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By Betty J. Laswell, Gerald W. Laswell

Rotary drilling in modern open-pit mining is usually considered the lead phase which not only establishes the production rates but frequently limits them. From this viewpoint alone, the drilling phase must be maximized. The drill phase is the step that permits all the other operational phases to function within their design limits. This means that, in most cases, the drill is literally run to destruction to ensure that the shovel will be able to smoothly and consistently load a manageably size muck, the haul trucks can carry a balanced load without having a boulder dropped through the bed, and the crusher can devour constant rock size.

Jan 8, 1978

By J. C. Bierlein, R. A. Dodd

Endurance strengths at 10' cycles, fatigue-hardening rates, and endurance strength/0.2 pct proof stress ratios have been determined jbr a range of Cu(Ni), Cu(Si), and S.R.0. Cu(Au) solid solutions. Some douht is cast on simple cross slip models of fatigue hardening in view of opposite composition dependencies of hardening displayed by Cu(Si) and Cu(Au). The temperature dependencies of hardening also are the opposite of predictions made on the basis of a cross slip model. A correlation apparently exists between the fatigue strength/0.2 Pc~ proof s1.re.s~ ratios and rates of fatigue hardening. An increase in PS/PS due to alloying or temperature change is accompanied by a decrease in hardening rate, and vice versa. In recent years there has been much interest in the determination of the dislocation structure of fatigued metals and alloys. The accumulated evidence, e.g., Refs. 1 to 5, suggests that the structure may be dependent on the stacking fault energy, 7, of the fatigued metal in the same way that fatigue hardening rates have also been shown to apparently depend on u .6' 7 The above research followed the various earlier theories relating crack nucleation to ease of cross slip, e.g., Refs. 8 to 131 so "ggesting that y may indeed be the parameter of principal significance in all facets of the fatigue process. However, comparatively little attention has been paid to correlating engineering fatigue data with observations of the above type. Certainly, it would be useful if potential engineering fatigue performance could be assessed from a knowledge of easily determined alloy properties, and the present research originated from this standpoint. TO investigate the widest Possible range of 7 would require the use of two solvent bases, e.g., aluminum and copper, but a reasonable coverage can be provided by copper-based solutions alone. Therefore, it was decided to work with Cu(Ni) and Cu(Si) solid solutions, the approximate stackillg fault energies of which are given in Table I. The y range extends from low, Cu(7.5 at- Pet Si), to moderately high in Cu(2-5 at. ~ct ~i) and two of the Cu(Ni) alloys. The values listed in Table I should be regarded as qualitative only, being derived as follows. Dillamore and smallman14 quote a value of 85 i 30 erg.cm-2 for the stacking fault energy of pure copper, based on an earlier value due to Howie and swannl5 corrected by Brown's formula.'' Since the ratios (alloy)h(pure copper) have been reported17,18 for Cu(Ni) alloys containing up to 30 pct Ni, approximate ) values for these alloys can be computed, and a rough estimate of 7 for Cu(50 at. pct Ni) obtained by extrapolation. The relatively low y value obtained in this way for Cu(50 at. pct Ni) coincides with the observation of Nakajima19 that the stacking fault probability is a maximum at this composition. Likewise, the y values for the three ~u(~i) alloys are estimates based on values given by Swann and Nuttingo corrected on the basis Of Brown's estimate that the true 7 values are probably 2.3 times greater than those originally computed. In addition to the above alloys it was decided to investigate short-range ordered (s.R.O.) CU(AU) alloys containing up to 25 at. pct Au. This last alloy has been shown to have a well-defined planar arrangement of dislocations when deformed,21,22 probably due to cross slip being restricted by the S.R.O. Engineering fatigue data was to be represented by the determination of endurance strengths, and these were to be correlated with fatigue hardening and mechanical property data. EXPERIMENTAL I, order to study the desired properties and property changes, the following alloys were prepared: Cu(2.5 at. pct Si), Cu(5.0 at. pct Si), Cu(7.5 at. pct Si), Cu(5.0 at. pct Ni), Cu(25.0 at. pct Nil, Cu(50.0 at. pct Ni), Cu(5.0 at. pct AU), Cu(15.0 at. pct AU), Cu(25.0 at. pct AU). The copper and gold were zone-refined, while the silicon was semiconductor grade. The nickel was of 99.95 p,t. purity.* All alloys were induction-melted in a *Kindly supplied by the International Nickel co. helium atmosphere, appropriate precautions being taken to avoid segregation in the Cu-Au series. Rod stock was obtained by rolling and swag,ng. A few Bridgman single crystals were grown for fatigue-hardening studies, but most material was machined into polycrystalline fatigue speciments of the design shown in Fig. 1, and into polycrystalline tensile and fatigue-hardening specimens of simple cylindrical design. All specimens except Cu(Au) were annealed; the latter were quenched from above T, to produce short-range order. A few of the quenched alloys were examined for long-range order by step-scanning over

