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By H. S. Kalish, F. J. Dunkerley

INTRODUCTION AND PREVIOUS WORK THE determination of the low temperature tensile properties of tin and tin-lead alloys was initiated as part of an extensive research program on the phasial equilibria of tin binary systems below 13.2°C and the property changes associated therewith. A survey of the literature revealed that, although some room temperature tensile data were available for tin and a few tin-lead alloys, there existed no survey report of the low temperature tensile properties of these alloys. Accordingly, the tensile data for tin and a series of pure tin alloys containing from 0.01 to 50 pct lead were measured at eleven temperatures from -196 to +20°C and are presented here in survey form. In addition to the importance of these tensile data as a preliminary to certain fundamental research, this information promises also to be of commercial importance because of the 'extensive use now being made of tin-lead solders in refrigeration and gas liquefaction equipment. Occasional failures of the solders in low temperature service have been attributed by some metallurgists to low temperature mbrittlement, while others hold that failure results from the transformation of the tin-rich phase of the solder from the solid white (beta) to the powdered gray (alpha) form. From the data previously available in the literature, neither of these explanations can be completely corroborated. Cohen and van Lieshout1 have established the beta to alpha tin transformation at 13.2°C and have shown that strain accelerates the transformation. Further, they showed that although I pct lead retarded the transformation, it was not eliminated. It will be pertinent, then, to note whether the beta to alpha transformation of the tin-rich phase will occur in a short-time tensile test. Polanyi and Schmid2 studied the tensile . properties of tin single crystals at -185°C and report that tin is brittle at-this temperature. In 1946, Kostenets3 reported that pure tin was brittle at -196 and -253°C, while lead remained ductile at both these temperatures. He also studied the tensile properties of tin-lead alloys containing from 10 to 75 pct lead at -253, -196 and +17°C. The ultimate tensile strength increased more than two times in going from room temperature to -196°C and about three times that value on further cooling to -253°C. All the alloys were brittle at -6°C except those containing more than 75 pct lead. Even at -253°C, the 75 pct lead alloy retained 36 pct elonga¬tion in a 30 mm-ga. length. Creep is also an important phenomenon

Jan 1, 1948

By Clarence Zener

Contents Page General Principles................................................................. 551 Equilibrium Diagrams......................................................... 551 Nucleation................................................................... 553 Kinetics of Phase-boundary Propagation......................................... 553 Kinetics of Growth of New Phase............................................... 556 Spheroidization............................................................... 560 Pure Iron-carbon System........................................................... 561 Formation of Pearlite.......................................................... 561 Interlamellar Spacing........................................................ 562 Pearlite C-curve............................................................. 563 Bainite Formation............................................................. 565 Formation of Martensite....................................................... 570 Loss of Tetragonality of Martensite.............................................. 570 Effect of Alloys upon Decomposition of Austenite..................................... 572 Pearlite...................................................................... 572 Bainite and Martensite......................................................... 574 Time-temperature-transformation Curves............................................. 576 Appendix A............................................................. ......... 579 Appendix B....................................................................... 580 Appendix C....................................................................... 580 The present investigation started in an attempt to understand certain details of the decomposition of austenite, and of the effect of alloying elements thereon. As the investigation proceeded it became apparent that not only these details, but all the general features of austenite decomposition, could be understood in terms of fundamental physical principles. Since the direct applicability of these physical principles has not been previously recognized, it was decided to incorporate the original results of the investigation into a review of the general subject of the kinetics of austenite decomposition. This review constitutes the present article. An extended summary of the results is given on pages 576 to 579. This article, which deals with the kinetics of phase transformations, may appropriately be considered as a sequel to two recent articles1,2 from this laboratory on the equilibrium relations in medium alloy steels.

Jan 1, 1947

By J. F. Wolff

CARL ZAPFFE, Brainerd, Minn. (communication to the Secretary*).¬Unless one has actually directed explorations for iron ore, it is doubtful whether the importance of Mr. Wolff's paper, the value of the information contained, and the large amount of detail work involved in what is set forth can be fully appreciated. It is indeed rare to get such a com-

