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By I. N. Knapp

I Herewith present some notes on the use of Portland cement to cement in the casing, and for plugging, to exclude water from oil and gas wells, and the methods employed. I have used my best efforts to. make each step of the operation of cementing wells perfectly clear. The information is the result of actual experience and observation. The illustrations are from original drawings made especially for this paper. Portland Cement It is not necessary to discuss here the manufacture of cement. Any established brand of the slower setting Portland cements may be purchased with the confidence that it will harden, if properly used, and exclude water from and plug wells efficiently. Setting.—By the setting of cement is meant its initial change from a soft or plastic mortar to a friable solid. After the cement has become thoroughly set it is still very weak and can be readily pulverized in the fingers. Setting is thought to be effected by the crystallizing out of the silicate and the aluminate of lime, which are soluble in water in their anhydrous form. After dissolving in the water they pass to the hydrated state, in which they are insoluble, and hence are precipitated in a crystalline form. Ordinarily neat Portland cement mortar remains perfectly plastic for from 1 to 1 1/2 hr. after mixing with water at about 70" F. A higher temperature accelerates and a lower retards setting.. Hardening.—This is due to a continual crystallization of salts from solution, and to further chemical and physical changes which develop slowly, but which continue for long periods of time. Testing.—It is no more necessary for an operator to go into the scientific testing of cement to be used in a well than to so test the pipe used. He must depend for the quality of each on the tests and reliability of the manufacturer. Cement or pipe may be damaged in shipment so

Jan 1, 1915

By George A. Jr. Dornin

A TRULY sound ingot can be made only from steel that is completely deoxidized. Given this condition, there is one further basic requirement-the steel in the ingot must solidify progressively from the bottom to the top. Any method of making the ingot that produces this type of solidification will yield sound products. Since a big-end-down ingot will not satisfy this condition, all sound steel today is produced in big-end-up ingots, the standard tool being the big-end-up mold fitted with some sort of refractory hot top. No one uses hot tops from choice, be cause of the bother and expense involved and because of the low yield resulting from their use-they are used because there has been no alternative where sound steel was required.

Jan 1, 1947

By F. V. Greene

This paper is based on my experience in the use of asphalt, for paving and other purposes, during the last ten years, part of the

Jan 1, 1889

By L. K. Welch, C.W. Macgregor

The past 20 years has seen a revolutionary change in the testing of materials at elevated temperatures. This has largely been brought about by the practical importance of the creep problem in the design of equipment for operation at high temperatures. The short-time tension test carried out at elevated temperatures has consequently assumed in many cases only a secondary role compared with the longtime creep test. In many problems, however, a knowledge of the short-time high-temperature properties of a metal is essential. To mention a few cases in which this is so, we might include all hot-forming operations such as rolling, forging, etc., the welding problem if residual stresses are to be computed, the development of new alloys for high-temperature service where, in the initial stages, time does not permit of long duration creep tests, and others. Usually a knowledge of the short-time properties is desired, if only to serve as a background against which to compare creep behavior. In conducting short-time high-temperature tests, it has been almost the universal practice to determine stresses based on the original area and strains referred to the original gauge length which is usually chosen as 2 in. It has been pointed out1,2 that one of the reasons that the true significance of certain tensile properties is not understood, which perhaps curtails their usefulness, especially when the material is applied under conditions differing considerably from the test conditions, is that true physical stresses and strains are not determined. It is essential to have a knowledge of true stresses and strains in order to correlate the values present in the tension test with those existing, for example, in hot metal-forming operations and in the general problem of the yielding and failure of metals under combined stress conditions. Stress and strain values based on the original dimensions of the test piece do not exist physically except in the early stages of the test. Since at the present time there is very little information in the literature on true stress-strain relations in the short-time high-temperature tension test it is proposed in the following pages to describe a

