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By Kavetsy A

In surface mining operations, the ease with which a muckpile may be dug is a dominant factor in mining efficiency. Within broad limits this is largely independent of the fragment size dis- tribution, since the equipment used to move the broken rock is generally larger than in underground mines. In such cases, muck- pile shape and voids ratio within a muckpile heavily influence mine productivity. In a particular operation, the muckpile shape after blasting should be tailored to the digging equipment being used. A front- end loader is best suited to a low, flat-lying, loose muckpile, because of its fairly good mobility and small break-out force with its bucket. In contrast, a rope shovel lacks mobility, generates a much larger break-out force with its bucket, and fills its bucket in a vertical filling motion. Therefore, it is ideally suited to well fragmented, steep faces. In situations where a dragline is used, the requirement for a suitable muckpile depends on the operat- ing scheme of the dragline. For a conventional highwall key method the preferred work- ing level of the dragline is the same as the highwall, so that the dragline may sit over its key. In this situation, the ideal muck- pile shape involves relatively little displacement of the fragmented rock, with a minimal "power trough" at the back of the blast. In throw blasting, on the other hand, it is desirable to cast as much of the spoil as possible across the pit. It is then necessary to optimize the blast design by maximizing the throw percentage under any necessary constraints (e.g. damage, vibration, flyrock, explosive cost).

Jan 1, 1988

By H. R. Tunnell

EVERY ONE connected with a mine knows that it is hard to keep down the costs of moving ore from the place where it is broken to the shaft or portal. Considered broadly, the subject of handling would cover all work done in a mine, but here it has been limited to handling ore in stopes and drifts, through chutes, and on levels. Good Ventilation and a strict enforcement of rules for the prevention of dust safeguard the health of the men and lower transportation costs. HANDLING ORE IN STOPES AND DRIFTS The object of all stoping is to mine ore of good grade at low cost. In Butte, the major part of the ore is mined, from Veins dipping from 60° to the horizontal to those which are vertical, by means of, square-set, rill, -timbered-rill, and back-filling stopes. When blasted, a part of the rock is carried by gravity to the grizzlies over the chutes, the rest is shoveled. Rock, when broken in a stope, may be deflected by inclined floors or slides toward the top of a chute leading to the level below. Ore broken clean enough to ship should be carried, by the force of its fall, into a chute or as nearly into that chute as the safety of the stope and the men permits. Ore that requires sorting, about 80 per cent. of all ore mined, is caught on a grizzly and the waste picked out. Waste rock broken in a stope is used to fill that stope and should be blasted into the gob with as little handling as possible.

Jan 2, 1922

By John Dresser

General THE controlling supply of asbestos for the world is obtained from southern Quebec, 150 miles or less north of the international boundary line between Canada and the United States, and about 75 miles south of the city of Quebec. The principal production is furnished by eight mines, seven of which occur within a distance of 6 miles, but there are also several smaller properties in the vicinity. The industry was begun in a small way some 35 years ago and has advanced more or less regularly ever since. The annual production now exceeds 100,000 tons and its value is about $3,000,000. It represents over 80 per cent. of the world's production. History Asbestos has been known in the eastern townships of Quebec since 1847, when attention was called to it in an official report by Sir William Logan, the first Director of the Geological Survey of Canada, but it was not until 30 years later that it came into commercial importance. The largest deposits, those of Thetford and Black Lake, were found in 1877 during the construction of the Quebec Central Railway. Work was begun upon them almost at once and has been continued ever since. The Danville mine, the next largest producer, was opened in 1879, and the slip-fiber deposits of East Broughton were located shortly afterward. For the first 15 years only the "crude" asbestos was recovered; that is, fiber long enough to be extracted by hand cobbing. Although this is still a valuable part of the production, it is now a relatively small part of the total output.

Jan 9, 1914

By E. R. Parker, C. F. Riisness

That grain size has a great effect on the mechanical properties of metals has been recognized for a long time. Bassett and Davis1 in 1919 did excellent work in determining the effect of grain size on the hardness of brass. About the same time Jeffries2 and Sykes3 ascertained the effect of grain size on the strength and ductility of several metals at temperatures ranging from 80°K. to their melting points. When creep was recognized as an important property of metals, those engaged in the study of this property tried to determine the effect of grain size4-9 on creep rates. Unfortunately, most of the investigations were conducted on only two grain sizes, often designated simply as "fine" and "coarse." It is well known that at high temperatures coarse-grained test bars creep less than fine-grained bars. The relation between grain size and size of test bar, however, has been frequently overlooked. In his early work, Jeffries2 showed that the number of grains in the cross section has a more important influence on the properties of the material than the actual grain size. More recently Hanson and Sandfordl0 and Pell-Walpole,ll in their measurements of the creep and tensile properties of tin, tested a wide range of grain sizes and correlated the grain size with the strength. Hanson9 later established the relation between the number of grains in the cross section and the creep rate. At high temperatures, generally a coarsegrained structure is considered superior in creep to a fine-grained structure, but it is evident that for a given bar size continuously increasing the grain size will

