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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 Paul Weir

BLEACHING clays have been used extensively in the oil-refining industries for a number of years. Their use in water purification is relatively recent and less extensive. They are frequently classified as (1) those naturally active and (2) those active after artificial activation with acid. Fuller's earths fall within the general group of bleaching clays and gradually the commercial term "fuller's earth" has been applied to natural clays originating, for the most part, in the south-eastern section of the United States. Bentonitic clays are usually classed as activable and are prevalent in the southwestern section of the United States.1 Bleaching clays vary considerably in chemical and physical properties throughout the country, or even in different parts of one deposit (Table 1). TABLE 1.-Physical and Chemical Composition of Different Types of Clays Composition, Per Cent Constituents and Properties Bentonite Fuller's Mud Clay (Wyoming) Earth (P Peak)' (Alluvial) Silica (SiO2) 60.0 69.6 61.67 Alumina (Al203) 19.0 14.3 20.34 Ferric oxide (Fe203) 2.8 3.90 7.70 Titanium oxide (Ti02) 0.13 0.70 1.01 Lime (CaO) 0.5 0.80 0.00 Magnesia (MgO) 2.0 1.00 0.24 Soda (Na2O) 2.4 0.40 0.31 Ignition loss 4.7 6.77 8.51 Moisture content 8.0 10.0 20.0 Isoelectric point, pH 9.2 9.2 6.5 Average swelling volume 15.0 0.0 0.0 Weight per cubic foot, lb 55.0 40.0 65.0 Material passing 200-mesh sieve, per cent 90.0 85.0 50.0

Jan 1, 1939

By G. R. Fitterer

BY means of the C-SiC thermocouple1, liquid metal temperatures have been found to vary much more than was previously supposed, and fortunately these variations can be directly associated with some of our former knowledge which combined to form the "art" of liquid-metal manipulation. COMMERCIAL DEVELOPMENT OF THIS DEVICE Several types of installations are operating in different plants. There are so many variables in steel plants in regard to operation, pro-cedure, arrangement of pouring platforms, ladles, etc., that most of the installations now in service in this country are "tailor-made"; never-theless, it is felt that satisfactory gains have been made inasmuch as each installation has indicated some effect of temperature upon the metal-lurgical operation, and has pointed the way toward technical and finan-cial benefits. In most cases, it has been necessary to accumulate the temperature data until sufficient metallurgical information is available for the drawing of conclusions. When mechanical difficulties have been eliminated, a distinct correlation of these factors has been obtained. The installations now in service. are used for the determination of temperatures in the basic open-hearth furnace prior to tapping and in ladles from both acid and basic furnaces prior to pouring. Some of the installations are in shops making the higher priced steels; others are in "tonnage shops." The errors of human element, smoke screens and emissivity corrections connected with the use of the optical pyrometer do not affect the C-SiC thermocouple readings. The accuracy of the C-SiC- thermocouple and the temperatures measured are discussed later in this paper.

Jan 1, 1936

By Leo L. Van Sambeek

An understanding of the creep and yield behavior of salt is required for the rock mechanics design aspects of solution mining. Most previous studies of salt behavior have been performed on small specimens of salt under homogeneous stress conditions; i.e., uniaxial and triaxial tests on specimens <0.002 m3. The corejacking test is a larger scale test (-0.75 m3) with inhomogeneous stress conditions that provides data on the structural response of salt. Interpretation of the responses from eight such corejacking tests provides verification of the requisite constitutive parameters required to predict salt behavior at different levels of stress and temperature. These constitutive parameters are not those studied in the usual laboratory test. Corejacking test results show almost inseparable elastic and plastic closures simultaneous with the corejack pressurization. Very rapid closure (on a relative basis) continues for a period of time after the pressurization. This rapid closure is shown to be both continuing yield deformation and creep deformation. After the period of rapid closure, the closure rate approaches a constant value. Numerical modeling of the corejack tests using a creep law containing both transient and steady-state creep functions does not provide results that agree with the responses measured in the corejack tests. Using an experimental design technique plus additional numerical modeling that includes yielding of the salt, results in identification of the significant parameters which allow agreement. The significance of the results from the study is demonstrated by comparing the postulated stability and creep response of a solution-mined cavern using the previous understanding of salt behavior and the understanding developed from this study.

