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By W. Philippoff

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

Jan 1, 1953

By W. Philippoff

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

Jan 1, 1953

By Robert Stefanko

Roof bolting in coal mines has progressed very rapidly in the last decade, and today this method of support is in general use. There are many theories concerning the functions of roof bolts, but the importance of beam building is indisputable. Proper tension in the bolts minimizes shearing along bedding planes and creates a thick, competent beam from individually weak layers. Bolting must be accomplished immediately upon exposure of the roof, and bolt tension must be maintained if roof failure is to be prevented. Seams are being mined today with roof bolt support where conventional timbering was not effective1. The widespread use of continuous mining equipment was made possible by roof bolts which permit long supported spans free of obstructions.2 Since adequate anchorage is the key to successful bolting, better methods for determining the efficiency of anchorage are continually being sought. Attempts have been made to measure bolt loads, thus assessing anchorage efficiency by employing sensing devices between the bolt head and roof. 3,4,5 None of the techniques appears to be very accurate, and all have at least one serious deficiency.

Jan 5, 1962

By J. J. Scott

INTRODUCTION Rock mechanics theory needs to be applied to solve ground control problems, but in the final analysis the mining method and equipment which is used will be those which solve problems in a practical manner. Equipment and its inherent productivity and safety as supplied as "off the shelf" items by manufacturers often dictate the size of mine openings. Operators may tolerate falls of ground and associated hazards if productivity and safety problems are not too severe. In this whole process the costs of mining finally dictates just what system will be employed and what equipment will be used. True solutions to ground control problems sometimes require that the mine operator step back and totally rethink his problems. The true cost of accidents are often missed and hidden in overhead costs. Losses in production and accompanying profit are not fully considered, false economics, such as using inappropriate roof support devices, are undertaken at times when using the most expensive devices to totally eliminate accidents may be the best overall solution. Automation to remove the worker from the hazard area is often over- looked as the initial capitol expense to apply it may be high. Cooperation between mine engineers, mine operators, safety personnel, equipment suppliers, and government inspectors, both state and federal, is required to reach workable solutions that best meet the goals of all parties.

Jan 1, 1983

By E. C. W. Perryman

On electropolishing, high-purity Cu-Sn and Cu-Sn-P alloys with more than 5 to 9 pct Sn were found to contain many grain boundaries with a ridge-and-furrow profile. The effect was not eliminated by solution treatment and was present at the new boundaries in recrystallized material. It could be produced by diffusing tin into the 3 pct Sn alloy and it is concluded that the effect is due to enrichment of certain boundaries in tin, or possibly in an impurity present in the tin, in solid solution. IN the hot working of tin bronzes, especially those with moderately high tin contents, considerable difficulty is frequently encountered from intercrystal-line weakness, which results in cracking at the edges in sheet on strip rolling and in the unsupported regions of the rod in rod rolling.' These difficulties are not at all pronounced with up to 3 pct Sn, but at 5 pct Sn impose serious limitations and at higher tin contents, especially if the phosphorus content is also high, they may become very severe. In some work carried out at the laboratories of The British Non-Ferrous Metals Research Association it was found that a notable lack of ductility in tension at elevated temperatures, associated with intercrystal-line failure, was characteristic of tin bronzes even of relatively high purity. That the intercrystalline fracture is not due to a brittle or molten impurity phase at the grain boundaries was shown by the fact that the temperature at which intercrystalline fracture first occurred decreased with decrease of rate of straining. Tensile tests on some commercial tin bronzes, reported by Goetzel,² show a similar fall in ductility with increasing temperature. As no visual evidence had been obtained showing that the grain boundaries of the tin bronzes were different from those in copper, a more detailed microscopical examination was carried out, and the results of this are given in the present report. Several workers"' have observed that electrolytic polishing is a powerful tool for detecting small amounts of a second phase and in particular for detecting high solute concentrations, "equilibrium segregation," at grain boundaries. Since it had been found that the suggested solutions for electropolishing bronze and the standard solutions for brass and copper did not give satisfactory results it was first necessary to find a suitable electropolishing solution.' Experimental Procedure Materials Used: The cast and wrought materials used for this work were the same as those used for the mechanical tests referred to above. They comprised 3, 6, and 9 pct Sn alloys without phosphorus and the same three basic alloys with 0.03 and 0.4 pct P. A 5 pct Sn alloy without phosphorus, of similar purity, was also examined. The basis materials were Chempur tin, high purity 15 pct phosphor-copper and cathode copper, and spectrographic analyses are given in Table I. Treatment: The cathode copper was first melted under charcoal, degassed by plunging marble chips beneath the surface, and cast through a coal gas flame into sand molds to produce a number of small ingots which after machining were of a suitable size for subsequent vacuum melting. Chill cast bars of the alloys, approximately 1¼ in. in diameter, were then made by melting and casting in vacuo, the tern-

