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By F. R. Hutto Jr., F. L. Kady Jr., L. E. Weymouth

The behavior of particulate non-metallic materials in moving contact with smooth surfaces is of interest and concern to manufacturers and users of abrasives, of fillers, and of pigments alike. The theoretical aspects of the subject have been treated to considerable extent in the literature, and correlatic,ns are available that attempt to relate various methods of hardness determination." 2 The particle size and friability are characteristics of the abrasive that are not related to the smooth surface. The hardness, on the other hand, may be visualized as relative to that of the smooth surface. In a study of abrasive action, the role that hardness, per se, plays is a complicated one. For it is necessary to compare the "hardness" of the abrasive, usually a non-metallic, with that of the smooth surface, generally a metal. Hardness of non-metallics is defined as resistance to scratch and is almost universally described with respect to the Mohs scale.3 Minerals have been rated by Mohs numerically from the softest (talc = 1) to the hardest (diamond = 10). By definition, a mineral has a designated hardness when it is scratched by the standard that is numerically just above it on the scale; and conversely, when it scratches the standard that is just below it. Hardness of metals. however.. implies resistance to indentation, a property that has been measured by a number of methods. In fact, the indentation hardnesses of the standard minerals on the hlohs scale have been determined by the Rockwell tester. Reproduced below are two versions of this correlation. 'A conversion chart, prepared by Wilson Mechanical Instruments Division of American Chain and Cable Co., merely gives the conversion from Rockwell to Knoop hardness. The relation between Knoop indentation hardness and Mohs scale has been reported by G. S. Smith — A New Scale of Hardness, The Engineer, Aug. 26. 1949. G. F. Kinney in Engineerin Properties and Aplications of Plastics reports the Rockwell hardness of the minerals directly in the Mohs scale. The question immediately arises as to whether this relation is valid when applied in reverse; namely,

Jan 1, 1961

By T. E. Brower

SHORTLY after our previous paper on this subject was printed,1 we located a source of uncertainty in the results arising from the unexpected fact that hydrogen slowly reduces silica at 1100° C. in presence of iron, even when the iron nowhere touches the silica, although in absence of iron it does not do so. This difficulty has been completely obviated by the use of a small high-frequency furnace, which enables us to heat the specimen for analysis without raising the temperature of the silica vessel to a point at which any appreciable reduction of the silica glass occurs. We now describe this modification of procedure, and present some typical results obtained with it. For any given specimen of steel, the results are entirely definite and. reproducible, but their precise significance is still open to some question, as indeed is true of all methods of oxygen determination so far developed. Further elucidation of this question is to be expected from the cooperative comparison of the several methods now under way under the auspices of the Bureau of Standards at the instance of the Iron and Steel Division of the A.I.M.E.

Jan 1, 1934

By Louise Reber

THE town of Jerome is located in Yavapai County in north central Arizona. It has a population of over 6000 people and the two important mines of the district, the United Verde and the United Verde Extension, lie almost within its limits. Perched high on the southwest side of the Verde Valley, at elevations of 4800 and 5500 ft.. (1463 and 1676 m.), both mines have long tunnels from their lower levels through which ore is hauled to their respective smelters. The two smelter towns of Clarkdale and Verde, out in. the center of the valley and about 2000 ft. (609 m.) below, form part of the wide panorama that meets the eye at Jerome. This panorama and the topographic and surface features and the geologic formations are shown in a separate pamphlet. In the vicinity of Jerome, the great southern escarpment of the Arizona plateau forms the northeast side of the Verde valley. The general level of this escarpment, or "the rim" as it is called, is about 4000 ft. above the Verde River. A corresponding elevation is reached only by the, highest parts of the Black Hills, which bound the valley to the southwest. The two lava-capped mesas, known as Mingus and Woodschute Mountains, form the culmination of the Black Hills. That part of the old Black Hills mining district which lies between their crests -and the Verde River is now known as the Jerome or Verde copper district. However, if the smelters are not included, a strip about 7 mi. long and 3 mi. wide (11 by 5 km.) embraces practically all the properties belonging to the Jerome district. This strip lies parallel to and along the side of the Verde valley from about First View, 2 mi. northwest of Jerome, to the neighborhood of Allen Spring, near the south end of Mingus. Mountain. The rank of the district in copper production, as well as features of peculiar geologic interest in connection with the ore occurrences, entitle the district to much more consideration than it has received in the literature of copper mining. Arizona stands preeminent as a copper-producing state. In 1918, it produced four-tenths of the total amount produced in the United States, and nearly equaled the, combined production of its three chief competitors, Montana, Michigan, and Utah. The production of the Jerome district places it in the sixth place among the copper

