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By A. S. Joy

Vacuum flotation tests carried out according to the method of Schuhmann and Prakash1 have shown that the acid limiting edge of the flotation area for a Brazilian hematite, in the presence of dodecylamine, is a straight line of slope approximately unity. The flotation tests and the structure, surface ionization, and electrokinetic properties of this hematite have been fully discussed elsewhere. 2 The numbers of adsorbed H+, and OH- ions and collector molecules have been determined in the range of critical conditions defining the acid limit of the flotation area. The total amine adsorption is shown in Fig. 1 as a set of contours superimposed on the straight part of the flotation area. These were determined by spectro-photometric estimation of the complex formed between residual amine and the anionic dye Orange II.3 The ionic strength of the solutions was kept constant and at a value in sufficient excess of the amine concentration to ensure that the diffuse part of the double layer was populated predominantly by indifferent ions. Adsorption of H+ and OH- in the absence of amine was found by potentiometric acid-base titration in the presence of hematite.4 The form of the adsorption-titration curves suggested that the hematite surface behaves in an amphoteric manner, and that positively charged sites arise through loss of a hydroxyl ion, and negatively charged sites by loss of a hydrogen ion. On this basis, curves 8 and 9, shown in Fig. 2, were calculated from the titration curves. These show the variation of the numbers of positive (s +) and negative (s—) sites with pH. To distinguish between ionic and other modes of adsorption, zeta-potential determinations have also been made using the streaming potential technique. The influence of amine on the zeta-potential of the mineral over a wide pH range is shown in Fig. 3. The change in charge ?s, due to adsorption of amine ions in the Stern layer, was calculated by applying the Gouy-Chapman theory, as modified by Stem, to the results shown in Fig. 3. The validity of this treatment has been shown by Ottewill and Jaycock.5 The three full lines, Nos. (1) through (3), included in Fig. 2 show the relationship between ?s and pH at three amine concentrations. The general conclusion from the zeta-potential curves is that adsorption of amine causes a reduction in the negative charge on the surface. Comparison of the values shown in curves (1) through (3) of Fig. 2 with the - curve shows that the magnitude of the reduction is comparable with that of s - at any given

Jan 1, 1964

By H. I. NORTON, H. O. Hofman

ZINC smelters in the central western. States have established a very high standard of purity for blende-concentrates, viz., zinc 60, iron less than 3, and lead less than 1 per cent. The very low percentage of iron is made possible by the blende containing less than 0.5 percent of isomorphous iron sulphide and by the sparing occurrence of pyritic material in the large blende-deposits of southwestern Missouri and southeastern Kansas. The blende in these districts occurs in sub-Carboniferous limestone, and is associated with chert, residual clay, calcite, pyrite or rnarcasite and bitumen. The different minerals are coarse and therefore readily separated by mechanical washing from the blende, with the exception of pyrite and marcasite, as blende has a specific gravity of from 3.9 to 4.1, marcasite, from 4.85 to 4.90, and pyrite, from 4.95 to 5.10. The common procedure of dressing the ores is to crush in a breaker, size in a trommel with 0.5-in. holes, pass the over-size through roughing-rolls and then jig the ore, now reduced to 0.5 in. maximum size, in roughing multiple-sieve jigs. The products of these are waste-tailings, sine-discharge coarse concentrates, side-discharge coarse middlings and bottom-discharge fine middlings. The coarse concentrates are sent to the market. The coarse middlings are crushed in middlings-rolls and brought back into the system by feeding into the main trommel. The fine middlings are cleaned upon finishing-jigs. Any pyrite or marcasite present follows the blende and increases the percent-

Mar 1, 1905

By Tegner C. Johnson

Just a few years ago, my company was referred to as the Marion Steam Shovel Company. Though we still make shovels, both two and eight-crawler types, the eight-crawler stripping shovel appears to have been replaced by the walking dragline for overburden removal and in some cases for the mineral as well. The walking dragline appeared in the coal fields in the early 1930's. It is popular because it can cope with overburden depths in excess of 100 ft and with blasted sedimentary rock, all at an O & O (ownership and operational) cost of ±10[c] per bank cu yd (bcy).

