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By Richard Hamburger

The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new & do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951

By David T. Day

In the summer of 1898, a demand suddenly arose for commercial quantities of the element osmium. At least half a ton was wanted for the manufacture of a new incandescent light. This led the writer to examine localities where platinum had been reported, in order to determine whether osmiridium mas contained in the crude platinum. With the co-operation of the concern most interested, the Welsbach Light Company, and in company with its President, Col. William E. Barrows, I visited most of the leading American localities where platinum has been obtained. I also wrote to every available placer-mine in the West for samples of the heaviest sands, in order to test them for platinum. The results of this inquiry are given in the present paper. Distribution. The notices of the occurrence of platinum in this country given in scientific journals include two interesting observa tions in the East. One concerns a nugget described by Peter Collier of Washington, D. C.,* and said to have been found on land adjacent to the village of Plattsburgh, N. Y., which weighed 104.4 grammes, and contained sufficient chromite to reduce the specific gravity from 17.35 for the heaviest portion to

Jan 1, 1901

By John H. Hollomon

The interpretation of notched-bar impact results has been a matter of controversy since the introduction of more or less standard tests by Fremont,' Charpy2 and others at the turn of the century. Many investigators3-l1 have contributed to the understanding of the significance of such tests. Several symposiums12,13 have been held with the express purpose of discussing the significance and interpretation of the impact tests. It is not the purpose of this paper to review all these contributions to the development of the knowledge on this subject, but rather to present an interpretation of notched-bar impact tests that appears to be in agreement with the available published data. Fundamentally, the interpretation discussed in this paper of the brittle failure of some steels in notched-bar impact test is similar to the qualitative analysis presented by Ludwik3 in the I92o's. Essentially, Ludwik stated that the function of the notch was to increase the tensile stress necessary for yielding, and that brittle failure occurred when the stress necessary for yielding exceeded the normal stress required for fracture (with no plastic deformation). Ludwik, however, had no means of measuring this normal stress necessary for failure of a plastically* undeformed metal, therefore he could not extend his interpretation beyond the qualitative stage. Kuntze14 and recently Mc-Adam15 attempted to determine the effect of deformation on the stress necessary for fracture by testing, in tension, specimens notched to various depths and angles. Because of the uncertainties in Kuntze's (and McAdam's) analysis of the stresses (which have been pointed out by Sachs16) and the inherent nonuniformity in the stress distribution in notched bars, the results of such investigations are difficult to interpret. A more direct method of measuring the effect of deformation on the fracture stress was suggested in previous papers"-18 and has been utilized in the present investigation. The present paper concerns itself primarily with the behavior of notched impact specimens. The effects of strain rate, temperature, and stress distribution, which are discussed with reference to the impact specimen, apply just as well to the behavior of metal at the bases of notches in any engineering structure. All that is necessary is to determine the stress distribution in the structure at the base of the notches.

Jan 1, 1944

By John H. Hollomon

The interpretation of notched-bar impact results has been a matter of controversy since the introduction of more or less standard tests by Fremont,' Charpy2 and others at the turn of the century. Many investigators3-l1 have contributed to the understanding of the significance of such tests. Several symposiums12,13 have been held with the express purpose of discussing the significance and interpretation of the impact tests. It is not the purpose of this paper to review all these contributions to the development of the knowledge on this subject, but rather to present an interpretation of notched-bar impact tests that appears to be in agreement with the available published data. Fundamentally, the interpretation discussed in this paper of the brittle failure of some steels in notched-bar impact test is similar to the qualitative analysis presented by Ludwik3 in the I92o's. Essentially, Ludwik stated that the function of the notch was to increase the tensile stress necessary for yielding, and that brittle failure occurred when the stress necessary for yielding exceeded the normal stress required for fracture (with no plastic deformation). Ludwik, however, had no means of measuring this normal stress necessary for failure of a plastically* undeformed metal, therefore he could not extend his interpretation beyond the qualitative stage. Kuntze14 and recently Mc-Adam15 attempted to determine the effect of deformation on the stress necessary for fracture by testing, in tension, specimens notched to various depths and angles. Because of the uncertainties in Kuntze's (and McAdam's) analysis of the stresses (which have been pointed out by Sachs16) and the inherent nonuniformity in the stress distribution in notched bars, the results of such investigations are difficult to interpret. A more direct method of measuring the effect of deformation on the fracture stress was suggested in previous papers"-18 and has been utilized in the present investigation. The present paper concerns itself primarily with the behavior of notched impact specimens. The effects of strain rate, temperature, and stress distribution, which are discussed with reference to the impact specimen, apply just as well to the behavior of metal at the bases of notches in any engineering structure. All that is necessary is to determine the stress distribution in the structure at the base of the notches.