Jan 8, 1920

By A. Hultgren

PAGE Outline of Progress of Knowledge and Theories about Gas Evolution in Steel Ingots, and Its Influence on Crystallization and Segregation 2 Object of Present Investigation 16 theoretical Discussion of Process of Solidification 17 Gas Given Off from Rimming Steel during Solidification 17 Equilibrium Diagram of the Iron-carbon-oxygen Alloys 19 Solidification of Pure Iron-carbon-oxygen Alloys 25 Solidification When Carbon Monoxide Is Given Off at Constant Pressure... 25 Solidification When Gas Evolution Is Suppressed 26 Schematic Application on Solidification of Rimming-steel Ingots 27 Influence of Manganese, Sulphur and Phosphorus 28 Experimental Work 30 Liquid Steel and the Mold Gas 30 Ingots Investigated and Methods Used 33 Ingot Structure 42 Structure of Rim Zone 42 Structure of Core 49 Structures Obtained under Special Conditions of Freezing 50 Distribution of Metalloids 55 Other Observations Made 60 General Discussion of Solidification Process 63 Condition of Liquid Steel before Casting 63 Rimming Period 70 Composition of Rim Zone 93 Freezing after Top Is Closed 96 Slag Inclusions and Ingot Scum 102 Reaction between Gas in Blowholes and Surrounding Solid Steel during Cooling 103 Summary 105 Appendix-Preparation and Etching of Ingot Sections 106 References 107 IN 1934, Jernkontoret (The Swedish Ironmasters' Association) appointed a committee for the study of the structure of rimming-steel ingots and the various phenomena associated with their solidification. The members of the committee, including those who have joined it later, have been: I. Bohm, B. D. Enlund, B. Kalling, M. Tigerschiöld, 1. Wohlfahrt and the authors. The present paper? is a somewhat

Jan 1, 1939

By Paul M. Tyler

MARKETWISE the year 1935 was rather a good one for most of the rare and minor metals; as a class they climbed out of the depression much faster than the common metals. The diamond market, too, was better than it had been for years, attributable only in part to investment buying, as there was a genuine pick-up in consumer demand. Wars and rumors of war tended to speed up purchases of certain metals, but consumption for peaceful purposes was the principal factor. Significant was the important role played by new industrial uses. New discoveries during the year were disappointingly few, considering the broad extent of this research frontier. Scientific developments were far from being at a stand-still, of course, but the dominant note was the cashing in on research consummated in former years. With even a moderate upturn in general business a surprising number of laboratory ideas donned overalls and found jobs in industry.

Jan 1, 1936

By Edward H. Robie

PONCA CITY proved an ideal selection as a place of meeting for the Petroleum Division this fall. The accommodations at the Conoco Club were just what was required for such a gathering; the committee having the arrangements in charge functioned with the efficiency of veterans and the enthusiasm of neophytes; and the members and guests followed the speakers with close attention, entered the subsequent discussions with gusto, and divulged the "low-down" at private conferences. No one minded the drizzling rain on the first day, which only served to keep up the attendance in the auditorium; the weather then cleared up in time for a group picture before the gathering went their separate ways.