Jan 1, 1985

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,900. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation,&apos; the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service. "It shall be within the discretion of the Board of Directors to establish a medal to be known as the Charles F. Rand Memorial Medal to be awarded at such a time and under such rules as may be determined by the Board of Directors, for Distinguished Achievement in Mining Administration." The establishment of this medal was announced at the annual meeting in February, 1932, the term "mining" being defined in its broad sense to include metallurgy and petroleum. Robert Linton is chairman of the Charles F. Rand Foundation Award Committee.

Jan 1, 1942

By A. H. Miller

THIS survey is one of the more recent tests of geophysical methods of prospecting by the Dominion Observatory and the Geological Survey of Canada, of which the purpose is to find out what application such methods may have to geological problems in Canada. The Malagash salt deposit lies on the north shore of Nova Scotia about 40 miles east of the New Brunswick boundary, and forms a part of faulted and folded Carboniferous strata. The salt beds are exposed only in the mine workings, which are about 1000 ft. deep and at one place extend for 1000 ft. along the strike. Lack of rock exposures, complicated folds, and faults make it impossible to predict the location of salt away from the mine. A survey of an area in the vicinity of the mine was therefore undertaken to find out whether the salt could be located by the torsion balance and whether its extension from the mine workings could be traced. As the gravitational effects at Malagash may be fairly typical of those at other concealed salt deposits in the Carboniferous rocks of the Maritime Provinces of Canada, the survey has a direct bearing on prospecting for other deposits. The survey was made in 1934 by A. H. Miller in collaboration with Dr. W. A. Bell, of the Geological Survey of Canada. Observations began on June 15 and were completed four months later, on Oct. 15. Definite gravitational effects including a lowering of gravity were observed over the deposit. The survey also disclosed one other area of low gravity east of the mine but whether this area is underlain by a large body of salt is not yet established.

Jan 1, 1936

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

By G. F. Tagg

Earth-resistivity measurements are often of service in obtaining information regarding geological formations, particularly when applied to structural problems. In such problems the masses of the various bodies are large, and have a corresponding effect on the average resistivity of the soil. Much work has been done using such measurements, but in general the method of interpretation employed is empirical. Since certain simple cases can be investigated mathematically, it appears to be quite sound to endeavor to apply the mathematical solutions to the practical results, in order to deduce from the latter such unknown quantities as depth. This paper deals with such a method of interpretation for the simple case of a single horizontal stratum. In the method described by Wennerl for measuring earth resistivity, four stake electrodes are driven into the earth in a straight line as shown in Fig. 1. A current I amperes is passed between the two outer stakes and the potential difference V volts between the two inner stakes is measured. Then if a is the electrode separation, the specific resistance of the soil, which is assumed to be homogeneous, is given by the formula P = 2?v/1 [1] v or if v/1 is called a resistance R ohms, p = 2?aR [2] If a is in inches, p will be in ohms per inch cube, or ohm-inches, and if a is in centimeters, p will be in ohms per centimeter cube or ohm-centimeters. As stated above, this formula is true only if the earth is homogeneous, and when this is not the case an application of one of these formulas

