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Ocean environmental factors are an intriguing new set of parameters to be dealt with in the prospecting and exploration phases of resource development for both the continental margins and the deep ocean. While information and data gathering programs for ocean minerals would parallel onshore procedures, their costs generally run higher. Commercial Prospecting-Identification of Mining Sites Two modes of prospecting can be identified-commercia1 prospecting (in which the ultimate objective is to define potential mining sites), and scientific prospecting, which is conducted with different objectives in mind. For ocean exploration, both types of prospecting are carried out prior to the obtaining of any exclusive rights to explore and exploit a specific deposit. Deepsea's John Flipse adds: "Any commercial prospecting program should by its very nature require the freedom to search wherever minerals might occur with maximum flexibility."

Jan 4, 1975

By G. A. Vissac

The drying of fine coal involves special techniques, which are discussed and analyzed. Types of dryers employing these techniques are described. Calculations are presented for new methods of deal ing with the entrained dust that is always present in fine coal drying operations.

Jan 10, 1953

By C. J. Bonnecarrere, P. A. Jr. Bloomer, J. Hunter

Since 1941 not more than 15 per cent of aii wildcat wells drilled in Louisiana have been successful. This figure is not too discouraging, especially in view of the fact that during the same period approximately 80 per cent of all wells (average 701 wells per year) drilled in or adjoining producing areas were successfully completed. However, a somewhat discouraging aspect concerning Louisiana's wildcat completions is that in 1942 only 12 out of 20 fields found were oil fields; in 1943, only 13 out of 24; and in 1944, only 8 out of 21. This means that an operator has less than a 50:50 chance of finding an oil field. In other words, it is more likely that he will find a gas-condensate field. This fact has become increasingly evident as the data for each year are compiled and compared. Yet, strangely enough, operators are reluctant to accept this fact and plan accordingly. Certainly they cannot continue to search for oil fields and, for the most part, end with shut-in gas-condensate wells. The reason for shutting in is that there is no immediate and satisfactory market for all the gas being discovered. The solution, and it is a very satisfactory one, as experience in Louisiana has already demonstrated, is cycling. The advantages of this type of operation of gas-condensate fields, especially where the entire field is pooled and unitized, should be self-evident. These advantages will become increasingly more important, especially now that legislatures, regulatory bodies, royalty owners, and others are beginning to realize that "reasonable development" in a field is not indicated by the number of wells completed, but rather by the method of development. To complete a great many wells that can produce at only, partial capacity is waste. Producing hydrocarbons from these wells and not subjecting them to processing by surface operations, in order to recover all liquefiable hydrocarbons, is waste. Permitting bottom-hole pressures to drop or gas-oil ratios to increase because of excessive production is waste. Loss of leases and of wells because of inability to produce or to meet lease obligations is waste. Therefore, it is becoming increasingly apparent that a reservoir entirely pooled and unitized with a minimum number of completions, but over which there is exerted careful control so as to provide maximum recovery and the processing of all hydrocarbons brought to the surface, is the only logical and reasonable method of developing a gas-condensate field. Oil Production Twenty-one new fields, including three rediscoveries, were found during 1944. Three of these new discoveries—Delhi in northeast Louisiana, Good Hope in southeast Louisiana, and West Tepetate in southwest Louisiana—should add considerably to Louisiana's oil reserves. The other discoveries were either gas condensate or of apparently little consequence. State-wide productioll for 1944 was 1366 million barrels of crude oil and condensate; amounting to about 8.1 per cent of the

Jan 1, 1945

By John R. Dyni

Colorado nahcolite deposits, estimated at 29 Gt, formed in an asymmetric permanent-lake basin whose waters were rich in algae and sulfate-reducing bacteria. Nahcolite (NaHCO3) occurs in oil shale of the Green River Formation (Eocene) as aggregates (62%), disseminated crystals (24%), and impure beds (13%). Because much of the nahcolite is nonbedded, it will be mined with oil shale and can be concentrated to marketable grade by crushing and screening. Impurities in nahcolite are kerogen, quartz, pyrite, and carbonate minerals. A promising new market for nahcolite is in the process of removal of sulfur dioxide from industrial stack gases. When heated, nahcolite reacts with sulfur dioxide to form sodium sulfate. Differences in thermally induced microporosity may explain why nahcolite is more reactive than trona, a Possible competitor with nahcolite for SO2 removal. Limited production of nahcolite at one or possibly two localities is expected in the next several years, but large-scale production is probably at least 10 years away.

