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I would like to congratulate the authors on an interesting paper and, in particular, on their justification of the use of superposition in treating gas wells. They state, however, that no theory has previously been developed lor treating the variable rate drawdown case. In a paper published a few years ago by my colleagues and myself, a method is described which allows a constant rate drawdown curve to be derived for any well. regardless of real rate variations. This method has the great advantage that it is not necessary to make any assumptions regarding the form or uniformity of the reservoir, and the derivation suggested by the present authors is simply an idealized case of our more general treatment. In the light of several years' experience in the derivation of constant rate drawdown curves: I would like to point out that the method proposed by Odeh and Jones may lead to confusing answers, particularly if applied over an appreciable time interval. The reason is that, if pressures are measured when a well is flowing, non-linearities in plots like Figs. 1 and 2 can arise due to either (1) changes in the skin factor with time and/or flow rate, or (2) an inhomogeneous reservoir. Separation of these two effects is only possible if some of the pressures used in the analysis are measured when the well flow rate is 0 or, in other words. during brief shut-in periods. REFERENCES 1. Arthur, K. B.. Metunomski, Z. G. and Ruche, Ms "Intetet ct methode d'utilisa tion des mesures de pression [)our Petude des gisemonts" Revue de T'I.F.P. (Nov., 1962) XVII, 1299. 2. Thomere, R. and Arthur, K. R.: "Analysis of the Pressure Bet~avior of a Production Well Subject to Interterence and Its Application to Reservoir Models", Paper SPE 1189 presented at SPE :Amund Fall Mecting Ireld in Denwer, Colo. (Oct. 3-6, 1965).

Jan 1, 1966

By William L. Batt

IT IS becoming increasingly evident to management that it has other obligations than merely to earn dividends for stockholders. The head of one of America's largest organizations has stated it in these words: "There rests upon them a far broader responsibility than the mere production of goods and services, or solely the interests of their stockholders. They must assume the important obligation, through proper policy, of attuning industry to a rapidly changing world, from social as well as economic standpoints." Stockholders might as well reconcile themselves, therefore, to the fact that management cannot always put their interests first in the obligation of business enterprise: and that the legitimate requirements of customers and employees have acquired a new significance which must be recognized if the business of today is to prosper.

Jan 1, 1938

By Walter Henoch

THE subject of my talk is, "What 'the college, student expects when he gets out of college." Since all of us, here tonight are engineers, I think it will be proper to limit the discussion to "What the engineering student expects when he emerges from college." It might be well to con-sider just why we chose engineering rather than some other of the many courses open to us. We certainly did not choose it because it is easy nor because we thought it would be a very pleasurable way to spend four years of our lives. The majority of students who choose this profession have a pretty well-formed idea of what an engineering course requires. They at least know that they must work to re-ceive their credits. The minority, which is no small num-ber, are soon disillusioned and as a result they either quit college entirely or they join the' Commerce School. I asked a number of my fellow students just what it was that induced them to join the engineering profession, but it was hard to obtain a clear cut statement from any of them. Some said it was due to environment; others said, they took it because they liked it, and still others said they took it because their folks wanted them to. These state-ments are rather vague and incomplete, but underlying them all is something that the fellows found hard to ex-press. I think it is this: To the layman there is something of romance and adventure about the engineering profes-sion, and this fact coupled with the reputed high salaries and high commands of certain noted engineers no doubt fired our imaginations and consequently led us to join the ranks of the engineers. No doubt many engineers have gone out into the world and have found little romance or adventure .attached to their work, but nevertheless it is an occupation of a wide diversity of interest, of constant change of scene, and of vivid and human relations.

