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By W. H. Emmons

INTRODUCTION THE deposition of metalliferous lode systems takes place at considerable depths and no one may observe the process. We see only the end results of the process and from these we seek to construct a theory that will account for them. Because there is an obvious relation between many lode systems and intrusive igneous masses, it is a natural inference that they have formed by fluids that were expelled from such masses. The metalliferous lode systems have been deposited by ascending thermal fluids that have risen mainly from great irregular bodies of intruding magmas which are called batholiths. Probably 95 per cent of such lode systems have formed in connection with acidic or "granitic" batholiths and probably less than 5 per cent have formed in connection with basic intrusives. The study of lode ores, therefore, should include the study of the intrusion and differentiation of the batholith. It was noted long ago1 that certain tin-bearing deposits are commonly associated with small stocks. That small stocks are cupolas of larger intrusive masses has generally been recognized. Butler,2 in his studies of the ore deposits of Utah, showed that the chief deposits in Utah are in and near the stocks; that is near the "apically truncated

Jan 1, 1933

By Donald W. Scott, L. A. Roe, B. J. Sweo

INTRODUCTION THIS paper describes the application of ore-dressing methods to the reclamation of milled frit from over-spray, or waste, porcelain enamel. Frit is the name given by enamelers to a granulated glass produced by the smelting and subsequent water quenching of various ingredients capable of forming a glass, usually including a compound to produce opacity. It is the major component of porcelain enamel, and normally commands a price ranging from 7 to 12 cents a pound. In the preparation of a white enamel slip, usually 6 or 7 parts of clay, 2 parts of opacifier, small amounts of electrolytes, in some cases inorganic color stabilizers and organic dyes, and 35 parts of water are added to loo parts of frit; the mixture then is milled to a fineness of the order of 92 to 95 pct through a 200-mesh sieve. The frit forms the base of the enamel; the opacifier imparts opacity or reflectance; the clay suspends the frit while in slip form and serves as a binder' in bisque form (dry and unfired); and the electrolytes control the workability. Spraying is used commercially, in many cases, to apply the finish coat of enamel to the ware, prior to drying and firing. In the spraying operation, only about 50 pct, by dry weight, of the enamel slip adheres to the surface of the ware, the remainder forms the over-spray. From 1/2 to 2/3 of the overspray goes up the flue where it is lost or recovered, depending on whether the plant is equipped with a dust-collecting installation; the coarser portion of the overspray is collected in the spray booth. The former product is termed flue reclaim enamel, and the latter booth reclaim enamel. Although the spraying operation is done in specially constructed booths, which are partially or completely enclosed, it is extremely difficult to keep out contaminating dirt, which joins the reclaim. Some present-day large enameling plants use 20 tons of frit a day, of which 10 tons go into reclaim with a potential value of $1400 to $2400. When two-coat finish enamels were common, the reclaim was used satisfactorily for the undercoat, but the relatively recent advent of one-coat finish enamels prevented use of the reclaim because, even when blended with first-run enamels, it gave dirty finishes with poor gloss. It was thought that the pitting and specking encountered with reclaimed enamels were caused by the contaminating dirt, and that the poor gloss was caused, primarily, by the high clay content; more clay usually was added to give proper suspension properties to the slip when the reclaim was used. A clay content in excess of about 10 pct usually imparted refractoriness to porcelain enamels. Present-day one-coat porcelain enamels must combine high gloss and opacity with freedom from surface defects. Methods of beneficiating the over-spray,

Jan 1, 1947

By B. Barlin, G. A. L. Smith, I. J. I. Delaney

A method was developed to quantify the three mineral species, sphalerite, galena, and pyrite in seven concentrator products. Intermineral effects were studied and a statistical analysis was undertaken to assess the accuracy and reproducibility of the method. The method is both rapid and suitable for plant control purposes. Furthermore, it requires only semiskilled laboratory personnel to carry out all the analyses.