Jan 1, 1932

By W. R. Crane

THE effect of mining in the red-ore mines of the Birmingham district has been observed for some time, but, except in a few localities, little difficulty has been experienced from disturbance of cover. Cave-ins near the outcrop and fracturing of the surface at greater distances are the most pronounced manifestations of disturbance, while limited areas at points distant from the outcrop and under greater depth of cover have actually subsided. There is no doubt but that in time, because of failure of pillars, extensive fracturing and widespread settlement of the surface will result, particularly along the slope of Red Mountain, where mining has been under way for many years. Were it not that the orebed is overlain by one or more water-bearing formations, the fracturing or settlement of the surface would not be serious; but because of these formations, fracturing of the top rock may in itself be of sufficient importance to warrant the adoption of protective measures. Until development openings and surface plants are transferred to Shades Valley, protection of the surface will probably not be considered imperative, as the area involved is not of particular value for agricultural or building purposes. Further, the collapse of pillars over a wide area may develop squeezes that, if not controlled, may jeopardize the integrity of the mines and necessitate a change in development, from slopes to vertical shafts, at a much earlier period than is now contemplated. The occurrence of heavy beds of strong tough materials at varying distances above the orebed make it doubtful whether any serious disturbance of the surface will be experienced at any considerable distance from the outcrop, although some settlement will probably take place. It is certain, however, that no great volume of water will enter the mines from fracturing of the Fort Payne chert bed, as this is known to be a compact and practically impervious formation beyond the leached zone. Not so much can be said, however, regarding other possible sources of water, as pervious beds and through faults that may be encountered in future mining operations.

Jan 8, 1925

By B. C. Allen

The solubility of chromium in liquid silver and that of molybdenum and tungsten in liquid tin have been determined by equilibrating Ike Liquid in a crucible of the solule metal. Generally the weight of solute in solulion was delermined both chemically and from crucible weight losses. The resulting weight percent solubilily of chromium in silver as a function of absolule temperature T is given by log w = -6660/T + 4.02 in the range 960° to 1445°C, and that of molybdenlttrl in tin by log w = —5050/T + 1. 79 in the range 1200° to 2200°C. The values appear unaffected by minor changes in solute composition. Calculations aye made of the parlial molar heal and excess entropy of mixing. The estimated solubility of tungsten in tin is 0.001 pct at 2000°C. Evidence is presented that molybdenwm dissolves in tin without compound for mation and that tungsten and tin form W10Sn. RECENT developments in coatings, heat transfer, and brazing require a knowledge of equilibrium solubilities in a variety of systems at elevated temperatures. Of particular interest are solid-liquid interactions in metal systems involving dilute solutions. This investigation was undertaken since little is known about the phase relations or solubility of chromium in liquid silver or of molybdenum and tungsten in liquid tin.1,2 EXPERIMENTAL WORK As indicated in Table I, high-purity metals or those of known impurity levels were used. Crucibles were machined from chromium, molybdenum, and tungsten bar stock 1.3 cm diam and 2.2 cm long. Chromium rod was prepared by arc melting and extruding iodide process crystals.3 The five chromium impurity alloys were in the form of 0.6-cm-diam swaged rod. A Cr-0.06N* alloy was prepared by exposure to NH3 at 1150°C in a closed quartz capsule for 24 hr. Because significant nitrogen was lost during annealing in argon at 1600°C,4 the estimated level was 0.01 pct N. Chromium and Mo,W crucibles were outgassed at 1200" and 1600°C, respectively, at 3 X 10-5 mm. The solvent was placed In crucibles of the solute metal- 6 g Ag in chromium, 0.4 g Ag in the five chromium impurity alloys, and 4 g Sn in Mo,W crucibles. The silver and tin series were outgassed at 900" and 110O°C, respectively, and held at the desired solution temperature in a tantalum resistance furnace under 1.05 atm 99.995 pct Ar. An equilibration time of 0.5 to 1 hr was chosen since 0.3-, I-, and 4-hr anneals at 1235°C for Cr-Ag yielded similar results. Temperatures were measured optically to +10°C under essentially black body conditions which were checked against the melting point of silver. The Cr-Ag and Mo-Sn,W-Sn series were respectively equilibrated at 990° to 1400°C and 1200" to 2000°C. Vaporization losses were generally held to <1 pct by the argon. In the 1800" and 2000°C anneals for 0.5 hr, the crucibles were placed in tightly sealed tantalum cans which kept tin losses to <5 pct. After the anneals, the specimens were furnace-cooled. One anneal was made on small Mo-0.02 C, Mo-0.5Ti-0.lZr, and tungsten crucibles containing tin at 2200°C. The metals were sealed in an electron-beam-welded tantalum can of minimum volume. After the anneal, tin was still present in each crucible, none of which was severely attacked. After equilibration, the saturated solvent metal was selectively removed from the crucible by acid leaching. Weight losses sustained by the crucibles were determined from the initial weight minus the final blank-corrected weight after acid leaching. Chemical analyses were performed on some of the samples. Hot 1:l HNO3-H2O removed silver from chromium with the blank running <0.1 mg or <0.002 pct on measured solubility. Tin was removed from molybdenum and tungsten by hot concentrated HC1 with the respective blanks amounting to -0.004 and -0.0004 pct in the presence of tin. The insoluble residues were weighed and checked for composition. The leaching solutions contained traces of the solute metals which were analyzed by colorimetric methods, Diphenyl Carbazide for chromium, Thiocyanate for molybdenum, and Dithiol for tungsten. The total of the two percentages found from the residue and leaching solution minus the blank gave the desired solubility values. On the basis of annealing empty molybdenum and tungsten crucibles, weight losses due to MoO3 or WO3 volatilization were found to be generally 10.4 mg and affect measured solubilities by <0.01pct. RESULTS AND DISCUSSION Chromium-Silver . Since no intermediate compounds are reported to form in the Cr-An system,&apos; crucible weight losses and chemical analysis of the entire melt should provide reliable measures of the chromium in solution. Values obtained by the two methods are in agreement as shown by the results for unalloyed chromium in Table II and plotted in Fig. 1. Furthermore, the results are consistent with those previously determined by melting equilibrated silver out of the crucible and analyzing calorimetrically for chromium.&apos; On the basis of limited thermal analysis data, the solubility of chromium in silver has been quoted as 8 pct at the monotectic temperature of -1445°C.1 This investigation indicates an extrapolated solubility of 1.38 pct which is believed to be more reliable. At the eu-

