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By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.' and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By L. P. Davidson

THE new electrolytic zinc plant of the American Zinc Company of Illinois commenced operation in April 1941. The simple flowsheet using the standard current density and the economic reasons that dictated it are given herewith. The Evans-Wallower Zinc Co. built an electrolytic zinc plant at Monsanto, Ill., in 1929 and .operated it for about two years. The plant stood idle from 1932 and was purchased by the American Zinc Co. in 1940. Because of the condition of the equipment, excepting the motor generator set, a complete rebuilding was necessary. The Fairmont City plant of the American Zinc Co. could treat the leach residues, the purification cake and the skimmings from the melting furnace in its various plants. This possibility permitted a simple flowsheet with good economic results. The flowsheet is shown in Fig. I. The calcined concentrates are leached in mechanically agitated tanks with spent electrolyte and such ferric iron solution as necessary. When the acid has been neutralized and the iron coagulated, the fluid is discharged to settling tanks. The underflow from these thickeners is filtered on a Moore filter; the filter cake leaves the plant for retreatment and the filtrate joins the thickener overflow. Zinc dust is added to this solution until the copper and cadmium are precipitated. The pulp is filtered through Shriver presses, which deliver the purified solution to storage tanks, and the copper-cadmium-zinc cake is shipped for retreatment and recovery of these three metals. The purified solution is electrolyzed; the regenerated acid is returned for use in the leaching plant and the cathode zinc, after stripping, goes to the melting furnace, from which it is cast in slabs. The skimmings from the melting furnace are shipped to the Fairmont City plant for reduction to metal in. the retort furnaces. The choice of this simple flowsheet was made possible only because of the facilities of the Fairmont City plant. The long leaching period, with high acid content and high temperature which characterize the high-density process, gives a higher zinc extraction but also dissolves more impurities, which must be removed. The same is true to a lesser degree of the multi-step leaching of the western low-density plants. By the sacrifice of some initial extraction, solutions can be obtained that are relatively easy to purify and give good ampere efficiency. This loss in initial extraction is made up in the retreatment of the residues in the Waelz plant. The impurities that accompany the zinc thus extracted are inconsequential when the Waelz product is treated in a distillation plant. It was recognized that this flowsheet would require a somewhat greater amount of sulphuric acid-either as acid or as sulphate sulphur in the calcine-because of poorer washing. The sulphuric acid plant at Fairmont City could deliver 60° Be. acid to compensate for the sulphate loss and the cost would be less than the cost of more intensive washing.

Jan 1, 1942

By H. C. Heard

The review by Professor J. C. Jaeger (Chapter 1) briefly summarizes and discusses a select group of papers by various workers dealing primarily with aspects of fracture in brittle rock materials. Professor Jaeger's treatment is primarily concerned with the correlation of phenomenological and theoretical failure criteria with empirical results from short duration tests at ambient temperatures and generally at low lithostatic and interstitial fluid pressures. As engineering rock mechanics becomes more concerned with new techniques of mineral exploration and production at increasingly greater depths in the crust, it is well to be aware of the effect of the environment -that of the superposed stress field upon the lithostatic and interstitial fluid pressure, the temperature and the duration of the loading upon the failure of rocks either by fracture or flow. All results to be discussed here are from laboratory tests on small homogeneous samples, thus caution should be used in the direct extrapolation of these results to large inhomogeneous rock masses having quite different boundary conditions in the earth. The purpose of this supplement is to briefly point out the major effects of these parameters as examined singly, with all others held constant, and to cite some recent results which apply to the main theme on the brittle failure of rocks. The total stress field imposed upon a small volume of porous and permeable rock in the earth's crust may be thought of as the sum of an applied differential stress, plus a lithostatic pressure, plus an interstitial fluid pressure. The differential stress portion may be completely specified by nine components, six shear and three normal. If the small volume element is in rotational equilibrium, by suitably choosing our coordinate axes we may resolve these nine components into the three principal com-

Jan 1, 1967

By Paul F. Kerr

QUARTZ of a certain kind, is one of our strategic minerals, and Brazil is probably the one important available source. Crystals of quartz of suitable size and perfection for piezoelectrical application are rare; their most outstanding use is in radio work. Clear quartz, or "crystal," free from twinning, cracks, foreign particles of other disturbing lines of growth, and gaseous or liquid inclusions, is cut into plates which provide excellent control of frequency in broadcasting. The squares or rectangles are less than a millimeter in thickness and ordinarily on the order of 1 in. along each side. They are cut at definite angles with respect to the axes of the crystal, and ground with opposite surfaces parallel. Each small slab must be a section of one crystal, uniform throughout in atomic alignment. The thickness of the chip controls the frequency of a broadcast and it is most important to have the plates oriented and ground with utmost precision. Opposite surfaces are parallel to within 0.001 mm. and expansion or contraction due to the temperature is limited to one part in a million.

