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By CHARLES M. A. STINE

IN fighting a war the all-absorbing intent is to win. There is little time to analyze the rush of events or to appraise their consequences beyond the war's end. The united objective is, rightly, success for our arms. Yet under the pressures of a great war there may be compressed scientific, economic and social developments that might have taken many decades to achieve under less urgent conditions. Their effects on our lives and all civilization may be more wide-reaching and lasting than any military conquest. They constitute one of the must imperative incentives to victory. No American, least of all any scientist worthy the name, conceivably could endorse war as a justifiable means to progress. The destruction of life and property wrought by the present war far exceeds the havocs of a century's earthquakes. Most of mankind is burning itself on an altar of paganism. Nonetheless, one fact is inescapable Despite the recurrent malady of war history's overall course is forward. Mankind has the habit of rising phoenix-like from its own ashes to attain greater heights. Progress is immortal.

Jan 1, 1942

By Charles Catlett

(Chattanooga Meeting, October, 1M.) THE terms " developed " and " undeveloped " are necessarily relative and cover a wide range; but the latter is here applied to cases in which the information at hand falls short of a clear demonstration of values, and conclusions must be reached from a study of the geological conditions of the particular deposit, interpreted in the light of similar and closely related deposits. Such an inquiry might be characterized as an effort to reach reliable conclusions from insufficient data. But the engineer engaged in commercial work finds himself often face to face with apparently such problems; and while he may realize with regret that a small amount of intelligent development would add enormously to the value of his conclusions, he is compelled to recognize the demand of a business situation for a prompt decision as the basis of immediate action. In a case within my knowledge, the question involved was the purchase of 50,000 acres of coal-land, and 10 days was the limit within which this question must be decided. Of course, it was impossible to make a satisfactory examination within that time; but the 'instructions were "to make the most complete examination and the most positive recommendation possible." Such instructions are often given; for, no matter how much time an investor may have, he is likely to put of his decision until the last moment, and then discover that he needs more light and advice. It does not follow that engineers, after full explanation and mutual understanding of the situation, should decline to undertake examinations thus limited. In the case just mentioned, while only the broadest view was possible, half the time available was sufficient to show that the property was a good purchase. The timber alone was subsequently resold for more than the entire purchase-price of the

Mar 1, 1909

By F. William Bloecher, William B. Plank

CURRENTLY 12,892 students are enrolled in the mineral engineering schools of the United States and Canada, marking an all-time record high for these schools. It shows a remarkably rapid recovery from the effects of World War II. Enrollment in all the other engineering branches has also increased but not so rapidly as in the mineral engineering branch. Almost all the data in this report are from the eighth questionnaire study of the mineral engineering schools made, as formerly, under the auspices of the Mineral Industry Education Division of the AIME. Every school is represented in the data, for which the authors thank the deans and professors who supplied the information. For this reason, the data of all the studies are comparable, an achievement not always possible in endeavors of this kind. For comparison with the general engineering enrollment situation, data are included from the January 1947 issue of the Journal of Engineering Education.