Jan 10, 1974

By Vince Poxleitner, John Delaney

Introduction In the mining industry, comminution typically begins in the mine with a blast of explosive to break rock so that it can be handled by the avail- able equipment. Though the breaking of the rock is essential for material handling in the mine and plant, this is not the only reason for ore reduction in the mineral industry. Comminution is primarily required to liberate minerals from ore so that they can be concentrated into valuable products or to prepare minerals, such as talc, for market as mined. The size of the equipment used for comminution ranges from small to massive. Regardless of equipment size, the power required to reduce the rock is a major expense. Years ago, mineral deposits could be mined more selectively and required less grinding to produce saleable products. However, as richer deposits were depleted, it has become necessary to mine low-grade deposits, with the valuables dispersed throughout the rock. Comminution equipment evolved in physical size and capacities to meet the new mine and process requirements. A modern, modestly sized mining operation, with a capacity of 25.000 TPD may use crushers two stories high weighing over a million pounds, SAG mills 36 feet in diameter driven by dual motors putting out 10.000 horse- power, and ball mills over 16 feet in diameter . Because of the increasing size and weight of modern equipment, the builder is faced with the problems of erecting massive foundations and field assembling equipment on these foundations. As equipment costs and plant construction costs increase, builders are finding that owners are asking for more detailed progress and cost data. Comminution construction projects are generally classified as grass roots plants or expansions or modifications to existing plants. It is estimated that 60-702 of the jobs involve existing plants. Today ' s costs for construction of small, new comminution plants can reach tens of millions of dollars; larger plants can cost hundreds of millions of dollars. Modifications, on the other hand, usually run from a few thousand to several million dollars. Though many problems are common to the construction of both new plants

Jan 1, 1982

Taking advantage of the lessons in administrative organizations which were taught by the war, Director Van H. Manning has put into effect a new form of organization in the Bureau of Mines. The Bureau is divided into two branches, one the investigations branch and the other the operations branch. F. G. Cottrell, who has been chief metallurgist of the Bureau, has been promoted to the position of assistant director and will be in charge of the investigations branch. F. J. Bailey, who has been chief clerk of the Bureau, has been placed in charge of the operations branch with the title of, assistant to the director. All research and technical control will be exercised through the investigations branch, while the non-technical work, administrative duties, and dissemination of the results of the Bureau's activities will be handled by the operations branch. Under the investigations branch comes the division of mineral technology, in charge of Dr. C. E. Parsons; the division of fuels, under the chief mechanical engineer, 0. P. Hood; the division of mining, under the direction of George S. Rice, the chief mining engineer; the division of petroleum and natural gas, under the direction of J. 0. Lewis, the chief petroleum technologist; and the division of experiment stations, under the direction of D. A. Lyon.

Jan 9, 1919

By NILS DANIELSEN

THE name of Swedish charcoal iron will probably bring to the memory of many old consumers an extremely tough and ductile iron which was formerly used in considerable quantities for common blacksmith purposes. To-day very little of this iron goes to such kind of work. Swedish charcoal iron is merely a speciality which is chosen whenever its remark¬able properties can be utilized. By giving a rough sketch of the manufacturing process of Swedish charcoal iron, the character of the iron, its weak as well as its strong points will more easily be understood. Swedish charcoal iron is a wrought iron also known in the United States under the name of Norway iron and Swedish Lancashire iron. The name Norway iron seems to have been attached to the product for the reason that in the earlier days it was generally brought into the States by Norwegian ships. However no iron of this kind is now made in Norway. The reason for the name Swedish Lancashire iron is that the manufac¬turing process emanated from Lancashier in England, the method being generally adopted in Sweden in the years 1831-1850. Today this iron is, with the exception of one plant in the United States, made in no place in the world outside of Sweden.

