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By George A. Macready

Trinidad, British West Indies, is an island near the north coast of South America, situated between latitudes 10" and 11" N., and opposite the numerous outlets of the Orinoco River Delta. It is separated from Venezuela by the Gulf of Paria (salt water) and straits over 5 mi. (8 km.) wide. The area of the island is approximately 1750 sq. mi. (453,-250 hectares) and the population is approximately 400,000. The climate is tropical with an annual rainfall of from 45 to 60 in. (114 to 152 cm.). The oil fields consist of several units, or fields, located in the southern half of the island. Approximately 90 per cent. of the total production has been yielded by fields situated within 7 mi. (11.3 km.) of the famous asphalt lake and on the southwest peninsula. The most important producing fields, or units, are the following, which are shown on the accompanying map: Brighton, or Pitch Lake Field, operated by the Trinidad Lake Petroleum Co., Ltd., is situated beside the famous Pitch Lake; it even encroaches on the lake. Vessigny Field, operated by the Trinidad Lake Petroleum Co., Ltd., is situated 2 mi. (3.2 km.) south of Pitch Lake. Lot One Field, operated by the Petroleum Development Co., Ltd., the United British Oilfields of Trinidad, Ltd., and Stollmeyer, Ltd., is situated 3 mi. south of Pitch Lake upon Lot One of Morne 1'Enfer Forest Reserve and adjoining properties. Parry Lands Field, operated by the United British Oilfields of Trinidad, Ltd., and the Petroleum Development Co., Ltd., is situated 31/2 mi. south of Pitch Lake on Lot Three of Morne 1'Enfer Forest Reserve and adjoining properties. Point Fortin Field, operated by the United British Oilfields of Trinidad, Ltd., is situated at Point Fortin, 6 mi. southwest of Pitch Lake. Fyzabad Field, operated by Trinidad Leaseholds, Ltd., is situated several miles southwest of Fyzabad Village and 6 mi. south-southeast of Pitch Lake. Barracpore Field, operated by Trinidad Leaseholds, Ltd., is situated several miles south of San Fernando and 15 mi. (24.14 km.) east of Pitch Lake.

Jan 1, 1921

By F. H. Rhines, A. H. Grobe

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By A. H. Grobe, F. H. Rhines

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By H. J. French

Within the past few years, particularly because of the rapid growth of the airplane industry during the war, considerable attention has been paid to the manufacture of light-wall cold-drawn seamless and welded steel tubing for structural purposes. While the manufacture of such tubing is not, in itself, a difficult matter, some difficulties have been encountered in producing the same under specifications requiring definite physical properties. It is the purpose of this paper to describe the methods of manufacture and the properties that may be obtained by such methods for tubing coming within about 1/2 to 2 in. (12.7 to 50.8 mm.) outside diameter and 10 to 22 Birmingham wire gage (0.134 to 0.028 in. wall thickness). Such tubing is largely used as structural material in the aircraft industry, and it is of the utmost importance that the physical and chemical properties should be known, and also that the various factors entering into the manufacture should be under such control as to allow these properties to be varied and held within definite limits. In general, tubing may be divided into four classes: namely, specialty tubing, such as riveted-sheet or plate, lock jointed, etc.; brazed tubing; welded tubing; and seamless tubing. Welded tubing may be divided into hot product, such as lap welded and butt welded, and cold product, such as acetylene and electric welded. Seamless tubing may be hot rolled or cold drawn. Specialty Tubing The first two classes present mainly mechanical or structural engineering problems. A simple form of tube is made by riveting together the overlapping edges of rolled sheets or plates formed into a cylinder. Because of the nature of its construction, such a tube is necessarily limited to relatively large sizes. Lock-jointed tubing is produced by passing low-carbon strip through a forming machine having suitable rolls and dies, its manufacture is almost entirely a question of design of the forming machine and its satisfactory operation. The chief application of such tubing is in the manufacture of bedsteads.

