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PUGET SOUND LOCAL SECTION. Executive Committee. CHESTER F. LEE, Chair roan. C. R. CLAGHORN, Vice-Chairman. JOSEPH DANIELS, Secretary-Treasurer, University of Washington, Seattle, Wash. W. C. BUTLER. AL K. RODGERS. On the evening of Tuesday, Sept. 2, an informal dinner was held at the University Club, Seattle, Wash., at which the Secretary of the Institute was present, and a valuable and interesting conference took place concerning the recent activities of the Institute and the relations of the Institute management to the Local Sections. SOUTHERN CALIFORNIA LOCAL SECTION. Executive Committee. THEODORE B. COMSTOCK, Chairman SEELEY W. MUDD Vice-Chairman. FREDERICK J. H. MERRILL, Secretary-Treasurer, 300 Germain Building, Los Angeles, Cal. C. COLCOCK JONES. FRANK ROBBINS. Maintains headquarters at 300 Germain Building, Los Angeles, Members of the Institute are invited to visit these headquarters whenever they are in the city. A reception was held at the headquarters of the Section on Wednesday, Sept. 10, at 8 p.m., to meet the Secretary of the Institute and discuss Institute activities and affairs. Light refreshments were served, and about 20 members of the Section attended.

Jan 10, 1913

By AIME AIME

THE coal classification session* on Monday morning, Feb. 17, was opened by a paper by M. R. Campbell, entitled "Natural Groups of Coal and Allied Fuels," in which he pointed out, by means of graphical presentation of selected proximate analyses of coal, that coals can be classified on the basis of their moisture content. He proposes four groups of coal, brown coal, hydrobituminous, bituminous, and anthracite, each subdivided into two or three sub-groups. In a written discussion of this G. H. Cady, of the Illinois Geological Survey, showed that there is, in general, a progressive decrease in the moisture of Illinois coals from north to south, and that it would be very difficult to draw any arbitrary line dividing the coals of the State into two groups on the basis of moisture content.

Jan 1, 1930

By R. E. Fryxell, E. C. Duderstadt, P. K. Conn

Permeation rates for nitrogen through are-cast tungsten were measured in the temperature range 1800° to 2600°C at nitrogen pressure differentials of 1.0 and 0.1 atm. Gas chromatography was used to measure the quantities of nitrogen which permeated through 0.26-and 0.53-mm-thick membranes. Permeation rates were proportional to the difference between the square roots of the nitrogen pressure on each side of the membrane and inversely proportional to membrane thickness, indicating that atomic nitrogen was the difjusing species and that diffusion was the rate-limiting step of the process. Permeation coefficients calculated from the rates may be represented by the equation: where P is expressed in the units cu cm (stP)-mm per 1/2 sq cm-min-atm"' and 70.0 * 0.8 is the activation energy in kcal per mole of permeating species. In a previous paper' permeation rates were reported for hydrogen and for oxygen through tungsten. The permeation cells used for the hydrogen measurements were suitable for measuring nitrogen permeation under similar conditions, so the study was extended to include nitrogen. Permeation rates of nitrogen through the polycrys-talline arc-cast tungsten membranes were measured in the temperature range 1800" to 2600°C using two membrane thicknesses and two nitrogen pressure differentials. Permeation coefficients were calculated and the activation energy of the process determined. THEORY For diatomic gases which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at an elevated temperature where bulk diffusion is the rate-limiting step of the process is given by the equation: where: q = total amount of gas permeating a membrane, P = temperature-dependent permeation coefficient, A = area of membrane, t = time, p1 = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, and d = thickness of membrane. When bulk diffusion is the rate-controlling step, and the solubility of the gas obeys Henry's law, a further relationship is that, for any given temperature and pressure, the permeation is the product of diffusivity and the amount in solution. The permeation coefficient, P, is temperature-dependent according to the equation: where: Po = permeation constant, Q = activation energy, R = gas constant, and T = absolute temperature. EXPERIMENTAL PROCEDURES Cell Design and Experimental Apparatus. Two of the permeation cells used for the previous measurements of hydrogen permeation are shown in Fig. 1. Each consisted of a cylindrical chamber divided into two parts by a permeation membrane fabricated from high-purity (>99.9 pct W) wrought tungsten sheet made from vacuum arc-cast tungsten. The membrane in one cell was 0.26 mm thick and the other was 0.53 mm. The fabrication of these cells was described previously.' The permeation cells were mounted vertically in a high-temperature tungsten resistance furnace and the membranes and the center portions heated to test temperatures. Temperatures were measured by sighting an optical pyrometer on the edge of the membrane through a small hole in a tungsten plate which was fastened to the side of the cell. This arrangement provided an approximate black-body condition and eliminated the need for emittance corrections. Appropriate corrections were made for the quartz window through which the temperatures were measured. Argon gas flowed through the 10-liter volume of the furnace at the rate of 4.7 liters per min. An impurity