Jan 1, 1942

By Theodore Marvin

NOW that real progress is being made in building airplanes that can stand up under adverse conditions in isolated parts of the world, utilization of aviation by mining and petroleum companies is proceeding rapidly. This isolation, offering such handicaps to ordinary methods of transportation, also was the thorn in the flesh of aviation until the recent advances in plane and englue design. The accompanying illustration shows one of the six new planes just delivered to the U. S. Government for map making. The planes will be used in Department of Commerce, Coast and Geodetic Survey, Navy Hydrographic, and Insular work. There is a trap door in the bottom of the hull for a Fairchild camera which takes five pictures-vertical, N60°, E60°, S60°, and W60°-at regular intervals. It is manufactured by the Grumman Aircraft Engineering Corp., Farmingdale, N. Y.

Jan 1, 1935

By A. J. Teplitz, R. J. Goodwin

A new type water shut-off for use in air drilling has been developed. The method has been 99 to 100 per rent effective in several different formations of inter-ranular-type porosity. Since costs for materials, time and equipment used are relatively small, the process should extend economies of air drilling to many new areas. The treatment involves a new technique for forming a water-inroluble precipitate within the pores of a rock. Advantage it taken of the difference in mobility of a liquid and a gas in porous media to achieve the greatest volume of precipitate in a given pore. Reactants selected for the laboratory (2nd field tests were aluminum sulfate solution and gaseous ammonia. This process has been tested in both intergranular and fractured-type porosities. It has consistently shut-of between 99 and 100 per cent of the water flowing from formations having intergranular-type porosity and perrlreuhilities ranging from a few millidarcise to over a darcy The treatment is not particularly suitable for shutting-off water from fractured formations although plugging of the order of 50 per cent or greater has been achieved in all such applications. Among advantages of the treatment are: (I) no reaction waiting rime after a relatively short placement time, (2) a low mate-rials cost of about $3/f1 of hole treated, (3) use of common service-type equipment for treatment, and (4) no unusual requirements for mixing and placement. INTRODUCTION In rotary drilling with air or gas it has been possible to increase bit life by tenfold and more than double rate of penetration over corresponding performance when drilling with mud. These factors have amounted to as much as 22 per cent savings on total cost of drilling a well. However, these advantages are rapidly lost when water is encountered in an air- or gas-drilled well because water interferes with the removal of cuttings from the hole and also gives rise to other difficulties. In attempting to combat water troubles, operators have commonly resorted to such measures as mist drilling, treatment with cement or chemicals, converting to conventional mud drilling, or setting casing. In many cases these measures have either been costly or ineffective. In an effort to overcome this problem, studies were undertaken to develop an effective and economical water shut-off technique for use in formations possessing inter-granular-type porosity. Extensive laboratory experimentation finally led to a unique method for producing a water-insoluble precipitate within the pores of a sandstone. The unique part of the treatment is use of a liquid and a gas to form the precipitate, and in this case the reactants used were aluminum sulfate solution and gaseous ammonia. The reaction between these two materials is shown in the following equation. Al2 (SO1)3 - 18 H20 6NH2? saturated Water- Solution Cat 2A1(OH)3 . n H20 3(NH4)2SO • n H20 Solid Solid That is, a solid precipitate consisting of aluminum hydroxide and ammonium sulfate is formed when ammonia reacts with aqueous aluminum sulfate. The aluminum hydroxide is insoluble in water and the ammonium sulfate, though soluble, can only be removed from the formation pores by diffusion—an extremely slow process. Although the precipitate formed by the reaction is not particularly firm, great strength is not needed for a precipitate to bridge and plug intergran-ular-type porosity. A flow path in such a system is extremely tortuous and involves a great variety of pore