Jan 1, 1944

By H. F. Bishop, F. A. Brandt, W. S. Pellini

The solidification mechanism of experimental steel ingots (7x7x20 in.) was studied by thermal analysis. It was determined that solidification proceeds in wave-like fashion at rates which are determined by the carbon level, superheat, and mold thickness. The thermal cycles of the mold walls were related to the course of solidification. ESPITE marked advances in the field of solid state transformation, metallurgical research has contributed comparatively little exact quantitative data on the mechanism of solidification of metals. There is, therefore, a great need for such data in the various metallurgical industries. The mechanics of solidification of ingots have been investigated in the past primarily by studies of the rate of skin formation as indicated by bleeding or "pour out" tests. The "pour out" method, however, is a tool which gives only approximate information. In the case of alloys with wide solidification ranges, such as irons and certain nonferrous alloys, the method will not work at all; in the case of alloys of intermediate solidification ranges, such as commercial steels, the information may be misleading. Thus, the general adoption of this method has resulted in divergent conclusions regarding the solidification process. Chipman and Fondersmith1 by means of bleeding tests have shown that the linear growth of a solidifying ingot wall follows a parabola of the general form, D = K C, with the start of solidification delayed until superheat is exhausted, as indicated by the constant C. These tests were carried only to a wall thickness of about 5 in. using an ingot of approximately 17x39 in. in cross-section; hence the latter stages of solidification were not studied. Matuschka2-3 indicated that linear solidification of ingots is rapid at first, then slow, but toward the end of solidification the rate becomes extremely rapid again. Spretnak's4 bleeding studies indicated that, wall growth is expressed more rigorously by two parabolas, and that their point of intersection corresponds to a change of solidification mode from columnar to equiaxed. Spretnak also showed that the K values of the first parabola are always the same regardless of superheat. Nelson bled ingots of square cross-section and found that linear wall growth is initially rapid but decreases continually until the end of solidification. He also concluded that rate of solidification in ingots of square cross-section increases 2.15 pct for every 10 pct increase in cross-sectional area of the mold. The mold ratios considered (ratio of cross-sectional area of the mold to cross-sectional area of the ingot) were all less than 2 to 1. The subject of solidification has also been treated mathematically in many cases, but because of the lack of accurate thermal constants and the simplifying assumptions required, as their authors generally acknowledge, they represent only approaches to the actual conditions of ingot solidification. A third method of studying solidification is the electrical analogue method promulgated by Pasch-kis6-7 and by Jackson and coworkers.8 This method treats solidification as a heat transfer problem with the solidification cycle synthesized on an electrical circuit. Paschkis in his treatment of solidification considered the fact, which was generally ignored, that solidification of steel is not simply the growth of a plane solid wall but a more complex process occurring over a temperature range as indicated by the constitution diagram. Undoubtedly, the anomalous results obtained by bleeding tests arise from the inability to measure quantitatively this mushy condition. The shape of Paschkis' solidification curves are more nearly in accord with those of Matuschka, in that they indicate rapid linear solidification at the beginning and end of solidification with intermediate solidification occurring at a slower rate. Paschkis indicates a definite lengthening of solidification time with increasing superheat. Thermal analysis is a direct method providing exact information for all types of metals regardless of solidification range and was thus adopted in the present program to follow the entire course of solidification from the surface to the centerline of the ingots. The method has the added advantage of being adaptable to following the thermal cycle of the ingot mold during the course of solidification. Test Methods The ingots studied were of square cross-section, 20 in. long, tapered from 71/4 in. at the top to 63/4 in. at the bottom, and fed with a hot top 7 in. in diam and 12 in. high. The molds were uniform in wall

