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By A. H. Geisler

The correlation of property changes during precipitation with structure has progressed, sometimes rapidly but other times more slowly, since the fundamental discovery of Merica, waltenberg and Scott.1 The predominent factor that hampered the progress has been limitations imposed by the various detection methods. Refiments in x ray diffraction tech-niques and in metallographic methods, which have been extended by the electron microscope, have contributed new information within the last few years. These permit an extension of the theory as proposed by Mehl and Jetter in 1940'2 Now that a sufficient number of alloys has been investigated to establish a general mechanism of the precipitation process, a correlation of the facts into a generally applicable theory of age-hardening is both warranted and desirable. The purpose of the paper is to provide an orderly correlation of the phenomenological facts of precipitation hardening. Speculation 011 mechanism of hardening will be confined to that consistent with existing theories of hardening, Age-hardening accompanies the formation of a new structure, the precipitate, as provided by a11 alloy system ill which solid solubility decreases with decreasing temperature. Upon this premise alone all such systems would be expected to include age-hardenable alloys. Alas, this is not always the case. Few attempts have been made to explain the variable degree of age-hardening among different alloys or to explain the influence of small alloying additions upon the hardening. Dispersion hardening as originally postulated3 is not adequate.* Coherency hardening—the term that will be used to distinguish the properties of a two-phase mixture in the unique and unstable transition state at which the phases are strained into precise atomic registry (continuity or coherency) in planes

Jan 1, 1949

New York Meeting, October 16 and 17, 1913.-The One Hundred and Sixth meeting of the Institute for the reading and discussion of professional papers will be held in New York City, on Thursday and Friday, October 16 and 17, 1913. Headquarters will be at the Institute office in the Engineering Societies Building, 29 West 39th Street. The sessions will be held in one of the assembly rooms of the building. Because of the many valuable papers on iron and steel obtained with the assistance of the Iron and Steel Committee, which papers could not appropriately be presented and discussed at the Montana meeting, this October meeting of the Institute is held for the purpose of reading and discussing these papers, most of which will be printed and distributed in advance. The members of the following societies have been invited to attend the meeting, and several have accepted and declared their intention of taking part in the proceedings: American Society for Testing Materials, American Iron and Steel Institute, American Society of Mechanical Engineers, American Society of Civil Engineers, American Institute of Electrical Engineers, American Foundrymen's Association. The meeting will be conducted under the auspices of the Iron and Steel Committee, and the latest revised program of the proceedings will be found on page xi, under the notes of this Committee.

Jan 10, 1913

By Henry Ferguson

THIS paper is a preliminary statement, intended to present the more important results of the recent studies of the ore deposits of the Alleghany district in advance of the publication of the complete report, now in preparation. The Alleghany district (Fig. 1) has been a producer of gold since the early days of California gold mining. As in other California gold camps, placers yielded the bulk of the earlier production, but during the last 30 years lode deposits have been the only important source of output. The district differs from other California gold-quartz districts in that nearly all the production is from small shoots of high-grade ore. The mining camps of Alleghany and Forest are on the western flank of the Sierra Nevada range about 20 miles west of the crest. The gently sloping lava-covered plateau which controls the upland topography has been trenched by deep canyons of the westward flowing streams, which are cut to depths of as much as 2000 ft. below the crests of the ridges. The district is about 18 miles from Nevada City but the automobile road which connects the two places is 31 miles long. The senior writer first visited the district in 1913 and published a short description of the lode deposits.1 The increasing importance of the district made further study desirable. A detailed topographic map was therefore made by W. B. Upton, Jr., of the U. S. Geological Survey, in the spring of 1924, and the senior writer spent parts of the field seasons of 1924 and 1925 in the district. For the second field season the Geological Survey was fortunate in securing the services of R. W. Gannett, who had already done geologic work in the district for several of the mining companies. Owing to the death of Mr. Gannett in October, 1925, just before the close of his field work, the work of preparation of the entire report fell to Mr. Ferguson. He takes this opportunity of acknowledging how deeply he is indebted to Mr. Gannett for his excellent work in the field, and his realization of how greatly the completion of the report on the district has suffered from lack of Mr. Gannett's assistance in the office. In October, 1.928, after the completion of the first draft of the manuscript, Mr. Ferguson made a short visit to the district.

