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By George S. Ramsay

The Appalachian system contains the largest area of all known Carboniferous coal-fields. Beginning near the north line dividing Pennsylvania and New York, it extends southwest through West Virginia, southeastern Ohio, Kentucky and Tennessee and terminates in Alabama—a distance of about 950 miles. The northeastern part of this field will be considered in this paper. The general dips of the measures are toward a trough about parallel to the Ohio river, from the Allegheny mountains and ridges on the west. The Potonlac field is an exception; the dip in this case being northeast, the folding to the east of the Allegheny mountains in Pennsylvania being of a greater degree and diminishing southwestward. The cause of the general dip to the west of the mountains seems to be the westward movement of the thrust east of the mountains, with the large Nittany fold including other folds to the east of the escarpment, raising the mountains high above the coal-fields to the west, making a general slope toward the Ohio river southwest, and crossing waves of anticlinals west ward. The synclinals contain the coals, while in many cases on the top of the folds or anticlinals some of the veins (or, in some cases, all) are eroded. The Coal-Measures of this field are generally divided into three principal divisions, known as the Upper, the Barren, and the Lower Coal-Measures, but there is a tendency to divide them into five groups, which is more convenient. Beginning at the bottom, the first would be the Conglomerate ; second, the Lower Coal-Measures; third, the Barren; fourth, the Upper Coal-Measures, and fifth, the Upper Barren or Permian Measures.

Jan 1, 1896

By F. M. Lewis, J. F. Meyers

This second progress report of grinding presents comments regarding ball consumption and data pertaining to the hydroscillator, which is closed circuited with the tricone mill. A study and postulate of how balls function is presented. The paper summarizes cost reduction obtained by the method of "grinding for the tail race" rather than for "mesh tons." AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of —200-mesh produced a very creditable figure. Hydroscillator Operation The machine as now developed has proved dependable and easy to operate. It starts easily under full load and responds quickly to operating adjustments. The hydraulic holes in the oscillating plate do not plug when shut down under full load. Absolutely clean hydraulic water is essential. An Elliott water screen or similar device should be an essential part of the machine to keep all scale and trash of all kinds from the hydraulic compartment. The shift operators have expressed approval of the machine. In table I we show a typical screen analysis of the hydroscillator rake sand as compared to conventional classifier rake sand on our ore. We have previously reported that of the 28.7 pct reduction in power, the hydroscillator contributed 6 pct, on a —200-mesh basis. This is a conservative figure. Some of our test runs indicated that the saving was as high as 10 pct. Laboratory studies by the Dorr Co. engineers indicate that still greater efficiency is possible. Nevertheless, the 10-ft plate is overflowing 2100 tons per day at 3 to 4 pct + 65-mesh, which is a very creditable performance by

Jan 1, 1951

By F. M. Lewis, J. F. Meyers

This second progress report of grinding presents comments regarding ball consumption and data pertaining to the hydroscillator, which is closed circuited with the tricone mill. A study and postulate of how balls function is presented. The paper summarizes cost reduction obtained by the method of "grinding for the tail race" rather than for "mesh tons." AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of —200-mesh produced a very creditable figure. Hydroscillator Operation The machine as now developed has proved dependable and easy to operate. It starts easily under full load and responds quickly to operating adjustments. The hydraulic holes in the oscillating plate do not plug when shut down under full load. Absolutely clean hydraulic water is essential. An Elliott water screen or similar device should be an essential part of the machine to keep all scale and trash of all kinds from the hydraulic compartment. The shift operators have expressed approval of the machine. In table I we show a typical screen analysis of the hydroscillator rake sand as compared to conventional classifier rake sand on our ore. We have previously reported that of the 28.7 pct reduction in power, the hydroscillator contributed 6 pct, on a —200-mesh basis. This is a conservative figure. Some of our test runs indicated that the saving was as high as 10 pct. Laboratory studies by the Dorr Co. engineers indicate that still greater efficiency is possible. Nevertheless, the 10-ft plate is overflowing 2100 tons per day at 3 to 4 pct + 65-mesh, which is a very creditable performance by

