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By B. C. Allen

Liquid surface tensions of copper and 18 Group IV-A to VIII transition metals (Ti, Zr, Hf, V, Cb, Ta, Mo, W, Re, Ru, Rh, Pd, Os, Ir, Pt, Fe, Ni. Co) have been measured by the static pendant-drop and dynamic drop-weight methods on the same rod sample. The drops were formed by electron-bombardment heating in high vacuum. Application of necessary corrections enabled determination of surface tensions to k2 pct and agreement between methods to * 1 to 4 pct for all the metals studied. Evidence is presented that the liquid surface was well screened by metal vapor, suggesting negligible adsorption of gaseous impurities and that the surface tensions measured are characteristic of the metals involved. Correlations between liquid surface tension and melting point, molar volume, heat of vaporization, and atomic number are presented and discussed. Temperature coefficients of surface tension were calculated using Eötvös' law. SURFACE tension and interface energies of metals are the result of incomplete atomic coordination resulting in a force perpendicular to the boundary, tending to minimize its area. These energies are important in many phases of metallurgy, including microstructure, sintering, joining, electronic emission, and lubrication, which in turn affect many physical and mechanical properties of metals. Liquid surface tension refers to the interface between the liquid and its own vapor or nonreactive atmosphere, and is considered a physical property of the liquid. Since equilibrium shapes can be readily obtained with liquids, the units of surface tension (force per length) and interface energy (energy per area) are interchangeable. Thermo-dynamically, the surface tension ?LV is given by the change in free energy F with surface area A at constant pressure P, temperature T, and composition N: for commercially important refractory metals, vanadium, columbium, tantalum,13,14 molybdenum,14 and tungsten,l5 and none for the rare platinum-group metals and rhenium. Measuring the surface tensions of transition metals is difficult because of their high reactivity and melting points. Of the many techniques available,16-18 the pendant-drop 19-21 and drop-weight methods17,22 are considered superior because they can be modified to eliminate persistent sources of contamination such as supports and capillaries necessary in the popular sessile drop, capillary rise, and maximum-bubble-pressure techniques. The necessary modification is to melt a drop on the tip of a vertical rod, which provides support through a solid of the same composition.13,15 The object of the work was to study the surface-tension behavior of copper and transition metals, having reasonably low vapor pressures. Liquid surface tension of each pure metal was systematically determined by using a combination of the static pendant-drop and dynamic drop-weight methods on the same rod. Liquid drops were formed by electron-bombardment heating in high vacuum. EXPERIMENTAL WORK As indicated in Table I, the metals studied were high purity and generally were obtained in rod form. The exceptions were titanium and zirconium, which were machined from crystal bars, and molybdenum (tot 11, osmium, and ruthenium, which were sintered and arc cast into rods. All the metals were ground or swaged to desired sizes between 1- and 7-mm diam, and centerless ground round and smooth to a finish better than 50 µ in., rms. Each rod was thoroughly cleaned with steel wool, degreased, acid etched, and dried. In a typical run, the rod was vertically clamped in a modified floating-zone electron-bombardment furnace designed after Calverley23 and Carlson.24 The specimen was outgassed and maintained positive at several kilovolts in a dynamic vacuum of 10-5 to 10-7 mm. The bottom end was enclosed by a tantalum pillbox and heated by electrons emitted from a hot concentric tungsten filament mounted on a movable bracket. The bombardment power was slowly raised until melting was observed. Power requirements ranged from 30 w for copper to 1300 w for 4-mm tungsten. The stabilized and out-gassed drop of near-maximum size was photographed at 4. 1X on panchromatic film at desired time inter-

Jan 1, 1963

Jan 1, 1925

By AIME AIME

IN accordance with the provisions of Art. XII, See. 3, of the By-laws of the American Institute of Mining and Metallurgical Engineers, the Board of Directors hereby give notice of their intention to amend the By-laws as follows : Art. V, Sec. 2. Amend by substituting the word "senior" for ('first" before the words "Vice-president" in line two of the third paragraph of said section which relates to the calling of special meetings of the Board in the absence or disability of the President.