Jan 1, 1920

By A. B. Kinzel, Walter Crafts

Inclusions of nonmetallic matter have long been recognized as objectionable in steel. A complete theory of the effect of inclusions, which is consistent with that held today, was outlined in Howe's early work on the metallurgy of iron and steel. This, by analogy with wrought iron, assumes that the observed difference in properties between specimens with and across the direction of rolling is due to slag enclosures. The fact that wrought iron shatters in ballistic test is taken as an indication of the effect of inclusions on the resistance to'shock. Since that time, the development of the metallurgical microscope has shown the discrete nonmetallic inclusions in the iron matrix. Better resolution has brought out the great number of inclusions, and the availability of good microscopes in steel mills and laboratories has constantly drawn more attention to these inclusions. This recent emphasis on inclusions has resulted in studies as to their nature, mode of formation and methods of elimination, such as the work of Wohrman, Dickenson, Herty and Schenk. In addition to the published works, many investigations which have not been published have been carried out by private laboratories and have resulted in the application of specifications intended to limit inclusions in many qualities of steel. Neverthless, a clear understanding of the quantitative effect of inclusions on the physical properties of steel has been lacking. It is the specific purpose of this study to determine the quantitative effect of inclusions on the physical properties of steel that determine its behavior under dynamic stress. The study has shown that a quantitative relation between counted inclusions and impact strength does exist in normalized steels, but that factors other than readily visible inclusions are equally important. Furthermore, the present commercial rating of inclusions is unreliable with respect to counted inclusions or dynamic tests, and this study indicates that the tensile-impact test is more reliable as a measure of quality. General Scheme The general plan of the study follows: (1) To develop or establish a satisfactory measure of dynamic strength; (2) to develop or establish a

Jan 1, 1931

By D. W. Frommer, M. M. Fine

Early in 1957 St. Joseph Lead Co. announced discovery of three new centers of iron ore deposition in east central Missouri.1 The discovery resulted from exploratory drilling in the vicinity of a magnetic anomaly or high. A deep hole, drilled into the Pre-Cambrian porphyry to determine the cause of anomaly, penetrated a magnetite-rich deposit.2 The magnetic surveys that revealed the anomalies were begun by the Missouri Geological Survey in 1929 and were continued into the 1930's 3. At that time an area in Crawford County known as the Bourbon magnetic high was located. A second anomaly, similar in size and intensity, was discovered about six miles to the northeast in Franklin County in the vicinity of Sullivan. This area was not studied in detail until the early 1940's.

Jan 3, 1959

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

INTRODUCTION TO COMPOSITING Individual drill hole samples may vary greatly in size, length, and weight. The sample interval may represent any convenient unit of hole length, and is usually related to the type of drill being used to obtain the sample. Depending upon the type of mineral deposit, it is desirable to group the individual sample values into composite weighted values representative of some particular zone or volume of the ore body. For example, values of several sequential samples of diamond drill core 3 m (10 ft) in length may be grouped together to represent a 12-m (40-ft) sample value over one bench height. On the other hand, several individual sample values taken across the thickness of a stratiform deposit or a vein zone may be weighted together to represent the value of the total thickness at the point of intersection. The choice of composite intervals is usually dictated by the type of mineral deposit and the mining method selected to produce the mineral. The techniques of weighting values from various lengths of samples into a composite value has already been discussed briefly in Chapter 3. Further examples of determining weighted composite values will be given in the following discussion on compositing for various types of mineral deposits. SAMPLE VALUE COMPOSITES AND TYPES OF MINERAL DEPOSITS There are many kinds of mineral deposits, each of which will require special treatment of sample data to obtain the best composite intervals for evaluating the deposit. It cannot always be known before hand what the optimum composite interval will be. Such composite intervals may properly be determined by geologic factors that are often unknown prior [ ]

Jan 1, 1980

CONTENTS PAGE East Texas, except the Gulf Coast-H. Vance 3 Gulf Coast-L. P. Teas 8 Texas Panhandle-C. C. Rae 16 North Central Texas-H. F. Smiley 23 North Louisiana, South Arkansas and Mississippi-B. C. Craft 25 Oklahoma-C. H. Pishny, Raymond M. Carr and E. J. Dickinson 31 Kansas-E. A. Koester 35 Rocky Mountain District-C. D. Johnson 46 Illinois and Indiana-T. Wasson 49 Michigan-T. Wasson 52 Eastern States-P. D. Torrey and W. H. Young, Jr 58 West Texas and New Mexico-W. V. Vietti. Published as a Supplement.

