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By D. W. Rudd, D. W. Vose, J. B. Vetrano

In an earlier paper the permeability character of Mo-0.5 pct Ti to hydrogen was described.' It was shown that this alloy is a more effective barrier to the passage of hydrogen than previously studied systems, i.e., copper,2 nickel,3 and several stainless steels.4 The permeability of Hastelloy B to hydrogen was investigated as a material having promising high-temperature structural properties which might have a low permeability to hydrogen. The general theory of permeation has been previously discussed,' and here only a summary of the more important results are given. It is found that except for very thin membranes, at low temperature, permeation of a gas through a metal barrier is determined by the rate of diffusion of the gas through the crystal lattice of the specimen, and that for hydrogen and the common diatomic gases, this passage involves dissociated particles as the diffusing species. The rate of permeation for hydrogen is therefore proportional to the square root of the pressure. It has also been found that the rate of permeation is inversely proportional to the thickness of the barrier. The apparatus used in this investigation was fundamentally the same as that employed in previous studies,' except that several simplifications result in the case of Hastelloy, since oxidation at the temperatures investigated is no longer a problem and welding of the specimen is relatively easy. A cross section of the membrane assembly is shown in Fig. 1. When finished, the assembly is about 5 in. long. The wall thickness is about 6 times the membrane thickness. The membrane (A) can be maintained at

Jan 1, 1963

By Thomas MacFarlane

In smelting copper, lead, and silver ores, it is scarcely possible in every case to make analyses of the various parcels of ore, with the view of combining these and the fluxes so accurately as to yield, in the furnace, slags of exactly the most favorable composition. This is even more difficult with ores which require previous calcination, or with mattes which have been roasted in heaps. Even in cases where the greatest pains have been taken and the most elaborate calculations made beforehand, it frequently happens that variations in the working of the furnace interfere with the result so much desired. Generally, the practical metallurgist must be content with ascertaining the average composition of his ores and fluxes, making a calculation once for all as to the most advantageous mixture, and leaving slight changes in its composition to be taken care of as it is passing through the furnace. The various products then afford him the best material whereon to base his judgment as to the manner in which his smelting mixture is working. Of course the character of the slag is one of his chief guides, but it is not always possible from its outward characters alone to form a correct judgment as to its composition. Neither would it be possible or practicable to apply chemical analysis for this purpose, as it would be impossible to wait for its results while working a furnace. Abich was, I believe, the first to point out the relation existing between the composition of volcanic rocks and their densities, and to show that, the latter being ascertained, very correct conclusions

Jan 1, 1880

By H. D. Hoskold

This instrument, shown in Fig. 1, is not generally known, though it has been used in England, and found very practical, handy and useful in work not requiring a transit or theodolite. It is not only a good miner's dial, but a circumferentor as well; that is, it can measure horizontal angles like a theodolite. The magnetic bearings are conveniently read on the inward-beveled upper divided circle; while another circle, graduated on the base-plate, is used for reading the horizontal angles with a vernier. Two leveling spirit-bubbles are sunk in the same base-plate. The vertical divided semicircle is attached to the compact-box by two short axes, which permit the semicircle, with its plain sights, to be turned down to a horizontal position, and rest upon a pin, which relieves the axes from strain. This adjustment gives a clear view of the needle and vernier, and protects the instrument from injury, when carried through low mine-workings. A groove in the semicircle receives a sliding-bridge which carries the plain sights, and a vernier for reading vertical angles. A ball-and-socket-headed tripod is used; but sometimes the instrument is mounted on parallel-plates and level-ing-screws; and sometimes a telescope is attached, instead of the plain sights. The instrument is admirable for all such Mexican surveys as Mr. E. A. H. Tays describes ;l and saves so much time and labor as to be vastly superior to the less accurate hanging-compass called by him a " bully " instrument. If the hanging-compass was ever used in England, it has long since given way to more modern and superior instruments.