Jan 1, 1943

By L. K. Welch, C. W. MacGregor

The past 20 years has seen a revolutionary change in the testing of materials at elevated temperatures. This has largely been brought about by the practical importance of the creep problem in the design of equipment for operation at high temperatures. The short-time tension test carried out at elevated temperatures has consequently assumed in many cases only a secondary role compared with the longtime creep test. In many problems, however, a knowledge of the short-time high-temperature properties of a metal is essential. To mention a few cases in which this is so, we might include all hot-forming operations such as rolling, forging, etc., the welding problem if residual stresses are to be computed, the development of new alloys for high-temperature service where, in the initial stages, time does not permit of long duration creep tests, and others. Usually a knowledge of the short-time properties is desired, if only to serve as a background against which to compare creep behavior. In conducting short-time high-temperature tests, it has been almost the universal practice to determine stresses based on the original area and strains referred to the original gauge length which is usually chosen as 2 in. It has been pointed out1,2 that one of the reasons that the true significance of certain tensile properties is not understood, which perhaps curtails their usefulness, especially when the material is applied under conditions differing considerably from the test conditions, is that true physical stresses and strains are not determined. It is essential to have a knowledge of true stresses and strains in order to correlate the values present in the tension test with those existing, for example, in hot metal-forming operations and in the general problem of the yielding and failure of metals under combined stress conditions. Stress and strain values based on the original dimensions of the test piece do not exist physically except in the early stages of the test. Since at the present time there is very little information in the literature on true stress-strain relations in the short-time high-temperature tension test it is proposed in the following pages to describe a

Jan 1, 1943

By Robert Mehl

THE system cadmium-mercury has attracted much attention, chiefly because of its importance in the study of electrochemical standard cells. The constitutional diagram, as it is accepted today, is essentially that FIG. 1.-BIJL'S DIAGRAM FOR CADMIUM-MERCURY ALLOYS. developed by Bijl1 (Fig. 1), though there has been a great amount of work done on the system by other workers.2 A year ago the senior author published a paper on the crystal structure of the system, in which were described determinations of crystal structure

Jan 1, 1929

By S. A. Shoop, J. J. K. Daemen

Site-specific blast vibration prediction can be more accurate than using a universal prediction equation. Vibrations from 37 blasts were monitored using three seismographs. Data analysis showed that square root, cube root, and site-specific scaling predicted ground motion with equal reliability. Imprecise prediction is caused by geologic and blast variability, particularly, inaccurate delay times. Vibrations at some mines were consistently lower or higher than vibrations predicted from US Bureau of Mines (USBM) equations. Vibration restrictions based on USBM studies could then be too conservative or too lenient. Predominant vibration frequencies were generally less than 50 Hz, but several blasts had significant energy up to 125 Hz. In some cases, energy was concentrated at frequencies corresponding to delay intervals.

Jan 1, 1985

By Fred K. Stieler

The largest updraft sinter machine built has a roasting area of 132 sq.m. Sinter machines with an area of over 200 sq.m. are under consideration. These large machines require new techniques with regard to drive thrust and sealing mechanism. To optimize the results of sinter plants, the charge preparation systems and the return fines circuits were improved. Special crushers were developed for crushing return sinter of up to 800 ºC to a size of minus 6 mm. Strand cooling of Pb-sinter was investigated. Different methods for plant ventilation were compared. New processes, which might replace sintering in the future, are in the stage of large - scale testing.

Jan 1, 1977

By E. H. Cho

INTRODUCTION Activated charcoal has been used for several centuries in many capacities including the recovery, isolation and purification of various materials (1). The first use of charcoal in a gold metallurgical system was in the extraction of gold after chlorination (2, 3,4). The gold was dissolved in a chlorine system and subsequently filtered through charcoal. The application of charcoal with cyanide extraction was patented by Johnston (5) in 1894 and adopted commercially in Australia in 1897. The process consisted of dissolving the gold and silver in a potassium cyanide solution and passing it through a series of charcoal filters. The charcoal was subsequently smelted to recover the gold and silver. The interest in the use of charcoal diminished in the first part of the twentieth century as the practice of the use of zinc as a precipitating agent increased. However, in 1916, the Yuanmi Mine in Australia replaced their zinc precipitation plant with a charcoal adsorption plant. In 1926, Scott and Gross (7) of the U. S. Bureau of Mines con- ducted extensive research on the adsorption of gold and silver from cyanide leach solutions. Among their findings was the result that the most important factor in improving the adsorptive power of charcoal was heat treatment with oxidation by air or steam. The work of Zadra (8) in 1952 stimulated renewed interest in the use of activated charcoal in gold and silver recovery with the development of a method of recovery of the gold and silver from the charcoal other than its destruction by burning. The process involved simultaneous desorption

