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By Joseph W. Roe

MANY questions arising in the work of the mining engineer may be solved quickly and with sufficient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool. for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of "innocuous desuetude " may lie in the unfortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer's attention in terms of every-day use they may prove of practical bearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in any way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To FIND THE STRIKE. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It will be assumed for the present that the vein is a plane.

Mar 1, 1910

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Jan 1, 1938

By F. S. McNicholas

In the first big blast at Climax, a "loop back" (three-wire system) was used (Fig, I), with the idea of securing a wiring system that would give to all series the same amount of current. Single-phase, 60-cycle, 13,800-volt power was furnished to the blasting transformers, each of which has a rated capacity of 600 amp. at 480 volts. Two blasting leads were taken from these transformers, giving a blasting current of single phase, 60 cycle, 480 volts, with an instantaneous capacity of more than 600 amp. The blasting switch was on the secondary leads from the transformers, to avoid lag in energizing them.

Jan 1, 1940

By F. S. McNicholas

In the first big blast at Climax, a "loop back" (three-wire system) was used (Fig, I), with the idea of securing a wiring system that would give to all series the same amount of current. Single-phase, 60-cycle, 13,800-volt power was furnished to the blasting transformers, each of which has a rated capacity of 600 amp. at 480 volts. Two blasting leads were taken from these transformers, giving a blasting current of single phase, 60 cycle, 480 volts, with an instantaneous capacity of more than 600 amp. The blasting switch was on the secondary leads from the transformers, to avoid lag in energizing them.

Jan 1, 1940

By J. Charles Miller

Natural carbon dioxide has recently been exploited in the United States in consequence of oil and gas developments in the Western States and the growing demand by transcontinental and transoceanic shippers for solid carbon dioxidc. The discovery by drilling of commercial deposits resulted in consideration of its geographic and geologic distribution and occurrence. Its wide distribution in nature is evidenced by its occurrence in the atmosphere, hydrosphere and lithosphere. The question of origin of carbon dioxide involves consideration of theories similar to those concerning natural hydrocarbons, although available evidence favors an inorganic rather than an organic source. Areas favorable to development of commercia1 production appear to be those in proximity to igneous rocks or in the vicinity of decadent volcanic activity, where, it has long been known, the gas is evolved either free or dissolved in the waters of fumaroles, geysers or mud pots. Structure contour maps are presented showing the Wagon Mound anticline in New Mexico and the Farnham anticline, Utah. A well drilled on the latter supplies gas to a 20-ton plant manufacturing solid carbon dioxide at Wellington, Utah, on the Denver and Rio Grande R.R., whence it is shipped to surrounding territory and to the West Coast. Before funds are invested in a plant for the manufacture of liquid or solid carbon dioxide, whether supplied by wells or springs, an effort to ascertain the volume of gas available is advisable. The use of present methods of estimation of gas reserves with modifications to account for the quantity absorbed by any water present in the producing formation is recommended. The Farnham anticline is used as an example and computations are made of the probable volume of gas originally present in the structure. No attempt was made to compute reserves in the Niland area, California, for the reason that in such areas it is believed the volume is indeterminate. Introduction Carbon dioxide, in liquid and solid form, has found a wide variety of uses other than its primary application in carbonating beverages. It is now used in more than 40 different ways, ranging from cooling or freezing to use in gas or liquid form for mechanical purposes, chemical industry, explosive, fire extinction, and tire manufacturing. Undoubtedly the chief supply of carbon dioxide is obtained from industrial plants or artificial sources and until recently natural deposits of the gas have received little consideration. Few will question the utility and perhaps dependability of artificial sources, which possess the advantage over

