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By W. R. Ingalls

Jan 1, 1922

By W. R. Ingalls

Jan 1, 1922

By Roland Kammel, Takeo Oki

A suspension electrolysis method has been developed which enabled a direct anodic extraction of zinc from zinc sulfide concentrate and simultaneously oxidized sulfide sulfur to elemental sulfur. The investigation was performed in a laboratory-scale electrolytic cell, where the zinc sulfide concentrate particles (chemical composition in weight percent: 61.1% Zn, 2.3% Fe, 30.6% S, 3.4% SiO2 were suspended with or without graphite powder in a dilute sulfuric acid electrolyte. The main parts of the cylindrical electrolytic cell are shown in [Fig. 1]. The cathode (1), a rod of aluminum, is set at the center of the cell. The anode (2), which consists of four plates, is mounted on the inner face of the cell wall. Both PbO2(Pb) and graphite anodes were used. The cathode compartment (3) is separated from

Jan 1, 1976

By H. M. Roche

MAGNETITE mining and milling in the Eastern States in 1939 showed considerable improvement over 1938. For the first eight months of the year production of magnetite proceeded at a normal rate but operations were stepped up in the last four months owing to increased domestic demand. In New York, the Republic Steel Corp. operated the Witherbee-Sherman mines at Mineville throughout the year. Chateaugay Ore and Iron Co. operated their low-phosphorus mine at Lyon Mountain for the first seven months, but on Aug. 1, Republic Steel took over this mine -and have since operated it. In Pennsylvania, the Bethlehem Steel Co, operated the Cornwall mine continuously. In New Jersey, Mt. Hops and Scrub Oak were in operation all year. The Washington mine went into production on Nov. 1 and the Richard mine on Dec. 1.

Jan 1, 1940

By Edwin H. Olson, Morton Smutz, Charles J. Baroch

IN 1949 an orebody containing some 10 billion lb of recoverable rare earth metals was discovered in the Mountain Pass district of San Bernardino County, California.1 The following year Molybdenum Corp. of America purchased a number of claims at the deposit and a mill on the property which had been constructed to process the district's gold ores. Average composition of ore from the San Bernardino deposit is less than 0.1 pct ThO2, 25 to 35 pet calcite, 10 pet rare earth oxides, 15 to 20 pet silica, and 30 to 40 pet barite.2 Rare earth content of the ore analyzes 50.7 pet CeO2, 4.2 pet Pr6O11, 11.7 pet Nd2O3, 1.3 pet Sm2O3, and 34.3 pet La2O3, and others.2

Jan 3, 1959

By S. G. Proctor, D. L. Baaso, W. V. Conner

A double crucible system was developed for I-g scale plutonium reductions. The equipment consists of an inner MgO crucible, an outer MgO crucible, and a stainless steel pressure vessel. The reduction charge is PIaced in the inner crucible and the annulus between the inner and outer crucibles is filled with a mixture of calcium and iodine. The exothermic reaction between the calcium and iodine in the annulus supplies the heat required for complete reaction of the reduction charge ana' good metal coalescence. Metal yields of 80 to 85 ,pct were obtained from I-g scale reductions and yields as high as 97.5 pct were obtained from 0.5-g scale reductions. The system was used to reduce charges containing as little as 0.1 g of Pu resulting in metal yields up to 90 Pct. THIN metal foils of highly enriched plutonium isotopes are used as targets for cross section and other measurements. The isotopes are separated in the calutrons at Oak Ridge and are very expensive to prepare. Often, only 1 or 2 g of material are available thereby emphasizing the need for a method of preparing these small quantities of metal. Procedures for 1-g scale plutonium reductions have been described, but these procedures require elaborate or expensive equipment. For example, the procedure described by Anselin et al.1 requires an inert atmosphere glovebox and induction heating equipment. The procedure described by Baker2 also uses induction heating equipment to obtain the recommended heating rates and liner temperatures. Baker's procedure also requires high purity PuF4 with very little PuO2 present. The procedure described in this paper resulted from a search for a simple and inexpensive method for making 1-g scale plutonium reductions. EXPERIMENTAL Equipment. The equipment required for the double crucible system consists of a pressure vessel, two MgO crucibles, a MgO crucible lid, and a resistance-heated, vertical crucible furnace. The crucibles were slip cast from high purity MgO and were supplied by the Coors Porcelain Co. and the Norton Co. The pressure vessel and lid were fabricated from 316 stainless steel. Materials. The PuF4 used for this study was obtained from the P1utoniu:m Metal Production Department at Rocky Flats. The PuF4 was prepared in a con- tinuous hydrofluorinator by reacting Pu02 with HF at 650°C. The isotopic composition of the plutonium was approximately 93 pct 239PU, 6 pct 240PU, and 0.5 pct 241PU. Some of this PuF, contained less than 1 pct Pu02 (Batch No. 6 and 7), while other batches contained up to 15 pct Pu02 (Batch No. 3). The chemical analyses of all the PuF4 used for this study is given in Table I. The calcium was 99 pct pure, AEC grade, and only that fraction which would pass through a 20 mesh screen was used. The I2 was USP grade re-sublimed I2 which was ground before being used. Procedure. Various charge compositions and methods for loading the double crucible system were tested. The optimum conditions for 1-g scale reductions are described below. The double crucible system was loaded as shown in Fig. 1. The outer crucible was placed in the pressure vessel and the annulus between them was filled with MgO sand. The inner crucible was placed in the outer crucible, supported by a layer of MgO sand in the bottom of the outer crucible. A mixture of 5.2 g of Ca and 25 g of I2 was placed in the annulas between the two crucibles. The upper portion of the annulas was filled with MgO sand. Next, a layer of a mixture of calcium and I, equal to 20 wt pct of the calcium and I2 used in the main charge was placed in the bottom of the inner crucible. The PuF, to be reduced was mixed with a 30 pct excess of calcium and 1 mole of I2 per mole of Pu and this mixture was placed in the inner crucible. The charge was topped with a layer of a mixture of calcium and I2 equal to 20 wt pct of the calcium and I2 used in the main charge. The pressure vessel was sealed with a flat copper gasket and was purged by alternately evacuating and filling with argon. The purge valve was closed and the vessel was placed in a vertical crucible furnace which was preheated to 950°C. The furnace was turned off after 20 min of heating and the vessel allowed to cool. Experience has shown that. this amount of heating is sufficient to assure complete reaction of the charge. RESULTS AND DISCUSSION The double crucible system has been used to produce plutonium metal on a 0.1- to 1-g scale. Reduction