Jan 1, 1983

By George Rupp

THE Sunrise iron mine of The Colorado Fuel and Iron Corporation is in Platte County, Wyoming, about 110 miles north of Cheyenne. It is served by the company-owned Colorado and Wyoming Railway, which connects with the Chicago, Burlington and Quincy and the Colorado and Southern railways at Guernsey, Wyoming, a distance of 6 miles from the mine. The original Sunrise claims were staked mainly by United States Army officers and soldiers stationed at old Fort Laramie, because of small showings of copper in the Carboniferous limestones that form a horizontal capping overlying the Huronian iron ore. A small copper smelter was operated for about three years at Fairbanks, now an aban-doned town on the North Platte River. As many of the copper shafts and test pits near the present Sunrise mine were deepened, they pene-trated the capping and encountered iron. ore or gray sericitic schist, and were abandoned. Evidence of an early interest in iron ore was found when the Chicago claim was stripped for mining. A narrow, winding crevice was dis-covered, which led downward 20 ft. through the capping to the underlying soft red hematite, in which a room 10 by 14 by 7 ft. had been excavated. Stone hammers and wedges and a few rusted pieces of iron were found on the floor, and the evidence is conclusive that the excavation was used up to rather recent times by Sioux Indian medicine men, to provide war paint.

Jan 1, 1939

By A. J. Sinclair

Sampling methods for feasibility studies are dependent on geological characteristics of the deposit being evaluated. A preliminary geostatistical study is required, taking into account autocorrelation aspects of variables under study in order that sample plan design can be optimized to produce grade and tonnage estimates within stipulated error limits. In general, regular sample distribution is to be aimed for, and regular sample lengths (from drill core or cuttings, for example) are preferred in order to facilitate statistical analysis. Sample plans are modified and improved (either technically or economically), as a sampling program proceeds and additional information is obtained. Bulk samples for metallurgical testing can be evaluated in terms of the variance shown by all such samples in a deposit and the internal variability of grade. Attention to these sources of variability will ensure proper evaluation of pilot test results from bulk samples. In addition, a general mineralogical study of a deposit is an important, often ignored, requirement in a more general but semi-quantitative evaluation of the representativeness of a bulk sample; and, moreover, provides information useful in optimizing plant design.

Jan 1, 1978

By Arthur Phillips

THE study of anisotropy in metals has been greatly stimulated in recent years by the rapid development of X-ray methods for determining the crystallographic relationships of wrought and annealed materials. Prior to this time the knowledge regarding the directional properties of commercial alloys consisted almost exclusively of observations of a practical nature made during the fabrication of metal objects, supplemented by a limited number of mechanical tests on specimens cut at various angles to the direction of working. Such observations clearly indicate that the common methods of cold-working metals cause both a crystallographic and a mechanical fibering varying in character and degree according to the nature and extent of the deforming process. Even after annealing, following certain not too well known combinations of reductions and anneals, a preferred orientation may exist, thereby constituting a residual fiber effect sufficiently pronounced to manifest directional properties. With the application of the X-ray the experimental horizon was extended chiefly because the study of anisotropic metals promised to offer direct and quantitative evidence regarding the involved mechanism of fragmentation and plastic flow. As a natural consequence the intensive studies in this direction have yielded a vast accumulation of data of ultimate potential value. Unfortunately, however, as is commonly the case in entering a virgin field of experimentation, many of the data cannot be molded into complete and coherent form because of the many unrelated conditions of the experimental projects. Again, the results of the study of single crystals have been rather naturally but at times indiscriminately applied to polycrystalline metals. Furthermore, sweeping statements have been made regarding the behavior during working and annealing of metals and alloys, entirely on the basis of similarity in lattice arrangement. There is abundant reason for believing that relatively small concentration variables, differences, in magnitude and distribution of applied stresses, and the character of associated annealing treatments may in some cases greatly influence the mechanics of flow and consequently largely determine the final structural characteristics of the metal.