Jan 1, 1969

By A. W. Asman

The problem of balanced design in a belt conveyor has been under constant study. Increased use of this method of transport in recent years has stimulated investigations. Conveyor belt, power transmission and other machinery should be adequate to perform the required service. All components of the belt conveyor should work as an efficient unit moving its load continuously between terminals. As part of a long term research project on belt conveyors, Hewitt-Robins established in 1954 a 2-year grant at Pennsylvania State University. Under terms of the grant, certain fundamental phenomena were to be studied. This work evolved a new concept in belt conveyor power determination based on the principle of belt tension. The Penn State contract furnished the foundation for later more detailed studies. From these most recent investigations, more specific factors were defined. In the final analysis, all of the data collected has been worthwhile in belt conveyor design. Units now operate over long distances at speeds of over 800 fpm. Long high lifts are commonplace. Where vertical or inclined shafts were the rule, belt conveyors receive first consideration. Although belt conveyors have moved forward rapidly, the future will see a tremendous gain in their use. The ideal test belt conveyor would be several thousand feet in length and have a maximum tension of at least 70,000 lb., Also, this conveyor should be horizontai and have a variable feed rate of more than one material. Data from such a field belt conveyor combined with laboratory information would permit accurate analysis. Since this type of conveyor was not available, many field locations were visited: An alternate would have been to erect a closed circuit system in the laboratory. Either method had limitations and the first was selected as having the best possibilities. Manufacturers of conveyor belting and machinery basically have been using the same horsepower formula. As more information became available from field installations, factors in the basic formula were modified. Practically all conveyors are designed today by adding together the horsepowers required to move the empty belt, move the load horizontally, and elevate the load. In selecting size of drive motor, the first two elements are relatively unimportant if the last is large. However, it is the combination of

Jan 1, 1961

THE man who forgot to mail the letters his wife gave him was for once justified at Tulsa, for envelopes, scratch paper and tablecloths were all in demand and through the two days of the meeting of the Petroleum Division, pencils were busy everywhere sketching out diagrams, drawing curves, figuring, or just taking notes. Those attending took the serious papers seriously, and discussion was wide-ranging but pointed. Despite the highly technical character of the papers presented, the chairmen had never to call for discussion; it was only necessary to say the paper was open for it. Both days the meetings lasted until after five in the afternoon, and it was enthusiastically voted to advance the meeting hour on Friday, in order to give more time. In all, ten papers, abstracts of which appeared in MINING AND METALLURGY for October, and copies of all but two of which were available in print, were presented in the two days, and no more could have been handled to advantage in that time. All but one of these dealt with problems of production engineering. That, the opening paper, was a general review of demand, supply and price in 1928, by Campbell Osborn, in which he argued for the price control of production and showed how the economic conditions determined development. J. Elmer Thomas presented a carefully prepared review of the same data, but came to somewhat different conclusions as to trend, and J. E. Pogue pointed out that in recent years it has been the manufacturing rather than the producing industries that have been notably profitable. These and other discussions were too long to be reported here, but will be printed in full later.