Jan 1, 1944

By John W. Padan, Thomas E. Howard

Most of what has been written during the past few years on marine mineral resources has emphasized the vast potential of the ocean, and its floor, as a source of the vital mineral raw materials upon which our modern technological society depends. Computations have been made to demonstrate that the sea contains sufficient minerals to support any reasonable world population indefinitely. The importance of these resources from the standpoint of strengthening the national mineral resource base has been pointed out. And though the information upon which these conclusions are based is sketchy, essentially qualitative, and often conflicting, there can be no doubt that the mineral potential of the sea is tremendous and that there are compelling reasons for working toward its exploitation. Unfortunately, there has been little emphasis on the problems that must be overcome, from the perspective of the economics of mineral production. Some of these problems have been noted, and some authors have appraised them realistically. However, many proposed solutions have been more romantic than practical, from the standpoint of both technology and economics. As a result the general impression has been given, particularly to those uninitiated in the realities of mineral production, that the mineral wealth of the sea is there for the taking-requiring only a good modicum of courage and technologic innovation to place it within easy grasp. But developing the capability necessary for substantial, profitable production of sea bottom minerals will be far from easy. It will be accomplished much more quickly if the problems are faced squarely, defined properly, and attacked in an orderly, logical sequence. While this approach may lack glamour, it offers the highest probability for success.

Jan 6, 1966

By J. T. Crawford

THE purpose of this paper is to present some data and comparisons regarding three types of Rheolaveur plants washing bituminous coal from the Pittsburgh seam. It deals only with the sections that handle coarse coal. The Rheolaveur system consists of launders or troughs in which coal and its associated impurities are conveyed by water. The impurities, being heavier than the coal, settle toward the bottoms of the launders and are drawn off through specially designed openings called Rheo boxes. Fundamentally, each plant consists of straight-sided, flat-bottomed launders of varying width and length, each launder equipped with one or more Rheo boxes for the removal of high-gravity fractions of the feed that are undesirable in the cleaned coal. Each launder has at least two longitudinal sections, the first with a slope of from 1 1/2 to 4 in. per foot of length, called the classification section. The single-box launder has a classification section followed by a washing section ahead of the box. A two-box launder is a single-box launder followed by a washing section and a second box. The slope of the washing section between the first and second boxes is determined to some extent by tonnage. At the end of the classification section, which may vary from 8 to 15 ft. in length, the slope abruptly flattens out to a slope of from ½ to 1 in. per foot of length. This flatter section of the launder, called the washing section, may vary from a few feet, in a single-box launder, to 15 ft., in a two-box launder.

Jan 1, 1938

By C. F. Riisness, E. R. Parker

That grain size has a great effect on the mechanical properties of metals has been recognized for a long time. Bassett and Davis1 in 1919 did excellent work in determining the effect of grain size on the hardness of brass. About the same time Jeffries2 and Sykes3 ascertained the effect of grain size on the strength and ductility of several metals at temperatures ranging from 80°K. to their melting points. When creep was recognized as an important property of metals, those engaged in the study of this property tried to determine the effect of grain size4-9 on creep rates. Unfortunately, most of the investigations were conducted on only two grain sizes, often designated simply as "fine" and "coarse." It is well known that at high temperatures coarse-grained test bars creep less than fine-grained bars. The relation between grain size and size of test bar, however, has been frequently overlooked. In his early work, Jeffries2 showed that the number of grains in the cross section has a more important influence on the properties of the material than the actual grain size. More recently Hanson and Sandfordl0 and Pell-Walpole,ll in their measurements of the creep and tensile properties of tin, tested a wide range of grain sizes and correlated the grain size with the strength. Hanson9 later established the relation between the number of grains in the cross section and the creep rate. At high temperatures, generally a coarsegrained structure is considered superior in creep to a fine-grained structure, but it is evident that for a given bar size continuously increasing the grain size will

