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By R. F. Mehl, C. E. Birchenall

SINCE Maxwell1 first considered the self-diffusion process in 1872 its importance in the kinetic theory of matter has been recognized. Until the discovery of isotopes in 1913, a direct measurement of this quantity seemed impossible. The only information that could be gathered indirectly was for gaseous systems for which the kinetic theory was well developed. When methods of direct observation be-came available, investigations on self-diffusion were carried out in condensed phases. In metals these data are presumably of potential importance in the study of recovery, recrystallization, creep, sintering, and related phenomena. Following the pioneer work of Von Hevesy2 and his collaborators, who determined the rate of self-diffusion in lead with the naturally occurring thorium B isotope, several metals have been investigated. Pb, Ag³, Au.6,5, and Cu6,7,8,9 are examples of isotropic crystals existing in only one phase modification. Anisotropy of diffusion has been demonstrated in Bil6 and Znll. This paper is a study of a single metal in two allotropic forms and also of self-diffusion in a body-centered cubic lattice. Despite the fact that the measurements in each of the papers cited on self-diffusion in copper seem to be internally consistent to about 10 to 15 pet, the curves reported by different authors differ by factors of 2 to 4 at the same temperatures. This uncertainty may account, in part, for the failure to establish a successful correlation between the self-diffusion rates and other physical characteristics of the metals. No satisfactory theory of metallic self- diffusion has as yet been proposed to account for all the existing data and to permit estimation in other metals. Experimental Part: Two units of radioactive iron were used in these experiments, each a mixture of Fe53 and Fe59 (12). Fe53 decays by K electron capture and the emission of an X ray with a half life of about 4 years. Fe59 emits two beta spectra, one with a maximum energy of 0.26 Mev, the other 0.46 Mev, and gamma rays of 1.1 and 1.3 Mev, with a half life of about 44 days. They were present in nearly equal concentration initially. The composite half life started at about 50 days and increased as the Fe59 decayed, leaving Fe55 relatively more abundant. After aging a year, the half life was too long to measure significant decay in a month. The absorption properties also changed with time. Because of the importance of the absorption coefficient in the diffusion calculations, it was necessary to determine this quantity frequently over the period during which these experiments were carried out. This correction was unsuspected at the time of publication of notesl3 on this work and accounts for the discrepancy in alpha iron and for part of the discrepancy in gamma iron.* * The data in the present paper supersede those given in the notes entirely. In one note the scale of log D was inadvertently reversed. In addition to the correction for the drift in absorption coefficient, the D values for gamma iron at low temperatures were high owing to insuficient correction for diffusion occurring during heating and cooling through the high temperature part of the alpha range at a rate much slower than that employed in the runs reported here. The high temperature alpha rates are much higher than the low temperature gamma rates and correspond to large equivalent times at these temperatures. These experiments were discarded and new measurements taken. Independent experiments with the same activity units indicated a radioactive contaminant in the iron, but exhaustive attempts to isolate and identify it chemically failed. These experiments? indicate † These experiments will be discussed in a later publication from this laboratory. that the contaminant represented only a trace of little importance in the diffusion results. The active iron was plated from an iron chloride solution. Enough of the solution was dropped on a 1% in. square of filter paper to wet it thoroughly.

