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By Abner Dixon

INTRODUCTION. IN India the production of mica, which in other countries is of very minor importance, is one of the staple, long established industries, and ranks high in the statistics of mineral products. Nearly two-thirds of the mica of commerce comes from India. The Indians have used mica for glazing and decorative purposes through many centuries. About 14,000 men are employed in and about the mines, and the indigenous and primitive mode of mining is still followed; but, by reason of the exhaustion of the surface supply hitherto won without intelligence or capital, it will not be many years before the present interesting and casual methods will be replaced by a less archaic and more profitable system. India on the whole has little mineral wealth, but the unique resources of its mica fields, cheap labor, and favorable natural conditions render it unlikely that any other country can ever more than temporarily contest her leadership in the production of this one minor but essential mineral. Mica plays a small but indispensable role in a variety of fields of dissimilar application. Its use and value depend upon characteristics which different kinds of mica have in varying degrees, each kind being adapted to 'its own special purpose. Its well-known characteristics of transparency, flexibility, elasticity, toughness, high dialectric, strength, perfect flatness; ease of splitting into thin films, ability to stand high heat and sudden changes in temperature, give it value in many industries. No other substance, natural or artificial, has this combination of qualities. The oldest use of mica is in glazing. By reason of the improvements in annealing glass, this is not now of great importance, but mica is still employed for the covers of ikon images in Russian churches, the windows of anthracite stoves, compass

Jan 5, 1913

By William Emmons

THE problem of the metalliferous veins has always been an outstanding one in the science of ore deposits. In recent years interest has been stimulated by Spurr, who maintains that veins have consolidated from magmas that have densities as great as the densities of ordinary rocks. Lindgren published a noteworthy paper1 in 1926, in which he supports the theory that veins are deposited chiefly by hot waters. Lindgren's paper was discussed by Singewald, Spurr, Kemp, Anderson, Colony, Bateman, Porter and others. The discussion, in the main, was centered on the interpretation of fragments that are included in veins. This paper also treats the problems of fragments in veins and includes a reply to a review by Spurr2 of a bulletin by Larsen, and myself published by the United States Geological Survey on the geology and ore deposits of Creede, Colorado. Mineral veins containing fragments of the wall rock are common. At many places the fragments are completely, isolated, one from the other, and are entirely surrounded by vein matter. It has been stated that the vein matter around the fragments was heavier than the fragments and that the latter were floated in a magma. J. E. Spurr, who is the leading advocate of this hypothesis,4 urges that normal mineral veins were deposited by solutions heavy enough to float fragments of the country rock, and it is mainly on this relation that he bases his theory that veins are deposited by solidification of magmas. If it can be shown that vein-forming solutions have a specific gravity greater than rock (2.77), one is justified in regarding them as true magmatic solutions. It is shown later in this, paper,. however, that at Lead, S. D., water not more highly concentrated' than ordinary drinking water is depositing vein matter around fragments of schist and of steel in such a manner that the fragments are completely isolated and completely surrounded by the mineral cement.

Jan 1, 1928

By Herbert Banks Johnson

During the past 10 or 12 years very little information has been made generally available concerning the commercial possibilities of separating materials by means of static electricity; and yet during that same period important improvements have been made in various branches of the science of electricity, which, when taken together, and applied to electrostatic separation, have resulted in important improvements in that art as well. For example, much improvement has been made in high-voltage electrical equipment such as full-wave vacuum-tube rectification and improved mechanical rectification. Great strides have likewise been made in the development of insulators for high-voltage work, not only in the materials used but also in the design of the insulators themselves. Again, in another field, the development of air-conditioning equipment has improved the technique of controlling the surface condition, through drying or humidifying, of the various materials that are passed through the electrostatic separator. In many authoritative publications and textbooks, the electrostatic separation process is declared to require a balance far too sensitive for general commercial application. For example, one publication1 in the past has referred to an unfavorable effect on the process caused by varying atmospheric conditions such as humidity. Some2 have even gone so far as to state that sunlight and shadows may seriously affect the separating efficiency of the process. Such statements may have been true in the early development of the art, when the source of static electricity was derived from a friction disk machine, such as the Wimshurst. The Blake Mosher equipment and the work of Huff in applying motor-generator sets, transformers and mechanical rectification overcame much of this kind of objection to the commercial application of the electrostatic separating process. Another objection made periodically is that it is generally considered necessary to feed the particles into the electrostatic field in a stream that

