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By Josiah Royce

To evaluate chemically the sample of rock obtained by diamond drilling, it has long been recognized that the analyses of the two components of the sample, core and sludge, must be given appropriate influence in computing the average analysis of any unit of depth. The purpose of this investigation is to set forth what means are available for apportioning the effect of core and sludge on the final analysis, what variables affect the problem, and what combination of applied mathematics will closest approximate the truth under each condition as these variables proceed within their limitations. A drill hole is bored in iron ore exploration principally to test variations in rock composition with depth and is usually directed as nearly normal to the bedding of a horizon to be tested as possible. This practice has a tendency to minimize variation in composition laterally which in any event is not likely to be great. It is obvious that the opportunity for change in analysis of a particular rock is not statistically as great radially in a diamond drill hole where the distance in which such a change may occur is from 0.719 in. (EX bit) to 1.469 in. (NX bit) as there would be longitudinally even in a' run as short as 5 ft. Variations in composition of bedded or layered rocks are usually greater normal to the bedding than parallel thereto. Even in massive rocks, like porphyries, variations are functions of distance. Hence. in either case, variations along the hole are of greater effect than across it. Let us examine Fig 1 briefly to observe a cross section of a unit of depth of a typical diamond drill hole. If we neglect radial change in chemical composition, which we have seen is small compared to lengthwise variation, we can see that if core recovery was 100 pct, the core and its surrounding area, which would be recovered as cuttings (assuming 100 pct sludge recovery), must analyze the same if the sampling is perfect. This is the foundation of this paper, namely, that if core recovery is complete we may assume that the core constitutes as nearly as possible a perfect sample of the ground drilled. Now let us pass to the methods of weighting core and sludge in the final analysis and then develop each in turn. One might employ core analyses only, sludge analyses only, or apportion the influence of each by one of several methods. The most common apportionment is by direct proportion to relative theoretical vol- ' ume occupied by each component in the cylinder hollowed out by the drill, known as the Longyear formula. Another logical treatment would be to consider core and sludge in the final analysis according to the weight of each recovered. This procedure was elaborately set forth and refined by R. S. Moeh1man.l Then to be sure that we have embraced all the possibilities, we must admit that some other method or methods may be devised empirically or by mathematical maneuvers. Should a drill machine be capable of recovering 100 pct of the core in all types of rock, certainly core alone need be analyzed and no complicated mathematics are required; but although some companies have had fair success in obtaining high percentages of core in certain homogeneous ores on the Mar-quette Range, their same methods have proved disappointing on the Menominee, Cuyuna, and Gogebic Ranges where the iron formation often varies widely from flinty chert beds interstratified with soft hematite to wholly leached ore material composed of an unpredictable mixture of hematite and limonite with occasional zones of sugary, recrystallized chert. In spite of numerous mechanical improvements in core barrels, few drilling programs can count on complete core recovery. The sludge alone might be analyzed but for practical reasons this is inadvisable when core is obtained due to the numerous opportunities for contaminating or losing portions of the cuttings. The Longyear formula involves a weighting of the core and sludge in proportion to the theoretical volume of each, that is, where the volume of the core recovered is one-third of the total cubic volume of the cylindrical hole made by the drill, the analysis of the core is given one-third of the weight in the final analysis. This approach to

Jan 1, 1950

By R. McEwen, G. W. Hansen, G. F. Lee

The effect of using an anionic collector, Reagent 308, a sodium petroleum sulfonate, with a cationic collector, Armac T, a tallow, fatty acid amine acetate, was studied in a series of monomineralic flotation trials with the alkali feldspars and heavy minerals, ilmenite, rutile, garnet, and monazite. This combination of cationic and anionic collectors is employed to float feldspar and heavy minerals from quartz in the beneficiation of sand in Normanville, South Australia, to produce a suitable quartz sand for glassmaking. In the alkali feldspar trials, Armac T additions were held constant, while the 308 additions were varied. In the heavy mineral trials, the 308 was held constant while the Armac T was varied. Peak enhancement of the feldspar recovery was noted when the 308 additions were between 25% and 150% that of the Armac T additions. At higher 308 addition, depression of feldspar flotation occurred. This appears to be due to a neutralizing effect in the combined collector system and to the formation of a nondissociating complex of both collectors. This variability in flotation response when Armac T is used with 308 suggests that the two collectors do not act independently of each other.