Jan 1, 1947

By William C. Harrigan, William D. Nix

Dynamic measurements of Young's modulus have been made for poly crystalline Ni-W alloys from room temperature to 800°C. The alloys studied range in composition from pure nickel to Ni-10 at. pct W. The results indicate that Young's modulus decreases linearly with temperature above the Curie temperature. The rate of change of Young's Modulus with temperature mas found to range from 104 psi per "C for pure nickel to 0.82 x 104 psi per °C for Mi-10 pct W. At all temperatures the elastic modulus decreases with increcrsing tungsten content up to 1 at. pct W, and increases as the tungsten content is increased above that level. Young's modulus decreases slightly as the carbon content is increased from 0.002 to 0.09 wt pct C THE knowledge of the elastic modulus of metals and alloys is important for a number of reasons. The first and most obvious reason comes from the need to predict elastic deflections under given loading conditions. A second and somewhat more subtle reason comes from the fact that the elastic properties of an alloy must be known before a proper account of the mechanisms of plastic deformation can be made. This is especially true for high-temperature creep of crystalline solids. Sherby and his coworkers have shown that the high-temperature steady-state creep rates of crystalline solids are inversely related to the elastic modulus1,2 and that the temperature dependence of the elastic modulus must be taken into account if reliable determinations of the activation energy for creep are to be made. In addition, measurements of the elastic constants of solid solutions are needed to allow one to assess the modulus interaction contribution to solid-solution Strengthening.3-5 Pelloux and Grant6 have demonstrated that substantial solid-solution strengthening at room temperature and elevated temperatures occurs when refractory metal solute atoms are added to nickel. While the high-temperature elastic properties of pure nickel have been measured by a number of authors,7-10 the elastic properties of nickel-based refractory metal alloys have not been determined. The purpose of this paper is to report on measurements of Young's modulus of polycrystalline Ni-W alloys at elevated temperatures. It is expected that these measurements will be valuable to studies of the mechanical properties of nickel-based refractory metal solid solutions. I) EXPERIMENTAL Young's moduli of polycrystalline samples were determined by a dynamic method in order to reduce high- temperature anelastic and plastic relaxations. The samples were forced in transverse free-free vibration; that is, both ends of the sample were unrestrained and the vibration was transverse to the long axis. The fundamental resonant frequency was determined by the Forster method.11 The analysis of this type of vibration which was formulated by Rayleigh,12 Timo-chenko,13 and pickett,14 and reviewed by Fine," leads where fn is the resonant frequency of the nth mode, r is the radius of the circular cross section. L is the specimen length, ßn is 1.5056 for free-free vibration in the fundamental mode of vibration, 6 is the mass density, and E is Young's modulus in the axial direction. This equation can be transformed into: E = 9.17605 x 10-6(L/D)E/Lf2 [2] where E is Young's modulus in psi, L is the length in inches, d is the diameter in inches, W is the weight in grams, and f is the resonance frequency in cps. Eq. [2] was further modified in order to take account of the thermal expansion of the samples. The resulting correct term is: where the thermal expansion coefficients for nickel and tungsten, respectively. Xw is the atom fraction of tungsten in the sample and T is the temperature in "C. The treatment of the thermal expansion coefficient as a linear function of composition seems sufficiently accurate since an error of 25 pct in the expansion coefficient will result in only a 0.3 pct error in the modulus at 1000°C. A) Apparatus. The equipment for this investigation has been described by Lytton et al.16 Several modifications of the equipment have been made. The most significant change involved replacing the detector crystal transducer with a magnetic transducer. A phonographic magnetic transducer was employed as a sensing device since the contact pressure necessary to produce a stable signal is much less than that for a crystal transducer. This magnetic transducer is also not affected by conditions of high temperature and vacuum which are present in these experiments. The vacuum was 10-5 torr at room temperature and about 5 x 10-4 torr at 900°C. This was sufficient to prevent surface contamination of the samples during the tests. The samples were heated in an elliptical furnace with a quartz lamp at one focal line and the sample at the other, as described by Lytton et a1.16 The temperature of the sample was measured by monitoring the

Jan 1, 1969

By H. Rush Spedden, Arvid Thunaes

R. R. Knobler and F. E. Albertson—Following the testwork done by Thunaes and Spedden, a Sullivan deck plant was built for the Colquiri mill. This plant started to operate in April 1945 and continues in successful operation. Since May 1950 the Colquiri mill has operated with a completely revamped flowsheet at a rate of 1000 tons per day. The old Sullivan deck section was retained with this new flowsheet. The "slime plant" in Colquiri consists of one 12-cell Denver No. 18-Sp. Sub-A flotation machine, one 16-ft and one 12-ft hydroseparator, six five-deck Sullivan-frames and six shaking tables for cleaning up the Sullivan deck concentrates, as well as 12 Deister plus three Plat-O tables on which the fine sands, which are not treated on the S-decks, are concentrated. Only —325-mesh fines are treated on the Sullivan decks. The combined hydroseparator overflows are fed to the S-decks. From 1946 to 1949, i.e. with the "old" flowsheet and an average mill feed of 800 tons per day an average of 45 tons per day was treated on four Sullivan rougher frames. The two additional frames were used as cleaners. At times, up to 90 and 120 tons of slimes were treated successfully on this Sullivan deck installation. The average operating data for the S-deck section in Colquiri for the year 1949 were as follows: The tests reported in this paper indicated a tin recovery of 42 pct. The actual plant results for 1949 show a 54 pct tin recovery from the Sullivan decks. The total average quantity of tin produced from the S-deck section in 1949 was 15 tons of tin per month. This corresponds to 3 pct of the total mill recovery. The difference between the 6 pct overall recovery-increase expected after the tests in 1943 and the actual plant results given for 1949 is explained as follows. According to the tests, a total of 170 tons was expected to be routed to the Sullivan decks, but because of certain changes in the flowsheet and mill amplifications,