Jan 1, 1928

By A. Raja, C. C. Harris

Apparatus for maintaining constant — but adjustable — pulp level and rate of froth removal are described. The results of preliminary experiments into the effect of scraping speed on the rate of solid and liquid recovery with a semi-batch system are presented. Glass spheres restricted to a narrow size range is the solid under investigation. Graphical methods for estimating the mass of recoverable material and the zero error are given. The semi-batch procedure1 is extensively used in laboratory flotation testing, though the method is subject to variability of moderate severity. Raffinot2 concluded from a statistical study of the difference between replicate tests, that the ptincipal source of errot was the test itself and not sampling or chemical analysis. These differences can be ascribed principally to changes in pulp volume and reagent concentration, and uncontrolled rate and depth of scraping. Semi-batch testing has been criticized1 on these grounds as a means of investigating flotation kinetics. This paper discusses and describes modifications to laboratory flotation equipment which reduce the number of manual operations and lead to improved control. Kinetic studies were the primary reason for developing the apparatus described. It should, however be a useful aid in normal flotation testing. Some preliminary results of experiments are presented.

Jan 1, 1967

Jan 1, 1911

By Yeatman, Pope

FOR many years geologists have felt that mining companies should adopt a more liberal policy in the publication of their reports. The increasing usefulness of the geologist to the mining profession in recent years demands that consideration be given to this question. Prior to 1900, the call for geologists of high reputation by mining companies was probably mainly in connection with lawsuits arising from the interpretation of rights or ownership as defined by the "Law of the Apex," and from problems such as finding the continuation of the vein or whether the vein followed was the main one or a branch. Later, outside of legal questions, the most intensive and general use of their services arose from the search for oil. Geologists to determine the position of the formations

Jan 1, 1938

By W. S. Holt, E. T. Tkac, R. A. Grange

QUANTITATIVE knowledge of the time element involved in austenite transformation in a particular steel provides a sound basis for understanding and planning heat-treatment. Such knowledge is conveniently obtained by measurement of austenite transformation as it occurs at each of a series of temperature levels. The results of these measurements usually are summarized in the form of the now familiar isothermal transformation diagram (I-T diagram, TTT diagram, or S-curve). Although a considerable number of such diagrams already have appeared in the literature, there remain many compositions of commercial importance for which no I-T diagram is available. The diagram for many such steels may be predicted from published data with sufficient accuracy for most practical purposes, but for others no satisfactory prediction can be made because the effect on austenite transformation of one or more of the important alloying elements present is not well enough known. Such a steel is Nitralloy, Type 135-Modified, which, containing about 1.25 per cent aluminum, differs from any whose I-T diagram has been published. This paper presents results of a study of the isothermal transformation behavior of a sample from a commercial heat of this aluminum-chromium-molybdenum steel, together with pertinent supplementary data including the equilibrium transformation temperatures (Ae3 and Ae1), the temperature range of martensite formation, and the end-quench hardenability. These data are directly applicable to the heat-treatment of this type of steel and are of interest in revealing some of the fundamental effects of aluminum as an alloying element in steel. MATERIAL All specimens were prepared from a 13-in. diam bar forged from a 5 by 5-in. billet from a commercial heat made in an electric arc furnace. The composition of the bar was; C, 0.41 per cent: Mn, 0.57: P, 0.016: S, 0.005: Si, 0.24: Ni, 0.17: Cr, i.57: MO, 0.36: Al, 1.26. The forged bar was normalized from 1750°F (955°C) and then tempered for one hour at 1200°F (650°C), this tempering treatment having been given to facilitate the machining of specimens. EQUILIBRIUM TRANSFORMATION TEMPERATURES In hypoeutectoid steel the minimum temperature at which austenite is completely stable, Ae3, and the maximum temperature at which austenite is completely unstable, Ae1, are of great significance in heat-treatment. Since these temperatures are dependent upon com-