Jan 1, 1953

By G. Birkbeck, T. C. Wells

Pearlite morphology in three commercially produced, low-carbon steels has been studied using optical and electron microscopy. A reduction in the cooling rate from 600° to 6°C per hr increased the interlamellar spacing but had little effect on pearlite content. The form of the lamellae was also assessed in terms of a new parameter, the ratio of lamellae length to interhmellar spacing. The variation of this parameter with cooling rate depended on steel composition. For each steel, it would appear that an optimum cooling rate exists at which lamellar pearlite can be produced to the greatest extent, though not necessarily the same extent in different steels. PeARLITE morphology depends principally on steel composition, prior austenite grain size, and either cooling rate or isothermal transformation temperature. Alloying with manganese,'" fine grain size,374 and slow cooling rates reduce the likelihood that a well-developed lamellar structure will be produced. Instead, imperfect structures usually consisting of partly globular carbides are formed in a ferrite matrix. Such structures have been described as granular.1,2,5 degenerate,6 or semi4-pearlite. Manganese additions also progressively lower the eutectoid temperature and the carbon concentration at the eutectoid so so that, for a given carbon content. the pearlite fraction is increased as manganese is added. While the effects of manganese are understood in a general way, quantitative studies of pearlite morphology have been carried out mainly on steels of eutectoid composition;9 little quantitative data is available for low-carbon steels. Certain anomalies exist in the behavior of steels containing -1.5 pct Mn, however. The pearlite morphology in niobium-treated steel differs from that which is generally accepted as typical of low-carbon/manganese steels in that a reasonably well developed lamellar structure is sometimes observed. In the present work, the effects of changes in cooling rate from 600° to 6°C per hr on the pearlite morphology in three commercially produced, low-carbon steels have been studied by both optical and electron microscopy. I) MATERIALS The steels were of the following types: 1) 0.1 pct C, 0.4 pct Mn steel (En 2, a composition similar to specification SAE 1010); 2) niobium-treated, 0.2 pct C, 1 1/2 pct Mn steel (BS 968:1962); 3) silicon-killed 0.2 pct C, 1 1/2 pct Mn steel (En 144, a composition similar to SAE 1320). The chemical analysis for each steel is given in Table I. To facilitate the comparison of pearlite morphology in the three steels, steels 1 and 3 (which were obtained as 1/2-in. plate and 1-in.-diam bar, respectively) were hot-rolled in the laboratory to $ in. thickness, finishing at around 850°C. The BS 968:1962 was received as 1/8-in. plate finished at 885°C and was not further worked. Specimens from each steel were heat-treated in vacuo at 950°C for 1 hr and cooled at rates of 600°, 60°, and 6°C per hr. 11) EXPERIMENTAL Pearlite contents were determined by point counting (500 points) on longitudinal sections mechanically polished and etched in 2 pct nital. Pearlite morphology is usually considered in terms of interlamellar spacing. For pearlite colonies randomly distributed in space and having a true, constant interlamellar spacing So Pellissier et al.9 determined the distribution curve for the apparent spacings of the lamellae on a random section plane. The areal fraction fs of the pearlite colonies occupied by apparent spacings up to a limiting value S is given by:

Jan 1, 1969

By E. R. Parker, R. H. Thielemann

The conventional short-time tensile test provides a reliable means of predicting the sustained load-carrying capacity of steels only when the temperature is such that continuous plastic flow does not occur. At elevated temperatures, stresses considerably less than the short-time rupture value may produce continuous flow, with fracture occurring only after long periods of time. The amount of flow or creep accompanying failure varies for different steels, and depends, to a large extent, on the temperature and the duration of the test. Service records of cracking stills, steam superheaters and high-temperature boilers have shown that brittle fractures sometimes occur with little or no warning. In installations of this type, localized stresses are often encountered, and steels must be capable of withstanding a certain amount of deformation without fracture. The sustained-load rupture test determines the expected life and corresponding ductility of steels at various stresses and temperatures. It also yields additional information regarding the effect of micro-structure and metallurgical stability on the high-temperature properties. Present Status of Sustained-load Rupture Test The sustained-load rupture test conducted at elevated temperatures is not entirely new. Dr. Zay Jeffriesl presented in 1919 the results of a large number of rupture tests made on copper, iron and tungsten. These tests were made with various strain rates and at temperatures ranging from the boiling point of liquid air to 1000° C. At that time he observed the interesting phenomenon characteristic of metals, that a temperature exists below which a metal is ductile and breaks with a transcrystalline fracture (through the grain) and above which the metal is brittle and breaks with an intergranular fracture (through the grain boundaries). He observed that this temperature varied with the testing speed, and that a minimum temperature, slightly above the recrystallization temperature, existed at which the cohesion of the grains themselves was