Jan 1, 1954

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979

By Arthur F. Colombo

The selective flocculation, desliming and flotation process developed by the U.S. Department of the Interior, Bureau of Mines, as part of its goal of maintaining an adequate supply of minerals to meet national economic and strategic needs is described. The application of the selective flocculation and cationic flotation process to three oxidized taconites from the western Mesabi Range in Minnesota is discussed. Data from the operation of a 408-kilogram-per-hour (900 lb/hr) pilot plant employing reclaimed water are summarized for the three types of oxidized taconites.

Jan 1, 1980

By R. C. Ku, A. J. McEvily, T. L. Johnson

AS reported in a recent paper,' we attempted to measure the response to stress of as-quenched Fe-Ni-C martensites (Ms of -35°C) in both the micro-and macrostrain regions. To avoid effects associated with the diffusion of carbon, tensile specimens were quenched from room temperature at 78°K and tested after 15 min in situ. It was assumed that the transformation had terminated and that the retained austenite was essentially stable. In the tensile tests microplastic strains of the order of 10"* were measured at stresses below 20 ksi. It was concluded that the observed strains were due to the motion of dislocations in the martensite, the dislocations having been introduced during transformation. It was argued that transformation or plastic deformation of the retained austenite did not contribute to the non-elastic deformation measured in the microstrain region. In contradiction to the above argument, Magee and paxton2 have more recently shown that the strain due to isothermal transformation of retained austenite to martensite can contribute to plastic deformation at low stresses even at 78°K. Moreover we were unaware (nost)-a culpa) of a paper by Machlin and cohen3 in which it was clearly shown by resistance measurements that isothermal transformation at 78°K leads to the formation of an additional 1 pct or so of martensite after the initial athermal transformation, even in the absence of external stress. We have verified Machlin and Cohen's results in the following manner. A capacitance microstrain gage was placed on a tensile specimen before immersion in liquid nitrogen. After 15 min at 78°K detectable burst phenomena had ceased and it was then possible to obtain a continuous record of the additional extensional strain due to spontaneous isotherma1 transformation. The results for the Fe-Ni-C series studied are shown in Fig. 1, and are similar to those of Machlin and Cohen who investigated a low-

Jan 1, 1968

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967

By E. C. Wright

The bessemer process is nearly one hundred years old. William Kelly, the American inventor, was able to demonstrate that he had accomplished the pneumatic purification of molten pig iron as early as 1847; Henry Bessemer's English patent was granted in 1855. The application of this steelmaking process since then and the present position of bessemer steel are concisely discussed on pages 355 and 356 of the fifth edition of "The Making, Shaping and Treating of Steel." The great expansion of the automotive, machine-tool, chemical and oil industries after I9I0 opened up a large market for special steels, whereas the output of steel before that time was mainly for structural purposes. The need for building more blastfurnace capacity complementary to bessemer operations, combined with the availability of the' necessary amounts of steel scrap, both contributed to the extension of open-hearth plants at the -exense of besskmer capacity. The ability of the open-hearth furnaces to consume virtually all types of raw materials as far as phosphorus content is concerned, and the need for selecting low-phosphorus ores of rapidly decreasing sources for the bessemer, also played a part in the reduction of bessemer steelmaking operations and the increase in basic open-hearth plants. As a consequence, the proportion of bessemer steel made, in this country decreased from 65.7 per cent of the total in 1900 to 37.1 per cent in 1910, and only 6.8 per cent of the total in 1937. The metallurgical concepts existent between 1910 and 1920 caused the writing of many specifications of very low phosphorus and sulphur content, which definitely barred bessemer steel from many commodities. Now sulphur is being added to many open-hearth and bessemer steels in amounts far exceeding the maximum sulphur content of good bessemer steel. Re-phosphorizing is also widely practiced for several specific applications. Even today, the chemical-analysis limits of many important steel specifications have an arbitrary and archaic tinge. The old standard "0.30 to 0.60 per cent manganese" might be mentioned in this connection as similar to the rigid requirements for maximum sulphur and phosphorus that were established at least 25 years ago. The literature is full of vague and complee discussions of the effects of nitrogen and oxygen where these elements existed in steel in amounts less than 0.02 per cent. Many failures have been attributed to these elements without reasonable proof on which to base the conclusion. Methods of determining oxygen in steel require such complicated equipment that only a few research laboratories have the required apparatus. Even so, the accuracy of oxygen determinations in steel has been only recently reproducible. Up to the present time, no one has succeeded in obtaining a sample of molten steel that accurately indicates the full oxygen content of the metal in the furnace or ladle because the molten sample