Jan 1, 1941

By J. Charles Miller

Natural carbon dioxide has recently been exploited in the United States in consequence of oil and gas developments in the Western States and the growing demand by transcontinental and transoceanic shippers for solid carbon dioxidc. The discovery by drilling of commercial deposits resulted in consideration of its geographic and geologic distribution and occurrence. Its wide distribution in nature is evidenced by its occurrence in the atmosphere, hydrosphere and lithosphere. The question of origin of carbon dioxide involves consideration of theories similar to those concerning natural hydrocarbons, although available evidence favors an inorganic rather than an organic source. Areas favorable to development of commercia1 production appear to be those in proximity to igneous rocks or in the vicinity of decadent volcanic activity, where, it has long been known, the gas is evolved either free or dissolved in the waters of fumaroles, geysers or mud pots. Structure contour maps are presented showing the Wagon Mound anticline in New Mexico and the Farnham anticline, Utah. A well drilled on the latter supplies gas to a 20-ton plant manufacturing solid carbon dioxide at Wellington, Utah, on the Denver and Rio Grande R.R., whence it is shipped to surrounding territory and to the West Coast. Before funds are invested in a plant for the manufacture of liquid or solid carbon dioxide, whether supplied by wells or springs, an effort to ascertain the volume of gas available is advisable. The use of present methods of estimation of gas reserves with modifications to account for the quantity absorbed by any water present in the producing formation is recommended. The Farnham anticline is used as an example and computations are made of the probable volume of gas originally present in the structure. No attempt was made to compute reserves in the Niland area, California, for the reason that in such areas it is believed the volume is indeterminate. Introduction Carbon dioxide, in liquid and solid form, has found a wide variety of uses other than its primary application in carbonating beverages. It is now used in more than 40 different ways, ranging from cooling or freezing to use in gas or liquid form for mechanical purposes, chemical industry, explosive, fire extinction, and tire manufacturing. Undoubtedly the chief supply of carbon dioxide is obtained from industrial plants or artificial sources and until recently natural deposits of the gas have received little consideration. Few will question the utility and perhaps dependability of artificial sources, which possess the advantage over

Jan 1, 1941

By H. M. Chance

(Butte Meeting, August, 1913.) ADEQUATE treatment of the difficulties surrounding the valuation of mineral lands requires that agreement be first reached defining value as understood for the purpose of appraisal. To define value as the price of a product is not sufficient, and does not assist us in using the factors that cause variations in values and in relative values. The real value of any product depends primarily upon its relation to the necessities, comforts and pleasures of mankind. As the necessities, comforts and pleasures of the civilized races differ-from those of more primitive man, the value of products varies with the degree of civilization and the environment of the consumer. Coal has no value to the savages of warm climates, and arrow-head flint none to the residents of New York. It has long been recognized that what has. been termed ?intrinsic value " must be limited to materials that are essential to existence-air, water, food. But " intrinsic value " cannot be measured in monetary terms. The intrinsic value of a bushel of wheat is due to the fact that it will support the life of an individual for a certain definite time, but this fact does not enable us to measure or to express that value in monetary terms. It has often been proposed to adopt as a measure of the value of any product the quantity of labor necessary to produce it, but this method is of limited application, and will not apply to what may be termed " intrinsic values." For many reasons it might be well, while assenting to the fact that any material may be intrinsically valuable, to abandon the use of the term "intrinsic value." One of these reasons is the tendency to confuse the idea of " intrinsic value with a value that is conferred by economic conditions, that is purely artificial and that may be permanent or evanescent. Intrinsic value must from its nature be permanent and unchangeable.

Jan 7, 1913

By Richard W. Smith

There are three distinct varieties of phosphate rock, in Tennessee, known commercially as: (a) the "brown" rock, which is the residual product of the weathering and natural concentration of certain phosphatic Ordovician limestones; (b) the "blue" rock, which is an unaltered phosphatic stratum of Mississippian or Devonian age; and (c) the "white" rock, which is the result of chemical replacement and deposition. Before 1894, South Carolina and Florida had supplied most of the phosphate of the United States, South Carolina leading until that date and Florida from then until the present time. In December, 1893, the blue phosphate of Tennessee was discovered almost simultaneously on Swan Creek, in Lewis County, by two independent parties—by one as the result of a careful and systematic search for a workable deposit of the long known kidney phosphate, and by the other through mistaking it for a "bloom" of coal. Leases were taken and, with further prospecting disclosing other deposits in the region, the development progressed as rapidly as could be expected without railroad transportation. In January, 1896, Judge S. Q. Weatherly, who was interested in the development of the blue phosphate, while riding along the road south of Mt. Pleasant, noticed some slabs of a brown rock in place above the limestone. He took samples, and had them analyzed, thus discovering the high-grade brown phosphate of this district. This discovery was kept a secret until July, 1896, when mining was started at the village of Mt. Pleasant. Development proceeded rapidly, many owners obtaining their capital by the sale of their rock fences, which were largely composed of slabs of high-grade brown phosphate. The development of the brown rock, which is richer and more easily mined than the blue, caused Tennessee to advance from a poor third in production to second, surpassing the output of South Carolina, and being excelled only by Florida.