Jan 1, 1946

By P. H. Mell

THE little village, from which this formation receives its name, is situated on a bluff of the Alabama River, 175 feet above water level. This bluff is a portion of high table land that begins in the western portion of Choctaw and extends through Clarke and Monroe counties. We find points on this ridge more than 100 feet higher than Tuscaloosa, and nearly as high as the Tennessee River at Tuscumbia. Through this the Alabama River cuts its way, exposing a beautiful cross-section of the strata, of which the accompanying sketch may give some idea. The fossils are found about 75 feet below the surface and 100 feet above the level of the river. There are seven distinct strata. 1. The lowest, extending from the water's edge up the bluff 80 feet, is a soft calcareous rock containing about 15 per cent. of carbonate of lime, with occasional specks of mica. In this a few Ostrea, Turritellce, and Flustrce were found, but so friable as to fall to pieces when handled. 2. Next comes a stratum varying from 2 to 8 feet, consisting of

Jan 1, 1880

By G. H. Wigton

THE oxidized ores of the Chief Consolidated Mining Co., in the Tintic mining district, have never yielded to metallurgical treatment by any standard method except smelting. These ores occur in comparatively small, irregular, siliceous replacements in limestone, and carry silver, lead, and gold as the principal valuable metals. But smelting methods. are unsatisfactory, as the lead smelters heavily penalize the large amount of silica in the ore, and the copper smelters do not pay for the lead in the ore; therefore, an alternative treatment method was sought. In 1916, a metallurgical research department was organized under; the direction of the writer. Many standard metallurgical methods were investigated but, on oxidized ore, none yielded extraction great enough to make its use feasible. During some chloridizing-roasting experiments in 1916, made in an assay muffle, the writer noted that large proportions of the silver, lead, and gold were volatilized from certain oxidized ores. The possibility of volatilizing the metals and collecting them in the form of a concentrated fume was then studied. But, as it was shown that satisfactory chloride-volatilization would be limited to a furnace feed with a high fusing temperature of the non-volatilizable constituents, and as the results obtained in a rotary kiln with the admixture of common salt with the ground ore were inferior to muffle tests, further volatilization experiments were discontinued until 1920. During this interval, an experimental sulfidizing and flotation plant was operated. After the cessation of attempts to float the oxidized minerals, chloride-volatilization experiments were resumed. The highly infusible flotation. tailing from the operation of the flotation mill was used for furnace feed. The first tests made on flotation tailing mixed with 10 per cent. common salt showed -nearly complete lead and gold volatilization but considerably less volatilization of silver than in muffle tests. In attempts to increase the silver extraction, the percentage salt in the furnace feed was varied, and it soon became apparent that the use of smaller percentages of salt raised the fusion temperature of the furnace charge and thus,

Jan 8, 1925

By K. A. Grange, W. S. Holt, E. T. Tkac

Quantitative knowledge of the time clement involved in austenite transformation in a particular steel provides a sound basis for understanding and planning heat-treatment. Such knowledge is conveniently obtained by measurement of austenite transformation as it occurs at each of a series of temperature levels. The results of these measurements usually are summarized in the form of the now familiar isothermal transformation diagram (I-T diagram, TTT diagram, or S-curve). Although a considerable number of such diagrams already have appeared in the literature, there remain many compositions of commercial importance for which no I-T diagram is available. The diagram for many such steels may be predicted from published data with sufficient accuracy for most practical purposes, but for others no satisfactory prediction can be made because the effect on austenite transformation of one or more of the important alloying elements present is not well enough known. Such a steel is Nitralloy, Type 13s-Modified, which, containing about 1.25 per cent aluminum, differs from any whose I-T diagram has been published. This paper presents results of a study of the isothermal transformation behavior of a sample from a commercial heat of this aluminum-chromium-molybdenum steel, together with pertinent supplementary data including the equilibrium transformation temperatures (Aeaand Ae,), the temperature range of martensite formation, and the end-quench harden-ability. These data are directly applicable to the hcat-treatment of this type of steel and are of interest in revealing some of the fundamental effects of aluminum as an alloying element in steel. Material All specimens were prepared from a 1 1/4 i-in. diam bar forged from a 5 by 5-in. billet from a commercial heat made in an electric arc furnace. The composition of the bar was; C, 0.41 per cent: AIn, 0.57: P, 0.016: S, 0.005: Si, 0.24: Ni, 0.17: Cr, I.j7: Mo, 0.36: All 1.26. The forged bar was normalized from r750°F (95s°C) and then tempered for one hour at rzoo°F (650°C), this tempering treatment having been given to facilitate the machining of specimens. Equilibrium Transformation Temperatures In hypoeutectoid steel the minimum temperature at which austenite is completely stable, Aep, and the maximum temperature at which austenite is completely unstable, Ael, are of great significance in heat-treatment. Since these temperatures are dependent upon com-