Jan 3, 1917

By John Jermain Porter

The chief purpose of this paper is to indicate the laws governing the fuel-economy of the cupola, to examine the feasibility of some of the proposals for increasing its fuel-economy, and to show that the conditions limiting fuel-economy here are altogether different from those prevailing in the blast-furnace. The two methods available for studying the thermal efficiency of the cupola and determining the factors limiting fuel-economy are: 1, by the determination of the total heat-balance; and 2, by the application of the theory of critical temperatures. The case selected as an example represents a cupola operating under fairly efficient conditions. The data are as follows : Cupola, GO in. in diameter, 15 ft. high to the charging-door, with a 9-in. lining. Bed-charge, 2,000 lb. of coke and 4,000 lb. of iron. Subsequent charges, 400 lb. of coke and 4,000 Ib. of iron. Total number of charges, 20. There was 800 lb. of coke recovered from the drop, hence the total coke burned is 8,800 lb., or 0.11 lb. of coke per Ib. of iron. Coke contains 90 per cent. of fixed carbon and 2 per cent. of moisture. 300 1b. of kindling-wood is used in lighting. 80 lb. of limestone (95 per cent. of CaCO,) is used per charge, or 0.02 lb. per Ib. of iron. Melting-loss, 4 per cent.; distributed thus : Fe, 3.5; Si, 0.25; Mn, 0.25 per cent. Average analysis of top-gases : CO2, 15.1; CO, 10.0 per cent. Average temperature of top-gases, 1,600" F. Temperature of air and stock charged, 60" F. Dew-point of air, 50 F. The items entering into the total heat-balance and their calculation are as follows: 1. Heat of combustion of fuel.—Total heat evolved = 14,580 x lb. of carbon burned + 7,200 X Ib. of wood burned. Hence B.t.u. per lb. of iron charged =

Jan 1, 1913

By C. D. King

A QUARTER century ago this country was producing an extraordinary quantity of iron and steel, with a decisive influence on the outcome of the first World War. Today this country is again demonstrating its industrial capacity with telling results. If this lapse of time has confirmed the opinion that man learns little from experience with respect to human relationships, at least we can derive some consolation from the knowledge that in the same period we have made huge strides industrially, and particularly in the steel industry. The differences represented by 25 years are striking, and have resulted from a multitude of changes that have contributed to the present-day high state of our pig iron and steel manufacture.

Jan 1, 1944

By AIME AIME

SECOND only to the February Annual Meeting of the Institute are the Regional and Divisional meetings held in the fall of each year. Six such gatherings are scheduled in the next the months, with something likely to interest every member of the Institute. A brief résumé of the programs follows. Regional Meeting Vancouver T HE regional meeting of the Institute will be held at Vancouver, Sept. 13 to 20, in conjunction with the annual western meeting of the Canadian Institute of Mining and Metallurgy. The pro gram appeared on page 350 of MINING AND METALLURGY for July and-proof of careful preparation-a month later re- quires no correction and little elaboration. On the technical side there are few changes. A new item on the Wednesday morning program is the paper, "Investigation of Residential-type Stokers," by H. F. Yancey, supervising engineer, Northwest Experiment Station. U. S. Bureau of Mines, Seattle. As to entertainment the meeting is taking on some most pleasurable aspects. Two notable excursions have been arranged.

Jan 1, 1937

By R. W. Powers, M. V. Doyle

ThE solution of a diatomic gas such as 0, or N2 in a metal usually follows Sieverts' law; i. e., Here C is the solute concentration at equilibrium and P, the gas pressure. The proportionality constant Ks is also the equilibrium constant for the reaction 1/2 02 (at pressure, P) - 0 (in solution at [21 concentration., C). to use oxygen as an illustrative gas. Sieverts' law is therefore interpreted to indicate that diatomic gases go into metallic solution atomically and that the solute "gas" atoms interact negligibly with each other. Of course, this interpretation is strictly valid only over the temperature interval in which the reaction indicated in [Z] can be investigated. At temperatures several hundreds of degrees below this interval, the possibility of interactions between solute atoms is conceivable. Indeed, from internal-friction measurements some evidence for the existence of groupings of oxygen atoms in tantalum solid solutions was presented a few years ago.1,2 Over a range of solute concentration, the experimental oxygen internal-friction peak in tantalum, measured as a function of temperature at constant frequency of vibration, can be described as the sum of two elemental peaks, each corresponding to a separate relaxation process. At 0.7 cps, the height of the elemental peak found at 137°C is proportional to the oxygen content, whereas the height of the one at 162°C varies as the square of the oxygen concentration. The 137°C peak was presumed to arise from the stress-induced ordering of oxygen atoms among various classes of octahedral sites in the manner proposed by Snoek.3 The 162°C peak was attributed to a somewhat similar stress-induced ordering process, in which each oxygen atom was interacting with a neighboring oxygen atom. Similarly, the experimental peak due to nitrogen in tantalum can also be described as the sum of two peaks. The height of one varies as the nitrogen concentration and the other as the square of this quantity. In fact, some evidence of solute interactions exist for all oxygen and nitrogen solid solutions of Group V transition metals. However, the interaction energy was not obtained previously for any alloy. The determination of this quantity, as a part of a more intensive study of the interaction between oxygen atoms in solid solution in tantalum, is reported in this paper. PRINCIPLE OF THE EXPERIMENT Consider an equilibrium in a solid solution of tantalum between oxygen atoms which are bound together pairwise and those solute oxygen atoms which are not so associated. 20 (Ta) - O2 (Ta) [3]