Jan 1, 1924

By Norman B. Pilling

The technical difficulties hampering the metallographic analysis of silicon steels are chiefly the result of the extreme corrodibility of these alloys. The addition of silicon to iron in increasing quantities, up to about 6 per cent., rapidly increases the susceptibility of the alloy to chemical attack, not only in acid solution, but in water. This renders the preparation of metallographic sections very difficult, because of a non-selective attack upon the finely polished surface by the water used as a lubricant in polishing. This water attack masks the true structural details revealed by suitable etching reagents. It is thus necessary to use alcohol as a polishing lubricant in the last stages of preparation and to avoid all etching reagents having an aqueous base. A specific reagent for the identification of iron carbide in ferrous alloys, and the one hitherto used almost' exclusively by metallurgists, is an alkaline aqueous solution of sodium picrate, which stains this constituent selectively. Its application to silicon steels has not proved successful, as its distinctive selective action is more or less completely hidden by the general attack of the aqueous solvent on the silico-ferrite, greatly accentuated by the fact that this reagent must be used at its boiling temperature (105' C.). Thus, a powerful metallographic aid to the study of the higher silicon alloys, such as transformer steels, is lost. A new reagent has been developed for the purpose of overcoming this difficulty. It is with some hesitation that the list of etching reagents, already overburdened, is increased, but the properties of this new reagent are advantageous in several ways and a definite field for it may be found in the metallography of ferrous alloys. The reagent consists of a dilute solution of nitric acid and methyl alcohol in nitrobenzol. It is a great advantage to secure an anhydrous solution, as a tendency toward acidic etching has been traced to small amounts of water. A convenient method of preparation is to make an anhydrous stock solution of nitric acid in methyl alcohol in the proportion 20 per cent. acid by weight (12.5 per cent. by volume). The alcohol can

Jan 1, 1924

By William Metcalf

ONE of the first questions that naturally occurs to one who handles steel is," Why does steel harden ?" To answer this question the chemist and physicist have devoted much thought and experiment, and while they have enriched our store of knowledge of the nature and composition of steel, it cannot be said that they have yet solved the problem involved in its hardening. In this communication I desire to direct attention to a line of investigation yet new, in the hope that it may receive the attention of those who have the time and ability to pursue it. I refer to magnetism. There are so many parallels between the action of magnetism on iron and steel and their behavior under different processes of manipulation that it would seem as if there must be some connection between the forces at work in the different cases, if, indeed, there be not an identity of force in all of these cases. Magnetism, as we know it, may be merely the visible manifestation of forces, which may serve as a guide to lead us to an exact knowledge of the structure, the strains, and the resistances with which we have to deal in iron and steel. If a magnet be brought close to a pile of iron filings, the little pieces of iron will fly to the magnet and attach themselves to it, with their longer axes lying in the direction of the force. If molten cast iron be poured into an iron mould,-a chill,-the iron upon crystallizing will form needlelike crystals, with their long axes normal to the surfaces of the mould. If the iron is at the proper temperature and the quantity small, compared to the mass of the mould, the whole of it will be chilled, or set, in' the hard needlelike crystals