Jan 1, 1968

By John Griffen

HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as follows:

Jan 1, 1943

By L. A. Cowan

IF the elements of personality be those characteristics in which humans differ, and if this definition be applied to the purchasing department for the Climax operations in Colorado, it must he concluded that this department has no distinguishing traits that would give it a departmental personality different from that possessed by the similar department of any progressive mining enterprise. Or, one may go further by stating that the rudimentary functions of any purchasing practice employed principally in the acquisition of maintenance, repair, and operating supplies are much alike, whether or not the industry involved be mining or milling. However, in the fact that the principal purchases of a mining company are materials for maintenance and repair and consumable operating supplies lies that essential characteristic which differentiates mining and milling purchasing functions from those of the manufacturer, the fabricator, or the ordinary processor.

Jan 1, 1946

By R. Dawson Hall

WHAT are the opportunities for the services of engineers in the coal mines? The best answer perhaps can be made by detailing the present lines of development in the bituminous coal mining regions. They are just at the beginning of a period that can be conservatively termed revolutionary. A few glimpses of new possibilities in economic mining that will reduce the cost of bituminous coal at the mines by at least one half have convinced almost everyone that a change must shortly come about. The cost of housing has become such a burden, especially in mountainous regions, that development which demands the hiring of more men and constructing more houses would not be profitable. The introduction of mechanical aids to mining, transportation and dumping suggests a way of obtaining a large tonnage with the same or a smaller number of men with no further house construction. At the same time the restriction of immigration has made it increasingly difficult to obtain men inured to hard labor. Modern civilization is not productive of muscular energy and at the same time it provides men who are not indisposed to the use of the mental effort required to direct the physical forces now available for the replacement of such energy.

Jan 1, 1924

Successful preliminary experiments at the University of North Carolina indicate that computers can provide speedy, accurate identification of the mineral content of rock samples. In just two minutes, the University&apos;s Univac 1105 computer solves the complex equations that would often require more than four hours using conventional methods. In addition, the computer is frequently spotting minerals that a geologist might miss simply because he wasn&apos;t looking for them.

