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By C. B. E. Douglas

In an interesting article on evaluation of the water problem at Eureka, Nev., W. T. Stuart describes how a difficult water problem, or one phase of it, may be evaluated by means of a small scale test. Test data are plotted by a method rendering, under certain conditions, a straight-line graph that can be projected to show how much the water table will be lowered by pumping at any specified rate for a given time. A formula is then used to determine the size of opening, or extent of workings, necessary to provide sufficient inflow to enable pumping to be maintained at that rate. At first glance this might seem the answer to a miner's prayer, but a word of caution is in order. It may not be the whole answer. Moreover, results obtained by the method described are reliable only for conditions approximating those assumed. Even where conditions do not meet this requirement, however, it may be possible to draw helpful inferences from the results, perhaps enough to facilitate another approach to evaluation of a problem.

Nov 1, 1955

By John Birkinbine

Since the presentation of the paper upon " The Concentration of Iron-Ore," which the writer, associated with Mr. Thomas A. Edison, read before the Institute in February, 1889 (Transactions, vol. xvii., 728-744), much time and money have been devoted to applications of various forms of concentrating apparatus, particularly in treating magnetic iron-ores. An indication of the interest which has been developed is shown in the four payers presented at and printed in advance for this meeting." The question, does magnetic concentration pay? is now being discussed by many owners of magnetite deposits, and affirmative answers can be readily obtained from patentees or agents of special machinery, while ultra-conservatism may give a prompt negative reply, based mainly upon the apparent impracticability of handling, crushing, sizing and separating large quantities of ore, and upon the generally

Jan 1, 1891

By AIME AIME

THE Industrial Conference appointed by President Wilson has presented the following tentative plan for preventing or retarding strikes and industrial conflicts by proposing new Federal machinery for the adjustment of differences between employers and employees. Theplan is signed by William B. Wilson, Secretary of the Department of Labor, 'as chairman of the conference; Herbert Hoover, former Federal Food Administrator, as vice-chairman; Martin H. Glynn; Thomas W. Gregory, former Attorney Gen¬eral; Richard Hooker; Stanley King; Samuel W. McCall former Governor of Massachusetts; Henry M. Robin¬son; Julius Rosenwald; Oscar S. Straus; Henry C. Stuart, former Governor of Virginia; F. W. Taussig; William O. Thompson; Henry J. Waters; George. W. Wickersham, former Attorney General; and Owen D. Young.

Jan 1, 1920

By H. Bernstein

WHILE the beryllium -copper (2 pct Be) alloy is nominally nonmagnetic, the presence of iron impurity causes variations in the magnetic proper- ties which, at times, attain excessive proportions. This investigation was carried out to establish the effect of small amounts of iron on the susceptibility of the material and to determine if the effect could be minimized. Beryllium-copper is an age-hardening alloy which

Jan 1, 1959

By William Campbell

In the olden days the making of alloys was an art, and the secrete of the craft were jealously guarded. To-day it has become a science, though the old ideas in regard to the secrets and formulæ are dying hard. Modern progress may be attributed to scientific research and testing of materials, and the substitution of chemical analytical control for " cook-book " methods. We know to-day a great deal about the constitution of alloys, the reasons of the change in structure and physical properties by heat and mechanical treatment; and this new knowledge is due for the most part to the physical chemist and metallographist, who have shown us that alloys are simply solutions, and as such obey definite laws. The application of the theories of solutions and of the phase rule tells us what ought to happen when our alloys are in a state of equilibrium. The working-out of the temperature-composition diagram (thermal diagram) for numerous alloys has thrown a light on the structure and constitution which has dispelled most of the darkness in which we labored before the advent of metallography. The work began with the determination of the freezing-point curves, and here the research of Le Chatelier,' Gautier,2 Roberts-Austen,3 and the other pioneers broke the ground. Next the physical chemists, Tammann,4 Rooseboom,5 Bancroft,6 and their colleagues, showed us the complete thermal diagram and its meaning. Then the researches of Heycock and Neville7 on the Cu-Sn series and of Shepherd 8 on the