By H. Stigzelius

FINLAND'S recent mining history is both dramatic and pitiful in its shifting fortunes, dominated as it has been, by the country's proximity to the border zone of opposing dictatorships and social traditions; Fascism to the south, Communism to the east, and Democracy to the west. After 108 years under Russia's more or less harsh rule, Finland gained its democratic independence during the 1917 revolutionary strife in Russia with the official help of Germany and spontaneous help of other neighbors. The young nation was attacked by Russia in 1939 and again in 1941. It is common knowledge how the Finns fought with everything they had and everything they could get against their overwhelming adversary, and how by force of circumstances they landed in the Axis camp in 1941. Finland has never been known as a mining country in the same way as near-by Sweden, whose abundant iron and copper smelters during long periods so greatly contributed to the nation's welfare. Its largely barren, Archaean-granite geology long seemed forbidding. Some mining was done, to be sure; copper and tin at Pitkaranta near the Russian border, and lead and copper at Orijarvi. But towards the end of the last century the absence of a single producing mine cast a pessimistic shadow of truth over the Finnish poet Runeberg's words, that

Jan 1, 1946

By H. M. Dess, S. R. Bolin

A modifiedl Czochralski technique has been utilized to grow single crystals of YVO, pure or doped with europium or neodymium, from 1 to 2 in. long and 4 to 1/2 in. in dianz. An oxyhydrog-en gas-fired furftace zuas used in this ulork, and melts were contained in iridium crucibles. Successful application of the Czochralski ~vzethod was found to depend upon atmosphere control to prevent crusting and to limit melt decomposition, the establishment of symmetrical thermal gradients in the melt to obtain stable growth, and the selection of high-quality single-crystal seeds to prevent propagation of misorientations during growth and subsequent catastrophic cracking. The suitability of YVO4 as a host for laser-active trivalent rare earth ions has long been recognized. However, the problems associated with the growth of sufficiently large, good-quality single crystals have, until quite recently, seriously hindered satisfactory evaluation of the laser potentialities of this material. Both flux growth and Czochralski growth techniques were investigated at an early stage of interest in YVO,. The former method proved incapable of yielding crystals large enough for practical use,ly2 and the latter was beset with difficulties which took some considerable time to understand and overcome. Recently, however, the Czochralski growth process for YVO, has been improved along separate but similar lines of development by groups working independently in the Crystal Products Department of Union Carbide's Electronics Division and Bell Telephone Laboratories3 so that now good-quality single crystals of satisfactory size can be produced on a routine basis. Stimulated emission from a neodymium-doped YVO4 crystal grown by the Crystal Products Department of Union Carbide was obtained by O'connor4 of MIT, Lincoln Labs. An oxyhydrogen gas-fired furnace was used in this work, Fig. 1, and melts were contained in iridium crucibles. The starting material was 99.9 to 99.99 pct pure YVO4 powder purchased from the Chemical and Metallurgical Division of the Sylvania Electric Products Co. Typical impurity levels, determined by spectrographic analyses, were as follows: Si, 50 to 500 ppm Al, Fe, Mg, 5 to 50 ppm Ni, Pb, Mo, Mn, Ce, Cs, 1 to 10 ppm Initially, YV04 powders predoped with neodymium or europium were obtained from Sylvania. Later, however, because of a desire to grow a series of crystals containing relatively broad concentration ranges of these dopants, it proved more convenient to start with pure YV04 and mechanically admix Nd2O3 or Eu@~ powders plus equimolar amounts of V2O5. The empty crucibles were preheated to 1900" to 1950oC, a temperature range where melting occurred readily. The powdered YVO4 feedstock was then added incrementally. However, a marked tendency toward

Jan 1, 1968

By Frank J. Anderson

IN the cement region of the Lehigh Valley, a difference of 2 to 3 pct in CaCO3 can make or break a new quarry development, and experience of the Dragon Cement Co. has shown that values of calcium carbonate, as reported from churn drill samples, have been increased as much as 6 pct on the average when the same area was diamond drilled. This calcium carbonate increase consequently lowered the values for silica, iron, and alumina, and made these sections much more attractive. Since 1950, the Dragon Cement Co. Inc. has been engaged in extensive diamond drilling in the local limestone of the Northampton, Pa., region, known as the Jacksonburg formation, and in the Lebanon, Pa., region in the Annville limestone, both of Ordovician age.