Jan 1, 1881

By R. S. Handy

THE properties of the Patiño Mines and Enterprises Consolidated, Inc., a New York corporation, are near Llallagua in the department of Chayanta in the west central part of Bolivia, South America, about 80 miles southeast of Oruro and 250 miles southeast of La Paz, the largest city in Bolivia and its virtual capital. The properties are accessible by railroad from three points on the west coast-from Mollendo, Peru, across Lake Titicaca, from Arica by way of La Paz, and from Antofagasta, Chile. The latter route, although the longest, is recommended by the companies as affording a more gradual introduction to the high altitudes; the mine being 13,000 ft. above sea level. The company operates its own railroad from its properties at Uncia to Machacamarca on the Chile & Bolivia R. R., a distance of 60 miles. This railroad is well equipped and well operated, and its location among the mountains surrounding Uncia represents excellent engineering skill. In fact all of the railroads, although they are of only a meter gage, are remarkable for the excellence of their construction, the arrangement of their dining and sleeping cars and the precision of their operation. There is only one drawback to rail- road and hotel accommodations and that is the absence of heating facilities, which does not seem to affect the natives but keeps a tenderfoot's teeth chattering continually. The company is a consolidation of the Patiño company, owning properties at Uncia, with the Compafiia Estanfera de Llallagua, a' Chilean corporation owning contiguous properties at Llallagua. Before the consolidation these companies were deadly enemies, and there still remain at the surface plant at Uncia the fortifications and underground defences provided during the warfare between the two factions. Also, in the Azul, or "Blue" tunnel at the junction line between the two properties is a strong steel barricade still bearing marks of the bullets fired during the various armed tilts between the workmen of the two companies. The headquarters for the mining operations and the milling plant have been moved since the consolidation from the original location at Uncia to the Llallagua side of the mountain, where the Chilean company's operations were carried on. The historic old town of Uncia, with its massive stone buildings of Spanish design, is a wreck, while the Llallagua side is being rapidly built up with modern structures.

Jan 1, 1929

By R. E. Reed-Hill

The shear continuity conditions under which one mechanical twin may cross another are considered. Twin intersections usually involve various types of slip deformation in addition to twinning. Because the shear of the crossing twin may be partly transmitted through the crossed twin by slip mechanisms, continuity of the twinning shear vectors is not required at a twin intersection. It is concluded that analyses based on twin intersections should not he used as an independent method for deducing twinning elements in newly observed twinning modes. WHEN one mechanical twin passes through another, a twin intersection is said to occur. In the simplest form of intersection, Fig. 1, the crossing of one twin by another is accomplished with the aid of a second-order twin induced, in the twin that is crossed, by the crossing twin. The subject of twin intersections is significant to the field of deformation studies because it has been postulated by cahn1 that twin intersections should occur only under the following continuity conditions: 1) the traces of the primary and second-order twin must be parallel to each other in the plane of the crossed twin; 2) the direction 771 and magnitude, S, of the twinning shear must be identical in the crossing and second-order twins; also, the sense of shear must be the same. If these postulates are valid they constitute a valuable tool for determining twinning elements of newly observed twinning modes in metals. In his classic paper in 1953 on the plastic deformation of a uranium, Cahn1 used these continuity conditions to deduce twinning elements for several uranium modes. However, in the same year, pratt2 showed that both of Cahn's continuity equations were violated for (1012) twin intersections in zinc. Later, Kiho and Maruyama3, 4 showed that Cahn's second postulate was violated in {301) and (101) twinning in tin and (101) twinning in bismuth. In spite of this documentation that Cahn's second postulate is often violated, several recent papers5'6 have been published which have attempted to use the condition of continuity of twinning shear vectors for the evaluation of twinning elements. The primary purpose of this paper is to call attention to the possible ambiguity inherent in applications of Cahn's postulate, and to present additional information concerning the nature of twin intersections.