Jan 1, 1905

By Arthur C. Simmons

The area producing Pennsylvania-grade crude oil declined sharply in 1943, with a daily average production in the entire area of 71,056 bbl. as against a daily average in 1942 of 77,786. The total decline in the Pennsylvania-grade area amounted to 2,456,311 bbl., and 1,g81,z71 bbl. of this occurrcd within the state of Pennsylvania. The principal decline occurred in the Bradford field, where it was caused primarily by a drastic reduction in well completions. All of the zones in the Pennsylvania-grade producing area showed a decline except the part of Ohio that produces that grade, where production increased very slightly over 1942. Table I shows the average daily production by months for the several districts of the area. Table z is a comparison of the production in the two districts within the state of Pennsylvania. It is interesting to note that the Bradford field produced approximately half the total quantity of Pennsylvania grade but accounted for nearly three-fourths of the decline in production from the previous year. It is believed that this decline is ocasioned by restrictive price ceilings and a lack of adequate manpower to drill the necessary wells to maintain production. Stocks of Pennsylvania Grade At the beginning of 1942, stocks of Pennsylvania-grade crude totaled 3,196,000 bbl. and at the beginning of 1943 they totaled 2,626,000 bbl. At the end of 1943 the stocks of Pennsylvania-grade crude had declined to 1,95z,000 bbl. The available crude stocks have been almost completely consumed, as nearly all of the present crude stocks are "unavailable" and required for

Jan 1, 1944

By A. A. Beard

ABOUT three years ago, I. L. Dunn, of Marietta, Ohio, found that wells could be cleaned by blowing with compressed air; this method has been used with great success on many wells in the Marietta, Ohio, district, where compressed air is being used to increase production, by forcing oil through the depleted sands. About a year ago, the process was successfully used to clean out wells in the Lenapah pool in Oklahoma, where an air plant had been installed, under the supervision of I. L. Dunn. Wells from 900 to 1000 ft. deep, with 40 ft. of sand and cavings in them, were cleaned out in from two to three days. The use of this process had, so far, been limited to properties using the Smith-Dunn process, where compressed air, under suitable pressure and volume, was available. For other properties, a portable compressor seemed essential; this was built and successfully demonstrated by Mr. Dunn, for the Tidal Oil Co. in September, 1924. The process of cleaning out with air has been described.1 It consists of lowering the tubing into the well, with a shoe or nipple of heavy pipe substituted for the perforated anchor on the bottom. Into the tubing, compressed air is introduced through a rotary swivel hose at the top, or by means of swing connections. The tubing is lowered to the top of the cave to be cleaned out, several barrels of water are put into the hole, and the compressed air is turned on. This blows out the material between the casing and the tubing, the tubing being lowered as the material is removed.

Jan 9, 1925

At a time when Congressional stiffening of health and safety regulations in the nation's coal mines seems all but an afterthought, when the problems confronting both mine operator and worker are being tossed about like a pigskin in an Australian- rules football match, what could be more appropriate to the times than to incorporate a discussion on these matters into the proceedings of an annual coal meeting. Integration of both technical and topical discussion provided the strength for this 28th Annual Meeting of the Central Appalachian Section of the AIME, convened at the The Greenbrier, White. Sulphur Springs. W. Va., Oct. 31-Nov. 1. Three technical sessions prepared for the occasion were served to those in attendance. First of these was held on Friday morning. Rendered excellent coverage, topics included Roof Structure Analysis at Blacksville No. I, presented by David Eyer, Christopher Coal Co.; Methane Monitors (evolution and evaluation of present day detection equipment); and Instantaneous Control Reaction to Mine Fires and Explosions, in which Elmer A. Fike illustrated the point quite vividly by showing a film on the potential of such control equipment. Indeed, the ability to snuff out a mine fire before it is allowed to spread even beyond its own igniting sparks speaks very well for itself. However, Fike hastened to point out that certain difficulties had to be overcome before these "fire watchers" could be implemented successfully in mines. These "bugs," inherent in virtually all coal mining environments, include ignition of sulfur pockets on mine facings and delivery of sparks on trolley rails, both of which may impede the accuracy of such control monitors.

Jan 12, 1969

By Eckley B. Coxe

At the first meeting of the Institute, a paper was read by Mr. Rothwell, calling attention to the importance of at once considering the great waste of anthracite coal under the present system of mining and preparing that fuel for market, and a committee was appointed to examine and report upon the method now in use. About the time the committee were selected, a general resumption of work, after the long strike, took place in the coal regions, and the members of the committee have not in consequence had as much leisure to devote to the study of the question as its importance demands. In the present preliminary report we shall merely sketch out the . plan which we propose to pursue in our investigations, so that when our fellow-members are called upon to assist us in our work by furnishing statistics, etc., they may understand more clearly for what object our inquiries will be made. As one of the most practicable methods of obtaining the information requisite for an intelligent consideration of our subject, we propose to send, from time to time, to members and others interested in the mining of anthracite coal, printed sets of questions relating to points under consideration. We would here impress upon our fellow members the importance of filling up these papers as far as they can from their own knowledge. We would, of course, wish each question to be answered as fully as possible, but we do not expect every one to answer them all. One question well answered would be of more use to us than the whole paper filled up with answers, many of