Jan 1, 1939

By Herbert Banks Johnson

During the past 10 or 12 years very little information has been made generally available concerning the commercial possibilities of separating materials by means of static electricity; and yet during that same period important improvements have been made in various branches of the science of electricity, which, when taken together, and applied to electrostatic separation, have resulted in important improvements in that art as well. For example, much improvement has been made in high-voltage electrical equipment such as full-wave vacuum-tube rectification and improved mechanical rectification. Great strides have likewise been made in the development of insulators for high-voltage work, not only in the materials used but also in the design of the insulators themselves. Again, in another field, the development of air-conditioning equipment has improved the technique of controlling the surface condition, through drying or humidifying, of the various materials that are passed through the electrostatic separator. In many authoritative publications and textbooks, the electrostatic separation process is declared to require a balance far too sensitive for general commercial application. For example, one publication1 in the past has referred to an unfavorable effect on the process caused by varying atmospheric conditions such as humidity. Some2 have even gone so far as to state that sunlight and shadows may seriously affect the separating efficiency of the process. Such statements may have been true in the early development of the art, when the source of static electricity was derived from a friction disk machine, such as the Wimshurst. The Blake Mosher equipment and the work of Huff in applying motor-generator sets, transformers and mechanical rectification overcame much of this kind of objection to the commercial application of the electrostatic separating process. Another objection made periodically is that it is generally considered necessary to feed the particles into the electrostatic field in a stream that

Jan 1, 1939

By N. Pessall, A. D. McQuillan

The phase relalionsllips in an isothernzal section of the Ti-Zr-H system at 750°Chave been investigated by measurement of hydrogen equilibrium pressures. The resulting diagram indicates that the hydride phase has an anomalously wide range of homogencity extending from 66.6 to 30 at. pct H in alloys containing about 15 al. pet Zr. Measurement of the heat of solution of hydrogen as a function of alloy composition in ß-phase alloys indicates no anomalous behavior in the region of 15 at. pet Zr, and suggests that the extensive range of homogeneity in the hydride phase at about this composition must he attributed to an enhanced stability of the, hydride phase. THE manner in which titanium and zirconium react with hydrogen and the constitutional diagrams of the two metal-hydrogen systems are qualitatively very similar,'-6 as can be seen from Fig. 1 which shows the constitutional diagrams of the two systems. Quantitatively, however, there are some differences. For example, the exothermic heat of solution of hydrogen in ß titanium is smaller than that in ß zirconium, and consequently the equilibrium hydrogen pressure of a Ti-H alloy is higher than a Zr-H alloy at the same temperature and hydrogen concentration. Other differences manifest themselves in the hydride phases which exist at high hydrogen concentrations. In the Ti-H system, above room temperature, there exists only a single hydride phase in which the metal atoms are arranged on a fee lattice, but in the zirconium system there are two hydrides, and whereas the hydride of lower hydrogen concentration has a fee structure, the higher hydride has a face-centered tetragonal structure. The tetragonal hydride retains its stability up to temperatures in excess of 450oC.7 From the foregoing, it would be expected that the constitutional diagram of the ternary Ti-Zr-H system would have a very simple form, especially as titanium and zirconium are completely miscible in both the a and ß forms.8 The present work, which consists of a study of an isothermal section of the ternary system, was carried out in order to check the assumption frequently made that the electronic structure of the two metals and the mechanism by which hydrogen is held in solution in the metals is the same for each. Although this proved largely to be true, certain inter esting and unexpected features of the ternary system emerged which must be explained before we can really say that the reactions of titanium and zirconium with hydrogen are fully understood. EXPERIMENTAL PROCEDURE The most convenient method of studying hydrogen-metal systems is by the measurement of the hydrogen pressure in equilibrium with the hydrogen dissolved in the metal as a function of hydrogen concentration and temperature. In binary systems, the results are easily interpreted in terms of alloy constitution, since two-phase regions can be recognized by the fact that the hydrogen pressure at constant temperature does not vary with the hydrogen concentration in the alloy when it is in the two-phase condition. This criterion does not apply in ternary systems, but there is usually a marked change of slope in the isothermal pressure-composition curves when a phase boundary is crossed, and with care, and a knowledge of the limiting binary systems, the phase structure of the alloys can usually be deduced. In the