Jan 1, 1944

By E. C. Wright

The bessemer process is nearly one hundred years old. William Kelly, the American inventor, was able to demonstrate that he had accomplished the pneumatic purification of molten pig iron as early as 1847; Henry Bessemer's English patent was granted in 1855. The application of this steelmaking process since then and the present position of bessemer steel are concisely discussed on pages 355 and 356 of the fifth edition of "The Making, Shaping and Treating of Steel." The great expansion of the automotive, machine-tool, chemical and oil industries after I9I0 opened up a large market for special steels, whereas the output of steel before that time was mainly for structural purposes. The need for building more blastfurnace capacity complementary to bessemer operations, combined with the availability of the' necessary amounts of steel scrap, both contributed to the extension of open-hearth plants at the -exense of besskmer capacity. The ability of the open-hearth furnaces to consume virtually all types of raw materials as far as phosphorus content is concerned, and the need for selecting low-phosphorus ores of rapidly decreasing sources for the bessemer, also played a part in the reduction of bessemer steelmaking operations and the increase in basic open-hearth plants. As a consequence, the proportion of bessemer steel made, in this country decreased from 65.7 per cent of the total in 1900 to 37.1 per cent in 1910, and only 6.8 per cent of the total in 1937. The metallurgical concepts existent between 1910 and 1920 caused the writing of many specifications of very low phosphorus and sulphur content, which definitely barred bessemer steel from many commodities. Now sulphur is being added to many open-hearth and bessemer steels in amounts far exceeding the maximum sulphur content of good bessemer steel. Re-phosphorizing is also widely practiced for several specific applications. Even today, the chemical-analysis limits of many important steel specifications have an arbitrary and archaic tinge. The old standard "0.30 to 0.60 per cent manganese" might be mentioned in this connection as similar to the rigid requirements for maximum sulphur and phosphorus that were established at least 25 years ago. The literature is full of vague and complee discussions of the effects of nitrogen and oxygen where these elements existed in steel in amounts less than 0.02 per cent. Many failures have been attributed to these elements without reasonable proof on which to base the conclusion. Methods of determining oxygen in steel require such complicated equipment that only a few research laboratories have the required apparatus. Even so, the accuracy of oxygen determinations in steel has been only recently reproducible. Up to the present time, no one has succeeded in obtaining a sample of molten steel that accurately indicates the full oxygen content of the metal in the furnace or ladle because the molten sample