By Nobuhiro Takahashi

PROLOGUE The Yaguki mine, which is located near the southern end of the Tohoku region, Japan, near the coast of the Pacific Ocean, had had a long history as a copper mine, but had not been operated since 1925. About 30 years later it was reopened by Nittetsu Mining Company, and in 1958 a small flotation and magnetic separation plant, a so-called test plant, started production. The ball mill the author first met, a 8x4x4x7 ft tricone mill, called No.1 mill, had started running at that time. With his experience in initial, running of this mill he realized that the ball mill was not simply a preparatory process to flotation, but a determinant factor for flotation performance, an energy-consuming and costly process, and that its operation control was an important task in the plant (1). The working part of an operating ball mill is the ball load inside, whose properties govern the grinding performance. Its size distribution affects the efficiency greatly and the capacity is nearly proportional to its weight. When a ball mill operates for a long period of time with a constant and consistent addition of renewal balls, wear and renewal of balls are balanced, and an equilibrium ball load is formed. A stable equilibrium load is the primary requirement for a stable ball mill operation. However, renewal ball size would be the most influential factor affecting efficiency and capacity of operating ball mills. To improve efficiency, to increase capacity, or to get finer product, attempts to find out the optimum size assortment of renewal balls should be made. When re-

Jan 1, 1976

By C. L. Berrien

BEFORE the present company was formed, in 1916, each group of mines comprising the old organizations made its detailed daily and monthly mine cost records along the lines used before the consolidation; that is, there was no attempt made to standardize and compare the stope costs of all mines. The general cost sheets for all mines, however, were standardized, and cumulative labor cost sheets were compiled in the general superintendent's office. At most of the mines, a daily record or distribution sheet for each working place was kept, showing the number of men, hours of drilling, hours of timbering, hours of tramming, cars of ore, cars of waste, sticks of powder and feet of fuse. This information was kept by each shift boss and entered on the distribution sheet by him or, at some mines, by a tram boss. The superintendent solved his own problems under the direction of the general superintendent, but without coming in touch with other superintendents, either through records or general conferences. Probably 95 per cent. of the stopes were square-set worked by day's pay; there were some back-filling and shrinkage stopes. Many of the development places, such as shaft sinking, station cutting, drifting and raises had always been run by contract. These contracts were given, for no definite period, at so much per linear foot and were measured monthly, or when completed; the men being paid monthly. In some cases, fairness to the employee, was not maintained. On the whole, there was no standardization. There were no stope contracts, because of the objections of the Western Federation of Miners to general contracting in the mines.

Jan 2, 1922

INTRODUCTION TO COMPOSITING Individual drill hole samples may vary greatly in size, length, and weight. The sample interval may represent any convenient unit of hole length, and is usually related to the type of drill being used to obtain the sample. Depending upon the type of mineral deposit, it is desirable to group the individual sample values into composite weighted values representative of some particular zone or volume of the ore body. For example, values of several sequential samples of diamond drill core 3 m (10 ft) in length may be grouped together to represent a 12-m (40-ft) sample value over one bench height. On the other hand, several individual sample values taken across the thickness of a stratiform deposit or a vein zone may be weighted together to represent the value of the total thickness at the point of intersection. The choice of composite intervals is usually dictated by the type of mineral deposit and the mining method selected to produce the mineral. The techniques of weighting values from various lengths of samples into a composite value has already been discussed briefly in Chapter 3. Further examples of determining weighted composite values will be given in the following discussion on compositing for various types of mineral deposits. SAMPLE VALUE COMPOSITES AND TYPES OF MINERAL DEPOSITS There are many kinds of mineral deposits, each of which will require special treatment of sample data to obtain the best composite intervals for evaluating the deposit. It cannot always be known before hand what the optimum composite interval will be. Such composite intervals may properly be determined by geologic factors that are often unknown prior [ ]