Jan 1, 1944

REJUVENATED is an apt word to apply to Chino, Kennecott's big open-pit mine at Santa Rita, New Mexico. Back in 1923 Chino was merged with Ray by an exchange of shares, and in 1926 the Ray-Chino combination was taken over by Nevada Consolidated through an issue of bonds that were traded for the Ray and Chino assets. Subsequently, of course, the whole package was acquired by the Kennecott Copper Corporation. On the basis of the terms of the Ray-Chino-Nevada exchanges, Chino was rated third in value, something less than thirty per cent of the total. In 1955 the appraisal would doubtless be forty per cent or more. But it is not only vis-a-vis Ray and Nevada that Chino has blossomed out. At the end of 1931, Chino ranked seventh among the Porphyries in point of output; whereas by the end of 1954 it was fifth,. having passed both Inspiration and Nevada Consolidated. Sharp curtailment in production in 1932-33-34 and total suspension in the two years following (see Fig. 21) found the property in a somewhat parlous position. However, the engineers had not been idle; they had been planning for the future, and in 1937 a far-reaching program of rejuvenation was launched. During the ensuing five years, capital expenditures totaled more than $8,500,000. Among the projects undertaken were the following: (1) Mine-Purchase of larger and better equipment for drilling, loading, and transporting the ore. (2) Mine-Beginning of the first systematic project to leach and recover copper in the waste dumps at the mine.

Jan 1, 1957

By A. G. H. Anderson, Eric R. Jette

A few years ago, while the writers worked on the constitution of ternary and quaternary alloys consisting mainly of iron, chromium and siliconl,2 some information on microstructures and hardness, not incorporated in the published work, alas obtained. It has not been possible to do any further work on the properties of the alloys. The information possessed is hereby presented for the interest it may have in connection with the constitution of the alloys. Microstructures Referring to the iron-chromium-silicon diagram,' the regions that received most attention were those in which the sigma phase appears. It was found that the mode of occurrence of this phase varied much with the condition under which it mas formed, and the mode influenced considerably the hardness of the alloys. In some slowly cooled alloys, well within the alpha + sigma-phase boundary, sigma occurs in pabterns suggesting a eutectic. The structure of such an alloy is shorn in Fig. 1, showing it to be partly coarsely laminated and partly globular mottled. In other annealed and slowly cooled alloys, the lanlinated structure is entirely absent, and sigma appears in an irregular distribution of sharply cornered elongated areas (Figs. 2 and 3). These areas all possess a more or less mottled structure. A carbide phase is also visible in these two photomicrographs; it is represented by bright white arras of various shapes, sometimes apparently enveloping the sigma. Quenched and aged specimens, whose compositions arc: located near the phase boundary between alpha and sigma + alpha regions, have structures not unlike martensite (Figs. 5 and 6). Fig. 4 shows the structurc of alloy No. 35 as quenched from 1100" C.; it is a typical solid solu-

Jan 1, 1938

By J. W. Wilson, S. Nakajima, B. D. Singh

According to the Project Independence blueprint, a 270 percent increase in coal production is expected from western coal fields compared to an increase of 100 percent for the nation as a whole. Furthermore, 30 percent of the total United States coal reserves lie in the western states, which are classified as beyond the strippable limits and can be recovered only by underground methods. In view of the fact that the majority of the seams in the West are thicker than those presently mined in other parts of the country, it is important to consider the parameters that relate to mining thick seams and the factors that affect such mining systems. Apart from thick seams, a common feature of many western coal fields is the occurrence of multiple seams that lie in close proximity to one another. These multiple seam deposits present difficult mining problems that have not been encountered to any degree in other U.S. coal fields; for example, ground pressure changes in one mine level caused by mining in the other, sudden water or gas influx from the adjacent levels, the danger of spontaneous combustion in gobs and large and complex subsidence displacements on the surface. Perhaps equally important is the fact that the country can ill afford the present systems of underground mining that attain only 50 to 60 percent coal recovery. With the probability of increased thick seam mining, conservation shall be a focal point in future mine design systems. It is possible that in the future it will be forbidden to adopt the present day wasteful mining methods to ensure that coal can be conserved for future generations.