Jan 1, 1982

According to Vorwärts, the German Mining Commission sent to ascertain the damage done to the mines of France says that the work of restoring these mines will furnish work for all the unemployed in Germany for the next 8 years. The commission said the work of reconstruction would have to be clone from. "the ground up," especially in the Departments of Pas de Calias, Courriere, Lens, Lievin, Drocourt, Mourchin, Carvin, and Dourgas, where the destruction was pronounced "terrible." Most of the mines have been "drowned," and in rebuilding new shafts would have to be protected against the inward pressure of water. The Germans declared the work of restoration would not only be one of great difficulty, but that in many cases it was impossible to ascertain the extent of the damage clone to each mine. They also said it was not easy to fix responsibility for the destruction because it was done by nu-merous groups of troops and the records showing where each military unit was located and at what period were not complete or available.

Jan 12, 1919

By John K. Hammes

INTRODUCTION This introductory paper presents a description and definition of what the finance function is and what it specifically means for the mining industry. In its simplest terms, finance is, "management of money matters". As an area within the discipline of business administration it draws heavily on the related fields of economics and accounting, and to a lesser extent on marketing and production. MINING FINANCE DEFINED In preparing to write about what finance means to the mining industry, I asked a number of mining people the question, "What does mining finance mean to you?" Most responded that mining finance was "How a company borrowed money for mine development", and perhaps half those questioned included "raising equity" in the definition. It is not surprising that the mining industry concept of finance is the providing of funds needed for the objectives of the business, for that was once a view shared by authorities in the field of business administration. Further, it is certainly the area where much of the emphasis has been placed in the past ten to fifteen years as the industry struggled with the development of more remote and more refractory or lower-grade orebodies while profitability and internal cash flow were below expectations. No wonder project finance became such a popular topic. Twenty years ago it is probable that the emphasis would have been on mine valuation, for that subject was the area of finance then most often examined in industry publications. Papers concerning the pros and cons of payback, internal rate of return, and discounted cash flow appeared regularly. Let's examine the following situations, each the result of a financial decision: - Funding the exploration program in a developing country was accomplished by buying the next six-months budget needs in local currency. One week later the currency devalued 30 percent. If the purchase had been delayed or the local currency borrowed short term, a substantial saving would have been made in funding the program. - A major mining company borrows heavily to finance both expansion of its primary mining business and its entry into several new industry segments. When markets for all of the commodities it produces turn down for a prolonged period, there is concern over the adequacy of cashflow to cover debt service in addition to other company needs. The company's financial officers, however, had arranged very large committed credit facilities from numerous financial institutions which assured the availability of funds for several years. This enabled the company to implement a strategy to conserve cash, sell assets and survive until conditions improved. Further, short term suppliers of credit also were comfortable with the assurance that longer term credit was there to support them. -A medium size mining company financed several mines independently with limited obligations on the part of the parent company. The company decided to refinance the operations under one agreement. More flexible terms, lower interest cost and a longer tenor financing were achieved in return for assuming the risk as a direct obligor. - The exploration and development group of a large mining company proposes to develop a new mine in a country in which the company does not presently operate. When the investment is rejected they are advised that one reason was that the reinvestment assumption inherent in the discounted