Jan 1, 1951

By AIME AIME

ON April 7 the twentieth national Open-hearth Conference of the A.I.M.E. will be held in Birming¬ham, Ala., in conjunction with a meeting of the Committee on Blast Furnaces and Raw Materials. At least 300 engineers and operators are expected to attend. Birmingham, the industrial city and iron, and steel center of the South, has been called the "Magic City." Men actively engaged in business in Birmingham today have seen practically every building in the business district erected, have witnessed the establishment of every existing industry, and have hunted birds cm the site now one of the busiest corners of the business district. Incorporated as a town in 1871, the city today has a population of more than 380,000 in its metropolitan area. It is

Jan 1, 1937

Seismological Society of America, University of California, Berkeley, Calif. Perry Byerly, Secretary. The Bulletin of the Seismological Society of America is issued quarterly. The four numbers each year are collected in a volume; in 1932 the 22nd annual volume was published. The articles contained in the copies of the Bulletin are not, perhaps, of direct interest to a mining engineer but many of them will interest geologists. To indicate the type of articles contained in the Bulletin, the following titles, taken from the current issue, for June, 1932, are given: The Japanese earthquake of march 28, 1925, and the Problem of depth of focus; the earthquake in Santa Monica Bay, California, on August 30, 1930; a new vertical seismography. For copies of the bulletin or information concerning them, address the above.

Jan 1, 1933

By George E. Erdman

Gouverneur Talc Co. had sought an effective means of depicting its mine at Balmat, N. Y. since it commenced operations in 1947. After considerable research the engineering department settled on the idea of a model made of plexiglas at a scale of 1 in. to 50 ft. The solid portion of this model represents the actual underground excavations. Talc is mined from two metamorphic tremolite-talc orebodies which are part of a complex fold system in this region. In the mine, stopes are laid out in panels and developed into openings 50 ft wide, 10 to 80 ft high, and perhaps 200 ft in length. Pillars usually approximate 30 ft in width. All present mining operations are contained within a block 2000 ft long, 1700 ft wide, and 1500 ft thick.

Jan 11, 1960

(This list. includes only those who have entered military service within the past month, or whose entry has only recently become known to us; it also includes a few names of those whose titles or assignments have been changed within the month. A complete list will he found in the Year Book mailed with this Bulletin. Another Honor Roll is maintained in the reception room of the Institute.) ALDEN, HERBERT W., Lieutenant-Colonel, Ordnance Dept. ALDER, ALFRED; Engineers' Reserve Corps. ALFORD, NEWELL G., Sergeant, Bureau of War Risk Insurance, Headquarters 84th Division. AMBLER, HARRY A., Lieutenant, 30th Infantry. ANDERSON, GEORGE K., JR., Sec. C, 1st Co.; 3d Officers' Training Camp. AYER, -FRANK A., 1st Lieutenant, 43d Squadron, 3d Prov. Regiment, Aviation Camp.

Jan 3, 1918

By H. Landsberg

SUBSIDENCE caused by mining operations has been a matter of interest for the mining engineer for just 111 years, since the Belgian Committee for study of subsidence in the city of Liege submitted its first report in 1825. This interest is fairly expressed in the enormous amount of literature that has since appeared on this subject. A bibliography, probably far from being complete, which preceded this study as a pre-liminary survey, comprises more than 800 titles. In spite of this fact the problem remains today as acute as it has ever been. The questions of as good a recovery as possible of the national resources, the safety of the operations, and the protection of private and public property are the important angles from which to look at the problem.

Jan 1, 1936

By S. C. Oliphant, George H. Fancher

Two samples of drilling mud from the Hastings oil field, Texas, were tested, and the solids in each were separated into small fractions of a limited range in particle size. The mineral composition of each fraction by X-ray analysis is reported, and the results are interpreted in relation to other measured quantities, such as the physical properties of the original samples and the density of the various fractions. It was found that only 7 to 8 per cent by weight of the solids was of colloidal dimensions and that neither of the samples contained montmorillonite but did contain illite. Considerable calcite was also found. These data should be useful to the geologist interested in the origin and history of sedimentary strata as well as to the petroleum engineer.