Jan 1, 1951

By H. N. Treaftis, J. W. Cahn

THE previous determinations of the solvus of tin in solid lead disagree with one another by as much as 40°C or almost 10 at. pct. Even determinations that appear to be careful differ considerably in both the solubility and its temperature coefficient. Recent kinetic workl -3 on the rate of precipitation of tin from lead-tin alloys and thermodynamic work4 on the heat of solution of tin in lead have given some insight into the time necessary to reach equilibrium in this system. As this time is longer than that used in almost all previous determinations of the solvus, these determinations are questionable. Since the interpretation of recent kinetic results requires accurate values of the equilibrium solubility the present work was undertaken. DISCUSSION OF PREVIOUS RESULTS The methods used in previous studies may be placed into three classes: 1) Several alloys covering a range of compositions are allowed to reach "equilibrium" at a certain temperature.5-7 Some property, such as the X-ray lattice parameter of the lead-rich phase or the re- sistivity of the alloy, is then measured as a function of composition. The solubility limit for that temperature is taken to be that composition at which a discontinuity in the property occurs. However, the recent kinetic work has shown that tin precipitates in two stages. The first stage is rapid but leaves the lead still supersaturated. The second stage is very slow, and it seems from the equilibration times quoted by the investigators of the solvus that the end of the first stage of precipitation was usually mistaken for equilibrium. This is especially true at temperatures below 100°C where the first reaction is still quite rapid (from minutes to months), but where the second stage is so slow that very long holding times are required to reach equilibrium. Alternatively micrographic work8 on several alloys of different compositions seems to have given good results if done carefully. 2) The beginning of precipitation in a homogenized alloy is measured as it cools slowly8-10. Since reactions in solids undercool easily, such determinations will always give too low a temperature for the solvus. 3) Some property of an alloy is measured as a function of temperature while the alloy is above the solvus.5,9,11 The range of temperature can usually be extended slightly into the two phase region. Then the alloy is precipitated at a much lower temperature and slowly reheated. The solvus is taken to be the lowest temperature where the property of the reheated alloy is equal to that previously determined for the homogeneous alloy. Usually one also expects a discontinuity at the solvus in the temperature variation of the property for the reheated alloy. The difficulty in this method is the sluggishness of the dissolution process, and this method may give too high a solvus temperature. EXPERIMENTAL The phase boundary or solvus temperature was determined by a modification of method 3 for a series of chemically analyzed high-purity alloys, ranging from 5.1 to 26.4 at. pct Sn. The resistance, as a function of temperature, of a sample of homogenized alloy (which could easily be undercooled) was compared with the equilibrium resistance which that alloy sample attained after precipitation at room temperature followed by long isothermal anneals at various temperatures. Before each anneal the sample was rehomogenized and reprecipitated. The solvus temperature could be located to within 1°C as the intersection of the resistance vs temperature curves for the homogenized and equilibrium alloys. No attempt was made to locate the phase boundary more accurately since the limiting factor was the precision with which the alloys could be analyzed. This precision was ±0.1 wt pct Sn and corresponds to an error of 1 deg in temperature. This use of isothermal anneals differs from some of the previous investigations in which method 3 was used with baths of slowly rising temperatures. It was found early in the investigation that solvus temperatures tended to be high if the latter method was used even at extremely slow heating rates. For example a

Jan 1, 1961

By C. G. Dunn

Identification of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereo-graphic projection with one pole per orientation.' However, accurate data based on calculations of the positions of all {1001 planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. Method of Computing Orientation OF a Twin It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given in terms of two angle variables, two sets of which appear in the following equations: Polar Net Wulff Net x = , sin ?p cos Fbp x = r COS ?w y = r sin ?p sin Fp y = r sin ?w cos Fw % = r cos ?p z = r sin ?w, sin +, The three numbers z, y and z determine a length r as well as a direction (0, 4) in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 + L2)1/2, where h, k and I are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {Ioo} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3,4' Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A' being one of the four {112} or {III} type* first-order twills of S. The orientation of S—i.e., the positions of poles of (I00)

Jan 1, 1945

C. M. Bishop (Aircraft Div., A. V. Roe Cnnada Ltd., Toronto)—Reference is made to the coherency hardening of ß due to ß' and also to the hardening of ß due to a coherent precipitation of the a phase. What is meant by the term "ß'?" Would not the coherency hardening of ß during cooling be due to precipitation of a sub-microscopic dispersion of a, as is the case during reheating a ß-quenched alloy? I feel that these two phenomena are essentially the same mechanism, i.e., precipitation of a from unstable or supersaturated ß. From the text, it would appear that Tables III and IV are intended to show the effect of the martensite transformation on the properties of Ti-Mn alloys. Referring to Table 111, the ß-quenched alloys would contain a greater proportion of retained ß than would the equilibrated alloy. Could not the increase in properties be attributed to this, along with possible coherency hardening of the ß? In the same way, the structures referred to in Table IV contain ß from which they could derive their hardness. It would appear to be difficult, if not impossible, to assess the role of the martensite transformation from the data contained in these tables. F. C. Holden, H. R. Ogden, and R. I. Jaffee (authors' reply)—In reply to the first question raised by Mr. Bishop, the term "ß"' designates an apparent retained-p structure which is harder than it is after the most rapid cooling from the ß field. It is thought to be the result of a coherent precipitation of a. The mechanism by which hardening takes place is undoubtedly the same as that involved in the early stages of aging of a re-tained-p structure, and we are in agreement with Mr. Bishop on this point. The term "ß'" to designate the anomalously hard retained-ß structure was agreed upon at a symposium in 1953." The authors do not agree that the quantity of retained ß and/or ß' in the ß-quenched specimens of Table III is necessarily greater than that of the 600°C equilibrated specimens. The ß-quenched specimen has a structure which appears to be completely a' formed by the martensite reaction. It is recognized that there could be some retained ß (or ß') between the a plates if the M, temperature is below room temperature. This is unlikely for the 3.4 pct Mn alloy where the M, is known to be at about 640°C. Therefore, the increase in strength cannot be attributed to the presence of a greater quantity of coherency-hardened ß, but, rather, the increase in strength must be attributed to the transformation products formed, e.g., a' (martensiti-cally formed a). Concerning the data in Table IV, we agree that it is difficult to estimate the role of the martensite reaction, since the 6.4 pct Mn alloy was retained ß in the quenched condition.