Jan 1, 1962

By William B. Harris, Leonard Greenburg, Gustav Werner

Haulage in tunneling operations generally has been done with electric locomotives. As a rule, on short hauls the source of electricity is a storage battery mounted on the locomotive, which, of course, must be removed and recharged periodically. Where the distance from the recharging point to the tunnel face is very long, and where loads are heavy, trolley-driven locomotives are used. Diesel engines have been used in mining and tunneling operations in Europe for a number of years. The recent reports of studies in Belgium1 and by the Bureau of Mines in this country2-4 have indicated the potentialities of this form of power for haulage, mucking, bulldozing and many other underground operations. The hazards attending the use of Diesel engines in more or less closed spaces have long been known. The exhaust constituents that may create a harmful or objectionable environment are carbon monoxide, oxides of nitrogen and sulphur, carbon dioxide, aldehydes and smoke. Lack of precise information regarding the concentration of these gases and the ventilation requirements to reduce them to safe levels has to some extent suppressed their general acceptance in tunneling and mining work. Not until the work of the Bureau of Mines referred to above, and certain experience gained in the construction of the Delaware Aqueduct, ‡ has there been available the requisite information regarding the conditions under which their use may be permitted. This paper concerns itself with the successful operation of Diesel engines underground in the construction of certain parts of the Delaware Aqueduct, and describes the conditions under which Diesel engines have been found to operate with a minimum production of noxious gases. The test data reported were obtained during the operation of Diesel engines over a period of two years.* Studies by the New York State Department or Labor Exhaustive tests were made by the Division of Industrial Hygiene, of the composition of the exhaust gases given off by a Diesel engine mounted on a test block. These tests showed that certain' quantities of the gases are discharged from the exhaust. On the basis of these figures, preliminary requirements of design and control

Jan 1, 1943

By Gustav Werner, Leonard Greenburg, William B. Harris

Haulage in tunneling operations generally has been done with electric locomotives. As a rule, on short hauls the source of electricity is a storage battery mounted on the locomotive, which, of course, must be removed and recharged periodically. Where the distance from the recharging point to the tunnel face is very long, and where loads are heavy, trolley-driven locomotives are used. Diesel engines have been used in mining and tunneling operations in Europe for a number of years. The recent reports of studies in Belgium1 and by the Bureau of Mines in this country2-4 have indicated the potentialities of this form of power for haulage, mucking, bulldozing and many other underground operations. The hazards attending the use of Diesel engines in more or less closed spaces have long been known. The exhaust constituents that may create a harmful or objectionable environment are carbon monoxide, oxides of nitrogen and sulphur, carbon dioxide, aldehydes and smoke. Lack of precise information regarding the concentration of these gases and the ventilation requirements to reduce them to safe levels has to some extent suppressed their general acceptance in tunneling and mining work. Not until the work of the Bureau of Mines referred to above, and certain experience gained in the construction of the Delaware Aqueduct, ‡ has there been available the requisite information regarding the conditions under which their use may be permitted. This paper concerns itself with the successful operation of Diesel engines underground in the construction of certain parts of the Delaware Aqueduct, and describes the conditions under which Diesel engines have been found to operate with a minimum production of noxious gases. The test data reported were obtained during the operation of Diesel engines over a period of two years.* Studies by the New York State Department or Labor Exhaustive tests were made by the Division of Industrial Hygiene, of the composition of the exhaust gases given off by a Diesel engine mounted on a test block. These tests showed that certain' quantities of the gases are discharged from the exhaust. On the basis of these figures, preliminary requirements of design and control

