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NEW MEMBERS The following list comprises the names of those persons who became members during the period June 10, 1919, to July 10, 1919. ANDERSON, JOHN EDWARD, Min. Engr., Lehigh Valley Coal Co., 121 N. Laurel St., Hazleton, Pa. BENBOW, B. L., Mgr., Cleveland Wire Division, National Lamp Works, General Electric Co., 1770 E. 45th St., Cleveland, Ohio. BLAIR, CHARLES S., Geol., Tennessee Coal, Iron & R. R. Co., Birmingham, Ala. BOLAND, FRED L., Chief Draftsman, Mine Dept., Chile Exploration Co., Chuquicamata, Chile, South America. COLLIER, OTTO L., Civil & Min. Engr., Secretary, Ernest M. Merrill Engrg. Co., Mullens, Wyoming Co., W. Va. DELAMATER, GEORGE RICHMOND, Asst. Supt:, By-product. Coke Oven Dept., Steelton Plant, Bethlehem Steel Co., Steelton, Pa. DOELL, WILLIAM R Chief Engr., Mahuomen Iron .Co., Crosby, Minn. ENDO, SHINZO 365 Komagome Shimmeicho, Hongo, Tokio, Japan. EVANS, CHARLES E., Chief Draftsman, American Smelt. & Refin. Co., Murray, Utah. FISCHER, OSCAR A 62S First National Bank Bldg., Denver, Colo. FISHER, GEORGE KINGSBURY, Met. Engr 47 Baker St., Saranac Lake, N. Y. FRAZEE, VERNE, Min. Engr Moweaqua, Ill. FURNICHI, ROKUZO, Supt. of Min. Dept., Besshi Copper Mine, Baron Sumitomo Co. Ehime Japan

Jan 8, 1919

By Anson G. Betts

A solution of lead-fluosilicate, containing an excess of fluosilicic acid, has been found to work very satisfactorily as an electrolyte for refining lead. It conducts the current well, iseasily handled and stored, non-volatile and stable under electrolysis, may be made to contain a considerable amount of dissolved lead, and is easily prepared from inexpensive materials. It possesses, however, in common with other lead electrolytes, the defect of yielding a deposit of lead lacking in solidity, which grows in crystalline branches toward the anodes, causing short circuits. But if a reducing-action (practically accomplished by the addition of gelatine or glue) be given to the solution, a perfectly solid and dense deposit is obtained, having very nearly the same structure as electrolytically-deposited copper, and a specific gravity of about 11.36—that of cast-lead. Lead-fluosilicate may be crystallized in very soluble, brilliant crystals, resembling those of lead-nitrate and containing four molecules of water of crystallization, with the formula PbSiF,,4H20. This salt dissolves at 150 C. in 28 per cent. of its weight of water, making a sirupy solution of 2.38 sp. gr. Heated to 60° C., it melts in its water of crystallization. A neutral solution of lead-fluosilicate is partially decomposed on heating, with the formation of a basic insoluble salt and free fluosilicic acid, which keeps the rest of the salt in solution. This decomposition ends when the solution contains, perhaps, 2 per cent. of free acid; and the solution may then be evaporated without further decomposition. The solutioi~s desired for refining are not liable to this decomposition, since they contain much more than 2 per cent. of free acid. The electrical conductivity depends mainly on the acidity of the solution. My first experiments were carried out without the addition of gelatine to the fluosilicate solution. The lead-deposit con-

Jan 1, 1904

By George K. Burgess

The suggestion has often been made that it would be highly desirable, at least for certain grades of steel, to be able to control more certainly, by pyrometric measurement or otherwise, the temperatures of the operation of the open-hearth and other furnaces used in the manufacture of steel and iron. That the properties of the ingot and finally of the finished steel product are intimately related to the final temperatures attained by the metal in the furnace and to the temperature of casting, has been recognized by metallurgists for a long time, and this question has been very thoroughly treated, especially by Prof. Henry M. Howe, and by A. W. and H. Brearley.1 It is the object of this paper to demonstrate that in so far as casting temperatures of furnaces, steel ingots, and similar operations involving the temperatures of streams of iron and steel are concerned, well-known pyrometric methods may be easily applied—if certain recently determined corrections are made and precautions taken—with a relatively high degree of accuracy. Greater but not insurmountable difficulties will be encountered in the case of open-hearth furnace temperatures, while for those of the converter type a ready solution does not seem practicable. It appears that certain essential data have always been lacking in reporting observations such as those of Le Chatelier in 1892. Thus the correction to be applied for the characteristic radiation—or emissivity— has hitherto not been adequately taken into account nor the limitations of the several possible pyrometric methods clearly recognized. In view of the fact that in open-hearth practice the temperature to be measured in the furnace itself, in the stream of metal and slag and in the teeming into molds or ingots is usually above 1,500" C. (2,700" F.)

