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By P. Pollard

A method has been developed for evaluating acid treatments in fractured limestone fields by breaking down pressure drawdown into three component parts: (I) pressure differcntial across "skin" near the borehole face, (2) pressure differential due to flow resistance in the coarse communicating fissures and (3) pressure differential between the fine voids and the coarse fissures. It is apparent that in most successful acid treatments the first term, skin resistance, has been reduced or eliminated. Further, it is often possible to estimate the volume of coarse fissures associated with the second term, coarse fissure flow resistance. In cases where this volume is comparable with practical acid volumes it seems likely that this resistance also may be attacked with a suitably retarded acid. INTROD UCTION Acid treatment has been successfully applied as a general practice in the limestone wells in the Mara/ Maracaibo districts of Venezuela for some 10 years. At the same time the need has been felt for a more precise method of: (1) evaluating the effect of an acid job and (2) selecting wells which should benefit from an acid treatment. The following method, based on an analysis of build-up curves for wells producing from fractured limestone, provides a means of forecasting the effect acid will have on a well and in many cases the probable order of production rate increase which may be expected. In certain cases it is also possible to calculate the fissure volume through which the acid has to be displaced for best results. Various approximations are introduced in the method, but within the limitations of these the analysis gives an indication of how a well, whether previously acidized or not, may be expected to respond to acid treatment. Suitable build-up curves cannot be obtained on "tight" wells which do not give sustained production and the method is not applicable to such wells. Figs. 1 through 7 illustrate various types of build-up curves obtained from limestone wells in Western Venezuela. Curves are included showing (1) both skin and coarse fissure resistance, (2) skin resistance only, (3 and 4) reduction of skin resistance by acidization, (5) fissure resistance only, (6) reduction of coarse fissure resistance by acidization, and (7) acidization failure. This theory has been successfully applied for over three years during which 22 acid treatments have been carried out specifically to reduce skin resistance and three treatments to reduce coarse fissure resistance. The method has been found to be a useful aid in the selection of wells for acidization.

By Noel Stearn

OF THE many instruments devised for the measurement of magnetic anomalies, the ordinary dip needle, by virtue of its superior simplicity of construction, facility of manipulation, and definiteness of interpretation, seems to merit serious attention as the instrument most readily applicable to the detection of magnetic anomalies of the higher order of magnitude. , In spite of the fact that it has been used for many years for the discovery of iron ore in Europe and in the Lake Superior region of America, its capabilities as a geological instrument have not yet been thoroughly plumbed. The Wisconsin Geological Survey, under Dr. W. 0. Hotchkiss, E. F. Bean, and H. R. Aldrich, has been most thorough in developing the technique of the instrument, and the results it has obtained have aroused a general interest in a more widespread use of geomagnetics as an exploration method and the dip needle as a geological instrument. The simplicity of the instrument is an especial advantage, as it can be used by anyone, regardless of his technical training; but to insure useful results not only is a knowledge of the background of geomagnetics necessary but also an understanding of the principles of the instrument itself.

Jan 1, 1928

By Clifford Frondel

THE aluminum oxide known as corundum has several varieties that have been used as gem materials since ancient times. These include the red variety called ruby, the blue variety sapphire, and the asteriated types of ruby and sapphire. Asteriated sapphire was known to the ancients under the name of astrios, and descriptions of this gem were given by Pliny and other early writers. The relation of these gem materials to each other as varieties of a single species, corundum, was first clearly established by Haüy in 1805 and J. M. Güthe1 in 1809. Natural gem corundum is obtained principally in Ceylon, Siam, Burma, India, and Australia. Star sapphires and rubies always have been highly prized and in recent years have become particularly popular in the United States. Natural star rubies of large size and fine quality are extremely rare and rank with large and fine emeralds and diamonds as the most valuable of gem stones. Interest thus attaches to the recent success in commercially synthesizing star sapphires and rubies of a size and perfection unmatched by nature.

Jan 1, 1954

The United States Employment Office of the Department of Labor, of which the division of engineering and education, under the direction of A. H. Krom, maintains an office at 29 La Salle Street, Chicago, Ill., is engaged in a classification of engineers in order to make their services more readily available in case of need. We have received a form used by this division, on which it requires only a very little time to indicate one's particular line of work, his experience and the salary that he desires. We have been asked to impress upon members of the Institute the distinct advantages that come through registration. Filling out the blank entitles an engineer to free employment service, provides him with direct contact with the Government, supplies him with information in regard to engineering affairs, and helps him to become successful in his profession. The Government wishes every technical man to register, so that it may know the strength and location of the engineering reserve. It is therefore the duty of every patriotic engineer, whether he needs a position or not, to register at once. Blanks can be obtained by addressing the office above noted.

Jan 10, 1918

By D. B. Grove

THE heavy media separation process plays an outstanding role in the concentration of 4000 tons of zinc ore per day at the Mascot mill of the American Zinc Co. of Tennessee. Of the total tonnage, 72 pct is treated in the heavy media separation plant to reject 56 pct of the ore as a coarse tailing, which has a ready market. Concentrates from this separation are beneficiated further by jigging and flotation. Approximately 25 pct of the total zinc concentrate production is made in the jig mill. Jig tailings are ground and pumped to the flotation circuit where the balance of the production is made. Fig. 1 shows a generalized flowsheet of the mill.