Jan 1, 1913

By D. D. Porter, C. Fairhurst

Crack propagation in the region of a statically pressurized borehole is investigated to determine a role of the sustained borehole pressure following detonation in a blast. The case of a single-hole bench blast is reduced to a plate model, which is considered both theoretically and experimentally. Based on the principle of least work, it is hypothesized that the path of any crack in the plate will coincide with one of a family of maximum principal stress trajectories. These trajectories were computed, and critical experiments in glass, designed to test the effects of controlled crack origin and of changed trajectories from different loading configurations, confirm this hypothesis. It is concluded that under ideal conditions the crack path can be predicted and that cracks can be produced in the absence of either high-amplitude stresses or stress waves. Energy considerations for crack extension are discussed, and, based on the strain energy distribution, a relationship between hole burdens and spacings is revealed, a critical burden is demonstrated, and a maximum crater width is shown to exist.

Jan 1, 1971

By William C. Alden

A great landslide occurred on June 23, 1925, in the valley of Gros Ventre River, about 35 miles south of Yellowstone National Park (Fig. 1). The relations of the north-easterly dipping rock formations of the slide scarp and of the dam formed by the slide are shown in the diagrammatic cross-section of the valley (Fig. 2). This generalized section is based on unpublished maps and notes by Eliot Rlackwelder, in the files of the IT. S. Geological Survey. Heavy rains and melting snow in the Gros Ventre Mountains had saturated clay layers in the Carboniferous strata, which dip toward the valley at angles of 18" to 21°, consequently an enormous mass of rock at the end of the north spur of Sheep Mountain became loosened and, on the afternoon of June 23, slid suddenly down into the valley. Within a few minutes this mass of debris—estimated as 50,000,000 cu. yd.—carrying

Jan 1, 1928

By George Smith

IN discussing present-day business and industrial troubles we easily drop into the habit of clinical diagnosis. Talk of this kind, with its emphasis on suspicious symptoms and abnormal tendencies, makes us all morbid. As an English essayist has put it, we may thus induce a melancholy, temper that simply in-vites the ministrations of social and political quacks. It is far better-because nearer the truth-for us to recognize that our condition is in no sense diseased, that our body politic, social and economic, is suffering merely from growing pains; that America is not de-cadent-indeed, that any lapses from staid normality are traceable to the, excesses of youth. Our chief .trouble, then, is only that our industrial state is still young; it may be that we have been growing too fast. The growth in the industrial development of our country from pioneer days to the present time has been marvelous. Too many of us, however, take all this as a matter of course-we credit this record of American progress to our American genius alone. Too often we overlook the fundamental relationship between resources and progress-that man is aided and even guided by Nature. The fact is, social advance, indus-trial progress, national prosperity all have their ma-terial basis in natural resources. In furnishing the needed mineral raw materials to the great manufac-turing industries of the United States there has been no halt, but rather a general acceleration. No other phase of American activity can show-equal advance. As the decades have passed, the winning of mineral wealth has progressed from the role of a stimulus for western exploration to that of the foundation for nation-wide business. In 1890 the Sherman law was passed; since then the population of the United States has about doubled. Since then, too, thevalue of the annual product of the mines of this country has increased better than eight-fold-from 650 millions to 51/ billions of dollars. Since then the four largest branches of the mineral industry, which supply the iron and copper, the bituminous coal and petroleum-the bone and sinew and the energy of all other American industries-have increased their annual output nearly ten-fold as to value and six-fold as to quantity. Such a growth in the volume of mineral output must be taken as a true measure of the ex-ceptional service rendered by the mines of the United States. Not only is this a much larger country than it was 38 years ago, but its growing mineral industry has met demands that have been out of all proportion to the growth of the population.