Jan 1, 1944

By C. A. Heiland

The Eötvös torsion balance permits the measurement of certain second derivatives of the gravity-potential, which are known as the gradients of gravity and the curvature values for an equipotential plane of gravity. These quantities are influenced on level ground by the configuration of the masses underneath. Hence, the torsion balance has gained great importance for the location of geological structures and thus indirectly for the discovery of oil and other mineral deposits. If the ground is not level, however, the measurements become more difficult, because the superficial mass-irregularities also produce more or less considerable disturbances. It is necessary, therefore, to determine the shape of the surrounding topography by leveling as well as by consulting topographic maps and to compute its influence upon the torsion balance. The correction thus determined is called, in general, the topographic correction; it is composed of two constituents, the terrain correction and the cartographic correction. The terrain correction would be that part of the topographic correction as derived from the direct leveling of the area surrounding the station, whereas the data for the computation of the cartographic correction are obtained from a topographic map, usually beginning with a radius of LOO meters, as under most circumstances it is difficult to level along a arger concentric circle about the station. Principle of Topographic Correction The principle of all topographic corrections is to assume a homogene-ous compositon of the masses around the station in regard to specific gravity as well as a mathematical shape of the topography. The results become the more accurate the closer this mathematical shape is to the actual configuration of the terrain, but naturally the amount of necessary computation also increases. If a standard correction with fixed dis-ances is adopted, the middle error of this method will, therefore, increase as the irregularity of the terrain. Hence, the application of the torsion balance in mountainous areas may be successful only if the disturbances due to heavy masses underneath the surface are so large as to exceed onsiderably the increased middle error due to rugged topography, or,

Jan 1, 1929

By Edward A. Capillon

The problem of scrap is probably of greater importance in the pro duction of gold, silver and other precious metal alloys than is the case for base metals and alloys. Remelting of gold and silver scrap in the shop is always a costly process because it involves losses by oxidation of thc base metals in the alloy with a consequent increase in the percentage of precious metal. This is most marked in the case of alloys containing the low-boiling and easily oxidized metals zinc and cadmium. Since it is not generally feasible to assay every shop remelt it follows that the possibilities of lost values arc large. So-called rolled gold and silver plate is made by soldering or welding the precious metal alloys onto base metal. Such plate when defective must be sent to the refinery to recover the gold and silver values, thereby involving additional expense in the form of refining charges. It is obvious therefore that gold and silver alloy scrap is an important item in manufacturing cost and must be reduced to a minimum. The amount of scrap resulting from poor metal will depend on a number of factors in the manufacturing operations, not least among which is the melting and casting practice. The notes which follow are a summary of experiments performed at various times to determine what variables in melting and casting are influential in the production of sound alloys. Metals Used in Alloying Pure gold, that is, gold of 24-kt. value is very much too soft for jewelry purposes and it is therefore always alloyed with other metals to increase its hardness and resistance to wear. For the same reason pure silver is seldom used alone but is alloyed with copper, the standard alloy being sterling silver which contains 92.5 per cent. silver and 7.5 per cent. copper. The metals commonly used for alloying gold are silver, coppcr, nickel and zinc. In addition to hardening the gold and producing alloys of different karat values the use of these metals makes possible the production of gold alloys of various colors such as yellow, red, green and white. The gold-silver-copper alloys vary in color from light greenish-white through green, yellow and red depending on the relative amounts of the three metals. Green or yellowish-green colored golds

Jan 1, 1930

By H. P. Moore, R. W. Fenn, Harold Margolin, W. R. Hibbard

DEFORMATION lines, also called etch markings or strain markings, are noneffaceable lines developed in individual grains by etching a metal specimen which has been cold worked sufficiently to cause atomic non-conformity or slight orientation differences within the grains. Etching occurs more rapidly at these lines of high chemical reactivity to produce a result similar to that revealing grain boundaries.1 Wider etching effects forming bands have been found. They are believed to be bands of deformation lines which form areas of measurably different orientation from the crystal matrix. The crystallite rotations causing these bands have been shown by Barrette to contribute to deformation textures. Although deformation lines have been observed in many metals, the amount of deformation required for their appearance has been established only in general terms. Mathewson and Phillips3 observed the first appearance of deformation lines in cold-rolled alpha brass at about 20 pct reduction in thickness using the standard ammonium hydroxide hydrogen peroxide etchant. Price and Davidson4 noted deformation lines in common high brass after 26.5 pct reduction by cold rolling using the same etchant. Johnson' observed dark thick forklike lines in 99.99 pct pure copper reduced 31.8 pct. Adcock6 observed deformation lines in 80-20 copper-nickel alloy rolled 50 pct. Samans7 found no deformation lines in alpha brass single crystals cold rolled 9.5 pct but they did appear after 25 pct reduction using ammonium hydroxide and hydrogen peroxide etchant. Barrett and Levenson8 observed deformation bands in drawn polycrystalline iron at very small reductions in area and noted that their initial appearance perhaps depends on grain size and other conditions. They reported deformation bands in a single crystal of iron reduced 6 pct by drawing. Brick9 noted that deformation lines in 70-30 brass apparently associated with {111} planes appeared after reductions of from 20-50 pct by cold rolling. Brick and Williamson10 noted that in single crystals of 70-30 alpha brass "as in polycrystalline brass, no deformation markings appeared until reductions exceeded 20 pct." Cook and Richards11 reported that in copper cold rolled less than about 50 pct few strain markings were apparent but for higher. reductions many strain markings appeared transverse to the rolled direction. In a review article Brick and Phillips12 noted that previous studies had not shown deformation lines in cold rolled alpha brass