Jan 1, 1932

By Frederick Laist

(Butte Meeting, August, 1913.) WHILE remodeling No. 1 section of the concentrator at the Washoe Reduction Works of the Anaconda Copper Mining Co. during the summer of 1912, for the purpose of ascertaining what additional metal recoveries could be made by improvements in concentration practice which had been developed by the staff of the Boston & Montana Reduction Department, at Great Falls, it was deemed advisable to carry on some experiments on the treatment of the regular mill tailings by roasting and leaching, to see whether the losses of metal values might not be still further decreased. In the course of these experiments about 5,000 tons of tailings were roasted, and of the resulting calcine about 200 tons were leached. The results were so satisfactory that it was decided to continue the work on a larger scale, particularly as regards the leaching end of the process, and construction work on an 80-ton roasting and leaching plant was accordingly commenced during the latter part of February, 1913, and is being pushed as rapidly as possible. 80-Ton Leaching Plant. This plant will consist of one 20-ft. roasting furnace of the MacDougall type, specially adapted to the work of roasting for leaching; two leaching tanks, .32 ft. in diameter by 12 ft, deep, together with the necessary solution tanks, air lifts, precipitating launders, etc. It has been decided to precipitate the copper from solution on scrap iron, so as not to hamper the roasting and leaching departments by any weakness that might develop in the precipitating department. It is, however, the intention to experiment with a number of different methods of precipitation ; for example, by electrolysis and by hydrogen sulphide.

Jan 7, 1913

By T. N. McVay, E. E. Creitz

INTRODUCTION Object RATHER large amounts of titanium minerals and some zircon and monazite are being recovered from dune sands about 10 miles west of Jacksonville Beach, Fla. The Mining Branch of the Bureau of Mines, Southern Experiment Station, has been interested in developing additional large deposits of similar sands in other areas of Florida. The results of a field study have been published1 concerning the sands occurring on Trail Ridge which runs north and south about 30 miles southwest of Jacksonville. This investigation was undertaken in order to identify the opaque titanium minerals occurring in Trail Ridge and because of the economic importance of Florida titanium minerals. Nature of the Problem The minerals present in the heavy fractions (sp gr > 2.94) of the sands are principally opaque minerals; staurolite, zircon, sillimanite, tourmaline, kyanite, rutile, a small amount of corundum, traces of the zinc spinel gahnite and garnet. Epidote, monazite, hornblende and titanite are present in other dune sands but these minerals were not noted in the samples collected on Trail Ridge. All of the minerals except those which are opaque can be readily identified by the usual petrographic methods. However, opaque minerals cannot be examined satisfactorily by transmitted light. Polished sections of the opaque-mineral grains were examined but these sections did not furnish useful information. Consequently, it was necessary to use means other than the usual petrographic methods to identify them. Previous Investigations of Heavy Minerals in Florida Sands Martens2 has described the heavy minerals in the Florida beach sands and has classified the opaque minerals as ilmenite with minor amounts of leucoxene. Miller3 studied a number of sands collected by Ross and Mertie in Florida. He states that the material from the Florida beach and dune sands that commonly has been called ilmenite has essentially the chemical composition of the material that has been called arizonite.4 The X ray diffraction patterns of several samples indicated that the supposed ilmenite is essentially amorphous, with only weak lines corresponding to ilmenite, and hence the material is unlike the type of arizonite from Arizona. Opaque Titanium Minerals Rutile is essentially titanium dioxide. However, as pointed out by Dana,5 important amounts of Fee and Fe3 as well as Cb and Ta are reported in some analyses.