Jan 1, 1943

By T. Sterry Hunt

This remarkable mine, to which attention has lately been drawn, is situated not far from the New River, in Ashe County, North Carolina, on a spur of the Blue Ridge which lies between the main crest of this name and the so-called Iron Mountain, a part of the Unaka or Smoky Mountain range. It is on a true fissure-lode, which cuts the strata of gneiss and mica-schist of the region. These, which have the lithological characters of what I have called the Montalban or White Mountain series, have here a dip of about forty-five degrees to the southeast, while the lode is vertical, with a course north 60' east. Both the country-rock and the lode, as is usual in this region, are decomposed to considerable depths; and the latter exhibits a cap of hydrous peroxide of iron or gossan, blocks of which, left by the denudation of the softer inclosing rock, are scattered over the surface, and first called attention to the locality as a source of iron ore. In sinking upon this lode, it was found that the porous gossan at a certain depth became charged with carbonate and red oxide of copper, and lower down was replaced by sulphuretted ores of this metal of remarkable richness. This deposit was worked for copper, in an irregular manner, before the late civil war, but was afterwards abandoned, and only reopened during the present year, by Messrs. S. S. & J. E. Clayton, of Baltimore. The outcrop has been traced for 1900 feet, and the sulphuretted copper ores have been met with in five shafts in a distance of 661 feet, a drift having moreover been carried for the above distance through the solid ore. The breadth of the lode, so far as opened, varies from six to eight feet to fourteen feet in places, and that of the outcrop of gossan is, in some parts, twenty feet. After comparing this deposit with the copper mines of Ducktown, Polk County, Tennessee, and those of Carroll County, Virginia, it is evident that we have, at Ore Knob, to do with the same kind of black ores as were met with in these mines, and will be noticed further on, Beneath the gossan, at Ore Knob, is found, in some parts, an iron-black, friable, drusy, crystalline, sulphuretted ore, inclosing grains of quartz, garnet, and magnetite, besides a black non-magnetic mineral, not attacked by nitric acid. This ore contains about 36 per cent. of copper, and portions have the mineralogical charac-

By W. P. Blake

FORGING under the hydraulic press, which was introduced by Haswell in the year 1861, at the machine shops of the Imperial State Railway Company of Austria, has since been greatly improved, so that at the present time there are very few parts of machines which cannot be produced in this way, and at no greater cost than iron castings. The process is now used at Vienna chiefly for such parts of locomotives as cross-heads, link-bars, axle-box frames, etc., especially where the form is intricate, and there are many angles and projections. These objects weigh from 50 to 150 lb. or more, and it is claimed for them that they are not only much cheaper than ordinary forgings, but are much more regular in form and stronger. The results which Mr. Haswell has attained, after years of patient experimenting, were well shown in the Austrian Department of the Vienna Exhibition by a collection of the pressed objects in iron and steel, just as they left the moulds, with some of them cut asunder longitudinally and the surfaces etched, so as to show the internal structure or direction of the grain. Through the courtesy of Mr. Haswell and his son I saw the hydraulic presses in full operation at the works, drawing down large Bessemer ingots, cutting them up into blocks of convenient size, and forming various parts of locomotives. They have two large hydraulic presses in use; the largest, with a piston 24 inches diameter, gives 1200 tons pressure, and the second, with an 18-inch piston, gives 600 tons pressure. The pressure in the pumps is 600 atmospheres. The action is vertical ; the piston descends upon the work, and for forging ingots is armed with a hammer-like head. An ingot of No. 7 soft Bessemer steel, which was forged in my presence, weighed 2030 lbs. One end being placed upon the anvil, the piston is brought slowly down and crowded into the mass as if it were putty or dough, forcing it each way, but chiefly in the direction of the length of the ingot, this being the narrowest section of the anvil and hammer. The piston is then raised and the ingot is moved forward for a second squeeze, and so on, until the first half of the ingot has been reduced in thickness, when it is turned on edge and the operation is repeated. The ingot is then turned end for end and forged until the whole length has been re-

Jan 1, 1874

By L. C. Snider

NO important discoveries of petroleum during 1932 are reported from Canada. New Brunswick, which has a small production from one field, was inactive, and the production showed a decline from 6600 bbl. in 1931 to about 6300 bbl. for the year 1932. The old fields in Ontario increased from 123,000 to about 131,000 bbl. Alberta showed a decline of more than one-third, from 1,413,631 bbl. in 1931 to about 913,000 bbl. in 1932. This decline was due principally to the restrictions placed on the flow of gas wells in the Turner Valley field, from which the crude naphtha is obtained that accounted for more than 93 per cent of the production of Alberta and for more than 80 per cent of the production of all Canada in 1932. The starting of new wells to the limestone that produces the naphtha-bearing gas was prohibited late in 1931, and only wells started before that time were finished during 1932. One well was drilled in the Turner Valley field to a depth of 7555 ft., establishing a depth record for Canada. It passed out of the Madison limestone at 5560 ft., and encountered showings of oil in the underlying formations, probably of Devonian age. Commercial production had not been established by the end of the year. Commercial oil wells were brought in in two areas in Ontario which had previously been considered as productive of gas only— in the Dawn gas field, Lambton County, and in Raleigh Township, Kent County. The discovery wells had initial productions of about 50 bbl. per day, but no production of major importance is indicated. In Alberta, outside the Turner Valley district, two wildcats were drilled northwest. of Lethbridge in the Keho Lake vicinity. Both failed to make commercial producers in the Madison limestone, but one was testing upper sands at the close of the year. Good showings of oil are reported. A very small production was found in the Madison limestone in a wildcat well on the Twin River structure southeast of Lethbridge and another well has been started near by on what is considered on geophysical evidence to be a better location structurally. About 15 locations were made on the Canadian side of the border north of the Cut Bank development in Montana.