Jan 5, 1928

T. W. ROBINSON, Pueblo, Colo.: Mr. Potter's review is a striking testimony to the important part played by science in this branch of practice. But, the question arises, In which department has science effected most ? The available raw material, the size of furnaces, the general design and equipment of the plant, and the daily management, are particulars, each of which contributes to the general result, while the effect of each merges into that of the others. The following notes concerning the operations of the furnace-plant of the Colorado Fuel and Iron Company (formerly the Colorado Coal and Iron Company), at Pueblo, may throw some light upon the question of their relative importance. This company operates three stacks, and when the plant first came under my observation, about nine months ago, the furnaces were constructed, equipped,and run as stated below: Raw Materials.—The main sources of ore-supply were, as they still are, the Orient and Calumet mines of the company. The Brecce and Morning Glory ores, mentioned below, were formerly brought from Leadville, but are practically now no longer used. The Orient ore is a porous brown hematite, easily reducible in the furnace. The Calumet is a magnetite, very refractory in character, requiring preliminary roasting. Both are fairly uniform in composition. The Breece and Morning Glory are red hematites, resembling in appearance the soft ores of the Vermilion range, Lake Superior. The coke here used is made of coal from the company's mines in southern Colorado, and is distinct from that produced by the company in the western part of the State. The structure is similar to that of Alabama coke. The limestone employed is a calcite. The analyses are given in Table I. I would note, parenthetically, that I know of no section of the country presenting harder conditions for furnace-practice than these materials impose. Results cannot be measured by the more

Jan 1, 1894

By Sir John Cadnan

The production from the Maidan-i-Naftun area for the year ending March, 1928, was 5,340,000 tons (40,210,200 bbl.), an increase of nearly 13 per cent. over the production for the year ending in March, 1927. The production by years since the opening of the field in 1912 is given in the following table: [1 ton = 7.53 bbl.] Year Ended MaRch Tons Year Ended March Tons 1912 (7 months)............. 43,084 1920....................... 1,354,631 1913........................ 80,800 1921....................... 1,767,070 1914........................ 273,635 1922....................... 2,310,098 1915........................ 375,977 1923....................... 2,913,908 1916........................ 449,394 1924....................... 3,583,000 1917........................ 644,074 1925....................... 4,221,000 1918........................ 897,402 1926....................... 4,470,000 1919....................... 1,081,919 1927....................... 4,735,000 1928....................... 5,340,000 The actual production represents only a small proportion of the potential production. The Masjid-i-Suleiman Field The present producing unit, the Masjid-I-Suleiman, is an anticline some 20 miles in length by 4 miles in width, including three domes as so far proved. The producing horizon is a very open, dolomitic limestone, which, while showing much variation in texture and porosity, is so connected that the lowering of pressure in one section of the field quickly affects the whole area. The topography of the field is broken, with differences of well elevations of as much as 1100 ft. The depths to the limestone vary from about 800 to about 5000 ft. The closed-in pressure of the oil wells varies from zero to 50 lb. per sq. in. and that of the gas wells is about 450 Ib. Although the static oil level may be several hundred feet below ground level, in oil wells of high elevation, all the wells flow continuously or intermittently after they are once started—the majority continuously. The gas is very high in hydrogen sulfide in gas-oil wells of low pressure.

Jan 1, 1929

G. Sherburne Rogers (written discussion*).—Mr. Kennedy's discussion1 of Mr. Matteson's paper takes the form of a criticism of my own comments2 on this paper. Mr. Kennedy is a respected authority on matters pertaining to the salt-dome oil fields, and his characterization of my "elaborate figures" as "worthless" is sufficiently candid and comprehensive to warrant a brief reply. My 'voluminous figures" consisted simply of a rough estimate of the minimum quantity of salt in the Humble dome, and a, calculation of the volume of sea water and of the volume of saturated brine which this salt would represent. Mr. Kennedy apparently interprets my remarks as opposing the idea that so,large a volume of salt could have been deposited from sea water, for he cites the area and thickness of European salt beds; but nothing was further from my intention. Given an arm of the sea, an arid climate, and evaporation under a hot sun, it is easy to conceive the formation of almost any thickness of bedded salt. I cited the figures in connection with Harris' theory of the origin of salt domes, according to which the plugs were formed by the deposition of salt from ascending brine solutions, owing to the drop in temperature as they neared the surface. I pointed out the well known fact that the solubility of salt is only slightly affected by temperature, and that a drop of 80" C. would cause the deposition of less than one-tenth of the salt in solution; hence that more than ten times the volume of salt actually forming the plug must have been involved. If ten times the salt actually in sight be computed in terms of brine and multiplied by 50 or 60 to take into account all of the known salt domes, the resulting figure is so enormous that I am not at all so sure as Mr. Kennedy seems to be that the porous stratified rocks of eastern Texas and western Louisiana could contain or furnish so great a volume of migratory brine. Mr. Kennedy, however, does not dwell on drop in temperature as the cause of the precipitation, but contents himself with ascribing the whole process to lateral secretion. As I understand it, this implies that the connate waters and brines contained in the rocks migrated to the Gulf Coast region, and there deposited their salt at various loci of crystallization. Just what started the crystallization or what force caused the