Jan 1, 1934

By D. M. Deason, R. M. Chhatre, G. Y. Onoda

INTRODUCTION The treatment of colloidal suspensions is a subject of increasing interest in mining and benefication (1). Colloidal suspensions are not readily operated upon by mechanical and physical methods useful with coarse suspensions, such as filtration, thickening, and flotation. This is because colloids are strongly affected by interfacial and interparticle forces that may be large compared with, and resistant to, external forces. The degree and type of interactions between colloids can be modified by small additions of reagents such as coagulants, flocculants, dispersants, and immiscible liquids. These alterations in turn change the properties of the suspension and provide possible opportunities for transforming suspensions to a more favorable condition for a given processing operation. Phosphate slimes are an example of a colloidal system of interest today. In the mining and beneficiation of phosphate rock in Florida, slimes are a waste product. The phosphate ore (called matrix in the industry) is slurrified hydraulically and pumped to a beneficiation plant, where the -150 mesh material is removed by cycloning from the coarser phosphate rock and silica. The resulting -150 mesh slurry, called phosphate slime, is pumped to large impoundments. The solid content of the slime entering the impoundment is around four weight percent, and over 80% of the solids is less than one micron in size. The immediate problems with phosphate slime relate to their disposal (2, 3). The disposal problem is associated with the very large volumes and the poor dewatering characteristics of the slimes. To have sufficient impoundment volume, large earthen dams are built around the mined areas. The volume above ground level approaches and

Jan 1, 1980

By A. Hamilton Garner

The occurrence of oil seepages in Venezuela has been known since the early days of Spanish occupation. It was not until 1912, however, that any serious exploration work was undertaken. In that year, the Caribbean Petroleum Co., then a subsidiary of the General Asphalt Co., employed a large staff of geologists to make a systematic survey of large areas in eastern and western Venezuela, selecting the most desirable localities out of the immense area covered by the Valladares concession. This preliminary work was completed in the fall of 1913, and in February, 1914, the company completed its first commercial well at Mene Grande. Development work has progressed slowly, for various reasons, but petroleum in quantity has been encountered in nine widely separated localities. The Mene Grande field has been put on a producing basis and approximately 4,000,000 bbl. of oil is being shipped annually. Increasing quantities of oil are now being drawn from El Mene and La Rosa. In the light of these developments, the world&apos;s need for oil reserves, and the proximity of Venezuela to the United States, American capital is being attracted more and more to Venezuela. Although considerable careful geological work has been done in Venezuela by the various oil companies now operating, most of the data is buried in the company files, and the published literature has been extremely meager. The most valuable contribution to date has been a map and report by Jahn, which, as it was printed in Spanish, is not generally available to the American oil public. Venezuela, located in the northwestern part of South America on the Caribbean Sea, lies between l° and 12° north latitude. Its principal

Jan 1, 1925

By E. J. Schmitz

The mining of the Triassic coals of the Richmond basin has been carried on, upon a larger or smaller scale, for more than a hundred years. Notwithstanding the close proximity of the field to a large city and to tide-water, assuring both a good home-market and cheap transportation, and notwithstanding the good quality of the fuel and the great thickness of the principal bed developed and worked, operations in this field have been conducted with but limited success. The basin comprises about 189 square miles, being from 24 to 31½ miles in length by 5½ to 10 miles in width. Not much more than one-tenth of this area has been explored in a practical and efficient way, and not over 1200 acres have been worked near and along the outcrops or edges of the coal. The practical mistakes which have been committed undoubtedly in a number of the mine-operations of the past, do not alone explain the unsatisfactory success and progress of the industry of this field ; nor can it be ascribed to the lack of local enterprise. Other reasons have to be looked for; and, as a principal one, the irregularity and the faulted conditions of the coal deposits must be pointed out. As a second cause, the indifference of the State government, which leaves the development of the field entirely to private enterprise, instead of aiding it by systematical and practical geological investigations, deserves to be mentioned. Nothing has been done by the State since the excellent work done more than fifty years ago by Professor Rogers, who could not at that time enter into the details of such

Jan 1, 1895

By Robert Bosworth

THE liability for damages to the surface caused by subsidence is an ever present threat in all underground mining. In ordinary lode mining, this threat rarely materializes into an action, due to the method of mining metaliferous ores, the dip of the veins, and the nature of the ground itself. In the mining of coal, however, this threat is very real. The coal frequently lies close to the surface, in beds underlying large areas of land the surface of which is suitable for agricultural or urban development. Furthermore, the coal is generally mined by the "room and pillar " method and when the pillars of coal are removed, the subjacent support is destroyed. This question of the duty of surface support has now become a very live one in Colorado. What was waste prairie land a few years .ago, has become valuable agricultural land dotted here and there with growing towns. Frequent references will be made here to Colorado conditions and adjudicated cases, but those conditions and cases and the conclusions to be drawn therefrom are equally applicable to all coal-mining states. Briefly stated, the question is "Does the owner of the substrata or underlying mineral, owe any duty of surface support to the owner of the superjacent strata or surface?" There is no absolute duty of support owed by the mineral owner and this assertion is made with full knowledge of numerous expressions to the contrary by courts of Pennsylvania, Illinois, Colorado and other coal-mining states. Whether or not any duty exists depends upon the circumstances surrounding each case, and since in the nature of things those circumstances are rarely identical, there can be no absolute rule.