Jan 1, 1933

By Shun-ichi Satoh

STUDIES by many authorities have proved that nitrogen exerts an injurious influence upon iron and steel, but in the casehardening of steel by carbon, nitrogen has the advantage of accelerating the process of cementation. Its influence upon special steels is quite remarkable; it can produce the hardest layer ever known in metallurgical products-a fact hit upon by A. Fry and studied and ascertained by L. Guillet. As there have been very few investigations on the influence of nitrogen on special steels, the writer has listed important articles dealing with this problem and has conducted experiments on nitrification. He also has tested the influence of nickel upon the penetration of nitrogen in electric-arc welding.

Jan 1, 1929

By A. T. Beckwith

This paper concerns measurements of low-velocity air currents and investigations on mine ventilation by means of chemical smoke. The chemical smoke used is produced without flame and at ordinary mine temperatures, and therefore presents no ignition hazard in gaseous mines. Mining men who have worked in open-light mines are familiar with the use of tobacco smoke in determining the direction of air travel and approximately measuring low-velocity air currents. The use of chemical smoke is merely a refinement on the use of tobacco smoke and the flameless low-temperature source of chemical smoke has the additional advantage that it can be used in gaseous mines. Ventilation smoke apparatus, Fig I, is a simple device for producing dense white smoke. The apparatus as shown consists of a rubber aspirator bulb which is used to force air through a glass "smoke tube" containing a chemical substance that produces a dense white smoke on contact with air. The apparatus was developed by engineers of the U. S. Bureau of Mines.' It is inexpensive, weighs less than 3 oz, is easily carried in a pocket, and requires no skill to operate. Smoke apparatus is invaluable in practical mine ventilation work for: (I) measuring low-velocity air currents, (2) detecting air leakage, (3) observing airflow characteristics. This paper is written to show the merits of the apparatus, and is based upon findings through its extensive use, during the past six years, in mines operated by the Lehigh Navigation Coal Co. Inc. The Apparatus Certain chemicals, such as stannic chloride (SnCl4) and pyrosulphuric acid (H2S2O7) produce "white smoke" when exposed to air. Stannic chloride gives off vapors which on contact with moist air cause the formation of solid hydrates, of which SnCl4.5H20 is the most important. Pyrosulphuric acid decomposes when exposed to air with the evolution of sulphur trioxide (SO3) fumes, which become white upon contacting moisture in the air. A chemical, such as one of the above, is the active substance in a smoke tube. The glass tubes are hermetically sealed during manufacture, and are made ready for use by merely breaking off the tips at the conveniently located file cuts. When the smoke tube is connected to the aspirator, depressing the aspirator bulb forces air into contact with the chemical, and smoke discharges from the open end of the tube. A white solid (a hydrate if stannic chloride is used, or sulphur trioxide if pyrosulphuric acid is used) may occasionally form a cake in the outlet opening of a smoke tube. A small wire such as an ordinary paper clip can be conveniently employed to dislodge the cake should it seal the tube. When the assembled apparatus is not

Jan 1, 1949

Jan 10, 1951

By Norman C. Britz, Mortimer P. Buck

THIS PAPER DEALS WITH the practices used at the Huntington, Nest Virginia works of The International Nickel Company, Inc., in hot and cold rolling nickel and high-nickel alloys. The practical metallurgical aspects are discussed and a brief description of equipment given. The alloys covered may he divided into three main groups. based on their major constituents: 1. Nickel alloys, 2. Nickel-copper alloys. 3. Nickel-chromium alloys. The nominal compositions of the various alloys which are produced in most common mill forms are given in Table 1. Nickel, a commercially pure grade of nickel containing about 0.05 pct carbon as' the chief alloying element, is produced in all common Mill forms. "L" Nickel is commercially pure nickel in which the carbon content is held as low as possible, usually less than 0.01 pct. This grade of nickel is used chiefly for spinning and for special high temperature applications where its low carbon content enhances its corrosion resistance. "D" Nickel contains 4.5 pct manganese to provide improved resistance to sulphur embrittlement at elevated temperatures. "Z" Nickel is an age hardening grade of nickel containing carbon, aluminum, and silicon as the age hardening elements. This alloy combines the cor-