Jan 1, 1917

By Milton Williams

It is generally recognized that fluid is lost from rotary drilling muds to permeable strata during normal drilling operations;1,2-3 but that this fluid is the filtrate from the mud, rather than the mud itself, has been shown by various workers.1,4,5 The presence of this filtrate in oil-bearing or gas-bearing strata is undesirable and harmful. The decreased permeability of the stratum to oil effected by the presence of water has been pointed out by several investigators,6,7 and since, in the production of the reservoir fluid, the greatest pressure drop occurs immediately adjacent to the borehole, it follows that infiltered water is particularly objectionable in this region. Again, this filtrate tends to make electrical logs less reliable, since oil in the proximity of the borehole is probably flushed out to an appreciable extent by the water.8 Observation of side wall cores may be misleading for the same reason. Drill-stem tests in low-pressure areas may be of doubtful value where no oil is recovered, unless sufficient time is allowed for production of water lost from the mud. The infiltered water may hinder drilling operations by softening shales and causing sloughing; the ['tight hole" occasioned by excessive deposition of filter cake in the hole is a common occurrence. The filter cake remaining on the face of the producing formation may itself sometimes be detrimental to production.9 In view of these implications of the importance of filtration of mud, an investigation was undertaken to determine the factors involved in the infiltration process, and to correlate these in such a manner that the values obtained in routine filter tests employing a conventional filter of the "wall-building tester" type,10 together with data on size of hole, drill pipe, and rate of mud circulation, could be used to estimate water loss and distance of penetration of the filtrate into strata. Quantitative relations of filter-cake permeability, filtrate viscosity, and rate of filtration have been developed for filtration in the simple laboratory filter.4a,11,12,13 It is obvious, however, that the conditions

Jan 1, 1940

By J. Koskinen, P. Vanninen, T. Leskinen, A. Leppala

Continuous and accurate analysis of slurries has become a critical requirement in mineral processing. With on-stream assay data, automation procedures can be employed to obtain higher recovery and improved control of production. The Courier system was developed by Outokumpu Oy, taking advantage of mineral processing know-how, to provide means for achieving these objectives in the company's ore concentrator operations. It became evident, based on early experience with on-stream analysis, that the Courier should be a complete system to fulfill all functions of the analysis operation. The system includes equipment and techniques for primary sampling, sample preparation for assaying, and processing of data for final assay results. In addition, the on-line X-ray spectrometer unit was developed specifically for industrial use, incorporating a number of technical advances. A new system for converting spectrometric data to assays is based on a physical model programmed on a digital computer. The Courier system is furnished on a turn-key installation basis incorporating all elements needed for operation including calibration. The experience to date with the Courier system at the Pyhäsalmi concentrator is summarized. Reference is also made to recent results with installations at the Outokumpu and Vihanti concentrators.

Jan 1, 1972

By R. P. Ehrlich, D. A. Dahlstrom

In the hydrometallurgical circuit, many phase separation steps are usually necessary. Typical steps are pregnant liquor - leach residue separation by counter- current decantation or continuous vacuum filtration, clarification of liquids prior to precipitation, ion exchange or solvent extraction, dewatering of final product, etc. The paper discusses the more recent advances in these areas and considers general operating parameters and cost factors. In addition, emphasis is placed on future needs because of the growing importance and necessity of hydrometallurgical processing of minerals.