Jan 1, 1930

By AIME AIME

NEARLY two hundred 'engineers attended the dinner given at the Hotel Pennsylvania on Monday-evening, Oct. 10, to the delegation from the American l3nginiering Societies to Great Britain and France when the John Fritz Medal was presented to Sir Robert Hadfield and to Eugene Schneider. Representatives of the British and French Governments ' and of foreign engineering societies gave to the event an international aspect unique in gatherings of engineers. Messages from men distinguished in science, statesmanship and diplomacy were read. Medals struck by the French Government were presented to the general chairman of the deputation, to the chairman of each' individual delegation and to the president's of the four Founder Societies. The meeting was regarded by engineers as formally ushering in a definite movement for world unity in the engineering profession. J. Vipond Davies, president of the United Engineering Society, acted as toastmaster. The speakers ,were Ambrose Swasey, Charles F. Rand, F. B. Jewett, A. S. Dwight, John R. Freeman, all members of the deputa- tion; and M. Gaston Liebert, French Consul General; Captain G. H. Armstrong, British Counsel General; G. G. Clapperton, representing the British Institution bf Electrical Engineers, and Prof. Jacques Cavalier, spokesman for the French universities. Among the engineers from other cities was Governor. James Hartness of Vermont.

Jan 1, 1921

Prof. H. O. Hofman, Massachusetts Institute of Technology, Boston, Mass. (communication to the Secretary): When Mr. Stetefeldt quotes me as saying that " silver-assays are uniformly made by scorification," he has evidently not understood that I was referring solely to the practice of silver-lead smelting-works. Everybody knows that silver-mills do not employ the scorification-assay for regular work ; and it is equally certain that in very few, if any, silver-lead smelting-works will the crucible-assay be found in use for determining silver. The second part of the quotation, "as it is adapted to all kinds of ores and gives excellent results unless organic matter is present," although, of course, also intended in a restricted sense, might very well be extended to a general one. Mr. Furman, in his Manual of Practical Assaying,* says, on page 123: "We believe that the Colorado practice is preferable, as most ores will yield higher silver-results by scorification." The fact that the scorification-assay is the accepted one in Colorado is strong presumptive evidence for its accuracy, as exactness would nowhere else be more jealously demanded. Mr. Stetefeldt cites Albert Arents- as a supporter of his preference for the crucible-assay, although I had already done so in favor of scorification. Looking up again the reference, I find that I was justified in quoting him, as, while Mr. Arents advocates the crucibleassay for low-grade gold ores, not on account of the greater accuracy of its results, but because it is quicker and less expensive, he condemns it§ for the assay of silver-ores, and prefers the scorifier for rich goldores, and for coppery ores, and in general for ores containing both silver and gold. As I, like Mr. Stetefeldt, have kept no detailed

Jan 1, 1895

By James P. Savely, Victor L. Kastner

Inspiration Consolidated Copper Company is currently mining in four pit areas; Live Oak, Red Hill, Thornton and Joe Bush Extension, near Globe, Arizona. Small satellite orebodies lying outside the main pits have been mined out in a series of small open pits. Major slope instability has affected production in every pit. Some consequences of the instability have been; (1) Serious interruption of mining plans, which resulted in deferred ore production, lost ore, reduced mining rates and increased stripping requirements. (2) Forced replacement of crushing facilities. (3) Serious effects on other production facilities. The introduction of a slope stability monitoring and control function as an integral part of mine planning has been successful in reducing the impact of these failures and will eventually result in economic pit design based on probabilistic slope analysis. This case history presents a brief review of the problems associated with slope instability at Inspiration's mines followed by a more detailed report on one specific failure area in the Thornton pit where the use of horizontal drain holes for slope stabilization appears to be successful. Relationships between slope movement rate, rainfall, and mining activity are shown.