Jan 1, 1927

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 P. LaRochelle, K. Y. Lo, A. L. Tamuly Phukan

In many civil or mining engineering works, the stresses and deformations of natural or excavated slopes due to the combined effect of self-weight and initial stresses are of interest. Because of the mathematical complexities of this problem, however, no complete exact solution exists for the simplest case, that of assuming the stress-strain relation of the rock to be perfectly elastic. Efforts have therefore been directed toward numerical and experimental technique. The stresses within an elastic slope have been obtained by LaRochelle,1 using the photoelastic and finite difference method to determine the difference and sum of principal stresses. Subsequently, Finn,2 Hoyaux and Ladanyi,3 and Duncan and Dunlop4 attempted to solve the same problem by using the finite element method. The problem was also investigated by Brown and Goodman5 and Brown and King6 who emphasize the importance of the effect of loading or unloading procedure on the stress distribution within the slope. Although the geometry of the slope and the boundary conditions involved are identical or similar, the results obtained by these various authors by no means agree. It is therefore necessary to review briefly the results of elastic analysis in order to lend credence to the methods used in the solution. Although the stress-strain behavior of some rocks may be reasonably approximated by the elastic modrl, other rocks generally exhibit an elasto-plastic behavior with strain hardening or strain softening as shown in Fig. 1. Experiments show that for most rocks, the stress-strain relationship is approximately linear from the origin to the point P (neglecting the small concave region under low stresses). At P, the curve deviates

Jan 1, 1970

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,400. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation,&apos; the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service. "It shall be within the discretion of the Board of Directors to establish a medal to be known as the Charles F. Rand Memorial Medal to be awarded at such a time and under such rules as may be determined by the Board of Directors, for Distinguished Achievement in Mining Administration." The establishment of this medal was announced at the annual meeting in February, 1932, the term "mining" being defined in its broad sense to include metallurgy and petroleum. Robert Linton is chairman of the Charles F. Rand Foundation Award Committee.

Jan 1, 1944

By R. W. Raymond

Richard Pennefather Rothwell, was born May 1, 1836, at Oxford, Upper Canada (now the province of Ontario). His father, Rev. John Rothwell, was a native of County Meath, Ireland, where the family (originally, no doubt, a Scottish one) still holds large estates, under a grant from William and Mary. John Rothwell was graduated at Trinity College, Dublin, and became a clergyman of the Established Church. He married Elizabeth Garnett, of Athearn Castle, Ireland, and subsequently came to Canada. It is said that he was a man of liberal views combined with sterling piety, an enthusiastic sportsman and yachtsman, and a pastor who refused for many years to accept any remuneration from his parishioners. After preliminary education, the subject of this sketch entered Trinity College, Toronto, with the intention of studying law; but a year later he resolved to become a civil engineer, and entered the Rensselaer Polytechnic Institute at Troy, N. Y., where he was graduated, with high standing, as civil engineer, in 1858. He then went to Paris, and entered the Imperial School of Mines, where, by reason of the proficiency he had already acquired in civil engineering, he was able to finish in two years and a half the full three-year course, and to take the degree of Engineer of Mines. In 1861 he took the "practical courses" in mining and ore-dressing at the Mining Academy of Freiberg, Saxony. After traveling in Italy, etc., he went in 1862 to London, where, for the purpose of familiarizing himself with business methods, he entered the offices of W. T. Henley, a manufacturer of wire