Jan 1, 1929

By John Johnston

ONLY two of the Institute's 26 Local Sections were unrepresented at the delegates' three sessions, held on Monday morning and afternoon and Thursday afternoon of the annual meeting. The Philadelphia and Wyoming Sections alone sent no delegates. In all, seven hours were spent most profitably in reviewing the work done by the Institute at headquarters and in the field, comparing ideas and practices in varied activities, and in establishing personal contacts. Cordiality and the co¬operative spirit marked the meeting and apparently no one had any serious grievances to air. Four motions were introduced and unanimously passed. The first, which was introduced by B. L. Sackett, was a recommendation by the delegates that a national committee be appointed to cooperate with Local Sections in the matter of student activities, to promote Institute welfare. It was agreed that this recommendation be made simultaneously to the Board of Directors and to the Mineral Industry Education Division. A subsequent resolution by A. M. Smith was passed asking that a part of the duties of this committee be to secure the opinions of Local Sections as to the most desirable methods of interesting students in the preparation of technical papers, by giving prizes or otherwise, and to report their findings at the Section Delegates' meeting next year.

Jan 1, 1933

By G. R. Love, M. L. Picklesirner

THE use of color adds a new beauty, power, and versatility to metallography. This has been amply demonstrated in a number of public exhibits and on the walls of corporate, government, and university metallographic laboratories around the world. Indeed, in a number of cases, the color not only is of esthetic value but is scientifically essential to the competent examination of particular samples and systems. Optical strain analysis,' determination of true grain size in U-A1 alloys: phase identification in Nb-base alloys,3 analysis of transformation rates in heat-treated Nb-Zr alloys,4 measurement of solidification segregation in cast Nb-Zr alloys,' study of the intermediate phases in Nb/Sn diffusion couples,6 investigation of the oxidation kinetics at various surface orientations in single crystals,7'8 and a number of other research efforts9'10 would have been vastly more difficult without the extra clarity and distinction introduced by color—either the colors resulting from particular polarized light techniques or the interference colors obtained by oxidation. It is unfortunate that the beauty of colored micro-structures cannot be shared more widely, but the economics of publishing a technical magazine apparently prohibits color plates except under extraordinary circumstances. It is doubly unfortunate that no convenient, general method exists for communicating the information available in colored microstructures to the scientific community. True, in some instances the color changes observed are dramatic enough that direct black and white photography is adequate. In photoelastic stress analysis, several orders of interference fringes may be produced and it is frequently desirable to suppress the color effects (use monochromatic light) to simplify interpretation. On the other hand, relatively minute color variations may be readily detectable by eye, be of considerable assistance in interpreting a structure, and yet be enormously difficult to reduce to an unambiguous black and white print. In order to illustrate a possible compromise or solution to the above problems, we wish to show three black and white photographs of the same region of an Nb/Sn diffusion couple whose interpretation depends heavily upon use of color techniques. These micro-structures were obtained from a section through a rod consisting of commercial-purity niobium tubing filled with 99.995 pct Sn (melt-filled in 10"6 Torr vacuum). The composite rod, measuring 500 mm long, was bent into a hairpin shape and inserted into water-cooled copper grips in a vacuum high-temperature furnace. The rod was outgassed for 2 hr at a furnace temperature of 800°C and was further heated by self-resistance using a 2.2-kva ac power supply. The rod was raised to 1910°C over a 4+-hr period, held for 15 min, slow-cooled to 1500°C over a -hr period, and free-cooled to room temperature (all temperatures were measured with W5Re/W26Re thermocouple). Throughout the heat treatment the ambient pressure was kept below 8 x lo-' Torr. Metallographic preparation of the sample was completely conventional except that it was necessary to extend the grinding steps to remove damage in the brittle NbsSn phase introduced by sectioning. No satisfactory chemical or electrochemical etch has been found for these diffusion couples; of those which have been tried, any that attack the niobium-rich phases at all attack the tin-rich phases disastrously. However, the final polishing steps did produce a slight relief effect and this, coupled with anodizing, yielded excellent clarity in the microstructures for direct observation. The anodizing voltage was chosen to give maximum change in color per unit change in composition. In this case, indeed normally, this maximum sensitivity occurred in the blue-to-red color range. The pure niobium tube wall anodized to a relatively bright blue