Jan 1, 1933

By John W. King

Uranium ore was first discovered in the Edgemont district of the southern Black Hills in the summer of 1951. The discovery was not made known for some time, but after the news leaked out prospecting became intense, and several hundred claims were staked in the spring of 1952. The Hot Springs Sub Office of the Atomic Energy Commission was established at that time and airborne radiometric surveys were commenced by the Government and by private companies. During the succeeding summer another important discovery was made by private airborne surveys in the northern Black Hills, and the area favorable for uranium ore was expanded many times. Between that summer of 1952 and the present, many individuals and groups have explored, developed, and exploited their claims until now uranium ore is produced in significant quantities and substantial reserves have been developed. The Black Hills portion of the geologic map of the U. S. issued by the U. S. Geological Survey is shown in Fig. 1. Sedimentary formations are exposed as a series of cuestas and hogbacks in a roughly annular pattern with the older sediments resting on the pre-Cambrian core, which is exposed in the eastern and southern portions of the dome.

Jan 1, 1956

By T. S. Fuller

THE experiments described in this paper constitute the preliminary work of an investigation outlined to determine the combined effects of steam and temperature on the endurance properties of certain steels. Essentially of a fundamental nature, it was found necessary, in order to make the investigation comprehensive, to test materials treated to give a wide range of properties. The work reported deals chiefly with nickel steel with one series of tests including nitriding steel. Such a study involves numerous variables, and requires an endurance-testing machine of rather special design.

Jan 1, 1930

By W. W. Coffeen, K. E. Doud

A singular mineral extraction and processing operation is conducted by Metal & Thermit Corp. in Hanover County, Va. The mine presently produces aplite rock, rutile and ilmenite. The deposit lies in the piedmont plain about 25 miles northwest of Richmond. It first drew attention as a result of discovery of float rutile on the surface about 1910. About seven years prior to this, Metal & Thermit through a subsidiary. American Rutile Co., had begun producing rutile'and ilmenite from a deposit in Nebon County, near Piney River, where aplite rock and ilmenite are mined today. Because of the interest in titanium minerals and the similarity of the new deposit to the Nelson County deposit, Metal & Thermit became interested and eventually acquired the Hanover County deposit.

Jan 10, 1962

By B. L. Seegmiller

Horizontally stratified lithologies of certain open pit or strip mines create unique stability problems for mine operations. Such problems may result when specific lithologies, such as sandstone and shale, exist in final or long-term slopes. Slope instabilities may occur when a sandstone unit directly overlies a shale unit and ground water drains into the mine along the lithologic contact. In essence, the ground water erodes the underlying shales and undercuts the sandstone. Large sandstone blocks fail in a toppling mode and cause safety and cleanup problems. Use of rock reinforcement including chain link fencing, roof bolt mats, rock bolts, rock anchors, and shotcrete offers a possible solution to the problem.

Jan 1, 1985

By J. J. Rutledge

The United States Bureau of Mines established at Bruceton, Pa., in 1909, an experimental mine, for the purpose of testing the means of preventing and limiting mine explosions. During the last ten years numerous explosions have been caused to originate in this mine for investigative purposes and the rate of propagation of the explosion wave, the pressure developed per unit of area by the explosions, and the general results of the explosions have been carefully recorded and studied. Means of preventing mine explosions or of limiting them to the areas in which they originate have been developed. A great deal of valuable information has been derived from the work in this mine and much more useful and Valuable information will be obtained in the future. The writer would plead, not for the opening of experimental mines in all the important coal-producing fields in the United States, but for the opening of demonstration mines, or mines in which experiments could be made with the various details of coal mining. The United States Department of Agriculture has established, in nearly every state, stations that undertake experimental work for the benefit of the agricultural interests. In addition, small demonstration plats are set aside, in suitable locations in the farming districts, where various crops are grown under scientific direction, so that the faimers in the neighborhood can note the results obtained and profit thereby. Something like this should be done for the coal-mining induatry. If experimental or demonstration mines were established, methods of working adapted to local conditions could be worked out. Owing to competition in the same markets, small capitalization, or low profits, it may be an utter impossibility for any one company to try a new method of mining. Labor conditions may prevent the trial of a new method of working. It may be impossible or inadvisable to disturb existing working conditions for fear of causing trouble among the miners through real or fancied changes in the scale of wages. The first and most important investigation to be undertaken in these demonstration mines would be the trial of various methods of working coal mines until a satisfactory plan had been demonstrated for each

