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By AIME AIME

CHARACTERIZING the annual meeting as the biggest and best one yet has happened so repeatedly that some may suspect it has become a conventional phrase, like "good morning," and yet, what else can be said when not only one but all the many who express an, opinion use exactly those words, while the first of the two adjectives refers to a physical fact that is established by count. Perhaps there were hose who thought it not the best, but if so they were too tactful to say it out loud. So without further ado . let us admit that the one hundred and thirty-ninth general meeting of the A. I. M. E. held; as our By-laws provide, in New York during the third week of February, was the biggest and best of them all. Perhaps it is because we appreciate friendliness more as we grow older, but somehow the friendly atmosphere seems to rise slowly in temperature with the passing of the years. The actual atmosphere on the opening morning was quite the contrary, Feb. 17 being the coldest clay, so far, of this winter, and the suburbanites claimed that their thermometers had registered 5" below zero when they got up, though the official records of the weather man did not go that low. From that time the temperature steadily rose until Thursday afternoon, when the official record of 66" constituted a record high for Feb. 20 at New York. The weather man explained it by learned discussion of highs and lows, but we suspect the A.I. M. E. members must have had something to do with it.

Jan 1, 1930

By A. N. Rogers

Jan 1, 1883

By E. H. Jr. Dix

THE consideration of alloying elements for aluminum has led to a series of investigations of the equilibrium relations between aluminum and those alloying elements. Therefore, the aluminum end of the aluminum-antimony diagram has been studied. The general form of the aluminum-antimony equilibrium diagram has been worked out by Campbell and Mathews1 and by Tammann.2 Campbell and Mathews described principally the beginning of solidification. They found the curve of beginning of solidification to rise gradually from the melting point of pure aluminum to a maximum at about 67 per cent. aluminum. After a slight lowering of the curve at a little greater antimony concentration the curve again rises to a maximum at 18.4 per cent. aluminum, which corresponds to the compound AlSb. The curve then drops to the melting point of pure antimony. Tammann explained the maximum occurring at about 67 per cent. aluminum as the result of the slow formation of the single compound AlSb. The space lattice of the compound AlSb, according to Owen and Preston,3 is face-centered cubic, the antimony atoms being intermeshed with an identical aluminum lattice. Very little, if any, work has been done on aluminum alloys containing small amounts of antimony.

Jan 1, 1930

By Herbert Clark Hoover, Lou Henry Hoover

DIGGING of veins I have written of, and the timbering of shafts, tunnels, drifts, and other excavations, and the art of surveying. I will now speak first of all, of the iron tools with which veins and rocks are broken, then of the buckets into which the lumps of earth, rock, metal, and other excavated materials are thrown, in order that they may be drawn, conveyed, or carried out. Also, I will speak of the water vessels and drains, then of the machines of different kinds,1 and lastly of the maladies of miners. And while all these matters are being described accurately, many methods of work will be explained. There are certain iron tools which the miners designate by names of their own, and besides these, there are wedges, iron blocks, iron plates, hammers, crowbars, pikes, picks, hoes, and shovels. Of those which are especially referred to as " iron tools " there are four varieties, which are different from one another in length or thickness, but not in shape, for the upper end of all of them is broad and square, so that it can be struck by the

Jan 1, 1950

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By A. A. Jr. Smith, J. S. Smart