Jan 1, 1983

By Randall L. Neal

This paper discusses the impact of taxes at the state and federal level on typical on-shore oil and gas exploration economics in the USA. Taxes considered are the windfall profits excise tax, state production (or severance) taxes, state income tax, and federal income tax. Also considered will be market prices for oil and gas in the USA. The effect of government take as a percent of revenue, on rate of return, discounted Payout, and discounted cumulative cash flow is shown on the attached tables. The conclusion drawn is that tax laws, while rarely the most important factor to be considered when drilling a well, can have significant impact on the profitability of oil and gas ventures, and should be considered when determining where to drill. Hypothetical exploration wells were analyzed for the impact of tax laws on project profitability. The results of this study show that when factors other than taxes are postulated to be the same (such as producing rate, capital, operating costs, and prices), cash flow can vary by as much as 68% due to the differences in the tax laws. Other significant findings for the cases studied include: (a) that discounted payout varied by as much as 1.8 years, (b) that rate of return differed by up to 67% and (c) the total tax rate as a percentage of revenue had a maximum variance of 33%.

Jan 1, 1982

I. MCLAUGHLIN, R. P.-Protecting California Oil Fields from Damage by Infiltrating Water. Discussed by M. E. Lombardi, A. F. L. Bell, A. C. McLaughlin, R. P. McLaughlin, William A. Williams, Mark L. Requa, C. D. Keen 2413 BEST, W. N.-Petroleum as Fuel Under Boilers and in Furnaces. Discussed by William A. Williams, Hennen Jennings, David T. Day, Mark L. Requa, A. F. L. Bell, W. N. Best 2420 JOHNSON, ROSWELL H.-Sliding Royalties for Oil and Gas Wells. Discussed by William A. Williams, A. C. McLaughlin, A. F. L. Bell, Roswell H. Johnson 2423 BELL, ARTHUR F. L.-Important Topping Plants of California. Discussed by William A. Williams, David T. Day, A. F. L. Bell 2426 LOMBARDI, M. E.-The Cost of Maintaining Production in California Oil Fields. Discussed by C. D. Keen, Mark L. Requa, H. M. Bacon, M. E. Lombardi 2427 HUNTLEY, L. G.-Oil, Gas, and Water Contents of Dakota Sand in Canada and United States, Discussed by E. W. Shaw 2428

Jan 12, 1915

By W. E. C. Eustis

During the last year I had occasion, on behalf of our New York copper works, to send to various chemists samples, intended to he accurate, of material which we were buying and selling, and I was astonished to find what differences were reported. After talking over the probable reasons for this with a number of chemists and metallurgists, it was suggested that it would be of real use and some scientific interest to send samples to the different chemists, and take such care in making up the samples that we could feel sure that each chemist had as nearly identical a sample as it was possible to make. After some consideration it was determined to send a mixture which should carry about 50 per cent. copper, and

Jan 1, 1883

By Henry D. Hibbard

A NOTED ordnance engineer once said to a friend, in speaking of the production of great steel guns, "How is it? We design our guns with a factor of safety of eight, and the guns burst." The vague way in which internal stresses and strains in iron and steel are often considered and spoken of makes it worth-while to examine them, as to their nature, their causes and results, how they may, for useful purposes, be advantageously dealt with, and how, when detrimental or dangerous, they may be reduced or kept within harmless proportions. Rankine defines ?strain " as a change of form or dimensions of a solid or liquid mass produced by a stress. This definition seems not intended to cover strains due to internal stresses, and it will help us in the present inquiry to consider strain as a tendency to change as well as an actual change of form. Internal strains in iron and steel are the result of stresses within the mass of the piece, some parts pulling and others pushing in resistance to them; or, in other words, some parts are in tension and some in compression, each part striving to relieve itself from strain and make the piece assume a form in which all parts are at rest. Subdivision, so that each part could relieve its strain by motion relative to the other parts, would, if carried out far enough, practically obliterate strain. The internal strains we are now to consider are not those due to the stresses of the service which the piece is rendering, either alone or as, a part of a structure, which may be termed service-strains, but those which originate or at least are contained in the piece itself. Internal stresses in a piece of metal are, like action and reaction, always equal and in opposite directions. The stresses