Jan 1, 1955

By V. L., McCutchan

FORM of ore bodies, strength of wall rock, and quantity of water that must be handled differ so greatly in the various districts in which the Corporation operates that a variety of mining methods have to be employed. All are underground, however, with the exception of glory holes at Cerro de Pasco from which siliceous silver pacos ore is obtained. In general, the ors is in many relatively small bodies unsuitable for hulk mining, such as caving or top slicing. The strength of the rock and ore rarely permit open stopes, though shrinkage is successfully used on various veins with strong walls, particularly in, Casapalca. Horizontal cut and-fill and square-set stoping with careful filling are the principal methods employed, with the necessarily higher cost for supplies and labor offset as much as possible by care in the avoidance of dilution. The mines at both Morococha and Casapalca are notoriously wet, and even at Cerro de Pasco the quantity of water was enough to retard deep development until the perfection of electric pumps. In Morococha particularly, the extension of successive levels, first from adits of moderate length, then from shafts and heavy pumping installations on the 750 and 1000 levels, and finally by the 30,564-ft. Kingsmill tunnel, was one of the most difficult and long continued fights against water and resulting heavy ground that is recorded in mining history.

Jan 1, 1945

By R. F. Mehl, M. L. Swanson, J. P. Hirth, G. M. Pound

The sorption of zinc in a-brass was investigated. By analyzing the elliPtically polarized light reflected from the surfaces of a-brass solid-vapor couples, their optical constants and surface compositions were determined. It was shown that the surface compositions approached an equilibrium value exponentially with time. The bulk diffusion coefficient, surface diffusion coefficient and condensation coefficient for a-brass solid-vapor couples were calculated near 350°C from the experimental results. It has been assumed during various diffusion experiments with bimetallic solid-vapor couples (Dunn,1 Seith and Kraus,2 Jenkins,3 Balluffi and Seigle,4 and others) that the surface composition of such couples reaches its equilibrium value immediately. Although this assumption is probably valid at elevated temperatures, it is certainly not expected to be confirmed at lower temperatures.* consequently, it was decided that a fundamental experiment, designed to solve this problem as well as to examine all aspects of bimetallic sorption, would be the investigation of the rate of approach to equilibrium of the surface composition of solid-vapor couples. The sorption (i.e., adsorption, absorption, and desorption) of metals is obviously dependent on the state of the metallic surface and substrate. Much recent theoretical8"9 and experimental10-12 work on condensation and evaporation of pure metals has shown that the surface contour in atomic dimensions is a critical factor in sorption, so that any deformation or contamination13,14 of the surface exerts a profound influence. It is also known that absorption or diffusion occurs much more rapidly along grain were and in other deformed regions. Thus an effective sorption experiment must utilize a strain-free and clean surface, or at least a clearly defined and reproducible surface state. A mechanically polished surface is in a highly deformed17-l9 state. Because the degree of this deformation is uncertain, it is clear that for most experimental purposes a strain-free (i.e., etched, chemically polished, or electropolished) surface is desirable. Although adsorbed gas molecules on metallic surfaces are unavoidable even in the highest vacuum,20 oxide films can in some cases be removed by suitable vacuum annealing. Electrolytically polished and annealed surfaces, being relatively without strain, smooth and free of bulk oxides, were considered adequate for the present sorption experiments. Measurement of the surface composition of a solid-vapor couple presents a unique problem. Since experiments to determine the approach to equilibrium of the surface composition must be performed at temperatures where diffusion is very slow, solute penetration is so small that conventional analytical methods are unsuitable. An optical reflectivity method utilizing a polarization spectroscope was employed because of the relatively small penetration (~200A) of visible light in metals. By this method, elliptically polarized light reflected from the metal surface was analyzed and compared with that reflected from samples of known composition. The a phase of the copper-zinc system was

