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By James Norman, E. W. Gieseke

Spodumene is a lithium-bearing pyroxene, and is an important source of lithium compounds. Because of its high alumina and lithia content, it might be a desirable constituent of glass batches. The use of spodumene in ceramics will undoubtedly increase, as it has been shown that a mixture of the proper proportions of this mineral with soda feldspar and potash feldspar has a much lower maturing temperature upon firing than has any one of the three components. The mineral spodumene seldom occurs as pure mineral, but ordinarily with feldspars, mica and quartz. All spodumene-bearing rocks tested contained these minerals as gangue. Small amounts of iron and manganese oxides also were present, usually as stains on the silicate grains. Mica associated with the spodumene carried a considerable amount of lithia. This was discovered in flotation tailings, which, although virtually free of spodumene grains when examined microscopically, showed 0.4 to 0.5 per cent Li²O on chemical analysis. The lithia content of micas picked from the North Carolina spodumene rock was variable. Some samples contained little lithia, others more than 3 per cent. In 1938, under the supervision of Oliver C. Ralston,S the Bureau of Mines, in cooperation with the Tennessee Mineral Products Corporation, undertook to study the beneficiation of North Carolina spodumene by froth flotation. The Bureau had previously published investigations on the beneficiation of spodumene.2,3The methods described in the second publication3 did not give good results with badly weathered spodumene rock, so that more thorough investigation of the subject was warranted. Study of Method of Flotation Separation Most of the work on concentration of spodumene was done with rock from near King's Mountain, North Carolina. Rock from two

Jan 1, 1942

By I. N. Zavarine

The present paper is a continuation of the work on the relationship between the magnetic and the phase transformations in carbon steels during quenching. An account was given by the author in a previous paperl† of an investigation of this relationship during a continuous quench. The experimental difficulties then encountered prevented a conclusive proof of the existence or absence of such a relationship. The conclusions of the previous paper were derived indirectly. The present paper deals with the same problem, but the method of attack is modified. The technique developed by Davenport and Bain2 in their well-known study of austenite transformation at subcritical temperature was adopted in the present investigation. They have shown that the austenite to martensite transformation can be caused to proceed at a relatively slow rate by quenching steels into a hot metal bath. Slowing down of the rate of transformation, together with an observation by Lewis3 that a eutectoid steel can be preserved in the nonmagnetic state by such quenching, pointed out a possibility of a study of both transformations under more favorable conditions than previously described. The preliminary steps were connected with the technique of the hot bath quench. To study this phase of the present work a modification of the apparatus previously described' was used. The modification consisted in the use of a hot quenching bath instead of brine, and in fixing the secondary and the primary coils of the apparatus in a stationary position in and around the bath. Tubular specimens, as in the previous investigation, were heated in a suitable furnace to a temperature in the austenitic range for the given steel and then were dropped into the quenching apparatus. The quenching bath was heated to a series of temperatures within the probable range at which the austenite to martensite transformation was expected to proceed at the slowest rate. Observations

Jan 1, 1936

By H. O. Hofman

The sudden decease, April 1, 1910, in Chicago, of Dr. Franklin R. Carpenter was a shock to his many friends. He died in his sixty-second year, of heart paralysis. To most fellow-members of the Institute who have followed the progress of the last twenty-five years in the mining and treatment of non-ferrous ores, the work of Dr. Carpenter in that line is familiar; but very few, even of those who knew hinl well in the later years, are acquainted with his earlier struggles to satisfy an inborn hunger for knowledge. The story of his life resembles that of the pioneer who opens up new country; overcoming hardships with indomitable courage, meeting doubts and difficulties with an alert and open mind, and exercising in the face of reverses an unconquerable perseverance. It seems appropriate to place on record in the Transactions a brief outline of the life and work of this eminent engineer. During the past 15 years of his life Dr. Carpenter was much interested in genealogy. In the pursuit of this study as an avocation, he traced his own ancestry to the time when ((Hugh," called "le Charpentier" on account of the dexterity with which he had swung his battle-axe as a crusader, settled in Sussex on lands received from William the Conqueror. The Carpenters came to this country with William Penn. A prominent member of the family was Joshua Carpenter, the founder of Christ Church, Philadelphia. Dr. Carpenter's branch of the family moved from Pennsylvania into that part of Virginia which is now West Virginia, where his grandfather settled in Harrison county, while the grand-uncle went further west, and built the first iron-furnace at Hanging Rock, Lawrence county, Ohio. In fact, since early times, the Carpenters appear to have been iron-masters. Franklin R. Carpenter mas born, Nov. 5, 1848, in Parkers-