Jan 1, 1948

By Philip W. Henry

There is a difference of opinion among engineers on the subject of depreciation in general, and still more on its application to any given case The committee which was appointed by the American Society of Civil Engineers to make a report on Valuation of Public Utilities, states "There is no subject connected with valuation about which there are more diverse views than those relating to depreciation;" and in the discussion which took place upon the presentation of the preliminary report of this committee in January, 1914, that part of the report dealing with depreciation called forth more discussion than any other. From this discussion it was evident that the word "depreciation" was not always used in the same sense, so it is quite important that some definition be adopted. As this paper relates to the proper method of treating depreciation by corporations or individuals operating oil properties, both of which must make a return of annual net income to the government in connection with the income tax, it will be in order to adopt the definition of the Internal Revenue Bureau. Under date of Mar. 29, 1910, the Commissioner of Internal Revenue of the Treasury Department stated "Deduction on account of depreciation of property must be based on lifetime of property, its cost, value and use." Again, on Form 1035, "Return of Annual Net Income" for miscellaneous corporations (Section 2, Act of Congress approved Oct. 3, 1913), a deduction from gross income is allowed for "Total amount of depreciation for the year." This item is defined more particularly as follows: "The amount claimed under Item No. 5 (b) for depreciation should be such an amount as measures the loss which the corporation actually sustains during the year in the value of buildings, machinery, and such other property as is subject to depreciation on account of wear and tear, exhaustion, or obsolescence. The amount taken credit for on this account in order to be allowable should be so entered on the books as to constitute a liability against the assets of the corporation. The amount claimed under this item should not cover losses in the value of stocks and bonds. Decrease in the book value of securities owned, so far as such decrease represents a decline in the actual value of such securities, should be deducted under item 5 (a) of the return. "Where depreciation of physical property is made good by renewals, replacements,

Jan 1, 1915

By Francis F. Lucas

A microscope objective of given numerical aperture, when used with light of given wave length, has some fixed limit of resolution. This may be expressed as potential resolving ability—the ability to resolve is inherent in the lens but whether this limit is achieved in practice is quite another matter. Nearly 50 years ago Abbe evolved theoretical considerations which indicated that the ability of a lens to resolve detail is directly proportional to twice the numerical aperture of the objective and inversely proportional to the wave length of the light used. It is true, unquestionably, that as the numerical aperture of the objective is increased the potential resolving ability of the lens is increased and likewise when the wave length of the light used is decreased, the degree of resolution is increased. Whether Abbe's formula expresses the exact relationship is not a matter of great concern. It suffices to know that to improve resolution, other things being equal, two avenues of approach are available. Either the numerical aperture of the objective may be increased or the wave length of the light decreased. With the apochromatic system it is possible to employ successfully wave lengths from 400 to 500 uu and still secure reasonably short exposures. The present limit for numerical aperture is 1.40 N. A. although objectives of 1.60 N. A. are now an experimental possibility for metallurgical work. Thus certain well defined limits are set for those who work within the range of the visible spectrum. In order to take advantage of the increase in resolving power which accompanies a decrease in the wave length of light employed, Dr. A. Kohler and Dr. M. Von Rohr of the Zeiss Scientific Staff developed the "monochromats." These are quartz objectives corrected for the single wave length 275 uu which lies in the ultra-violet region of the spectrum. They also developed a series of quartz oculars and a complete photo-micrographic equipment with which to use the quartz optics. Quartz must be used for the optical parts because glass absorbs ultra-violet light almost completely. Thus there was made available about 20 years