Jan 1, 1969

By E. A. Breitenbach

A computer program has been developed to afford rapid and complete quantitative log analysis for exploration and production decisions. The computation consists of automatic selection of tops and bottoms of porous intervals from the digitized data, and then point-by-point calculations within each selected interval. Nearly all log types can be analyzed. This paper presents the calculation techniques found to be appticable to machine evaluation and gives examples of their use. INTRODUCTION As the quantitative interpretation of well logs entails repetitive use of charts and equations, it is natural that digital computer programs would be written. A Universal Log Interpretation Computer Program (ULICP) has been developed to afiord rapid and complete analysis for exploration and production decisions. Application of this program enables the log analyst to: (I) apply rapid quantitative log analysis for exploration and production decisions on either a field, a well or on a single zone basis; (2) apply concepts of interpretation requiring detailed numerical analysis; (3) analyze all porous intervals on each log, rather than a few selected zones, and complete the analysis in less time than previously required. Computations are reported for every digitized point in each zone; (4) use empirical techniques applicable to a given area as an integral part of the computation; (5) experiment with the empirical coefficients and exponents in the interpretation equations to find the best possible solution; and (6) automatically plot both the original and computed data to scales analogous to the field prints. The primary utility of a log interpretation program stems from its ability to do an overwhelming amount of work with very little man-power. If a calculation procedure or thought process can be formalized to the extent that step-by-step logic can be written, a computer program can be developed that follows this logic. The major question is one of economics. A feasibility study of the costs for such a program indicates that digital processing is economical primarily as a means of increasing the productivity of the log analyst. In effect, the probability of missing productive intervals in any well, because of a lack of time to do detailed calculations, is greatly reduced. The nucleus of ULICP is programmed to compute large sections of a suite of logs by selecting zones automatically and then performing all pertinent computations on a data point by data point basis within each zone.'.' An entire suite of logs can be processed in this manner with very little manual intervention. Sufficient programming logic is available so that each log analyst can request computations pertinent to his area. These requests are made by simple additions or deletions of information on the input header cards. Hence, the log analyst is always in complete control of the computation process. The evaluation of a suite of logs requires pre-editing, digitization, computation, presentation of results and interpretation. Work by the log analyst is reqilired only in pre-editing and interpretation. Thus, he is allowed more time for comprehensive interpretation, rather than calculation. For continuity, the discussion of ULICP is organized sequentially: pre-editing, digitization, computation and presentation of results. DISCUSSION PRE-EDITING The extent of pre-editing prior to computation is dependent on the format of the original data. For analog prints, it requires inspection, correlation and editing of the logs, plus the entering of required data an special forms. For digitized data such as magnetic tape field recordings, only the special forms are necessary. The process for analog prints will be given here. The inspection and correlation process involves the selection of sections for digitization and the correlation of the traces to a common depth. To decrease the cost of digitization, traces that exhibit large variations in shale formations can be redrawn to a non-zero baseline. The next step is to enter all pertinent data on the input header cards. The header cards presently used for ULICP are presented as Figs. 1 through 6. Cards 1, 2, 3 and 4 (Fig. 1) are defined as the Main Header Cards. They describe the particular well for output identification and give basic information. Cards 5 through 15 (Figs. 2 through 6) are defined as the Block Header Cards. As such, they define the log types and the interpretation parameters for the block of data immediately following. Cards 1 through 10 are required for every computer run. Cards 11 through 14 pertain only to nuclear logs. Card 11 is required if any nuclear log is supplied, and cards 12 through 14 are required only when gamma-ray, density or neutron log data, respectively, are supplied. Card 15 (Fig. 6) must be supplied when cross-plot calculations are required. Either two- or three-component

