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By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper' that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By Charles A. Schffer

Several months ago, some specimens of the minerals occurring at the Etta tin mine, Dakota, were received at the laboratory of the Cornell University. On examining the heavy brownish-black portion, which I presumed was the tin-stone, I was surprised to find only a faint indication of tin. Further investigation showed the mineral to be tantalite. On searching carefully all the fragments received, a considerable quantity of that mineral was found, and only a single streak of cassiterite, which was attached to a mass of spodumene. Another lot of specimens, from the same locality, consisted of

Jan 1, 1885

In discussing Mr. Keller's paper, I quoted the results obtained by Mr. Allan Gibb, correctly crediting them to Mr. Gibb, with due reference to the report in which they were published. But in the table immediately following, and in my further remarks, following the table, I find that, by some clerical or other error which I cannot, after the lapse of time, explain, I spoke of Mr. Gibb as Mr. "Dean"—a metallurgist who had written on a related subject, but not on the point I was discussing. In short, my reference throughout was to the work of Mr. Gibb; and by reading a Gibb " for a Dean " in all places on pp. 832 and 835 where the latter name occurs, my remarks will be brought into accordance with my intention, and with the facts.

Jan 1, 1901

By Marcel R. Daly

The writer has devoted a number of years to practical operations and to the study of geology in the oil fields. In consequence, he has been brought to investigate the theories advanced to account for the accumulation of oil and gas in commercial deposits. It is the result of these investigations and his personal conclusions that he wishes to sum up in this paper. The writer is an advocate of the organic origin of petroleum found in pools. He has been led to believe that the present theories of oil and gas accumulations are incomplete and, in certain respects, incorrect, although they may embody certain elements of truth; that the forces that are called upon to explain the movement are only secondary forces in the process, and insufficient, by themselves, to cause this movement; and that the phenomenon of accumulation is of much larger order than heretofore admitted and bears an intimate relation with the general as well as with the local deformations of the crust and is a direct consequence and a mechanical effect of these deformations to which the term " diastrophie " has been applied. As a complement to this theory, the writer offers a new interpretation of the "rock pressure" and of the mechanism of the "sealing up" of this pressure in oil and gas pools. The Anticlinal Theory The theory most generally accepted to account for the accumulation of hydrocarbons in commercial deposits is the anticlinal or structural theory. This theory, the principles of which have been laid down by I. C. White, Orton, Winehell and others, and which has since been modified and perfected, is too well known to need a detailed statement. A clear interpretation of it may be found, in the paper of W. T. Griswold, in Bulletin No. 318 of the United States Geological Survey, and the reader is

Jan 1, 1917

By Paul Sterling

The general impression regarding the preparation of merchantable anthracite is that it is confined to a colossal, grimy structure, called a " coal-breaker." This name is a misnomer; for the desired result is not to break the coal, but to prevent its being broken. Preparation may be said to begin at the face of the chamber, with the mining and loading of the coal. Local conditions vary, not only ill the same field or basin, but also in the same mine, so that there is no fixed empirical rule governing the method of blasting or cutting coal. Tests should be made, when possible, to determine the explosive, or the mechanical coal-cutter, which will produce the largest percentage of what are locally known as " lump " and " prepared sizes " of anthracite. The prepared sizes are those mostly consumed for clomestic purposes. All other sizes might be called by-products of the anthracite industry; for they are not especially desirable, being the degradation resulting from the mining and handling of a brittle or laminated material. Being low in volatile combustible matter, anthracite burns most successfully when nearly of a uniform size, permitting the easy passage of air through the voids. This accounts for the large number of sizes into which the coal is separated. Table I. gives the various sizes, the diameter of ring over and through which each size is made, and the usual purpose for which it is employed.