Jan 1, 1964

By R. W. Raymond

THE death of Privy Councilor Bruno Kerl, on March 25, 1905, terminated a distinguished and useful career. Bruno Kerl was born March 24, 1824, at St. Andreasberg in the Harz, and entered in 1840 the mining school of Clausthal, where he studied for three years, working at the same time in the mines and stamp-mills. After an additional year of practice in the silver-reduction and iron-works of the Upper Harz, he passed his examination as a metallurgical graduate, and studied for a year at Göttingen under WV filer in chemistry, Hausmann in mineralogy, and eminent teachers in other branches. In 1846 he was employed at the Oker works, but very soon left this post, to become a tutor in chemistry, metallurgy, etc., at Clausthal, where he continued to labor until 1867. During this period the Clausthal school became a completely equipped Mining Academy, and Kerl was made in 1862 a full professor. Meanwhile, in addition to the work of instruction, he discharged, simultaneously or successively, the duties of many responsible official positions in the Royal Hanoverian administration of mines and smelting-works, and also published many valuable books and treatises. Among these were professional guide-books to the Upper and Lower Harz, and their characteristic metallurgical processes; a manual of qualitative and quantitative blow-pipe analysis; another of metallurgical assaying ; and, most important of all, a Handbook of Metallurgy in four volumes, the second edition of which was issued in Leipzig, 1861-1865. This book was speedily recognized as the leading authority in its field. In this country, the English translation and revision, by Crookes and Röhrig, published about 1869, had a large circulation. In addition to these literary labors, Prof. Kerl became in

Jul 1, 1905

By Donald J. Drinkwater, M. C. Fuerstenau

Many important contributions to the more fundamental aspects of mineral processing have been made this past year. Mular1 researched the flotation characteristics of pure zinc oxide and also samples that had been doped with Al+++ and Cu++. Correlation of the response of pure zinc oxide to oleate flotation with a calculated zpc (from solution equilibrium) suggests that adsorption of oleate ion is coulombic in nature. Doping the sample with Al+++ (which will make the ZnO more n-type) had a marked effect on the maximum value of pH at which 50% recovery was obtained at constant collector addition. That is, when 0.5 mole percent Al+++ was added, the pH for 50% recovery was reduced by about four units. Treatment with Cu++ was found to have little effect on the flotation response of zinc oxide, even for additions of one mole percent. Since the zero points of charge of the Al+++ doped powders were not measured, it was not possible to correlate flotation data of these samples directly with charge phenomena.

Jan 2, 1966

By A. G. Jordan, W. Jeitschko, Paul A. Beck

The occurrence qf the V phase structure /Zr,Co,Ge, type) in ternary syste7ns (titanium, zivconium, niobium, lanta1urn) -(nickel, cobalt, iron)-(silicon, germanium) was incestigated. Nine V silicides and four V gertrlanides were found and their lattice constants are reporled. The lattice constants of twenty-one preri-ously identified E phases (TiNiSi type) are given. The average atomic volumes of these phases are discussed in relation to similar binary phases. ThE occurrence of a phase Ti4Ni4Si7 was first reported by Westbrook. DiCerbo, and peat' who gave it the name "V phase". They also reported the existence of an E phase TiNiSi. Subsequently a systematic study was undertaken in this laboratory to explore the occurrence of E' and V phases3 in related ternary systems. In the meantime the crystal structure of the E phase TiNiSi 4 and of the V phase Zr4CO4Ge 75,6 was determined. In the present paper the details of the V phase investigation and the lattice constants of the E and V phases are presented. V PHASES Alloy specimens of approximately 10 to 15 g were prepared by arc melting under argon (99.996 pct Ar) atmosphere. The starting materials were all of purity higher than 99.9 pct, with the exception of cobalt. which contained 0.14 pct Fe as the only major impurity. The weight losses were in all cases less than 2 pct, in most cases less than 1 pct. The samples were encapsulated in fused silica tubes with sufficient argon to yield about 1 atm pressure at the annealing temperature. After the homogenization anneal. Table I. the specimens were water-quenched. A representative portion of each specimen was then examined metallographically (etchant: 20 pct HNO,. 10 pct HF. 25 pct glycerine, 45 pct H20). Only minor amounts of second- and third-phase particles were observed in the specimens listed in Table I, with the exception of alloys Zr4Fe4Si7 and Ta,Fe,Si,. which contained an estimated 10 pct by volume of foreign phases. X-ray powder photographs were taken with a Seeman-Bohlin type focusing camera and Fe-KO radiation. Of the thirty possible combinations of elements in the ternary systems (titanium, zirconium. vanadium. niobium. tantalum)-(iron. cobalt, nickel)-(silicon. germanium) thirteen V phases could be identified. In the remaining seventeen ternary systems and also in the systems Cr-Ni-Si and (M0.W)-(Ni.Co)-Si no V phase was found at the composition 4:4:7 after annealing at temperatures between 900" and 1200'C. For the determination of the lattice constants of the V phases Debye-Scherrer photographs were taken using the asymmetric film arrangement and CrKcr radiation (ka1, = 2.28962A). Using the positional parameters, as determined6 for Zr,Co,Ge,. Table 11. intensity calculations were carried out for each of the V phases with the aid of a computer program.: Thus unequivocal indexing of the diffraction patterns was greatly facilitated. The lattice constants. Table I. were then computed by a least-squares fit of the high-angle lines with f (0) = cos2 Q as extrapolation function. Only few. if any. very weak impurity lines were observed, with the exception of the three iron alloys Zr,Fe,Si7. Zr4Fe,Ge7. and Ta,Fe,Si7. The agreement