Jan 1, 1942

By John Hays

AT the December Board meeting, the report of the William Lawrence Saunders Medal Committee, recommending the award of the medal to John Hays Hammond, was received and unanimously approved. The citation is: "For his notable work as an engineer and developer of mines at home and abroad, his industrial leadership and his public services." The medal will be presented as usual during the meeting in February, presumably at the annual dinner at the Waldorf, on Feb. 20. The other medals to be given on the same occasion are the James Douglas, which goes to Paul D. Merica, and the Robert W. Hunt, which is awarded this year to Edgar C. Bain, as already announced. This will be the third award made of the Saunders Medal for "Achievement in Mining," previous recipients having been David W. Brunton in 1927, and Herbert Hoover in 1928. The list is a distinguished one and Mr. Hammond's name is appropriately included. His career is so widely known that it is not necessary to repeat the account, published in MINING AND METALLURGY last April.

Jan 1, 1929

By L. Adler

The author recently proposed a technique for handling the effect of planes of weakness on failure in geologic material.1 The technique employed an "extended" Mohr's rupture envelope, on which was superimposed a generalized three dimensional stress representation. Subsequently, the method was applied to so-called two-dimensional stress states" which were in reality degenerate three-dimensional ones. Since a two-dimensional stress solution usually refers to a plane stress condition, the terminology was confusing. The distinction between a plane stress state and a degenerate three-dimensional one is shown in Fig. 1. The solution of problems involving a generalized three-dimensional stress state is greatly aided by continual reference to the basic principle that no stress components can act on a plane, oriented as is the weakness plane, which lies outside of the weakness plane's rupture enVelope.2 This is shown in Fig. 2; and if it is also remembered that the radii of the Mohr's Circles give the orientation of such a plane, solutions are easier to follow, and perform. Sample Problem 1: Site Location (generalized three-dimensional case).' Given: 1) Both rupture envelope for the solid and plane of weakness. 2) Existing principal stresses and orientations in space (?12, ?13) obtained from a stress analysis of the proposed structure. Find: Permissible orientations of the weakness plane in order to select a suitable site.

Jan 1, 1963

By V. Jares

DESPITE the fact that a combination of metals-aluminum-zinc-tin, and sometimes aluminum-zinc-cadmium-is extensively used for aluminum solders, as well as for die-castings, the constitution of these alloys has not yet been made clear. I. BINARY SYSTEMS The system aluminum-zinc is the basis of the ternary alloys under consideration. Their composition was made sufficiently clear by the investigations of Rosenhain and Archbutt,1 Bauer and Vogel,2 Sander and Meissner,3 Hanson and Gayler4 and Isihara.5 Only the temperature of decomposition of the crystals 0 seems still to be doubtful, whether it is considered as a compound of Al2Zn3 (according to Bauer and Vogel) or as an intermediate phase of variant composition (according to Hanson and Gayler). This temperature is given by most of the authors as in the neighborhood of 256° C., only Isihara giving 280° C. As its accurate determination is of special importance in the study of the ternary alloys under consideration it was experimentally controlled in the following manner: An alloy corresponding in composition to the formula Al2Zn3 was made, in which the temperature effect was found to be the greatest. This was drilled and a silver-constantan thermoelement inserted into the cavity so as to be in direct contact with the alloy. The whole was then very slowly heated and the heating and cooling curves determined. The transition temperature from the heating curve was found to be 281° C., whereas from the cooling curve it was 252° C.

Jan 1, 1927

By Edward Saibel, W. T. Lankford

DURING the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instability frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining will proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogeneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to. as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators 1,2.3,12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It is also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test specimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combined stresses on flow and rupture, account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By Paul M. Tyler

FOR the same reason that water is not missed until the well runs dry, the roles of many industrial minerals in wartime are often overlooked. In contrast to the growing shortages of many metals, our supplies of most nonmetallic minerals are limited only by our machinery for taking them from the ground and by our processing facilities. With few exceptions, the demand for increased supplies has been met without fanfare or delay. Only Brazilian quartz crystals, certain kinds of mica, and, latterly, industrial diamonds are on the so-called strategic list, although asbestos, beryl, corundum, cryolite, fluorspar, crucible-grade graphite, ilmenite, iodine, kyanite, monazite, nitrates, rutile, and zircon have caused more concern among those responsible for procurement and are included in our preclusive buying programs. Such specialties are needed urgently, but they are far less important in the over-all picture than the more abundant minerals.