Jan 1, 1912

By Alan Bauer

DRILLING CONSIDERATIONS In considering blasting it is necessary to consider the drilling and explosives since one is generally concerned with the total cost of muck of a certain size in the pit or through the crusher. To get a current idea of the drilling situation in open pit mines plotted in Fig. 1 are the drilling costs per ton of material vs. hole diameter for rotary drill holes in large limestone, iron ore and taconite operations. The exception is the 2-in. diam hole which was drilled with a percussion drill in limestone. Each curve in Fig. 1 represents a different operation and the data cover many months of production drilling. The costs are total operating and maintenance and do not include machine depreciation. As the hole size is increased so are the machine size and the investment. Providing the tonnage is available to be drilled, then as the machine size goes up so does the productivity-markedly-and this same shape of curve applies. In some instances it is even steeper. The interesting thing to note is that in each case studied there is a substantial drop-off in cost/ton as the hole size is increased. This is true for the softest material considered, limestone, through to the hardest, taconite. How has this come about? In going from 10-in. to 123-in. diam holes, the powder factors have generally stayed about the same and the same type of muck has been produced. To date this has been mainly in the softer materials but it has also been steadily taking hold in the harder ones. On this basis, then, patterns are generally expanded as the ratio of the hole diameters or close to it, if the explosive type is kept the same. In the harder rocks the cost per foot of hole has increased somewhat so that the overall reduction in drilling cost per ton is about 25 pct. In somewhat weaker rocks of about 25,000 psi compressional strength the drilling cost per

Jan 1, 1968

By Michel L. Bilodeau

The objective of delineation drilling is to provide a data base for the tonnage and grade estimates required to evaluate the economics of mine development. As drilling information is accumulated, geological risk is reduced and more reliable estimates of tonnage and grade are obtained. Investment in drilling is justified by the benefits which result from improving the reliability of the economic criteria evaluated. These benefits are subject to diminishing returns, i.e. as drilling information is accumulated the reliability of the economic criteria evaluated is improved but at a decreasing rate. At the same time, costs are incurred -- the direct investment cost associated with additional drilling and the time cost of delaying possible production revenues. The economic sampling limit is de- fined by the point at which the marginal benefits from drilling investment just balance the marginal costs. The paper describes the formulation of an economic model to optimize investment in delineation drilling. The model is applied to a simulated mineral deposit to illustrate the economic effects of a sequential drilling program.

Jan 1, 1977

By C. W. Hall

Owing to its isolation and comparatively small tonnage, the Yoquivo district is not widely known; though financially important and, geologically, quite interesting. San Francisco dc Yoquivo, the center of the mining district, is in the western part of the state of Chihuahua, Mexico; about 35 miles west of. San Juanito, on the Kansas City, Mexico & Orient R. R. The town can be reached from the railroad by a good trail over a rugged country. The elevation of Yoquivo is 6500 ft., and peaks surrounding the town are 2000 ft. higher. The mining towns of Concheno and Ocampo are 25 miles northwest, and Uruachic is 20 miles southwest. The climate, temperate and healthful, is almost ideal. The rainy season begins in July and ends the latter part of September. There is usually, though not always, some precipitation in all months except April, May, and June: The mountains are covered with pine and scrub oak. Water, wood and lumber are plentiful for all ordinary purposes, and hydroelectric power is available for. about six months of the year, when wood for steam, power is utilized as an expedient. The district has been worked: recurrently for over 60 years. The Yoquivo province lies on the steep western-slope of the Tara-humara division of the Sierra Madre range of mountains. The province is traversed by many deep canyons, most of which flow west. The town is situated on the San Francisco arroyo, which makes a confluence with the Huevachic stream 212 m. southwest; the Huevachic in turn joins the Candemeña river farther down and these two drain the western flank of the Tarahumara mountains and form the headwaters of the Mayo river. The claims of the Yoquivo Development Co., which, is the only organization in the district with a record of any considerable production,: lie within an area roughly 112 m. square. The area extends from the, San Francisco arroyo north, and from the Dolores arroyo west, and is confined to the andesitc formation.