Jan 1, 1926

By J. W. Fuller

During the last 20 years, experimenters have sought to utilize pulverized coal in boiler plants, but refractory and slag troubles have usually overbalanced any gains in efficiency that were obtained. These troubles were caused largely by lack of knowledge of the proper methods of coal preparation and lack of a furnace design that would be adaptable to pulverized-coal firing. When this information was obtained the results were so much more satisfactory that within the last 5 years approximately 80,000 boiler hp. have been installed in plants ranging from 1000 to 20,000 boiler hp. rated capacity, which are operating at an average of 174 per cent. of rating. The first commercial installation for burning pulverized coal under boilers was made at the Parsons shops of the M. K. & T. railroad in 1916. Of eight 250-hp. water-tube boilers thus fitted, six were operated continuously for 3 yr., when oil was obtained at such a low price as to warrant its use. Since then, this plant has been operating alternately on pulverized coal and oil, depending on prevailing prices. Recently gas has been discovered within 20 mi. of this plant, so that this fuel may also be used. No change in furnace design was made when changing from pulverized coal to oil or gas firing. One of the principal advantages of this method of firing is its ability to utilize, with maximum efficiency, all kinds of coal, irrespective of quality or physical characteristics. In fact, quite a number of the present pulverized-coal installations were made for the purpose of utilizing coal that could not be marketed or used in any other way. The Pacific Coast Coal Co., at Black Diamond, Wash., formerly hand fired the boilers, using approximately 125 tons of prepared steam-size coal daily. The Black Diamond steam coal is the best quality of coal for steaming purposes mined in that section of the country, and there is a market for all that can be produced. By installing a pulverizing plant, it was possible to substitute coal of a size and quality that had no commercial value, so that 125 tons daily of the best steam coal formerly used at the mines is now marketed. This company made a similar installation, at its New Castle, Wash., mine with approximately similar results. Each of these two plants has a

Jan 1, 1922

By J. B. Austin, R. L. Rickett

Measurements of the rate of decomposition of austenite at constant temperature are commonly represented by plotting the percentage transformed on linear coordinates against time on either a linear or a logarithmic scale, a method that yields a curve that in shape resembles an integral sign (Fig. 1). A graph of this kind is not always convenient because extrapolation to the beginning or end of the transformation, or even intebrpolation, may be uncertain unless there are a large number of observations, which seldom happens; furthermore, the degree of consistency of a set of measurements is difficult to judge from such a curve. It is desirable therefore to find some mode of plotting, or even better to find a standard variety of graph paper, that gives a straight line instead of the integral shape. The straight line has many advantages; the number of readings required to fix the position of the curve is greatly reduced, interpolatiorr is easy and rapid, extrapolation can be carried out with greater confidence and, finally, the consistency of the measurements is readily estimated from the scatter of the points. The last advantage is particularly valuable when the data are obtained by direct microscopic examination alone, because they are influenced by the skill of the observer in estimating the relative size of areas, possibly also by undetected inhomogeneity of the specimen. A search for ways of representing the observations as a straight line yielded two methods which are described in this paper. The paper also includes an account of some interesting relations brought to light in applying these methods to the available experimental data. Usually the best way to derive such a method of plotting is to base it on established principles of chemistry and physics, as has been done, for example, for the temperature variation of the equilibrium constant of a chemical reaction. But so little is known of the mechanism of the decomposition of austenite, and so little is available in the way of well established background for changes of this kind, that it is simpler to rely upon purely empirical means. The general plan therefore is to study existing data with a view to finding some function of the direct observations that will