Jan 1, 1985

By Albert R. Ledoux

In Great Britain all analytical chemists are styled assayers, but in the United states a slight distinction is made, assayers being considered those analytical chemists who have chiefly to do with the determination of the precious metals. There have grown up around the assayers of precious metals a number of customs and traditions which, as a rule, do not fetter American chemists when called upon to determine the composition or constituents of any samples submitted to them for analysis. In Great Britain, on the other hand, trade-customs even go to the extent of enforcing the employment of an admittedly erroneous atomic weight in certain alkali-determinations. If the American chemist is asked to determine the amount of lime in a water, potash in an alkali, or silica in an ore, the owner of the sample does not presume to suggest what method he shall employ, nor does he question his report on the ground that he should employ another method. But even in America it is different with the assayer. Unfortunately for the guild, as well as for those who have to base business operations on the reports of assayers, customs and traditions as well as divergent interests seek to circumscribe him in his choice of method and sometimes dictate how he shall perform his operations. This was true at one time of copper, which to-day in England is still determined by the so-called Cornish fire-assay, an attempt to imitate in the laboratory the various metallurgical operations in the smelting-works; but nowhere in this country is the assayer forced to employ any particular method for determining copper so long as his certificate indicates the true total percentage of copper in the sample. It is true that both buyers and sellers demand use of the electrolytic method, but only because it is the most accurate. In America the trade accepts the assayer's statement as final, and makes

Jan 1, 1895

By E. D. Williamson

DURING the wartime rush to prepare the glass necessary for the needs of our army and navy, the problem of the temperature control of the annealing kilns became most serious. The narrow limits of strain allowable (all the specifications called for less internal strain than the average of the previously used German glass) made necessary a very exact procedure and the methods had to be used on a much larger scale than theretofore. At the Charleroi plant of the Pittsburgh Plate Glass Co., the members of the staff of the Geophysical Laboratory, which was cooperating with the company, had occasion to study the methods available, and reached a number of conclusions (many of them by no means new except in their application) that may interest and assist those who have to meet similar problems in other fields. The following is a short account of the essential features of the system of temperature control evolved, along with a rather abridged statement of the reasons that led to the adoption or rejection of various schemes.

Jan 8, 1919

Albin, B. R Billings, Mont. '28 Amster, Nathan L . , 25 Broad St, New York, N. Y. '28 Bache, Jules S 42 Broadway, New York, N. Y. '28 Barrett, C. P 5338 Harper Ave, Chicago, Ill. '28 Baum, Frank G Hobart Bldg., San Francisco, Cal. '28 Bayless, Ron. William S Russ Bldg , San Francisco, Cal. ' 28 Bean, Louts H., V.P., Dwight P. Robinson & Co, Inc 125 E. 46th St, New York, N Y. '23 Beatty, Ross J 1105 First National Bank Bldg., Chicago, Ill. '28 Benwell, Oswald F 205 Colorado National Bank, Denver, Colo. '28 Beymer, Albert S., V.P., Keystone National Bank Pittsburgh, Pa. '28 Bingham, Charles W 1542 Hanna Bldg, Cleveland, Ohio. '28 Blumenthal, Hugo 44 Pine St, New York, N. Y. '28 Boettcher, Charles Ideal Cement Bldg., Denver, Colo. '28 Bowlus, Thomas H Iola, Kans. '28 Bragg, E. B Carmel, Cal. '28 Brown, Colvin B Chamber of Commerce, Washington, D. C. '28 Burt, Maxwell Struthers Southern Pines, N. C. '28

Jan 1, 1923

By R. T. Gallagher, C. G. Brennecke

This paper is the result of a research program entered into cooperatively by the General Reinsurance Corporation and Lehigh University in January 1944. The research program was instituted to find a more positive method to determine the presence of hazardous roof conditions in mining operations. The co-authors, together with Mr. R. D. Currie, Engineer for the General Reinsurance Corporation, started working on the project in January 1944, first undertaking a library search; second, a preliminary study based on some existing equipment; third, the design of new and more suitable equipment; and finally, the field testing of equipment and methods. PURPOSE Any study of the accident statistics of mining operations will disclose the rather startling fact that approximately 50 to 60 per cent of all fatal underground accidents in the anthracite and bituminous mines are caused by falls of roof and coal, the metal and nonmetal mines showing only a slightly smaller percentage. Advancements in safety engineering have produced definite results in the decrease of accidents due to blasting, haulage, electricity, and explosions but no such decrease is shown in those caused by falls