Jan 1, 1960

By L. S. Darken

IN the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be repre-sented satisfactorily by the simple equilibrium expression K - (p1)p1 (p2)p2 . (R1)r1(R2)r2 . where (P) denotes the concentration of a product and (R) the concentra-tion of a reactant in the reaction r1R1 + r2R2 + . . . Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a com-ponent is not proportional to its true mol fraction, But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple com-ponents and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satis-factorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature as ionization or the occurrence of polar and nonpolar molecules-are presumably less effective in metal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By P. G. Shewman, T. L. Wilson

Using published surface-diffusion (D,) data and published sintering equations, it is shouln that surface difusion should dominate the neck-growth stage of intering for all materials in which D, has been measured (six metals and A1as). Also, grain boundary diffusion can be expected to contribute appreciably to shrinkage and possibly to neck growth below some critical temperature of the order of 70 pct 01- the absolute melting temperatuve. In view of the widespread conclusion in previous sintering work that volume diffusion dowzinates neck gvowth, experiments were conducted using spherical copper powders to test this conclusion. Scaling studies on neck growth at 950°and 1020°C clearly demonstrated that suyface diffusion dorninates. Kinetic studies on shrinkage gave more equivocal results that indicated an increasing role of' grain boundary transport at lower temperatures. Five diarszeters from 100 to 300 u were used in the scaling sludy and a temperature range of -650' 10 950 C was covered in the shrinkage studies. All experiments were conducted in dvy hydrogen. In 1949, Kuczynski published his now classic paper on the determination of the transport mechanism in sintering from the time laws of neck growth. In the interim, these laws have been applied to many systems and slightly modified by several authors. Essentially all these authors concluded that, for crystal- line materials, the dominant transport mechanism in neck growth is volume diffusion. This stems from the observation that the neck radius increases about as t"5 and that the activation energy approximates that for lattice diffusion. A related but independent series of studies stems from Mullins' rigorous analysis of the growth of the groove formed where a grain boundary meets a free surface." xperimental work stemming from this analysis has shown that for each crystalline material studied (Au, Ag, Cu, Ni, Fe, Pt, Al2O3) surface diffusion was clearly the dominant transport mechanism for groove widths up to the order 10 to 20 p. The ratio of the quantity of material being carried by lattice diffusion to that carried by surface diffusion increases linearly with the groove width, so surface diffusion is dominant for all widths under 10 to 20 u. The analysis of the relative contributions of surface and volume diffusion to grain boundary grooving, and to neck growth in sintering, shows that they are quite similar. Thus, using the available surface-diffusion data and the approximate equations of Kuczynski, or the more rigorous recent equations of Nichols and Mullins, 3 it can be shown that the small necks between particles must grow almost entirely by surface diffusion. The purpose of this study was to re-examine the basis for the conclusion that the neck-growth stage of sintering proceeds by volume diffusion. Using spherical copper powders, of several different diameters, precise experimental measurements were made of both neck growth and shrinkage. Application of Herring's scaling laws to the neck-growth data clearly indicated that neck growth occurred by surface transport, even though the neck radius increased as or Using the recent analysis of Mullins and Nichols as well as published data on surface diffusion, it is shown that the observed time law, as well as actual rate of neck growth, can be satisfactorily explained by a surface-diffusion mechanism.

Jan 1, 1967

On the following pages are abstracts of papers published by the Institute during the year 1934 as TECHNICAL PWLICATIONB, CONTRIBUTIONS, m bound volumes and in MINING AND METALLURGY. For abstracts of papers that appear In bound volumes in 1934 but that were published as TECHNICAL PWLICATIONS m 1932 or 1933, see the TRANSACTIONS for 1932 and the YEAR BOOK dated January, 1934. Many of the TECHNICAL PWLICATIONS have been reprinted In bound volumes Information regarding this disposition, and number of pages in each paper, may be found m the list beginning on page 92 Volume numbers are given as listed at the beginning of the index, page 99 The abstracts are grouped as follows:

Jan 1, 1935

By AIME AIME

MODERN metallurgy is an art and a science. The art is process metallurgy-extracting metals from their ores, refining them, and alloying them with one another and with certain nonmetals to produce thereby a variety of metallic materials which, owing to a wide range of useful properties, are for many purposes more valuable to man than the individual metals themselves; process metallurgy also includes shaping or otherwise treating metals and alloys to form objects useful to a complex industrial world. The science is physical metallurgy-organized knowledge of the constitution and internal structure of metals and alloys, of the relation of their composition and structure to properties, and of the laws, theories, and hypotheses that purport to explain this relation.