Jan 1, 1970

By J. D. Mooney, D. L. Darnell

The accompanying chart has been drawn for the convenicncc of engineers as' a means of quickly determining the correct number of plies of conveyor belts operating under specific conditions. The calculations are based on the average safe strength (factor of safety, 15) of the various standard rubber conveyor belts. The calculations assume maximum loading conditions; that is, the belt is considered as carrying the greatest load that it will handle without spillage at ordinary belt speeds. This not only produces the most economical operating conditions, but also the maximum tension in the belt. The chart is a graphical representation of the formula: Where, p = kg W(L + 10H) p = the correct number of plies k = a constant, depending on the type of drive g = the weight 'in pounds per cubic foot of material handled W = the width of the belt in inches L = the length of the belt in feet (approximately twice the center distance). H = the difference in elevation between the head and tail pulleys, in feet. For a simple drive, with a bare pulley, k = ----1 For a simple drive, with a rubber-lagged pulley, k = --- 1 For a, tandem drivej with bare pulleys, k = 1/375.000 For a tandem drive, with rubber-lagged pulleys, k = ---1 The chart is drawn for a simple drive, with a bare pulley (k — =e)1 ; therefore, the number of plies obtained from the chart should be multi- ' plied by the factor 0.83 or 5/6 for simple, lagged drive; the factor 0.67 or 2/3 for tandem, bare; and the factor 0.55 or 11/20, for tandem, lagged. The formula p = kgW(L + 10H) has been developed mathematically

Jan 1, 1916

By H. S. Fleming

My original intention was to give a full account of Southern furnaces, ores and cokes; but, owing to the difficulty of getting reliable information, I confine this paper to a general description of the ores used in, and immediately around, Chattanooga. Mr. L. S. Colyar, Manager of the Rising Fawn furnace, wrote me in answer to an inquiry as to what ores they were using, " Below I give you analyses of the mixture of ore we have been using for the past seven or eight years. We haven't a complete analysis of any ores, but I will give them to you as I have them. Attalla Soft Rising Fawn Hard Rising Fawn Red Ore. Red Ore. Soft Ore. Iron,.... 50.60 38.48 46.82 Silica,. .. 11.69 7.32 22.69 Phosphorus,. .. 1.06 .319 .350 This is a fair average of all the ores we get in this section." The following analyses of Birmingham soft ore were received from the Morris Mining Co., of that place. No. 1. NO. 2. No. 3. No. 4. Iron.....51.60 54.88 51.04 51.20 Silica,. .. 19.32 10.60 17.32 17.08 Alumina,....19 .88 1.18 Phosphorus,. ..129 .287 .116 .464 Mine No. 1, second vein, shows: iron, 46.40; alumina, 4.92; phosphorus,.212; silica, 19.60. Mine No. 1, by analyses obtained from the Mary Pratt Furnace CO., shows: Iron. Silica. Fine red ore,.49.00 18.38 Lump red ore,...54.42 17.10 Bottom vein,.50.00 21.38 Bottom vein,.41.24 13.52 A lot of this ore delivered in Chattanooga gave : iron, 53.32; alumina, 2.10; phosphorus,.529; silica, 18.03.