Jan 1, 1976

By Robert Ammon

THE milling practice at Mascot, at present, consists of dry crushing to 5/8 in., jigging, fine grinding, and flotation. The ore arrives at the mill from two mines, No. 1 mine shaft being located in the mill proper, and No. 2 mine shaft being situated about 2000 ft. east of the mill. No. 2 mine is served by a coarse-crushing plant and aerial tramway to the mill bins. In jigging the No. 2 mine ore, 50 per cent. of the mill feed is rejected by the jigs as a jig tailing ranging from 5/8 in. to 10 mesh; the balance of this ore, after removing a jig concentrate, is ground to flotation feed. In jigging No. 1 mine ore, approximately 80 per. cent. of the mill feed is rejected as a coarse jig tailing, and the balance is ground to flotation feed without the removal of a jig concentrate. The difference in the treatment is due to the fact that No. 2 mine ore carries a higher content of zinc than that from No. 1 mine. Of the total concentrates produced, 30 per cent. are made on jigs and 70 per cent. by flotation. At present, 1350 tons of No. 2 ore and 800 tons of No. 1 ore are treated each 24 hours. The recoveries for a typical week are as follows: Heads 3.55 Jig concentrates 61.30 Jig tails 0.80 Flotation concentrates 60.60 Flotation tails 0.09 Extraction 86.50 The associated minerals are a straw-colored sphalerite, dolomite, calcite, pyrite, quartz, and a small amount of greenockite, which occurs as a stain and sometimes small crystals along with sphalerite, but is comparatively rare. Pyrite is present in small quantities, usually less than 0.5 per cent.; quartz occurs in bands a few inches thick. A complete analysis of the ore is as follows:

Jan 9, 1924

By F. W. Bremmer

THE drilling of constantly deeper oil wells has made it imperative that the manufacturer of casing be ever searching for new methods and new materials to meet the increased demands. One phase of this search constitutes the subject matter of the present paper. Starting from the original Drake well in 1859, the depth of wells has advanced by leaps and bounds, until today depths of 6000 to 8000 ft. are common. Conditions point to the necessity for drilling to greater depths, and it is not at all improbable that much of the future oil produc- FIG. 1.-TREND IN DEPTH OF OIL WELLS. tion will be from, wells around 10,000 ft. deep. The trend to deeper wells is nicely illustrated by the curve in Fig. 1.1 The points plotted are the maximum depths attained in the various pools which were at their peak for the years given. It may be of some interest to observe the change that has taken place in the tensile and collapsing stresses over the last 25 years. The pressure at the bottom of a 900-ft. hole, equivalent to the pressure caused by an equal column of water, is only 450 lb. per sq. in. The equivalent