Jan 8, 1951

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

Jan 1, 1918

By Arthur Coffinberry

EVE have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, com-bined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was, undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atones, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such informa-tion is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By Gifford Pinchot

The proposition that forest reserves are, from the mining point of view, not only desirable but necessary, is not one which would have received enthusiastic support in. the West a year ago. It is, nevertheless, easily susceptible of proof. A short and simple statement of the facts has seldom failed to carry conviction as to the wisdom of the forest-reservation policy. Hostility to mining interests was never contemplated by the men to whom the forest reserves are chiefly due, and it is most unfortunate that the opposite belief should have obtained wide

Jan 1, 1899

By Arthur S. Coffinberry, Ralph Hultgren

We have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By Arthur S. Coffinberry, Ralph Hultgren

We have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

At a special inaugural ceremony in Blue Hill, Maine on August 3rd, Governor John H. Reed detonated the first blast to signify the beginning of development work on a new copper-zinc mining venture that seems destined to focus increased interest in the mineral potential of that State. The property which is the first new base metal mine to be discovered in the northern Appalachians in 30 years, is owned by Black Hawk Mining Co., a subsidiary of Denison Mines Ltd. of Toronto. When it goes on-stream in 1966, it will join Ducktown, Tenn., as the only active copper producing region, east of the Mississippi River. According to official reports submitted by the Company to Robert G. Doyle, Maine's State Geologist, Black Hawk has found ore reserves totalling 4.5 million tons. Assays show 2.8 million tons of 2.0'; copper and 0.4 oz. of silver per ton; 1.2 million tons of 16.75% zinc and 0.58% copper; and 0.5 million tons of 6.75% lead with 4.25 oz. of silver per toil and some zinc.

Jan 9, 1964

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (-=,6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by Pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (=10-6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By Stanley C. Herold

A few hates on the occurrence and significance of mud volcanoes in Colombia may be of interest at the present time, owing to the renewed activity in geological exploration of the coastal regions bordering the Caribbean Sea. The best-known volcanoes are found a few miles from the seacoast. One is situated to the south of Puerto Colombia; the second, to the east of Cartagena near the village of Turbaco; and the third, near the village of Puerto Escondido south of the Sinu River. Others are reported in more inaccessible localities. Usually they stand 2 1/2 or 3 ft. (0.762 or 0.914 m.) above the surrounding ground at the crater, though several craters from 10 to 20 ft. -(3.04 to 6.09 m.) "apart will often build up an extensive mound at low gradient. The shallow mound may cover 1/2 or 3/4 acre (0.2 to 0.3 ha.) with an elevation of 12 or 15 ft. (3.65 or 4.57 m.) at the, center. The craters are formed of hardened blue clay; the inside diameters vary from 14 to 24 in. (35.56 to 60.96 cm.). The rim is continuous, except on one side where there is usually a cut 3 or 4 in. deep, thus allowing an overflow. The craters are filled to the' rim-cut with a thick mixture of blue clay mud and water, which is kept in agitation by escaping gas. Fig. 1 shows the bubble in the act of bursting and Fig. 2 the appearance of the surface of the viscous fluid a second or so later. The frequency of the explosions is determined by the weight of the column of fluid in the neck of the volcano, consequently, such explosions are not synchronous in a group of craters. Ordinarily, there arc two or three explosions in about 3 minutes. The supply of gas is small but steady and sufficient pressure must accumulate before the bubble can enter the column of fluid. The water is derived from the surface and enters the scdirnentary strata not far distant from the volcano. During long dry seasons, as the supply of water fails the volcano dries and geyser action ceases. The temperature of the muddy fluid is normal; the gas is dry and inflammable. - No petroleum products come with the gas. On the surface of the fluid, there is sometimes a dark brown streaky scum, which