Jan 1, 1918

By R. G. Treuting, W. C. Ellis

D. Whitwham, M. Mouflard, and P. Lacombe (British Council Research Fellow, Labratoire du Professor Chaudron, Vitry-sur-Seine; Inqenieur de Recherches, Labratoire de Vitry; and Maitre de Recherches, Labratoire de Vitry, Professeur Adjoint de Metallurgie, Ecole des Mines, Paris)—The authors' work is of great interest in bringing out the geometrical relations existing between twinned lattices, and for the notion of a coincidence super lattice developed from this. We should like to point out that a similar idea was put forward by Friedel8 in his book on the subject of lattice merohedrism "merihedrie réticulaire:"—When two crystals A and B are twinned with respect to a mirror plane, there exists a common superlattice, "réseau periode," which is independent of the contact surface between the two crystals. The volume V of this superlattice is a simple multiple of the volume v of the lattice of crystals A, or B, (Fig. 5). This "multiple cell" is defined by the twin plane (p q r) and a row of atoms [h k l] normal to this plane, the base being taken as the smallest unit (two-dimensional) of this plane. Two cases must be considered. First when the multiple cell, as defined, has no atom site at its center nor at the center of its faces other than (p q r), v the twinning index is defined by —. In the second v case, when one of the two above conditions does not v apply, then the twinning index is V 2v A more intuitive definition of the twinning index would be the proportion of atoms of C, which would coincide with those of C1 when the C, lattice is imagined to extend on the other side of the contact surface. In the case of cubic crystals, the twinning index

Jan 1, 1952

By L. C. Graton

Although marked by numerous well-known attributes of its own, gold does not possess a kind and range of physical, chemical and geological characteristics wholly different and apart from those of other metals. Instead, it is merely one of the family of metals, with its individual and distinctive traits subordinate to the underlying family relationships and resemblances. The geologist concerned with pure science will pursue, therefore, the same general course and will examine the same broad kinds of facts and interrelations when studying the occurrence of gold as when studying that of copper or cadmium, or any other metal. But when we come to consider the use and economics of the metals, we discover that gold differs strikingly from all the others. Gold, in short, is unique, not by virtue of its inherent characteristics, but because of a peculiar and concerted psychological regard in which it is held. It will be evident, therefore, that the geologist who would deal with gold supply must give far greater weight to economic considerations than is required in his contacts with any other metal. If the geologist be called the scientist of occurrence, and the economist the scientist of use, the economic geologist stands as the necessary link between them. Perhaps it is in part because the economic geologist has made himself more familiar with the science of occurrence than with the science of use and has thus in some degree failed to bridge effectively the gap between the two fields, especially with regard to gold, that the usen1 of gold now appear to be in a state of general concern and even of alarm for the security and adequacy of future supplies. In the case of no other mineral commodity do the users, as a rule, trouble themselves greatly about the adequacy of supply except in so far as that may affect the price which they shall have to pay for the commodity. Oversupply, with resulting low price, they regard as a gift of good fortune. As to long-term undersupply, they are generally content to go ahead on faith, leaving the producer to discover as best he may the means for meeting their requirements or the inventor to find a substitute. But history has shown that for gold a different situation exists. While