Jan 6, 1964

By Robert Linton

SPECIFICATIONS for clays serving raw materials in the ceramic industry usually contain the following items: (1) Chemical analysis, sometimes with mineralogical structure determined by microscopic investigation. (2) Maturing temperature and firing range, usually expressed in terms of pyrometric cone equivalent. (3) Shrinkage (drying and firing shrinkage separately). (4) Degree of plasticity. (5) Color after firing. Clays may be classified, according to the purpose of the classification, in several different ways, based on (1) Geological occurrence-transported, altered An place, indurated (shales). (2) Physical properties-plastic (bonding clays, ball clays) and nonplastic (flint clays, kaolins or china clays, bone clays). (3) Color. (4) Use. A common classification of clays for commercial designation, and one fol-

Jan 1, 1936

By JOHN R. SUMAN

COMMENCEMENT exercises this year have a peculiar significance because the graduating students are entering upon their life&apos;s work at the most critical time in the history of the United States. We are engaged in a great struggle the outcome of which is none too clear even to the best informed students of international affairs. We are starting late in a vicious world conflict where it is generally recognized that our adversaries have distinct superiority over us in armament on the land, on the sea, and in the air. We have the gigantic task of building up our armed forces and armament and at the same time supplying our allies with equipment which they must have. We can do this job if we are given sufficient time, but there is a possibility that the war will be over before we are ready. Few realize the seriousness of this situation. If this fight is to be won-and we dare not try to visualize the future of this country if it is lost-all dissension and bickering between Congress, capital, labor, and agriculture must cease. When and where voluntary co-operation proves inadequate for the successful conduct of the war effort, laws must be enacted or strengthened to achieve our purpose.

Jan 1, 1942

By AIME AIME

WIDESPREAD interest in the better utilization of coal is indicated by the attendance of over seventeen hundred men interested in the pro- cessing and utilization of coal and its by-products, at Pittsburgh, Nov. 15 to 18. The conference was truly international in scope and of a scientific character, and must be considered a real success. There were dele- gates--official and unofficial-from America, Belgium, Canada, Czechoslovakia, France, Germany, Great Britain, Japan, Mexico, and Sweden. Several Federal and 28 State departments had representatives, also many colleges and universities, and many leading industrial and mining corporations throughout the country. A feature of the sessions was that papers were mostly read in full and attentively listened to, although in some cases they were of a technical nature. The proceedings were opened by the president of Carnegie Institute of Technology, Thomas C. Baker, who spoke of the importance of the conference and felt that without foreign cooperation it could not have been held. There was no need to apologize for the movement of Carnegie Institute of Technology in the matter. Coal is commanding attention in every part of the world; so is power; and coal will remain the chief source of power for generations to come. The coal chemist is working with the engineer, and nobody can forecast what developments there will be in fuel technology. This conference may be the turning point of fuel technology in America. The development and application of these new processes may be of great benefit to Pittsburgh.

Jan 1, 1926

By Roy E. Dickerson

CUBA differs considerably from the other Greater Antilles in many geologic fundamentals. Cuba is geosynclinals; whereas Jamaica, Hispaniola. (Haiti), and Puerto Rico are geoanticlinal. (Scliuchert, Chas., Historical Geology of the Antillian. Caribbean Region, p. 13, 1935.) Rocks of lowermost Cretaceous age exist in large volume in Cuba, where- as they are generally absent in the other islands. Since many of the surface indications of petroleum are intimately associated with lowermost Cretaceous rocks, the Vinales limestone,, this difference is most important. The Vinales limestone in many places in Pillar del Rio and Santa Clara provinces reeks with light tars when broken with a hammer. The late David White and his associates on the U. S: Geological Survey studied

Jan 1, 1937

By Dozier Fircley

SOME nonmetallic minerals and their products, such as portland cement, common brick and hollow tile, sand, gravel, crushed rock, vitrified salt-glaze clay pipe, and the like, are a necessity in every community. They are mineral in nature but the establishment of plants for their production is usually a local and elementary problem. Yet it is probable that an economic study of the problem in every locality will show that such nonmetallic mineral commodities are not always obtained in the most economical way, or in the best quality. Other nonmetallic minerals are of such value that they may be shipped for long distances and sold in sufficient quantities to establish prosperous commercial ventures. Among these are phosphates, barium compounds, borates, nitrogen compounds, magnesium compounds, sulfur, asbestos, and potash. Success in marketing such products depends on quality, production cost, transportation, and similar conditions.