Jan 1, 1947

By Lloyd R. Jackson

IN the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: I. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalid strains in determining the effect of plastic flow on the work-hardening of metals. FUNDAMENTALS INVOLVED IN PLASTIC FLOW In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Never- the less, as will be shown, metals are close enough to being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of .isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables-six being stress variables, and six being strain variables. ) From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining. This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses . and one for strains) that have received most attention are the following: [ ]

Jan 1, 1946

By H. R. Reed

THE cost of hoisting with electricity in deep mines is a matter about which little information has been published. This paper makes a detailed study of such costs and presents the information in a series of curves. In particular the curves show the cost of hoisting ore from depths varying from 500 to 7000 ft. vertical with the shaft at 70º incline for the double cylindroconical and double cylindrical drums, the hoists operating balanced, using Ward Leonard and Ilgner-Ward Leonard control, and designed for most economical operation from each depth. Operation with the double cylindrical drum is expanded to cover hoisting from 2000 to 5000 ft. using equipment designed for 5000 ft. and from 4000 to 7000 ft. using equipment designed for 7000 ft. Additional curves are included to show the ratings of the necessary hoist motors, energy input per hoisting cycle and size of flywheel in tons for complete equalization when the Ilgner-Ward Leonard system is used, also hoisting efficiency. The duty imposed on a mine-hoist motor fluctuates between wide limits during a cycle of operation. The demand on the motor may vary from a large horsepower value near the beginning of the cycle to a small or a negative demand near the end of the cycle. Such factors as tonnage to be raised per hour, depth of shaft, and balanced or unbalanced operation have such a marked effect on the operating cycle and vary to such an extent for different mines that no set of rules can be formulated for quickly determining the size of the motor required. The duty cycle from which the motor rating is derived must be determined for each case according to the conditions of the proposed hoisting operations. The motor torque required at the cardinal points of the duty cycle is determined from the moment or torque in pound-feet necessary to raise and lower the load and ropes, accelerate and retard the load, ropes, drum, etc. The torque diagram depends largely upon the type of drum. Two different types of drums, if used on exactly the same duty cycles, may have widely different peak demands and capacities of hoist motors. The essential feature in the design of hoisting drums and in determining

Jan 1, 1937

By Henry Faul

Measurement of radioactivity of rocks and ores has developed into a complete method of geophysical exploration. The problem falls into three natural categories: (1) surface radiation measurement in the field and underground; (2) radioactivity logging of drillholes; and (3) laboratory analysis of samples. Portable counters are used in the field for tracing radioactive formations and for quanti tative estimates of radioactive content of surface rock. Wartime advances in battery design make it possible to construct small precision counters that can be carried easily. Even the smallest conventional diamond drillholes can be logged, and actual content of the radioactive element can be measured. The exact grade of very thin active layers or veins can be estimated only approximately. Samples may be analyzed for their alpha, beta or gamma activity, and beta assaying is the best suited to rapid routine operation. Simple calibration with standard samples is sufficient for rough work, but a density correction is necessary when greater precision is required. Samples with high emanating power should be fixed and stored for three weeks to reestablish the radium-radon equilibrium prior to precision assaying. Carno-tite can be fixed by sintering or molding with plastics. Among the important new developments, a low-voltage Geiger tube has been 'designed recently, and crystal scintillation counters hold great promise for high-efficiency gamma-ray measurement. Introduction During the last few years we have witnessed an unprecedented rise in the demand for radioactive minerals, coming as a direct consequence of the discovery of nuclear fission and subsequent developments, the full impact of which is by no means in sight even now. It remains certain, however, that radioactive minerals, and especially those which can be used as ores of uranium and thorium, will continue to be of great interest not only to the prospector and mine operator but also to the various inspection parties envisioned by most of the schemes advanced for the control of nuclear energy on a world-wide basis. It is clear, therefore, that the measurement of radioactivity in rocks in the field as well as in samples in the laboratory has become a method of geophysical exploration of some importance. If we consider the recent technological advances in the general fields of nuclear physics and electronics it seems proper to review the present status of the methods and procedures of radiological exploration. General Considerations Equilibrium If we take a fixed amount of uranium that has just been purified, some of it will immediately start decaying into its first daughter element which in turn decays into its own daughter and so on down the line until the last daughter is reached—a stable isotope of lead. The rate at which a radioactive element decays is frequently expressed as the half-life, which is the length of time required for the decay of half the atoms in a given amount. The half-life is inversely proportional to the decay constanl X which is defined as the number of atoms which decay in one unit of time divided by

