 [1] g = 981 cm per sec, acceleration of gravity, and L = thickness of the particle of specific gravity (s) and velocity (v). The initial acceleration dv/dt = g (1-u/s ) [2] is a function of the specific gravity of the particle, only for a given medium, and independent of its dimensions—an ideal separating condition. The terminal velocity Vt = gxL- (s-u)/u, [3] for a given value of u, is a function of s and L. Two particles, L, s, and L2 s2, are said to be equivalent if they have the same terminal velocity, and accordingly L1/L2=s2-u/s1-u. [4] Two such particles cannot be separated by continuous currents, in any concentrating device. Because the initial accelerated motion, which provides for efficient separation, is followed by a constant velocity, which has a limiting effect, it is essen-

Jan 1, 1956

By A. W. Hale

IN a work published in 1838, De Morgan, the author of the article on "Probabilities,' in the Encyclopedia Metropolitana, says " The method of least squares is not yet introduced into the affairs of common life,….that many things which are demonstrable only by the higher branches of mathematics are looked upon as useless." And he mentions an instance in which "a method was suggested for estimating the relative importance of boroughs, by considering their population and contributions to the revenue com-

Jan 1, 1881

By I. H. Warren, E. Devuyst

A review of the physical and chemical aspects of the direct leaching of metal oxides has been given and com- pared to recent data of the authors and co-workers. The physical aspects, including the anisotropy of the dissolution, the hydration and the zero point of charge of some metal oxides are discussed first and then the kinetics of the dissolution of metal oxides are considered. A general mechanism of the leaching of oxides which describes most of the observed results is proposed.

Jan 1, 1973