Jan 1, 1939

By R. H. Thielemann, E. R. Parker

The conventional short-time tensile test provides a reliable means of predicting the sustained load-carrying capacity of steels only when the temperature is such that continuous plastic flow does not occur. At elevated temperatures, stresses considerably less than the short-time rupture value may produce continuous flow, with fracture occurring only after long periods of time. The amount of flow or creep accompanying failure varies for different steels, and depends, to a large extent, on the temperature and the duration of the test. Service records of cracking stills, steam superheaters and high-temperature boilers have shown that brittle fractures sometimes occur with little or no warning. In installations of this type, localized stresses are often encountered, and steels must be capable of withstanding a certain amount of deformation without fracture. The sustained-load rupture test determines the expected life and corresponding ductility of steels at various stresses and temperatures. It also yields additional information regarding the effect of micro-structure and metallurgical stability on the high-temperature properties. Present Status of Sustained-load Rupture Test The sustained-load rupture test conducted at elevated temperatures is not entirely new. Dr. Zay Jeffriesl presented in 1919 the results of a large number of rupture tests made on copper, iron and tungsten. These tests were made with various strain rates and at temperatures ranging from the boiling point of liquid air to 1000° C. At that time he observed the interesting phenomenon characteristic of metals, that a temperature exists below which a metal is ductile and breaks with a transcrystalline fracture (through the grain) and above which the metal is brittle and breaks with an intergranular fracture (through the grain boundaries). He observed that this temperature varied with the testing speed, and that a minimum temperature, slightly above the recrystallization temperature, existed at which the cohesion of the grains themselves was

Jan 1, 1939

By T. L. Joseph

IT is a distinct privilege to participate in this meeting convened to honor the memory of Henry Marion Howe, a distinguished scientist and metallurgist. Many have added to our rapidly growing fund of metallurgical knowledge but few have made the unique contribution of formulating basic concepts essential to an over-all comprehensive view of the subject of metallography. Of those previously selected to deliver this lecture, several have added a personal touch to their discourse because they were able to refer to their associations with Dr. Howe. It was not my good fortune to know him or to enjoy his inspiring influence. Like most of you, my contact has been with his published works, which are outstanding in that they provide lucid, detailed expositions of the nature and behavior of metals and alloys. His deep understanding and clarity of expression have greatly accelerated our progress in metallography and in the use of metals. The degree to which a man's thinking, experimentation and writing contribute toward an understanding of basic laws and phenomena determines whether his life's work is of transitory or permanent value. This occasion appropriately recognizes the fundamental importance of Dr. Howe's pioneer work in the field of metallurgy. On two former occasions, gray iron was selected as a subject for discussion. The fact that the production of pig iron has not been discussed before does not reflect any lack of interest on the part of Dr. Howe or former lecturers in the process that under- lies the production of steel. Although Dr. Howe's work in his later years centered around metallography, his earlier publications show a considerable interest in the production of iron and steel. He recognized that in the ascending spiral of metallurgical advancement we are not winding a single thread but are weaving a complex fabric. Specific evidence of his interest in the production of pig iron may be found in his book1 on The Metallography of Cast Iron and Steel. In explaining why blast furnaces have been in constant use for about 600 years, he says: "The process is economical because it utilizes with extraordinary completeness the calorific power of the coke due to the thorough transfer of heat from the gaseous products of combustion to the charge." This emphasis on heat transfer, overlooked in many more extended and more recent discussions of the blast-furnace process, illustrates Professor Howe's ability to see the essentials. Other distinct advantages of the blast furnace, such as the removal of much of the sulphur and practically all of the oxygen, were mentioned. It was also stated that although the blast- furnace process is complex in nature, its outward form is comparatively simple, thus permitting large-scale production at small labor costs. All who contemplate the production of metallic iron from its ores by any other process might well consider the