Jan 1, 1970

By J. H. Canterford

The adsorption of uranium onto Wyoming bentonite was measured in carbonate media over the pH range 8 to 11. Uranium was removed from solution onto the solids by a rapid reaction, proposed to be adsorption of the anionic uranyl tricarbonato complex onto edges of the clay platelets, and a slow reaction that may be precipitation of a hydroxide. The changes in uranium content of the aqueous and solid phases of a uranium ore carbonate leach slurry were also measured as the slurry was progressively diluted. There was an increase in the uranium content of the solids as the pH of the suspension was lowered, as observed with the Wyoming bentonite. Results indicate the conditions that should be met with respect to pH control to prevent the problem of excessive uranium adsorption in the counter-current decantation washing circuit of a conventional leaching process, as well as in the leaching and restoration phases of carbonate solution mining.

Jan 1, 1985

By Donald L. Colwell

THIS is a metallurgical war. More than ever before, the mechanized forces and the air-borne warfare are deciding campaigns. Both of these are primarily dependent upon metals. There are two ways of increasing the effective supply of these metals when the demand is greater than the total over-all supply. The American custom, when a shortage of anything develops, is to get more. In the case of some nonferrous metals this has been done. For example, our potential peak output of magnesium will be almost one hundred times the prewar production. Output of aluminun has also been tremendously increased, and production of other metals is being stimulated by every possible means. Our enemies, however, have another successful method of increasing the effective supply of a material, and that is, to eliminate entirely all nonessential uses, and also to use, in essential applications, alternate materials wherever possible. Sometimes, ersatz material is inferior to the original, and consequently does not do the job as well. Often, however, it has been found superior, and many substitute items are now being used both by industry and by the military which will continue even when the original material again becomes available.

Jan 1, 1943

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 Raymond O. Ladoo

FUSED quartz is a glass made by the fusion of nearly pure silica. Some confusion in terminology exists but in the trade today "fused quartz" generally refers to the perfectly transparent colorless product made from rock crystal whereas "fused silica" is a white, translucent product made from silica sand. Vitrified silica is the term preferred by purists for all quartz glass, but it lacks the definiteness of -the trade terms. Since the raw materials, methods of production, and properties of the finished products arc different for the two types, the trade terms are preferred. As fused quartz is amorphous, it-physical properties differ greatly from those of quartz crystal. Lacking crystallographic directions and having no piezo-electric properties, fused quartz. of course, has no value for the making of radio oscillator plates; but it does have other valuable and unique properties. Perhaps the 'best known and most useful properties are its extremely low coefficient of expansion and its ability to transmit short-wave ultraviolet radiant energy. Crystal quartz not only has an aver-