Jan 1, 1962

By Walter R. Hibbard, Harold Margolin

DURING preliminary tests on the aging of a Cu-plus 5 pct Ag alloy,' a specimen which had been overaged 24 hr at 550°C was annealed in a nitrogen-hydrogen atmosphere first for 2 hr and then for an additional 28 hr at 600°C. After each anneal the specimen was cooled to room temperature in about ½ hr and X-ray photograms were made. The first film, Fig. la, revealed two sets of copper-base lines, one intense and corresponding to the parameter at 550°C, the other fainter and shifted away from the beam, corresponding to the larger parameter at 600°C (see arrows). The 30-hr film, Fig. lb, revealed the same two sets of copper-base lines with a reversal of intensity. In neither case do the copper lines form a broad band which would be indicative of a range of compositions. This phenomenon is thus a "discontinuous" type of solution. A similar phenomenon was observed in a Ag-rich Cu-Ag alloy.' Finlay and Hibbard9 have suggested that directional rather than random solution of precipitate occurs in some alloys. Conceivably, for Cu-Ag alloys, the matrix-transition-precipitate precipitation sequence is reversible for the re-solution of the precipitate caused by rapidly raising the annealing temperature of an overaged specimen. A copper-base transition structure supersaturated with solute might be formed around the precipitate as it dissolves, thus obviating the necessity for a gradually changing solute composition of the matrix. The solute atoms then might be transferred rapidly and locally from the transition to the matrix phase in the proper amount and at the proper location to obtain directly the new ex- panded solid solution. The theory implies a minimum of diEusion of solute in the matrix (i.e., no significant range of matrix composition) and possibly suggests that the composition of the transition structure will vary with the conditions of re-solution. A transition copper phase found in aged Cu-Ag alloys1 might fulfill this function. Evidence regarding this suggestion could be obtained in Cu-Ag alloys by overaging a specimen until no trace of the expanded copper lattice is present and then subjecting the specimen to a retrogression treatment. Re-appearance of the transition copper phase would confirm the theory. Additional details could be secured by varying both aging and retrogression temperatures. References 'H. Margolin and W. R. Hibbard, Jr.: Effect of Ternary Additions on the Age Hardening of a Copper-Silver Alloy. Trans. AIME (1951) 191, p. 174; Journal of Metals (Feb. 1951) TP 3002E. 2 W. Ageew, M. Hansen, and G. Sachs: Decomposition and Changes in Properties of Super-saturated Silver-Copper Alloys. Ztsch. Physik (1930) 66, p. 350. 3W. L. Finlay and W. R. Hibbard, Jr.: Some Effects of Applied Stresses on Precipitation Phenomena. Trans. AIME (1949) 180, p. 255; Metals Technology (Sept.

Jan 1, 1952

By H. Landsberg

The curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag Io years behind the times. Rather, instead of being prodded by industry, they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table iA represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one tO the other (e.g., because of a different aspect in the mployment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited—just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1946

By H. Landsberg

The curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag Io years behind the times. Rather, instead of being prodded by industry, they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table iA represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one tO the other (e.g., because of a different aspect in the mployment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited—just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1946

By A. H. Daane, B. J. Beaudry

The Sc-Y and Sc-Zr systems were studied by thermal and X-ray methods. Both systems are characterized by complete solid solubility in the low temperature hexagonal form and in the high temperature bcc form. In the Sc-Y system, there is a minimum in the solidus at 50 at. pct and 1365°C, while the solidus in the Sc-Zr system follows a nearly straight line relationship between the melting point of scandium and zirconium. There is a minimum in the temperature of transition from hexagonal to bcc in the Sc-Y system at 43 at. pct Y and 1175°C; while the temperature of transition is raised in the Sc-Zr system to a maximum of 1415 °C at 30 at. pct Zr. INTEREST in the metals of the first transition series has usually stemmed from their useful properties; however, there is now a great deal of interest in determining the fundamental nature of these metals. Since scandium is the first of these transition metals, a study of the preparation and Properties1 and the alloying behavior of scandium2 was initiated. In a continuing study of the alloying behavior of scandium, the systems of scandium with zirconium and yttrium have been established. Extensive solid solubility in both the Sc-Zr and Sc-Y systems was expected from application of the classical rules of Hume-Rothery. Also, the modified Darken and Gurry plot as suggested by Gschneid-ner3 showed ideal conditions for solubility in the Sc-Zr system with less favorable conditions in the Sc-Y system. The effect of scandium on the transformation temperature of zirconium and yttrium was of interest, since a recent empirical observation by Uly and Burr4 predicted that the solute scandium would raise the transformation temperature of zirconium and lower the yttrium transformation. In addition to noting the validity of the above predictions, the SC-Y and Sc-Zr systems were established. EXPERIMENTAL METHODS Materials. The metals employed in this investigation were crystal bar zirconium, distilled scandium prepared by the method described by Spedding, et al.1 and yttrium prepared by the method described by Carlson, et a1.5 The major impurities present in these metals are listed in Table I in ppm. Alloy Preparation. All the alloys examined were initially formed by comelting the two metals in a nonconsumable electrode arc-melting furnace under an atmosphere of purified helium or argon. The buttons were inverted at least five times and re-melted each time to ensure homogeneity. During preparation of Sc-Zr alloys, approximately 1 wt pct was lost which was attributed entirely to the loss of scandium by distillation. When preparing Sc-Y alloys, approximately 1.5 wt pct was lost, but it was assumed that the intended composition was maintained, since the relative weight lost when arc melting the component metals was nearly the same. Samples weighing 15 to 20 g were prepared for time-temperature thermal analysis, while only 1- to 2-g samples were prepared for the optical pyrometer and X-ray diffraction studies. Thermal Methods. The solidus and the melting points of the metals were determined by an optical pyrometer method described previously.2 The temperatures at which the transformation from hexagonal to bcc occurs were determined by differential thermal analysis. Several points on the solidus and liquidus in the Sc-Y system were also determined by this method and are in good agreement with those obtained by the optical pyrometer method. The procedure followed in the preparation of samples for thermal analysis and the furnace used have been described elsewhere.2'6 Since a limited quantity of scandium was available, most of the alloys were not melted during thermal analysis, thus avoiding contamination by the crucible. The alloy could then be reused and the composition changed by adding the desired quantity of solute to obtain the next alloy. Heat Treatment and X-Ray Methods. In order to ensure homogeneity, the "as arc-melted" alloys Were wrapped in tantalum foil, sealed in quartz capsules and heated at 1100°C for 15 hr and then cooled at a rate of 8 deg per min. Samples for X-ray diffraction were filed from these heat-treated alloys, sealed in 1/8 in. by 1/2 in. tantalum capsules under