Jan 1, 1951

By H. Rush Spedden, Arvid Thunaes

R. R. Knobler and F. E. Albertson—Following the testwork done by Thunaes and Spedden, a Sullivan deck plant was built for the Colquiri mill. This plant started to operate in April 1945 and continues in successful operation. Since May 1950 the Colquiri mill has operated with a completely revamped flowsheet at a rate of 1000 tons per day. The old Sullivan deck section was retained with this new flowsheet. The "slime plant" in Colquiri consists of one 12-cell Denver No. 18-Sp. Sub-A flotation machine, one 16-ft and one 12-ft hydroseparator, six five-deck Sullivan-frames and six shaking tables for cleaning up the Sullivan deck concentrates, as well as 12 Deister plus three Plat-O tables on which the fine sands, which are not treated on the S-decks, are concentrated. Only —325-mesh fines are treated on the Sullivan decks. The combined hydroseparator overflows are fed to the S-decks. From 1946 to 1949, i.e. with the "old" flowsheet and an average mill feed of 800 tons per day an average of 45 tons per day was treated on four Sullivan rougher frames. The two additional frames were used as cleaners. At times, up to 90 and 120 tons of slimes were treated successfully on this Sullivan deck installation. The average operating data for the S-deck section in Colquiri for the year 1949 were as follows: The tests reported in this paper indicated a tin recovery of 42 pct. The actual plant results for 1949 show a 54 pct tin recovery from the Sullivan decks. The total average quantity of tin produced from the S-deck section in 1949 was 15 tons of tin per month. This corresponds to 3 pct of the total mill recovery. The difference between the 6 pct overall recovery-increase expected after the tests in 1943 and the actual plant results given for 1949 is explained as follows. According to the tests, a total of 170 tons was expected to be routed to the Sullivan decks, but because of certain changes in the flowsheet and mill amplifications,

Jan 1, 1951

By H. M. Wilten

THIS article presets a view of a problem encountered in petroleum refining in the deterioration of equipment used in condensation of vapors and cooling of liquids. Discussion is limited to the problems of shell- and tube-type exchangers and condensers. In this service shell- and .tube-type equipment is gradually displacing other types and, for this reason, its economic importance ill oil-refining practice is also increasing. Considering oil - refinery practice during the last two decades one can readily see many important improvements in the apparatus used. Briefly, the present equipment is safer, more efficient, and Ignore economical. Improvement in apparatus used for the condensation of distillates has, in my opinion, been less than that in other essential distilling apparatus. So it is hoped that this discussion will stimulate research among the producers as well as among the consumers of this equipment with a view to ameliorating this condition.

Jan 1, 1937

By J. M. Callow

H. A. MEGRAW, New York, N.,Y.-One interesting thing that might be brought out in this connection is the cost of making sulphide gas. I had a communication the other day which suggested that, in view of the high cost of oil, sulphur and sodium sulphide, we might make use of a well-known chemical reaction to form this sulphide gas by the use of aluminum sulphide. It is difficult to see any advantage in this, however, since aluminum has been affected just as much as any other commodity by the rise in prices, due, to war conditions. RUDOLF GAHL, Miami, Ariz. (communication td the Secretary*) Mr. Callow refers to my paper, History of Flotation at Inspiration, which was presented at the Arizona meeting of the Institute. These notes of Mr. Callow's contain much valuable information on flotation practice, as is to be expected from an article written by an author of Mr. Callow's experience in this branch of metallurgy. Nevertheless, I cannot help contradicting a number of the statements made in the references to my paper. In passing, I will also say a word about the reference in Mr. Callow's paper to the article by Messrs. Laist and Wiggin entitled "Flotation Concentration at Anaconda, Mont." Mr. Callow calls attention to the fact that evidently Callow flotation machines are not very sensitive, inasmuch as one man per shift handles four 800-ton sections of Callow machines or 3,200 tons per day at the Inspiration plant. While-it has been the experience of the Inspiration company that the four sections of Callow machines in the Inspiration concentrator are easily handled by one American operator per shift, it is only fair to state that each man operating four sections is assisted by two Mexican helpers who constantly clean the bottoms of the machines. The tonnage per section, by the way, whether equipped with Callow,, Inspiration or Minerals Separation machines, is considerably in excess 4 800 tons.. Mr. Callow further says that local opinion at Inspiration is that, two 800-ton sections consisting of two 10-compartment and four 6-compartment Minerals Separation machines (these machines are of the Hebbard type) is the limit that one man can properly attend. I do not hesitate to say that I consider it perfectly feasible to have four such sections operated by one man, perhaps assisted by "one helper. The Minerals Separation machines of this type have undoubtedly an advantage as far as easiness of operation is concerned,