Jan 1, 1947

Jan 1, 1908

By D. M. McFarland

IN mining, quarrying, and construction, drilling and blasting have an important influence on the operations that follow. If the fragmentation of material being disrupted is inadequate, loading and transportation equipment will not operate at or near full capacity. Any operator faced with this difficulty should not be satisfied until he is convinced by a careful study of his methods of drilling and blasting that no improvement can be made. Rock in a certain quarry in Ohio seemed to defy any grade of explosive or means of detonation that the explosives industry had to offer. The average result of a blast was that a great part of the burden would be pushed out from the face in a number of large sections that would jokingly be referred to as "boxcars." These were no credit to the explosives man and a costly problem for the quarry company. Such blocks retard shovel operation as they have to be uncovered and subjected to secondary drilling and blasting which, if extensive, is an expensive operation. It was an attempt to improve the fragmentation obtained in primary blasts that led to the development of milli-second-delay electric blasting caps. The reasoning that prompted the trial was that even with wide spacing of the drill holes it seemed that the burden was separated too quickly from the face by the cutting action of the explosives from hole to hole. If the time of firing of the holes could be regulated so that

Jan 1, 1948

By A. E. Worthington, R. F. Meldau

An analog computer study was made of the reduction of the magnitude of the SP by formation geometry and resistivity effects. Practical field .situations were studied. The analog data were converted to the form of departure charts. These charts may he used to determine the reduction in the SP due to the above eflects pith good precision Quantitative interpretation of the SP log in terms of formation water resistivity is presently based on the premise that the observed SP is equal to the electrochemical potential developed across a shale between the mud filtrate and the formation water. This procedure inherently assumes that, first, no electro kinetic (streaming) potential is present, and, second, that the SP is not reduced by resistivity or geometry effects in the formation. When, however, such a reduction of the observed SP does occur, one may write, SP = b,E, b, E, (1) where SP is the observed self-potential opposite the center of the bed under consideration. In this case, E, is the electrochemical potential, E, is the electrokinetic potential, b, is the electrochemical reduction factor, and h, is the electrokinetic reduction factor. The first assumption above is equivalent to assuming E, = O in Eq. 1 and the second assumption is equivalent to h, = b, = 1. Examination of electric logs shows that for many formations of interest the observed SP is reduced below its maximum value. The object of this work is to aid quantitative SP interpretation in at least some of these situations by obtaining values for b, and b, in Eq. 1 as functions of realistic combinations of bed thickness, depth of invasion, and formation resistivity. The only previously published work in this field known to the authors is by H. G. Doll' in 1948. He evaluated b, under conditions permitting exact analytical solution. His work clearly established the importance and qualitative nature of formation geometry and resistivity effects upon the SP, but the necessity of obtaining analytical solutions restricted his study to situations of limited practical interest. In order to extend such studies to practical combinations of formation parameters which do not lend themselves to feasible analytical solutions, the results reported in this paper were obtained by use of a special analog computer. THE ANALOG MODEL The analog model used for this study was the Guyed Analog Computer which originally was designed and built for resistivity log departure curve studies. It consists of a two-dimensional mesh of resistors, with the vertical mesh corresponding linearly to vertical distance along the borehole, and the horizontal mesh corresponding to radial distance from the borehole axis. By proper choice of horizontal resistor values, a three-dimensional, axially symmetric, borehole-formation problem can be modeled with this two-dimensional array. These and other details of the model are contained in a paper by H. Guyod'. The geometry used for the SP studies with the analog is depicted in Fig. 1. This configuration has a horizontal plane of symmetry, and, hence, the model, and the following discussion, need only to be concerned with one quadrant such as shown in Fig. 2. A further simplification arises by considering that both the natural potential sources and those used in the model have fixed internal impedance. Therefore, the current flows produced by these sources can be separated and studied independently ( i.e., the superposition theorem can be applied). SP = SP, i SP, = h,E, + b,E, ,(7)