Jan 1, 1977

By A. F. Knoll, T. Clinton Taylor

Qualitatively, galena (native lead sulfide) reacts with aqueous solutions of the xanthates,1 and has its surface sufficiently altered so that there is a tendency for air bubbles to attach themselves to the mineral crystals where there was no such effect before the treatment. This property is utilized in froth flotation operations where the mineral sulfide particles are raised into the froth and the gangue whose surface is not altered remains behind. The results of a study of this reaction were reported2 recently and certain tentative suggestions about the interaction of galena and the alkali xanthates were offered. In this paper, there is set down the results of a detailed quantitative investigation of the ions involved in this interaction with a view to finding out more about the condition existing immediately at the surface of a crystal like a heavy metal sulfide after treatment with an organic reagent. Past experimental experience showed that finely ground galena shaken with aqueous potassium xanthate abstracts xanthate ion and at the same time sulfate ion, reducing ions of the type (SmOn)= where the ratio of m to n is less than 4:l (as in sulfate), sometimes hydroxyl ion, are thrown into solution.3 Ions Involved in Xanthate-galena Interaction The present quantitative study of the galena-aqueous potassium xanthate system shows that at the lower concentrations of potassium xanthate (less than about 25 mg. per liter) the amount of xanthate ion abstracted by the galena can be accounted for by the amount of reducing ions of the (SmOn)= type and sulfate ion thrown into solution. At these

Jan 1, 1935

By Thomas Carnahan

THE mining property of the Utah Copper Co. is situated in the West Mountain mining district, Salt Lake County, Utah, in the Oquirrh Range of mountains. GEOLOGY In a general way the rock formation of the district consists of a series of beds of quartzite and limestone intruded by a body of monzonite porphyry roughly elliptical in shape, with an east-west axis over a mile in length and a north-south axis of about 3,000 ft. This porphyry intrusion, accompanied by strong mineralizing action and fracturing, resulted in the formation of orebodies in the adjacent sedimentary rocks, and was itself sufficiently mineralized to make it one vast orebody. The Utah Copper Co.'s mining property comprises within its boundaries practically the entire outcrop of the monzonite mass, of a commercial grade. GENESIS OF PORPHYRY ORE Following an intricate system of fracturing, mineral solutions circulated freely through the porphyry, depositing small quantities of copper and iron, and resulting in a considerable silicification of the monzonite. The quantity of copper originally deposited was undoubtedly too small to have ever given the porphyry a commercial value, had not secondary enrichment, due to the leaching of the copper from the surface of the mass and re-deposition in the sulphide zone, been active over a long period of years. A large portion of the leached material has probably been .removed by erosion, but there still remains a blanket of leached and oxidized porphyry of varying thickness covering the sulphide ore, known as capping. Over certain sections of the orebody, this capping contains commercial quantities of copper carbonates, but most of it contains little or no copper.

Jan 1, 1916

By Eric R. Jette, A. G. H. Anderson

A few years ago, while the writers worked on the constitution of ternary and quaternary alloys consisting mainly of iron, chromium and siliconl,2 some information on microstructures and hardness, not incorporated in the published work, alas obtained. It has not been possible to do any further work on the properties of the alloys. The information possessed is hereby presented for the interest it may have in connection with the constitution of the alloys. Microstructures Referring to the iron-chromium-silicon diagram,' the regions that received most attention were those in which the sigma phase appears. It was found that the mode of occurrence of this phase varied much with the condition under which it mas formed, and the mode influenced considerably the hardness of the alloys. In some slowly cooled alloys, well within the alpha + sigma-phase boundary, sigma occurs in pabterns suggesting a eutectic. The structure of such an alloy is shorn in Fig. 1, showing it to be partly coarsely laminated and partly globular mottled. In other annealed and slowly cooled alloys, the lanlinated structure is entirely absent, and sigma appears in an irregular distribution of sharply cornered elongated areas (Figs. 2 and 3). These areas all possess a more or less mottled structure. A carbide phase is also visible in these two photomicrographs; it is represented by bright white arras of various shapes, sometimes apparently enveloping the sigma. Quenched and aged specimens, whose compositions arc: located near the phase boundary between alpha and sigma + alpha regions, have structures not unlike martensite (Figs. 5 and 6). Fig. 4 shows the structurc of alloy No. 35 as quenched from 1100" C.; it is a typical solid solu-