Jan 1, 1948

By W. S. Holt, K. A. Grange, E. T. Tkac

Quantitative knowledge of the time clement involved in austenite transformation in a particular steel provides a sound basis for understanding and planning heat-treatment. Such knowledge is conveniently obtained by measurement of austenite transformation as it occurs at each of a series of temperature levels. The results of these measurements usually are summarized in the form of the now familiar isothermal transformation diagram (I-T diagram, TTT diagram, or S-curve). Although a considerable number of such diagrams already have appeared in the literature, there remain many compositions of commercial importance for which no I-T diagram is available. The diagram for many such steels may be predicted from published data with sufficient accuracy for most practical purposes, but for others no satisfactory prediction can be made because the effect on austenite transformation of one or more of the important alloying elements present is not well enough known. Such a steel is Nitralloy, Type 13s-Modified, which, containing about 1.25 per cent aluminum, differs from any whose I-T diagram has been published. This paper presents results of a study of the isothermal transformation behavior of a sample from a commercial heat of this aluminum-chromium-molybdenum steel, together with pertinent supplementary data including the equilibrium transformation temperatures (Aeaand Ae,), the temperature range of martensite formation, and the end-quench harden-ability. These data are directly applicable to the hcat-treatment of this type of steel and are of interest in revealing some of the fundamental effects of aluminum as an alloying element in steel. Material All specimens were prepared from a 1 1/4 i-in. diam bar forged from a 5 by 5-in. billet from a commercial heat made in an electric arc furnace. The composition of the bar was; C, 0.41 per cent: AIn, 0.57: P, 0.016: S, 0.005: Si, 0.24: Ni, 0.17: Cr, I.j7: Mo, 0.36: All 1.26. The forged bar was normalized from r750°F (95s°C) and then tempered for one hour at rzoo°F (650°C), this tempering treatment having been given to facilitate the machining of specimens. Equilibrium Transformation Temperatures In hypoeutectoid steel the minimum temperature at which austenite is completely stable, Aep, and the maximum temperature at which austenite is completely unstable, Ael, are of great significance in heat-treatment. Since these temperatures are dependent upon com-

Jan 1, 1948

By S. P. Ray, B. D. Sharma

THE activation energy values for self-diffusion in pure metals have been correlated with a number of physical properties such as melting points,1 valences,' Debye temperatures,3 and cohesive energy densities.4 Extending the melting point correlation, the self-diffusion activation energy values for the alloys can be similarly correlated with the solidus temperatures. For metals and alloys which exhibit phase transformations, such a correlation is not feasible because of the uncertainty of various physical properties of the corresponding phases. Using thermodynamical approach, Ardell5 calculated the hypothetical melting points of the low melting phases of the polymorphic metals. However, these calculated melting points do not show reasonable correspondence with the activation energy of self-diffusion. Recently, a new approach treating metals and alloys as electron concentration phases has been developed by Engel6 and Brewer.7 These workers have attempted to correlate the crystal structures with the electron configurations of the atoms existing either in ground state or in an excited state of low promotion energy. The basic postulate of this theory is that whereas the contribution to the bonding of the metal comes from the interaction of both d and (s-p) electrons existing either independently or in hybridized states, the existing crystal structure is controlled by the (s-p) electrons alone. Specifically, a metal is supposed to crystallize in bcc, hcp, or fcc phase provided the metal has one, two, or three valence electrons per atom in the (s-p) configurations. The diamond, or ZnO and ZnS structures, occur with four (s-p) electrons per atom. Secondly, the contribution of d electrons to bonding is supposed to increase with atomic number