Jan 1, 1930

By E. I. Organick, B. H. Golding

A simple correlation is presented for the prediction of saturation pressures in condensate-gas and volatile-oil mixtures. Saturation pressure is related directly to the composition of the mixture with the aid of two generalized composition characteristics, B, the molal average boiling point, and W, the modified weight average equivalent molecular weight. The need for hydrocarbon equilibrium constants is entirely eliminated. Only the values of the two conlposition parameters need be obtained, and these are calculated in a simple and reproducible manner from the stream analysis of the mixture and the ASTM distillation for the heavy ends. The correlation is given .in the form of a set of 14 working charts in which saturation pressures, either retrograde dew points or bubble points, are plotted cs temperature, forming partial phase envelopes for mixtures having discrete values of the composition parameters, B and Wul. A locus of critical states on each chart intersects the partial phase envelopes, distinguishing retrograde dew point pressures from bubble pressures. A comparison Between experimental and predicted saturation pressures reveals that: the probable error of the predicted values, when considering the data as a whole (214 experimental points), is five per cent; for high gasjoil ratio condensate fluids (approximately 40.000 or more cu ft/bbl) the probable error is about 8 per cent. In either case, however, the probable error is comparable with the overall uncertainty of the data from which the correlation is derived. INTRODUCTION There is a present need for a simplified, yet reasonably accurate method for predicting upper phase boundaries of reservoir fluids. In the case of high gas/oil ratio fluids, namely the so-called highly volatile oils and the condensate gases, no simple method, accurate within 5 to 10 per cent, is now available by which bubble point and retrograde dew point pressures may be predicted. In order to calculate the upper phase boundary of a volatile reservoir fluid, using correlations now available, it is necessary to find and employ the proper K-values (equilibrium volatility ratios of the hydrocarbons in that fluid). This process of finding the Proper K-values usually involves a double trial and error computation. Since the K-values are in themselves dependent upon the composition of the fluid, their use in the calculation of a saturation pressure actually represents an unnecessary complication. The correlation described in this paper relates saturation pressure directly to the stream composition, entirely eliminating the need for K-values. The only data required to calculate the Stream composition are obtained from the customary low temperature fractional analyses of separator gas and liquidt and from the ASTM distillation of the c,+ fraction of the separator liquid. A considerable simplification in the procedure for predicting saturation pressures is thereby effected without significant loss in accuracy. BASIS FOR A CORRELATION Empirical relationships between the saturation pressure and the composition of the fluid in question have already been partially explored by one of the authors.V n particular, a relationship between the critical pressure for a hydrocarbon mixture and its composition was developed. The critical pressure is in reality a saturation pressure, as it repregents a limiting case either of a dew point or of a buhhle point pressure for any given mixture. It was found that the critical pressure may be correlated as a function of two generalized composition characteristics or variables. One characteristic expressed a molal average prop-erty, the other a weight average property of the mixture. Specifically, the molal average boiling point (MABP, or B as it

Jan 1, 1952

By Wesley G. Josephson

THE MINING PROPERTY of the Argonaut Mining Co., Jackson, Calif., is one of the oldest on the Mother Lode. A vein outcropping on a hill in this section could not long elude the eye of the forty-niner, so it was first discovered in 1850. From that time until 1893 the Pioneer mine, as it was then called, limped along under various poorly equipped and financed operators who tried tapping it by trenching and tunneling. Then the Argonaut Mining Co. took over the property and sank the present 65° inclined shaft in the hanging wall of the vein. The mine workings have now reached the 6000-ft. level, which is 5283 ft. vertically below the surface, or just 3 ft. over a mile. The total production of the mine is uncertain, because of lack of early records, but from 1893 to 1932 it is known to have produced in excess of $17,000,000.

Jan 1, 1932

ON FEBRUARY 4, 1952, the Phelps Dodge Corporation signed Contract GS-00P(D)-12068 with the United States Government. This interesting document dealt with the "Bisbee East" project as part of the Government's program to increase the supply of needed copper by encouraging private enterprise to expand production. The ore deposit involved was a relatively small body of low-grade ore lying east of the remnants of the old Sacramento Hill deposit that was exploited with indifferent success from 1923 to 1931, as related in THE PORPHYRY COPPERS. Planning for the entire enterprise had been directed from the start by Harrison M. Lavender, who in 1945, succeeded Percy G. Beckett as vice-president and general manager for all of Phelps Dodge's Western mines and smelters. The untimely death of Mr. Lavender in 1952 prevented him from seeing his plans brought to fruition; but in his honor the mine was fit- tingly named "The Lavender Pit" and was so dedicated on August 7, 1954. The Copper Queen Branch operates under- ground mines at Bisbee (production in 1955 was 28,000 tons) ; but, as this volume is concerned only with Porphyry operations, this chapter deals only with the Lavender Pit project, or as the Government knows it, Bisbee East. My reason for going into some detail regarding the floor-price contract is that it is fairly typical of contracts made by the Government in connection with a half-dozen other copper-expansion projects; and, incidentally, with various projects involving other strategic metals. Phelps Dodge did not seek a loan or other financial aid. The only encouragement asked consisted of (a) the privilege of a five-year write-off (commonly called rapid tax amortization)