Jan 1, 1977

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By Charles Morgan

AN increased demand for brown iron ore in the Birmingham district during the past 18 months has caused renewed activity both in prospecting and mining these ores. In recent years the production in Alabama has ranged from 41,559 tons in 1932 to 639,351 tons in 1928. During the last 9 years about 83 per cent of the total brown ore produced in the United States has come from Alabama (Tables 1 and 2). PROSPECTING Two methods of prospecting are used in this district: (1) test pits, (2) churn-drilling. Usually there is certain quite definite information on an area to be prospected; some of the indications are float ore such as small gravel or small and large boulders known as "dornicks" scattered over the surface, and ore exposed by erosion in gulleys and ravines, which have cut or eroded through the overburden. Often these natural erosions furnish an indication of the thickness of the ore and to some extent of the area of the ore body.

Jan 1, 1937

By Lauren A. Wright

The principal talc deposits in California are in a 200-mile belt paralleling the state's eastern border. The southernmost deposits represent selective alteration of early pre-Cambrian (?) carbonate strata, and are associated with granitic rocks. Deposits in the Death Valley area are at or near contacts between late pre-Cambrian carbonate rocks and diabase sills. Those in the Inyo Range area are chiefly alterations of Paleozoic carbonate rocks and silica rocks. Most of the state's talc output is used in ceramics.

Jan 1, 1950

By J. W. Downey, R. A. Morris, M. V. Nevitt

An experimental survey has determined the occurrence of Ti2 Ni-type phases in binary and ternary alloys of Ti, Zr, or Hf with first, second, or third long-period transition metals and also in ternary systems in which 0 is the third component. The existence of eleven previously unreported isomorphs is cited and some approximate phase boundaries are given. Lattice parameters are reported for the new phases. The periodic table relationships involved in the occurrence of the phase are discussed. A previous paper' reported the occurrence of a group of Ti2Ni-type phases (structure-type E93) containing Zr in combination with Rh, Ir, and Pt, and Hf in combination with Rh, Pd, Ir, and Pt, and cited evidence to show that all of the Zr phases and the Hf-Pd phase are not binary phases but occur only when 0 is present. More recently one of the present authors found that in the ternary systems of Ti and 0 with Cr, Mn, Fe, Co, and Ni the occurrence of the Ti2Ni-type phase could be correlated qualitatively with valency electron concentration, and that the role of 0 appeared to be that of an electron acceptor.' This paper describes the results of a broader investigation of the occurrence of Ti2Ni-type phases in binary and ternary systems containing Ti, Zr, or Hf. EXPERIMENTAL PROCEDURE Alloys were prepared by arc melting. The purity of the metals Zr, Rh, Hf, Ir, Pd, and Pt was given in the previous paper.' The additional materials used for this work were metals with a minimum purity of 99.9 pct and reagent grade ZrO2, TiO2, Cr2O3, and NiO. Chemical analysis of several alloys in each system indicated good agreement between intended compositions and cast-button compositions. For the heat treatment precautions were taken to avoid oxygen contamination. The specimens were wrapped in Mo foil and sealed in fused quartz tubes at a room temperature pressure of 1 x mm of Hg. These capsules were then annealed in a vacuum furnace at an external pressure of 5 X mm of Hg. Since the major constituent in most of the alloys studied was the brittle Ti2Ni-type phase, Debye-Scherrer patterns with sharp lines could be obtained with powder crushed from the annealed solid samples without being reannealed. Metallographic, X-ray diffraction, and density determination techniques previously described1, 2 were used. RESULTS AND DISCUSSION Zr-Rh-O, Zr-Ir-Oand Zr-Pt-O Systems-Figs. 1 through 3 show the approximate boundaries of the Ti2Ni-type phase fields at the temperatures indicated in the ternary systems Zr-Rh-O, Zr-Ir-O and Zr-Pt-0. In each isothermal section the Ti2Ni-type phase field is labeled E and the unidentified binary phase found in the previous work' is labeled ?. The dotted lines, which are not phase boundaries, correspond to the composition (Zr2 B)1-xOx. In each system the Ti2Ni-type phase field is displaced to the high-Zr side of this composition line. However, the departures from Zr2B stoichiometry for the metal components are not as high as Zr3B, as was inferred from the previous work. Lattice parameters of the Ti2Ni-type phases in the alloys shown as triangular data points in Figs. 1 through 3 are given in Table IA. The probable compositions of the Ti2Ni-type phases have been estimated from the isothermal sections. Although there are a few exceptions that probably result from uncertainties in phase boundary location and from the effect of variation of oxygen content, the generalization can be