Jan 12, 1954

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By J. S. Marsh

AN incomplete statistical analysis performed wearily on the morning after Thursday, Feb. 12, indicates that the unavoidable items of conversation among steelmen were the current shortage of sleeping time and the "Normandie." No analysis is needed, however, to be certain that many thousands of valuable words were uttered, both in and out of technical sessions, concerning matters of deep interest to members of the Iron and Steel Division. The opening session consisted mostly of papers that have appeared, or will appear shortly, in Metals Technology. One, however, that was not finished in time to be printed in any form, but that aroused great interest, was by E. L. Ramsey and L. G. Graper (Wisconsin Steel Works). Its subject was the production of high-sulphur steel by treatment with sulphur dioxide derived from anhydrous sodium sulphite or bisulphite added to the ladle or to the mold. The sulphide distribution in the finished steel is such that increased machinability and longer tool life result. Both items are of obvious importance in these days of mighty production.

Jan 1, 1942

By Edward H. Robie

PONCA CITY proved an ideal selection as a place of meeting for the Petroleum Division this fall. The accommodations at the Conoco Club were just what was required for such a gathering; the committee having the arrangements in charge functioned with the efficiency of veterans and the enthusiasm of neophytes; and the members and guests followed the speakers with close attention, entered the subsequent discussions with gusto, and divulged the "low-down" at private conferences. No one minded the drizzling rain on the first day, which only served to keep up the attendance in the auditorium; the weather then cleared up in time for a group picture before the gathering went their separate ways.

Jan 1, 1932

ALTHOUGH I have told you before (in the chapter on making the main mould for guns) how to support the core, I wish to repeat it here briefly and in a more orderly fashion, so that you may understand it better. For it is a thing of great importance to the profit of the owner as well as to the honor of the master, because he who does not locate the core in the middle makes the gun weak and incapable of shooting straight, and shows great lack of skill as a master. In short, it is very necessary to do this well. The first of these methods that I described to you is an iron, one dito wide, made into a ring which has four arms in a cross, or sometimes three. This is put in the mould where [88v] the last cornice begins, one palmo or half a braccio from the foot. Secure it in the middle of the diameter,

Jan 1, 1942

By A. H. Smallbone, R. Lathe

Considerable efforts have been expended to apply multiple regression techniques to quantitative determinations in x-ray fluorescence analysis. Multiple regression has been shown to be an effective method for correlating x-ray fluorescence intensities to elemental concentrations. Although many other techniques have been devised to solve the problem of matrix effects in x-ray fluorescence analysis, there are few as efficient in terms of storage requirement or ease of programming for digital computers as the multiple regression method. In the case of ore slurry, it has the additional advantage of allowing a unified approach to the problems of slurry density correction and matrix effect corrections. The data used in the present work were obtained with an on-stream x-ray analyzer capable of analyzing 15 slurry streams for as many as nine elements simultaneously. One of its fixed monochromators was set to accept scattered radiation at a discretely selected wavelength as a means of monitoring the slurry's pulp density. The data were reduced to obtain the correlation equations and a computer program combining slurry density with matrix corrections was written in FORTRAN IV to calculate concentrations.