Jan 1, 1967

By Edward I. Salkovitz

THE determination of the orientation of metal single crystals and the studies of plastic deformation are greatly facilitated by the use of the stereographic projection. To draw a standard projection of the crystal it is necessary to have a tabulation of the angles between the various crystal-lographic planes of the particular crystal studied. Bozorth' has published such a table for the cubic system which can be found in many reference books; such convenient tabulation for the hexagonal metals, however, does not appear to be in the literature, although scores of workers have calculated these angles. Therefore, Table I of angles for magnesium, zinc, and cadmium has been compiled. Since the c/a ratio is different for each of these metals, three separate calculations are necessary. The angles 4 between (HKIL) and (hkil) were calculated by means of the formula: Hh+Kk+½(Hk + hK)1+~3aLl cos The c/a ratios were calculated from data given in the 1948 edition of Metals Handbook. Fig. 1 is a typical (0001) standard projection of zinc. For all practical purposes, it serves for cadmium as well, as can be seen from the table. For magnesium, however, it is necessary to construct another net. R. M. Bozorth: Physical Review. (1925) 26, 390.

Jan 1, 1952

By Herbert K. Kutter

This paper is concerned with the physical phenomena in the fracture process of presplitting and only indirectly with the establishment of the optimum presplitting parameters. Its nature is therefore qualitative, rather than quantitative.

Jan 1, 1968

By F. N. Rhines, A. S. Nemy

The mode of high-temperature tertiary creep of 523-0 aluminum alloy was found to be strongly stress dependent. The occurrence of necking and/or fissures during tertiary creep exhibited a sequence with varying stress, wherein fissures with no necking occur at a minimum stress and necking with no fissures occur at a maximum stress. At an intermediate stress, tertiary creep begins without necking but with fissures in a region just beneath the external surface, followed by necking and the development of fissures along the axis of the specimen. The results are interpreted in terms of grain boundary gliding and the hydrostatic stresses produced by restraints to grain boundary gliding. THERE appear to be two possible reasons for the existence of a period of accelerating elongation prior to rupture during high-temperature creep in metals; namely, 1) a change in the structure of the metal itself, leading to a change in its response to loading, and 2) a reduction in the cross section of the metal resulting in a higher unit loading. Howe,' by annealing and retesting broken low-temperature creep specimens, found that irreparable damage is done once a metal is subjected to creep. Andrade2 first pointed out the association between the reduction in cross section and the increase in creep rate. The present research was designed to investigate both of these factors by retesting specimens machined from material which had been subjected to high-temperature creep testing short of rupture. EXPERIMENTAL METHOD An aluminum alloy, 52s-0, was selected for these studies because it is constitutionally simple, is strong enough to be relatively insensitive to mechanical damage during machining,3 and undergoes accelerating creep in a convenient temperature range. This alloy is hardened by 2.6 wt pct Mg in solid solution and is not subject to overaging effects; it has a very small quantity of an insoluble impurity phase, Mg2Si, finely dispersed throughout its micro-structure. Creep specimens, similar in design to ASTM 0.252-in. tensile specimens, were machined from 3/4-in. round stock and the surfaces were electro-polished. A 24-hr anneal at 500°C was then applied to stabilize the grain size to an average diameier of 0.27 mm. Subsequent heating for as long as 700 hr at the intended test temperatures produced no change in the tensile properties, indicating a well-stabilized state of the material. Corresponding to each of the typical testing conditions listed in Table I, one creep specimen was tested to destruction and this test was employed as a guide in the selection of times for subsequent tests. Duplicate creep tests were then run to various points along the creep curve to produce specimens which were used to determine changes in mechanical properties and microstructures. The latter were examined at the midsections of the specimens. Other specimens were tested to various stages of tertiary creep, after which they were remachined to new cylindrical test specimens, electropolished and re-tested in creep. RESULTS The major findings of this investigation may be illustrated by a comparison of the results of three sets of creep tests. These were run at 400°C at three stress levels, namely 750, 1000, and 1500 psi. In presenting these results in Figs. 1, 5, and 8, the creep curves are given in pairs: That curve of each pair which is drawn through filled circles corresponds to the initial test, and the curve drawn through open circles (and designated by - R) represents the result of retesting the same specimen after machining to a new cylindrical surface. The load was readjusted to the original unit stress at the beginning of each retest.