Jan 1, 1967

Jan 1, 1925

By M. L. Fuller

MOST commercial alloys undergo changes in phase composition after casting. This is a natural result of the fact that the alloys are not in a state of phase equilibrium as cast and phase changes will therefore take place, with more or less rapidity, in an attempt to attain equilibrium. The practical aspect of aging in zinc-alloy die castings concerns the changes in physical properties and in dimensions that may accompany aging phase changes. Harmful alterations have been reduced to a minimum and zinc-alloy die castings are being produced today that are so stable with respect to dimensions and physical properties that they are entirely suitable for most practical purposes1. In the first paper2 of this series, and in this paper, aging phase changes of zinc alloy die castings have been investigated and the possible influence of these changes on dimensional changes of the castings has been evalu-ated and compared with the dimensional changes actually experienced. The change of dimensions has been selected for practical comparison in these papers because the effect of phase changes on the dimensions of a casting is directly calculable; from X-ray crystal-analysis data of the phase structure. The die-casting alloys considered contain, in addition to zinc, 4 per cent of aluminum, about 0:03 per cent magnesium, and from 0 to 3 per cent of copper. It was shown in the former paper that the eutectoidal decomposition of the beta aluminum-zinc phase, while intrinsically capable of causing a considerable shrinkage, can have very little effect on the observed shrinkage of die castings because it takes place within a few days of aging, whereas the observed shrinkage continues for five weeks. It was therefore concluded that the other existing phase change,

Jan 1, 1935

By N. E. Maccallum

(Cleveland Meeting, October, 1912.) ALMOST half a century has passed since the Siemens brothers, after tedious and costly experiments, finally began the manufacture of open-hearth steel. The furnace of that time was very small, having a hearth-capacity of from 3 to 4 tons, and we can appreciate the wonderful development that has taken place in those 50 years by the knowledge that to-day furnaces of 50 times the original capacity are in operation. As the new steel process assumed importance, and furnaces began to grow in number and in size, a question arose, to which no satisfactory answer has ever been given, and that was: ?What is the safe and economical limit of the open-hearth furnace?" Various stopping-places have been suggested, and 20, 30, 40, and 50 tons have each been advocated, but all such arbitrary restrictions have been passed, and 60 tons would probably represent the average furnace, although in a few instances from 70 to 80 tons are regularly tapped into one ladle. The furnaces which are the subject of the present paper have gone far beyond even these limits, and since, in my opinion, they mark another step in the progress of open-hearth steel, they will be considered fairly and frankly, in order that those to whom the matter may be of interest may be able to judge and form their own Conclusions. Short accounts of the work of these furnaces have appeared from time to time in various technical journals, of which the following is a brief résumé. These furnaces are the property of the Phoenix Iron Co., of Phoenixville, Pa., and their distinctive and important feature is, that they charge to twice the capacity of one ladle, and tap simultaneously into two ladles, with a device for controlling the flow into either. In this way the capacity of the furnace is not limited, as formerly, but heats of any size within the capacity of two ladles may be charged.

Oct 1, 1912

By G. K. Manning, P. C. Rosenthal

USE of copper as an intentionally added alloy in steel and cast iron has rapidly expanded with-in the last fifteen years. It is estimated that in 1931 not more than 2000 tons of copper were so used; by 1941, however, this figure had grown to 13,000 tons. Tonnage figures during the war years have been restricted just as copper itself has been restricted, but copper-bearing cast irons and steels have played a part in the production of ordnance equipment. They are used in gun carriages, airplane landing-gear assemblies, scout cars, bulldozing equipment, army trucks, armor plate and many other instruments of war. These wartime applications have their counterpart in many peacetime applications; derricks, dredges, mine equipment, railway equipment, trucks, farm implements, automobiles, and tractors, all usually contain some parts made of copper-bearing steel or iron. An example of this is the Ford tractor which in 1940 contained over 300 lb. of copper-bearing steel castings. To this list should be added corrugated building sheet for exterior use most of which, at the present time, contains upward of 0.15 per cent copper. With the return to peacetime economy and the removal of wartime restrictions, it appears certain that copper cast irons and steels will find increasing application in civilian goods.