Jan 8, 1928

By G. M. Ellis

When developing a mineral processing facility, the mining company management and engineering staff should have some knowledge of the construction industry in order to work with the contractors involved as a team. Of course, the situation varies with the nature of the project and its size, but relations among owners, engineers, and contractors always will be enhanced if the mining company has a knowledge of three construction industry facets: (1) the makeup of a construction company, (2) the functions performed by its staff, and (3) the various types of contracts and tendering procedures available. There are several options open to a company wishing to bring a new mine into production from the grass roots, depending upon corporate structure, capabilities, and financial strength. A company that already employs a substantial engineering staff may elect to manage and perform the design requirements itself, and may handle some or even all of the actual construction work. But in cases where bank financing is required, the loan is often dependent upon adequate professional construction help being used.

Jan 1, 1978

By H. R. Peiffer, R. Geckle

The silver phase of silver and finely divided alumina composites is shown to grow as single crystabs upon solidification from the melt. These crystals grow without the aid of an externally applied thermal gradient or a mold. The single-crystal growth is more readily disrupted as the alumina content varies from the optimum concentration of 20 wt pct. Pretreatment such as variation of fabrication pressure, and presintering of the specimens appear to play a lesser role in this phenomenon. In actual practice the growth of single crystals of metals from the melt is a tedious, painstaking process.' Care must be taken to insure the proper thermal gradients and rate of growth in a vibration-free environment. Excellent single crystals can be grown when these variables are controlled. When a second insoluble and finely divided phase is present in the melt the growth of single crystals is difficult, if not impossible, even under the most favorable conditions outlined above. During the past few years, a composite of silver and alumina has demonstrated an ability to resist flow even though the major phase, silver, is mo1ten. 2 A more surprising feature of this material is the ease with which single crystals of silver grow upon cooling the composite from temperatures above the melting point of silver to temperatures near room temperature. Observations have been made that demonstrate that single crystals of silver will grow even when conditions most unfavorable for growth of pure silver crystals exist. The crystals grown in this manner are imperfect in that a great deal of subgrain structure exists. It is the purpose of this manuscript to qualitatively describe this process and to attempt to isolate the influencing factors of this behavior. MATERIAL PREPARATION The composite material is prepared by powder-metallurgical techniques. Two items of great importance are the introduction of oxygen into the system and the obvious need for a thorough mixing of the metallic and refractory oxide phases. The oxygen is necessary in order that the silver wets the alumina. Without oxygen the phases separate and the material shows no unusual properties. In order to supply the needed oxygen the silver is added in the form of silver oxide which is readily decomposed to oxygen and silver upon heating. The silver oxide is readily obtained in a finely divided form that allows a uniform mixture of the alumina and silver oxide to be prepared. The correct ratio of alumina to silver oxide is mixed in the presence of alcohol in an ordinary food blender. The mixture has the consistency of a thin slurry and after mixing for approximately 20 min is dried and pressed into billets at various pressures. As is shown in Fig. 1, there is no limit to the shape of the specimens obtainable as single crystals. These billets are heated in air in a predeter-

Jan 1, 1964

By Robert Keeney

THE electric smelting of manganese ore and the production of ferro- manganese did not exist as an industry, in the United States or elsewhere, previous to the outbreak of war in 1914. Ferromanganese had been produced, electrically, during times of high prices by two companies at Niagara Falls and by several European companies, but the production. was spasmodic, and none was electrically produced when ferromanganese sold at from $35 to $40 per ton. Thus the electric smelting of manganese ore must be considered as a development caused by the high prices prevailing during the years 1916, 1917 and 1918, and the necessity of smelting domestic ore in order to fill the ferromanganese requirements of the steel industry of the United States, which increased from 189,088 tons in 1914 to 356,356 tons in 1918. The electric furnace is well adapted to smelting domestic-ore because it can be located in small units near the source of ore supply. In 1918, the ferromanganese production of the United States was 333,027 tons, of which about 7 per cent., or 23,000 tons, was produced in the electric furnace. The electric furnace not only assisted materially in the development of a domestic-ore supply but made a considerable saving of coke, as it requires about 1,4 tons of bituminous or lignite coal per ton of ferromanganese compared with a blast-furnace consumption of 2.9 tons of coke per ton of ferromanganese. Some of the plants in the United States that smelted manganese ore in the electric furnace during the war and in 1920 are listed in Tabled. From early in 1919 to about February, 1920, little ferromanganese was produced in the electric furnace. During this period the price of ferro-manganese (78 to 82 per cent. manganese) was about $100 per ton. During the first half of 1920, several plants resumed operation when the, price of. ferromanganese (76 to 80 per cent. grade) gradually increased to $200 per ton, delivered.