Jan 1, 1961

The Tuscarora mining district, which has been highly productive of gold and silver ores in past years, is situated about 50 miles north- west of Elko, Nevada. The town of Tuscarora lies at an altitude of about 6,000 ft on the west side of the Independence Valley. Precipitation, particularly the winter snowfall, is considerably greater than in many other parts of Nevada, and temperatures are lower. From Tuscarora can be seen-across Independence Valley in the mountains to the east, a distance of about 12 miles, the Freeport Minerals Jerritt Canyon mine, which seems to be-destined to become one of the great gold mines in the western hemisphere. Tuscarora, a gold and silver camp, was active from the early 1870s to 1903 and produced about $10 million in those 30 years. Ten major mines and several smaller ones were operated in an area of about 1.45 square kilometers (one-half squaremile). The deepest shafts were only 230 m (750 ft) but most of the ore came from about the 105 m (350 ft) levels. Mineralization above the water table, at about 30 m (100 ft), was mostly native silver and cerargerite with free gold. Below the water table the ore was rich in sulfides including argentite, stephanite, proustite, pyrargyrite, enargite, arsenopyrite, bornite, chalcopyrite, pyrite, sphalerite and galena. A number of the properties contain sizeable dumps of what was con- sidered waste rock when it was mined. These dumps aggregate over 408,000 mt (450,000 st) with one dump, the Navajo, containing over one-third of the total. A few grab samples taken in the summer of 1978 from some of the dumps indicated interesting silver values with minor gold content. AgAu Exploration Ltd., was organized to explore and develop these dumps into a heap leaching operation. In the fall of 1978 a campaign was started to lease, with front money payments on a royalty basis, three groups of claims on which were located a few hundred thousand tons of dumps. In September and October of 1978, a systematic program of sampling was started on the Navajo dump which was most favorably situated in that it was near to an area which would furnish good sites for heap leaching pads. At the time it was fully recognized that sampling of dumps was a most difficult problem. Because of the topography on which they were situated and the manner in which they were formed, each dump required its own special sampling technique.

Jan 1, 1981

MAY began with a general strike of the bituminous and anthracite coal miners in the United States in progress, while in Great Britain about three quarters of a million workers became idle by a lockout, caused by a dispute respecting the question of the rights of management in their shops. The employers opened their shops on May 3 to men wishing to resume work, but few availed themselves of the opportunity. Up to this time the statistics had been showing a little increase in the rate of employment in Great Britain and business conditions were considered to be improving. From Russia came reports that the results of the famine had not been so bad as had been prophesied, which is not to say that they were not grievous. In prognostications such things are habitually overesti-mated. Seeding for the new crop has now begun in Russia, with hopes for better results than last year. However, the general economic situation in Russia steadily becomes worse. We had advices during May to the effect that the Soviet Government had decided to abolish the gold ruble even as a theoretical calculating unit and substitute a "goods index." This idea would be somewhat on the lines of Professor Fisher for stablizing the dollar, and there may be a chance to see how it will work in practice. There was a contradictory report from Russia, however, that it had been decided to revert to the gold basis. This is the more plausible report, for if there be anything to be deduced from economic theory and history the present paper rubles will completely collapse and return to gold basis will ensue simply because the people will refuse to sell their goods on anything else. The civil war in China came to a head during the first week in May when General Wu-Pei-fu crushed the forces of General Chang Tso-lin around Pekin. The victor declared his intention to be to reunite the North and the South and in course of time to arrange for a constitutional convention. We probably do not under-stand the conditions in China, but recent events do not appear to have solved the grave difficulties there, though they may be a step toward it. However, the immediate outlook does not appear good, General Chang having retired to the north and declared the secession of Manchuria and Mongolia.