Jan 1, 1957

By William H. Marlowe, Thomas E. Ban, Eric Johnson

Introduction In recent years, the industries of the US have been caught between ever increasing environmental concerns and an increasing uncertainty in availability of fuel. An obvious solution is to use our vast reserve of coal by direct combustion or gasification. The problem involves development of a fuel that is environmentally acceptable for these purposes. In order to resolve this problem in the shortest period of time, it would be ideal if an existing technology could be modified to produce a clean fuel from coal. Shortly after World War II, the iron ore industry was compelled to develop a high quality ore from low grade resources. This need led to the development of the taconite industry which involved milling, concentrating, and pelletizing technologies. These technologies are now fully established and applicable to conversion of coal. This presentation introduces a process for converting high sulfur coal into carbonized composite pellets, which emit low quantities of sulfur and particulate matter and may be produced by employing proven elements of technology. The new product, a clean pellet fuel (HelifuelTM) was initially developed by McDowell-Wellman Co., a subsidiary of Helix Technology Inc., at their Dwight-Lloyd Research Laboratories

Jan 1, 1982

By R. H. Card

The geophysicist is interested greatly in the resistivities of different formations or parts of the earth's crust; sometimes he is interested in a single figure in the nature of an average, or what may be called the effective resistivity, of all the formations or parts of the crust at a given location to a certain depth. Conversely, the engineer whose work is concerned with the coordination of power and communication lines in such a manner as to avoid electrical interference between these two types of facilities is concerned very much with this effective resistivity; to a lesser extent he is interested in the resistivities of individual formations. In connection with his work the coordination engineer often estimates the effective resistivity of the earth from measurements of the mutual impedances of lines; in other instances he derives from measurements of a different type the resistivities of different layers of the crust and synthesizes these to obtain an estimate of the effective resistivity. In connection with problems concerning the coordination of power and telephone lines, measurements from which earth resistivities can be estimated have been made at many points in the United States by the American Telephone and Telegraph Co. and its associated companies, in cooperation with various power companies and with railroad companies having electrified sections of line. Other such measurements have been made by the Joint Subcommittee on Development and Research of the Edison Electric Institute and the Bell Telephone System. A study has been made of the correlation of these data with the ages and types of materials of the strata of the earth's crust at each of the test locations. The purpose of this study has been primarily to provide information to assist in predicting the order of magnitude of effective resistivities to be used in the preliminary consideration of problems concerned with the coordination of power and communication lines. To make the results of such a study most useful, it is essential that the geological data to be secured when such a prediction is wanted be readily obtainable. Data on the ages of strata and the types of materials composing geological structures can usually be obtained, therefore particu-

Jan 1, 1940

By R. H. Card

The geophysicist is interested greatly in the resistivities of different formations or parts of the earth's crust; sometimes he is interested in a single figure in the nature of an average, or what may be called the effective resistivity, of all the formations or parts of the crust at a given location to a certain depth. Conversely, the engineer whose work is concerned with the coordination of power and communication lines in such a manner as to avoid electrical interference between these two types of facilities is concerned very much with this effective resistivity; to a lesser extent he is interested in the resistivities of individual formations. In connection with his work the coordination engineer often estimates the effective resistivity of the earth from measurements of the mutual impedances of lines; in other instances he derives from measurements of a different type the resistivities of different layers of the crust and synthesizes these to obtain an estimate of the effective resistivity. In connection with problems concerning the coordination of power and telephone lines, measurements from which earth resistivities can be estimated have been made at many points in the United States by the American Telephone and Telegraph Co. and its associated companies, in cooperation with various power companies and with railroad companies having electrified sections of line. Other such measurements have been made by the Joint Subcommittee on Development and Research of the Edison Electric Institute and the Bell Telephone System. A study has been made of the correlation of these data with the ages and types of materials of the strata of the earth's crust at each of the test locations. The purpose of this study has been primarily to provide information to assist in predicting the order of magnitude of effective resistivities to be used in the preliminary consideration of problems concerned with the coordination of power and communication lines. To make the results of such a study most useful, it is essential that the geological data to be secured when such a prediction is wanted be readily obtainable. Data on the ages of strata and the types of materials composing geological structures can usually be obtained, therefore particu-