Sep 1, 1906

By George D. Dub

Owens Lake is at present a source of important nonmetallic minerals, sodium carbonate (soda ash, Na2CO3); sodium sesquicarbonate (trona, Na2CO3.NaHCO3.-2H2O) and borax, (Na2B4O7.10H2O). Owens Lake is a closed basin in the southern part of Inyo County, California, at the southern end of Owens Valley, east of the Sierra Nevada Mountains and west of the Coso and Inyo Mountains. Broadly considered, it is in the Great Basin area, but at no time was it a part of Lake Lahontan. Closed Basins Closed basins are phenomena of arid or semiarid regions where outflow is considerably less than inflow and where accordingly soluble salts concentrate in residual liquid. When inflowing waters originate in areas where the rocks are predominantly marine sediments, the residual basin liquid is primarily a chloride, brine; if the rocks are largely igneous, the residual brine tends to be alkaline containing carbonates, and sometimes borates as well. Since normally, both types of rocks occur in regions contiguous to closed basins, residual liquids do not often fit into the two broad divisions mentioned. No two residual brines are exactly alike, just as no two ore deposits are exactly alike. Even out of the same closed basin, it is possible to get widely different analyses of liquids since underground and surface flows, as well as local evaporation rates and other conditions might have a marked influence on residual-liquid compositions. At Searles Lake, The American Potash and Chemical Corporation is building a plant to process a lower-level brine which is considerably higher in sodium carbonate and borax, and lower in potassium chloride, than that company has processed for many years. F. W. Clarke1 has classified waters of closed basins as follows: I. Chloride type; largely sodium chloride (NaC1) and of oceanic type, such as Great Salt Lake. Related is -the Dead Sea, a bittern residue of magnesium, potassium and sodium chlorides. a. Sulphate type; largely sodium sulphate (Na2SO4) with considerable sodium chloride such as Sevier Lake, Utah; Laramie Lakes, Wyoming; Dale Lake, California. 3. Carbonate type; high in carbonates and fairly high in sulphates, such as Moses Lake, Eastern Washington; and the Nebraska Potash Lakes. 4. Carbonate—chloride type; lower in carbonates than type 3 and about equally rich in sulphates, such as Pyramid Lake, Nevada. 5. Sulphate—Carbonate type; quite high in sulphates and carbonates, such as Pelican Lake, Oregon. 6. Triple type; considerable quantities of carbonates, sulphates and chlorides

Jan 1, 1948

By George D. Dub

Owens Lake is at present a source of important nonmetallic minerals, sodium carbonate (soda ash, Na2CO3); sodium sesquicarbonate (trona, Na2CO3.NaHCO3.-2H2O) and borax, (Na2B4O7.10H2O). Owens Lake is a closed basin in the southern part of Inyo County, California, at the southern end of Owens Valley, east of the Sierra Nevada Mountains and west of the Coso and Inyo Mountains. Broadly considered, it is in the Great Basin area, but at no time was it a part of Lake Lahontan. Closed Basins Closed basins are phenomena of arid or semiarid regions where outflow is considerably less than inflow and where accordingly soluble salts concentrate in residual liquid. When inflowing waters originate in areas where the rocks are predominantly marine sediments, the residual basin liquid is primarily a chloride, brine; if the rocks are largely igneous, the residual brine tends to be alkaline containing carbonates, and sometimes borates as well. Since normally, both types of rocks occur in regions contiguous to closed basins, residual liquids do not often fit into the two broad divisions mentioned. No two residual brines are exactly alike, just as no two ore deposits are exactly alike. Even out of the same closed basin, it is possible to get widely different analyses of liquids since underground and surface flows, as well as local evaporation rates and other conditions might have a marked influence on residual-liquid compositions. At Searles Lake, The American Potash and Chemical Corporation is building a plant to process a lower-level brine which is considerably higher in sodium carbonate and borax, and lower in potassium chloride, than that company has processed for many years. F. W. Clarke1 has classified waters of closed basins as follows: I. Chloride type; largely sodium chloride (NaC1) and of oceanic type, such as Great Salt Lake. Related is -the Dead Sea, a bittern residue of magnesium, potassium and sodium chlorides. a. Sulphate type; largely sodium sulphate (Na2SO4) with considerable sodium chloride such as Sevier Lake, Utah; Laramie Lakes, Wyoming; Dale Lake, California. 3. Carbonate type; high in carbonates and fairly high in sulphates, such as Moses Lake, Eastern Washington; and the Nebraska Potash Lakes. 4. Carbonate—chloride type; lower in carbonates than type 3 and about equally rich in sulphates, such as Pyramid Lake, Nevada. 5. Sulphate—Carbonate type; quite high in sulphates and carbonates, such as Pelican Lake, Oregon. 6. Triple type; considerable quantities of carbonates, sulphates and chlorides