The controlled amounts of phosphorus, arsenic, sulphur or selenium found in commercial coppers perform a variety of highly useful functions. Indeed, a large segment of modern copper technology is essentially dependent upon the presence of one or more of these elements. Consequently, the literature contains many references to their effects but the scope is broad and has been only partly covered. New data are presented herewith directed toward a better understanding of the basic behavior of these elements in copper, with particular emphasis on the composition range o to 0.05 per cent. These data are a part of a general program of research on the effects of impurities on the properties of oxygen-bearing and oxygen-free copper, other portions of which have been reported previously. Schematically, the behavior of individual elements is determined from measurements of conductivity and softening temperature,'v2 and the binary alloys employed are synthesized from high-purity copper in order to eliminate interference from the effects of extraneous impurities. Alloys of selected composition were first prepared in the oxygen-free form by continuously casting the melts in the form of %-in. diameter rod. Oxygen was added subsequently to portions of the alloys, either by remelting or by diffusion at 8jo°C. from a surface scale. Test wires wcre drawn one B. and S. number per pass, using four 30-min. 600°C. anneals at 0.3125, 0.257, 0.204 and 0.162 in., and a final cold reduction of 75 per cent to 0.081 in. Oxygen-bearing slugs made by remelting nere hot-rolled to 4ia in.. drawn to 0.162 in., annealed for 30 min. at 6o0°C. and cold-drawn 75 per cent to 0.081 inch. The alloys containing phosphorus, having been compounded very early in the program, were prepared in the form of 3i6-in. rod, and processed to wire with only the last three intermediate anneals listed above, all of these having been conducted in commercial nitrogen. In addition, the conductivity anneals on these alloys were also performed in the same atmosphere, and the small amount of oxygen present as an impurity in the gas resulted in some loss of accuracy at temperatures of 700' to 8o0°C., as will be shown later. Subsequently, the anneals for all oxygen-free alloys were conducted in hydrogen to prevent oxidation, and purified nitrogen was employed only for oxygen-bearing samples. All conductivity anneals wcre of one hour duration followed by a rapid quench in 10 per cent HZSO*. Effect of Phosphorus The widespread use of phosphorus as a deoxidant has resulted in universal appreci-

Jan 1, 1946

By A. A. Jr. Smith, J. S. Smart

The controlled amounts of phosphorus, arsenic, sulphur or selenium found in commercial coppers perform a variety of highly useful functions. Indeed, a large segment of modern copper technology is essentially dependent upon the presence of one or more of these elements. Consequently, the literature contains many references to their effects but the scope is broad and has been only partly covered. New data are presented herewith directed toward a better understanding of the basic behavior of these elements in copper, with particular emphasis on the composition range o to 0.05 per cent. These data are a part of a general program of research on the effects of impurities on the properties of oxygen-bearing and oxygen-free copper, other portions of which have been reported previously. Schematically, the behavior of individual elements is determined from measurements of conductivity and softening temperature,'v2 and the binary alloys employed are synthesized from high-purity copper in order to eliminate interference from the effects of extraneous impurities. Alloys of selected composition were first prepared in the oxygen-free form by continuously casting the melts in the form of %-in. diameter rod. Oxygen was added subsequently to portions of the alloys, either by remelting or by diffusion at 8jo°C. from a surface scale. Test wires wcre drawn one B. and S. number per pass, using four 30-min. 600°C. anneals at 0.3125, 0.257, 0.204 and 0.162 in., and a final cold reduction of 75 per cent to 0.081 in. Oxygen-bearing slugs made by remelting nere hot-rolled to 4ia in.. drawn to 0.162 in., annealed for 30 min. at 6o0°C. and cold-drawn 75 per cent to 0.081 inch. The alloys containing phosphorus, having been compounded very early in the program, were prepared in the form of 3i6-in. rod, and processed to wire with only the last three intermediate anneals listed above, all of these having been conducted in commercial nitrogen. In addition, the conductivity anneals on these alloys were also performed in the same atmosphere, and the small amount of oxygen present as an impurity in the gas resulted in some loss of accuracy at temperatures of 700' to 8o0°C., as will be shown later. Subsequently, the anneals for all oxygen-free alloys were conducted in hydrogen to prevent oxidation, and purified nitrogen was employed only for oxygen-bearing samples. All conductivity anneals wcre of one hour duration followed by a rapid quench in 10 per cent HZSO*. Effect of Phosphorus The widespread use of phosphorus as a deoxidant has resulted in universal appreci-