Jan 1, 1980

By Heinrich Ries

The clay-resources of Colorado are but little known, for the reason that little has been published concerning them, and also on account of the hitherto small demand for clay products in the Rocky Mountain region. At the present day the wares manufactured from clay which are used in Colorado include common and pressed brick, terracotta, sewer-pipe, pottery and refractory articles. Most of these are brought from a considerable distance; but with an increasing demand for such goods in the West and a better knowledge of the available materials, there should be considerable expansion in the clay-working industry of Colorado in the future. The notes here presented are an abstract of those collected by the writer in October, 1896, in a reconnaissance of the clay-bearing formations of Colorado. Clay-bearing Formations. We may roughly divide the clay-bearing formations of Colorado into three groups : 1. Loess and alluvial deposits. 2. Jura-Trias and Cretaceous clays. 3. Tertiary clays. . The loess forms an extensive deposit of large area, though not very thick, extending from north to south across the State, and eastward from the foot-hills. It is generally a very sandy clay, with little plasticity, and is underlain by a gravelly stratum, which determines the workable depth. Clay similar to the loess is found underlying the river terraces in many of the broader valleys, such as those of the Arkansas, Grand River, etc. The Mesozoic formations extend along the eastern edge of the Rocky Mountains, and also occur in some of the deeper valleys tributary to the foot-hill belt. They consist of a great series of interbedded shales, sandstones and limestones of Jura-

Jan 1, 1898

By S. R. B. Cooke, C. E. Thurston, G. Kudo

The trend toward utilization of low grade iron ores means that more efficient methods must be developed for their concentration. The collecting ability of fatty acids derived from fish oils has been extensively investigated by Cooke.' Tuna oil, a byproduct of the tuna canning industry, is one of the lower priced fish oils. Utilization of tuna oil fatty acids as collectors in the flotation of iron ore might be economically feasible under certain market conditions, especially if their efficiency were high. Crude or unfractionated tuna oil fatty acids, and five fractions derived therefrom, were tested for their ability to concentrate a commercial specularite ore from northern Michigan. A commercial fatty acid derived from tall oil, and commonly used in nonsulfide flotation, was used as a reference. The crude fatty acids were obtained by simple saponification of tuna oil. Fractions A and B were obtained by acetone precipitation of the crude acids at -5O and -2S°C, respectively. Fraction C was obtained by a partial fractional distillation at 12S°C and at a pressure of 3y in a centrifugal molecular still in order to remove the shortest and longest chain fatty acids of tuna oil as well as oxidation products present in the original mixture. Fractions D and E were prepared by a chilling process in order to precipitate the unwanted saturated fatty acids. Yields and iodine values of the materials used are listed below: The seven samples were used as collectors in a laboratory procedure patterned after the commercial process for flotation of Michigan specularite ore. The outline of the procedure is that previously described1

Jan 1, 1962

By Harold M. Mooney

RESISTIVITY measurements for determining depth to bedrock, water table, and other geologic discontinuities have had only limited success. Many of the difficulties can be attributed to complex geology and to basic limitations of the method; current flow through a continuous medium is a diffusion phenomenon, emphasizing irregularities near the source and smoothing out those at a distance. Some of the failures, however, are due to careless field work and incompetent interpretation. A forthcoming publication1 may help to reduce difficulties of this sort. The writer here attempts to bring order into the multiplicity of interpretation methods and, to a limited extent, to evaluate them. For all methods, the field data to be interpreted consist of apparent resistivity values plotted against electrode separation, Fig. 1. The interpretation should give depths to one or more geologic horizons. Direct currents and the Wenner four-electrode configuration will be assumed, since these are widely used, although the interpretation problems remain essentially the same for other electrode configurations. Alternating currents higher than, say, 20 cycles per second introduce complications beyond the scope of this paper. Three approaches to the interpretation problem have been used. These may be called empirical, theoretical curve matching, and direct. Many techniques have been proposed, but each can be reduced to one of these approaches and to a single geologic idealization. This idealization rests on the following assumption: the earth in the limited volume of interest can be approximated by a horizontal sequence of layers, each homogeneous and isotropic in its electrical properties. This seemingly restrictive assumption has proved to have practical value, although future work should aim at removing some