Jan 1, 1932

By S. A. Falconer

D. A. Dahlstrom—Mr. Falconer has done an admirable job of proving the adaptability of the cyclone to the beneficiation of a very difficult size range in the preparation of coal. The addition of the cyclone to other coarser size methods makes it economically feasible for the coal operator to rigorously control his marketed products at a high and uniform quality level down to the 48 and 100-mesh size. Furthermore, it should be pointed out that by utilizing the cyclone as a deslimer or classifier the —3 200-mesh fraction, usually containing large percentages of undesirable material, can also be quickly and cheaply removed from the clean coal. Advantages of such a step are several: (1) Reduction of ash content, especially where clays and slimes are serious. (2) lower moisture content of the final coal. (3) easier mechanical and thermal de-watering of the fine coal due to higher cake and bed permeabilities. The author has indicated that adjustable control means should be installed on the cyclone operating on a heavy-media slurry. This also holds true for the cyclone acting as classifier, deslimer or preliminary dewatering agent and is worthy of special emphasis. Such controls, while not necessarily automatic, must be simple, rapidly adjustable, and require a minimum of attention. Three methods available to the operator are (1) throttling valve on the feed line, (2) back pressure valve on the overflow, and (3) adjustable diameter underflow nozzles. The first two, while fulfilling the specifications, suffer the disadvantage of restricting capacity if severe throttling is necessary. The third method has little effect on capacity and easily maintains an underflow of correct moisture content. Several designs are possible, but two find the widest application. The first was developed by Robert Piros of The Truax-Traer Coal Co. and uses a simple casting containing two holders for underflow nozzles which can be rotated about an axis parallel to the cyclone centerline. These holders retain the underflow nozzle flush with the conical section walls. When a change in nozzle diameter is required, the new size is placed in the spare holder and rotated into place. A second design utilizes a soft rubber cylindrical tube which is compressed or released from three sides, causing the inner diameter of the tube to decrease or increase. This is achieved by using a machine-threaded,

Jan 1, 1951

By S. A. Falconer

D. A. Dahlstrom—Mr. Falconer has done an admirable job of proving the adaptability of the cyclone to the beneficiation of a very difficult size range in the preparation of coal. The addition of the cyclone to other coarser size methods makes it economically feasible for the coal operator to rigorously control his marketed products at a high and uniform quality level down to the 48 and 100-mesh size. Furthermore, it should be pointed out that by utilizing the cyclone as a deslimer or classifier the —3 200-mesh fraction, usually containing large percentages of undesirable material, can also be quickly and cheaply removed from the clean coal. Advantages of such a step are several: (1) Reduction of ash content, especially where clays and slimes are serious. (2) lower moisture content of the final coal. (3) easier mechanical and thermal de-watering of the fine coal due to higher cake and bed permeabilities. The author has indicated that adjustable control means should be installed on the cyclone operating on a heavy-media slurry. This also holds true for the cyclone acting as classifier, deslimer or preliminary dewatering agent and is worthy of special emphasis. Such controls, while not necessarily automatic, must be simple, rapidly adjustable, and require a minimum of attention. Three methods available to the operator are (1) throttling valve on the feed line, (2) back pressure valve on the overflow, and (3) adjustable diameter underflow nozzles. The first two, while fulfilling the specifications, suffer the disadvantage of restricting capacity if severe throttling is necessary. The third method has little effect on capacity and easily maintains an underflow of correct moisture content. Several designs are possible, but two find the widest application. The first was developed by Robert Piros of The Truax-Traer Coal Co. and uses a simple casting containing two holders for underflow nozzles which can be rotated about an axis parallel to the cyclone centerline. These holders retain the underflow nozzle flush with the conical section walls. When a change in nozzle diameter is required, the new size is placed in the spare holder and rotated into place. A second design utilizes a soft rubber cylindrical tube which is compressed or released from three sides, causing the inner diameter of the tube to decrease or increase. This is achieved by using a machine-threaded,

Jan 1, 1951

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,&apos; based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry&apos; has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962