Jan 1, 1946

By R. S. Archer

SILICON is one of the most important elements in the metallurgy of aluminum. It is always present in small amounts in the ordinary grades of "pure" aluminum, and hence in all alloys made therefrom. Within the last few years binary alloys containing up to 13. per cent, of silicon have come into extensive use for castings. Silicon is also added, beyond the amount present as an impurity, in alloys containing one or more other elements such as copper, manganese, magnesium and nickel. The binary aluminum-silicon alloys are not yet heat treated to any extent in commercial practice, although, as will be shown, their properties are affected to a very considerable degree by heat treatment. There are other aluminum alloys that develop higher strength, but the special characteristics of the silicon alloys may well lead to the application of heat-treating processes on a commercial scale. The role of silicon in the heat treatment of aluminum alloys is more important than would be indicated by consideration of the binary alloys alone, because many of the alloys that are heat treated in regular commercial practice contain some silicon in addition to that derived from the aluminum ingot as an impurity. Among these may be mentioned the heat-treated 195 alloy castings, and the wrought alloys 258, Special 178 and 51S of the Aluminum Co. of America, and the German wrought alloy, Lautal. It is the purpose of this paper to present the results of experimental work and the conclusions derived therefrom regarding the heat treatment of the binary aluminum-silicon alloys. The products heat treated included forgings, chill castings and both "normal" and "modified" sand castings.

Jan 1, 1927

By Benjamin Miller

FROM earliest recorded times, limestone has been employed in the industrial life of peoples of all sections of the world where it exists. It is widely distributed and therefore has been available in almost every country and has been employed for a variety of purposes. Its earliest use was for buildings, since it is more easily quarried and dressed than most other kinds of rocks and so could be utilized by early inhabitants, poorly equipped, with tools. The next use was in the manufacture of lime, which was employed by the ancients in mortar. These two uses of limestone are still all important, but they have been overshadowed in scores of regions by literally hundreds of new applications for raw lime-stone or products made from it. Anyone familiar with modern manu-facturing processes can quickly call to mind many industries in which limestones are essential, and new uses are continually coming to notice. Any enumeration would probably be incomplete and soon out of date.

Jan 1, 1935

By George S. Rice

Ten years ago: October, 1914, the author had the privilege of giving an illustrated address on investigations of coal-dust explosions1 to this Institute at one session of its fall meeting in Pittsburgh, Pa,. On the following day, the members had the opportunity of seeing a large-scale explosion test at the Experimental Mine near Bruceton, in which the explosion was made to follow a predetermined path by means of rock-dust barriers of various types, which had prevented the explosive waves from reaching the outlets of the mine by the shortest paths.2 There was also shown a ((home-made" rock-dusting machine discharging the dust from a flexible nozzle, and a cement gun operated for the quick erection of a fire or ventilation stopping, such as might be put up after an explosion. Following that paper, there was presented a paper by J. Taffanel, Director of the Lìévin testing station in the Pas de Calais, which reviewed the French coal-dust investigations.3 A paper4 by Howard N. Eavenson contains lists of explosions that occurred in North America and Great Britain, from early in the 19th century to 1912; in France to 1903, and Belgium to 1909. Although explosions still occur, we are hopeful that we have entered a happier freedom from these visitations, as the result of increased knowledge of the causes and means of prevention. Looking back over coal-dust investigations, there appear to have been periods of advance and of stagnation. Coal-dust Investigations From the earliest times of coal mining, which chiefly affected Great Britain as the first nation to take up coal mining on a large scale, to the beginning of the 19th century, no one thought of coal dust as an explosive agency; firedamp was the cause dreaded. It was believed, when Sir Humphrey Davy invented his safety lamp in 1815, that a solution had been found for the prevention of mine explo-

Jan 1, 1925

By Morgan Walker

Intermittent injection of gas in gas-lift pumping is a variation of the common practice in that the gas is delivered to the well for a short period, called the "on time," followed by a period during which none is admitted, called the "off time," instead of being admitted continuously at a constant rate or by intermittent flowing in which it is occasionally delivered to the well in just sufficient quantity to flow off the accumulated head of fluid. The term "gas" is used throughout this discussion but it should be remembered that in so far as the operation is concerned either air or natural gas may be used. The equipment at the well is the same as commonly used in gas-lift installations and gas may be admitted to either the tubing or the casing. It seldom occurs that all the wells on a lease can be pumped economically by intermittent injection from one header. Wells that have flow characteristics which permit their being handled together have their intake lines grouped at a central compressor station. Well groups may consist of two or more wells. The total volume of gas delivered by each group of compressors goes to one well at a time through a quick opening valve, each well connected to the header receiving its charge of gas in turn. Special cases may require a deviation from this arrangement. The distribution of the gas to the different wells is effected by an automatic timing device which operates quick-opening valves on the intake lines. The timing mechanism may be actuated by electricity, liquid or gas pressure, The essential factor in the operation of the timing mechanism is that as one intake valve is closed another must be opened. Water-operated Timing Device Timing devices operate the intake valves either directly, or indirectly by pilot valves. Of the former type one that is operated by water and has given satisfactory service is shown in Fig. 1 and can be made on the lease. The horizontal cylinder is a piece of 10-in. casing about 7 ft. long, closed at each end and free to oscillate about a fulcrum at the center.