Jan 1, 1946

By William H. Spice

Drilling activities in South Central Texas for the year 1945 continued the steady increase over the past two years, while new fields discovered for the year included four new gas fields and one field extension. In the 30 counties included in this area, which comprises district No. 1, Oil and Gas Division, Railroad Commission of Texas, 141 exploratory wells were completed, compared with 61 drilled in 1944 and 29 drilled in 1943. Of these 141 tests, 55 were field well and 86 were wildcats; 38 were completed as oil wells, S as gas and gas-distillate producers, and 95 were abandoned as dry. Atascosa and McMullen Counties were the most active in the district, accounting for 73 of the wells drilled.

Jan 1, 1946

By AIME AIME

OCTOBER will be western month for the Institute. With meetings at Spokane, Tulsa, Los Angeles, and San Francisco, and with a large number of American Institute of Mining Engineers members and their families in the party sailing out through the Golden Gate to Japan on the afternoon of the tenth, the major activities of the Institute will, for this month at least, be west of the Mississippi. Despite cancellations due to necessity, most of the officers of the Institute will be present and taking part in some one or more of the Western meetings. Prof. Robert S. Richards, our senior past-president, will attend both the Spokane and San Francisco meetings and then go to Japan. President Bradley will preside at the San Francisco meeting and then head the party going to Tokyo. At Tulsa and Los Angeles, the principal officers of the Petroleum Division will be present and active and at all the meetings, directors, ex-directors and -present and past officers will be on the job and keeping things moving.

Jan 1, 1929

NORTH AMERICA Number Members Alaska 32 Canada 300 Mexico 165 Newfoundland 3 United States Alabama 43 Arizona 121 Arkansas 9 California 674 Colorado 184 Connecticut 94 Delaware 19 District of Columbia 120 Florida 17 Georgia 5 Idaho 66 Illinois 211 Indiana 56 Iowa 8 Kansas 32 Kentucky 31

Jan 1, 1934

By AIME AIME

A DOCUMENT of progress and of great interest to engineers is the report of the Military Affairs Committee of 'the Engineering Council, which has just been accepted and sent to the secretary of War. It provides .a plan whereby civilian engineers holding commissions in the Reserve Corps may; with their con- sent, be called into service of the army during peace at any time, either with troops in the field or in a consulting capacity on any government engineering work. The Military Affairs Committee finds ample authority in the military bill passed by Congress on June 4, 1920, for this arrangement and also for extending the privilege to military engineer, officer-s of the regular army to engage in civilian work during times of peace. It is hoped that the Secretary of War will adopt the suggestions and put the program outlined into effect. This is a constructive piece of work comparable to the efforts of the military Committee before the war which developed so much in the way of preparedness, particularly in the program of military lectures which, held in the auditorium in the Engineering Societies Building, became so popular that each lecture had