Jan 1, 1942

By H. N. Thomson

(Butte Meeting, August, 1913.) GENERAL. THE Tooele plant. off the International Smelting & Refining Co. is situated at the mouth of Pine canyon, Tooele county, Utah. It is connected with the main line of the San Pedro, Los Angeles & Salt Lake railroad by the Tooele Valley. railway, and is about 7 miles from Tooele Junction. Fig,. 1 is a general view of the plant. The copper plant has been in operation since July, 1910, and the first blast furnace it the lead plant was blown in on Feb. 29, 1912. The location of the plant was selected on sloping ground with the idea of using gravity to the fullest extent and thus keeping labor at a minimum. Practically the entire plant is constructed of steel, reinforced concrete, and. brick.

Jan 7, 1913

By R. H. Swallow, George Hess

C. G. BALL*—These maps are obvi-~,usly quite helpful in many types of mining engineering, but I want to find out if the prints which you obtain in the first step toward making any aerial contour map have already been corrected for tilt. Is that done afterwards only if you are going into the process of making a contour map ? GEORGE HESS (authors' reply)— The tilt correction is the first step in either compiling the mosaic or compiling the total map. They must be corrected. C. G. BALL—But are the contact prints themselves corrected for tilt? GEORGE HESS—They are not corrected. E. R. KAISER†—I enjoyed this paper very much, and am glad to learn that the methods have a high degree of accuracy and are in use in the coal industry. Accuracy in dimensions is understandable from the paper. Would you tell us how accuracy can be obtained in the vertical dimensions by means of the photographs so as to permit drawing contour lines? GEORGE HESS—To explain our process, even in a limited way, is quite a large order. However, the basic principle involved is the measurement of parallax by viewing two overlapping photographs stereoscopically. It would almost be necessary to have the various instruments here on view to adequately explain their operation. E. R. KAISER—Are the elevations for reference obtained at more than four points ? GEORGE HESS—The pattern of control is four points obtained in the corners. Primarily. that is to restitute the picture and horizontalize it. The vertical control points are read ill on the stereometer and a direct comparison is made while draw- ing the contour lines. You do have to have those four points. But one stereoscopic pair of 5 ft contours has some 340 acres on it, consequently for every four points picked up 340 acres are contoured. E. R. KAISER—How does your method compare with that used by the military reconnaissance during World War II? GEORGE HESS—The Army did not get into this refined mapping. Most of their work has been reconnaissance mapping by taking one vertical and two oblique views. Basically, the same principle is used. Our maps are for engineering purposes. The Army was primarily interested in reconnaissance. E. R. KAISER—You could take more than 48 pictures in one flight? GEORGE HESS—Yes, the Brock camera accomodates 48 pictures per magazine. We are limited by the hours of greatest light, though, 2 hr before high noon, and 2 hr after high noon. Shadows do affect the picture. The shadows can-

Jan 1, 1950

By A. J. Bartlett

ISLAND Creek conditions are generally referred to as ideal; yet, as at all other properties, there are all known hazards of coal mining. The hardest of these hazards to combat is the human element. The basic thought in the minds of the management of these properties is to produce coal with the utmost safety, and it has impressed upon its supervisory force that it does not want a ton of coal unless it can be produced safely. This company has instituted a mine inspection department, which reports direct to the general manager, and all matters pertaining to safety come under the direction of this department. Through the medium of the inspection department, the management is kept in touch with the actual conditions existing in general at all mines. Inspections are made regularly and continuously; that is, at all times while the mines are in operation some sections of some mines are being examined. These inspections cover all active and inactive workings. Miners are con-tacted in their working places and other employees at their respective work. A thorough check is made to see that the state mining laws are complied with and that company safety rules are being observed. Night shifts receive the same attention as day shifts. All violations and dangerous practices are brought to the attention of the plant supervisory force with suggestions and recommendations; major hazards of emer-gency nature are taken up immediately with the management. Peri-odical inspections are also made of all tipples, preparation plants, dumping and hoisting equipment, to see that all machinery is properly guarded, and walkways and platforms properly fenced; conditions of equipment and mechanical defects are also reported. Reports of inspection are written in letter form and in such a manner as to give the management a picture-of the existing conditions at the time of inspection. Copies of inspection reports are forwarded; to the superintendents with the general manager's comments.