Jan 1, 1887

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By F. C. Langenberg, J. Chipman

New data on the distribution of silicon between slag and carbon-saturated iron at 1600oand 1700oC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1700°C for slags containing up to 20 pct Al2O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A1203-SiO2 slags over a range from zero pct A12O3 to saturation with A12O3, or CaO.2A12O3. The upper limit of SiO, is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently, 4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/A12O3 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al2O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al2O3 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al,O3 and of A120,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO, (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2 The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960

By A. M. Gaudin

THIS paper presents, with the help of colored photomicrographs, the new method of mineral identification termed "selective iridescent filming." This method pertains to the field of determinative mineralogy, which it provides with tools for: (1) phase identification, (2) solid solution analysis. The method should be particularly useful in the applied fields of: (1) paragenesis of ore deposits, (2) mineral dressing, (3) mineral synthesis and study of phase equilibria.

Jan 1, 1938

By A. M. Gaudin

THIS paper presents, with the help of colored photomicrographs, the new method of mineral identification termed "selective iridescent filming." This method pertains to the field of determinative mineralogy, which it provides with tools for: (1) phase identification, (2) solid solution analysis. The method should be particularly useful in the applied fields of: (1) paragenesis of ore deposits, (2) mineral dressing, (3) mineral synthesis and study of phase equilibria.

Jan 1, 1938

By J. Gordon Parr, M. J. Bibby

In addition to the (bcc) - (cph) transformation at 882°C a second distinct change of slope has been observed on a titanium cooling curve between 905" and 960°C.1,4 Duwez,1 commenting on work by McQuillan,2-4 attributed this arrest to contamination of the specimen with oxygen—a possibility that existed even at the reduced pressure of 10-5 mm Hg at which the experiments were conducted.

Jan 1, 1963

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 T. M. Gurr

The United States is the world's leading producer of phosphate rock. In 1975 according to the US Bureau of Mines' statistics, 44.3 million tonnes (48.8 million st) of phosphate rock were produced in the United States, 1 which is 40.6% of the world's production.2 The major phosphate producing areas of the United States are located in Fig. 1 and the production for 1975 is listed as follows:

Jan 6, 1979

[Trans. No. Place Date Vol. Page 1. Wilkes-Barre, Pa May, '71.. 1 3 2. Bethlehem, I's Aug., '71.. 110 3. Troy, N. Y Nov., '71.. 113 4. Philadelphia, PaFeb., '72.. 117 5. New York, N. YMay, '72120 6. Pittsburgh, Pa Oct., '72.. 125 7. Boston, MassFeb., '73.. 128 8. Philadelphia, Pa.*May, '73.. 23 9. Easton, PaOct., '73.. 27 10. New York, N. Y Feb., '74211] [ ]

Jan 1, 1925

By C. C. Harris

The 3-parameter equation* was introduced1 as having the necessary form and flexibility for describing the major features of size distribution curves. Also, Eq. 1 was shown to contain most of the widely used 2-parameter equations as special cases. Special methods are necessary in order to determine the parameters of 3-parameter equations by graphical means. The procedure given previously required double graphical interpolation followed by regraphing the interpolated data. The theoretical basis of the method was a difference equation eliminating y. Several other methods for obtaining the parameters have been under development and one method appears to overcome the disadvantages of the earlier method and satisfies several procedural requirements. The points in favor of the new method as compared to the earlier method are as follows: 1. Estimation of the quality of fit is direct, and is in fact an essential part of the procedure. 2. The data is plotted directly without the necessity of interpolation from a graph. 3. The method makes use of Rosin-Rammler2 paper which because of expanded scaling in the coarse sizes leads to improved accuracy1 as compared with the log-log plot for the Gates3-Gaudin4-Schubann5 representation. 4. There is a gain over the earlier method in overall accuracy and in simplicity.

Jan 1, 1970

By L. Adler

The author recently proposed a technique for handling the effect of planes of weakness on failure in geologic material.1 The technique employed an "extended" Mohr's rupture envelope, on which was superimposed a generalized three dimensional stress representation. Subsequently, the method was applied to so-called two-dimensional stress states" which were in reality degenerate three-dimensional ones. Since a two-dimensional stress solution usually refers to a plane stress condition, the terminology was confusing. The distinction between a plane stress state and a degenerate three-dimensional one is shown in Fig. 1. The solution of problems involving a generalized three-dimensional stress state is greatly aided by continual reference to the basic principle that no stress components can act on a plane, oriented as is the weakness plane, which lies outside of the weakness plane's rupture enVelope.2 This is shown in Fig. 2; and if it is also remembered that the radii of the Mohr's Circles give the orientation of such a plane, solutions are easier to follow, and perform. Sample Problem 1: Site Location (generalized three-dimensional case).' Given: 1) Both rupture envelope for the solid and plane of weakness. 2) Existing principal stresses and orientations in space (?12, ?13) obtained from a stress analysis of the proposed structure. Find: Permissible orientations of the weakness plane in order to select a suitable site.

Jan 1, 1963