Jan 6, 1922

By C. R. Schumacher, W. H. Moyer

Cornwall, Pa. magnetite ore, containing recoverable sulfides in the form of chalcopyrite and pyrite, has been mined continuously since 1742 1 Beneficiation of the ore was begun in 1905, at the Lebanon concentrator located six miles from the mine. At first, only magnetite was recovered, using Grondal magnetic separators. In 1907, copper minerals were recovered by means of Wilfley tables. Copper flotation, attempted as early as 1912, was finally successful in 1919. In 1940, flotation of the cobalt- bearing pyrite was begun, and Cornwall ore became the major domestic source of cobait for many years. In 1916, the Bethlehem Steel Corp. began to purchase interests in the Cornwall mine and Lebanon concentrator properties, and by 1926 had acquired complete ownership. Metallurgical practice at the old Lebanon concentrator was good, but by today's standards the plant was outdated. The flowsheet was complex, due both to the mineral content of the ore and to the low capacities of much of the equipment. As the flowsheet developed, buildings were added and the plant was spread over a relatively large area, with resulting high manpower requirements. Another disadvantage was the six-mile rail haul from the mine to the Lebanon concentrator.

Jan 3, 1966

By H. M. Chance, T. M. Chance

The term 'Llow-sulfur coal," as used in this discussion, is limited to coals containing less, or very little more, than 1 per cent. sulfur. For certain purposes it might be advantageous to include coals that contain as much as 1.25 per cent. sulfur, because such coals have been considered as available for making metallurgic coke of fair grade; but the same reasoning might apply to coals containing as much as.1 1/2 per cent. sulfur, if facilities exist for utilizing such coal by admixture with coal containing less sulfur. , In Pennsylvania, it is not possible to define the exact geographic limits of the areas in which coals relatively low in sulfur exist, because variations in the percentage of sulfur occur irregularly and often abruptly. It is not uncommon to find areas, more or less circumscribed in extent, in which the coal is relatively high in sulfur although all the surrounding territory contains low-sulfur coal; and, similarly, small areas of low-sul. fur coal exist in districts where the coal is normally high in sulfur. These generalizations apply, with few exceptions, to the whole area underlaid with bituminous coal in the State of Pennsylvania, and also to each of the individual beds of coal in this state. Pennsylvania is poorly supplied with coals of the low-sulfur class. We find, however, as an offset to this condition, very large areas in which coal ranging from 1 to 2 1/2 per cent. sulfur exists in beds of good workable thickness. This coal, by washing, can be reduced in sulfur low enough to make coke of a high grade. While a considerable tonnage of workable low-sulfur coal remains in the Pennsylvania bituminous districts, it has been necessary to turn to the areas of higher sulfur coal for the supply of metallurgical coke. This utilization of the higher sulfur areas has been made possible either by washing or by selective mining. Washing.—Fine crushing of the entire feed is not generally necessary to the successful washing of Pennsylvania coals. This is due to the fact that the pyrite is rarely finely and uniformly disseminated throughout the coal but is usually confined to high-sulfur benches in the bed or to concentrations on the cleavage planes of the coal. Hence, by graded crushing and sizing it is frequently possible to at once reclaim those portions of the coal bed containing coal that is relatively free from pyrite.