Jan 1, 1940

By Walter P. Jenny

I. The Reducing Action of Carbon and of Hydrocarbons,. .. 445 11. Protective Action of Carbon and of Hydrocarbons,. 451 111. Contributory Action of Carbonic Acid Gas,..452 IV. The Stability of Carbonic Acid and of Water,..453 V. Occurrence of Carbon and the Carbon-Compounds,. 455 VI. The Occurrence of Carbon, Alone,.... VII. The Occurrence of Carbon Combined with Hydrogen,. .. 460 VIII. The Relative Reducing Power of Minerals,..487 I. The Reducing Action of Carbon and of Hydrocarbons. Carbon has long been recognized as one of the most powerful reducing agents in the deposition of ores. Investigations, made by myself, of the zinc- and lead-deposits in Southwest Missouri, in the region centering about Joplin, where the formation of the metallic sulphides has been due to the action of bitumen, carbonaceous shales and bituminous coal, have afforded abundant evidence that the solid oxygenated hydrocarbons, particularly when in fine powder and in suspension in the waters circulating through the ore-bodies, are the most energetic and powerful reducing agents known. Bitumen, liberated by the decomposition of the ore-bearing limestone, is found in the Joplin mines in all degrees of fluidity and hardness, dependent on the amount of oxidation it has undergone. From semi-fluid maltha it grades into partly oxidized mineral-pitch, which, by further oxidation, changes to hard asphalt, finally breaking up, from continued absorption of oxygen, into a fine powder resembling in appearance powdered coal. In this condition oxidized bitumen, from its light gravity, is transported readily in suspension in the underground circulating-waters. Bituminous coal and black carbonaceous clays and shales occur as surface formations, often in intimate association with

Jan 1, 1903

By Lawrence Burkhart, S. B. Joo

Axially unsymmetric ordered circulation patterns on the surface of a hemispherical constant volume drop with forced Internal motion were considered as a manifestation of hydrodynamic instability, which was affected by internal flow as well as by the properties of the interface A simplified mathematical model was analyzed In order to study the mechanism of onset of interfacial circulation from a non-circulatory basic state. Values of the critical Reynolds numbers were obtained when the basic state became a fully developed rotational flow and the values changed for different interfacial properties. The work describes a heretofore unreported surface flow pattern on drop surfaces From a practical point of new, any motion in the interface of a droplet can have a significant effect of mass transfer rates in solvent extraction processes Although surface motion in droplets actual processing equipment is very complex, continued study of the fundamental nature of such phenomena should ultimately lead to more effective equipment design procedures.

Jan 1, 1981

By G. H. Walrod, J. M. Mutmansky, Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths, from 150 m to 300 m (500 ft to 1000 ft), and six different diameters, from 4.27 m to 7.32 m (14 ft to 24 ft), were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1979