Jan 4, 1917

By D. H. Wertz, R. R. Furlong

Dry room equipment at Donora Zinc Works is of the design which prevailed at the time the plant was built in 1915. It consists of 11 adjoining rooms, each being 99 ft long, 11 ft wide, and 7 ft high and having a capacity for 1040 retorts. Heat is supplied by steam coils beneath the slatted wood floor and by warm air ducts at the ceiling. Drying practice is about the same as that generally followed in the industry except that, under normal zinc furnace operations, the maximum drying time is 45 days. During certain seasons of the year the drying process was seriously affected by varying weather conditions which frequently resulted in a scrap loss of 5 to 7 pct. Because of these unfavorable conditions, which caused uneven drying and strains in the retorts, increased retort failures in the zinc furnaces were recorded. Regulation of temperature and humidity under all conditions appeared to be the logical solution of this problem. Controlled drying had been developed for a number of ceramic products and investigation of several such drying processes in this area revealed favorable results. Along with control of drying conditions and the attendant decrease in scrap losses, plant operators also reported a material reduction in drying time. Another factor affecting the decision to proceed with this development was the drastic change in market conditions for retort clay. Curtailment of shipments from the chief source of supply made it necessary to proceed with blending of other available clays, but quality of these clays was questionable for adequate retort life in the 24 hr furnace cycle. Rapid furnace testing of new mixtures was desirable but impossible with the prolonged drying schedule. Therefore development of a controlled drying process for zinc re- torts offered the solution to the problem of rapid testing of retort mixtures. Description of Process and Equipment The freshly extruded retort is cylindrical in shape, 58 in. long, 9 in. id and has 1 1/8 in. side walls. One end is closed and approximately 2 in. thick. The moisture content of this "green" retort is about 17 pct which means a necessary removal of 30 lb of water per retort. Retorts are set on the slatted floor of the dry room with the closed end down. The controlled drying process depends upon the circulation of a large volume of conditioned air at low velocity. To provide for uniform distribu-

Jan 1, 1950

By AIME AIME

THE STANDARD herewith submitted is the result of several years of research and consideration by the A.I.M.E. Technical Committee on Milling Methods. In the early work of this committee it was found necessary to undertake the development of a standard laboratory method for screen testing of ores. During the research stages the desirability of having this standard, when completed, approved as American Standard was brought out. In accordance with this idea, its initiation as a project of the American Standards Association (then the American Engineering Standards Committee) was approved by the latter body and the A.I.M.E. designated as sponsor. In 1929, the A.S.A., on recommendations of its advisory committee, the Mining Standardization Correlating Committee), authorized the A.I.M.E. to be sole sponsor for this project. The personnel of the Institute's Committee on Milling Methods was then increased to make it thoroughly representative of all diversified interests in the mining field. Two years ago the standard was circulated and has been given wide distribution. Early in 1932 the committee voted unanimously, with 38 affirmative votes, that the standard be recommended to the Board of Directors of the Institute for submission to the American Standards Association for approval as American Recommended Practice. This was accordingly done, at the Feb. 1.6, 1932, meeting of the directors, and the American Standards Association approved the standard on July 6; 1.932, designating it as ASA M5-1932.

Jan 1, 1932

By O. W. Ellis

The writer has dealt with the effect of various methods of melting copper upon the gas content of the metal.' The copper referred to in his earlier paper was melted in the foundry both in the oil furnace and the electric furnace. As the metal did not measure up to conductivity standard, the term "casting copper" was applied to the material in the title of the paper. It was thought that some information in regard to the gases in a sample of overpoled copper might also be of interest, and through the courtesy of C. R. Stevens, superintendent of the copper mill of the West-inghouse Elec. & Mfg. Co., such a sample was obtained. The metal was chill-cast in the form of an ingot about 7 in. long, 2 1/2 in. deep (from the base to the raised surface of the ingot) and from 1 3/8 to 1 7/8 in. wide. A photograph of part of the ingot is shown in Fig. 1. The effect of over-poling on the surface of the metal is here quite clearly shown.