Jan 1, 1920

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Jan 1, 1940

By F. C. Stanford

The work of an engineer is to direct natural forces so that the: bring about the results that he wishes to secure. Heretofore he ha concerned himself chiefly with physical forces and inanimate objects until he has secured a truly marvelous degree of control over them The great problem of the present age is to secure a like degree of know1 edge and control of the human factor. Progress has already been made along this line, but it is only a beginning. Wilhelm Ostwald says tha scientific knowledge enables a man to be a true prophet; but it must be remembered that a good many people do not seem to be able to main tain a high average in prophecy. In short, 'the average of knowledge is not equal to the average needs of the present time, but continually fails to keep pace with it. It has been aptly said that the really essentia need of the period is for more brains; if we only had sufficient knowledg and sagacity we could not only solve all difficulties, but prevent then from arising. This generalization holds good for an industrial organization. Th most vital need of the management is for more brains. The logica course for an engineer in charge of an industrial organization is, therefore to direct whatever forces may be at his command toward the development training, and guiding of all the brains in his organization. This is easie said than done, for it involves the carrying on toward two objective: the maximum of productive work, and the development of the individual who perform it. This is essentially like the rebuilding and enlarging of plant, keeping it in full operation the while. On the other hand, if th aim is merely for maximum production from an organization, withou offering opportunity for development, the final outcome will necessari be like that of a plant that is driven at full capacity without stoppin for repairs or improvements; it eventually becomes so run down th either a complete rebuilding is necessary or else it has to be abandone

Jan 1, 1918

By Leonard P. Colvin

Like all successful American enterprises, the mining industry is constantly trying to increase production, lower costs and improve working conditions. Companies are, of course, intensely interested in new equipment to help them gain these important ends, and one recent development-the mechanical raise climber--contributes to all three goals. Properly used, it increases production, cuts costs and has a number of important safety aspects all of which are the subject of this article.

Jan 1, 1962

By Christopher Haycocks, J. Richard Lucas

The growth of computer and ground control technology in recent years, combined with an urgent demand for low-cost fossil fuels and mineral resources, has set the stage for full-scale utilization of computers in mine planning. Steeply rising production costs and the need to preserve the environment are placing great demands on engineers to improve their mining efficiencies, which can best be accomplished by applying the full capabilities of the computer. Pressure to develop and perfect programs with an immediate potential for improving mine design, reducing mining costs and extending the viable coal reserves of the country has already come to bear in the form of exploding energy requirements, environmental considerations and the visible limitations of other energy sources.

Jan 4, 1973

By Guy R. B. Elliott

If chemical mining is to work, it is extremely important to watch heat balances. Some reactions with coal give off heat and others absorb heat. The reactions of coal with oxygen or air give off heat, but the reactions of coal with steam or with carbon dioxide absorb heat. By balancing the proportions of the two types of reactions, the energy of the coal can be almost completely recovered and environmental damage is minimized. The chemical reactions are listed in Table 1 in the usual form with subscripts (s) and (g) indicating solid or gaseous materials. In reaction 1, solid corbon, C(s), reacts with gaseous oxygen, O2(g), to produce gaseous carbon dioxide, CO2 (g). H means enthalpy or available heat in the material; F is free energy, and it measures whether the reaction can go at all, and if so, how much.

Jan 9, 1973

By R. J. Lipp, I. Iwasaki, R. H. Heerema

The presence of calcium ion in iron ore pulps that are upgraded by selective desliming can result in indiscriminate flocculation of both iron oxide and siliceous gangue slimes. In order to overcome this adverse effect, deflocculation by three complexing agents, namely ethylenediaminetetzaacetate (EDTA), sodium tripolyphosphate (STPP), and sodium hexametaphosphate (SHMP), was investigated. The precipitates and complexes of these agents with calcium ion were characterized by potentiometric and conductometric titrations, and the surface properties of quartz and goethite were studied in the presence of calcium ion and of the complexing agents by means of streaming potential measurements and flotation tests. The results were then correlated with selective flocculation tests on an artificial mixture of quartz and goethite. EDTA markedly improved the selectivity of flocculation when added in near stoichiometric amounts, whereas STPP was less effective and SHMP was totally ineffective due to strong, indiscriminate dispersion. Remanent calcium polyphosphates on the goethite surface interfered with the adsorption of starch flocculant.