By Maurice E. Peloubet

This discussion of accounting will describe the statements and the information that the accounting system produces, from the point of view of those who use such systems rather than of those who prepare them and who do the detail and technical accounting work. In any well organized mine, quarry, or other enterprise exploiting a mineral deposit, no matter how small, some clerical and accounting work must be done. Miners and other employes must be paid, supplies must be purchased and issued, and various tax and information returns, which even the smallest enterprise must file, have to be prepared. In this chapter it is assumed that the enterprise has employes of this type and that they understand the fundamentals of record keeping and accounting. It would be impossible here to give sufficiently full explanations to enable a man with no previous clerical and accounting training to set up and operate an accounting and cost system for even the simplest extractive operation. Rather, we shall hope first, to tell the investor and the operator, from the chief engineer or president down to a subforeman, what to expect from the accounting statements and records and how to use this information in his daily work; and second, that it will enable the man with some knowledge of accounting or bookkeeping, but with little or no experience in any extractive industry, to set up and operate a satisfactory system for a mine or other extractive enterprise. For readers who wish to go further, the bibliography at the end of this chapter contains many references. The emphasis has, therefore, been placed on the statements to be produced and the purposes for which they are to be used rather than the underlying books and records. These are, with a few exceptions which will be described later, essentially what might be found in any industrial enterprise and would probably, in the extremely small enterprise, consist of handwritten journals, ledgers, analysis books, payroll books, and stores ledgers. In the larger enterprise, various types of mechanical accounting would be introduced in proportion to the complexity of the operation.

Jan 1, 1959

By C. J. Osborn

In oral discussion at the Columbus midyear meeting, September 26, 1949, these pertinent questions were asked: Was a satisfactory separation of metal and matte obtained? The matte was quite fluid and in most cases the separation was satisfactory. Were the mattes chlorinated after aging? The mattes were stored in sealed glass mason jars, and chlorina-tion experiments made after standing for several weeks gave satisfactory results. Was ferric chloride volatilized? Most of the iron content of the matte was converted to ferric chloride. However, because of the low chlorination temperatures used (150" to 250°C) the major part of the ferric chloride remained with the residue. Undoubtedly, some ferrous chloride was also formed, because of the reducing conditions within the reaction vessel, but no effort was made to separate it from the ferric chloride. Could the reaction be stopped before making metallic iron? No attempt was ever made to stop the reaction before making metallic iron. Generally, 20 to 60 pct of the iron in the charge was obtained as metallic iron which could be readily separated from the matte. In certain cases, metallic iron was dispersed through the matte in the form of globules, which could be removed by magnetic separation. Could other sulphides, i.e., calcium sulphide or sodium sulphide be used in place of iron sulphide? No other sulphides were investigated. It was felt that titanates of calcium and sodium would be formed should these sulphides be used to replace the pyrite. What were the sulphur volatilization losses during matte smelting? In the course of this laboratory investigation, a rather wide variety of variables was introduced from highly oxidizing to reducing conditions and various ratios of pyrite, rutile, and coke. These and other factors all have a definite bearing on the sulphur losses. In general, the higher the sulphur in the charge the higher were the sulphur losses and the percentage of titanium in the matte decreased. With sulphur additions more nearly the theoretical amount, the sulphur losses averaged approximately 10 to 15 pct. With a higher percentage of sulphur on the charges, the losses were in the order of 15 to 30 pct.

Jan 1, 1951

By C. Schlumberger

IN the course of the past few years the authors and their associates have had different opportunities to study the electrical phenomena which accompany the oxidation of pipe lines. The causes of such phenomena are very similar to those which have been described under the name "spontaneous polarization" with reference to metallic orebodies,1 and can be investigated in the same manner. These investigations, however, until recently were of a scientific and theoretical character, and had not found any important practical application. During the year 1931, however, the authors treated several industrial corrosion problems for public utility companies. These problems usually had to be studied in towns or in densely populated areas, where it was well-nigh impossible, or very expensive, to dig pits and trenches in order to make electrical measurements on the pipe itself. The authors were thus led to evolve a method and apparatus permitting the study, from the surface, of the direction of the currents flowing from pipe lines. The purpose of the present paper is to discuss the results obtained in the course of these investigations. However, in consideration of the importance and interest of the work carried out by other scientists along the same lines, a separate chapter will be devoted to a summary of the results achieved up to the present time in the study of pipe line corrosion.