Jan 1, 1911

By James Norman, E. W. Gieseke

Spodumene is a lithium-bearing pyroxene, and is an important source of lithium compounds. Because of its high alumina and lithia content, it might be a desirable constituent of glass batches. The use of spodumene in ceramics will undoubtedly increase, as it has been shown that a mixture of the proper proportions of this mineral with soda feldspar and potash feldspar has a much lower maturing temperature upon firing than has any one of the three components. The mineral spodumene seldom occurs as pure mineral, but ordinarily with feldspars, mica and quartz. All spodumene-bearing rocks tested contained these minerals as gangue. Small amounts of iron and manganese oxides also were present, usually as stains on the silicate grains. Mica associated with the spodumene carried a considerable amount of lithia. This was discovered in flotation tailings, which, although virtually free of spodumene grains when examined microscopically, showed 0.4 to 0.5 per cent Li²O on chemical analysis. The lithia content of micas picked from the North Carolina spodumene rock was variable. Some samples contained little lithia, others more than 3 per cent. In 1938, under the supervision of Oliver C. Ralston,S the Bureau of Mines, in cooperation with the Tennessee Mineral Products Corporation, undertook to study the beneficiation of North Carolina spodumene by froth flotation. The Bureau had previously published investigations on the beneficiation of spodumene.2,3The methods described in the second publication3 did not give good results with badly weathered spodumene rock, so that more thorough investigation of the subject was warranted. Study of Method of Flotation Separation Most of the work on concentration of spodumene was done with rock from near King's Mountain, North Carolina. Rock from two

Jan 1, 1942

RECENTLY seven Boy Scouts were chosen from all the troops in the United States for their all-around ability, excellence in' scouting, and special ability as writers. Two of the members of this selected group were sons of In-stitute members. In the accompanying illustration, Ber-nard Queneau, son of A. L. J. Queneau, of the U. S. Steel. Corp., can be seen at the extreme left, just behind Theo-dore Roosevelt, who is shaking hands with the boy next to. Carl Zapffe (standing in the middle with his hands behind him), the son of Carl Zapffe, manager of the iron ore prop-erties of the Northern Pacific Railroad.

Jan 6, 1928

The Committee appointed by your Board of Directors to nominate Officers for the Institute for the year 1915 invites the participation of all members in the nominations. The suggestion of names for the various offices will be appreciated and given full consideration when making the selection of candidates which this Committee will recommend. The officers to be elected at the annual meeting in February, 1915, are: One officer, known as Director and President. Two officers, known as Director and Vice-President. Five officers, known as Director. The attention of members is called to Articles V and VII of the Constitution, and to By-Law XIII, which reads as follows:

Jan 6, 1914

By William B. Plank

STATISTICS just released by the American Society for Engineering Education and given in the table, show that the total current enrollment of 200,227 in the 220 engineering schools of the U. S. and Canada represents a gain of 9.8 pct over a year ago, while the mineral engineering enrollment in the U. S. of 9826 shows a gain of only 4 pct in that field. The spurt in the mineral group shown last year is thus slowed down to less than one half of that in the whole engineering student body. Last year, it was growing more rapidly than the whole engineering group.

Jan 5, 1954

EVERY forward-looking mining company realizes the need for employing graduate mining engineers so that there will be a supply of qualified men from which to draw for company officers, executives, and mine managers. The mining industry is competing today with numerous other fields of engineering for its supply of technical men, many of which are more attractive than mining because of better pay, living conditions, and well- regulated company training programs. The Ontario Mining Association and the mining companies of Ontario are conducting a postgraduate training plan which if adopted in the United States, might well encourage top quality men to study mining.

Jan 3, 1950

The Howe Memorial Lecture, in memory of Henry Marion Howe, Past President of the Institute, was authorized in April, 1923, as an annual address to be delivered by invitation under the auspices of the Institute by an individual of recognized and outstanding attainment in the science and practice of iron and steel metallurgy or metallography, chosen by the Board of Directors upon recommendation of the Iron and Steel Division. The following were the Howe lectures and lecturers for the years indicated: 1924 What is Steel? By Albert Sauveur. 1925 Austenite and Austenitic Steels. By John A. Mathews. 1926 Twenty-five Years of Metallography. By William Campbell.