Jan 1, 1920

By E. R. Johnson

The copper concentrator of the Braden Copper Co. is at Sewell, Chile, on the westem flank of the main Cordillera of the Andes, at an air distance of approximately 50 miles southeast of Santiago, the capital of Chile. The region is mountainous and space is at a premium because of the rough terrain and the danger of snowslides. The ore, a porphyry copper, is mined by a block-caving method in the El Teniente mine. It is hauled to the crushing plant, a distance of 2.6 miles, through a tunnel because of the severe climatic conditions. The usual large, coarsely set, primary reduction machines found in many ore-treating plants are not required because of the mining method employed and the limiting 12-in. spacing of the grizzlies at the head of each ore pass in the mine. It is the purpose of this paper to describe the numerous improvements made in the crushing section of this large flotation concentrator during the past I5 years to increase the efficiency of the plant and to raise the daily output from around 20,000 to 30,000 tons. The reader should keep in mind that all changes were made within the existing building because of the limited space and the high cost of the heavy mill construction required to withstand the snow loads. The present plant, as well as the former, operates on a 24-hr, 7 days a week basis. The crushing plant commenced operations at its present site in 1921, the main equipment being No. 7½ gyratories, followed by 48-in. horizontal Symons disk crushers. Fines were removed by I-in. stationary grizzlies ahead of each unit. In 1924 a third stage of crushing was provided by the addition of 55½-in. rolls in open circuit. During 1925, the Symons disks were replaced by 73½-in. rolls. All the rolls were changed to closed circuit, with elevators and screens to give a final product of 9 pct plus 3-mesh. The flowsheet of a typical crushing section of this period is shown in Fig I. The ore was withdrawn from a common bill serving the five crushing sections in the plant by means of any number up to six 36-in. wide-apron feeders, which discharged onto a common conveyor belt. This conveyor was equipped with a magnetic head pulley and the crusher attendant was stationed near the discharge end to pick out pieces of mine timber that might be in the ore. The ore was discharged over a 13/4-in. spaced bar grizzly and the oversize of this grizzly was crushed by a No. 7½ McCully gyratory crusher set at 13/4-in. opening on the closed side. The grizzly undersize joined the gyratory discharge and was conveyed to a set of 73½ by 20-in. Garfield rolls set at I in. These rolls operated in closed circuit with a bucket elevator and two vibrating screens placed in parallel.

Jan 1, 1949

By Haakon Styri

In discussion of Dr. Fitterer's paper on electrolytic separation of slag inclusions, some results from experiments on electrolyzing high-carbon steels at the SKF Research Laboratory were given. l We had been working for a number of years on chemical methods of separating the inclusions but could not find any solvent that would dissolve the steel without attacking some of the inclusions, particularly the sulfides in which we were mostly interested at the time, nor any that would dissolve all sulfide or silica in filings as fine as 300 mesh without attacking the iron. Electrolytic methods had also been tried without any real progress until we learned from the Bureau of Mines about the use of the collodion membrane around the anode. Our early difficulties were to some extent different from those of the Bureau of Mines, perhaps because of experimenting on steels of higher carbon content, but most of our difficulties were of the same nature as those of the Bureau. Formation of large quantities of basic hydroxides was traced to the use of impure and oxidized ferrous sulfate. To protect from oxidation from the atmosphere during electrolysis, after purer chemicals were obtained, a thin layer, 54 in. or less, of molten paraffin was poured over the surface of the cathode liquid, where it solidified. It was found desirable also to hold the cathode chamber slightly acid by initial addition of 0.1 per cent acid (sulfuric or hydrochloric) to prevent precipitation of the hydroxide. This acidity would decrease gradually and the cathode chamber would become neutral before the end of the electrolyzing. The increase in acidity in the anode chamber during our early experiments had appeared to cause attack of the precipitated sulfides in the residue, which originally was analyzed by volumetric method for sulfur, and for this reason a 10 per cent sodium citrate solution was substituted for the sulfate in the anode chamber. With the use of the more reliable Eschka method for sulfur determination (as in coke), there was however no serious attack on the sulfides in the anode chamber with a variety of different liquids, as shown in Tables 2 and 4. The Eschka method gives a higher sulfur value than

Jan 1, 1933

By D. L. Ritter, N. J. Grant, B. C. Giessen

The crystal structures of eight of the nine intermediate phases in the Nb-Rh system were investigated by X-ray techniques. The following structures occur: a,Nb3Rh (Cr3O type);o(ofe - cr type) (H.T. phase, structure unknown); Q2 (AuCU type); a, (orthorhombic, analogous to a,, (Ta-Rh)); a (AuCd type); a,, (monoclinic, related to samarium type); a-8 (VCo3 type); a, NbRh, (AuCu, type). Structural relationships between the six close-packed intermediate phases are discussed and a comparison with the Nb-Ir, Ta-Rh, and Ta-Ir systems is made. In the Nb-Rh phase diagram,' nine intermediate phases were encountered. In order to understand the phase sequence in the diagram and to be able to plot atomic volumes, several unknown crystal structures had to be worked out. These and the evi-