Jan 1, 1931

THE great subject of interest in American affairs during February was the consideration of the proposed soldier bonus. This proposal was based upon the idea that, because most of the workers of the United States had enjoyed high wages during war, the soldiers were entitled to "adjusted compensa-tion" in order to equalize things. It overlooked the fact that the soldiers, themselves, had the opportunity to enjoy high wages in 1919 and 1920, when rates were highest. Apart from this, the whole project was founded on fallacies and involved what would be nothing less than economic crime. Although it looked as if the measure were destined to be railroaded through Congress, so great a storm of protest was pelted upon Congress that the present outlook is that the whole project will be abandoned. There was probably some increase in the physical volume of business during February. A rise in prices for agricultural products assisted the farmers mate-rially. These developments, however, are not to be construed as presaging any general upward movement. On the contrary, the current year is to be contem-plated as one of serious labor troubles, following inevit-able reductions of wages. These began in February in the form of an extensive strike in the cotton textile industry of New England, accompanied by some rioting in Rhode Island. The coal miners have had numerous conferences, without coming to any encouraging results, and the stage appears to be fully set for a general strike beginning Apr. 1. About the only question now is whether this will comprise both the bituminous and anthracite miners. If the latter refuse to go out, no serious shortage of coal is anticipated, the belief being that the existing stocks together with the output of the non-union mines will supply the demand, which is sub-normal even now. In the metal industries, lead and zinc were dull but stable. The weakening tendency in iron and steel that was manifest during January appeared to be checked, at least temporarily. Copper was charac-terized by a distinct weakness and a considerable decline in the market. This downward movement was inspired by the news during January that several of the important mining companies were taking steps to resume production. During February the demand for copper, both foreign and domestic, was poor.

Jan 3, 1922

By Herbert H. Kellogg

C. M. Decroly (University of Brussels, Belgium) — The importance of the fluorides in the process metallurgy of special metals has already been accepted and it will probably increase in the future. Free energy diagrams as such established by Professor Kellogg are therefore very useful. It is interesting to note that the absolute value of the standard free energy of formation of HF increases with temperature, whereas for almost all the other fluorides it decreases; consequently it should be theoretically possible to reduce all the fluorides of the metals which, at low temperature, have a greater affinity for fluorine than hydrogen by this last element, provided a sufficiently high temperature is used in order to have a good efficiency. However, with regard to the reduction of UFe by hydrogen, I doubt that it will be possible to obtain directly the metal at comparatively low temperatures. There are other uranium fluorides which are more stable than UF6 and it is very likely that such fluorides will be obtained first. For example, in considering the reaction: UF6gas + H2gas + UF1so1id + 2 HFgas it is found, using the thermodynamic data of Brewer et al, that ?H298 = —66 kcal and ?G°298, = —65.2 kcal. As a result, the reduction of UF6 to UF4solld should proceed spontaneously even at ordinary temperature. On the other hand, the standard free energy of formation of UF4solid at 298°K is AG°298 = -209 kcal per mol of F2. The reduction of UF4 by hydrogen will be practically difficult and, as it is known, the only practical way of reducing this compound is to use alkaline-earth metals such as calcium or magnesium. I should like to point out, further, that the fluorination of many metal oxides can be carried out very easily by using the ammonium difluoride method of preparation, which renders the use of fluoride gas unnecessary. The first compound formed is generally a double fluoride of the metal and ammonium. This compound can be decomposed by heating either in a vacuum or in an inert atmosphere, ammonium fluoride being volatilized leaving the metal fluoride in a very pure state. H. H. Kellogg (author's reply)—Professor Decroly is quite right in pointing out that the formation of lower halides of uranium may complicate the reduction of UF6 by H2. I was unable to find his reference to the free energy of formation of UF4 in the compilation of Brewer.13 however. The value of AG°298, = —209 kcal for formation of ½ UFa seems rather high, and I hope the source of this value may be made clear.