Jan 1, 1963

By D. M. James, J. C. Martin

The results are presented of a study of the application of analytical methods to the solution of two-phase flow into single wells. Approximate analytical expressions for the pressure distribution in two-phase flow are found ;;; a number of conditions. The results obtained from the analytical solutions me found to be in good agreement with results obtained by finite difference techniques using a high speed digital computer. Mathematical solutions for four sets of boundary conditions are presented. All of these solutions are composed of a short-term transient plus a steady or quasi-steady state. The rates of decay of the short-lived transients are analyzed. It is found that the durations of the short-term transients may be characterized by a parameter defined as the time constant which can be determined from simple relations. It is shown also that if the outer radius is much greater than the radius of the well. the short term transients decay at rates which are proportional to the square of the exterior radius, and the rates of decay are only slightly dependent upon the radius ratio. Numerical solutions based on finite difference techniques are presented for a number of conditions. The numerical solutions are in good agreement with the predictions based on the theoretical analysis for small and moderate drawdowns. Examples involving large drawdowns indicate that the nonlinearities in the equations of flow do not appreciably alter the longevity of the short-term transients. In all cases the time required for the short-tern transients to disappear is predicted satisfactorily. INTRODUCTION The mechanism by which oil and gas flow into a single well is of vital interest to the petroleum industry. The fundamental equations of two-phase flow which describe this mechanism are nonlinear partial differential equations. Numerical solutions of these equations describing pressure transients have been obtained with the aid of electronic computers. Although solutions obtained in this manner take into account a large number of effects, the reduction of this information to useful generalities is difficult. One method of obtaining generalities is the use of linearized approximations of the nonlinear equations. Since it is possible to obtain explicit solutions of the linearized equation, general properties of the role of pressure in the flow mechanism may be ascertained. Results obtained from this approach are limited to some extent by the linearizing assumptions. The severity of these limitations may be evaluated by comparing solutions of the linear equation with numerical solutions of the more exact nonlinear equations of two-phase flow. In the past considerable amount of work has been devoted to studying pressure build-up using the single-phase flow theory. Unfortunate1y, most prep sure build-up tests involve multiphase flow. A small amount of work has been done studying pressure build-up where the flow is two-phase. The encouraging results of these studies suggest that useful results may be found from additional studies of not only pressure build-up, but also the rapid transients associated with placing a well on production. This paper presents the basic theory of the pressure transients associated with placing a well on production and with closing it in. The paper is concerned chiefly with two-phase compressible flow; however, the results also apply to single-phase flow. The results are based on analytical solutions of the flow equations, and they are verified by numerical solutions using finite difference techniques. Much of the previous work on compressible flow into wells has been confined to single-phase flow. Some work has been done on compressible two-phase steady state flow, and solutions of the equations of flow have been found by finite difference techniques using high-speed computers. Muskat1 presents some rather general solutions to the equations of single-phase compressible flow into wells. Much work has been done on pressure build-up in wells (see, for example, Refs. 2-6). Almost all of the work on pressure build-up concerns single-phase flow with the exception of Ref. 5 and part of Ref. 2. Some work has been done on pressure fall-off in injection wells.718 Muskat9 presents the solution of the equations for radial steady state two-phase compressible flow. Handyl0 extends Muskat's solution to obtain