Jan 1, 1940

According to the June 27 issue of Business Week, Rep. Kearns (R., Pa.) introduced a bill in Congress along lines suggested by the National Society of Professional Engineers, to amend the Taft-Hartley Act to permit scientific, technical, and professional groups to discuss wages, hours, and working conditions with management-with the protection and support of the federal law. The article reports that the bill is opposed by a loosely knit group of professional and technical unions, the Engineers & Scientists of America. This group wants Taft-Hartley amended to make it an unfair labor practice for employers to discuss collective bargaining matters with professional organizations.

Jan 9, 1953

Two career employees of the US Dept, of the Interior, in a recent study, indicated that by the end of 1974, 73% of all public lands had been entirely or partially closed to exploration and development of essential resources for leasable minerals and 67% had been similarly restricted for locatable minerals.1 This has come about because of the lack of coordination within the executive branch and between the executive and legislative branches of the federal government and without regard for the cumulative, depressing effect on future domestic mineral production. Much of the withdrawn land is felt to have great potential for discovery of significant mineral deposits.

Jan 5, 1976

By E. C. Wilson

The knowledge concerning the lubrication of open gearing for mining machinery has contained many unknowns and at its best has relied to a great degree on a "Rule of Thumb" procedure. It will be within the scope of this paper to explain what we have learned to date and what must be learned in the future. Action of Two Gears in Mesh Let us review some of the basic fundamentals concerning the action of two gears during mesh. Most of the gears we use are involute and may be spur, helical, or herringbone. The gear contact is a combination of rolling and sliding action.

Jan 12, 1968

By Corale Brierley

The effect of hydrogen peroxide (H202) on growth and respiration of Thiobacillus thiooxidans and Thiobacillus ferrooxidans, organisms involved in acid leaching of copper sulfide minerals and uarnium oxides, was examined. Oxygen uptake and growth by T. thiooxidans were totally inhibited after contact with 0.82 mM H202. Complete inhibition of oxygen uptake by T. ferrooxidans occurred at 8.75 mM H202, and growth was inhibited after 6 hr exposure to 2.06 mM H202. Higher concentration of H202 can be used without detriment to thiobacilli if it is dissipated prior to reaching the oxidation pond or dump surface.

Jan 1, 1980

By J. C. Jr. Vaughan

ALTHOUGH a considerable amount of practical importance attaches to systems involving gases and molten metals, little is known regarding the effects of alloy elements upon the solubility of gases in liquid iron. The solubilities of hydrogen1 and nitrogen2,3 in pure liquid iron are known and it has been shown that small amounts of silicon and aluminum3 exert only a small effect upon the solubility of nitrogen but greatly increase its rate of solution. This paper presents the results of a study of the Solubility Of nitrogen, at pressures approximately one atmosphere, in molten iron containing up to 1.5.5 per cent silicon.

Jan 1, 1939

By Arch J. Alexander

This paper is a resume of a study undertaken by the West Virginia Department of Mines. The underlying and direct causes of accidents are determined in each occupational group. Then from this study, accident prevention courses, visual and written, are to be taken to the various working groups in the mines. THE causes of accidents in West Virginia mines follow the main pattern of coal industry accidents in the United States—falls of roof, ribs and face, 56 pct; from haulage, 25 to 30 pet; blasting, 3 pet; electrocutions, 3 pct; explosions, 2 pct; and other causes, about 10 pct. To arrive at some satisfactory conclusions regarding causes and prevention of mine accidents, the Department of Mines has made a study of all mine accidents, from 1945 to 1948, inclusive. During the last two years of this period, we did not have a major explosion, one that took the lives of as many as five men. The direct cause of these accidents is apparent in the reports but we who are making a close study into their frequency think that the virus lies much deeper, and we want to suggest an underlying cause. The rapid growth of the coal industry in West Virginia, the largest producer of bituminous coal, has resulted in a demand for manpower which probably has never been equaled in mining history. At the turn of the century, West Virginia had 24,635 men employed in and about her mines, and they produced 21,153,341 tons of coal a year. In 1948, there were 125,669 men employed, and coal production for the year was 168,589,033 tons, an average increase of 35 pct for each year since 1900. Over 100,000,000 tons of this increase were mined in the southern counties of the state. A safety analyst might read into the history of this development an underlying cause for accident occurrence. He might say that in such a vast, rapid development the available supply of trained miners became exhausted and that young, inexperienced men were employed in the mines by the thousands. Being unacquainted with the hazards of mining, it would be only natural for these young men to be injured or killed in too great a number. This assumption would not be borne out by the records. Men were not injured or killed in disproportionate numbers during their first years in a mine. The only reason we can give is that, during these years, they possessed an attribute of safety—CAUTION—to a much greater degree than in the years following. The coal companies in West Virginia that have been operating over a number of years have a nucleus of employees who have been with them ten, twenty, thirty, and forty years; many of them having gained all of their mining experience with one company. Their habits of work have been