Jan 1, 1939

By J. B. Austin, R. L. Rickett

Measurements of the rate of decomposition of austenite at constant temperature are commonly represented by plotting the percentage transformed on linear coordinates against time on either a linear or a logarithmic scale, a method that yields a curve that in shape resembles an integral sign (Fig. 1). A graph of this kind is not always convenient because extrapolation to the beginning or end of the transformation, or even intebrpolation, may be uncertain unless there are a large number of observations, which seldom happens; furthermore, the degree of consistency of a set of measurements is difficult to judge from such a curve. It is desirable therefore to find some mode of plotting, or even better to find a standard variety of graph paper, that gives a straight line instead of the integral shape. The straight line has many advantages; the number of readings required to fix the position of the curve is greatly reduced, interpolatiorr is easy and rapid, extrapolation can be carried out with greater confidence and, finally, the consistency of the measurements is readily estimated from the scatter of the points. The last advantage is particularly valuable when the data are obtained by direct microscopic examination alone, because they are influenced by the skill of the observer in estimating the relative size of areas, possibly also by undetected inhomogeneity of the specimen. A search for ways of representing the observations as a straight line yielded two methods which are described in this paper. The paper also includes an account of some interesting relations brought to light in applying these methods to the available experimental data. Usually the best way to derive such a method of plotting is to base it on established principles of chemistry and physics, as has been done, for example, for the temperature variation of the equilibrium constant of a chemical reaction. But so little is known of the mechanism of the decomposition of austenite, and so little is available in the way of well established background for changes of this kind, that it is simpler to rely upon purely empirical means. The general plan therefore is to study existing data with a view to finding some function of the direct observations that will

Jan 1, 1939

By J. D. Rice, S. C. Pitzer, C. E. Thomas

Interpretation of pressure build-up data obtained in the conventional manner has often been difficult because of the deviation from theoretical behavior. Major causes of this deviation have been attributed to damage and afterflow, and to fluid redistribution in the wellbore which, in extreme cases, can result in a pressure hump in the early portion of the build-up curve. Theoretical investigations show that bottom-hole pressure is definitely influenced by phase redistribution in the tubing column during surface shut-in tests, and that the magnitude of the effect is sensitive to the producing gas-oil ratio and stabilized rate of flow in the well. For field experiments a wire-line tubing packer, which can be run in the tubing against a stabilized flow rate, was developed for bottom-hole shut-in tests. By use of this bottom-hole .shut-in method, pressure humps previously observed in surface shut-in tests were completely eliminated and the effects of afterflow minimized. Analog and digital computer studies have been made to obtain theoretical curves for comparison with field curves, and remarkable agreement between the results of bottom-hole shut-in tests and theoretical curves has been obtained. INTRODUCTION Pressure build-up data from shut-in wells have been used by the petroleum industry to determine the permeability of the formation, to estimate wellbore damage, to evaluate the static reservoir pressure and to speculate reservoir volume. Calculation of these factors is based on methods of analysis developed for theoretical systems whose build-up curves have a charac- teristic shape when the wells are shut-in at the sand faCe.1,2,3,5,8,10 However, field curves obtained by conventional surface shut-in methods do not always exhibit this characteristic. Such factors as stratification, rock heterogeneities and irregular reservoir geometry can cause the character of a build-up curve to deviate from that predicted by theory for a simple system. In addition, all field build-up data are affected by the methods utilized in obtaining the measurements. Conventional surface shut-in techniques allow two effects to occur which contribute directly to the manner in which pressure builds up at the sand face. The first, afterflow, has been recognized for some time and methods are available for estimating the magnitude of its effect and for correcting its influence.' The second, phase segregation in the tubing column after shut-in, has been reported only recently and appears to exert a considerable influence on the character of field build-up curves.!' In extreme cases, phase segregation can produce "pressure humps" in the early portion of the build-up curve. Such curves have been considered anomalous and have defied analysis. It is the purpose of this paper to discuss the effect of phase segregation in the tubing string during build-up and to present a bottom-hole shut-in technique for obtaining field build-up data which minimizes the influence of afterflow and eliminates phase segregation effects. It will be shown that reliable reservoir information can be calculated from build-up measurements obtained using this method, even though conventional surface shut-in tests on the same wells yield anomalous data. DISCUSSION OF PHASE REDISTRIBUTION EFFECTS Some of the effects of phase redistribution on pressure build-up curves have been described previously by Matthews and Stegemeier" who have presented evidence that phase segregation is responsible for the pres-