Jan 1, 1946

By Joseph L. Patrick

Geologic exploration, which has experienced an upward trend in the United States since 1962, continued with increasing activity through 1965. New, spectacular discoveries of recent years and continued questionable economic and political climates in many areas of the world have continued to focus the exploration attention of an increasing number of companies on the United States. Traditional geologic field methods are being bolstered by development of new methods, techniques and geophysical instruments. Reports from the states emphasize that successful exploration is dependent upon the combined effort of geochemistry, geophysics and geology, with high quality laboratory support of the field effort becoming increasingly necessary. PROGRAMS NOW UNDERWAY IN WEST During 1965 mineral exploration reached an all- time high in Nevada. Although examinations are being carried on throughout the State, much of the work is limited to two areas. The first area to attract recent exploration interest, initiated by discovery of the Carlin gold mine by Newmont Mining Corp., is an area of windows near the leading edge of the Roberts Mountains thrust fault in northeastern Nevada. Included in this area are the old camps of Mountain City, Battle Mountain, Cortez, Mineral Hill and Eureka. Major mining companies are using a combination of surface mapping, geochemistry, geophysics (largely induced potential surveys), following up with drilling. The second area of exploration is along the Walker Lane, a wide shear zone that parallels the Nevada-California boundary from Virginia City to Las Vegas. Activity has been intense in the Tonopah-Yerington area. Discovery of a large copper-iron deposit following an airborne magnetometer survey first focused recent attention on Walker Lane. Sixteen major companies are involved in exploration in the State.

Jan 2, 1966

The Western World's gold reserves now exceed 23,000 mt (750 million oz), 65% of which exist in South Africa. Although several major mines are reducing production or closing because of depletion of reserves, new mines or expansions of existing mines are coming on-stream which will maintain an annual production of 684 mt (22 million oz) of gold well into the 1990s. These new operations by the South African mining industry represent the largest expansion since the opening of the Witwatersrand gold fields in 1886. Included in three new mines being opened is that of Anglo American Corporation's Elandsrand plant, their fir& new gold venture in South Africa in seventeen years. Current average grade of South African mines is 8.2 g Au per mt (0.24 oz per st); and while the cost of the Elandsrand 135,000 mt (149,000 st) operation, including mine development, was about $314 million, it is estimated that the cost of a comparable operation started today and completed in the mid-1980s would be of the order of $480 million. New mines to exploit low-grade ore bodies are, therefore, likely to be few in number, and further expansion will undoubtedly be in the form of extensions to existkg operations where cash flow can be used to finance development. The authors' first monograph, "Gold and Silver Cyanidation Plant Practice," devoted a section to South African cyanide plant operation; and it is believed that this new volume would not be complete without a description of Elandsrand, South Africa's newest gold plant. The Elandsrand mine is adjacent to Anglo American's Western Deep Levels on the Far West Rand. The decision to go ahead with the development was taken in mid-1974 from the results of exploration drilling carried out over a period of .lo years. Results of 17 bore holes and 68 intersections of the Ventersdorp Contact Reef had indicated a gold-.bearing reef less than one meter thick at a depth of 1,800 to 3,000 meters (5,900 to 9,840 ft). Preliminary studies indicated a mine of 900 km (560 miles) of underground workings would yield 725,000 kg (23. 3 million oz) of gold from 60 million mt (66 million st) of ore to be milled over a period of 34 years. Eventually, when the mine is in full production, the total hoisting capacity will be 300,000 mt per month (331,000 st) for a milling capacity of 225,000 mt per month (248,000 st). The Elandsrand surface facilities have been built on a low range of 0 hills to take maximum advantage of the 10 slope in transporting ore

Jan 1, 1981

By Walter A. English

The four papers making up this symposum have been prepared especially for those who have no knowledge of seismograph prospecting. To many people mathematics is a formidable subject, and many are discouraged from studying seismograph prospecting under the mistaken assumption that the mathematical requirements are severe. In the papers presented here there is not a single mathematical equation. We believe that considerable competence in dealing with some of the most important problems of this work can be attained without any mathematical training whatever. At the present time, there is a real need for interpretation of results by persons thoroughly competent to bring geologic experience and imagination to bear on data that are subject to multiple interpretation from a strictly physical viewpoint. Likewise, those charged with the responsibility of planning seismograph exploration campaigns would do well to become familiar with as much as possible of the technical aspests of the work. They would then be in better position to judge of its success in individual cases. It has often been said that the seismograph is a new structure-finding tool for the geologists to use. Using a tool and using its product are two different things. One does not use an automatic screw-threading machine when he buys a box of screws at the hardware store. Neither does the geologist