Jan 2, 1926

By E. M. Tory, P. T. Shannon

An analysis of batch and continuous thickening in terms of the movement of planes of constant concentration (i.e. continuity waves) is presented. Use of solids flux as a primary variable greatly facilitates the analysis and clarifies the relationship between batch and continuous thickening. An "ideal" slurry is defined as one whose settling rate is a function only of the local solids concentration. An analysis of continuous thickening of this ideal slurry in an ideal thickener explains many aspects of the steady — and unsteady — state behavior of real slurries, such as the main features of a thickener's "solids profile" (including the break attributed to rake action), the sudden appearance at abnormally high feed rates of a zone of constant concentration and the velocity with which it rises, and the effect of detention time at constant weight of sludge per unit area. Where deviations exist, they are explained in terms of the batch settling behavior of real slurries. The purpose of this paper is to interpret continuous thickening phenomena in terms of batch settling behavior. Both types of thickening may be considered as the process of propagating concentration changes, due to the downward movement of the solids, from the bottom of the settling vessel upward through the slurry.' These concentration changes may be either finite or infinitesimal as in the case of the propagation of a continuous concentration gradient. The slurry itself may be moving downward as in the case of continuous thickening. The downward velocity of the slurry may be such that the concentration changes being propagated up from below remain stationary relative to the thickener walls. This is the case for steady-state thickening. It seems appropriate to analyze continuous thickening in terms of the movement of planes of constant concentration. This has already been done for batch settling."3 Although our main interest is in real slurries, there are certain aspects of both types of settling which can be deduced from a theoretical analysis of highly idealized systems. To this end, an "ideal slurry" is defined as one for which the dimensionless settling rate at any point is a function only of the local solids concentration.1,2 An "ideal thickener" is one in which there is no radial variation in either the solids concentration or in the downward component of slurry velocity. The underflow outlet is a point sink. It is to be expected that the behavior of non-ideal systems will deviate in some measure from theoretical results. However, the same characteristics which cause deviations in continuous thickening should be evident in batch settling, permitting a rational explanation of the former in terms of the latter. PREDICTED RESULTS FOR AN IDEAL SLURRY IN AN IDEAL CONTINUOUS THICKENER General Theory: In continuous thickening, the downward solids flux (mass/area-time) relative to the thickener, G, results from two different

Jan 1, 1967

By Earl Oliver

This paper is based on the formula that the petroleum industry is sick—find the cause, eliminate it, and the industry will get well. There is perhaps no difference of opinion that the cause is overproduction, actual or potential. But that, again, is a result rather than a cause. The problem is to study the influences that serve to keep production and consumption out of balance. Production control is a popular theme and a natural one at this time when the whole world is unstable; but production control in its popular sense means little more than the application of emergency measures while danger threatens. Economists differ as to the effectiveness of these, most of which are designed to alleviate and not to cure, but we assume there are none who question the wisdom of promoting conditions under which economic forces are permitted to operate freely in bringing about stable conditions. The petroleum industry suffers from two classes of economic ills that serve to promote overproduction; namely, those which are common to all industries and those which are peculiar to this industry. It is of the latter I wish to speak. Strange to say, government is responsible in large part for this latter class of ills that affect the petroleum industry and we are coming to recognize that only through the assistance of government can they be corrected. Instability of the petroleunl industry, in so far as human agency was involved, had its inception in 1875 when a Pennsylvania jurist, called upon to make a decision for which there was no precedent and fancying he noted some resemblance between the so-called fugitive nature of oil and gas and that of wild game, made mention of that resemblance. Other courts being impressed by the analogy enlarged upon it, and gradually fixed upon oil and gas a legal status in certain important respects similar to that of wild game. Although later the courts abandoned this analogy, certain practices that developed out of that early concept have continued to this day and are largely responsible for the industry's present plight. Thus, instead of ownership in place that is characteristic of private property generally, the law of capture was applied to oil and gas. Now, the rapid and wasteful depletion of game