Jan 1, 1955

By Adolf Gurlt

It has long been known that minute quantities of foreign substances, when alloyed with steel, are capable of materially altering its physical properties. Thus, half a century ago, Faraday and Stodart, in England, discovered in the famous Indian steel, known as " wootz," small quantities of aluminum, from 0.0728 to 0.693 per cent., and attributed its extraordinarily good quality to the presence of such minute quantities of that metal. Since aluminum is now produced by electrolytic means on a large scale and at low cost, its addition to cast-steel has been frequently recommended of late. Chromium was alloyed with steel fifty years ago by the celebrated French metallurgist, Berthier, of Paris, and has recently been successfully applied to the same purpose by Holtzer, of Terre-Noire. In 1860 titanium was alloyed with crucible steel by Robert Mushet, of Coleford, the alloy containing up to 0.50 per cent. of titanium, which was extracted from Norwegian ilmenite. The titanium-steel was much vaunted by him for its excellent qualities. Rhodium, a very rare metal of the platinum series, was maintained by Berthier to improve steel materially in strength and hardness. Manganese has always been held by Sheffield steel-melters to provide steel with excellent qualities, and this influence was quite recently investigated by H. M. Howe and L. Campredon. Nickel was tried as an addition by Berthier, not to speak of gold, silver and platinum ; and nickel-steel has recently been brought into prominence by J. Riley and others, who recommend it for its great strength and toughness, particularly as material for armor-plates.

Jan 1, 1894

By J. M. Gaines, C. H. Herty

It is a matter of frequent record in the literature that manganese will desulfurize molten iron under proper conditions. Particularly has much been written with regard to this action in the mixer, and numerous reports have been published describing experiments in which advantage was taken of this phenomenon in order to obtain a purer iron for the open hearth. The question of sulfur elimination in the ladle has, however, received comparatively little attention. The reaction by which sulfur is removed is considered to be: FeS + Mn = MnS + Fe. The manganese sulfide, being but sparingly soluble in the iron, and of a lower density, will rise from the body of the metal and collect as a slag on the surface. It is therefore an action taking place solely in the metal, and independent of interaction between slag and metal. As will be shown later the presence of slag on the metal tends to offset the effect of manganese elimination. It is this fact which distinguishes desulfuriza-tion in the ladle from desulfurization in the mixer, for it has been shown1 that the amount of sulfur eliminated in the mixer is closely tied up with the composition of the slag. Experimental Procedure In order to ascertain the extent of and the factors controlling this elimination in the ladle, several casts were sampled carefully at the blast furnace and again when the ladles were being emptied, either at the mixer, open hearth, or foundry. If the sulfur content varied from ladle to ladle at the blast furnace the average sulfur content of each ladle was obtained by integrating the curve "sulfur vs. time " for the cast under

Jan 1, 1927

By G. E. McElroy

MUCH attention has been directed to mine-air flow in recent years, more especially in Great Britian where there is frequent reference to a theory of fluid flow developed by English engineers. Briefly stated, this theory is that for similar passages of the same relative roughness, in which fluid flow occurs, the conditions of flow are exactly the same for equal values of the product W D V/ µ, where W = density of the fluid, D = diameter of the passage through which flow occurs, V = mean velocity of flow, and µ = absolute viscosity of the fluid flowing. This, the "Reynolds Criterion" of fluid flow, had its origin in the work of Prof. Osborne Reynolds' more than 40 years ago. Later, Lord Rayleigh amplified the theory2 which has been conclusively proved for small pipes by the experiments of Stanton and Pannel3 over a large flow range, and by Lacey4 over a somewhat more limited range. Concordant results on small pipes have also been obtained by numerous other investigators with single fluids over more or less limited ranges of flow. According to this theory results in one medium, such as water, are immediately applicable to another, such as air; and experimental results on models are (theoretically, at least) applicable to full-scale designs. This is of great importance in aeronautics and can be of considerable value in mine ventilation research. Hodgson, in a recent paper,5 has outlined the application of this theory to mine-air flow and recent English experiments" on the resistance of a timbered mine airway have been expressed in this form.

Jan 10, 1926

By Henry Hanson

A STUDY of the ore to be treated should be the first step in deciding on a machine for crushing or grinding. Coarse crushing is practically confined to the jaw and the gyratory crushers, the large-size jaw type being often employed in large installations as a primary crusher, followed by the gyratory type for secondary reduction. In small plants where mine-run ore is reduced in a single step, either of these machines will do the work. In intermediate and fine grinding, various machines are used. The relative merit of the different types will be governed in no small measure by the size of the installation, the character of the ore to be reduced and the final product desired for subsequent treatment. It should be possible, nevertheless, with the data available, if properly classified, to arrive at an approximation of the relative efficiency of these intermediate and fine grinders. It should be possible, also, to determine the economic grinding range of the different machines. With this in mind, it will be the object of this article to indicate, in rough outline, how the data available may be classified, rather than to attempt to discuss any particular practice and compare the results with other practices. Conclusions or generalizations can not be drawn without an exhaustive classification of data; in fact, many vital points will have to be determined by additional experiments which can be carried on most advantageously in the laboratory. The expense en-tailed in such experiments would be worth while if the data obtained should lead to definite conclusions that would aid in standardizing and simplifying grinding practice.