Jan 8, 1969

By R. I. Jaffee, F. C. Holden, H. R. Ogden

ECENT papers dealing with the properties of unalloyed iodide titanium have been directed primarily at the determination of base-line properties for alloy investigations. Early work was limited to a few tests because of the limited availability of iodide titanium at the time. In the results of papers by Campbell et al.,1 Gonser and Litton,2 Jaffee and Campbell,3 inlay and Snyder,4 and Jaffee, Ogden, and Maykuth, data on mechanical properties are presented for unalloyed iodide titanium in the annealed and cold-worked conditions. Data are presented in this paper which show the effects of heat treatment on the structure and mechanical properties of commercially produced iodide titanium. Correlation is made between microstruc-tural variables and the mechanical properties. Experimental Procedures Melting Stock: The melting stock used was as-deposited iodide titanium, produced by New Jersey Zinc Co. The furnished analysis showed the following range of impurities: N, 0.004 to 0.008 pct; Mn, 0.005 to 0.013; Fe, 0.0035 to 0.025; Al, 0.013 to 0.015; Mo, 0.0015; Pb, 0.0045 to 0.0065; Cu, 0.0015 to 0.002; Sn, 0.001 to 0.01; Mg, 0.0015 to 0.002; and Ni, 0.003. Hydrogen content as determined by vacuum-fusion analysis was 0.0091 wt pct (0.44 atomic pct) after arc melting and fabrication. Nitrogen analysis on the arc-melted and fabricated titanium showed a content of less than 0.002 pct N. The average hardness of the furnished stock was Rf 70, or approximately 85 VHN. Melting Procedure: The as-deposited rods were rolled, sheared, and degreased in preparation for arc melting. The charge was arc-melted with a tungsten electrode in a water-cooled copper crucible under a positive pressure of high purity (99.96 pct) argon. The final ingot was approximately 2 in. in diameter and showed no increase in hardness over that of the initial stock. Fabrication: Heating for fabrication was done in air. It was begun by forging the ingot into a 3/4 in. diam rod, at an initial temperature of 1600°F. Scale was removed by sandblasting. The rod was then swaged to 1/4 in. diam at room temperature through a series of 20 dies, with approximately 10 pct reduction in area between each die. An anneal of 1 hr at 850 °C in air was given after the 1/2 in. die, such that the final cold reduction was 75 pct. Sections cut from this rod were used for test and microstructure specimens. Heat Treatment: Heat treatments were carried out in resistance tube furnaces with stainless-steel linings, under an atmosphere of gettered argon. As further protection against contamination, the specimens were packed in titanium turnings in a titanium sleeve. Control experiments have shown negligible hardness increases with this method, indicating that contamination from oxygen and nitrogen is slight. Three cooling rates were employed in this work; these have been designated as water quenching, argon cooling (to simulate air cooling under a controlled atmosphere), and furnace cooling. The cooling rate for an argon cool is 100°C per min for the first minute, with an average cooling rate of 35°C per min over a 15-min period. A furnace cool requires about 10 hr, with an average cooling rate of 3.6oC per min during the first hour, and an average cooling rate of 1.2°C per min over the 10-hr period. Microimpact Test: The specimen adopted was based on the cylindrical Izod Type Y specimen (ASTM, E23-41T). All dimensions were reduced to half scale, including the notch radius. Specifications are shown in Fig. 1. The specimen is held vertically in an adapter and broken as a cantilever beam. Impact tests were run on a constant-velocity (11.34 ft per sec) Tinius Olsen impact testing machine with a total available energy of 100 in.-lb. Tests were made to determine the correlation between this microimpact and the standard V-notch Charpy impact test. Curves showing impact energy as a function of temperature for both impact tests are plotted in Fig. 2. Transition temperatures, when they occur, are about the same for both impact tests. All three titanium-rich materials have the same conversion factor, 10. Tensile Testing: Tensile tests were conducted on Baldwin-Southwark testing machines using the 600, 2400, or 3000 1b range. Specifications for the test specimen were taken from the 1948 edition of the ASM Metals Handbook, and are shown in Fig. 1. Strain measurements were made using an SR-4 resistance gage (Type A-7) cemented to the reduced section in conjunction with a lever-type extenso-meter. Readings on the SR-4 strain indicator were

Jan 1, 1954

By N. G. W., Cook

When an excavation is made underground the original rock stresses are removed from the surfaces of the excavation. These surfaces converge to partially close the excavation and the superincumbent rock mass moves down towards the excavation. If the convergence of the surfaces of the excavation were controlled, energy generated by their motion against the controlling forces could be extracted. Since the total forces in the rock mass are not significantly affected by the excavation, stress concentrations arise around the excavation, which compensate exactly for those stresses no longer transmitted through the excavation. These phenomena give rise to two general principles which provide the basis for analyzing the effects of making any underground excavation. The first of these is that the total force resulting from the stresses across any plane in the rock, including any plane through the excavation, must be the same before and after the excavation is made. The second of these is that energy must necessarily be released as a result of making an underground excavation.