Jan 1, 1960

By W. L. Saunders

IMPORTANCE OF ROCK DRILLING. IT has been estimated that the value of the mineral products of the United States is about $2,000,000,000 a year; that about $25,000,000 is expended. annually for explosives and that about double this sum is paid in wages where blasting is done. The value of the mineral products does not adequately express the importance of the industry involved in the excavation of rock and ore because of the enormous sums of money expended in tunnel driving, in quarries, and in open-cut excavation generally. We know that the Catskill Aqueduct in the neighborhood of New York, which is now nearing completion, has cost some $165,000,000 and that about one-third of this may be rated as rock excavation. These illustrations are given in order to call attention to the great importance of an industry the extension and development of which in our industrial life depend so much upon the economics of rock drilling. Reference has been made to the new Catskill Aqueduct. There are three aqueducts leading into New York, each built at periods separated by some 20 years of time. 'The first one, known as the Old Aqueduct, conveys the waters of the Croton river to New York City in a manner which reminds one of the old Roman aqueducts, the ruins of which are still in evidence. The engineers who laid out these old conduits sought to direct their lines around the hills and into the valleys, at all times avoiding the rock. When it was necessary to cross a river or a deep ravine, a bridge or causeway was constructed. High Bridge, over the Harlem river, is an arched masonry viaduct differing in no essential features from the aqueducts of the Romans. When the second Croton Aqueduct was built, about the year 1890, the art of drilling rock had been so far perfected, and the use of explosives, through the invention of dynamite, had become ,so general, that this waterway was planned and executed on straight lines, following rather than avoiding the rock. The second Croton Aqueduct is a tunnel through rock, about 32 miles in length; material gneiss, almost as hard as granite. Its construction was made practicable by sinking

Jan 9, 1913

By Patrick H. O’Neill

The Choco placers, mined continuously since the earliest expeditions of the Spanish conquistadors, were exploited by the Indians prior to the conquest. Platinum is found in varying percentages with gold throughout the Choco placers and is found in minor percentages in some placers in other parts of Colombia. The Choco Department is on the west coast of Colombia between the western range of the Andes and the Pacific Ocean and extends from the San Juan River north beyond Panama to the Caribbean. The first reference in European literature to platinum was by Julius Caesar Scaliger in 1557. He did not assign any name to it but referred to it as an infusible metal found in the mines in the New World. The Spaniards had given it the name platina, which is the diminutive for plata, the Spanish word for silver. Don Antonio de Ulloa first recorded the name while on an official visit to the Choco from Spain in 1735.

