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By T. N. Williamson

The art of drilling tunnels is still in its infancy, although it is 70 years since the first tunnel driver was put into operation. (It was used to drive 6000 ft of tunnel under the English Channel.) But during the next 60 years neither government agencies nor private enterprise could find much of a future in tunnel drivers. It was difficult to justify the heavy investments, labor was opposed to the machines, and there had been some spectacular failures. In the last ten years, however, there have been changes. Tunnel drivers are being tried with increasing frequency-in spite of the fact that a large number of them have had to be abandoned on site.

Jan 7, 1965

By L. R. Shoenberger

Boron has been used to produce nonaging low-carbon sheet steel. Retention of the necessary minimum amount of about 0.006 pet partially killed the steel. Amounts exceeding about 0.012 pet increased the degree of deoxidotion, piping tendencies, and possibility of hot tearing in primary rolling. Semikilled practice resulted in good ingot yields and satisfactory surface quality. Aluminum added with the boron provided a protective de-oxidizer. Good drawobility was indicated by performances of the steel in a limited number of deep-drawing trials. Some problems with hot-tearing and boron-analysis procedures were overcome. Metal lographically, the boron semikilled steels revealed some structures not usually found in plain low-carbon steels. IN 1943 Low and Gensamer1 reported that strain aging, which hardens and embrittles ordinary low-carbon rimmed steel, was due to nitrogen and carbon, and that oxygen played a relatively unimportant role. Since then, many investigators have substantiated their findings and indicated that nitrogen is particularly potent. Commercially, today's most widely produced non-aging sheet steels for deep drawing are either aluminum killed or vanadium rimmed types. The difference in deoxidation practice, alone, is evidence that oxygen is apparently not an important consideration in control of strain aging. The fact that nitrogen is important is apparent in the consideration that has been given, knowingly or unknowingly, to the amount combined with aluminum and vanadium. Patents were granted to Hayes and Griffis2 for the processing of aluminum-killed steel, and to Epstein" for the manufacture of vanadium rimmed material. Certain prescribed steps in producing these steels can be correlated with the formation of the respective nitrides within certain temperature ranges below the usual hot-finishing temperatures. The potential nonaging properties of either type can be reduced or suppressed by cooling too rapidly to permit the aluminum or vanadium to combine with nitrogen. Subsequent suberitical annealing of the cold-rolled strip, however, normally forms the nitrides and produces the resistance to strain aging. Titanium-killed nonaging steel, described by Comstock,1 forms a nitride in the molten state and is essentially nonaging throughout its processing. Zirconium-killed steel, which was investigated briefly by the author,* appeared to have similar nitride- forming characteristics. It is known" that chromium can produce nonaging rimmed steel, but relatively little is known of the potentialities of some of the other nitride-forming elements such as boron, silicon, columbium, and cerium. In attempting to develop a new nonaging cold-rolled sheet steel with good drawability, the following factors were considered pertinent. Such a steel would necessarily have a low carbon content and therefore have a relatively high degree of oxidation when made in a basic open-hearth furnace. If the denitriding element were also a deoxidizer, a part of the addition would be lost as oxide. The degree of deoxidation would determine whether the steel is rimmed, semikilled or killed, and also could be expected to have an important bearing on ingot yields and ultimate surface quality. Assuming that the pattern for the production of cold-rolled sheets would not be changed to any great extent, the nitride must form in the molten steel, in hot rolling, in subsequent cooling, or in annealing. The nitride, once formed, should resist dissociation and be stable in the final product. Usually an excess of the nitride-forming element is required to combine with sufficient nitrogen. If the element used is a strong ferrite strengthener, a small excess may markedly decrease drawability. With aluminum and vanadium, about 0.03 to 0.05 pct in the steel is preferred. Epstein has said" that about 0.30 pct chromium is required. Titanium nonaging steels are hard unless a sufficient amount (about 0.30 pct) is added also to combine with the carbon. The cost of the necessary amounts of these latter two elements discourages commercial acceptance. Silicon was considered as a possible nitride former, but since amounts up to 0.10 pct in rimmed and semikilled steels do not induce marked resistance to strain aging, larger amounts are apparently required, which would tend to harden and strengthen the ferrite. Of the other elements mentioned, all but boron are expensive heavy-metal elements. Stoichi-ometrically, almost an equal weight of boron would be required to combine with the nitrogen—-ordinarily about 0.003 to 0.006 pct in scrap-practice open-hearth steels. Boron is a slightly stronger deoxidizer than carbon but is less powerful than zirconium, aluminum, or titanium. Thus a rimmed-steel practice might be possible. There is much in the technical literature concerning the hardenability effects of minute amounts of boron in killed steels but very little about its behavior in low-carbon material—particularly as a ferrite strengthener. The available data indicated a need for better information concerning the effects of boron in low-carbon strip steels. Experimental Work Development of a Boron-Treated Nonaging Strip Steel—Initial attempts to produce a boron-rimmed strip steel employed 3-ton basic open-hearth heats which could be teemed into molds large enough to sustain a normal rimming action. Boron as ferro-boron was added to the ladle in small amounts because of the reported hot-short character of aluminum-killed heat-treating grades containing more than about 0.005 pct boron. Actually, the amounts used, i.e., 1/8 and 1/4 lb per ton, would be large for

Jan 1, 1959

By S. Stutz

COAL, like most other minerals, only exceptionally occurs in a sufficiently pure state to he directly available for general manufacturing purposes. And even where this is the case, the small coal or slack is usually more impure than the lump coal, as the slate, clay, etc., from the roof and bottom of the vein become mixed with it in the handling it undergoes. These impurities often exceed ten or more percent in addition to the impurities of the coal itself. The most common impurities of the coal are slate, or shale, clay, and sulphur. The latter occurs in different forms, but most frequently as bisulphide of iron, or iron pyrites, and as sulphate of lime, or gypsum. In both cases the impurities add greatly to the amount of ash, and where they are present in considerable quantities the raw coal, and still more the coke made from it, is unfit for the, manufacture of iron. Coke will contain on an average at least ;fifty per cent, more ash and sulphur than the raw coal from which it is, made. To the manufacturer of iron every additional per cent. of ash which his coal or .coke contains is a source of additional expense, seemingly small, and yet very important in the aggregate. In the blast-furnace, for instance, the ash must be heated up to the melting-point, and, since it is composed largely of refractory substances, the consumption of carbon in melting it will be equal to at least one-half of its weight ; that is, a certain part of the coke is consumed for the melting and fluxing of the ash and is lost. Besides this, it is well enough known to the-iron-master that coke containing less ash makes the slag or cinder more liquid and less inclined to stick to- the walls of the furnace. Fuel containing much sulphur produces generally a white iron, poor in carbon, while from the same ore and flux, with a pure fuel, a good foundry iron might be obtained. The work of separating slate, sulphur, etc:, from the coal 'has as yet only been succesafully accomplished by the washing process. This process depends for its success on the differences in the specific

Jan 1, 1881

By G. W. Jarman

The purpose of this paper is to present briefly a description of some of the special methods of separation or concentration, either singly or in combination with others, and to give certain operating data and examples. Explanation of the usual methods of large-production mill treatment, such as flotation or wet tabling, or of chemically treating industrial minerals, is not included in the scope of this paper, although one of these methods might be, in certain instances, augmented by one or more of the special methods that will be enumerated herein. Description of these special methods will be centered on magnetic separators, electrostatic separators and air flotation or air tables. Magnetic Sepaeatohs In general, separation is achieved by exerting upon a particle some kind of force opposed to gravity, either directly or at an angle. For example, in the Wetherill or cross-belt type of magnetic separator some particles are lifted vertically from the others because they have been exposed to a force to which they respond more readily than particles of lesser magnetic susceptibility. Of course, there is a limitation to this vertical rise, for the particle must be of a high enough susceptibility to receive a magnetic force greater than the 980 dynes per gram of gravitational urge. To overcome this limitation, the induction type of magnetic separator was developed, so that it is only necessary to instill, say, 30 to 60 dynes per gram instead of the 080, to cause a deflection away from the vertical in falling, and that deflection can be used advantageously when falling by inserting a dividing knife-edge. The induction magnetic separator (Fig. 1) has become a fairly well known method of concentrating and purifying. For example, abrasive grain was among the materials that did not respond to the previously best known type of magnetic separator, such as the Wetherill type, and the development of the induction magnetic separator in the plant of a

Jan 1, 1942

By G. W. Jarman

The purpose of this paper is to present briefly a description of some of the special methods of separation or concentration, either singly or in combination with others, and to give certain operating data and examples. Explanation of the usual methods of large-production mill treatment, such as flotation or wet tabling, or of chemically treating industrial minerals, is not included in the scope of this paper, although one of these methods might be, in certain instances, augmented by one or more of the special methods that will be enumerated herein. Description of these special methods will be centered on magnetic separators, electrostatic separators and air flotation or air tables. Magnetic Sepaeatohs In general, separation is achieved by exerting upon a particle some kind of force opposed to gravity, either directly or at an angle. For example, in the Wetherill or cross-belt type of magnetic separator some particles are lifted vertically from the others because they have been exposed to a force to which they respond more readily than particles of lesser magnetic susceptibility. Of course, there is a limitation to this vertical rise, for the particle must be of a high enough susceptibility to receive a magnetic force greater than the 980 dynes per gram of gravitational urge. To overcome this limitation, the induction type of magnetic separator was developed, so that it is only necessary to instill, say, 30 to 60 dynes per gram instead of the 080, to cause a deflection away from the vertical in falling, and that deflection can be used advantageously when falling by inserting a dividing knife-edge. The induction magnetic separator (Fig. 1) has become a fairly well known method of concentrating and purifying. For example, abrasive grain was among the materials that did not respond to the previously best known type of magnetic separator, such as the Wetherill type, and the development of the induction magnetic separator in the plant of a

Jan 1, 1942

By Richard T. Ely

Conservation, narrowly and strictly considered, means the preservation in unimpaired efficiency of the resources of the earth; or in a condition so nearly unimpaired as the nature of the case, or wise exhaustion, admits. And broadly considered, it means more than the word itself implies, for it naturally includes an examination of methods whereby the natural inheritance of the human race may be improved; and still more broadly considered—and as used in popular discussion—it includes a treatment of the effects of productive conservation measures upon distribution. We shall give our attention briefly to the main points in this informal definition before we pass on to the thesis that conservation is largely a matter of property relations—-that a wise conservation policy means wise property relations.

Jan 1, 1916

By C. A. Shook, W. H. W. Husband, D. B. Haas

Introduction Although previous studies1,2,3 have been made, no correlations for pressure drop have been proposed. This is probably because severe particle breakage occurred and pressure drops changed substantially with time. A quantitative statement of the relationship of pressure drop to the parameters of the system is desirable for lignite since, unlike higher rank coals, lignite slurries are thixotropic. The present investigation was undertaken to quantify the pipeline behavior and required continuous monitoring of pressure drop and size distribution.

Jan 1, 1980

By F. G. Tryon, F. E. Berquist

Our task is to make a prospecting trip over the whole field of mineral economics which other lectures of this series will explore in detail. The old timers who really understand mining warn us that its economic aspects are often neglected, and this we find to be true. We shall try to show that mineral economics deserves recognition as a separate branch of economic science with urgent and distinctive problems of its own; that to cultivate it requires a fusing of the viewpoint of economics with that of geology and engineering; and that the help of both economists and technical men is needed in exploring its problems and in training workers in the field. To save time, we shall pass over the familiar subjects of production, consumption, and distribution which bulk as large in the market analysis of the minerals as they do in other commodities. The existence of these problems may be taken for granted and attention centered rather upon those that differentiate mining from other branches of industry. What then is the case for an economics of minerals? Why set up a new compartment in a branch of knowledge that is already well subdivided? Do not the established principles of economic theory apply here as elsewhere? In pleading for recognition of mineral economics one often finds that

Jan 1, 1932

By G. Sherburne Rogers

One of the features of oil-field work that puzzles operator, chemist, and geologist alike, is variation in the gravity of the petroleum produced on neighboring leases or even from adjoining wells. Few fields in the United States yield oil that is of uniform gravity throughout; in some fields the different grades are produced from different sands, in a few from different formations, and in many from different areas in the same sand. In a few cases, perhaps, a common assumption—that the heavier oil is derived from the lighter through the escape of the more volatile constituents—is valid, but many cases can not be explained in this way. Although in the California fields the specific gravity of the oil generally decreases with depth, there are numerous exceptions to this rule; and, as in many other regions the light oil is found nearest the surface, it is evident that evaporation underground is generally an unimportant factor. It is generally recognized that the great differences between petroleum from widely separated fields are due largely to differences in age and degree of metamorphism and to variation in the composition of the original organic matter; but in the writer's opinion some of these broader differences, as well as most of the minor variations in the character of the oil from any one field, are due to the local action of natural reagents such as sulphur or oxygen. This is particularly likely to be true if the oil has migrated from one formation to another, as in the California fields; and in some arcas it appears that variation in sulphur content may even afford a rough index of the extent or distance of the migration. It is the purpose of this paper to call attention to the chemical action of sulphur and oxygen on petroleum, to show that the gravity of the oil from any one field is intimately related to its sulphur content, and to discuss the possi-

Jan 1, 1918

By A. B. Hildebrandt

P. B. Baxendell is to be complimented for an exccllent piece of work. To our knowledge there has been no previous publication of field data on the flow of oil and gas through the annulus of a well. It is certainly gratifying to see this work on annular flow confirm the previous published correlation procedure on tubing flow. It extends considerably the range under which reliable gas-lift calculations can be made. Baxendell discussed this work with us about a year ago and was kind enough to send a large scale plot of his correlation. We had been designing gas-lift installations on flow through the annulus, assuming that the original correlation of the f factor based on tubing flow' was valid as long as we stayed within the same mass velocity range on which the correlation was based. Doing this work necessitated the use of an equivalent diameter for the annular flow. The equivalent diameter is defined as area' of stream cross section wetted perimeter and for the case of an annulus is D, — D,. Substituting this in the basic equation correlating energy loss along with the area to flow required to convert the velocity, to volumetric flow rate, D (Baxendell's Eq. 7) becomes dell's expression, D,). Similarly, the D in 1.4737 X 10 (M&/D) becomes (D, + D;) for annular flow. On receipt of Baxendell's data, we. of course, recalculated it to put it into the form we were using, and to see how well it agreed with the correlation based on tubing flow. Fig. 1 shows the results, which were certainly gratifying. For low values of (D, - D,) pv, the data coincide with the data on flow through tubing, whereas at high values the data on flow through the annuli appear to be leveling off to a constant value. For very high rates of flow where the turbulence is very high, one might expect the value f to level out and become constant. A bulletin published in 1914 by the U. of Wisconsin presented results of a large number of laboratory teats in air lifting water through short lengths of 1.25-in. tubing. It was possible to correlate a random sampling of

Jan 1, 1924

By M. Stuart, R. F. Down

The Copper flotation concentrate produced at Gortdrum mines contains about 1% Hg. This article deals with the treatment used to produce a substantially mercury-free copper concentrate. Metallic mercury is a byproduct. Nearly all the mercury in the Gortdrum concentrate is present in the copper mineral tennantite-tetrahedrite. This mineral is variably distributed throughout the ore body so that by selective mining it was possible to produce salable concentrate relatively low in mercury while the treatment plant was being built. Roasting was the only feasible method found for removing the mercury from the concentrate, and it was decided that this should be done in an atmosphere with limited oxygen. A multiple hearth furnace is used. Mercury soot is condensed from the gas stream and treated to produce prime virgin mercury. Problems were experienced at first with materials handling, oxygen control, cooling of the calcined concentrate, treatment of the mercury soot, and in the metallurgical accounting. Precautions were necessary to avoid health problems. The plant is now operating reasonably well. The value of the mercury produced does not warrant the cost of the plant but without it, the copper concentrate could not be sold.

Jan 1, 1975

By A. Haas, L. Bubenicek

The Lorraine deposit of minette iron ore has been mined for more than a century. During this time, the economic conditions have changed frequently, and especially during the past decade. Thus, it has become economically prudent to proceed to new iron ore reserves with consideration of many and varied parameters. In the past, only traditional mining parameters were considered. Today, the quantity of information that must be taken into account is of such magnitude that the only practical means of data processing is by use of a digital computer and a mathematical model. One such model, based on geostatistics, was developed by G. Matheron. Much of the required input information, such as the petrology of ores, has been generated through IRSID investigations. This paper deals with several aspects of data processing in mining including information recording, reserves calculation, and stages of shrinking data in the calculation of mining iron beds, variograms, kriging, and tonnages.

Jan 1, 1969

Jan 1, 1909

By P. W. Bridgman

Flow and fracture are admittedly complicated phenomena of which we are yet only partially masters. There is not even nni-.persal agreement as to the details of the language best adapted merely to describe the phenomena, to say nothing of any theory. Certain points of view, however, are widely held, and there are certain general expectations as to what sort of procedures will prove permissible. A complete description of any situation involving fracture would demand a complete history of all the variables in the control of the experimenter. The experimenter endeavors so to choose his independent variables that they are adequate to determine completely the situation in the sense that when an experiment is repeated on the same initial material and with the independent variables running through the same sequence, all the other measurable properties of the system will also run through the same course. It is, I think, the universal conviction that when we are dealing with phenomena of flow and fracture, the most important of the necessary variables are the external forces acting on the various parts of the body; when the force history repeats, with certain obvious restrictions such as that temperature must be constant and non-mechanical forces, such as magnetic field, must be small enough to be ineffective, then the history of all measurable properties will repeat; in particular the alteration of geometrical shape due to flow will run through the same course, and when fracture comes, the character of the fracture will be reproduced. Complete mastery of merely the descriptive aspects of flow and fracture would demand the ability to predict the entire course of flow and complete characterization of the final fracture for every possible combination of forces, varying in time in all possible ways, when applied to bodies of all possible shapes. This full situation is obviously of prohibitive complexity. The first stage in reduction to manageable simplicity is to resolve the total situation into the sum of contributions made by small elements. Our thesis is that if each of the elements is adequately characterized, the behavior of the whole system is fixed. The element is usually taken of a simple geometrical shape, suggested by the mathematics best adapted to the particular situation. The forces acting across the faces of the elements are ultimately determined by the forces acting across the free faces of the whole system. The detailed process of finding the precise forces on the faces of all the elements in terms of the external forces involves the use of a special mathematical invention, the stress, a constructional quantity consisting of six components. The stress at any point in the body is determined by both the external force system and by the physical properties of the body at all points; quite different stresses prevail at the interior of bodies of the same shape under the same external forces in the elastic and plastic ranges. The forces on the faces of any element are, however, uniquely determined by the stress system at the element. Our fundamental thesis

Jan 1, 1945

By Ingvar Janelid

DURING the last ten years, in the effort to save manpower and costs, methods of drilling and blasting in Sweden have changed and developed in a revolutionary manner. These developments have been accompanied by extensive alterations in methods of tunneling and in mining technique. Since the end of the 1940's there has been a 100 pct change-over in Sweden to the use of tungsten carbide tipped drill steel. Both investigations and practical results have shown clearly that a tungsten carbide chisel bit fastened directly on the drill steel is the most economical for Swedish conditions. This applies to drill steel up to the longest size it is practical to handle. In terms of drilling footage, durability of the drill steel and the tungsten carbide bit is generally the same. In this respect, therefore, a detachable bit offers no advantage over integral steel. Transportation of integral steel to the grinding plant, instead of detachable bits only, involves heavier work, but this is counteracted by placing grinding plants closer together or by grinding at the working place itself. The drilling rate with integral steel is higher, the trouble of changing bits is avoided, and the difficulties which always arise with joints are eliminated.

Jan 6, 1954

By Parke A. Dickey

Potential differences between strata of shale and sandstone have been recognized for about years, and they form the basis of the electrical logging of oil wells. Hitherto these potentials have been ascribed solely to electrochemical reactions caused by the disturbing effects of the water in the drill hole through which they are generally measured. Observations by the author in wells empty of water and in a mine shaft suggest that potential differences between sandstones and shales are natural and specific properties of the rocks, although they are modified in measurement by the disturbing effects of the water in the drill hole. The cause of these potentials probably is to be sought in the relative polar adsorptive capacities of quartz and clay particles. Introduction The existence of potential differences in the surface of the earth has been known for some time, and their measurement has facilitated the discovery of geological discontinuities such as ore bodies. The technique of measurement has been well established.'-a In measurements in oil wells, it has been found that the potential of shales with respect to some arbitrary reference is very nearly constant in any one well, at least below the zone to which meteoric water has gained access. Sandstones and some other types of sedimentary rocks have a difference of potential with respect to shale that is negative and may attain a value of 200 millivolts or more. The difference of potential, as usually measured commercially with water in the hole, is distributed over about one foot vertically at the top and bottom contacts of the sandstones. The sharpness of the curve at the formation contacts can be improved by using a short electrode that is close to the wall of the hole. These potentials generally have been ascribed to the disturbing effects of the water in the drill hole. Potentials have been found, however, in wells in which no water was present. In the course of experiments in electrical logging in Pennsylvania, carried out by the Pennsylvania Geological Survey, observations were made of several phenomena that hitherto have not been described, to the author's knowledge, in the published literature. The potential differences across the contacts of sandstone and shale are called in this paper "natural potentials," as distinguished from the potentials caused by electroendosmosis (electrofiltration) and concentration differences, which will be discussed subsequently. Potentials in Cored Well In the spring of 1942, the author measured the potentials in an exploratory well (Day 13, near Grand Valley, Pa.) which had been cored with diamond tools. The potentials were first measured with fresh water in the hole. A null balance potentiometer was used in this and all the other measurements described in this paper. One nonpolarizing porous pot electrode, containing copper sulphate solution and crystals surrounding a pure copper elec-

Jan 1, 1944

By Parke A. Dickey

Potential differences between strata of shale and sandstone have been recognized for about years, and they form the basis of the electrical logging of oil wells. Hitherto these potentials have been ascribed solely to electrochemical reactions caused by the disturbing effects of the water in the drill hole through which they are generally measured. Observations by the author in wells empty of water and in a mine shaft suggest that potential differences between sandstones and shales are natural and specific properties of the rocks, although they are modified in measurement by the disturbing effects of the water in the drill hole. The cause of these potentials probably is to be sought in the relative polar adsorptive capacities of quartz and clay particles. Introduction The existence of potential differences in the surface of the earth has been known for some time, and their measurement has facilitated the discovery of geological discontinuities such as ore bodies. The technique of measurement has been well established.'-a In measurements in oil wells, it has been found that the potential of shales with respect to some arbitrary reference is very nearly constant in any one well, at least below the zone to which meteoric water has gained access. Sandstones and some other types of sedimentary rocks have a difference of potential with respect to shale that is negative and may attain a value of 200 millivolts or more. The difference of potential, as usually measured commercially with water in the hole, is distributed over about one foot vertically at the top and bottom contacts of the sandstones. The sharpness of the curve at the formation contacts can be improved by using a short electrode that is close to the wall of the hole. These potentials generally have been ascribed to the disturbing effects of the water in the drill hole. Potentials have been found, however, in wells in which no water was present. In the course of experiments in electrical logging in Pennsylvania, carried out by the Pennsylvania Geological Survey, observations were made of several phenomena that hitherto have not been described, to the author's knowledge, in the published literature. The potential differences across the contacts of sandstone and shale are called in this paper "natural potentials," as distinguished from the potentials caused by electroendosmosis (electrofiltration) and concentration differences, which will be discussed subsequently. Potentials in Cored Well In the spring of 1942, the author measured the potentials in an exploratory well (Day 13, near Grand Valley, Pa.) which had been cored with diamond tools. The potentials were first measured with fresh water in the hole. A null balance potentiometer was used in this and all the other measurements described in this paper. One nonpolarizing porous pot electrode, containing copper sulphate solution and crystals surrounding a pure copper elec-

Jan 1, 1944

By K. P. Wang

Under the Communist regime marked industrial progress has been achieved on the China mainland. Within a decade, the country has been transformed from an economy primarily agricultural to one bristling with industrial possibilities. The industrial capacity of Communist China is beginning to approach that of Japan and will probably surpass it by 1962, the last year of the Second Five-Year Plan. The slogan already is Beat the United Kingdom by 1972, a goal which most observers feel will be achieved ahead of schedule. During the early years of the industrialization program in Communist China, emphasis has been placed on basic goods; hence additional time will be needed to make large quantities of the more complicated products. However, regardless of the current stage of industrial development, it is apparent that the necessary forward momentum has been created. The many capital construction projects being brought into production and the additional projects being initiated confirm this observation. The accuracy of Communist China's industrial statistics can be questioned, but their order of magnitude is clear. To properly evaluate the industrial capability of the country, differentiation must be made between the absolute quantities that reflect overall strength and the per capita quantities that reflect living standards. While Communist China is well on the road to becoming a world power, its living standards will remain below European levels for many years to come.

Jan 8, 1960

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory state of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which are 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 in 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. In its first form, as stated by P. R. Rittinger, 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. Gaudin2 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' that 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 relatively harder to grind at 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 theory' 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 2.5 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-1.5 If 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, 1952