Jan 2, 1923

By Milton E. Wadsworth

INTRODUCTION The purposes of this conference are aimed mainly at the treatment of fine or ultra fine particles in terms of beneficiation and chemical processing of minerals. For this reason the discussion on leaching will be confined to processes which treat slurries rather than those which treat a large variety of low and medium grade materials by vat leaching or dump leaching techniques. This eliminates such hydro-metallurgical systems as solution mining from consideration. This discussion will focus predominantly upon the behavior of fine particles as associated with their chemistry in leach reactors. Four major sub-headings may be pointed to as encompassing the major areas in which research and engineering design activity should be directed. These are: 1) generation of fine particles, 2) heterogeneous kinetics of leaching, 3) solution chemistry, 4) engineering design and control of flow reactors. Each of these topics will be addressed briefly in this presentation to illustrate current developments and future needs. GENERATION OF FINE PARTICLES As will be pointed out more quantitatively in the next section the generation of fine particles has great influence upon leaching systems inasmuch as in most cases the rate of leaching is related to the surface area of the particles involved. This is true for acid or base leaching of oxide minerals as well as a large variety of sulfides which have been considered in commercial processes and which have in the case of copper received increased attention during the past decade. Mean particle sizes of slurries vary broadly depending upon the type of grinding equipment being used. For example, in the agitation leaching of uranium ore the slurry typically consists of particles approx-

Jan 1, 1979

By C. E. Beecher

THE application of gas or air under pressure to obtain more oil from a sand which has been practically exhausted by ordinary production methods has been practiced to a limited extent for many years. Until recently such methods were confined to the Eastern fields, principally those of Ohio and West Virginia, where in many cases the production obtained after applying pressure for a few years was nearly equal to the total production prior to that time which had been obtained by the usual production methods.' As early as 1917, J. 0. Lewis1 called attention to this method of increasing the recovery of oil and cited the phenomenal results obtained by H. E. Smith, I. L. Dunn and 0. C. Dunn, who pioneered the application of air or gas pressure recovery methods. With this information available it would appear that other oil-producing sections of the country have been extremely slow to realize the advantages of repressuring. However, after a few successful projects in the Mid-Continent area, the oil producers appreciated the value of this method for obtaining further and profitable production from their practically exhausted leases and are now making extensive use of it. In general, it has been the practice to apply pressure to the sands when production has declined to a small yield per well. The purpose of this paper is to discuss some of the advantages which may be expected from returning gas under pressure to the oil sands during the early stages of development, before the rock pressure has been dissipated and the gas exhausted, and to stimulate discussion of this subject on which comparatively little actual field data are available.

Jan 1, 1928

By Sylvain J. Pirson

The question of the interpretation of apparent resistivity curves is still a much disputed subject although the discussion has been going on for several years, mainly since Gish and Rooneyl made their first measurements on the Tidal Basin at Washington, D. C. As a first approximation, they interpreted the depth to a horizontal discontinuity in terms of the electrode spacing at which a maximum or a minimum occurs in the resistivity curve. Later on, Lancaster-Jones2 proposed a closer approximation of depth determination by evaluating the depth to a horizontal discontinuity as the two-thirds of the electrode spacing at which a point of inflection occurs in the resistivity curve. An accurate determination of the depth was recently proposed by Tagg3 for a two-layer problem. It is a graphic solution of the problem by means of charts calculated from the formula of the apparent resistivity based on the theory of electrical images. Tagg's method is theoretically sound but the fact that the layers have been assumed to be homogeneous and isotropic must not be overlooked. Abusive use of the method has been made by geologists who have failed to recognize the fact that nature offers only few cases where the conductivity of the rocks may be assumed to be the same parallel and perpendicular to the bedding plane. Actually the ratio of the two resistivities in those directions may take values ranging from one (isotropic medium) to three for shales. In such conditions Tagg's method leads to disappointments. A method recently advocated by Manhart4 and Tattam6 forces Tagg's method to give a solution where manifestly the case under

Jan 1, 1934