Jan 1, 1948

By W. C. Winegard, C. Feng, C. Elbaum

SEVERAL investigations have been made concerning the effect of oxygen on the mechanical properties of titanium 1-6= In particular, the yield strength has received considerable attention. Finlay and snyder2 report a 0.2 pet strain offset yield strength if 49 kg per sq mm in titanium containing 0.1 pct 0 and 61 kg per sq mm in titanium with 0.2 Pct 0. These results are in good agreement with those of Jaffee, Odgen, and Maykuth3 who report values of yield strength

Jan 1, 1960

By Walter R. Crane

PAGE I. Apparatus and Methods.......... 406 1. The Magnetic Circuit...........406 2. Apparatus Employed in the Traction-Method...... 406 a. The Coils............409 b. The Pole-Pieces..........409 3. Methods of Testing Fields Produced by Different Pole.Pices.. ..409 c. Testing with a Search.Coil........410 d. Testing with Iron-Filings and Glass Tube.. .. .410 4. General Forma of Pole-Pieces.........411 e. Flat Poles............411 f. Conical Poles........... 411 g. Spherical Poles...........411 h. Chisel-Edged (Chamfered) Poles.......412 II. Magnetic Fields...........412 5. Methods of Testinq for Magnetic Permeability...... 421 i. The Rod-Method..........423 j. Method Employed in These Experiments......424 k. Difference in the Results of the Two Methods..... 425 l. The Traction-Method.........427 m. Effect of Loosening the Charge.......430 n Corrections...........432 6. Theory.............433 o. Effect of Varying Weight on Tractive Force..... 434 p. Effect of Varying Pole-Distance.......436 q. Effect of Varying Magnetization.......436 T. Effect of Varying Size.. .......437 a. Summary,........... 441 III. The Relative Magnetic Permeability of Various Minerals,. 443 The form and strength of magnetic fields have attracted much attention. especially in connection with the designing of dynamo-electric machinery—an art which has been revolution-

Jan 1, 1902

By W. E. Bruce, R. J. Morrell, James Paone

This chapter is a partial summary of an investigation by the U.S. Bureau of Mines (USBM) made in response to a recent request by the Assistant Secretary, Water and Power Development of the U.S. Department of the Interior, for a comprehensive review of horizontal boring technology related to underground power-line installation. This review is concerned primarily with 3 to 36-in. diam horizontal holes from several hundred to several thousand feet in length. An electric power system consists of three essential functions: generation, transmission, and distribution. The generation component includes the generating station and step-up substation; the transmission component includes the transmission line and stepdown substation at typical voltage levels ranging from 69 to 345 kv for underground lines and 69 to 500 kv for overhead transmission lines; the distribution component includes the distribution line carrying the commonly used voltages of 120, 208, and 240 v, the distribution transformer, and the line to the service customer.l The Federal Power Commission reports that 1600 miles of underground transmission lines of 60 to 345-kv capacity are now in service in the United States. By 1980, it is estimated that approximately 3000 miles of trans- mission lines will have to be placed underground.2 The cost of burying electric transmission lines underground in metropolitan areas, approximately 30 miles from the center of each of the most populated cities, will exceed $1.5 billion with the methods now available. The wide spread in unit costs of overhead and underground transmission lines narrows as right-of-way costs for overhead transmission in congested areas increase. Improved methods of underground emplacement will certainly reduce this difference in costs and even further favor underground emplacement. Also, in the future, overhead transmission lines will probably not be permitted in highly built-up areas.

Jan 1, 1970

By R. A. Walker, R. G. Bradburn, B. C. Flintoff

The events which led to computer control of the grinding circuit at Brenda Mines are described, beginning with mill operating philosophy. High production rates are encouraged so that, despite severe upstream disturbances, a manual control method to meet this philosophy had developed. Unfortunately, due to the time interval between manual control adjustments, losses in production resulted. An analog control method was devised and, although superior to manual control in some situations, was found to suffer from several practical limitations. The data logging capabilities of a control computer seemed warranted. Circuit testwork combined with an analysis of operating data showed that (1) metallurgical personnel at times could increase production rates by as much as 10% over that achieved by grinding operators; (2) the chosen data base required an increase of 2% or more to be statistically significant; and (3) for a 2% increase there would be a significant rate of return of investment in computer installation. Consequently one grinding circuit was fully instrumented, and a rented computer was installed by Brenda personnel. Prior to installation, Brenda metallurgical and instrumentation personnel were trained in the use of the computer. An experimental program was devised with short and long-term objectives. The short-term objective was to develop a practical control strategy which would yield immediate production improvement. This goal has been successfully met as described in this paper. Statistically significant increases in excess of 2% have been established. Work is being completed for the permanent installation of computer control on all four grinding circuits at the present time. Long-term objectives are (1) off-line analysis of the circuit using mathematical models of process units; (2) on-line experiments to study alternative control tactics; and (3) possible expansion of computer facilities to the crushing plant.