Jan 1, 1945

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

By M. R. Geer, H. F. Yancey

Four coals were treated in the Humphreys spiral concentrator, and the products were examined by float-and-sink and screen-sizing tests to determine fundamental performance characteristics. The efficiency of the separation between coal and impurity was shown to be influenced greatly by particle size.

Jan 1, 1950

By Oscar H. Hershey

COMPLAINT has been made that in the literature of economic geology the work of the "company or practical" mining geologists does not get enough attention. I propose to attempt to overcome this com¬plaint in reference to one important lead-mining district, that of the Coeur d'Alene in northern Idaho. Furthermore, I will assume that the reader is not so much interested in the geology of the district as in the methods of application used and incidents that have arisen in the work. All the important discoveries of ore in the Coeur d'Alene were made without benefit of geology. Certainly I would not claim the reputed discoverer of the Bunker Hill mine as a fellow geologist. It appears also that the mines were operated quite successfully for many years without geological specialists, though doubtless certain properties were visited at long intervals by such men as Waldemar Lindgren. It was known that the ores occur in quartzite, graywackes and slates as stated by J. R. Finlay in 1903. (TRANS., VOL. 33.) He described the ore as occurring in typical fissure veins that occupy fault-planes of indeterminate displacement. The Bunker Hill lode was based on a definite fissure with the mineralization all on the hanging-wall side, extending as far as 300 ft. from the fissure.

Jan 1, 1933

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

[Separates of all the Pamphlets published within the last three years (starting with No. 1469) are available, with few exceptions, at Institute headquarters. Separates of all the Technical Publications are also available. All the papers are on file in public, university and technical libraries, and when so indicated in the list, may be found either in the TRANSACTIONS or in the special volumes issued by the Institute.] METAL MINING TRANS. PAMPHLET VOLUME NUMBER TITLE AUTHOR MEETING AND PAGE* -1033 Relation of Air Pressure to Drilling H. W. Seamon New York 66,743, 766 Speeds of Hammer Drills Feb., 1921 1034 Time Factor in Depletion of Mines J. W. Roberts New York - 66,711 Feb., 1921 1 1035 Calculation of Ore Tonnage and Grade J. E. Harding New York 66, 117, 122 from Drill-hole Samples- Feb., 1921 1038 Discussion of Papers Presented in 1920 1041 Run-off and Mine Drainage - H. N. Eavenson New York 66, 624, 630 Feb., 1921 1043 The Health of the Underground Worker A. J. Lanza New York Feb., 1921 1045 Dust-ventilation Studies in Metal D. Harrington New York 66, 272, 282 Mines Feb., 1921 1046 Discussion of Papers Presented at New York Meeting, 1921 1072 Breakage and Heat Treatment of Rock- B. F. Tillson New York 66,758 drill Steel Feb., 1921 1073 Discussion of Papers Presented at New York Meeting, 1921 1076-M Analysis of Some Drill-steel Tests F. B. Foley New York - 66,789 Feb., 1921 1077-M Application of Magnetic Analysis to C_ W. Burrows New York 66,796 Root Drills Feb., 1921 1078-M Heat Treatment of Rock-drill Steel G. H. Gilman New York 66,779 Feb., 1921 1080 What is the Ideal Drill Steel? F. H. Kingdon New York 66,807 Feb., 1921 1081 Rock Drill Steels, etc. W. T. Ober New York 66,814 Feb., 1921 1082-C Underground Mine Development, Its J. B. Dilworth Wilkes-Barre 66, 715, 721 Definition and Valuation Sept., 1921 1084 Drill Steel from Hollow Ingots P. A. E. Armstrong New York 66,809 Feb., 1921 1088 Authors' Replies to Recent Discussion 1092 Heat Treatment of Rock Drill Steel A. E. Perkins New York 66,811 Feb., 1921 1096-M Octagonal Ventilation Shaft of Davis- J. L. Bruce Wilkes-Barre 66, 252, 268 Daly Copper Co. Sept., 1921 1100-C Determination of Electrical Equip- G. Bright Wilkes-Barre 66, 580, 605 ment for a Mine Hoist Sept., 1921