Jan 2, 1921

By M. J. Duggin

Evidence is produced below to show that the carbide "Mn,C," reported by Kw,and ersson' is really a mixture of two carbides. One is an Fe-Mn carbide which is probably isomorphous with hexagonal Mn15C4, reported by Bouchand and Pruchart.' The othev is a tetragonul Fe-Mn carbide with cell dzmensions close to those reported previously by the author3 for an Fe0.1Mno. carbide. IN a recent investigation several Fe-Mn carbide specimens, each weighing about 5 g, were prepared in a manner previously reported.3 Debye-Scherrer X-ray photographs were taken of at least two samples from different parts of each specimen using a 114.6-mm-diam camera. The exposure time was 2 hr using filtered chromium radiation, a tube voltage of 35 kv and a tube current of 10 ma. In the case of one specimen, which contained nominal weight percentages of iron, manganese, and carbon of 9.40, 84. 6,, and 6.0, respectively, duplicate chemical analyses indicated f1.2 and 5.5 wt pct C to be present in the two samples taken of the specimen: no graphitic carbon was detected. One powder-diffraction pattern of this specimen indicated the presence of the tetragons: carbide reported earlier,3 (a = 6.772A, c = 9.427A), plus cementite (O), plus an unknown structure. The second powder-

Jan 1, 1970

By R. A. Spitz, T. C. Frankiewicz, R. E. Lueders, D. S. Davies

Further development of the Nitric-Sulfuric Leach (NSL) process has led to an improved design of the leach and nitric acid recovery steps. NO produced in the leach step is reacted with oxygen, regenerating NO2, which is sparged directly into the leach reactor. Leaching is simplified to two steps, and the nitric acid plant is replaced with an oxidation recycle gas system. Laboratory work substantiated the concept and led to selection of operating conditions. The lab work also pointed to improved process control compared to use of nitric acid as the sole oxidant. Recovery of copper from purified pregnant liquor is modified to use air agitation electrowinning improving cathode quality and lowering tankhouse costs. Economic evaluation shows reduction of capital requirements from $2640 per annual ton to $2220 per annual ton in 1978 dollars for 45 kt/a of copper production.

Jan 1, 1982

By Sidney W. Poole

THE control of deoxidation, together with other factors involved in electric-furnace melting practice, to consistently produce heats of high-quality alloy steel to stringent specifications as to nonmetallic inclusion content is a problem of considerable magnitude. Steel melting as an industrial process is subject to many variables that can influence the quality of the product made. In order to modify the size, amount and distribution of inclusions and to promote their elimination, deoxidation, among other practices, plays a major part. The primary purpose of deoxidation in the production of electric-furnace alloy steels is the removal of dissolved oxygen present as FeO in the bath, which is produced as a result of prior oxidizing conditions. The elements usually added to effect this removal of soluble oxygen are those that will, upon addition, cause the formation of an oxide compound insoluble in the molten steel bath as silica, alumina or silicate combinations.