Jan 1, 1973

Electro-mechanical actuator, self-protected for mechanical and electrical overload, is developed by RACO. Tubular housing consists of squirrel cage motor with hollow rotor shaft and inner threads in the rotor. Features stroke distance of 2-72 in. and wide range of trust (20 lb-10 tons). (100) Agglomeration systems, offered by Ferro-Tech, incorporate pelletizing, briquetting and extrusion systems to agglomerate materials too fine to convey, load or feed to a process. Equipment includes disc and drum pelletizers, briquetter presses, compactors, extruders, pugmills and mixers, dryers, coolers, feeders and conveyors. (101)

Jan 9, 1973

By Arthur W. Rose

Statistical techniques are being widely used in geochemical exploration to answer questions involving sample spacing, analytical and sampling errors, thresholds, data smoothing, and optimum combination of several elements into one measure of favorability. The applications of sampling theory, mean and standard deviation, trend surfaces, moving averages, factor analysis, cluster analysis, discriminant analysis, and regression analysis to these questions are discussed with examples. Although the techniques are very useful as means of handling large amounts of data, they require as much geological and geochemical judgment as any other approach to data interpretation.

Jan 1, 1973

By Theodore Simons

The rapid and comparatively recent development of flotation has opened so fascinating a field for study and research that the older processes of gravity concentration no longer receive the attention they deserve. The early work of Munroel and Richards12 and the more recent contributions by Clevenger and Coe,3 Laist and Wiggin,4 Ammon,5 Bardwell,6 Crowfoot,' and Hayden8 (to mention only some which have appeared in our own Transactions) and by Schu1z,9 have furnished so much data that to offer something new seems a difficult task. It is still possible, however, to present known facts from a different point of view, and, with this in mind, the writer has undertaken to express basic principles of gravity concentration in terms of simple mathematics and mechanics; the conclusions thus reached will be found to correspond, in general, with those obtained by experimental methods. Rittinger, in his classic Aufbereitungskunde (1867)) reached analogous conclusions by way of intricate higher mathematics, for which reason his interesting investigations have remained a sealed book to most of us. The writer hopes that a more elementary treatment of the subject, based in part on Rittinger's metheds, may arouse new interest in the study of basic principles.

Jan 1, 1923

By C. C. Henning

In any line of human activity logical handling requires an amount of attention to each phase that is in keeping with the importance of that phase. In the complex and rapidly changing field of modern ferrous metallurgy it is difficult to allot the proper degree of attention to the various subjects, and it is not surprising that one or more subjects of major importance should for a time be neglected. Bessemer steel is a good example of a neglected subject. It is largely taken for granted, inferior physical quality is assumed for it, and there is a • lack of interest in its technical development and commercial application. Availability of supply is limited. In spite of this technical indifference, limited source and lack of commercial exploitation, bessemer steel constitutes a large volume of tonnage in daily use. There is a fairly prevalent idea even among technical people that bessemer steel survives mostly because of low cost and by reason of a dwindling residue of applications sufficiently common to permit of its use. The difference in cost between bessemer and open-hearth steel is governed largely by the relative cost of manufacture of pig iron and the market price of steel scrap. During the past four years there have been long periods of time during which the price of steel scrap was low enough so that open-hearth steel was considerably lower in manufacturing cost than bessemer. As to application, it may be pointed out that thousands of tons of this material in the form of bessemer screw steel are applied for moving parts in automotive and other equipment. Some forging work and considerable heat-treating, particularly carburizing, is performed on this grade. From an economic standpoint the most effective contribution of bessemer steel lies in its free machining qualities. It is by far the freest

Jan 1, 1935

By Kenneth B. Ray, George R. Gardner

The application of wet cleaning processes for the beneficiation of bituminous coal has created in some localities a problem in the recovery and disposal of fine solids in the washery water. The maximum allowable concentration of these solids in the washery circuit that is consistent with satisfactory operation of the cleaning units remains a controversial point. It has, however, been generally recognized for a number of years that some degree of control should be exerted over the concentration of such material. Early methods of control involved intermittent or continuous discharge of a portion of the plant slurry into near-by streams or settling ponds, and this persisted even after the adoption of settling tanks or cones. The practice is not always economical, for two reasons: first, because of the waste of coal, and, second, because it is sometimes difficult and expensive to obtain an adequate supply of water. The latter condition often is aggravated by chemical treatment of the make-up water that is necessary to prevent excessive corrosion of plant equipment. The modern approach to this problem has been the adoption of continuous thickening devices. However, because such equipment occupies considerable plant space and is somewhat expensive to construct, the practice of loading these thickeners beyond their rated capacity is widespread, therefore often the performance of such units is not altogether satisfactory. In recent years, European washeries have increased the rate of settling of the fine coal from the slurry by the addition of specially prepared starch solutions. These reagents cause flocculation of the solid particles and thereby increase the rate of sedimentation. The first important work on the flocculation and clarification of coal slurry was done by Henry, who developed the Henry process and used it successfully in Belgian preparation plants. Soon after the initiation in Belgium, the process was introduced into England, where subsequent, investigation developed similar processes, which were successfully used in