May 1, 1956

By William G. Pariseau

Advances in numerical methods of analysis and computer technology during the past decade have brought many formerly intractable ground control problems within easy reach of present day graduate mining engineers. However, the new technology brings with it new problems. The identity of these problems are largely those arising from a lack of familiarity with the capabilities and limitations of the new technology. In this regard, the central problem in ground control planning is the calculation of ground motion associated with mining. The fundamentals of this problem leading to a form suitable for computer programming are therefore reviewed. Solution procedures in the broad sense including the gathering of input data and the interpretation of output are described. Computer program capabilities necessary for ground control analysis are discussed and the steps necessary to implement an analysis are outlined.

Jan 1, 1983

By Michael J. Messel

OF the various minerals that occur in fibrous form known as asbestos, chrysotile is the variety most in demand for commercial uses, and, last year, over 683,000 tons of the various grades were produced in Canada and United States, exclusive of African and Russian production, which figures are uncertain. Production has not been able to keep up with the increased demand, and an acute shortage exists. Canada, Russia, and Africa are still the most important producers. However, Russia consumes most of its production at home and exports very little. The United States consumes over 60 pct of the total production and produces only about 4 pct of the total from deposits in Vermont and small quantities from Arizona. This paper will review mainly, some of the more recent developments concerned with the extraction and processing of this fibrous mineral for various industrial uses, such as textiles, insulation, building materials and brake linings.

Jan 1, 1949

By C. C. Wright, R. J. Day

Although data on the exact tonnage of recoverable coal silt are not known, the quantity produced in 1943 was estimated to be over five million tons for the anthracite region of Pennsylvania alone. Since that time the recovery of the No. 5 buckwheat size previously included in silt estimates has increased greatly thus reducing the total silt tonnage. As a compensating factor, however, the methods of recovering silt previously escaping into the rivers and streams have been markedly improved so that the net figure may not have changed materially. Comparable estimates for bituminous coal are lacking, but undoubtedly the silt represents a significant tonnage. With the trend toward increased wet cleaning of the smaller sizes of bituminous coal, it is to be expected that even greater quantities of silt will be available in the future. The raw silt from anthracite collieries usually contains a high mineral matter content, but technological developments in fine coal cleaning have been making rapid advances and it appears probable that more extensive use of these methods will be employed in the near future. Bituminous coal silt in many instances contains a similar high mineral matter content. As with anthracite silt, however, the cleaning of this material, where necessary, appears both technologically and economically feasible. With a view to upgrading the size and value of silt, considerable laboratory and pilot plant work has been conducted by a number of organizations on what is commonly known as pelletization. Actually the process is one of extrusion in which the moist silt is extruded from a die in the form of rods, which usually break into relatively short lengths—a few inches long—as they fall from the die. Fig I is a photograph of some extruded 3/8-in. diam pellets and of the anthracite silt from which they were produced This technique of producing larger sized material from fines is by no means new, having been used extensively by the industrial carbon and clay industries for years.' The application of the process to coal silt appears, however, to be relatively new. The first major program of investigation dates back only to July 1945, when a group of engineers representing the Anthracite Institute, The Pennsylvania State College and the J. F. Pritchard and Co. conducted preliminary tests on the extrusion of anthracite silt at the Floridin Co. plant at Warren, Pa. Since that time these three organiza-tions—individually, together, and in cooperation with other interested groups— have actively pursued work on various phases of the problem. Much of the early history and details of the laboratory and pilot plant work by the Anthracite Institute, has been reported by Mulcey and Eckerd.2 It is the purpose of this paper to report additional information on the process, especially with respect to the factors influencing the quality and use properties of the product, and the current develop-