Jan 1, 1951

By Arch J. Alexander

This paper is a resume of a study undertaken by the West Virginia Department of Mines. The underlying and direct causes of accidents are determined in each occupational group. Then from this study, accident prevention courses, visual and written, are to be taken to the various working groups in the mines. THE causes of accidents in West Virginia mines follow the main pattern of coal industry accidents in the United States—falls of roof, ribs and face, 56 pct; from haulage, 25 to 30 pet; blasting, 3 pet; electrocutions, 3 pct; explosions, 2 pct; and other causes, about 10 pct. To arrive at some satisfactory conclusions regarding causes and prevention of mine accidents, the Department of Mines has made a study of all mine accidents, from 1945 to 1948, inclusive. During the last two years of this period, we did not have a major explosion, one that took the lives of as many as five men. The direct cause of these accidents is apparent in the reports but we who are making a close study into their frequency think that the virus lies much deeper, and we want to suggest an underlying cause. The rapid growth of the coal industry in West Virginia, the largest producer of bituminous coal, has resulted in a demand for manpower which probably has never been equaled in mining history. At the turn of the century, West Virginia had 24,635 men employed in and about her mines, and they produced 21,153,341 tons of coal a year. In 1948, there were 125,669 men employed, and coal production for the year was 168,589,033 tons, an average increase of 35 pct for each year since 1900. Over 100,000,000 tons of this increase were mined in the southern counties of the state. A safety analyst might read into the history of this development an underlying cause for accident occurrence. He might say that in such a vast, rapid development the available supply of trained miners became exhausted and that young, inexperienced men were employed in the mines by the thousands. Being unacquainted with the hazards of mining, it would be only natural for these young men to be injured or killed in too great a number. This assumption would not be borne out by the records. Men were not injured or killed in disproportionate numbers during their first years in a mine. The only reason we can give is that, during these years, they possessed an attribute of safety—CAUTION—to a much greater degree than in the years following. The coal companies in West Virginia that have been operating over a number of years have a nucleus of employees who have been with them ten, twenty, thirty, and forty years; many of them having gained all of their mining experience with one company. Their habits of work have been

Jan 1, 1951

By Louis Moyd

The Concrete Research Division, U.S. Corps of Engineers, has developed a simple procedure for determining the coefficients of linear thermal expansion of rocks by means of resistance wire (SR-4) strain gauges. Gauges are cemented to the surfaces of specimens, which are then brought alternately to temperatures of 35OF and 1350F. Results are accurate to the seventh decimal place. IN the course of investigations of the thermal properties of various rocks proposed for use as aggregates in concrete structures, a relatively rapid method of determining coefficients of linear thermal expansion was required. A method which proved to be satisfactory for this purpose was developed in the petrographic laboratory of the Concrete Research Division, U.S. Corps of Engineers, at Clinton, Miss. The method is based on the fact that strain effects in a specimen can be determined by measuring variations in the resistance of an electrical conductor firmly cemented to the surface of the specimen. Equipment for the determination of strain, electrically, has been developed by the Baldwin-South-wark Division of the Baldwin Locomotive Works in Philadelphia. This equipment includes small strain gauges made of coils of resistance wire bonded between thin sheets of paper (SR-4 gauges), and a portable "Strain Indicator" which records variations in the length of the gauges in microinches per inch. Gauges of this type are now in general use for determinations of various mechanically-induced strains, but their use for the determination of coefficients of thermal expansion appears to be a new application. The advantages of the method are that the test specimens may be relatively small and require only a minor amount of preparation, that a large number of tests can be run at the same time, and that the installation and operation of the equipment is relatively simple. The method and equipment described are now in regular use for determining the coefficients of linear thermal expansion of rock samples submitted to this laboratory. Rocks which have been tested include granites, syenites, gabbros, and other igneous rocks, limestones and dolomitic limestones, sandstones, and quartzites. Specimen Preparation: To standardize the conditions of the tests, the rock specimens are sliced by diamond saw into slabs about 11/2x11/4 in. In the case of bedded or foliated rocks, three oriented slabs are cut from the same specimen, and represent, respectively, a direction in a plane of the bedding or foliation of the rock; a direction along the bedding or foliation and at a right angle to the first; and a direction across the planes of bedding or foliation. One of the large surfaces of each slab is lapped for a few minutes with No. 100 abrasive powder to remove saw scars and irregularities. The slabs are soaked in petroleum ether and then dried in an oven to remove all traces of oil picked up in the sawing