Jan 1, 1902

By Charles Albert Ashburner

Natural gas has been known to exist for many years in the St. Lawrence Valley, between Quebec and Montreal, and more partirularly in the vicinity of Louisville and Three Rivers, 74 and 94 miles respectively northeast of Montreal, and 98 and 78 miles respectively southwest of Quebec; the distance from Montreal to Quebec along the St. Lawreuce River being about 175 miles. It was not until 1880 that any practical explorations were begun with the hope of finding gas in sufficient quantities for commercial uses. In this year Messrs. Piret and Genest, of Three Rivers, sank a well near St. Maurice to a depth of 50 feet, where solid rock was encountered. A similar well was drilled through the glacial and allavial drift, in the same district, in 1883, by the Messrs. Renaud Freres and Dubois, to a depth of 70 feet before solid rock was encountered. In this latter well a strong flow of gas was obtained. The gas was an outflow from a very limited reservoir in the porous glacial gravel, which had been filled from the gas resulting from the decomposition of vegetable remains, which had been buried in the gravel at the time of its deposition. Subsequently, other wells were sunk in the same way, with the hope of getting gas in commercial quantities from similar reservoirs. Commercial Gas.—By gas in commercial quantities I mean gas in such quantity that, if utilized with proper care and economy, it would generate steam at a cost below the cost at which the same duty could be obtained from the use of coal or wood at current prices, and that

Jan 1, 1890

By H. M. Chance

In recent years an important function of the mining engineer has been the appraisal of the value of mining-properties required by those planning consolidations of a number of&apos; individual operations. In no field of productive industry have the economic results attainable by consolidation been more clearly shown than in the mining-regions of the United States. In many important mining-centers unification of ownership of the most valuable properties has already partially or completely been attained, and, in other districts, projected absorptions and consolidations await only favorable financial conditions for their consummation. The iron-ore districts of the Lake Superior region, the coal-mines of Colorado, of Wyoming and of Utah, the anthracite mines of Pennsylvania, the Connellsville coking-coal mines, and large areas of bituminous coal-land in Pennsylvania, in Ohio, in the Indian Territory and in other portions of the United States, are now largely controlled by a few corporations operating on a large scale, or by a number of corporations working in harmony because of an affiliation and interleaving of interests. The tact of keen financiers and the diplomacy of men of great administrative ability are the chief operative forces in conceiving and accomplishing such consolidations, but in formulating and maturing them, the services of the mining engineer are often required to supply the facts upon which they must be based. For this purpose the expert is expected to furnish full and complete reports covering the quantity of ore, coal or other mineral available, its value per ton, cost of mining and treatment, etc. In reporting upon gold-, silver-, lead-, zinc-, copper- or iron-

Jan 1, 1905

The introduction and development of the flotation process have proved to be of such momentous importance to the mining industry of the United States that they deserve to be considered historically.* The origin of the use of oily matter in separating minerals in ores is obscure, because its beginnings were unregarded. The story told by Herodotus concerning the recovery of gold from the mud of a lake by means of feathers daubed with pitch in the hands of apocryphal virgins is as pertinent to our inquiry as the yarn, two thousand years later, of a young school-teacher in Colorado that was washing oil-stained ore-sacks in her brother&apos;s assay-office when she noted the floating of pyrite on the water contaminated by the oil. In any event, the method patented by Carrie Everaon in 1885 was a complete failure, except as factitious evidence for trying to disprove the originality of subsequent inventions. An early and inadvertent use of the affinity of oil for metallic surfaces is suggested by the story of Jason and the Argonauts, who extracted gold from the gravel of the river Colchis by means of sheepskins. The woolly hide sewed, like the blankets used in our early stamp-mills, to arrest the gold, which was further detained by the oil on the fleece. Strabo, referring to a later period, says that in the country of the Soanes, who inhabit the valley of the Colchis, “the winter torrents are said to bring down even gold, which the barbarians collect in troughs pierced with holes, and lined with fleeces; and hence the fable of the Golden Fleece”.† William Pryce

Jan 1, 1932

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&apos;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&apos;s law, which formerly was preferred to Rittinger&apos;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