By A. D. McMaster, M. L. Gimpl, N. Fuschillo

Low-power, high-speed, radiation-resistant, monolithic thin-film integrated circuits require thin-film resistors of high sheet resistance which are compatible with the processing requirements for monolithic silicon devices. For this purpose the structure and electrical resistance as a function of temperature were investigated for Nichrome-silicon monoxide cermet films on passivated single-crystal silicon substrates. A suitable material was found to be a mixture of 50 vol pct Nichrome-50 vol pct silicon monoxide. This mixture, when evaporated onto 300°C substrates. showed a low temperature coefficient up to 400°C, at both 270 and 1100 ohms per square. Resistors deposited on room-temperature, 300°, and 500°C substrates were heat-treated at 600°C in air for short periods of H- seed, low-power, radiation-re sis tant, monolithic thin-film integrated circuits'-3 require thin-film resistors of high sheet resistance and low temperature coefficients of resistance which are compatible with the processing requirements for monolithic silicon active devices. The present investigation is directed towards the replacement of the Nichrome in the sandwich-type SO2-Nichrome-SiO resistors, currently used for DTL monolithic thin-film integrated circuits, with codeposited Nichrome-SiO cermet resistors. These Nichrome-SiO resistors are provided with an overcoat of SiO and are deposited onto thermally oxidized silicon wafers used in monolithic mi-crocircuit technology. The cermet resistors are shown to provide a lower temperature coefficient of time totaling up to 45 min. Electron nzicrogvaphs and diffraction patterns were taken of the as - deposited and heat-treated films. These results were then compared with electrical-resistance measurements for each condition. The room-temperature and 300°C substrate films showed a large decrease in resistance. The 500°C substrate film remained stable throughout the entire cycle. Electron-microscopy results show that the increased stability after heating to 600°C is largely due to crystallization of the films which begins in the vicinity of 400°C. The slight oxidation of the films when heated in air had a negligible effect on the resistance. The resistance of the film was a function of the substructure. resistance and a more versatile compatibility with silicon monolithic processing. Previous work3, on chromium-SiO coevaporated cermet resistors on glass and ceramic substrates without overcoats of SiO has been reported. For the present application, the thin films should possess the following ideal requirements: a) a temperature coefficient of resistance as near zero as possible up to 300°C; b) have a sheet resistance higher than 200 ohms per sq to conserve space on the chip; c) be easy to evaporate; d) be oxidiation- and radiation-resistant; e) show long-time stability at 100°C; } be stable in N2 atmospheres up to 600°C for short periods of time (5 to 45 min). Requirements a to e are well-known. The last requirement was optional and was due to a mask elimi-

Jan 1, 1967

By G. B. Walker, S. A. Falconer, S. J. Swainson, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By G. B. Walker, S. J. Swainson, S. A. Falconer, H. H. Vogel

During the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue of Mining and Metallurgy, Professor Taggart made the statement that " preconcentration by heavy suspension was Miss A.1.M.E 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By G. B. Walker, S. J. Swainson, S. A. Falconer

DURING the past few years much interest and attention has been focused on a relatively new method of ore concentration, which utilizes the principles of sink and float and employs as the heavy medium a suspension in water of a finely ground solid, such as galena or ferrosilicon. Although a relatively recent development, much progress has already been made in applying heavy-media separation processes to a considerable number of ores. Eight plants in this country and abroad -are now treating approximately 10 million tons of ore annually by heavy-media separation (sink-float) processes, including lead-zinc, lead, iron, garnet, tin and tungsten. At the annual meeting of the A.I.M.E. in 1941, three interesting papers (unpublished) dealing with heavy-media separation (sink-float) processes of ore concentration as practiced in four commercial units in the United States were presented by Victor Rakowsky, Grover Holt, Elmer Isern and Robert Ammon. These papers gave an excellent exposition of the principles of sink and float, as well as the operating practice in two iron-ore-beneficiation plants, the Harrison and the Merritt, of Butler Brothers, in Minnesota; the Central mill of the Eagle Picher Mining and Smelting Co.; and the Mascot mill, of the American Zinc, Lead and Smelting Co. Augmented by pictorial descriptions and a working model demonstrating the processes, these papers evoked a great deal of interest and discussion. In fact, in reporting the high lights of the meeting in the April 1941 issue Of MINING AND METALLURGY, Professor Taggart made the statement that "preconcentration by heavy suspension was Miss A.I.M.E. 1941 so far as milling is concerned." Although to date the greatest application of heavy-media separation from the tonnage point of view has been for the treatment of lead, zinc and iron ores, these processes have a much wider field of usefulness. In this regard, it is to be noted that recently new heavy-media separation plants for treating cassiterite ore and garnet ore have been placed in successful operation. Moreover, numerous other types of ores have been found to respond well to these processes when tested on a semi-commercial scale, and it is expected that in the near future a considerable number of new plants will be erected. In view of the fact that heavy-media separation processes offer such attractive possibilities, particularly now, when the mining industry is being called on for an even larger production than ever before has been attempted, despite shortages of labor and supplies, it was felt that a description of some of the successful separations that have been worked out during the past year in the Ore Dressing Laboratory of the American Cyanamid Co. on a variety of ores of strategic importance would be of interest. The purpose of this paper, therefore, is to present the essential data relating to investigations of heavy-