Jan 1, 1938

By R. M. de Carvalho

Empirical and phenomenological models of SAG and AG mills have dominated the scene for the last few decades, being used nearly every time a mill is scale-up or an attempt is made to improve its performance. However, in spite of their success, these models fail to describe the details of both the grinding environment and the breakage mechanisms. The result is a generally good track record, with a few – but very important – instances when these models fall short in their predictions, which can be very costly. Further, nearly all of these models require detailed calibration to industrial and pilot plant data, being costly in their application, although still with limited predictive capabilities. Recognizing these challenges, a new model framework has been proposed which overcomes the limitations of currently used models by coupling the microscale population balance model, the discrete element model and functions that describe internal classification at the mill grate. This model framework has already been applied to describe breakage in ball mills, with showing very promising results. However, in the case of SAG and AG mills a much greater level of complexity is involved in the model, given the interaction between the mechanical environment that is formed totally or, in part, by the ore itself, and the breakage response in the mill. The paper describes the model framework, demonstrating how it can address appropriately effects such as mill speed, mill filling and size distribution, on the response from the mill. Some of the advantages of the model are related to its intrinsic multi-component and dynamic nature, which allows simulating appropriately mixtures of ores of different competences in a transient manner.

Jan 1, 2012

By Earl R. McMillan

Though much has been written during the past several years about the Russian success in using hydraulic jets for coal mining, little or none of the published information, in so far as this writer has observed, has been of any use or practical application in this country. It is true, according to their published reports, that the Russians were pioneers in the use of high-pressure water jets in the mining of coal. They report the use of water jets for this purpose as early as 1936. However, according to a survey of foreign literature on the subject made by the U.S. Bureau of Mines1 a few years ago, water jets in the USSR, as well as in other nations including New Zealand, Poland and West Germany, were used principally to sluice the loosened coal after it had been previously drilled and blasted, rather than to cut or break it from the solid face. The interest of the Northern Pacific in the potential application of a high-pressure water jet to the actual extraction of coal, particularly in steeply dipping beds, originated in a visit by this author to the operations of the American Gilsonite Co. at Bonanza, Utah, in March 1958. After seeing the extraction, on a commercial basis, of gilsonite from a 22-ft wide vertical vein of this solid material with a 3/8-in. diam stream of water under approximately 2200 psi, it was felt that, with some modifications, water jets were the solution to the problem of economically mining the steeply dipping (i.e., steeper than 20º) coal beds in the State of Washington.

Jan 6, 1962

By Thomas S. Carnahan

The mining property of the Utah Copper Co. is situated in the West Mountain mining district, Salt Lake County;Utah, in the Oquirrh Range of mountains. Geology In a general way the rock formation of the district consists of a series of beds of quartzite and limestone intruded by a body of monzonite porphyry roughly elliptical in shape, with an east-west axis over a mile in length and a north-south axis of about 3,000 ft. This porphyry intrusion, accompanied by strong mineralizing action and fracturing, resulted in the formation of orebodies in the adjacent sedimentary rocks, and was itself sufficiently mineralized to make it one vast orebody. The Utah Copper Co.'s mining property comprises within its boundaries practically the entire outcrop of the monzonite mass, of a commercial grade. Genesis of Porphyry Ore Following an intricate system of fracturing, mineral solutions circulated freely through the porphyry, depositing small quantities of copper and iron, and resulting in a considerable silicification of the monzonite. The quantity of copper originally deposited was undoubtedly too small to have ever given the porphyry a commercial value, had not secondary enrichment, due to the leaching of the copper from the surface of the mass and re-deposition in the sulphide zone, been active over a long period of years. A large portion of the leached material has probably been removed by erosion, but there still remains a blanket of leached and oxidized porphyry of varying thickness covering the sulphide ore, known as capping. Over certain sections of the orebody, this capping contains commercial quantities of copper carbonates, but most of it contains little or no copper.

Jan 1, 1916

By Cyril Stanley Smith, Earl W. Palmer

FOR several years an investigation has been in progress in the research laboratory of The American Brass Co. to determine the thermal and electrical conductivities of most copper alloys of commercial importance and several of scientific interest. This paper contains such data on the binary alloys of copper with silicon, aluminum, manganese and nickel, and on a large number of ternary or more complex alloys. Some interesting general relationships between the thermal and electrical conductivities for all copper alloys at all temperatures are pointed out. The data for the copper-zinc, copper-phosphorus and copper-tin binary systems have already been publishedl 1,2 † except for the electrical conductivity at 200° C., which is given in the appendix of this paper. LITERATURE ON THERMAL CONDUCTIVITY OF COPPER ALLOYS The papers referred to above contained a summary of the figures available in 1929 for the thermal conductivity of copper alloys. There is given in Table 1 herewith a selection of the data that have appeared since that time. The measurements of Hanson and Rogers3 are particularly interesting since they cover a series of alloys in the alpha solid solution range and show the effect of heat-treatment. Their alloys were tested as annealed castings, and are not therefore directly comparable to the worked alloys measured in the present investigation, although the difference is small. Bailey's determinations4 were carried out on the alloys used by Lees5 in 1906, and extend his results to higher temperatures. It is most unfortunate that the alloys were not analyzed, for the approximate compositions given are hardly sufficient identification of the