Jan 1, 1969

By J. R. Wylie, L. C. Huntley

Drilling for oil in the eastern producing states was fairly active during the first part of 1931, although less so than in 1930. With low prices development declined during the year, until the low prices of the summer resulted in an almost complete shut-down of drilling. This coincided with the action of the Conservation Board of the Pennsylvania Crude Oil Producers Assn, in limiting pipe line runs to 50 per cent of the 1930 normal for the Bradford district and upper country, and to 70 per cent for the balance of the region. Not only was new drilling halted but in many cases oil-producing properties were shut in. In November crude prices were partly restored, and all oil offered was being taken except in the Bradford district which was restricted to 80 per cent of the 1930 normal. During the latter part of the year drilling was being resumed on a moderate scale, and new production indicated a resumption of the proration order. The interest in gas development which has been under way for several years, maintained its supremacy over the search for oil in 1931. New reserves of importance were developed during the year in the Western Kentucky Coal Basin, in the Eastern Kentucky shale gas territory, in Stark County, Ohio, as well as the Oriskany sand development in northern Pennsylvania and central New York. A gas line was completed to the Eastern Seaboard serving Washington and Baltimore, and other lines were under construction designed to serve portions of the territory not hitherto supplied with natural gas. The low price of fuel oil at seaboard is understood to be the deterrent factor against further extension of natural gas lines to these markets at present. The development of these new reserves, as well as those developed by intensive drilling in old areas, resulted in the building up of large potential gas production and a lowering of rates paid to the producer. This, coupled with the country-wide tendency to lower the consumer rates of all public utilities, resulted in a general threat to reopen rate cases before various state commissions. Oil Development The past year was marked only by the almost complete shut-down of new development, reaching its low point during the summer, with its

Jan 1, 1932

By AIME AIME

THE second session on geophysical prospecting at the February meeting of the Institute was a discussion of the mining law and the bearing of the new method of search on location of claims and assessment work thereon. Allen H. Rogers was chairman of the meeting, which he opened by reviewing the present law and the proposed changes. W. R. Ingalls commented (by letter) on the Arentz bill, as introduced into the House of Representatives in 1921 and the need for revision of the present mining law. L. W. Douglas explained (by letter) the bill that he introduced and which has been passed by the House. SAMUEL S. ARENTZ, Nevada: It is my opinion that if the American Institute of Mining and Metallurgical Engineers is to sell this proposition to the people in the West, they have to sell it to the lawyers, because, after all, they are heard loudly when it comes to speaking in Congress. One man tells the other, "This thing is a vicious piece of legislation"; it might not be, but they will pass it on if it affects them. If the Institute would impress on the people affected that we need a re-codification of the mining law and that such is necessary along certain lines; that things have changed during the past decade or two, so today instead of doing our prospecting alone through the sinking of a shaft, through a discovery that may be seen, we are now moving on to more modern means of discovery through geophysics, through the churn-drill, through geology, through geological inference, I think we could get somewhere.

Jan 1, 1929

By P. H. Dudley

A quarter of a century of service of steel rails on our oldest railroads, many of which have changed their standard sections three or four times, has furnished, and is furnishing, excellent opportunities to study their wear and behavior in the track. Such experience is valuable for the design of new sections, now required to meet the constantly increasing severity of railroad service. Before presenting the new sections for consideration, I will briefly call attention to some features of past experience. For convenience of study, rails may be separated according to their weight and height into four groups, viz.: 1. Hails weighing per yard from 52 to 60 pounds, and 34 to 4 inches high. 2. " " " " " 60 " 72 " " 46 to 44 " " 3. " " " " " 72 " 90 ' 41/8 to 5 4. " " " " " 85 or more " " over 5 " I Experience in this country is confined mainly to sections in groups Nos. 1, 2 and 3. • During the past few years I have had the opportunity to run my car over many thousands of miles of railway laid with the principal sections in use, and to obtain diagrams showing their deflections, permanent set, and, in a great measure, their manner of wear. The First Group.—The first steel rails imported, and those manufactured here, were light sections—included in the first group—and many of them, being rolled in rolls used for rolling iron sections, have pear-shaped heads, 2 3/8 to 2 1/2 inches wide, the base being heavy and from 1/4 to 1/2 inch narrower than the height. These rails were laid upon ties of solid timber, at least 8 inches face, spaced 2 feet from center to center. The moments of inertia of these rails were low, only ranging from 8 for the lightest sections to 12 for the heaviest. The deflections were, of course, great; but the quality of the metal was excellent. It was physically hard and

Jan 1, 1890