Jan 1, 1943

By H. Landsberg

THE curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag 10 years behind the times. Rather, instead of being prodded by industry, -they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table IA. represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one to the other (e.g., because of a different aspect in the employment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited-just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1941

By G. W. Imholz

The effect of new discoveries and development of other pools recently discovered is reflected in the increase in production from 586,000 bbl. during 1940 to 758,000 bbl. during 1941 in Coleman County. The States Oil Company's No. I Hudson, Coleman County, was the discovery well of the Silver field, with a total depth of 3540 ft.; initial production, 10,000,000 cu. ft. of dry gas and 60 bbl. of oil per day from the Gray sand, topped at 3482 ft. The first well drilled in the new Jim Ned field was the Merry Bros. and Perini No. I Greer, also in Coleman County. It had a total depth of 3937 ft. and an initial production of 152 bbl. of 42" gravity oil in 6 hr., through I-in. choke, from Gray sand encountered from 3909 to 3937 feet. J. E. Farrell's No. I Rose, Haskell County, was a new discovery, around which no additional wells have been drilled. Total depth was 3002 ft., plugged back to 2780 ft. to test an oil sand encountered from 2663 to 2685 ft., which when perforated with 76 shots at that depth was good for 85 bbl. of 40" gravity oil. In Fisher County, General Crude drilled its No. 12 Flanagan to a total depth of 6746 ft. After plugging back to 4578 ft. to test a sand encountered from 4515 to 4528 ft. it was abandoned as a dry hole. The top of the Ellenburger was reported as 6094 feet. Interest in Jones County continued unabated, largely through the development of the Wimberly pool in the southern part of the county, where five Cisco sands are producing. At present the pool has been defined on the south and the southwest. The structure has 170 ft. of closure; the lower limestone pays producing on top of the structure and the fist pay encountered, the Akard sand, producing on the flanks of the structure. Five deep wells were drilled in Stonewall County (H. and T.C. survey)—the Shell Oil Company's No. I-A Patterson, in block D, with a total depth of 6827 ft., dry and abandoned; the Shell Oil Company's No. I Rutherford, block I, with a total depth of 6239 ft., dry and abandoned; the Leader Oil Company's No. I Bilberry, block D, with a total depth of 5700 ft., dry and abandoned; Forest Development Company's No. 2 Boyd, block D, with a total depth of 4753 ft., dry and abandoned; and the Hunter et al. No. I Boyd, block D, total depth 4757 ft., dry and abandoned. J. E. Farrell drilled his No. I Tipton south of a well that produced from a Strawn sand for some time, to a total depth of 5202 ft., where it was abandoned. The well is in the southwest corner of sec. 43, block 19, T. and P. survey, Nolan County.