Jan 1, 1949

By H. E. Elliott, R. S. Busk, A. T. Peters

One of the problems of the fabricator of metals and alloys is the propensity of some composition rarnges toward abnoermal grain growth during certain stages of fabrication. In this respect magnesium alloys are no exception among alloys. Fortunately, convenient foundry control methods have been developed by which the abnormal grain growth possible in certain magnesium-alloy castings can be suppressed. An unusual characteristic of magnesium alloys, however, is that castings of some composition ranges are subject to local grain growth during heat-treatment without the necessity of intentional mechanical stressing of the part prior to heat-treatment. This effect occurs only under certain critical casting conditions, and only in certain alloys of greater than about 8.5 per cent aluminum content, such as C alloy (Mg, 9 per cent A1, 2 Per cent Zn, 0.2 Per cent Mn) and G alloy (Mg, 10 per cent Al, 0.2 per cent Mn). The first observation of this phenomenon in cast magnesium alloys occasioned much surprise, since it is not observed in other meta1s- Jeffries and Archer1 have stated that "the grain size of cast metals, provided they have not been plastically deformed, cannot be changed by heating below the melting point." The study of the conditions leading to abnormal grain growth in cast magnesium alloys, and of the mechanism of this phenomenon, has led to some very interesting observations. Perhaps the most significant of these was the observation that stresses originating from cooling contraction in magnesium-alloy castings are the only stresses necessary, under certain conditions, to cause local recrystallization and subsequent grain growth in the casting during heat-treatment. Before recent developments, this phenomenon of abnormal local grain growth Was a definite problem in the production foundry on C alloy sand castings. Illustrated (Fig. I) is a picture of a casting scrapped because of this defect. A mottled effect is produced in coarse-grained areas by suitable etching solutions. The properties of metal in the affected area are much impaired by such grain coarsening. Ultimate tensile strengths of half the normal value have been measured in metal of this nature. In this paper are described the techniques that have been developed by The DOW Chemical Co. for studying, and in large measure solving, this production problem. Also discussed are studies of the mechanism by which excessive grain coarsening occurs, and the fundamental conditions that produce this effect. The abnormal grain growth discussed in this paper will be referred to as "germinasium since this term has been definedl as any process leading to an abnormally coarse grain size. This paper deals only with abnormal local grain growth that may occur during the solution heat-treatment of certain magnesium-alloy castings, as dis-

Jan 1, 1945

By N. E. Maccallum

(Cleveland Meeting, October, 1912.) ALMOST half a century has passed since the Siemens brothers, after tedious and costly experiments, finally began the manufacture of open-hearth steel. The furnace of that time was very small, having a hearth-capacity of from 3 to 4 tons, and we can appreciate the wonderful development that has taken place in those 50 years by the knowledge that to-day furnaces of 50 times the original capacity are in operation. As the new steel process assumed importance, and furnaces began to grow in number and in size, a question arose, to which no satisfactory answer has ever been given, and that was: ?What is the safe and economical limit of the open-hearth furnace?" Various stopping-places have been suggested, and 20, 30, 40, and 50 tons have each been advocated, but all such arbitrary restrictions have been passed, and 60 tons would probably represent the average furnace, although in a few instances from 70 to 80 tons are regularly tapped into one ladle. The furnaces which are the subject of the present paper have gone far beyond even these limits, and since, in my opinion, they mark another step in the progress of open-hearth steel, they will be considered fairly and frankly, in order that those to whom the matter may be of interest may be able to judge and form their own Conclusions. Short accounts of the work of these furnaces have appeared from time to time in various technical journals, of which the following is a brief résumé. These furnaces are the property of the Phoenix Iron Co., of Phoenixville, Pa., and their distinctive and important feature is, that they charge to twice the capacity of one ladle, and tap simultaneously into two ladles, with a device for controlling the flow into either. In this way the capacity of the furnace is not limited, as formerly, but heats of any size within the capacity of two ladles may be charged.