Jan 1, 1935

By S. Ostap

INTRODUCTION Paradoxically, it has been found that the people who are the most aware of the origin, mineralogy and composition of bauxite are also the people who are the least aware of how bauxite composition affects its treatment by the Bayer process. These people are the exploration and mining geologists normally associated with aluminum producing companies. The purpose of this paper is to give some idea of how the concentration and physical nature of the different minerals found in bauxites affect the operation of the Bayer process used to extract their alumina content. The bauxites we will consider here will be only the tropical bauxites such as occurring in Jamaica, various countries in South America i.e. Guyana, Surinam, Brazil, African bauxites, Malaysia and in Australia. When we speak of the Bayer process, it will be the North American version of the Bayer process using low caustic concentrations and bauxite digestion temperatures varying between 130° to 250°C. TABLE 1 shows the minerals and elements of interest occurring in tropical bauxites. The minerals and elements listed in the table do not by any means represent all of those identified in bauxites. Using mass spectrographic analysis on six bauxites from different geographic locations, we managed to identify between 50-60 different elements. Fortunately, only about 13-14 of these elements possess the necessary chemical properties to be able to accumulate in caustic Bayer solutions. The remainder are either not attacked, or form insoluble reaction products with some main liquor component, i.e., hydroxide, aluminate or carbonate, or reprecipitate with alumina trihydrate during the precipitation stage.

Jan 1, 1984

By R. P. King

INTRODUCTION It is now 21 years since Wiegel and Li published their paper on a random version of Gaudin's model for the mineral liberation phenomenon (Wiegel and Li, 1967). This paper was to revitalise interest in North America in one of the most fascinating, difficult and important problems in the field of theoretical mineral processing. Gaudin had many years previously (Gaudin, 1939) already presented a penetrating analysis of the problem and Wiegel and Li based their analysis very closely on the Gaudin model but they realised that the indeterminate geometrical structure of mineralogical materials demanded that only probabilistic models could provide the necessary quantitative information when working with real materials. They proposed and solved a randomised version of the Gaudin model but retained the essential geometrical simplicity of cubic mineral grains and a cubic fracture pattern. Although their model met with some limited success it was to be superseded in due course. During the 1940's and 1950's the classical field of geometrical probability spawned the mathematical discipline of integral geometry and as early as 1965, Bodziony (1965, a,b) showed that the techniques of integral geometry could accommodate the problems associated with the indeterminate nature of the geometrical mineralogical structure, provided that these were couched in probabilistic terms. In particular he showed that the quantitative description of the comminution process and that of liberation could be decoupled with the resulting economy of effort. This idea has profoundly influenced the course of research in liberation theory and has greatly facilitated its application and the measurement of liberation in a practical way. Bodziony demonstrated also that any theory that required the specification of the mineral "grain

Jan 1, 1989

By Fred Bond

THE process of comminution by grinding is properly classified as an art, rather than as a science. Like most other operations concerned in ore dressing, or in the treat-ment of nonmetallic minerals, the mathe-matical relationships of rock breaking are still obscure, and much disputed. If some basic formula exists, comparable for in-stance to E = RI in electricity, it has not yet been placed in common use. The absence of such a comprehensive mathe-matical background undoubtedly is the cause of many inefficient designs and installations, as well as of much poorly oriented experimental work. On the other hand, the mathematical immaturity of the process constitutes an opportunity for a real contribution on the part of those who enjoy mental pioneering. Some of the statements made in any such exploratory work may be little more than opinions, and it is to be expected that some will later be proved untrue; but such an evolutionary development is necessary if we are ever to arrive at the fundamental laws, the discovery of which can change the empirical art into a mathematically exact science. The most significant principle of com-minution that we possess is probably Rittinger's law, which states that the work done in crushing or grinding is proportional to the area of the new surface produced. There is an alternative theory, known as Kick's law, which formerly was preferred to Rittinger's but which now is rather dis-credited. According to Kick, the work done in comminution is proportional to the volume, or weight, of the pieces broken, or to the cube of their diameters, while accord-ing to Rittinger it is proportional to the square of the diameters.

Jan 1, 1940