Jan 1, 1970

By AIME AIME

SOME 65 members of the Institute, including most of the Local Section delegates and several Directors and officers, were on hand for the Annual Business Meeting of the Institute held in the Engineering Societies Building on Monday, Feb. 21, at 4:30 p.m., immediately following the second session of the Local Section Delegates Conference. President Mathewson presided. The meeting was largely taken up with the presentation of committee re- ports, discussion of which was invited. F. E. Wormser presented the report of the Admissions Committee ; Philip Kraft, Papers and Publications Com-

Jan 1, 1944

By AIME AIME

Award of a Gold Medal : to the Institute. The Jury of Awards of the Jamestown Ter-Centennial Exposition has conferred a gold medal, the highest distinction within its power,. on the American Institute of Mining Engineers for the excellence of its publications during the past decade. ; A half-tone photographic reproduction of both sides of the medal is given in the accompanying illustration.

Jan 7, 1908

The plans involve about ten technical sessions, a day spent in Cripple Creek and in Pueblo, where there will he optional visits devoted to steel, non-ferrous metals, etc.; half-a-day each to mills in Colorado Springs district and an auto trip to the top of Pike's Peak. Finally, a day at Leadville devoted to visits, including the molybdenum works.

Jan 4, 1918

By Waldemar Lindgren

Discussion of the paper of WALDEMAR LINDGREN and CLYDE P. Ross, presented at the New York meeting, February, 1916, and printed in Bulletin No. 106, October, 1915, pp. 2171 to 2190. WALDEMAR LINDGREN, Boston, Mass.-I happened to go down to Cuba rather unexpectedly in the winter of 1914, and spent a few very interesting days at Daiquiri and Mayari. To C. F. Rand and his associates I am greatly indebted for permission to visit the mines and for many courtesies received. A few months after that, I met Professor Kemp who informed me that he had just returned from a geological study of Daiquiri. We talked over what to do in a case like that. We both liked to publish our opinions, and so finally agreed to write two papers entirely separately, I not knowing any of Professor Kemp's conclusions,1 and vice versa. We were rather interested in seeing what would happen. Of course, as might be expected, we disagreed on some points; not, of course, that we ordinarily disagree, but simply because when two men work in the same field and with different ideas, probably they are apt to vary slightly in their conclusions. Some years ago A. C. Spencer went down there for the military interim government and published the results of his study. His view of the origin of the deposit differed from that of Professor Kemp and from mine. So here are three different results obtained by three different geologists. Such differences in opinion on obscure subjects sometimes tend to bring geology into disrepute. It is perhaps not surprising that different opinions have been expressed, for this occurrence of iron ore is one of the most difficult to explain that I have ever seen. MAX ROESLER, Great Neck, L. I.-I had the opportunity this summer of spending about two months down at the Juragua deposits, and studied them with the idea of writing a paper on them, which I hope will come out later. The interpretation of the occurrence at Ocania Mine is the thing which particularly struck me, in the last paper. At the Ocania Mine we may have these large blocks of limestone which have been utterly and entirely altered, to a remarkable extent.

Jan 5, 1916

By R. F. Rolsten

VAN Arkel 1 prepared ductile tantalum by the thermal decompoiition of tantalum pentachloride on a resistively heated wire (2000° C) in an evacuated bulb maintained at 100°C. Burgers and Basart2'3 observed the formation of a mixture of tantalum carbide and free metal when a carbon deposition base was used. campbel14 suggested the thermal decomposition of the iodide if a lower decomposition tem- perature was desired. To date, the details for preparing high-purity iodide tantalum have not been disclosed. EXPERIMENTAL The tantalum to be purified was symmetrically placed around the clear quartz deposition surface centrally located within a 64 mm cylindrical Vycor bulb. The deposition vessel usually employed5 was modified6 by incorporating a reentrant fin,mer in place of the customary metal filament in the head

Jan 1, 1960

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in