Jan 1, 1926

By M. A. Grossman

THE hardenability of most steels can be predicted within 10 to 15 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter"; namely, the diameter of bar, in inches, that will just harden all the way through (absence of unhardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test. The data bring out certain features rather clearly. For example: I. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals," are known; thus an "incidental" chromium content of o.-2o per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful as would appear to be common experience; observe that an increase from no manganese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.2o per cent Mo provides a factor of 1.63, an increase of over 6o per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the first small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater harden ability will be obtained by using, for example, o.5 per cent of each than by using 1.0 per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain steels of high hardenability. It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, undissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum possible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the absence of Cr, and V up to 0.04 per cent), the charts provide reasonable approximations. The precise figures on the charts are suggested as tentative, subject to some modification as more data accumulate, but the fundamental concept appears to be supported by tests made on a wide variety of steels, a few of the correlations being shown in Fig. I.

Jan 1, 1942

By Williams, J. A.

THE Alaska Juneau mine has been developed through an adit driven at the elevation of the top of the mill and all mining is done above this main haulage level. As a result of wholesa1e"mining operations about 11,000 tons rock containing one dollar' per ton in gold is, hauled to the. concentrator during every 24 hr. Due to the method of mining, whereby a system of oreways delivers-the.ore direct from the stope to the bottom level of the mine, no tramming of ore is done on any of the upper levels. However, ;in doing exploratory drifting and crosscutting on the upper levels, the broken material is trammed by hand in 1-ton 18-in. gage cars to a nearby raise connecting with one of the several oreways. This constitutes the only tramming operation except that on the main level.

Jan 1, 1931

By Fulton B. Flick

The micrography and macrography of aluminum and its alloys present certain difficulties. Many of the difficulties attendant on the micrography have been removed by methods developed during the past few years, notably those of E. H. Dix, Jr.1 The development of grain size in aluminum and its alloys may be equally troublesome, yet comparatively little detailed attention appears to have been given to it. Satisfactory reagents are available for the development of such structurcs in ferrous and most non-ferrous metals, but those applied to aluminum and its alloys, i. e., alcoholic or aqueous solutions of sodium hydroxide or hydrofluoric acid are not entirely satisfactory. Hanson and Arch-butt,2 in speaking of these two reagents, state that "These two reagents give fairly satisfactory results, but they sometimes produce badly tarnished surfaces from which the surface deposit is difficult to remove." It has been our experience that neither of these reagents is to be entirely relied on for developing structures suitable for study or photography. This means that when the etch fails to produce satisfactory results the specimen must be repolished, through the 000-paper at least, and then etched with another reagent. This procedure entails a considerable loss of time, and the final results may not be all that might be desired. However, the reagent to be described, although not a panacea for all etching troubles, has improved results so markedly that it is felt that it & worth offering as a grain-size etch generally applicable to aluminum and aluminum alloys. Czochralski3 in 1915 mentioned the application of a solution of 10 to 20 c. c. concentrated hydrofluoric acid in 100 c. c. absolute alcohol, etching in this reagent being followed by dipping in concentrated hydrochloric acid soliltion.

Jan 1, 1925

By AIME AIME

NEW place was assigned to the women for their headquarters at the annual meeting of the Auxiliary but they, as usual, occupied a large place in the activities of the annual meeting. The alcove on the Thirty-ninth Street side of the building was a busy place on Monday morning, as the members of the various sections from New York to California greeted each other. The registration was conducted under the supervision of Mrs. Wolfes, Miss Georgene Davis and Mrs. Jennings, while Mrs. Hursh, Mrs. Hyde, Mrs. Charlton Reynders, and others dispensed tickets to the various functions that had been provided for entertainment. There seemed to be the usual number registered, but when only one member of the District of Columbia Section made herself known everyone wondered why the large delegation of last year had so dwindled. The explanation appeared next day, when a number of others from that Section arrived, telling of a delightful reception on the night before, at the White House. Mrs. Hoover had honored the "Canaries"¬(the organization of Lone Girl Scout' workers) the officers of the Section, and their husbands, who for once became only "so and so's husband." Luncheon was served on the fifth floor on Monday, the hostesses for that day being Mesdames C. F. Ayer, Willis Burns, G. W. Farny, H. G. Moulton, and T. T. Read. A number of sight-seeing trips had been arranged for the afternoon. The most popular proved to be an expedition to the new Riverside Church; where Dr. Fosdick is pastor. Guides were there to conduct

Jan 1, 1931