Jan 1, 1949

By Henry Faul

Measurement of radioactivity of rocks and ores has developed into a complete method of geophysical exploration. The problem falls into three natural categories: (1) surface radiation measurement in the field and underground; (2) radioactivity logging of drillholes; and (3) laboratory analysis of samples. Portable counters are used in the field for tracing radioactive formations and for quanti tative estimates of radioactive content of surface rock. Wartime advances in battery design make it possible to construct small precision counters that can be carried easily. Even the smallest conventional diamond drillholes can be logged, and actual content of the radioactive element can be measured. The exact grade of very thin active layers or veins can be estimated only approximately. Samples may be analyzed for their alpha, beta or gamma activity, and beta assaying is the best suited to rapid routine operation. Simple calibration with standard samples is sufficient for rough work, but a density correction is necessary when greater precision is required. Samples with high emanating power should be fixed and stored for three weeks to reestablish the radium-radon equilibrium prior to precision assaying. Carno-tite can be fixed by sintering or molding with plastics. Among the important new developments, a low-voltage Geiger tube has been 'designed recently, and crystal scintillation counters hold great promise for high-efficiency gamma-ray measurement. Introduction During the last few years we have witnessed an unprecedented rise in the demand for radioactive minerals, coming as a direct consequence of the discovery of nuclear fission and subsequent developments, the full impact of which is by no means in sight even now. It remains certain, however, that radioactive minerals, and especially those which can be used as ores of uranium and thorium, will continue to be of great interest not only to the prospector and mine operator but also to the various inspection parties envisioned by most of the schemes advanced for the control of nuclear energy on a world-wide basis. It is clear, therefore, that the measurement of radioactivity in rocks in the field as well as in samples in the laboratory has become a method of geophysical exploration of some importance. If we consider the recent technological advances in the general fields of nuclear physics and electronics it seems proper to review the present status of the methods and procedures of radiological exploration. General Considerations Equilibrium If we take a fixed amount of uranium that has just been purified, some of it will immediately start decaying into its first daughter element which in turn decays into its own daughter and so on down the line until the last daughter is reached—a stable isotope of lead. The rate at which a radioactive element decays is frequently expressed as the half-life, which is the length of time required for the decay of half the atoms in a given amount. The half-life is inversely proportional to the decay constanl X which is defined as the number of atoms which decay in one unit of time divided by

Jan 1, 1949

By O. M. TUPPER

REQUIRING a finer ground clay than that obtainable with a dry pan or hammer mill, the Clay Corporation of California installed a five-roller, low- side Raymond impact mill at its Lincoln plant in 1925 and since then has been economically grinding fire clay with a moisture content as high as 15 per cent. This was one of the first, if not the first, of this type of mill to be used in the grinding of clay on the Pacific coast. The pulverizer consists of a die-ring, lying in a horizontal plane, enclosed in a sheet-iron housing. A vertical shaft supports a spider from which five rolls are suspended in such a way as to always have them bearing on the die-ring. The vertical mill shaft is driven by means of beveled gear and pinion from a horizontal shaft which is connected by belt with a 60-hp. motor with suitable pulleys to give a speed of 175 r.p.m. A large fan which has a speed of 1100 r.p.m. and is belt connected to a 40-hp. motor is connected to the mill housing. The discharge end of the fan is in turn connected to a cyclone dust collector.

Jan 1, 1929

By Francis Freeland

An examination of accessible English literature shows that but small space has been allotted to the determination of faults ; most suggestions being confined to Schmidt's rule of the downthrow on the hanging-wall of the fault, or the coal-miner's rule of the obtuse angle. Von Carnall's modification of Schmidt's rule is sometimes given without the important exception, and Zimmermann's rule is

Jan 1, 1893