Jan 1, 1942

By G. W. Imholz

The effect of new discoveries and development of other pools recently discovered is reflected in the increase in production from 586,000 bbl. during 1940 to 758,000 bbl. during 1941 in Coleman County. The States Oil Company's No. I Hudson, Coleman County, was the discovery well of the Silver field, with a total depth of 3540 ft.; initial production, 10,000,000 cu. ft. of dry gas and 60 bbl. of oil per day from the Gray sand, topped at 3482 ft. The first well drilled in the new Jim Ned field was the Merry Bros. and Perini No. I Greer, also in Coleman County. It had a total depth of 3937 ft. and an initial production of 152 bbl. of 42" gravity oil in 6 hr., through I-in. choke, from Gray sand encountered from 3909 to 3937 feet. J. E. Farrell's No. I Rose, Haskell County, was a new discovery, around which no additional wells have been drilled. Total depth was 3002 ft., plugged back to 2780 ft. to test an oil sand encountered from 2663 to 2685 ft., which when perforated with 76 shots at that depth was good for 85 bbl. of 40" gravity oil. In Fisher County, General Crude drilled its No. 12 Flanagan to a total depth of 6746 ft. After plugging back to 4578 ft. to test a sand encountered from 4515 to 4528 ft. it was abandoned as a dry hole. The top of the Ellenburger was reported as 6094 feet. Interest in Jones County continued unabated, largely through the development of the Wimberly pool in the southern part of the county, where five Cisco sands are producing. At present the pool has been defined on the south and the southwest. The structure has 170 ft. of closure; the lower limestone pays producing on top of the structure and the fist pay encountered, the Akard sand, producing on the flanks of the structure. Five deep wells were drilled in Stonewall County (H. and T.C. survey)—the Shell Oil Company's No. I-A Patterson, in block D, with a total depth of 6827 ft., dry and abandoned; the Shell Oil Company's No. I Rutherford, block I, with a total depth of 6239 ft., dry and abandoned; the Leader Oil Company's No. I Bilberry, block D, with a total depth of 5700 ft., dry and abandoned; Forest Development Company's No. 2 Boyd, block D, with a total depth of 4753 ft., dry and abandoned; and the Hunter et al. No. I Boyd, block D, total depth 4757 ft., dry and abandoned. J. E. Farrell drilled his No. I Tipton south of a well that produced from a Strawn sand for some time, to a total depth of 5202 ft., where it was abandoned. The well is in the southwest corner of sec. 43, block 19, T. and P. survey, Nolan County.

Jan 1, 1942

By K. L. Young

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection case. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. INTRODUCTION When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressures. The two methods are Cullender and Smith1-" (numerical integration), and average temperature and com-pressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correcton. The average temperature and compressibility method, in addition to neglecting kinetic energy change, asumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. l or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. where 111.1 qeC2/d p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation,

By S. D. Michaelson

[CONTENTS PACE See TP 2377, Min. Tech, May 1948 for discussion of A Technique for Photographing Difficult Subjects through a Petrographic Microscope (TP 2092 by DONALD W. SCOTT, Min. Tech., Nov. 1946. Discussion by HORACE WINCHELL). Metallurgical Efficiency-a Yardstick in Lead-zinc Flotation Metallurgy (TP 2141 by R. A. ....... PALLANCH, Min. Tech:, March 1947. Discussion by S. D. MICHAELSON). I Symposium on Milling Devices and Practices. (TP 2162 by J. F. MYERS and R. J. TOWER, Min. Tech., May 1947. Discussion by HARLOWE HARDINGE). ............ 2 Rod Milling-Plant and Laboratory Data. (TP 2175 by J. F. MYERS, S. D. MICHAELSON and F. C. BOND, Min. Tech., July 1947. Authors' supplement and discussion by HARLOWE .......................... HARDINGE, and B. H. IRWIN) 2 A New Separating Vessel for Sink-float Concentration. (TP 2182 by E. C. BITZER, Min. Tech., May 1947. Discussion by E. H. CRABTREE, JR.) .................. 5] Metallurgical Efficiency-a Yardstick in Lead-zinc Flotation Metallurgy S. D, MICHAELSON*-The method of determining the efficacy of a separation described in this paper, gives the metallurgist a most useful guide for keeping his ship on an even keel When the ore Waves vary from placid seas to high breakers. Now that such a method of evaluating metallurgical efficiency has been developed and proven practical, it Would seem logical to introduce the next, and more final, factor of Economic Efficiency. I choose to define this term as the percentage ratio of net return from milling to the theoretical maximum net return. The actual operating cost subtracted from the actual mill return represents the net actual amount received for the material treated. Experienced operators of most plants Would ordinarily have enough data on hand to estimate a theoretical milling cost per ton, based on labor, power, supplies and maintenance When operating at maximum tonnage With minimum trouble and under ideal ore conditions. When this theoretical estimated cost is subtracted from the theoretical maximum ore return (calculated by Pallanch's method) the resulting figure is the maximum theoretical net amount the mill operator could hope to realize in processing the ore. The percentage ratio of these sums, of actual to theoretical, is the economic efficiency of the operations. This economic efficiency, if determined on the basis of a fixed market price for metal and similarly fixed base rates for labor, power and supplies, Will reflect the effect of changes in milling practice, labor efficiency and equipment condition. When computations made on the basis of actual current rates for labor, power and supplies are compared With similar actual figures for past periods they will show forcefully how energetic our hunt must be to develop man saving controls, more effective metallurgy, and better equipment to maintain profitable operations. Such computations also offer a simple means of determining how much more labor, supplies and power can be put into the mill operation to obtain an increase in metallurgical recovery at a profit.

Jan 1, 1947