Jan 1, 1929

R. W. Guard (General Electric Co., Schenectady)— The method of fractional replication discussed by the author has proven very valuable to us in applied research connected with alloy and process development where many of the same experimental difficulties exist. Several of our experiences may be of assistance to those who want to apply the method in these fields. Contrary to the author's observation that interactions are rarely significant, we have found in a number of cases that first order interactions exist which are significant and metallurgically important. Because of this difference there are two further precautions which should be taken in order to minimize the difficulties from this point. First, in evaluating the importance of

Jan 1, 1957

By Charles A. Ashburner

The manufacturing and domestic consumers of anthracite are beginning to realize the fact more fully, that the coal purchased for any one year does not seem to burn so freely, does not fire with so little trouble, and does not last so long as that purchased during other years, or vice versa. Where coals of different sizes, or from different districts, are offered to the trade by the same or competing salesmen, the question suggests itself, which shall we buy ? Among housekeepers, who are the most numerous class of consumers, though on the smallest scale, distinction is seldom recognized among these anthracites. By other consumers the coals are grouped into those which, when burned, will produce either a white or a red ash, special qualities being arbitrarily attached to each. Others, again, know only of three varieties : (1) Those from the WYoming and LacKawanna fields, or the coals shipped from the northernmost basins over the railroads running through northeastern Pennsylvania direct to New York—notably, the Delaware. Lackawanna and Western, Delaware and Hudson, and Erie railways; (2) those shipped by the Lehigh Valley Railroad and the Lehigh and Susqaehanna division of the Philadelphia and Reading Railroad down the Lehigh Valley ; and (3) those shipped over the main line of the Philadelphia and Reading Railroad down the Schuylkill Valley. In special localities, where a favorite coal is largely used, the consumer will speak of one class, composed of his favorite coal, which possibly comes from two or three collieries, with a total aggregate annual production of less than a million tons; and of a second class, composed of the coals from all the other collieries in the anthracite

Jan 1, 1886

By Richard Hamburger

(1) Introduction: The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new,',2 do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951

By R. V. Ramani, G. W. Luxbacher

The approach proposed in this paper is, as stated by the authors, an update of methods well discussed in the literature. The authors are to be congratulated for their excellent effort in quantifying a difficult problem with realistic cost data. Economic analysis of the components of a mine ventilation system is complicated by both the dynamic nature of the system and the uncertainty as to the time when system changes occur. We wish to address three specific areas of this paper which require further consideration: shaft designed air capacity, shaft location, and economic criteria used within the analysis. With regard to ventilation shaft size optimization, the system complexities are illustrated in the quantity flow through the shaft. Obviously, the capacity chosen by the designer is a static parameter while the utilized capacity is usually a dynamic variable over the life of the shaft. The designed capacity may be used for a short or a long period, and this may occur during the beginning, middle, or near the end of the shaft life, leading to different operating costs at different times. Operating costs, as shown by the authors' Eq. 8 are more dependent on air quantity than any other single factor (quantity cubed as compared with other factors to the single power); hence, extreme accuracy in the assessment of some of the other factors discussed by the authors may be secondary to the quantity estimation. Incorporation of a variable usage factor for air quantity over the life of the shaft in this optimization problem deserves some consideration. Although the authors have chosen to examine optimum ventilation shaft sizing, it must be remembered that optimization of the whole system-is the primary objective of any optimization process; unit optimization of such items as shafts may not complement the overall process. We have discussed this subject in some detail in another paper in this Transactions volume (Luxbacher and Ramani, 1979). While the recommended process by Wang, et al. can be used in shaft sizing, the shaft operating conditions (pressure head and air quantity) are intertwined with the shaft location within the mine infrastructure:

Jan 1, 1980

By J. Steininger

The Hallimond tube flotation of sphalerite and pyrite with sulfhydryl collectors has been found to be inhibited near neutral pH in the presence of copper salts. Alkalimetric titration studies of the reactions between collector and activator indicate that this effect is apparently related to the formation of basic copper collector complexes. The conditions of formation of these compounds and their stability are in good agreement with the depression observed in flotation experiments. The general procedure employed in the flotation of zinc sulfide minerals requires activation of the mineral surface by heavy metal ions, usually copper, which react more easily than zinc with the common short-chain ionic sulfhydryl collectors.' Commercially, zinc flotation is carried out under alkaline conditions (pH 7 to 10.5), but small-scale experiments indicate that zinc sulfide minerals can also be activated and collected under acid conditions. Selectivity, however, becomes poor at low pH and undesirable materials such as pyrite, silicates and carbonates tend to report in the float. Several years ago, Wark and Sutherland~, measured the contact angles of air bubbles on copper-activated sphalerite immersed in various sulfhydryl collector solutions. When represented, as in Fig. 1, on pH-sodium cyanide diagrams, the results are characterized by 'islands' of non-contact near neutral pH and

Jan 1, 1969

By A. L. Fentress, P. R. Bucky

The purpose of this paper is to present a scientific method for determining the proper span and shape of roof for safe and economical mining; at present, these two vital factors wherever pillars are left to support the roof are determined by local practice or general experience. To develop the method described here, experimental laboratory work was done. The arch adopted was a segment of a circle, a flat roof being considered an arch with an infinite radius. Hitherto, arches have been used underground without the background of stress analysis that generally precedes arch construction on the surface. In many cases results have not been as expected, because of the lack of knowledge of the factors affecting its strength and behavior. A theoretical and experimental study of arches should furnish information that will make it possible to design safe and economical surface structures as well as underground openings. For example, on the subject of mine drifts and tunnels, the present idea is that arching their backs increases their strength; this paper will indicate that this is not always true, and if it can be shown that under certain conditions arching becomes unnecessary an economic saving will result. In room-and-pillar work a question may arise as to whether arching the roof and gobbing the excavated material will result in timber saving, and a decrease in the dangers from falls of roof. It is to be distinctly understood that each mine must be treated as an individual problem, and that answers to these questions and many others can now be found after experimental laboratory data have been obtained. Mine-Arch Structure Fig. 1 shows the elements that affect the strength or behavior of the experimental arch. They are the span, crown thickness, radius of curvature, rise and restraint. The restraint in all cases was made sufficient to cause the arch to fail without displacing the restraining sides. Fig. 2a is a photograph of a model arch prepared for testing in the centri-

Jan 1, 1934

By A. W. Hull

The new valves described in this article are the latest product of the Research Laboratories of the General Electric Co. Some of them are still in the laboratory stage, others have already found important applications. Some of the larger ones, which have graduated from the laboratory, are waiting for their apprenticeship in industry, there to refine their frailties and complete their preparation as electrical servants. The career that awaits them, though dimly foreseen, appears fascinating. And as surely as history repeats itself, scenes still more romantic, now beyond the horizon, will unfold as we approach them. This is the romance of science. Counting Electrons Let the smallest tube lead the march of review. It is a special Pliotron, designed to measure currents smaller than any yet detected. It goes by the unromantic name of Pliotron FP-54. Fig. 1 shows this miniature tube—miniature in performance rather than size, for it is the size of an ordinary radio receiving tube. Its appearance has nothing distinctive, except the quartz beads above and below the plate, which support the grid. They minimize insulation leakage. In principle, the FP-54 is like any grid-controlled high-vacuum electron tube; but in structure and operating characteristics it is entirely special. An extra "space-charge" grid, maintained at 3 volts positive with respect to the filament, holds back the small but pernicious current of positive ions emitted by the filament; the normal plate voltage is 6 volts, grid bias 3 volts, thoriated-tungsten filament temperature 1700" K., plate current 40 microamperes. These conditions are essential to the avoidance of grid-currents, which may consist not only of insulation leakage and positive ions from the hot filament and from residual gases, but of high-speed electrons from the filament, photo emission from the grid due to the light of the filament, and electron emission caused by X-rays generated by the impact of electrons on the plate.

Jan 1, 1932