Jan 1, 1940

By Walter A. English

The four papers making up this symposum have been prepared especially for those who have no knowledge of seismograph prospecting. To many people mathematics is a formidable subject, and many are discouraged from studying seismograph prospecting under the mistaken assumption that the mathematical requirements are severe. In the papers presented here there is not a single mathematical equation. We believe that considerable competence in dealing with some of the most important problems of this work can be attained without any mathematical training whatever. At the present time, there is a real need for interpretation of results by persons thoroughly competent to bring geologic experience and imagination to bear on data that are subject to multiple interpretation from a strictly physical viewpoint. Likewise, those charged with the responsibility of planning seismograph exploration campaigns would do well to become familiar with as much as possible of the technical aspests of the work. They would then be in better position to judge of its success in individual cases. It has often been said that the seismograph is a new structure-finding tool for the geologists to use. Using a tool and using its product are two different things. One does not use an automatic screw-threading machine when he buys a box of screws at the hardware store. Neither does the geologist

Jan 1, 1940

By Sylvain Pirson

THE number of seismograph field crews employed in the active survey of potential oil territories is still on the increase, owing to the ever pending threat of a shortage in the supply of crude oil. It is to be expected that for years to come the seismograph will be responsible for discovering many new oil fields, both in wildcat territories and in deeper formations, and that the seismographic campaign will go on unabated. Yet improvements in instrumental design, in the field and interpreta-tive techniques, are brought about year after year, and lead to the reshooting of areas many times surveyed previously. Notwithstanding the experience gained by the past eight years of active work in reflection seismographic surveys, the results given by this method of mapping deep formations have in many instances been at variance with the information subsequently obtained by the drill. To overcome this shortcoming, geophysicists have used closer spacing of the shot points and closer control of the depth points. The method dis-cussed here is being used actively in the Mid-Continent region and endeav-ors to reduce the interpretation work to a mere mechanical technique, leaving as little as possible to the opinion of the interpreter.

Jan 1, 1937

By E. S. Bardwell

DURING the period extending from May, 1922, to September, 1923, the copper-refining furnaces of the Great Falls Reduction Department of the Anaconda Copper Mining Co. at Great Falls, Mont., were operated exclusively with pulverized coal as fuel. The installation was made first as an experiment. It proved successful from the start and was abandoned solely because fuel oil from the Sunburst field became available at a price sufficiently low to make its use desirable from an economic standpoint. The equipment required for pulverized coal has, however, been kept intact and is available for immediate use should the oil supply fail. Inasmuch as pulverized coal had been used on two large reverberatory smelting furnaces and was, at the time we were considering its application to the copper-refining furnaces, being used on the Wedge furnaces roasting zinc concentrate for the electrolytic zinc plant, we were equipped with a coal-pulverizing plant of ample capacity to supply pulverized coal for the furnace refinery. The only problem was to devise suitable means for transporting pulverized coal from the pulverizer plant, located in the smelter building, to the refinery about 1000 ft. distant and about 150 ft. above the level of the pulverizer plant. When studying this installation, it should be borne in mind that the layout represents an adaptation suited to the existing conditions at this particular plant. The installation was entirely satisfactory and uniformly dependable but might be modified to advantage from an operating point of view if an entirely new installation were being planned.