Jan 1, 1932

By J. R. Thoenen

THE consensus of opinion in the published literature on. Grecian magnesite is that it has been formed by alteration of the serpentine, which in turn was itself a product, of metamorphism from the original olivine intrusion. The general opinion seems to be that the magnesite was formed by descending waters heavily charged with CO2. Inasmuch as this opinion is held by engineers far better qualified than I to speak authoritatively on this subject, I hesitate to dispute that theory. However, certain occurrences coming under my observation do not, to me at least, seem to-entirely substantiate this theory. LOCATION Most of the Grecian magnesite comes from the Island of Euboea, although more recently some deposits have been opened on the mainland near the City of Saloniki, which prior to the war was Turkish. The island, comprising a state or province in the Greek political structure, is roughly 110 miles long and varies from 10 to 30 miles in width. It lies off the east coast of the Greek peninsula in the AEgean Sea with its long axis extending in a northwest-southeast direction. It is separated from the mainland by a long narrow arm of the sea known as the Atalanti Canal. Chalkis (Halkis), the capital on the west coast of the island, is the northern terminus of a branch of the state-owned railway and is connected with the mainland by a single-span, movable, highway bridge, roughly 150 ft. long.

Jan 1, 1928

By Charles Fulton

The study of the condensation of zinc from its vapor was undertaken to shed light on certain problems encountered in large-scale electric zinc-furnace work recently conducted. It is a matter of common knowledge that one of the disadvantages of the arc type, electric zinc furnace, is the production of a large amount of blue powder and proportionately little liquid spelter, for, as stated by Stansfield,1 "A notable defect in the electric smelting of zinc ores is the difficulty experienced in obtaining the distilled zinc in the liquid state; when zinc ores are smelted electrically, very little liquid metal is commonly obtained, nearly all of the zinc being in the state of powder."

Jan 8, 1918

[The following discussion, comprising both remarks made at the Chicago meeting and contributions since forwarded to the Secretary, is based upon the following papers, presented at that meeting : "Segregation and its Consequences in Ingots of Steel and Iron," by Alexandre Pourcel, Paris, France. (See p. 105, mans. xxii.) " Microscopic Metallography," by F. Osmond, Paris, France. (See p. 243, Trans. xxii.) " Microstructure of Ingot-Iron in Cast Ingots," by Prof. A. Martens, Berlin, Germany. (See p. 37.) " Microstructure of Steel," by Albert Sauveur, South Chicago, Ill. (See p. -546, Trans. xxii.) "Farther Observations on the Relations Between the Chemical Constitution and Physical Character of Steel," by William R. Webster, Philadelphia, Pa. (See p. 113.) "The Heat-treatment of Steel," by H. M. Howe, Boston. Mass. (See p. 466.) Since all these papers were considered together, no attempt has been made to separate the discussion strictly under the several heads.] William R. Webster, Philadelphia, Pa.: I desire to say that in my first paper (Trans., xxi., 766) the actual ultimates were subtracted from the estimated ultimates, whereas in the paper submitted at this meeting the estimated ultimates are subtracted from the actual, thus giving contrary signs. The latter method corresponds with the direct effect. of low and high finishing-temperatures ; that is, a plus difference indicates low, and a minus difference high, finishing-temperature. I make this explanation to prevent confusion in comparing the two papers. Mr. Sauveur has shown that there is a close relation between the size of the grain and the ultimate strength, and also that the size of the grain depends on the temperature at which the material is finished in rolling, and on the chemical composition of the steel. I have shown that there is a close relation between the chemical

Jan 1, 1894

By Stephen Taber

INTRODUCTION THE term asbestos, as commonly used, includes half a dozen minerals all having a well-developed fibrous structure, but differing in chemical composition and in some of their physical, properties. In its strict application the name is limited to the fibrous varieties of the monoclinic amphiboles. Commercially, however, the most important of the asbestiform minerals is chrysotile, a fibrous variety of serpentine. About 95 per cent. of the asbestos used in manufacturing is chrysotile, and it commands a much higher price than any of the other fibrous minerals now on the market. Although the production of asbestos has increased rapidly in recent years, comparatively little has been published concerning its origin. The present paper is preliminary in its nature, and therefore does not pretend to exhaust the subject. The ideas herein developed are the result of field investigation, laboratory experiments in the growth of fibrous

Jan 10, 1916

By Arthur Taggart

THIS paper describes the result of a series of experiments run in the laboratory of the School of Mines, Columbia University, during the winter of 1927-28. It shows that the several operating adjustments of a pneumatic table produce effects in the action of a, given coal that may be grouped into two classes, viz.: stroke length, speed and rocker-arm angle, which affect longitudinal travel; air supply and table slope (transverse and longitudinal), which determine transverse travel. The magnitude of the effect of the different adjustments varies. Some of the adjustments affect stratification of the bed, both as respects size and specific gravity of the bed components, as well as direction of travel. Operation of a pneumatic table is fundamentally different from that of a wet table in that the former exerts, through the air supplied, a force on the particles upward away from the deck which is lacking on the wet table while, on the other hand, it lacks the positive control over cross travel that is supplied by the wash and feed water.