Jan 1, 1939

By J. N. Hummel

The methods of electrical prospecting, which employ contact electrodes to produce an electric field in the ground, furnish information concerning the constitution of the material beneath the surface, as indicated by the distortion of this artificially produced field and anomalies therein. To reveal the distortion of such field of known character, it is only necessary to measure qualitatively the direction of the field, using sensitive compensation methods. In such a case, the survey is relatively simple, and that is an important factor from a practical point of view. The distortion of the normal field thus determined permits an easy interpretation and gives approximate information as to the subsurface conditions, without the necessity of a thorough theoretical knowledge of the electrical field. The true field of application of the equipotential lines and search-coil methods, which are based on this principle of directional determination of the electrical field in the ground, is that of search for deposits of economic minerals for the mining industry, although they can also be used in solution of other problems; for example, in the determination of the strike of anisotropic beds. The distortion of the electric field as represented by the picture of equipotential lines or other measured curves is striking only when bodies having conductivities different from that of the country rock are embedded in the underground, or when the underground is anisotropic. It is obvious that methods based on such a simple principle and capable of solving directly many of the practical problems of mining geology have found a widespread application. However, these methods are unable to furnish any information as to the presence, depth and physical properties of layers in the underground, which have different conductivities, but are parallel, or only slightly inclined, to the surface. Where such conditions exist in the underground, the picture of the field

Jan 1, 1932

By George R. Gardner, Kenneth B. Ray

The application of wet cleaning processes for the beneficiation of bituminous coal has created in some localities a problem in the recovery and disposal of fine solids in the washery water. The maximum allowable concentration of these solids in the washery circuit that is consistent with satisfactory operation of the cleaning units remains a controversial point. It has, however, been generally recognized for a number of years that some degree of control should be exerted over the concentration of such material. Early methods of control involved intermittent or continuous discharge of a portion of the plant slurry into near-by streams or settling ponds, and this persisted even after the adoption of settling tanks or cones. The practice is not always economical, for two reasons: first, because of the waste of coal, and, second, because it is sometimes difficult and expensive to obtain an adequate supply of water. The latter condition often is aggravated by chemical treatment of the make-up water that is necessary to prevent excessive corrosion of plant equipment. The modern approach to this problem has been the adoption of continuous thickening devices. However, because such equipment occupies considerable plant space and is somewhat expensive to construct, the practice of loading these thickeners beyond their rated capacity is widespread, therefore often the performance of such units is not altogether satisfactory. In recent years, European washeries have increased the rate of settling of the fine coal from the slurry by the addition of specially prepared starch solutions. These reagents cause flocculation of the solid particles and thereby increase the rate of sedimentation. The first important work on the flocculation and clarification of coal slurry was done by Henry, who developed the Henry process and used it successfully in Belgian preparation plants. Soon after the initiation in Belgium, the process was introduced into England, where subsequent, investigation developed similar processes, which were successfully used in

Jan 1, 1939

By Philip Morse

THE Australian lead-smelting plants began to use charges carrying high zinc percentages somewhat earlier than was common with American plants. When lead smelting first started in Australia the immense deposits of oxidized lead at Broken Hill were available but later these oxidized ores became exhausted and were replaced by sulfides. This was before the days of flotation and these sulfides when concentrated carried about 1 per cent. of zinc to 6 per cent. of lead. The works of the Sulphide Corpn. at Cockle Creek was perhaps the pioneer in high-zinc slags but the Port Pirie plant of the Proprietary Co. was a close and very able second and has continued the work to the present time. The Cockle Creek lead furnaces remained in operation until shortly after the war when most of the Broken Hill companies combined and took over the Port Pirie plant to treat their concentrates. As it was the practice both at Cockle Creek and Port Pirie to carry 20 per cent. or more of lead on the charge, it was found that under these conditions of large amounts of zinc in the charge, good roasting was absolutely necessary and matte production was unwise. The Huntington-Heberlein system of roasting was introduced and later the Dwight & Lloyd process. In this way, by roasting the sulfide portions of the charge as thoroughly as possible and making no matte, a method of smelting was developed where the slag over long periods carried as high as 20 per cent. ZnO without serious furnace troubles, and slags carrying even up to 33 per cent. ZnO have been reported. The zinc slags were not very different in appearance from the ordinary slags produced in American practice except that they gave off more smoke and fume on tapping. The slag usually ran hot and freely, coming from the tap in a full stream. Normally there was little crust on the sides' of the furnace and the tuyeres gave no trouble though they were always rather dark.