Jan 1, 1951

By Louis Moyd

The Concrete Research Division, U.S. Corps of Engineers, has developed a simple procedure for determining the coefficients of linear thermal expansion of rocks by means of resistance wire (SR-4) strain gauges. Gauges are cemented to the surfaces of specimens, which are then brought alternately to temperatures of 35OF and 1350F. Results are accurate to the seventh decimal place. IN the course of investigations of the thermal properties of various rocks proposed for use as aggregates in concrete structures, a relatively rapid method of determining coefficients of linear thermal expansion was required. A method which proved to be satisfactory for this purpose was developed in the petrographic laboratory of the Concrete Research Division, U.S. Corps of Engineers, at Clinton, Miss. The method is based on the fact that strain effects in a specimen can be determined by measuring variations in the resistance of an electrical conductor firmly cemented to the surface of the specimen. Equipment for the determination of strain, electrically, has been developed by the Baldwin-South-wark Division of the Baldwin Locomotive Works in Philadelphia. This equipment includes small strain gauges made of coils of resistance wire bonded between thin sheets of paper (SR-4 gauges), and a portable "Strain Indicator" which records variations in the length of the gauges in microinches per inch. Gauges of this type are now in general use for determinations of various mechanically-induced strains, but their use for the determination of coefficients of thermal expansion appears to be a new application. The advantages of the method are that the test specimens may be relatively small and require only a minor amount of preparation, that a large number of tests can be run at the same time, and that the installation and operation of the equipment is relatively simple. The method and equipment described are now in regular use for determining the coefficients of linear thermal expansion of rock samples submitted to this laboratory. Rocks which have been tested include granites, syenites, gabbros, and other igneous rocks, limestones and dolomitic limestones, sandstones, and quartzites. Specimen Preparation: To standardize the conditions of the tests, the rock specimens are sliced by diamond saw into slabs about 11/2x11/4 in. In the case of bedded or foliated rocks, three oriented slabs are cut from the same specimen, and represent, respectively, a direction in a plane of the bedding or foliation of the rock; a direction along the bedding or foliation and at a right angle to the first; and a direction across the planes of bedding or foliation. One of the large surfaces of each slab is lapped for a few minutes with No. 100 abrasive powder to remove saw scars and irregularities. The slabs are soaked in petroleum ether and then dried in an oven to remove all traces of oil picked up in the sawing

Jan 1, 1951

By G. Sachs, C. C. Chow, L. J. Klingler

Most structural parts which are heat treated are designed using strength properties which have been determined in the principal direction of the wrought material. For example, for rolled or drawn materials, properties are given for the rolling or drawing direction. The structures, however, may be loaded so that the critical stress is in some direction other than that for which the properties of the material are known. Investigations of forged products,123 have shown that while the yield strength and tensile strength of carbon steel billets and bars vary little with the direction of the test specimen in relation to the fiber, the contraction in area in tension tests and the impact strength in notched bar impact tests decrease in the transverse direction. The contraction in area and, consequently, the fracture stress of hard aluminum and magnesium alloy forg-ings have also been found to be lower in the transverse direction. An investigation on aluminum alloy plate4 likewise has shown the dependence of the fracturing characteristics upon the direction* of the test specimens, the longitudinal direction being considerably stronger than the transverse direction and the normal direction, with the normal direction being the least strong. The variation of properties with direction has been explained by a type of anisotropy called mechanical anisot-ropy. This anisotropy results from the elongation, in the direction of the principal strain, of certain phases, inclusions, and/or cavities in the metal during working. A mechanical fibering is thus produced which seems to persist through annealing and heat treatment. This investigation was initiated to determine the flow stress and fracture stress, at high hardness levels, at 90° to the rolling direction in a round steel bar. It is this direction which receives the critical stress in drawing dies machined from round bars. Preliminary tests showed a large difference in properties between the 0° and 90° directions. Consequently, it was felt that a more complete investigation, utilizing several types of tests, was warranted to determine the flow and fracture characteristics of a steel at various orientations, for a number of hardness levels. This investigation was conducted on an air hardening nondeform-ing die steel. Material and Procedure The distribution of properties was made on a 3-in. round bar of annealed high-carbon, high chromium steel of the following analysis: Pct Carbon................... 1.53 Manganese................ 0.39 Silicon.................... 0.27 Chromium................ 11.76 Vanadium................. 0.25 Molybdenum.............. 0.81 The 3-in. bar was produced from an 8-in. ingot, which was annealed and forged to a 4-in. square billet. The billet was annealed and rolled to a 3-in. round which was then annealed and straightened. This steel is an air hardening die steel which has very good dimensional stability on hardening; therefore, the residual stresses resulting from hardening would be expected to be low. A hardness survey across the diameter of the annealed bar showed no difference in hardness from the center to the outside. However, the test sections of all the specimens were taken approximately half way between the center of the bar and the surface to avoid any surface effect or possible porosity at the center. Tension, compression and bend tests were made on specimens hardened and tempered at six different temperatures. The tension test specimens, Fig 1, were machined from the bar at orientations of 0, 22.5, 45, 67.5 and 90° from the axis of the steel bar. The specimens were rough machined, heat treated and then ground to size. The test section on each specimen was lapped in a direction parallel to the axis of the specimen to remove any transverse scratches which might act as stress raisers. The specimens were tested in fixtures which insured concentricity of loading of less than 0.001 in.5 The transverse strains were measured with a radial strain gauge,5 the least count of which was 0.0001 in. change in diam. The compression specimens, Fig 1, were machined from the bar at ori-