Jan 1, 1964

By W. E. D. Stokes

THE application of aviation to mining and petroleum operations, on the basis of economy and attainment, has become a demonstrated fact. According to Dominion Government records, 30 Canadian companies engaged in air transportation with northland mining camps, carried 13,000 tons of freight in 1935, and in 1936 carried 16,000 tons. In addition, many mining companies used planes to transport prospectors with canoes, outboard motors, gasoline drums and supplies to remote locations, and one company maintained a plane to take radium-bearing ore from its mine on Great Bear Lake nearly 1000 miles south to the rail- way at Waterways, Alberta. Heavy pieces of mining machinery weighing 2 tons are being carried by Ford trimotor planes over the Andes, at an altitude of not less than 15,000 feet. At Bulolo, New Guinea, 17,500 tons of disassembled gold-dredging equipment has been flown over inaccessible terrain, while supplies and building materials for a community of 1000 whites have been transported by airplane. A 3 1/2-ton shaft was carried on one notable trip, while at another time an automobile, 2 tons of rice and a large safe went over the mountains in one plane. Fig. 1 shows an electric generator that was carried by plane to Bulolo. Many large American oil companies operated fleets of planes during 1936, ranging from fast, luxurious air liners for executives to elaborate geological prospecting units, ambulance planes, freight carriers and pipe-line repair crews. According to the U. S. Geological Survey, commercial firms photographed 16,291 square miles during 1935, while the Government compiled from aerial photographs by the Geological Survey in the United States 85,544 square miles. It was found that information could be determined in a fraction of the time required by surface methods. However, sounding a word of caution, a Commonwealth of Australia government report on aerial survey operations had this to say: It is necessary to repeat ad nauseam that aerial photographic survey is in no sense a substitute for geological investigation, though it is a very valuable adjunct thereto, and greatly facilitates and accelerates geological mapping. There are many details