Jan 1, 1937

By W. T. Lankford, Edward Saibel

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By Edward Saibel, W. T. Lankford

During the course of an investigation of the plastic flow of aluminum aircraft sheet under combined loads, several problems arose in which analyses of the conditions leading to unstable plastic flow were needed. In order to provide these analyses, and in the hope of attaining a better understanding of the general problem of unstable plastic flow, the present study was undertaken. It is well known that unstable plastic flow is associated with a form of mechanical instabi!ity frequently observed during the plastic deformation of ductile metals. This instability is characterized by the fact that, at its onset, plastic straining mill proceed at a constant magnitude of the externally applied forces. It is further typical that the resulting unstable flow is generally accompanied by the formation of a neck, a local bulging, or some other form of heterogcneous deformation. Perhaps the most familiar example of unstable plastic flow to the metallurgist is the formation of the neck in the ordinary tension test. It is well known that in this test most metals exhibit a maximum in the externally applied load, followed by the process commonly referred to as "necking down." Instability in the simple tension test has been frequently discussed and numerous investigators1'2'3'12 have derived the criterion for instability in terms of a critical rate of strain hardening. It is the purpose of the present study to extend the criterion for unstable flow to the more general case where the body undergoing flow is subjected to combined loads. It is hoped that the problems considered will provide a more consistent picture of the general features of this important form of mechanical instability. The most practical implications of instability in plastic flow arise in connection with sheet metal forming operations. In the formation of a great many sheet metal parts, the deformations are produced primarily by stretching. If the conditions which lead to unstable flow are fulfilled in such a formation, and if the resultant instability leads to a pronounced localization of flow, then the useful limit of ductility of the material will have been reached. It i; also essential that the effects of instability be taken into consideration in any study of the plastic flow and rupture of metals under combined stresses. In general, when unstable plastic flow is initiated, straining becomes localized, the geometry of the test splecimen changes, and the state of stress in that portion of the specimen undergoing plastic flow is no longer under external control. In many past studies of the effects of combinetl Metals On flow and rupture) account has not been taken of the fact that, although a given test may be started under constant

Jan 1, 1947

By R. T. DeHoff

A new approach to the measurement of the size distribution of particulate structures imbedded in opaque bodies is developed. The method is based upon the assumption of a general two-parameter distribution curve, and the estimation of these two parameters from three well-known counting measurements made upon metallogvaphic sections. The total number of particles in the system is also a product of the analysis. Application of the method with the assumption of the logarithmiconorma1 disfribution function is developed in detail. A complete description of the geometry of a particulate structure requires the determination of the size distribution of particles. The problem of estimating the size distribution of particles of a particular phase in a multiphase system, or the grain-size distribution in a homogeneous system, has been approached by many investigators.'-'0 All of the solutions proposed by these investigators share the following characteristics. a) A minimum of several hundred particle sections in the microstructure must be examined, and some characteristic dimension recorded, such as area,3'5 intercept length,6"9 or diameter.1'2'4'10 b) The resulting data must undergo a series of fairly complex calculations to generate the empirical histogram which describes the size distribution in three dimensions. c) In order to manipulate the result, the histogram must be fitted to some assumed mathematical formula, using the attendant statistical procedures. d) With two notable exceptions,8,10 the particles must be spherical. The measurements and calculations involved are in general very tedious and time-consuming, with the logical result that much effort has been expended in the development of equipment which will perform these tasks automatically and semiautomati-cally.9,11-15 considerable success has been achieved in this area, but the equipment is in general expensive, and usually places stringent requirements On the quality of microstructure which can be reliably analyzed. In laboratories which do not possess such equip- ment, the analysis of geometry is usually limited to measuring total properties of the microstructures, such as volume fraction and interfacial area, because the measurements required are much simpler to make. The determination of size distributions rarely is undertaken. The development which is presented in this paper permits the estimation of size distributions of three-dimensional structures from the same simple counting measurements which are required to determine the surface area and volume fraction of the particulate structure, and one other counting measurement. The basic approach that is used is to assume a general mathematical form for the distribution, which is described by two parameters (as the normal distribution is described by assigning values to the mean and the standard deviation), and then estimate these two parameters from the results of the counting measurements. The introduction of a third counting measurement also permits the evaluation of the number of particles per unit volume, Nv.

Jan 1, 1965