Jan 1, 1952

By R. J. Linney

Reserve Mining Co. produces 5 million tons of iron ore pellets per year. The finished product runs about 65.50 pct Fe, with 7.75 to 8.00 pct SiO2. Less than 12 pct arrives at the blast furnaces smaller than % in. This plant was originally designed to produce 3.75 tons annually—not 5 million. To handle the increased tonnage a fifth fine crushing line was added, and some very minor changes were made. When production can be stepped up 33 1/3 pct without extensive additions or changes—within the short period of a year—basic engineering has been sound. Operators of the plant consider it the best design job they have seen or heard of, and competent authorities have said that start-up was quicker and easier than for any previous large-scale minerals beneficiation plant. One big advantage is the elbow room allowed. Generally speaking, there is an eternal conflict between operator and designer over space. The designer has his costs per cubic foot, and he is keenly aware that if he permits the number of cubic feet to rise unnecessarily, total costs will be too high. But this was a new operation, and on a large scale. There were no proven standards to go by. Realizing this, Reserve's engineers provided ample and efficient access to machinery, allowing extra space for unanticipated situations. In three years of production this planning has paid off handsomely. Gravity Flow Saves Time and Money: This plant is on a rocky hillside, the car dumper about 270 ft above Lake Superior. In locating buildings and placing machinery the designers mad= good use of gravity flow, at considerable financial savings. In the concentrator building from rod mills to filters, gravity carries the material between all stages of the operation except one—the closed circuit pumping of concentrate between cone classifiers and ball mills. Since no machine is located directly above any other, an observer can stand on the truck ramp adjacent to the offices and laboratory and see practically every phase of activity in the huge building. The first mill section started in August 1955. After a day's run several modifications were made on auxiliary chutes and launders where spillage had occurred. This procedure was followed for the first

Jan 1, 1960

By Gilbert P. Moore

The production of petroleum in Argentina during 1932 was greater than in any preceding year. The total amount produced was 13,012,-756 bbl. This figure represents a decided increase in the production of oil in Argentina and can be attributed largely to the increased activities of the Royal Dutch operations at Kilometer 27 in the Comodoro Rivadavia district and those of the Standard Oil Co. of Argentina in the Salta region. Production from the Royal Dutch wells amounted to considerably more than 10,000 bbl. per day over quite a long period during the year. Of the 13,012,756 bbl. of oil produced during 1932, the Government Agency (Y. P. F.) was responsible for some 5,578,954 bbl., while 7,433,-802 bbl. were produced by private companies. Although in 1930 the Y. P. F. produced about 55 per cent of the total production and in 1930 50 per cent of the total, in 1932 its production had fallen to about 42 1/2 per cent of the total. This decrease in the proportion produced by the Y. P. F. was not due to a decrease in its production but to the decided increase in the production of private companies, particularly those two whose names are given above. One new discovery was recorded during the year. This was a well drilled by the Y. P. F. at Cacheuta in the province of Mendoza which came in pumping 80 bbl. of 15" gravity oil from a depth of 673 meters. This well was completed at approximately the same time that the provincial government of Mendoza granted a concession to the Y. P. F. and declared the whole province as a reserve in which no concessions may be granted for a period of 10 years. Under these conditions, the federally operated Y. P. F. will have no competition in the Cacheuta area from private companies such as they have in the other three fields of the republic. The Y. P. F. wildcat west of Comodoro Rivadavia at Pampa Maria Santissima on the Rio Senguerr was completed as a dry hole during 1932. This we11 was reported as a producer in 1930 by persons returning to this country from Argentina but it appears that they had been misinformed. The site of this test has been abandoned and a new location made north of the Rio Senguerr.

Jan 1, 1933

By AIME AIME

IN ORDER to carry on its work most effectively, the Committee on Industrial Organization (now known as the Committee on Industrial Relations) consists, of .a number of sub-committees, each composed of a chairman and members who are especially fitted to carry out the work designated by its title. With only one or two exceptions, all of these committees made reports at the New York meeting of the Institute, in February of this year, abstracts of which follow.