Jan 1, 1950

By W. J. Houk, F. C. Hull

To clarify interpretations of grain structures and to assist in calculations of spatial grain size distributions, plane distribution curves have been determined for random sections through four regular polyhedrons approximating the shapes of metal grains. The characteristics of the distribution curve for the average metal grain are predicted. IT was realized early in the history of metallurgy that metals are polycrystalline aggregates and that the size and shape of crystals affects the properties of the material. Reaumur1 in 1722 employed the microscope to examine the fractured surfaces of steel and of white and gray cast iron and suggested a polyhedral arrangement of the crystals. The first extensive investigation of the form of crystal grains was carried out by Desch.2 He examined the disintegrated grains from a ß brass sample and noted that the number of faces per grain ranged from eleven to twenty and that the number of edges per face varied from three to eight and the maximum occurred at five. While it has been found practical to examine isolated grains only in exceptional cases, it is always possible to make a plane section through the metal and examine the shape of the grain sections on the plane of polish. Desch2 tried to determine the relation between the form of a polyhedron and that of its plane sections for comparison with distribution curves of numbers of sides per grain section of actual metal samples. The polyhedrons investigated were the rhombic and pentagonal dodecahedrons and the orthic tetrakaidecahedron. However, the frequency distributions of the number of sides of plane intersections were not sufficiently characteristic to decide which polyhedron most closely approximated the average grain in a metal. Determination of Statistical Shape of Grain in Space Scheil3 was interested in the problem of calculating the distribution of grain sizes in space from the easily measured distribution of grain section sizes on the plane of polish. Assuming that the grains were spheres and using the plane distribution curve for a sphere shown in Fig. 1, he employed a successive subtraction method to calculate the spatial distribution. In order to evaluate the accuracy of these calculations, Scheil and Wurst4 determined the actual distribution of grain sizes in space in their sample of ingot iron by polishing off successive layers and following every individual grain in a series of micrographs. From curves of mean radius of intersection of a given grain vs thickness of metal removed in polishing, Scheil and Wurst attempted to derive the statistical shape of a grain in space. Their calculated plane distribution curve for this shape is compared with the distribution curve for a sphere in Fig. 1. A table of values based on this curve was prepared for calculating spatial distributions of grains. The calculated and measured spatial distributions of their sample then agreed much better than when a spherical shape had been assumed. In the present paper, an attempt has been made to learn something about the average metal grain by studying in detail the effect of the shape of regular polyhedrons on the plane distribution of areas and shapes of areas produced by random sections through them. From the data presented below, it can be concluded that the plane distribution curve for the average metal grain differs in three fundamental respects from the curve derived by Scheil and Wurst. Polyhedrons Selected for Study The polyhedrons selected for the statistical study are illustrated in Fig. 2 and consisted of a cube, a figure formed by cutting off the corners of a cube at the midpoints of the original edges, a tetrakaidecahedron, and a pentagonal dodecahedron. The length of edge on any one figure is a constant. For the above models the edge lengths were 3.50, 4.00, 2.00, and 2.08 in., respectively. A cube was selected for one of the polyhedrons because of its simple geometry, because it is a form that by repetition can completely fill space, and because it represents a convenient degree of departure from compactness beyond which the shape of

Jan 1, 1954