Jan 1, 1948

By S. M. Marshall, B. M. Bird

For a number of years European investigators have used laboratory methods of predicting the probable strength of coke made from coal, and recently several investigators in the United States have reported the use of various tests for this purpose. There is at present no method accepted as standard, however, nor is there even agreement as to the general type of test that should be used. Furthermore, because the details of most of the tests have not been worked out carefully, one investigator can not hope to duplicate the work of another. The extension of coke manufacture to new localities in the United States, and the increasing need for cokes of exceptional qualities made from the most economical mixtures, made it desirable to have some simple laboratory test which will determine whether given coals, alone or blended with other coals, are more satisfactory from the standpoint of coke strenpth- than others of different cost. The work described herein has resulted in the development of a simple laboratory test which, it is believed, can be generally adopted in coal laborat,ories, and which will give concordant results even though performed by different investigators in different laboratories. The general method of predicting whether a coal or a mixture of coals will produce a strong coke, resistant to crushing and shattering, has been to correlate the known strengths of the cokes produced in commercial ovens with some measurable constituent or with some property of the coals, and then to use the relationship so found for forming an estimate of the coking strengths of coals unknown. Several such correlations have utilized the percentages of the various ultimate constituents of coal, such as the oxygen content and the hydrogen-oxygen ratio;(39)§ other correlations have involved the proportion of a, B and r com-pounds, (17,21,30c) or of "oil and solid bitumens."(16,30) Also a relationship has been traced between the coking properties of coal and the rate of change of the resistance offered to the flow of an inert gas by fine particles of the coal while being slowly heated. (11,176) But the most general corre-

Jan 1, 1930

By B. S. Old, E. R. Poor

PRODUCING more steel without major capital investment in new plants is one of the most perplexing difficulties which confront the nation's postwar steel industry. The lack of scrap at a reasonable price results in an especially heavy pressure being brought to bear on the pig-iron production facilities which consist of 245 blast furnaces scattered throughout the country but concentrated most heavily in the Pittsburgh-Chicago area. Present demands exceed the total optimum output of these existing blast-furnace plants. Management hesitates to authorize erection of new plants on a scale sufficient to satisfy 'the demand for pig iron for two main reasons: first, extensive building under the present high costs of construction would greatly increase . the over-all capital investment per ton of iron capacity; and, second, the amount of steel necessary for a major construction program would upset the already tight supply-demand situation. The answer to the problem would then seem to be the development and application of a method which would increase the capacity of existing blast furnaces with a minimum of alterations and expense. Experiments consisting of operating a blast furnace at higher-than-normal top pressures, as proposed by Arthur D. Little, Inc., were carried out by the Republic Steel Corp. initially during World War II, and much more extensively during the past twenty months. The results of the Republics trials indicate that pressure blowing is a solution to the problem of increasing pig-iron capacity without necessitating major changes to existing equipment.