Jan 1, 1920

By Jill Dill Pasteris

Several mineralogical prospecting techniques are used in diamond exploration. Most are concerned with identifying indicator minerals such as pyrope garnet and magnesian ilmenite, which are derived from mantle xenoliths hosted by kimberlites. The first goal of such prospecting is to locate kimberlite intrusions; the second goal is to identify the diamond-bearing kimberlites. Explorationists have worked much less on the indigenous kimberlite phases. The kimberlitic opaque oxides, ilmenite and particularly spinels, promise to be useful in discriminating between intrusion episodes in identified kimberlites, and perhaps in the evaluation and prediction of diamond grades. Several petrologists have showed that spinel compositions and zoning patterns are specific to certain intrusive facies in South African and Canadian kimberlites. Careful evaluation may indicate a correlation between spinel parameters and diamond content.

Jan 1, 1984

By Thomas E. Howard

Recipient of the 1975 D. C. Jackling Award - "For his vision and initiative in defining, planning, directing, and accomplishing mining research programs; for his leadership in focusing worldwide attention on the need for research to improve underground excavation for mining and civil applications; and for his lecture. . ."

Jan 1, 1976

By C. W. Brown

In the author's experience and contact with engineering students the old form of recitations had grown into the lecture system in which the student was a passive receiver of digested material. Later, the tutorial system was developed because it was felt that the lecture system was breaking down. The student was too passive and was simply trying to absorb what was given him. The seminary method was then introduced and for the particular field the author believes that there is no better method, but that for 20 years he has been trying to change the attitude of the student in certain courses from a passive, almost noncommittal, to an active participation, to change him from a receiver to a doer. The student cannot look over the whole field. That must be presented by the instructor in charge. A topic such as structure or glaciation is taken up and from that standpoint are argued all the geologic problems that might confront the engineer. Problems relating to dams and foundations, and structures, tunnels and excavations, are particularly adaptable to the method. Usually, however, the problem comes to the engineer in more complicated form. By virtue of the character of the material the same topic cannot be assigned to the entire class. Different phases of the topic must be assigned. The greatest difficulty in after life comes in that the student cannot analyze the problem and has not the ability to see that there is a problem. He has had little or no training in the gathering of material and very little training in the arrangement of a report. Consequently, selecting different problems, putting them before small groups, and then starting the student on the way to make the knowledge of his particular topic an integral part of his own mentality, is something that will fix that part of the work firmly in his mind. Professor Brown has insisted on an introductory step in a great many classes, in that without the student knowning very much more than the general outline of the topic or problem, he is made in inductive fashion to take up the entire problem, look it over, and prepare an outline as far as he can; in other words, to expose the problem to his own mind. This preliminary outline is discussed with the student and if the arrangement or logic, with regard to the end in view, are faulty, he is shown where

Jan 1, 1929

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 J. R. Finlay

Every business man who has reached the age of forty, or perhaps even thirty, must know from his own experience that there are occasional periods of "good times'' and others of "bad times "-booms and panics. Those who give to business some complexion of science have invented a semiscientific name for these alternations-the business cycle-indicating that it is a normal phenomenon which by its own nature repeats itself. The longer one lives and the more one enlarges his own experience by the study of history, the more of these cycles he knows and the more disposed he becomes to take their recurrence for granted. If these alternations can be put into the category of common- places, why not treat them as such? We are in a sharp depression right now, why worry about it? Is there not a certain average value for business that can be depended upon in spite of depressions? By way of rejoinder one might answer that war is the great commonplace of history, but when we get into one we generally find it worthy of attention. In the present case, many a man has lost two-thirds of his income, and he is extremely nervous about finding it again. The Southern Pacific Railroad earnings have dropped 75 per cent in the past year; Pennsylvania, 60 per cent; United States Steel Corp., about the same. The drop in current earnings is

Jan 1, 1932