Jan 1, 1937

By S. R. Goodman, Hsun Hu

The formation of secondary - recrystallization tex-tlires in cube-textured 18-8 stain less steel (Type 304) Ilas been studied at three temperatures. Prolonged annealing at 100°'C protluces a PredoninanGly (520) [OOZJ-type texture, which is related to the cube te.ture of the primary lnatrix by a rotation of approxivzately 22 deg around the [001] axis in the rolling direction. Annealing at 1200 or 1300°C facers the formation of the (123)[272/-type texture, which is related to the matrix texture by a [111] rotation of app.voxiniately 40 deg. These observations suggest that in the secondary recrystallization of cube-texlut-ed stainless steel an apparent actilation energy for growth is higher for grains related to the tncrtuix Og [111] rotations thun those reloted by [100] rotations. THE formation of secondary-recrystallization textures in cube-textured primary matrices of fcc metals has been studied widely by various investigators. For Fe-40 pct Ni alloys, Pawlek' and wassermann2 reported that the orientations of secondary grains were related to the cube texture by rotations of 30 and 38 deg around [001] in the rolling direction. However, Rathenau and custers3 found that, while in one Fe-48 pct Ni alloy, most of the secondary grains were oriented with respect to the cube-textured matrix by rotations around [001] of 26.5 deg, in another alloy of a different origin, the orientations of secondary grains were related to the cube texture by rotations of approximately 35 deg around a [lll] axis. Similar orientation relationships were also observed between the secondary grains and the cube-textured primary matrices of copper.4"a No attempt was made to differentiate these two types of orientation relationships; reorientation by either a [111] or a [100] rotation was considered to be equally favored. The present investigation consisted of a study of the secondary recrystallization textures in cube-textured stainless steel. It was noted that the secondary grains formed in stainless steel were considerably smaller than those of Fe-Ni alloys or copper. This offered the advantage that the secondary recrystallization texture could be determined by the texture-goniometer technique, and a more detailed study of the textural development during the course of secondary recrystallization could be made. The effect of annealing temperature on the formation of secondary-recrystallization textures was also investigated. MATERLAL AND METHOD It was shown earlier"-" that a strong cube texture can be obtained in 18-8 stainless steels by rolling at 800°C to produce the copper-type deformation texture, followed by annealing at 800" to 1000°C for recrystallization. To improve the cube texture for the present study, a commercial-grade 18-8 stainless steel (Type 304) was rolled at 800°C first to 5 mm (0.2 in.) thick plates. Three of these plates were then stacked and welded together along the edges into a sandwich assembly. After annealing at 900°C for 20 min: the assembly was finally rolled at 800'C to 90 pct reduction in thickness with reheats and end-for-end reversals after each pass. Only the central strip, which was reduced from 5.0 to 0.50 mm (0.7 in. to 0.020 in.) thick, was used. The chemical composition of the steel in weight percent was as follows: C, 0.06; Mn, 0.38: Cr, 18.71; Ni, 9.56: P, 0.011; S, 0.009; and Si, 0.39. The purpose of rolling the strip in a sandwich assembly was to prevent direct contact between the central strip and the rolls. It was observed earlier" that, when the strip was rolled at 800°C without being enclosed in a sandwich assembly, the cube texture obtained by subsequent annealing at 900" or 1000° C for recrystallization was largely confined to the central section of the strip, while most of the recrystallized grains formed in the surface section of the strip were not cube-textured. This was obviously due to the fact that the actual temperature at the strip surface during rolling, as a result of direct contact between the strip and the cold and massive rolls, was considerably lower than 800°C. By using a sandwich assembly for hot rolling, the cube texture obtained upon subsequent annealing for recrystallization was found to extend through the entire thickness of the strip. After rolling, the central strip was taken from the sandwich assembly. and cut into specimens. Prior to annealing. the specimens were etched to 0.25 mm (0.010 in.) thick. A tube furnace provided with a purified, dry argon atmosphere was used for annealing. Textures were determined by the reflection technique. using a Siemens automatic texture-goniometer and ZrOz-filtered MoKa radiation. With a time constant of 4 sec. the preferred orientation of the secondary grains could be measured satisfactorily by the integrated intensities. Both (111) and (200) reflections were measured, and corresponding pole figures were constructed according to the techniques described previously.10 The agreement between results deduced from these two reflections was excellent. RESULTS AND DISCUSSION Secondary-Recrystallization Texture due to Prolonged Annealing at 1000°C. Fig. 1 shows the primary-recrystallization texture of a specimen annealed at 1000°C for 30 min. A substantial improvement in both sharpness and intensity of the cube texture, owing to the present processing method, can be noted readily by comparing Fig. 1 with similar pole figures shown earlier in Refs. 9 and 11. Secondary recrystallization

Jan 1, 1967

By A. B. Parsons

LAST YEAR (1934) saw the completion of a ten-year program of reconstruction and modernization of the world's largest lead- smelting plant, that of the ' Broken Hill Associated Smelters Proprietary, at Port Pirie, South Australia, which has a capacity for smelting and refining 220,000 (short) tons of lead per year. It deals with the entire output of lead concentrates from the famous Broken Hill district in Australia, being owned .jointly by the three leading companies: North Broken Hill, Broken Hill South, and the Zinc Corporation. These companies, together with the Sulphide Corporation, are credited with a production of 198,000 tons of lead in 1934. When one says regarding any metallurgical plant that modernization is "completed" he should add "for the moment." Development in the art of metallurgy and in the equipment used never ceases; that which seems close to the last word today is likely to be obsolete in a few years even in a process so well standardized as smelting and refining lead. However, the reconstruction at Port Pirie has altered the procedure materially. More im-

Jan 1, 1935

By J. F. Myers

AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of -200-mesh produced a very creditable figure.

Jan 1, 1950

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model