Jan 1, 1983

THE story of Miami really is two stories. First, that of an excellent Porphyry Copper mine, ably managed as a business enterprise, and always among the leaders in technical progress. Concentrating its first ore in 1911, it had by 1925 paid dividends totaling $30,000,000 or $40 per share on stock that had cost the public $5 per share in March, 1908. The ore, containing 2.5 per cent copper at the start, had become progressively leaner but the recovery had tended to improve. Production costs had gone up during the World War and the early post-war period; and had come down again. In all these respects it had followed the norm. If the mine had been abandoned as exhausted and the company had been liquidated late in 1925 (a program that had been given earnest consideration in 1924), Miami would have gone down into history a first-rate mining venture; as an active and progressive participant in the great Porphyry achievement. But Miami was not liquidated in 1925; instead it started to write the record of its second and really amazing story. Near the old mine was a large body of low-grade ore containing, in place, less than 20 lb. of copper to the ton, and without, incident- ally, any considerable sweetening of gold and silver. Any method of underground mining that was cheap enough would certainly entail some dilution, so that ore as sent to the concentrator necessarily would average much less than 20 lb. As a matter of record, the average for 1929 was 16.6 lb., from which 11.726 lb. was recovered as concentrate. As already said, the exhaustion of the older orebody during 1925 was foreseen; but in 1924 the decision was reached to enlarge the concentrator and develop a new mine. An expenditure of $2,500,000 was entailed in this program. By October, 1925, the

Jan 1, 1933

By C. B. Barlow, T. A. Mekelburg

Due to a tight ash constraint on the clean coal product and difficult middlings washability characteristics, a considerable amount of coal was being lost in the jig middlings at the Monterey No. 2 Mine. An investigation was conducted into circuitry to recover this lost coal with minimal effect on the total clean coal ash. A reverse two-stage hydrocyclone system cleaning at low specific gravities was selected. This system is currently recovering approximately 5.8 kg/s (23 stph) of 11.5% to 12.5% ash coal. The specific gravity of separation for the system is about 1.5 and the probable error is 0.13.

Jan 1, 1986

By V. R. Garfias

. EVEN before the arrival of Cortes in 1519, the history of Mexico was closely linked to that of its mineral production; the mining activities of the Aztecs being thus described by Clavigero, one of the early historians: In the mountains of Anahuac there abound in veins all kinds of metals, and infinite variety of other fossiliferous products. The Aztecs obtained gold from the countries of the Cohuijques, of the Mixtecas, of the Zapotecas and from various other places. They gathered that precious metal usually in grain, from the sands of the rivers, keeping a certain portion for the crown. They obtained silver from the mines of Taxco, of Tzumpango and others; however, this metal was not as esteemed by them as by other neighboring nations. They had two kinds of copper; one hard, which they used instead of iron to make sickles; lances and all kinds of rural and military instru-ments and another, soft, with which they made kettles, goblets and other receptacles. This metal abounds mainly in the province of Zacatula and in that of Cohuijques, which at present is in the kingdom of Michoacan. They obtained tin from the mines of Taxco and lead from those of Izmiquilpan, located in the country of the Otomies. From the tin they made money, and the lead, we know they sold in the market places, but we ignore the uses to which they applied it. They also had mines of iron in Tlaxcala, in Taxco and in other places; but they either had not discovered them, or did not know how to make use of the metal they contained. In Chilapa there were mines of mercury, and in other places there were mines of sulphur, alum, vitriol, cinnabar, cohre and of a white earth which they esteemed highly. As regards mercury and vitriol, we do not know of what use (they were to them; the other metals they used in paintings and dyes. There were then great abundance of amber and asphalt-bitu-men of Judea-on the coast of the seas and many cities of that territory paid tribute of one and the other to the kingdom of Mexico. They mounted the amber in gold, and it was only used as ornament and display by them. With the asphalt they made certain perfumes.

Jan 1, 1937

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951