Jan 1, 1978

By S. J. Rothman, J. J. Hines, D. Rokop, R. Bastar

Self-diffusion has been measured along each principal axis of mosaic-structured and relatively perfect a uvaniuln single crystals. The anisotropy reported before,' D[loo] = D[001] » D[010 , has been confirmed. and is shown to represent volume diffusion. Diffusion along the dislocations in the imperfect crystals increases the measured value of D significantly without changingr either the shapes of the penetvation plots or the anisotropy. SINCE a uranium is orthorhombic, the diffusion coefficients along the principal crystallographic axes need not be equal. A previous measurement of self-diffusion in three mosaic-structured a uranium single crystals1 showed that Dil00| =D[001 >>D[010 This result was deduced from penetration plots similar to those in Fig. 1. That is, the plots for diffusion along [loo] and [001] were the straight lines expected from the solution of the diffusion equation for the boundary and initial conditions of the experiment, while the plot for diffusion along [010] was curved so that the part near X = 0 had a much steeper slope than the straight lines did. The observed anisotropy could have been due either to volume diffusion or to diffusion along the very large number of dislocations in such crystals, according to the model proposed by aart.' The authors of Ref. 1 argued that the latter possibility was unlikely, but did not exclude it. To settle the question, a simultaneous measurement of self-diffusion in mosaic-structured and mosaic-free crystals was carried out. This paper reports the results, as well as a measurement of the temperature dependence of self-diffusion in a uranium. EXPERIMENTAL The single crystals of a uranium used in this experiment are listed in Table I, together with other experimental details. '(Mosaic structured" here means crystals grown by solid-state phase change.3 The Laue spots from such crystals spread over about 6 deg of arc, which indicates that the density of dislocations is very large. "Perfect" crystals are ones grown by Fisher's grain-coarsening tehnique; the Laue spots from these are quite sharp,4 which shows that the dislocation density in these crystals is much lower. All of the crystals were made from high-purity uranium; a typical analysis is given in Ref. 1. The actual diffusion directions were within a few degrees of the nominal. The thin layer-sectioning method was used. The experimental techniques were similar to those described in Ref. 1, except the sectioning. Crystals Za, 2b, 2c, 4a, 4b, and 4c were sectioned on a lathe. Crystals 3a, 3b, and 3c were sectioned by grinding on glass plates, with 1 p diamond powder in butyl alcohol as the abrasive. The use of glass plates eliminated the crowning noted in Ref. 1, and the use of butyl alcohol as a lubricant simplified the chemical processing of the sections. Material from the sides of these three crystals was removed by spark machining before sectioning. The sectioning of crystals 4a and 4c was botched. A small cylinder of metal was extruded from the center of crystal 4a while turning off material from the side of the sample. Crystal 4c was misaligned by 2.1 x 10"3 cm because the dial gage jammed during the alignment. Notwithstanding these errors, useful data were still obtained from these crystals. The points

Jan 1, 1967

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By E. L. Jr. Spain

THE deposits described in this paper occur over much of Wayne County and in the southeast portion of Hardin County, Tennessee, and in the northeast and northwest portions of. Mississippi and Alabama respec-tively. The presence of tripoli in this region has been known for some time and descriptions of various occurrences in Tennessee have been made by Jewell1 and Miser2, while Hilgard3, Lowe4 and Logan5 have treated the deposits that occur in the adjacent portions of Alabama and Mississippi, but there has not been a general survey of the entire field summarizing completely the geology of the deposits with respect to their origin and stratigraphic relationships. During 1934, while engaged in surveys of mineral resources through this region for the Tennessee Valley Authority, the writer collected data with this in mind, and has assembled them in this report. He is indebted to H. S. Rankin and N. A. Rose, of the Tennessee Valley Authority Geology Division, for field assistance.

Jan 1, 1936