Jan 1, 1929

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.'TheRittinger In its first form, as stated by P. R. Ritted.'tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin' as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.'TheRittinger In its first form, as stated by P. R. Ritted.'tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin' as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Walter Remmers

THE fact that gray iron increases in volume, cracks and distorts upon repeated heating and cooling is rather common knowledge. In ingot molds, Diesel engine pistons, carburizing boxes, continuous furnace parts, grate bars, stoker parts, and all castings that are subjected repeatedly to high and low temperatures, the phenomenon of growth presents a vital problem. Ingot molds distort and produce cracks which result in seams or laps and later appear as defects in the finished product. The heads of Diesel pistons frequently fail by cracking in a stellar shape. This is attributed usually to the result of permanent growth. Distortion and change of dimension of furnace parts frequently renders them entirely unusuable. In chain grate stokers, mechanical difficulties frequently are caused by the growth of the links. In proper operation these links should never attain a temperature sufficiently high to start growth; nevertheless, some have grown 1/8 in. on an 8-in. length when improperly operated. Even though the phenomenon is generally known there still exists a deficiency in the explanation of the mechanism of this growth. The field of investigators of this subject has a decided variation in opinion concerning the causes. The problem is of sufficient importance therefore to warrant further consideration.

Jan 1, 1930

By Rudolf Gahl

THE history of flotation in America is very short, at least as far as the large-scale application of the process is concerned. It is remarkable how many important developments have taken place inn the last few years and are already being extensively utilized. What was new a year ago, seems almost commonplace now. For this reason it is with hesitation that I follow the suggestion: of Dr. Ricketts, President of the Institute, to describe the experiences of the Inspiration Consolidated Copper Co. with the flotation process. TESTS CONDUCTED IN SMALL TEST-MILL When the Inspiration company first decided to build a concentrating plant, nothing was known about flotation, and the process was to be gravity concentration pure and simple. Demonstration Tests Conducted by Minerals Separation Co. While plans were being prepared by H. Kenyon Burch (who had been intrusted with the design and construction of the concentrator) the Minerals Separation Co., a concern at that time little known in America, asked and obtained permission to demonstrate the value of its flotation process for Inspiration ore. As. a consequence, a small 50-ton flotation machine of standard design was added to the company's test plant and started to operate in the beginning of 1913. This marks the beginning of flotation at Inspiration. The results obtained with this machine, which was operated by members of the Minerals Separation staff, so far surpassed what this company anticipated that it was decided to continue flotation tests for this purpose, and two of the flotation experts of the Minerals Separation Co., I. L. Greninger and G. A. Chapman, were retained. L. R. Wallace, now superintendent of the Miami works of the International Smelting Co., was at that time metallurgist of the Inspiration company and in that capacity took an active part' in these tests. Great credit is due to him for his quick recognition of the possibilities of flotation.

Jan 9, 1916

By Joseph Hartshorne

Ever since the introduction of the Siemens regenerative furnace, it has been recognized that a certain amount of gas is lost each time the furnace-action is reversed. This loss comes, first, from the gas which passes through the free connection between the stack and the gas-main, which exists during the time the reversing-valve is turning over; and, secondly, from the gas which is in the chamber and flues, from the hearth to the reversing-valve, and which flows back into the stack when the valve is reversed. The amount lost each time is, of course, small; but, since a furnace is reversed from four to six times every hour for, say, 300 days in the year, the aggregate is large enough to be well worth attention. The estimate has been published1 that, in Germany aloue, the loss from the first of the above causes amounts to 500,000 barks per year. The loss from the second cause is, of course, much greater.

Jan 1, 1907