Jan 1, 1929

By O. W. Ellis

The writer has dealt with the effect of various methods of melting copper upon the gas content of the metal.' The copper referred to in his earlier paper was melted in the foundry both in the oil furnace and the electric furnace. As the metal did not measure up to conductivity standard, the term "casting copper" was applied to the material in the title of the paper. It was thought that some information in regard to the gases in a sample of overpoled copper might also be of interest, and through the courtesy of C. R. Stevens, superintendent of the copper mill of the West-inghouse Elec. & Mfg. Co., such a sample was obtained. The metal was chill-cast in the form of an ingot about 7 in. long, 2 1/2 in. deep (from the base to the raised surface of the ingot) and from 1 3/8 to 1 7/8 in. wide. A photograph of part of the ingot is shown in Fig. 1. The effect of over-poling on the surface of the metal is here quite clearly shown.

Jan 1, 1929

By B. T., Colley

AS always when metallurgical operations are conducted within or close to agricultural and stock-raising regions, the question of damage due to fume and smoke presented itself when the Cerro de Pasco Copper Corporation's new smelter commenced to operate in La Oroya in 1922, For more than twenty years the Corporation had operated its old plant close to Cerro de Pasco without encountering difficulties from smoke claims, owing to the fact that it was in an open plain where more or less constant air currents carried and dissipated the smoke over large areas, affording ample dilution. But Oroya is in a deep canyon formed by four contributing valleys up and down which the smoke travels for long distances in a more or less concentrated form. Though the altitude of Oroya is more than 12,000 ft., and the surrounding country rises to much greater elevations, nevertheless there exists there a large and important stock-raising industry and also a considerable development in agriculture, consisting of the cultivation of potatoes, barley, etc.

Jan 1, 1945

By George A. Hill

WE of the oil industry, devoted to freedom of initiative, free competitive enter- prise, and free American institutions, applaud, with one voice, affirmation by the President of the national will and purpose to preserve and to protect, against all aggressors, "our American way of life with our individual and national freedom." We subscribe utterly and completely to this guiding declaration and seek its further definition as applied to the oil industry. Fortunately for all, the policy of the Government, after adequate study and deliberation, has been given precise definition. The National Defense Advisory Commission, with its patriotic, highly qualified, and distinguished personnel, has unanimously agreed to and adopted twelve general principles governing national defense contracts and also fair labor standard requirements. The President of the

Jan 1, 1940

By Donald C. Myntti

INTRODUCTION A major segment in a successful heavy equipment maintenance and repair program is the provision of well-laid out and well-equipped shop and service facilities The facilities described here will be those required for a large, high tonnage hard rock open pit mine utilizing rotary drills, shovels, haulage trucks, support equipment, and service trucks. The term support equipment covers the equipment required to support the drill, shovel, and truck operations, these are crawler tractors, road graders, front-end loaders, water trucks, rollers, rubber-tired tractors, etc. Service trucks are the automotive type consisting of rubber-tired over-the- road equipment. The primary structures generally involved in the total maintenance effort are as follows. (1) the main shop with an attached warehouse (the structure could also house the tire and lube shops plus the equipment cleaning stalls), (2) a service station with bulk petroleum product storage tanks, (3) a heating plant, (4) a security station (lf this is a corporate requirement), (5) operating department and employee assembly buildings, and (6) an electrical substation. Under certain conditions, many of these facilities with the exception of the substation could be combined In one or several structures. This arrangement could have a great advantage especially in areas where the heating of the structures is extremely critical.

Jan 1, 1979

By B. F. Tillson

ALTHOUGH most accidents occur through the A carelessness or misfortune of the workmen; that is no reason why we should not take all physical precautions practicable. The best way to approach the problem of mine safety is to acquire a personal feeling of responsibility for the accident and then plan how it might have been prevented had we known that it was to occur. A statistical analysis of the physical conditions contributory to accidents will give an indication of some of the methods or mechanisms that should be revised or safeguarded. The handling of rock or ore is a common source of minor injuries. Freedom from accident when mucking largely depends on the skill and care of the workman; this also is true, to a certain degree, to loading cars from chutes, but much can be done in the layout of chutes and their equipment to provide equal safety with less skill. Permanent stagings, or rigid units that may be easily assembled, should be provided so that the men handling the chute boards or gates and barring the jammed chunks will have a convenient safe footing for their operations. A stance to the side of the chute mouth is to one in front, because a man will not be liable to be struck by flying lumps or his bar, should it he caught in the mass, yet in many mines the workmen face the chute when loading a car. Fig. 1 shows the operation of a plank chute having special latches which support the chute boards in such manner that they may be conveniently dropped into place to stop the flow of ore.