Jan 1, 1927

By L. C. Aycock, J. Hunter, P. M. Lyons

In view of the unfavorable discovery trend that has set in during the past few years, it seems permissible to infer that the large, more easily found crude reserves in Louisiana are now known. Without doubt, many new producing areas will be located, but in the light of development during the past few years the majority of new areas probably will be found at greater depths and from relatively poorer sands. f Although sufficient reserves exist in Louisiana to last at the present rate of production for a considerable period, additional reserves must be found in more intensive development of the presently known structures. In order to ensure the greatest ultimate recovery from such structures, the most advanced technical methods must be employed in their exploitation. Wherever possible, cycling and repressuring plants should be installed. 'here are presently in Louisiana, especially in south Louisiana, a great many fields that contain gas-condensate reservoirs. These reservoirs cannot be produced for their liquid hydrocarbon content under present conditions without wasting an enormous quantity of gas and creating underground waste. Although some of these reservoirs are being produced, such production must be considered in the nature of a salvage operation rather than as a sound economic proposition. Such reservoirs, however, can become profitable ven- tures through the use of cycling and repressuring plants. Cycling operations now operating in Louisiana have increased the ultimate recovery from gas-condensate reservoirs anywhere from 10 to 30 per cent. Cycling operations will also provide a considerable reserve of gas, without which Louisiana cannot hope to develop any program of industrialization. During the past year, Louisiana attained the rank of third among the oil-producing states of this country. With a proper program of exploitation and development, and with emphasis on conservation, Louisiana can maintain this position for a great many years. Production On Dec. 31, 1943, oil and/or gas were being. produced in 52 parishes, or 81 per cent of all the parishes in the state. Thirty-three of the parishes produced oil and gas, 14 produced oil, and 5 produced solely gas. Tensas Parish in north Louisiana and Assumption Parish in south Louisiana formerly contained no producing fields but during 1943 joined the ranks of the producing parishes. Twenty-three new fields, including one rediscovery, were found during 1943-—a rate of discovery almost comparable to that of the preceding year. Eleven of these new discoveries were either gas or gas-condensate fields. Thus, the trend of development in finding new reserves was also comparable to that of 1942. Many reasons of considerable merit have been advanced to account for the discouraging lack of crude-oil reserves found during the past year. None are, however, completely satisfactory.

Jan 1, 1944

By J. Hunter, P. M. Lyons, L. C. Aycock

In view of the unfavorable discovery trend that has set in during the past few years, it seems permissible to infer that the large, more easily found crude reserves in Louisiana are now known. Without doubt, many new producing areas will be located, but in the light of development during the past few years the majority of new areas probably will be found at greater depths and from relatively poorer sands. f Although sufficient reserves exist in Louisiana to last at the present rate of production for a considerable period, additional reserves must be found in more intensive development of the presently known structures. In order to ensure the greatest ultimate recovery from such structures, the most advanced technical methods must be employed in their exploitation. Wherever possible, cycling and repressuring plants should be installed. 'here are presently in Louisiana, especially in south Louisiana, a great many fields that contain gas-condensate reservoirs. These reservoirs cannot be produced for their liquid hydrocarbon content under present conditions without wasting an enormous quantity of gas and creating underground waste. Although some of these reservoirs are being produced, such production must be considered in the nature of a salvage operation rather than as a sound economic proposition. Such reservoirs, however, can become profitable ven- tures through the use of cycling and repressuring plants. Cycling operations now operating in Louisiana have increased the ultimate recovery from gas-condensate reservoirs anywhere from 10 to 30 per cent. Cycling operations will also provide a considerable reserve of gas, without which Louisiana cannot hope to develop any program of industrialization. During the past year, Louisiana attained the rank of third among the oil-producing states of this country. With a proper program of exploitation and development, and with emphasis on conservation, Louisiana can maintain this position for a great many years. Production On Dec. 31, 1943, oil and/or gas were being. produced in 52 parishes, or 81 per cent of all the parishes in the state. Thirty-three of the parishes produced oil and gas, 14 produced oil, and 5 produced solely gas. Tensas Parish in north Louisiana and Assumption Parish in south Louisiana formerly contained no producing fields but during 1943 joined the ranks of the producing parishes. Twenty-three new fields, including one rediscovery, were found during 1943-—a rate of discovery almost comparable to that of the preceding year. Eleven of these new discoveries were either gas or gas-condensate fields. Thus, the trend of development in finding new reserves was also comparable to that of 1942. Many reasons of considerable merit have been advanced to account for the discouraging lack of crude-oil reserves found during the past year. None are, however, completely satisfactory.

Jan 1, 1944

By R. L. Bleifuss

Most pellets swell only slightly during reduction, but some swell so enormusly that their increase in size is termed catastrophic. Since catastrophic swelling produces irregularities in blast furnace operation, an understanding of the phenomenon is of practical as well as theoretical interest. Observations have shown that catastrophic swelling is characterized by the growth of a network of fine iron filaments. Evidence is presented to show that the growth of these filaments is promoted by the presence of calcium in the magnetite lattice of the original ore. During reduction, the limited mutual solubility of CaO and FeO produces an unstable condition that inhibits the uniform nucleation of metallic iron. Other elements in the magnetite lattice whose oxides are continuously soluble in FeO in the critical temperature range have no effect. Magmatic segregation or pyrometasomatic replacements are the most likely deposits to contain calciferous magnetite. Over the past few years there has been an increasing concern throughout the iron and steel industry over the tendency of pellets to swell during reduction. Although the tendency for swelling is only one of several attributes that determine the behavior of pellets in the blast furnace, swelling-reduction tests are now part of the normal evaluation procedure of many pellet consumers. During a swelling-reduction test, pellets display either the moderate increase in size known as normal swelling, or the enormous expansion known as catastrophic swelling. This paper is concerned with the origin and control of catastrophic swelling and how it is enhanced or inhibited by the presence of minor elements. Swelling Behavior The swelling behavior of pellets during reduction is indicated in Fig. 1. The lower curve represents normal swelling and the upper curve catastrophic swelling.' During the initial stages of reduction, that is, up to about 20-25% reduction, the two curves are considered to be equivalent. Beyond this point normal pellets undergo a gradual decrease in size with increased reduction. By contrast, pellets which exhibit catastrophic swelling show a second dramatic expansion between 25 and 70% reduction. The initial normal swelling develops as the hematite of the pellet is successively reduced to magnetite, and then to wustite. Work by Edstrom' and others has shown that the reduction of hematite to magnetite is accompanied by a 25% volume increase, whereas the magnetite to wustite stage shows a volume decrease. The volume increase overlaps the wustite field because magnetite is formed simultaneously with the wustite during topochemical reduction of the pellet. The catastrophic expansion is clearly related to the wustite, to

Jan 1, 1971

By Robert E. Tally

Underground fires have been common in the mines of the United Verde Copper Co. for the past 22 years. The first fire started in the 300 Hampton stope in the fall of 1894, following a cave in that orebody. The soft and highly pyritic nature of the ores is responsible for most of these fires. Since ore characteristics, methods of mining and ventilation, have an important influence on mine fires, they will be described in this paper. Orebodies The ores are mostly chalcopyrite except on the upper levels where considerable chalcocite, black oxides and other secondary minerals occur. The orebodies are in the form of lenses and vary in size. Some are small, while others are several hundred feet in length by a hundred or more feet in width. These orebodies extend, in some cases, from the surface to the lowest levels of the mine and usually at a steep angle of inclination. There are three different classes of ores, classified in accordance with the gangue rock. The copper in all cases, except as above specified, is in the form of chalcopyrite. The largest and most important of these reserves are in a pyrite gangue. Next in order of importance are the schist ores and lastly the quartz porphyries. The pyrite, locally termed iron ores, average from 30 to 42 per cent. sulphur. The schist and quartz porphyries vary from 3 to 25 per cent. sulphur. Mining Methods All the orebodies were worked by the overhand square-set method of mining prior to 1908; since then the cut-and-fill, shrinkage and mill-hole systems have been largely employed. But 15 per cent. of the total tonnage now extracted is from timbered stopes. Most of this is from the upper levels where the ore is soft, heavy and more or less broken to the surface. Large reserves of these ores are being conserved for more efficient methods of mining.

Jan 1, 1917

By Robert Gorham Morse

This paper presents the results of an investigation made in the metallurgical laboratory of Columbia University, New York City. The object of the investigation was to determine how the tensile strength, the elastic limit, and the size of the grain, of a pure medium-carbon steel are affected by heating to successive temperatures between 500° and 1300° C., with slow cooling therefrom. Since Dr. Sorby's first investigations into the microstructure of steel, the study of the subject has been continued by Professor Martens, Mr. F. Osmond, Professor Arnold, Professor Howe, Mr. A. Sauveur, Mr. J. E. Stead, and many others. Among many valuable and interesting papers I mention the following as having a special bearing upon this investigation.* " Microstructure of Steel," by Albert Sauveur, Trans., xxii., 546 (1893); Microscopic Metallography," by F. Osmond, Trans., xxii., 243 (1893); "The Microstructure of Steel and the Current Theories of Hardening," by Albert Sauveur, Trans., xxvi., 863 (1896); "The Crystalline Structure of Iron and Steel," by John Edward Stead, J. Iron and Steel Inst., 1898. II.—Statement of Experiments. Through the kindness of Mr. N. Lilienberg, New York City, round rods 3/4 of an inch in diameter were obtained, which had been rolled from one ingot. The analysis of the steel was as follows : C, 0.343; Si, 0.027; Mn, 0.221; I?, 0.0266; S, 0.0037 per cent.

Jan 1, 1900

Jan 1, 1903

By Waldemar Lindgren

Jan 1, 1905

By Norman Pilling

The micrographic analysis of silicon steels is possible if a dilute solution of nitric acid and methyl alcohol in nitrobenzol is used. The action of this reagent differs from that of sodium picrate in that there is no persistent deep-seated staining and the solution is used cold. THE technical difficulties hampering the metallographic analysis of silicon steels are chiefly the result of the extreme corrodibility of these alloys. The addition of silicon to iron in increasing quantities, up to about 6 per cent., rapidly increases the susceptibility of the alloy to chemical attack, not only in acid solution, but in water. This renders the preparation of metallographic sections very difficult, because of a non-selective attack upon the finely polished surface by the water used as a lubricant in polishing. This water attack masks the true structural details revealed by suitable etching reagents. It is thus necessary to use alcohol as a polishing lubricant in the last stages of preparation and to avoid all etching reagents having an aqueous base. A specific reagent for the identification of iron carbide in ferrous alloys, and the one hitherto used almost exclusively by metallurgists, is an alkaline aqueous solution of sodium picrate, which stains this constituent selectively. Its application to silicon steels has not proved successful, as its distinctive selective action is more or less completely hidden by the general attack of the aqueous solvent on the silico-ferrite, greatly accentuated by the fact that this reagent must be used at its boiling temperature (105° C.). Thus, a powerful metallographic aid to the study of the higher silicon alloys, such as transformer steels, is lost. A new reagent has been developed for the purpose of overcoming this difficulty. It is with some hesitation that the list of etching reagents, already overburdened, is increased, but the properties of this new reagent are advantageous in several ways and a definite field for it may be found in the metallography of ferrous alloys.

Jan 1, 1924

By J. L. Bruce

AFTER six years of war-enforced idleness, Cyprus copper mines are operating again. This relatively long shutdown seems infinitesimal when compared with something like seventeen hundred years of inactivity that followed the important operations of the ancient Romans, and continued until the twentieth century. The historical records of the ancient operators are scarce but full of interest to those who realize that Cyprus copper production was important more than two thousand years ago. This paper, however, will give only a brief review of the ancient history and the evidence of ancient mining which have been quite fully covered in other publications.1-6 The purpose of this paper is to give a general sketch of the Cyprus Mines Corporation's enterprise in the Island of Cyprus, with special emphasis on those conditions and practices which are unusual. The picture is not intended to be complete, and many interesting details will be omitted. Some of these may be described in subsequent papers covering departmental practices. The principal operations of Cyprus Mines Corp. are in Cyprus, where it has leasehold concessions from the Cyprus Government covering about 50 square miles. It holds additional areas under "Prospecting Permits." The consideration for the concessions is a royalty on production, coupled with minimum annual rentals. Cyprus is a British Colony in the Eastern end of the Mediterranean with an area of about 3000 square miles and a population of about 400,000, of which 65 pct may be classed as Greeks on the basis of language, religious training, and traditions. About 25 pct are Moslems, principally of Turkish extraction. Prevailing languages are Greek and Turkish. A large proportion of the supervisory and administrative staff and practically all of the skilled and unskilled craftsmen and laborers are drawn from the native population. The "overseas" staff constitutes not more than 2 pct of the employees. The majority of these are from the United Kingdom, the British Dominions and Colonies. About one-third are from the United States of America. The topography of the Island is rugged, with mountains and foothills covering more than two-thirds of the area. Between the Kyrenea range rising to 3000-ft elevation, along the north coast, and the Troodos range (maximum elevation 6400 ft) occupying the southwest half of the Island, lies a cultivated rolling plain, the "Mesaoria," dry in summer and watered only by the winter rains and by scanty irrigation from small mountain streams and wells in the spring and summer. Climate and natural vegetation are characteristic of semi-arid conditions. The "urban" population, about one-fourth of the total, lives in the five port towns, Famagusta, Larnaca, Limassol, Paphos and Kyrenia, and in the capitol Nicosia, near the center of the Island. The suburban population lives almost entirely in villages or small towns, with very few people residing in isolated country homes.

Jan 1, 1947

By R. B. Yerxa, C. F. Green, H. O. Hofman

MASSACHUSETTS INSTITUTE OF TECHNOLOGY, In refining copper, the metal is melted down in a reverbera tory furnace in a more or less oxidizing atmosphere and then further subjected to an oxidizing smelting in order to eliminate the common impurities, most of which have a stronger affinity for oxygen than has copper. In these operations some of the copper is oxidized to cuprous oxide and dissolved by the metal bath. When the quantity of dissolved cuprous oxide has reached about 6 per cent, the metal is said to have been brought to " set-copper." A button-sample will show a depressed surface and, when broken, a single bubble at the apex of the depression; the fracture will be brick-red and dull. It is essential to carry the oxidation to this point in order to know that the impurities have been oxidized as far as it is possible under the given working-conditions. Nearly all the cuprous oxide of the set-copper is now reduced to the metallic state by poling, when "tough-pitch" copper will be obtained. A button-sample will show a flat surface. Upon breaking, it will be found that the former bubble has disappeared and that the fracture has become rose-colored and shows a silky luster. The quantity of cuprous oxide allowed to remain in the copper will vary with the impurities still present in the metal and with the degree of pitch that it is desired to reach. It is essential for the general physical and the mechanical properties of the resulting copper that such impurities as arsenic, antimony, bismuth, lead shall be present in the oxidized state, as they are

Jan 1, 1904

Jan 4, 1953

By DeVerle P. Harris

Risk for most mineral investments is greater than that of average business ventures, because the physical and economic characteristics of the mineral deposit are never known with certainty. Inasmuch as the merits of a potential mineral investment cannot be fully appraised without consideration of the impact to the investor of the possible unfavorable events associated with the adoption of the project, methods of risk analysis are important in project evaluation and investment selection. The conceptual framework for risk analysis and the means by which some of the recommended practices might be implemented are examined. In addition to the normal business risk due to market forces, the physical and economic characteristics of the mineral deposit are never known with certainty, for only partial or indirect information is available, such as data from drill cores or surface and underground workings. Consequently, risk for most mineral investments is greater than that of average business ventures. Inasmuch as the merits of a potential mineral investment cannot be fully appraised without consideration of the impact to the investor of the possible unfavorable events associated with adoption of the project, methods of risk analysis are important in project evaluation and investment selection. This paper examines the conceptual framework for risk analysis and means by which might be implemented some of the recommended procedures. Utility Theory A discourse on risk and its impact upon investment selection quite often leads the reader into the concept of utility theory, for utility theory is a device constructed by economists to measure the satisfaction an individuai receives from a good; in the case of investment analysis, that good is the outcome of an investment. It briefly is reviewed here to describe the reaction of the individual to risk and as a stepping stone to other techniques more suited to risk analysis at the level of the firm. Utility theory proposes that an investor possess a utility map (curve), such as indicated in Fig. 1, which indicates the value in utiles of potential monetary rewards to an individual with some specific endowment of resources. Points on this map are obtained from the following relationship:

Jan 1, 1971