Jan 1, 1920

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 Joseph E. Pogue

THAT the domestic consumption of gasoline displays a marked seasonal variation, with a low in the winter and a high in the summer, is well known. It is logical to expect that the nature of the variation has itself been undergoing a change as a result of improvement in roads, general employment of closed cars; and growth of mass haulage; but so far as I am aware the change in seasonal variation has never been investigated and measured. It is the purpose of this paper to present the method and results of such an investigation undertaken as a contribution to the technique of planning operating schedules now so prominent in connection with the functioning of the industry under a Federal quota system. For the method employed I am in-debted to the suggestions and help of Frederick R. Macaulay', who kindly looked over the work sheets; and credit is due Barnabas Bryan, Jr., for assisting in the computations and the graphic work. Ideas for the approach to the problem were also derived from an article by Aryness Joy, and Woodulief Thomas of the Division of Research and Statistics of the Federal Reserve Board*-.

Jan 1, 1934

By Robert R. Brookshire

Brush plating has been thought of by many as black magic bordering on alchemy. Actually it is a science that uses both electro-chemical and mechanical engineering skills and technology. We are not sure when brush plating was first used or by whom. I do know that many times when we would put in for patents on things we thought of as new and innovative, we would find that someone had done it many years before. It took World War I1 to get brush plating off and running. Now at this point, someone may be asking just what is brush plating? And why are we plating brushes? One way of describing what brush plating is, is by telling what it is not such as tankless plating. Brush plating-is an electro deposition of an electro-platable element or alloy onto a conductive surface. To do this a source of direct current is required; this can vary widely. I prefer stepless voltage control from 0-35 volts with a capacity depending on the size job to be done. This can vary up to 500 amps for normal applications. In one case we have used 7500 amps.. In the beginning a brush was actually used with a wire in the middle of the bristles and a jelly-like paste made up from tank plating solutions. The bristles were saturated with the gunk and the spot to be plated was muddled with the concoction at a potential which was the same as the applied tank Voltage. Metal was deposited but only thin coats were achieved. Today we use graphite wrapped or covered with cotton to form a Q-tip type anode. By using graphite rather than a specific metal we are able to either plate, de-plate or strip, electro- mill, electropolish, or anodize--all with the same equipment. Only the electrolyte needs to be changed.

Jan 1, 1984

By W. D. France, H. l. Burghoff

FABRICATORS of copper and copper alloys have contended with the problems of reconversion during the past year in endeavoring to return to the full-scale production that is demanded of them. The problems have not been easy, for the industry, like so many others, has had to deal with strikes of long duration, and material shortages, particularly in the raw materials, copper, zinc, lead, and tin. Despite all these obstacles, it was possible to gear production to new peacetime records during the latter part of the year. This was made possible not only by the use of multiple shifts of personnel, but also by the improved production equipment, the development of which had been stimulated by wartime necessity. The work of installing new and better equipment is still continuing, and virtually every company is engaged in improving or planning to improve its processes.

Jan 1, 1947

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By Robert Glass Cleland

IN SPITE of its widely ramified interests in manufacturing, mines, lumber, railroads, and real estate, Phelps, Dodge & Co. remained primarily interested in exporting and importing, in buying and selling, and William E. Dodge, the directing-partner, consistently styled himself a merchant. After 1849 the profits of the company mounted steadily for seven years until they approached the half-million mark, but in 1857 another severe panic ended the long period of national prosperity that had begun some fifteen years before. Extravagance, indebtedness, and inflation again took their costly toll; or, as the New York Herald of June 27,1857, declared: Governmental spoliations, public defaulters, paper bubbles of all descriptions, a general scramble for western lands and town and city sites, millions of dollars, made or borrowed, expended in fine houses and gaudy furniture; hundreds of thousands in the silly rivalries of fashionable parvenues, in silks, laces, diamonds and every variety of costly frippery are.only a few among the many crying evils of the day. The worst of all these evils is the moral pestilence of luxurious exemption from honest labor, which is infecting all classes of society. The country merchant is becoming a city stock-

Jan 1, 1952