Jan 1, 1926

By F. S. Crawford

IRON and copper are mined in the Lake Superior district. The iron mines of the district have the best safety record for that industry in the country as a whole, while the copper mines of the district rank second in two of the four years recorded (Table 1). In Utah copper comes mainly from open-pit mines, which enables that state to lead easily in safety. All of the Michigan production comes from deep under-ground workings. About 60 per cent of the iron miners in St. Louis County, Minnesota, are employed at open-pit mines; this favorably affects the combined open-pit and underground accident-frequency rate, as this county pro-vides most of the Minnesota-mined iron ore. In Michigan, however, there are few open-pit mines, the bulk of the production coming from underground mines, while all of the Wisconsin production, just across the state line from Michigan, is from underground mines. In spite of the fact that fewer mines in Michigan use the safer open-pit method, the iron-mining industry of that state maintained a consistently low record from 1931 to 1934; however, it was many points behind its nearest com petitor, Minnesota, with its much greater production from open-pit mines.

Jan 1, 1939

By William M. Shepard

The Tintic mining districts of central Utah com- prise one of the major silver-lead producing areas in the United States. Ore valued at nearly $450 million has been produced from these districts since the initial discoveries, in 1869, of veins cutting the Silver City monzonite stock. Subsequent production from the famous manto-type "ore runs", which characterize the Main Tintic district, was followed during the past 40 years by discovery of the blind orebodies of the East Tintic district, including the famous Tintic Standard mine and the most recent discovery, the Burgin mine, currently being brought to full production by Kennecott Copper. The occurrence of blind orebodies of exceptional size and grade in both the Main and East Tintic districts has made this area a field laboratory of major importance for the study of geochemical dispersion halos and alteration features associated with known ore, and has led to the discovery of additional concealed orebodies. The larger share of the basic data-gathering and interpretation has been done by members of the U.S. Geological Survey who have been studying the Tintic mining areas since before the turn of the century. These studies have been supplemented and expanded by the geological staffs of the local operating mining companies, by exploration geologists and by students.

Jan 4, 1966

By Arthur L. Walker

In June, 1893, while I was with the Old Dominion Copper Co. at Globe, Ariz., I received an offer to take charge, as manager, of the Baltimore Electric? Refining Co. which had recently built a plant at Baltimore, Md., having a capacity of about 1200 tons of electrolytic copper per month, using the Hayden series system. This was a very large output, for in those days the plants were small and the art was in its infancy. At the beginning of 1893 there were 11 electrolytic refineries in the United States, most of them using the multiple system. The Hayden series system was used at Baltimore and Bridgeport and the Smith series system was in operation at the Electrolytic Copper Co. at Ansonia, COM., and at the Pennsylvania Salt Co. at Philadelphia. In the latter system the plates were placed in a horizontal position, but the operating difficulties were so numerous it was soon discarded. The total production of these 11 plants in 1892 was very small; I have not been able to discover reliable figures of production. There were about thirty electrolytic copper refineries in the world that year, according to Titus Ulke, and the entire production of these

Jan 1, 1932

By A. L. Mular

lnput energy-size modulus relation at small reduc-tion ratios is expressed by Et = (M, -Mt) k;. In some cases 13 is close to Schuhmann's distribution modulus a in value. Experimental results in conjunc-tion with the equation demonstrate the fact that energy input which produced fracture is not expended on unbroken starting material inside the mill at any time. Recently, schuhmann1 derived the Charles equation2 using the postulate that complex com-minution operations can be considered as a summa- tion of many comminution events. The fragments resulting from each event are assumed to follow the Gaudin-Schuhmamn distribution. In his derivation, Schuhmann implies that the size distribution of the total mass of a material is determined by the fraction of that mass actually subjected to comminution. Consider a feed to contain a volume, Vo, of uni- formly sized homogeneous material. After t seconds of grinding, let the volume of broken material be Vo - Vt where Vt is the volume of starting material not yet broken. The size distribution of the broken material is given by: where V is the cumulative volume less than size X, and k, is the size modulus of the broken material at time t. The distribution for the total volume at this

Jan 1, 1962