Jan 1, 1947

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By N. J. Grant, C. Stein

A more complete determination of the chromium-rich portion of the Cr-Ni phase diagram was made, based in part on resistivity measurements. The existence of a eutectoid reaction at 1215°C,made,based in addition to the previously reported eutectic reaction at 1343°C, was confirmed. Metallographic studies, lineal analysis, and diffusion-couple evidence were utilized to support Metallographicand extend the findings of the resistivity measurements. Delineation of the a chromium solvus line shows that the maximum solubility of nickel in a chromium decreases rapidly from 25 wt pct Ni at the eutectoid temperature to 16 wt pct. Ni at 950°C. IN recent years alloys of high chromium and nickel content have become of more interest as better performance of metals at higher temperatures is sought. It has become increasingly important, therefore, that the Cr-Ni binary diagram, which is composed of two of the elements commonly found in many high temperature alloys, be known more accurately. In particular, the chromium-rich portion of this diagram has for a long time remained incompletely determined and has been reported in the literature with a great deal of conflicting evidence. In general, electrolytic chromium of nominal purity was used by most of the earlier workers, who, except for Jenkins et al., made no further attempt to purify the metal. In the present redetermination of the chromium-rich portion of the Cr-Ni phase diagram, every effort was made to use the purest component metals available and to retain this purity throughout the preparation of the alloys and their subsequent handling. Early work by Voss, Bain," and Phebus and Blake4 indicated that the Ni-Cr binary diagram was a simple eutectic system with rather extensive terminal solid solutions. Later, Nishigori and Hamasumi," Tasaki, Weaver and Jellinghaus,' Matsunaga, and Jette, Nordstrom, Queneau, and Foote attempted to determine the limits of the phase fields. Except for Jette and coworkers, the other investigators agreed that the temperature of the eutectic reaction occurred between 1320" and 1340°C and at a composition of 50 or 51 pct Cr. There was, however, considerable disagreement as to the melting point of the chromium-rich alloys and the limits of the solid-solution fields. As a result of the studies of Jenkins et al., the liquidus and solidus curves up to 80 and 90 pct Cr, respectively, were outlined. In addition, the solid-solution phase fields at higher temperatures had been investigated and showed only two phases. The boundary of the chromium-rich a phase was not determined precisely according to these authors, but indications were that it tended to confirm the earlier work of Nishigori and Hamasumi. A more recent investigation by Taylor and Floyd,'" using X-ray methods, essentially corroborated the diagrams proposed by Jenkins et al., and by Wise and Eash (see Fig. 1). Again, no indication of a third phase in the chromium-rich portion of the diagram appeared. The earlier observations, however, are not substantiated by the modifications to the Ni-Cr binary diagram proposed by Bloom and Grant." In the investigation carried out by Bloom and Grant, X-ray methods showed that an eutectoid reaction existed at approximately 1180°C, in addition to the eutectic reaction at 1343°C (see Fig. 1). Their determination of the melting point of pure chromium was 1930°C (later revised to 1903"C)." Experimental Procedure and Results The chromium used for this study was electrolytic chromium, made available by the United States

Jan 1, 1956

By W. O. Philbrook, R. H. Spitzer, F. S. Manning

The steady-state operation of an isothermal, counter-current reactor in which a mouing bed of hematite particles is reduced by hydrogen has been modeled mathematically using a generalized single-particle kinetic formulation for topochemical reduction with formation of the intermediate oxides, wustite and magnetite. Reduction prof iles have been generated for various oper- REDUCTION of iron ore, as practiced industrially, approaches counter current, granular-bed operation. The total process is extremely complex. Quite under- ating conditions selected to demonstrate the influence of major variables such as gas and solid flow rates, bed length, and particle size. These profiles illustrate , among other things, that the reducing-gas requirement in a countercurrent bed hinges upon the iron-wüstite equilibrium or 'pinch-point" in much the same way as in a staged reactor. standably, nearly all research has been focused on reduction of single particles of oxide under controlled conditions. While this approach simplifies the problem by eliminating interparticle interactions, the remaining intraparticle transport and kinetic processes still constitute a most formidable challenge. Only within the last few years has knowledge of single-particle reactions been developed sufficiently to make modeling of counter current-bed reduction a realistic and useful study of process behavior. The authors have analyzed1"3 extensive laboratory