Jan 1, 1932

By A. Hamilton Garner

Northern Venezuela has been divided into three provinces, as follows: The Llanos, the Andean, and the Maracaibo Basin and Falcon. The first and third are large sedimentary basins offering, possibilities for oil accumulations. Oil is known to occur in many formations ranging in age from Cretaceous to Quaternary. The most prolific source of oil is probably the Cretaceous shales and limestones, from which the oil appears to have migrated into overlying porous beds. Faulting or fracturing, folding, and porosity are governing factors in the localization of commercial deposits. THE occurrence of oil seepages in Venezuela has been known since the early days of Spanish occupation. It was not until 1912, however, that any serious exploration work was undertaken. In that year, the Caribbean Petroleum Co., then a subsidiary of the General Asphalt Co., employed a large staff of geologists to make a systematic survey, of large areas in eastern and western Venezuela, selecting the most, desirable localities out of the immense area covered by the Valladares concession. This preliminary work was completed in the fall of 1913, and in February, 1914, the company completed its first commercial well at Mene Grande. Development work has progressed slowly, for various reasons, but petroleum in quantity has been encountered in nine widely separated localities. The Mene Grande field has been put on a producing basis and approximately 4,000,000 bbl. of oil are being shipped annually. Increasing quantities of oil are now being drawn from El Mene and La Rosa. In the light of these developments, the world's need for oil reserves, and the proximity of Venezuela to the United States, American capital is being attracted more and more to Venezuela. Although considerable careful geological work has been done in Venezuela by the various oil companies now operating, most of the data is. buried in the company,, files, and the published literature has been extremely meager. The most valuable contribution to date has been a map and report by Jahn, which, as it was printed in Spanish, is not. generally available to the American oil public.

Jan 10, 1924

By Henry Howe

FIG. 1 shows a volute aging break which developed spontaneously in a hardened and tempered steel helmet between 19 and 38 days after it had been tested ballistically. A similar break, shown in Fig. 2, developed spontaneously in a similar helmet about 40 days after the ballistic testing. In this case the rupture occurred abruptly and with a loud report. The path of rupture in this second case, though much the less regular, is the more interesting of the FIG. 1. FIG. 2. two, in that it is an approximation to two parallel volutes centered at the point of impact of the projectile, just below D. Several weeks later, after the photograph for Fig. 1 was taken, a similar doubling of the volute crack occurred in this helmet, starting from the end of the eyelash crack near A and spreading thence to the left contra-clockwise for about ½ in. The negatives from which these pictures are made have not been touched up in any way, save writing the letters on them. In both cases the trajectory of the bullet was normal to the initial surface at the point of impact, and in both the helmet passed the ballistic

Jan 2, 1919

By Harry Roeser

Short cuts for determining the constants of oil decline curves, with the method of least squares as a starting point, are presented and applications made to practical examples. The nature of the raw data does not justify rigid adherence to the orthodox theory but does lend justification to convenient methods of approximation within reasonable limits. If the conventional form y = kxn were changed to y = k(x + c)', methods of determining the curves would be simplified and greater uniformity in calculated results would probably follow. As A result of the publication, several years ago, of some articles on determining the constants of empirical formulas, the determining the constant's of types of curves used for estimating the production decline of oil wells was brought to the writer for study. Methods requiring a minimum of time and labor and a maximum of rigor were sought, as it appeared that the nature of the data from which such curves are computed and the relative uncertainty of occurrence of the events predicted from them did not justify close adherence to the theory on which the solution of such problems is ordinarily based. The technical deficiencies of the solutions presented in this paper, from the standpoint of the method of least squares, are readily apparent to those familiar with that method, but their presentation in detail here is irrelevant to the subject matter. However, it is the author's conviction, after a rather exhaustive study of the problem, that the value of the solutions lose little by the approximate application of the conventional theory. It must be understood by those who use these formulas that the solutions herein given, and the formulas based on them, are merely facilities to aid the valuation engineer in forecasting future events. It is assumed, also, that before application is made of them, prescient judgment based on the circumstances in each case, shows that the forecast has some probability of realization. On this basis only will these formulas be found useful.

Jan 6, 1924