Jan 9, 1925

By John M. Gallow

Discussion of the paper of JOHN M. CALLOW, presented at the New York meeting, February, 1916, and printed in Bulletin No. 108, December, 1915, pp. 2321 to 2339. R. H. RICHARDS, Boston, Mass.-I think there is one note which would be interesting to have recorded in connection with this paper, and that is another form of flotation machine. The Minerals. Separation machine has a vortex action, with a vertical shaft and a propeller. This new frother has been developed for the Copper Queen Co. at Bisbee, Ariz. It has a horizontal shaft and a paddle wheel for a frother. It has eight cells, I think, all connected underneath in one continuous tank, and the only separation of the cells is in the upper chambers where the froth is. When this paddle wheel goes around it throws out the froth and the sand goes to the bottom and drifts over from the first to the second cell, where it is paddled again, and comes out with its froth; the sand goes to the third cell where it is again beaten. In that way the sand is continually drifting toward the last cell, while each new froth remains in its own cell. You can see in the working of this machine just the same effect that you see in Callow's machine, i.e., the earlier cell has the darker or richer froth, and the latter has the lighter or poorer froth until you get to the farthest one-which has very little froth, and is very light. JOSEPH W. RICHARDS, So. Bethlehem, Pa.-Speaking from the metallurgical standpoint, it is quite desirable, in many cases, that the oil be removed from the concentrate in order to facilitate the metallurgical work, and I think attention should be directed to the desirability of removing from zinc sulphide concentrates the oil which interferes with their subsequent roasting. The value of the oil is not large; in Mr. Callow's plant, for instance, it would be $20 a day, and it may be possible that a process might be developed which, within the limits of the value of the oil, would remove it, and thus facilitate the metallurgical treatment. LEONARD WALDO, New York, ,N. Y.-The question came up about a year ago as to why-Mexican crude was not an admirable oil for flotation. I have never heard any satisfactory answer to the question. The Mexican crude has the peculiar property of comparative freedom from dangers of fire, a very great reluctance to part with its water, and a specific gravity almost identically the same as water.

Jan 5, 1916

By R. W. Shoenberger, J. D. Clendenin, W. L. McMorris, N. Schapiro, B. R. Kuchta, A. A. Terchick, R. J. Gray, J. G. Price

INTRODUCTION * The United States is fortunate in having enormous reserves of metallurgical-grade coals. Although these coals are better in quality and more accessible than most coals found throughout the rest of the world, the best grades of these coals are being depleted. Consequently, more efficient exploration tools and techniques, such as advanced methods of core drilling and logging, correlation by palynology,** stratigraphy, paleontology and petrography are being used to help assess the extent and quality of the remaining coal reserves. Exploration and assessment of new and existing coal properties become of utmost importance in determining (1) the economic justification for mining the coal, (2) the optimum design of the preparation plant and (3) the most effective use of the coal. Fortunately, the cost of mining coal has remained stable because of better mine planning, more efficient operations and increased mechanization of mining operations. However, increased mechanization raises the amount of impurities in the coal mined, and this requires more and better coal beneficiation to meet the more stringent quality requirements set by the market. Besides, mechanical miners also produce relatively fine coal and, to ensure maximum liberation of impurities, much of the coal presently being used must be crushed to a finer size prior to preparation. The bulk of all coals presently used in this country is mechanically cleaned, much of it at a lower specific gravity than in the past. This necessitates the use of new and improved processes and equipment for coal washing and recovery, such as heavy-medium cyclones and vessels, and froth flotation cells. However, because wet-cleaning processes are pre- dominant in the United States and fine coal retains large amounts of moisture, the increased production of cleaned fine coal accentuates the need for new or improved methods and equipment for dewatering and drying this coal. The larger amounts of coal being beneficiated and the use of new and improved beneficiation processes will aid in controlling and ultimately eliminating sources of pollution. Modem coal markets demand coals that meet rigid specifications. Most coals are purchased under contracts that specify moisture, ash, and sulfur contents, or heating value, depending upon the end use. There has also been a growing trend toward specifying other properties, including particle size and coking capability. These specifications may include not only the * Editor's note: Because of the numerous and varied contributions of the associate authors of this chapter, the text does not differentiate between sections prepared by each individual as has been done in other chapters. ** Palynology is the study of plant microfossils, especially spores, pollen, and other types of fossils not usually studied by paleontologists.

Jan 1, 1968

By Charles Berry

Conventional and nonconventional insurance is examined from the point of view of a financier of a major mining and minerals project. The paper reviews the elements of a conventional insurance program; explains why such a program is not fully responsive to the project financier's needs; examines some of the new insurance coverages that can supplement a traditional program; and emphasises that these insurance markets are still in the early stages of their development with consequent effects on capacity (insured amount) and to some extent price (insurance premium).

Jan 1, 1985

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae'd is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m' is the slope of the line tangent to the curve at the point (p', 2').

Jan 1, 1940