Oct 1, 1912

By T. M. Girdler

INDUSTRIAL progress and development in this country from the earliest daps to the present has proceeded at an ever-quickening pace. Yet during recent decades the nature of our industrial progress and development has undergone a change of great significance. The earlier days were a period of tremendous expansion. Population was increasing by leaps and bounds. Vast areas of new land were being .2 opened to settlement. And almost boundless new sources of timber, coal, oil, ores, and power were being opened to ever-expanding markets. Today, however, that picture has al- most completely changed. Today, with population increase tapered way off and the opportunity for free expansion into western frontiers gone, the great industrial development of our country continues on a vastly different front. Industrial progress and development today rest on a foundation of technology. The key- stone is research. Our frontiers to- day are frontiers of sciencec

Jan 1, 1939

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Mining Engineer. Graduate of Colorado School of Mines, 1912, experienced in coal, lead manganese and limestone mining, wishes execu¬tive position. A-2146. Graduate Mining Engineer.-Discharged, reserve officer, age 32, single, 7 years' experience holding responsible executive positions, in iron, copper, and talc mining. Well recommended. A-4913. Mine Manager, Superintendent or Engineer. Age 41, graduate of Michigan College of Mines; 20 years' experience in responsible positions in connection with large operations; in iron, copper, pyrites, lead and zinc mines; successful in finding and developing orebodies, increasing production, and reducing costs. Desires a position with a future. A-4081. Mining Engineer.-Graduate from Polytechnicum, Stockholm; 14 years' practical experience in Sweden, United States, Belgium, and Spain, in iron-ore development, mining, and milling; thorough knowledge of English, French and Spanish; desires position as superintendent or assistant manager. Good references; member; now in Sweden. A-4914. Research Engineer. Now in Chile on the erection of a 50-ton mill with modern machinery for the treatment of Chilean nitrate. Desires connection from the first of next year; with firm operating in South or Central America. A-4915. Metallurgical Engineer. Junior member, age 26, single, graduate Columbia School of Mines; recently discharged as lieutenant in the heavy artillery. A-4916. General Superintendent. Technical graduate, age 35, desires position over a group of four or five mines or as assistant general superintendent for a large. company. Has had experience in superintending mines, construction work, opening new and abandoned mines, safety and effi-ciency engineering and handling organized labor. At present employed by a coal company in the middle West. A-4917.

Jan 11, 1919

By R. E. Allen

THERE was once a time when a practical oil man would appraise or buy a producing property on the basis of from $200 to $500 per barrel of average daily settled production. Curtailment-has, for the present at least, caused a virtual abandonment of the "barrel -of settled production" as a yardstick of, oil property value and in its place has come the "barrel of allowable production," which, although an artificial thing, is nevertheless now the principal factor governing the rate of ?pay out? or investment return. The potential production of a well, settled or otherwise, is of less importance in determining the present worth of a well than is the rate at which it may be produced. Speaking only of true potential for the moment, it is obvious that of two similar wells having the same potential, the one having the highest rate of allowable production would be worth proportionately more than the one of lesser allowable. The discount factor for deferred return and risk can easily vary the present values of the two wells by as much as 20 per cent when allowable rates are not greatly different.

Jan 1, 1934

By T. A. Wright

THE-Institute of Metals Division opened on Tuesday afternoon with Wheeler P. Davey as chairman and G. E. Edmunds as vice-chairman. Four papers were on the program, two being of a fundamental character. A paper on "Internal Surface in Minerals and Metals," by R. S. Dean and J. Roster, was presented by the latter; C. H. Gottschalk discussed coercive forces in powders. In answer to a question by the chairman. The author stated that he had not investigated [he temperature coefficient of resistance. A paper on "Recrystallization and Grain Growth in Cold Worked Polycrystalline Metals," by L. W. Eastwood, Arthur E. Bousu, 'and C. T. Eddy, was presented by Mr. Eastwood. A. great many quantitative data were given, with little reference to the theory. Theoretical considerations were discussed by Dr. Gottschalk, and C. A. Edwards of the University College of Wales, contributed very interesting comment on the relationship of size and critical strain. Dr. Edwards discussed the necessity of considering strain with time and temperature.

Jan 1, 1935

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields