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By Glenn Southward

This describes a highly concentrated mining system consisting of a series of short faces arranged to get complete recovery of coal with the maximum protection for the men and equipment. A series of conveyors collect the coal from eight faces and discharge into mine cars at a central loading point on a main haulageway. The conveyor is sectional and, by a multiple-drive arrangement, the same standard parts are used to construct a unit of any length. THE. V system of mining used at the Norton mine of West Virginia Coal & Coke Co. was designed as a modified longwall with face conveyors, FIG. 1.-GENERAL DESIGN AND ARRANGEMENT OF FACES IN V SYSTEM. for use under roof conditions that would not permit regular longwall methods. This mine is in the Lower Kittanning seam, which averages about 6 ft. in height. There is from 20 to 30 ft. of slate and shale immedi-

Jan 2, 1924

R. S. MACPHERRAN,* Milwaukee, Wis. (written discussion?);-Mr. Stork's paper is very interesting, but I am unable to agree with some of his conclusions. He argues very strongly for the beneficial effect of oxygen, but gives no actual determinations of this element to support -his views. He states that the oxygen resulting from a high bed, heavy charges, low coke ratio, etc. must not be confused with the oxygen under normal conditions. I will be glad to know in what respect these oxygens differ or in what state they occur. Is it his opinion that the beneficial type is present as a dissolved gas and the other as metallic oxide? I will not discuss the first five of his six points, as I have not seen enough trustworthy determinations of oxygen in cast iron to form any conclusions as to its effect. I have never known the addition of manga-nese, however, to reduce the strength of cast iron. Under the sixth point, I would say that the addition of steel lowers the total carbon content, and by this action will increase the strength independently of oxygen. This reduction of carbon operates also to raise the melting point. It is interesting to note here that the author, in order to get proper fluidity for his cylinders, was obliged to reduce his oxygen by raising the manganese in the charge.

Jan 12, 1919

By Harrison Schmitt

The definitions of the terms commonly used in connection with metamorphism at elevated temperature near igneous contacts are re-examined. As the study of tactite zones associated with igneous contacts progresses, more and more emphasis is put on the localization of the ore by structural forms. The generally early age of the silicates and late age of the sulphides is well established. Postsilicate structural deformation is likely to localize ore bodies. The silicates are often replaced by the ore minerals. we may not be far from proving that the elements involved in the formation of silicate aureoles are merely normal "volcanic" emanations, that silica, lime, magnesia, and alumina, and probably soda and potash, are likely to undergo local transfers only. The work of Newhouse suggests the agents of the formation of sulphides in deposits of various classifications are the volcanic emanations. Introduction The purpose of this paper is to define the terms commonly used in connection with the subject, to briefly review and discuss the broad features of the aureoles, to indicate some of the features lately recognized: to discuss the genesis, and to suggest how the associated ore deposits can best be studied and developed. When developing a subject in mining geology one is soon conscious of the vast amount of pertinent literature and that most relevant ideas, no matter how obscure, have been considered. One can only hope to make some small contribution in point of view, a few confirmatory observations, or, perhaps, suggest a small new idea indebted to the most recent data. It is nearly impossible, also, to give specific credit, and adequate credit, to all the contributors to a given subject. This study, furthermore, was not intended to cover the field exhaustively, nor is the bibliography complete. Definition OF Terms There is much confusion in the use of the broad terms concerned. Needless to say, metamorphism means change of form; metasomatism, change of substance. The term contact metamorphism, however, has been widely misused possibly by a majority of economic geologists and engineers. As originally adopted by European investigators it meant changes effected largely by heat (thermal effects) in the rocks invaded by plutonic intrusives, but did not include those local changes usually at the immediate contact brought about by the addition of substance, i.e., by metasomatism. The term has become clouded. In Europe it has

Jan 1, 1949

By Alden H. Emery, J. J. Forbes

The data contained in this paper were collected during the course of an investigation which covered 15 representative coal mines in six coalmining states. The purpose of the investigation was to determine by atmospheric sampling how much dust was raised into the air during the various operations of coal mining, such as undercutting with machines, loading coal by hand and transporting it from the working face to the surface. The data thus obtained were considered from two angles; namely, the possible physiological effect of inhalation and the explosion hazard of the dust. No attempt will be made to discuss the former factor in this paper. ConDitions of Mining The mines in which this investigation was conducted were considered representative, and it is believed that the results obtained will suffice for the average dustiness encountered in most coal mines. All of the coal mined was bituminous, from beds 30 to 120 in. thick. Only the ordinary room-and-pillar system of mining was employed. Daily production ranged from approximately 700 to 1500 tons and the men employed from 150 to 450. Coal was undercut by shortwall mining machines in all mines, with the exception of one in which pick mining was employed. Loading at the face wets done by miners; none of the mines used mechanical loaders. Electric drills, both for brushing roof and for shooting coal were commonly used, although some roof work was done with jack-hammers and a little of both with augers. Coal was hauled by motor, mule, or rope power in end-gate cars with capacities ranging from 1800 to 3600lb. With few exceptions, coal was won at the face by dry methods, that is to say, no water was employed for wetting down the dust either during undercutting, loading or transportation. Observations of Sources of Dust The common sources of coal dust as observed, arranged by decreasing amounts, were as follows: (1) Undercutting with mining machines; (2)

Jan 1, 1927

By Harrison Schmitt

The definitions of the terms commonly used in connection with metamorphism at elevated temperature near igneous contacts are re-examined. As the study of tactite zones associated with igneous contacts progresses, more and more emphasis is put on the localization of the ore by structural forms. The generally early age of the silicates and late age of the sulphides is well established. Postsilicate structural deformation is likely to localize ore bodies. The silicates are often replaced by the ore minerals. we may not be far from proving that the elements involved in the formation of silicate aureoles are merely normal "volcanic" emanations, that silica, lime, magnesia, and alumina, and probably soda and potash, are likely to undergo local transfers only. The work of Newhouse suggests the agents of the formation of sulphides in deposits of various classifications are the volcanic emanations. Introduction The purpose of this paper is to define the terms commonly used in connection with the subject, to briefly review and discuss the broad features of the aureoles, to indicate some of the features lately recognized: to discuss the genesis, and to suggest how the associated ore deposits can best be studied and developed. When developing a subject in mining geology one is soon conscious of the vast amount of pertinent literature and that most relevant ideas, no matter how obscure, have been considered. One can only hope to make some small contribution in point of view, a few confirmatory observations, or, perhaps, suggest a small new idea indebted to the most recent data. It is nearly impossible, also, to give specific credit, and adequate credit, to all the contributors to a given subject. This study, furthermore, was not intended to cover the field exhaustively, nor is the bibliography complete. Definition OF Terms There is much confusion in the use of the broad terms concerned. Needless to say, metamorphism means change of form; metasomatism, change of substance. The term contact metamorphism, however, has been widely misused possibly by a majority of economic geologists and engineers. As originally adopted by European investigators it meant changes effected largely by heat (thermal effects) in the rocks invaded by plutonic intrusives, but did not include those local changes usually at the immediate contact brought about by the addition of substance, i.e., by metasomatism. The term has become clouded. In Europe it has

Jan 1, 1949

By R. W. Vander Laan

Conneaut has a long and illustrious history as a major Great Lakes port for coal and iron ore. The first dock was built in 1892 for unloading iron ore from the Mesabi Range for shipment to the Pittsburgh steel mills via the Shenango & Lake Erie Railroad, later to become the Bessemer & Lake Erie Railroad. The Pittsburgh & Conneaut Dock Company was incorporated in 1893. The world's first Hulett automatic ore unloader was constructed at Conneaut in 1899. Steam operated, it was the model for the giant electric Huletts used today, named after its inventor, George Hulett, who was a Conneaut resident.

Jan 3, 1974

By R. R. Nash, W. F. Sheely

Experiments were conducted on magnesium monocrystals in order to collect quantitative information on the mechanisms which limit the rate of basal slip. Using critical shear stress and creep data, activation energies for creep at low aid at high temperatures were derived. The activation energy at low temperatures is the same as that for jog formation and the activation energy at high temperatures agrees with that for climb. COTTRELL has suggested that at low temperatures, the expansion of dislocation loops under stresses near the yield strength is limited by the rate at____ which the expanding loops can cut the "forest" of dislocations passing through the glide planes.' On the basis of this mechanism, seeger2 has derived expressions for low-temperature creep and for the relation of flow stress of single crystals to temperature. In the work reported here, the authors have performed experiments designed to obtain quantitative data on the physical properties of the dislocation intersection mechanisms operating during basal slip in pure magnesium monocrystals. Above a critical temperature, dislocations thread-

Jan 1, 1961

By Herbert Hoover

THE time has arrived in our national development when we must have- a definite national- program in the development of our great engineering problems. Our rail and water transport, our water supplies for irrigation, our reclamation, the provision of future' fuel resources, the development and distribution of electrical power, all 'cry out for some broad-visioned national guidance. We must create a national engineering sense of provision for the nation as a whole. If we are to develop this national sense of engineering wand its relations to our great human problems, it must receive the advocacy of such institutions as this. We, together with our sister engineering societies, represent the engineers of the United States. It is our duty as citizens to give voice to those critical matters of national policy which our daily contact with this, the fundamentally constructive profession, illuminates to us. Just as our medical associations voice the necessity of -safeguards to national health; as the bar associations of safeguards to our judiciary, so the engineers should exert themselves in our national engineering policies. We have none; but we need some, or the next generation will face a lower instead of a higher standard of living than ours.

Jan 1, 1920

By W. B. Morrison

The principal factors influencing the total percent elongation of a lead-tin eutectic and several low-alloy steels which exhibit superplasticity were investigated. These factors are: a) Strain-rate sensitivity of the stress (m). b) Specimen geometry; in particular, diameter-to-length ratio (d0/l0), and surface irregularity (e.g. notches). A feature of the tensile deformation of a superplastic alloy is the early appearance of a neck which continues to extend throughout the test. As a result the total elongation is directly related to the diameter-to-gage-length ratio. The strain-rate sensitivity of the stress varies during extension, mainly because of microstruc-tural changes. A satisfactory correlation exists between the minimum strain-rate sensitivity and total elongation, as indicated in the equation shown below. Notches cause a considerable reduction in total elongation and their effect is greatest at high values of strain-rate sensitivity. An initial notch depth exists below which there is no appreciable effect on elongation. An equation relating elongation to strain-rate sensitivity and specimen geometry is proposed, THE total percent elongation of a tensile specimen is usually regarded as a measure of superplasticity. However, little attention has been given to the fact that total elongation is also a function of specimen diameter and gage length, even though the importance of geometry has long been recognized in the tensile testing of materials in which elongations are relatively small.* In the present study, the effect on superplas- tic extension of the ratio of specimen diameter to length was investigated and an analysis was made of strain distribution along the gage length. Superplastic alloys are characterized by having a flow stress sensitive to strain rate but relatively insensitive to strain.2"' In an earlier study,5 it was found that the strain-rate sensitivity of several low-alloy steels changed during the test and that the minimum value correlated best with total elongation. In the present study, the variation of strain-rate sensitivity during the straining of a lead-tin alloy was investigated. EXPERIMENTAL PROCEDURE Lead-tin eutectic alloy (32 pct Pb 68 pct Sn), made from high-purity lead and tin, was cast in the form of 1-in. diam rod. The rod was cold-rolled in stages to 0.25 in. diam and then swaged to 0.125 in. diam. Samples were cut from the rod at various stages of the mechanical working process. Tensile test specimens were then made by attaching threaded steel ends to the rods by an epoxy-base thermosetting adhesive which required a setting treatment of 2 days at room temperature. The rods were seated in the steel ends in holes approximately 0.01 in. oversize. The test pieces thus made were of various diameters and gage lengths. These were stored at a temperature of about -70°C (-94°F) until required for testing. The distribution of strain along the gage length of a specimen was determined at various stages of the tensile test. The lead-tin alloy was superplastic at room temperature and direct observations during testing were simple. The gage length was divided by reference marks into five initially equal units. These reference marks were made with ink and were reinforced during the test when the initial marks became faint. Photographs were taken, at intervals, of the deforming specimen and measurements of the elongation in each of the gage units were made on these photographs. Tests were also done on several superplastic low-alloy steels whose properties were described earlier.5 The chemical compositions of these steels are given in Table I. A diagram of the notched tensile specimen used in the steel tests is shown in Fig. 1. The specimens were tested at 900°C (1650°F) in a furnace through which a mixture of He + 2 pct H was continuously circulated.5 RESULTS Strain Distribution. Approximately 20 tests on lead-tin alloy specimens were conducted to determine the strain distribution during the test. An example is shown in Fig. 2 of the strain distribution in the gage

Jan 1, 1969

In response to Dr. Ledoux's paper, a large number of metallurgical establishments and individual assayers expressed their willingness to co-operate in the plan he proposed. The necessary samples were prepared as follows : Matte.—A car-load of matte was put through a Blake crusher, then automatically subdivided into tenths by a Taylor and Brunton sampler, and one-tenth passed through Cornish rolls and through a 12-mesh screen. This was again subdivided by an automatic sampler into tenths, and a final tenth, representing 1 per cent. of the original lot, was finished by hand-sampling on an iron floor until 100 pounds remained. This was pulverized to pass a 40-mesh screen and then thoroughly mixed and divided in the presence of my assistant for distribution to the parties co-operating. Copper Borings.—These were taken from a lot of anodes, the dip-samples from several batches having been united, remelted and cast into a plate, which was proved by assay to be of uniform quality in its different parts. Borings from this plate were intimately mixed and divided in the presence of my assistant. Samples were sent out November 1,1894, with the following letter: New York City, November 1, 1894. Samples of matte and copper (about I pound each) carefully prepared in the presence of my assistant and sealed with his seal as below, are sent you by express for assay and report according to the plan of Dr. Ledoux. These samples are constituted about as follows: Matte. Copper. From. To. From. To. Copper, per cent.,.....50 60 ..........., Gold, oz. per ton,.....2 3 0.20 0.50 Silver, oz. per ton,.....100 150 140 180

Jan 1, 1896

By Robert J. Willard

The scanning electron microscope (SEM), became commercially available in 1966. Embodying some unique features not provided by conventional electron microscopes, this new electron-optical instrument offers the scientific community a new way of observing the surfaces of materials. In rock mechanics research, the SEM should prove a useful basic tool in characterizing rock fracture on a very small scale and thus contribute to a better understanding of rock behavior at larger scales. This article presents one example of how the SEM is being applied to such research at the Twin Cities Mining Research Center operated by the U.S. Bureau of Mines in Minneapolis. This research center conducts theoretical and experimental studies on a broad range of mechanisms that induce disintegration by the application of energy to rock.1 Some of these studies are concerned with the relation of microstructure to rock behavior and are carried out mainly with the petrographic microscope. At the same time, however, the center recognizes that this relation must be studied through several orders of magnitude, from lattice-size units of rock-forming minerals to field-size rock units. The SEM fits this scheme by extending the capability of the petrographic microscope into smaller orders of magnitude. However, because its resolution is limited to about 200 A at 10,000x, the SEM is not capable of resolving lattice-size units, and hence a conventional electron microscope with a much greater resolution capability is necessary at this order of magnitude.

Jan 6, 1969

By D. L. Albright, R. W. Kraft, J. A. Ford

HE unidirectional solidification of A1-CuAl, eutec-tic specimens to produce an essentially parallel lamellar structure has been described previously.' Ingots solidified in this manner ordinarily exhibit three macroscopic zones. In Zone I, at the head end of the ingot, a large number of slightly elongated grains occur in which the lamellae are highly distorted and twisted. After a few centimeters of growth, this distribution gradually changes to a small number of coarse grains elongated in the growth direction and in which the lamellae are quite regular, Zone 11. Zone 111, at the tail end of the ingot,

Jan 1, 1963

By Raymond S. Weimer

OF the several characteristics of a coal that influence its suitability for use in a given piece of burning equipment, the clinkering and slagging characteristics of the ash of the coal are highly important. They determine the maximum rate at which the coal may be burned on a stoker or in pulverized form without difficulty from damage to metal parts, from erosion of refractory walls, or from stoppage of gas passages by accumulation on the tubes. They also determine the minimum rate at which a slag-tap furnace may be operated without difficulty in removal of the ash in fluid form. NEED FOR A BETTER CRITERION In common with other producers and users of coal, the Northern Illinois Coal Corporation has long used the available methods for the measurement of the clinkering characteristics of coal ash, chemical composition and fusion temperature of the ash, as criteria for the selection of coal that would suit the particular requirements of its customers. These two available criteria have greatly helped in the problem of selection but it is unnecessary to dwell upon the fact that they are not completely adequate for the purpose. The composition of the ash and its clinkering tendency vary widely over the company's mining area. In a certain period, some years ago, an unusual amount of severe clinkering of the ash of coal shipped made extremely acute the need for a better criterion of the clinkering that might be expected. It was also desirable that the criterion result from a reasonably rapid method, so that the clinkering characteristics of the coal would be known before shipment. Complaints on the severe clinkering of the ash came from only a fraction of the output of the mine but the occurrence of the clinkering seemed quite unpredictable. Attempts to relate the chemical composition of the ash and the fusion temperatures to the clinkering were unsuccessful. Coal from the area of the mine in which the fusion temperature of the ash was the lowest gave the least trouble from clinkering. Chemical analysis of the ash from that section giving the most trouble showed high contents of iron and low contents of silica, but frequently these were not greatly different from those of coals that gave little trouble from clinker. Aside from the clinkering difficulty, the coal was quite satisfactory. The ash content was normal and high rates of burning could be obtained, but again and again such severe clinkering would occur that the furnace would be shut down because of the accumulation of clinker. Examination of the clinker from the customers' plants showed that the clinkers that adhered to the grates and fouled the fuel beds were hard, flat, dense, and usually dark in color. Coal that was satisfactory gave clinkers that were softer, bulky rather than flat, of low density, and usually lighter in color.

Jan 1, 1944

By Paul Weir

BLEACHING clays have been used extensively in the oil-refining industries for a number of years. Their use in water purification is relatively recent and less extensive. They are frequently classified as (1) those naturally active and (2) those active after artificial activation with acid. Fuller's earths fall within the general group of bleaching clays and gradually the commercial term "fuller's earth" has been applied to natural clays originating, for the most part, in the south-eastern section of the United States. Bentonitic clays are usually classed as activable and are prevalent in the southwestern section of the United States.1 Bleaching clays vary considerably in chemical and physical properties throughout the country, or even in different parts of one deposit (Table 1). TABLE 1.-Physical and Chemical Composition of Different Types of Clays Composition, Per Cent Constituents and Properties Bentonite Fuller's Mud Clay (Wyoming) Earth (P Peak)' (Alluvial) Silica (SiO2) 60.0 69.6 61.67 Alumina (Al203) 19.0 14.3 20.34 Ferric oxide (Fe203) 2.8 3.90 7.70 Titanium oxide (Ti02) 0.13 0.70 1.01 Lime (CaO) 0.5 0.80 0.00 Magnesia (MgO) 2.0 1.00 0.24 Soda (Na2O) 2.4 0.40 0.31 Ignition loss 4.7 6.77 8.51 Moisture content 8.0 10.0 20.0 Isoelectric point, pH 9.2 9.2 6.5 Average swelling volume 15.0 0.0 0.0 Weight per cubic foot, lb 55.0 40.0 65.0 Material passing 200-mesh sieve, per cent 90.0 85.0 50.0

Jan 1, 1939

In the time it takes you to read this sentence, you'll be "zapped" by about 40 cosmic rays. Though harmless, their existence is being probed by a team of Texas A&M University physicists. What's most unusual about the research project is the design and location of the telescope required to detect the particles-it's made of fluorescent light tubes and is 457 m (1500 ft) underground at United Salt Corp.'s mine in Hockley, Texas, about 80 km (50 miles) southeast of Texas A&M's College Station campus. Cosmic rays are actually particles smaller than atoms traveling at extremely high speeds. Scientists believe their source is the same as that of starlight, and that these primary particles entering the earth's atmosphere create secondary particles in collisions with oxygen and nitrogen atoms.

Jan 6, 1978

Underwood & Underwood HERBERT C. HOOVER ALBERT SAUVEUR CHAIRMAN OF WASHINGTON, D. C. CHAIRMAN OF BOSTON SECTION SECTION FREDERICK LAIST R. V. NORRIS CHAIRMAN OF MONTANA CHAIRMAN OF PENNSYLVANIA LOCAL SECTION ANTHRACITE SECTION CHAIRMEN OF SOME OF OUR LOCAL SECTIONS

Jan 6, 1919

By F. P. Dewey

Recent discussions have furnished to the members of the Institute much information concerning aluminum and its applications. The present paper will be devoted almost entirely to the description of a process by which the metal is produced in the form of alloys. The characters which especially distinguish the Heroult process consist in electrolyzing a mass of molten alumina (Al2O3), and at the same time alloying the separated aluminum with a heavy metal, the heat necessary for the fusion of both the alumina and the alloying metal being supplied by the direct passage through the molten Al2 0, of an electric current of high amperage and low voltage. The process has been in active operation at Neuhausen in Switzerland for about two years. It is also in active operation at Froges in southern France. Both these locations were selected for this purpose on account of the presence of large and desirable water-powers. The apparatus consists of a carbon containing-vessel, which may be a single crucible for small operations, or may be built up of slabs or blocks of carbon for large and industrial operations. When built up of slabs or blocks, the whole is surrounded by an iron casing. In the earlier crucibles this iron casing was cast around the carbon, in order to secure close electrical contact. This, however, has been found unnecessary; and in the later crucibles the casings consist of plates bolted together, while pulverized carbon is packed between the carbon blocks and the iron. Electric conductors are united direct to this iron casing, and the current passes from this through the carbon lining to the interior of the crucible. By this

Jan 1, 1890

By Ralph H. Sweetser

IN these days of the almost exclusive use of byproduct coke as the blast-furnace fuel in this country, it may seem out of place, and smacking too much of reminiscing, to say anything about the use of anthracite coal for blast-furnace fuel. Viewed in the light of present day research and of developments in alloy steel, some observations seem appropriate regarding this raw material that played such an important part in the development of the iron and steel industry during 50 years of the past century. The research work of that period, in which the whole iron and steel industry was revolutionized, passing from wrought iron to steel and from charcoal to three new mineral fuels for blast furnaces, was done chiefly in the full-sized plants of that day; and it was done largely by the ironmasters themselves. The laboratory had not become a part of the ironworks, and scientific instruments were lacking around the blast furnaces; "rule o' thumb" and erroneous theories prevailed-and have not yet all been eliminated. The recent interest in meteoric iron in connection with nickel steels and other alloys proves that it is worth while to search for the reasons for excellence and the causes for failures in the metallurgy of bygone days. Turner1 gives the reasons why the blast furnace of Dr. F. W. Geissenhainer on Silver Creek, Schuylkill County, Pennsylvania, about 10 miles northeast of Pottsville, was operated successfully with anthracite2 in August and September, 1836, and why several other attempts failed. It has taken a long time for us to find out that there are great differences in the behavior of anthracites from the several parts of the anthracite region, as well as differences in coking coals from the bituminous fields.

Jan 1, 1935

By R. W. Smith, C. Schroeder, R. Haddenham

Amphoteric surfactants are heteropolar organic compounds which possess at least two functional (ionic) oppositely charged groups per molecule. The ones studied are manufactured by General Mills and possess one or more long hydrocarbon chains plus a carboxyl group (s) and an amino or imino group. Hallimond tube and M. C. Fuerstenau micro flotation cell flotation tests were performed on quartz and hematite as a function of pH using amphoteric, cationic, and anionic surfactants as collectors. For the most part, flotation could be correlated with an interaction of charged groups on the collectors with oppositely charged sites on the minerals plus association of hydrocarbon chains. The comparison of flotation in a Hallimond tube and an M.C. Fuerstenau cell shows that one should use care in using the latter if one excludes an additional frother from the system. Also, it is interesting to note that sometimes greater collector concentrations are required in the Fuerstenau cell for comparable flotation recoveries.

Jan 1, 1974

By C. G. Dunn

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

Jan 1, 1945