Jan 1, 1929

By A. S. Adams

A glance at the list of papers1 that have been published since 1920 on the general subject of flotation suggests the variety of ideas that exist regarding the underlying cause of the phenomenon. Among these ideas, we find several coherent theories, but none that adequately and completely explain the phenomenon. Ralston2 and Bains3 suggested an electrical theory which has to do with the attachment of mineral particles to a bubble by the attraction of unlike electrical charges. This theory has its root in the fact that a bubble of air in pure water is electrified in such a way that the surfacc is negatively charged while the body of the water is positively charged. This result, which was first discussed by Helmholtz, also obtains when the water contains anything except a high concentration of hydrogen ions, or ions which are trivalent or tetravalent. The theory also holds that the mineral particles have positive charges on their surfaces, and so there is attachment between bubble surface and mineral particles by the old law of electrostatics, which states that unlike charges attract. Contact Angle and Oil Attraction The contact angle—the angle formed by a fluid-fluid boundary when both are in contact with a solid-—has been indicted several times for complicity in the phenomenon of flotation. This angle is supposed to indirectly measure the surface energy of a solid. Thus if we have two fluids in contact with a solid, we may express the difference between the two fluid-solid tensions as equal to the fluid-fluid tension times the cosine of the angle between the two fluids.4 If the two fluids are in contact with the solid, this is, no doubt, an excellent way of establishing relative surface energies. However, in flotation, we deal with substances which are not wetted by water. What assurance have we, then, that the angle

Jan 1, 1928

By K. Unrug, G. Herget, A. Smith

SUMMARY Statistics on roof falls indicate that the cost of just removing the unwanted waste from roof falls in US coal mines amounts to about $20 M per year. Almost 40 percent of fatal accidents occur under permanently supported roofs, indicating that the assessment of roof stability is still a very difficult task. In an effort to obtain a better understanding of roof fall occurrences, rock strength and ground stresses were determined in the roof of one mine each in Western Kentucky, northern West Virginia, and Eastern Kentucky. Triaxial ground stress determinations clearly show that horizontal stresses were higher than vertical stresses, and that maximum stresses in the horizontal plane were concentrated between the NE-SW to E-W direction, with the exception of the Eastern Kentucky site which was above the drainage. Magnitudes of stress components may vary considerably in one drlll hole. Strength tests of roof strata materials were done on core samples. Mapping of roof falls showed that the geometry of an opening or maximum span were not the overruling factor because in the same general area, a roof fall was observed in a room (entry) which connected two stable four-way intersections. It should be noted that, in very wet areas, the roof can break up to the bed where water is carried, and a very low ratio between extent of roof fall to height of roof, fall is observed. Geometry is, however, a contributing factor because nearly 70 percent of roof falls are intersection falls. The frequency of fractures parallel to bedding in failed roof strata is much higher than that observed in the original strata, indicating a significant amount of working in the roof before failure.

Jan 1, 1984

By C. C. Henning

In any line of human activity logical handling requires an amount of attention to each phase that is in keeping with the importance of that phase. In the complex and rapidly changing field of modern ferrous metallurgy it is difficult to allot the proper degree of attention to the various subjects, and it is not surprising that one or more subjects of major importance should for a time be neglected. Bessemer steel is a good example of a neglected subject. It is largely taken for granted, inferior physical quality is assumed for it, and there is a • lack of interest in its technical development and commercial application. Availability of supply is limited. In spite of this technical indifference, limited source and lack of commercial exploitation, bessemer steel constitutes a large volume of tonnage in daily use. There is a fairly prevalent idea even among technical people that bessemer steel survives mostly because of low cost and by reason of a dwindling residue of applications sufficiently common to permit of its use. The difference in cost between bessemer and open-hearth steel is governed largely by the relative cost of manufacture of pig iron and the market price of steel scrap. During the past four years there have been long periods of time during which the price of steel scrap was low enough so that open-hearth steel was considerably lower in manufacturing cost than bessemer. As to application, it may be pointed out that thousands of tons of this material in the form of bessemer screw steel are applied for moving parts in automotive and other equipment. Some forging work and considerable heat-treating, particularly carburizing, is performed on this grade. From an economic standpoint the most effective contribution of bessemer steel lies in its free machining qualities. It is by far the freest