Jan 1, 1920

By C. Bezemer, I. Havenaar

An investigation was carried out on the dynamic liltration behavior of drilling fluids. In a set-up consisting of a porous pipe through which the drilling mud was circulated, dynamic liltration rates and cake thicknesses were determined as a function of flow rate and filtration time. Eventually, a state of equilibrium was reached; i.e., both cake thickness and filtration rate attained constant values. Concurrently, dynamic filtration tests were carried out in a simple dynamic filter apparatus where mud flow was similar to that in a rotational vismmeter. In both arrangements the relation between equilibrium liltration data and rate of shear at the cake surlace was studied. Filter pipe and dynamic filter apparatus were lound to give identical relations. It was therelore concluded that the latter apparatus, which is suitable lor routine measurements on small amounts of mud, could be used to determine the dynamic liltration behavior of mud under borehole flow conditions. Some data are presented on the effect of filtration pressure and temperature on equilibrium filtration rate and cake thickness. INTRODUCTION In oil well drilling, the drilling fluid used generally forms a mud cake on the permeable sections of the borehole wall while filtrate is lost into the formation. As to the conditions under which this filtration process takes place, a distinction should be made between static mud filtration (mud is not circulating) and dynamic mud filtration (mud is circulating). In recent years several investigatorsl-5 have studied the process of dynamic mud filtration about which little had previously been known. This type of filtration is the subject of this paper which confirms several findings of previous investigators. It differs from already published works, however, in the following respects. 1. It contains a description of a simple laboratory apparatus developed for dynamic filtration measurements on small amounts of mud. 2. The effect of rate of shear at the cake surface on dynamic filtration has been studied. As a result of this study, dynamic filtration data pertaining to the borehole conditions of mud flow can be found from laboratory tests. 3. Some data are presented on the effect of filtration pressure and temperature on dynamic filtration. The work was limited to a small number of muds. No attempt was made to compare data on API filtrare loss with dynamic filtration rates. Previous workers have clearly shown that no correlation exists between static and dynamic filtration rates. EXPERIMENTAL ARRANGEMENT To establish whether the effect of mud flow conditions on dynamic filtrations is governed by the rate of shear at the cake surface, two different types of mud flow were used. In this connection the experiments were partially conducted by means of a porous pipe through which mud was circulated, partly in a dynamic filter apparatus which somewhat resembles a rotational viscometer. In both cases the flow conditions of the mud were well defined, thus making it possible to-calculate rates of shear at the cake surface. The filter pipe was 200 cm long with an internal diameter of 3 cm. Its perforated wall was covered on the inside with filter cloth on which the mud cake could form. Mud was pumped through the pipe at linear rates varying from 20 to 186 cm/sec. The required filtration pressure was obtained by means of a lack-pressure valve downstream of the filter pipe. In this arrangement the type of flow existing in the borehole is reasonably well simulated. The dynamic filter apparatus (Figs. I. and 2) consists mainly of two concentric cylinders with a clearance of about 0.5 cm. The outer cylinder (rotor) can be rotated at rates up to 1,000 rpm. The outer surface of the inner cylinder (radius about 2.5 cm) is covered with filter cloth or paper supported by copper gauze. The two cylinders are mounted inside a pressure

Jan 1, 1967

Jan 1, 1895

By T. Leser, A. W. Jenike

The problems of caving and underground subsidence can be considered as the failure of a highly compacted rock and its subsequent flow in the form of broken rock. The problem is complex because the propagation of failure and flow have to be considered simultaneously; the yield strength of the virgin rock and the broken rock are different; and, while under certain conditions it is sufficient to consider the virgin rock as homogeneous, the density and the yield function of broken rock are both pressure and time dependent. A study of the failure and flow of solids with a pressure dependent yield function has been published recently by Jenike.' In this paper the density of the broken rock is assumed to be only time dependent and the consequences are examined in the case of one-dimensional vertical subsidence into an initial cavity. The following describes an attempt to develop a tool which, in combination with other tools, may lead to mathematical solutions of real problems of caving and subsidence. STATEMENT OF THE PROBLEM An underground cavity of horizontal cross section 4 = 1 and height 6 is assumed to exist at some depth below the surface. At the time t = 0 rock above the cavity fails and completely fills out the cavity with expanded broken material. With passing time the broken rock consolidates and subsidence proceeds continuously upuard in a vertical shaft. The phenomenon is one-dimensional (see Fig. 1). The problem consists of finding the displacement and the velocity with which the frlmt of the subsidence (wave front) moves upward as a function of the time and of the rock properties. DIFFERENTIAL EQUATIONS CONTROLLING THE PHENOMENON With the assumptions that the broken rock is a continuum and that the subsidence occurs continuously, we can apply the one-dimensional differential equation of contitiuity (conservation of mass) and the equation of preservation of momentum The latter equation is replaced by an assumed relation based on experience, which takes care of the

Jan 1, 1962

By John A. Church

In a recent paper read before the Institute it was said of faults that "the sensible expression of the fracture is an earthquake." This notion, which has been expressed before, though usually as a theory and not as an admitted conclusion, is based upon the early belief that faulting is a violent rupture of the earth's crust. Faults are of different kinds, from great dislocations of the earth —hundreds of miles in length—down to the still more mysterious displacements with which miners have to deal. The latter are usually quite short, from 1000 to 20,000 feet in length, but are distinguished even above their greater brethren by the excessive pro-

Jan 1, 1893

By O. W. Walvoord

To those working in the mineral industry, the flowsheet is a familiar and valuable tool, seldom used, unfortunately, to its fullest advantage. As with so many other commonplace and simple items, there is little or no attempt to expand on the forms, and types of flowsheets. A flowsheet or flow diagram may be defined as an illustration showing circulation of the ore stream in a concentrating plant. It may be further described as an explanatory graphic design or picture. A flowsheet is obtained by interpreting the metallurgists' research and ore test data, usually with some adjustments to suit the economies of the project. It brings together, in compact form, information from a number of sources.

Oct 1, 1956

By Arthur S. Coffinberry, Ralph Hultgren

WE have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electronto-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938