Jan 1, 1942

By Charles Barrett

SINCE 1925, when the preferred orientations in compressed aluminum were first determined1, 2 the orientations have been described as a fiber texture in which a face diagonal, [110], of the face-centered cubic lattice is parallel to the compression axis. Subsequent experiments have seemed to confirm this texture,3-5 and a number of theories (recently summarized in references 6 and 7) have been proposed to explain it and to relate it to the behavior of single crystals during compression. 3,8-11 The experiments reported in this paper prove that the orientations are not adequately described as quoted above-i.e., as a [110] fiber texture-although this is a first approximation to the actual texture. They also show that the texture cannot be thought of as a stable orienta-tion that is reached and maintained after a sufficient amount of deforma-tion. The actual texture, when studied in detail at successive stages of compression, indicates that a hitherto unsuspected range of orientations is present, both in the polycrystalline metal as a whole and in various individual grains in its interior, and that a state of dynamic equilibrium exists within this range. The reasons for the failure of previous theories to predict the actual texture become obvious when the heterogeneous nature of the flow is considered. In addition to the deformation texture, the manner of its develop-ment, and its theory, this paper presents data on the following related subjects: the identity of strain markings in aluminum; the orientation changes in aluminum single crystals during compression and a com-parison of these with the conditions in individual grains of a polycrystal-line specimen; the origin of asterism in deformed single crystals, which heretofore has been regarded as a distortion localized at the surfaces of slip planes; and the relation of plastic strain in individual grains in an aggregate to the strain of the whole.

Jan 1, 1939

By Gerald Edmunds

CASTINGS of pure metals and many alloys usually have a coarse-grained structure characterized by long columnar grains throughout the main body of the casting. Frequently, the surface exhibits finer, some-times nearly equiaxed grains, and such grains may also compose other parts of the casting. This paper deals primarily with determinations of the grain-orientation textures of the columnar and surface grains of polycrystalline zinc castings. It includes some results upon a cadmium casting and a magnesium casting. A hypothesis is devel-oped to account for the observations on columnar grains and to use as a basis for predicting orientations in other cast metals. A general description of the position of the columnar grains in castings is that their long axes are approximately parallel to the direction of the thermal gradient during crystallization. Thus, in cylindrical castings the columnar grain axes tend to be radial, and in large flat castings where most of the cooling is through one or both of the large mold surfaces they tend to be perpendicular to the mold surfaces. At the edges and corners the direction of heat flow and there-fore the position of the grains is more com-plex. Actually observation shows that even in castings made in flat molds the cooling seems to be somewhat irregular, since columnar grains tend to emanate from certain areas of the cooling surface, indicat-ing that thermal contact was better there than in neighboring areas.

Jan 1, 1940

By C. M. Smith

DELEGATES from 26 Local Sections and- Divisions of the Institute had three stimulating sessions during the Annual Meeting, a few topics still remaining to be discussed after the two Monday sessions.. The final session was held on Thursday morning. An abstract of the discussion will be transmitted to each delegate present. The topics included: Student relations. Section operation, membership, employment, MINING AND METALLURGY, a new nonmetallic minerals Division. licensing of engineers, and increased allotments of money to Local Sections. Some of the Sections felt that the present limit of $250 allotted to them - from the national treasury was insufficient to carry on their activities, and that this maximum should he increased. A resolution to this effect was passed for transmission to the Board of Directors.

Jan 1, 1935

By W. E. D. Jr. 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 31..4-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 19:36, 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 photo-graphed 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.

Jan 1, 1937

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

By AIME AIME

THE organization of the Board of Directors was effected Tuesday afternoon in ' executive session. Messrs. Bassett,. Buehler, Cates, Daveler, Eavenson, Eilers, Elliott, Evans, Guess, Lovejoy, Moulton, Rickard, Tally, Turner,, Wraith and Wright being pres¬ent. Messrs. Tally, Bassett, Rickard, Mathews and Cates were chosen to form the Executive Committe with Mr. Tally as Chairman, and Messrs. Krumb, Guess and Moulton for the Finance Committee with Mr. Krumb as chairman. Karl Eilers was reelected as Treasurer and H. Foster Bain as Secretary, after which the Directors adjourned for the usual dinner reported elsewhere. At the open session of the Board, at which in addition Messrs. Allen and McAuliffe were present, the work of organization was continued with appointments to committees as listed herewith. Various actions of the Executive and Finance Committees were confirmed, the budget for 1931 formally approved, the meeting dates for the year adopted, 34 new Members and Associates, 13 Junior Members and 31 Student Associates admitted by election and transfer and 29 resignations accepted.