Jan 1, 1948

By James E. York

AT a meeting of the American Society for Testing Materials at Atlantic City, June, 1908, Dr.. C. B. Dudley, in his presidential address,' showed the vital necessity of not only making a steel rail as good as in the past, but of making it considerably better in order to meet the present and prospective require¬ments of railroads. Doctor Dudley requested the co-operation of all who from personal experience could give information that would result in bringing about the production of a steel rail that could be relied upon to meet the present requirements. I have had considerable experience in the practical manufacture of steel of almost every grade, during the past 40 years, and I shall suggest changes that will bring about the results desired. Doctor Dudley has had a long experience as chemical and metallurgical expert for the Pennsylvania railroad, but he frankly admits that up to the present time both he and other metallurgical experts lack the practical knowledge of steel-making that is necessary to state correctly the reasons for the unreliability of the steel rails now produced. The necessity is self-evident for more positive practical knowledge on the part of these experts of what is possible and what is impossible regarding the practical manufacturing of steel rails from the ingot to the, finished product. Chemical knowledge in steel-making is far in advance of what it was years ago, and might be said to cover every requirement (in that department) for producing reliable steel. The study of the metallography of steel has been of great value, also the physical testing of steel, but this knowledge will only de-

May 1, 1909

By Gary B. Williamson, Barton K. Cross

Digital simulation is a modern analysis tool which allows the mine operator to evaluate the result of making a decision without actually changing the organization or buying the equipment. The purpose of this paper is to demonstrate the use of digital simulation in evaluating a decision of whether or not to introduce dispatching in an open pit mine. The analysis shows that appreciable savings can be realized by dispatching. In certain cases, an operator can reduce the number of trucks required to move a specified tonnage. A second analysis evaluates the alternatives of using one large shovel or two smaller units. In this case, the operating cost of the haulage equipment necessary to support the shovels turns out to be the critical factor in this decision.

Jan 1, 1969

By E. P. Pfleider, W. G. Pariseau

This paper reports the theoretical and experimental results of an analysis of ore pass drawdown as a problem in soil plasticity. The method of analysis developed appears to be a promising technique of investigating the mechanics of fragmented materials. A reconstructed plasticity theory brings experiment and theory into reasonable agreement, and hence may provide the foundation needed for rational ore pass design. The gravity-induced movement of broken rock through ore passes is an economical method of transporting fragmented materials through large vertical distances in underground mines, provided the ore pass is well designed. Unfortunately, the design procedures now followed do not very often result in ore passes that function properly. On the one hand, the huge accumulation of empirical data pertaining to the movement of materials in gravel bunkers, storage bins, deep grain silos and other structures that have features in common with ore passes remains uncorrelated. On the other hand, there is a dearth of experimental data substantiating theoretical models of material behavior. Consequently, reliable generalizations encompassing the broad spectrum of problems involved have not been forthcoming. AS an initial step towards improving the situation, a detailed case study of two-dimensional ore pass drawdown was made. The mechanics of the process were analyzed theoretically as a problem in soil plasticity and tested experimentally through observations of a laboratory ore pass model. THEORY Taylor1 defines a soil as a "mass commonly considered to consist of a network or skeleton of solid particles, enclosing voids of varying size." Broken rock in an ore pass is such a material. In plasticity theory this material is replaced by an idealized substance that deforms elastically up to some state of stress at which slip or yield occurs,2 For com-pressive states of stress, the Mohr-Coulomb criterion is a satisfactory yield condition. After the yield point is reached, the ideal soil deforms in accordance with the concept of plastic potential.4 Under plane strain conditions the governing equations separate into a system of stress equations and a system of velocity equations.' Only stress variables appear in the stress system. The velocity system, however, contains a stress variable. The two systems are, therefore, coupled. Both systems are hyperbolic, and each has two real, distinct families of characteristic curves that coincide according to the classical theory of ideal soil plasticity. The

Jan 1, 1969

By AIME AIME

THIS year the Petroleum Division holds its fall meeting at Houston, Texas, Oct. 2 and 3, with head- quarters at the Lamar Hotel. Technical sessions will be held in the morning and afternoon of both days. A smoker on Friday afternoon will afford an opportunity to get together socially. Saturday evening is left free for private parties to the beach at Galveston, where a wide variety of entertainment is available. On Oct. 4 there will be an excursion to Sugarland oil field, with luncheon at Boling and a visit to Boling sulfur mine and plant in the afternoon. There are nine technical papers on the program for Friday. Saturday morning will be devoted to oil production control and it is planned to make the discussion more