Jan 1, 1969

By W. H. Emmons

A DIATREME is a hole blown through a rock by gases, presumably of volcanic origin. Not all pipes of ore have formed by deposition of metals in such openings, but a con-siderable number have so formed. In this paper are described peculiar vein patterns that are believed to be incipient diatremes or "perforation pipes." Grading into this group is one showing thorough brecciation without rotation of fragments and into the latter a group of ore pipes showing brecciation with rotation of fragments-many of them with well rounded fragments. Also, volcanic craters or volcanic necks are explosion pipes. These may carry ore deposits along their contacts and some carry deposits within the pipes. As new data appear this group becomes increasingly impressive. It has been shown that veins are concentrated in and about cupolas of batholiths and that such veins commonly lienearly parallel to the long axes of cupolas as these are shown on plans. It would be supposed that conical cupolas would have radial patterns, but few vein systems exhibit radial patterns. It is probable that explo-sion pipes also may form in areas above conical cupolas. From these the gases escape more violently because the loads above them are less than above an elongated cupola where larger bodies of rock are affected. The hypothesis is sound mechanically, for the top of an elongated cupola is a line whereas the top of a conical cupola is a point.

Jan 1, 1938

By R. E. Cech

Metallographic observations on hydrogen-reduced nickel oxide crystals suggest that nucleation of nickel occurs at structural singularities in the oxide. The fully reduced structure contains micron-diameter, worm-like voids occupying 40 to 50 pct of the volume. The crystallographic orientation relationships between nickel oxide and nickel resulting from oxide reduction are recorded and discussed. THE process of reduction of oxide to metal is one of considerable complexity involving a chemical reduction reaction, mass transport of reducing agent to the point of reaction and of reaction product away from it, and finally a transformation whereby metal atoms released from the oxide rearrange to form a stable reduced phase. In addition, nucleation of the reduced phase affects the overall reaction kinetics. Thus far only the thermodynamic aspect of reduction has received the attention warranted by the importance of

Jan 1, 1960

By James E. Harding

The usual method of sampling mineral deposits is to drill holes and assay the sludge or core. Though the results thus obtained may not represent the true average value of the deposit, it is on these results that estimates of practically all large orebodies are made. In a large number of cases, the results of exploitation fall far short of the estimated value of the orebody. The standard method of making these estimates is to find the cubic contents of triangular prisms, in the apexes of which the drill holes are placed, by. multiplying the surface area by the average depth of the ore in the three drill holes and then multiplying the cubic contents by the specific gravity of the ore or rock to find the tonnage. The assay value is found by dividing the sum of the products of the depth of ore in each hole and the corresponding assay value by the sum of the depths of the ore in the three holes. As the latter part of this method is subject to many mathematical errors, it should not be depended on. Some engineers, therefore, use a discount factor, but as this factor is either arbitrarily selected or is obtained by obscure methods, the results are no better than guesswork. The standard method is correct when the drill holes are so laid out that the triangular prisms are equilateral in cross-section. But as ore deposits cannot always be drilled into at regular intervals and because of the human factor, if many holes are drilled, triangular prisms of all degrees of angularity are produced. In such cases it is necessary to assume that the influence of the different holes is not the same in all directions, which assumption of course is absurd. The area of the triangular prism is usually found by scaling; an ore-body of sufficient size to justify churn drilling is too large to be handled conveniently on maps having a scale larger than from 1000 to 1 to 1,500 to 1 and maps of such scales cannot be accurately measured. A variable is thus introduced in the first operation. In addition, the scaling is frequently done from blueprints, which sometimes shrink as much as 4 per cent. between printing, washing, and drying. The error due to scaling may be eliminated by surveying the location of each hole and

Jan 1, 1922