Jan 1, 1931

[FUQUA, H. B. and Thompson, B. E.: Oil and Gas Development and Production in North Texas for 1933, 107, 320; for 1934, 114, 417 Oil and Gas Development in West Texas 114, 438 FURMAN, W. F.: Heat and Corrosion-resisting Alloys. Printed in Oil & Gas Jnl., June 13, 1935 Furnace-bottom sand, uniformity, 73, 390 Furnace control, Isley apparatus, M27, 502 Furnaces (See also Holt-Dern; Blast Furnaces; Roasters; Wirebar, etc.): annealing: electric, 89, 424 gas-fired, 89, 425 gas vs. wood for nonferrous metals, 89, 422]

Jan 1, 1936

By W. Hurst

What is entailed here is the extension of the sinzplified material balance formulas to encompass interference between oil fields. As previously reported, the ex-plicitness as so revealed for the cunzulative pressure drop as a function of all factors contributing to its change in the material balance equation, is now transcribed through the inter-conzmunicating aquifer to effect an increased pressure drop on an adjoining field by interference. Such is performed by mathematical analyses and the application of the Laplace transformations. What is accomplished is that the reiteration problems previously associated with interference studies are nullified, since volumetric changes for the fluids in situ are automatically adjusted by the explicitness so expressed, and what pertains to the superposition principle applies only to the impeded water drive upon a su.bject field, which is likewise incorporated in the over-all pressure drop that results. The mathematics treats with the rigorous solution of the problem, as well as with methods easily amenable to numerical interpretation by the practicing engineer. In all cases, however, what is deduced for areal extents, reveal interference between wells when time becomes large that further substantiate the analyses. Probably of equal significance, all variables and for/nation characteristics are accounted for. This applies to the differences in PVT analyses that occur from field to field and the physical parameters associated with the lithology of the reservoirs. The latter is deduced from a rigorous interpretation of the unsteady-state flow problem for sands of different permeabilities in series. Thus, what purports to be a trial-and-error calculation to include variations in sand conditions within the intercommunicating aquifer to define water drive has little importance compared to the designation of such paranzeters at the reservoir to constitute the essential criteria. INTRODUCTION In a recent publication, the reader has been introduced to the simplified material balance formulas,' It has been shown that the complexities formerly associated for identifying and determining reservoir pressure in the material balance relationship can be resolved by treating with the Laplace transformations, the inversion of which reveals pressure as an explicit function of all factors contributing to its change. For an under saturated oil reservoir, this constitutes an integrated effect from the inception of production; and for a saturated oil reservoir, such represents a survey traverse. However, what is most important, for the first time we are able to express the pressure change in a reservoir directly to the oil, gas and water produced, and to the physical parameters of the formation, in the same manner that reservoir pressure has served in the past to define well interference — which opens up this avenue of endeavor for investigating interference between oil fields. The occurrence of interference is by virtue of the juxtaposition of two or more oil reservoirs producing in the same aquifer. Thus, in any one field, the extended production so incurred creates a pressure lowering in the field, as well as in the aquifer, which can now be transcribed by these simplified material balance formulas to the adjoining reservoir to observe the increased pressure change so induced. These effects are retroactive from field to field, to reveal a pressure drop far in excess of normal depletion to evidence the interference pattern that can result. Such is the purpose for the present undertaking — to develop the mathematical physics treating with this phenomenon of interference between oil fields, employing the simplified material balance formulas. Since Ref. 1 often will be referred to in the text, it is identified as "The Simplification", in the same connotation that another paper has been referred to as the "Laplace Trans-formation. However, the amount of material to be covered in these passages is substantial; therefore, the total emphasis will be placed upon developing these fundamental ideas treating with interference rather than attempting to offer work curves, which always can be prepared. For the practical application of these simplified material balance formulas that form the framework of the present development, the reader will find a comprehensive treatment in the Appendix of Ref. 1, illustrating a factual field example. In essence, what is proposed by this presentation is to make available to the practicing engineer a simplified means to treat with interference between oil fields, independent of the complex machine computations that have attended such undertakings in the past. As the problem unfolds, a common pattern will be discernible, whereby the many reiteration processes that previously required computing devices are eliminated.