Jan 1, 1931

By Fred Hale

OWING to the large area included in the Yellow Pine mining district, and the-varied nature of its mineral deposits, a detailed geological description of the district could be covered only in an extensive monograph. This paper is intended as a description of the most prominent geologic features only with special reference to those of economic importance. The first mention of the district was in 1903 by J. E. Spurr,1 who briefly describes the structural geology of the Spring Mountain range. In 1906, H. F. Bain2 briefly described the Potosi mine. James J. Hill,3 of the United States Geological Survey, visited the district for a brief period in 1912, the result of which is an excellent reconnaissance report, covering the district in some detail but necessarily with brevity. Since that time, articles covering special features of the district have appeared in the technical press, including some by the writer, and a notable description of the Boss mine, by Adolph Knopf,4 appeared in 1915. Development of the district during the past few years has progressed so rapidly and with so many notable discoveries, particularly with reference to the rare metals, that a further description at this time may prove of interest. The writer's acquaintance with the district is based on 7 years' continuous residence in the vicinity, beginning with the spring of 1910.

Jan 2, 1918

By U. N. Bhrany, N. Arbiter

F. C. Bond (Consulting Engineer, Processing Machin-Dept., AllisChalmers Manufacturing Co., Milwaukee) This is a very comprehensive paper. It deals with 1) size distribution functions, 2) energy-particle size relationships, and 3) criteria for grinding efficiency. The method of analysis used consists of tracing the increase and decrease of successive Tyler scale screen fractions as grinding progresses. The treatment is based upon the assumption that the work done in grinding is concentrated entirely upon the coarse size fractions in the mill. It is postulated that when a feed consisting entirely of particles of one size fraction is batch ground that finer fractions increase at a constant rate as grinding progresses, until finally each in turn begins to be ground and to decrease in amount. It is shown that under these conditions the empirical Gates-Gaudin-Schuhmann log-log size distribution plot can be logically explained. It is difficult to imagine any condition of ball mill operation, or any probability analysis, which would result in no grinding contacts on the finer particles present. However, the authors' postulate must be accepted if their conclusions are to be sustained. They conclude that the equation expressing the for mation rate of each size fraction can be resolved into the G.-G.-S. size distribution equation, and that the curvilinear portion of the log-logsize distribution line represents the only particle sizes which are being ground as well as produced. The author's statement that the G.-G.-S. Eq. 4 applies only to the finer portion of the size distribution while the Rosin-Rammler Eq. 6 applies over the whole size distribution range certainly supports the view that an exponential equation of the Rosin-Rammler type corresponds more closely to actual size distribution than does the power law G.-G.-S. equation. However, the G.-G.-S. equation is used to derive Eq. 8 and Eq. 9, which state that the energy required to grind a ton through a particular mesh varies inversely as the particle size to the exponent -a , whic h is the slope of the extended G.-G.-S straight line. This is stated to apply to both batch and continuous grinding. The G.-G.-S. slope exponent thus becomes very important in all crushing and grinding analyses by this method. The authors include some data which can be used to test their conclusions, as described below: We will consider grinding a feed composed of 14 mesh (1190u) to -200 mesh (74u). The average of 17 Allis-Chalmers grindability tests on quartz gives a work index (Wi) of 12.77. The -200 mesh product should have 80 pct passing 41.6u or P = 41.6. The equivalent 80 pct passing size of the 14 mesh feed particles is considered to be the particle diameter, as is true for spherical particles. Thus F is 1190u. In the work index equation 10 wi 10 wi 127.7 127.7 P f 41.6 1190 = 16.1 kw-hrperton. In Table I the ball mill exponent for quartz is 1.0 and from Eqs. 9 and 10: w=kw-hr/ton =Constan/(do/di) = 16.1 ton so that (1190) Constant/ Constant and the Constant equals 259. The tons per horsepower-hour value is 0.0464, in agreement with Table IV. The exponents for other minerals are listed in Tabl e 11. In Table IIA, the kilowatt hours per ton required to grind these minerals between the same sizes as the quartz, both by the authors' method and the work index equation, are listed. According to the authors kw-hrperton = 259/(16.1)".

Jan 1, 1961