Jan 1, 1935

By R. C. Hall

In the present work, experiments determined the effect of the order-disorder reaction near the Fe,Al composition on the magnetic anisotropy and magnetostriction of single crystals: A material which is more difficult to magnetize in one direction than in another is anisotropic, that is, the ease with which ferromagnetic materials may be magnetized in different crystallographic directions determines the anisotropy. Two investigators have estimated the anisotropy of the aluminum iron alloys from poly-crystalline data;1,2 however, these estimates should not be considered to be reliable. Siege1 made two accurate measurements of the first anisotropy constant* from single crystals of 4.0 wt pct aluminum sotropy throughout the ferromagnetic aluminum iron system have been described. These results were obtained from single crystals which were slowly cooled and, hence, ordered near the Fe3Al composition.4 Magnetostriction is the change in length per unit length resulting from applying a magnetic field to a ferromagnetic material. For the purpose of this report, the saturation magnetostriction was measured. This is the maximum change in length per unit length resulting from an applied magnetic field large enough to saturate the material in a given direction. This magnetostriction has been determined for single crystals of the ferromagnetic aluminum-iron system.' The crystals near Fe3Al were also ordered. PREPARATION AND TREATMENT OF SINGLE CRYSTALS Single crystal bars were grown from the melt.' The raw materials for these crystals were iron and aluminum of 99.9 and 99.99 pct purity, respectively. From the bars, crystals in the shape of circular

Jan 1, 1959

By Albert Sauveur

As director of the Division of Metallurgy of the Technical Section of the Air Service, American Expeditionary Forces, from August, 1917, to January, 1919, I devoted much time to the study of the steels best suited to the construction of aircraft. It became apparent at a very early stage of my investigation that the practice of builders varied greatly in regard to the number of different steels to be used, to the kinds of steels, and to their treatment. Some manufacturers employed as many as fifteen steels while the builder of one of the newest motors, favorably passed upon in the United States, assured me that two or, at the most, three kinds of steel was all he needed to produce satisfactory results. In the matter of treatment, the manufacturers were also greatly at variance.. Some treated their steel with considerable refinement, while others paid but scant attention to this feature. Some manufacturers case-hardened many parts, while others used the case-hardening process sparingly, if at all. Nickel-chromium steels were used at some works for case-hardening while at other plants this treatment was applied exclusively to carbon steels. Air-hardening nickel-chromium steel was used extensively by some and not at all by others. Considerable variance existed likewise in regard to the steels used for admission and exhaust valves. The conclusion was obvious, that no two manufacturers of airplane motors held like opinions as to the steels to be used or as to the treatment they should receive. Was it to be inferred from this that the many committees and associations that had been created, in part at least, for the standardization of aircraft steels had failed to make proper recommendations or that the manufacturers had ignored their recommendations? Confining our inquiry to the committees and associations that had dealt with this question in England, France, and the United States, it was found that in Great Britain the British Engineering Standards Committee, now the British Engineering Standards Association, had devoted much time to the problem of satisfactory standards for aircraft steels. In April, 1918, this Association presented a set of specifications

Jan 9, 1919

By Theodore Simons

The rapid and comparatively recent development of flotation has opened so fascinating a field for study and research that the older processes of gravity concentration no longer receive the attention they deserve. The early work of Munroel and Richards12 and the more recent contributions by Clevenger and Coe,3 Laist and Wiggin,4 Ammon,5 Bardwell,6 Crowfoot,' and Hayden8 (to mention only some which have appeared in our own Transactions) and by Schu1z,9 have furnished so much data that to offer something new seems a difficult task. It is still possible, however, to present known facts from a different point of view, and, with this in mind, the writer has undertaken to express basic principles of gravity concentration in terms of simple mathematics and mechanics; the conclusions thus reached will be found to correspond, in general, with those obtained by experimental methods. Rittinger, in his classic Aufbereitungskunde (1867)) reached analogous conclusions by way of intricate higher mathematics, for which reason his interesting investigations have remained a sealed book to most of us. The writer hopes that a more elementary treatment of the subject, based in part on Rittinger's metheds, may arouse new interest in the study of basic principles.

Jan 1, 1923