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By D. J. Varnes

Rocks in mines, quarries, and many outcrops commonly show evidence of being under high stress. Saw cuts and drillholes close in, partly mined coal bursts violently, and pillars crush and rock spalls in mines even at moderate depths. Similarly, strong and massive rocks such as granite and sandstone naturally divide themselves into sheets that lie more or less parallel to their outward topographic form. The sheets may be either convex or concave. Thin plates of bare rock surfaces bow up and buckle. Such effects often cannot be explained by the obvious loads now acting on the rock, that is, by loads resulting from overburden, topographic irregularities, or stress concentration around openings. The stresses exceed those that would result from such loads. Two interpretations of such excess stresses have been made. In one, the stresses are assigned in origin to now active tectonic forces. In the other, they are regarded as leftover and locked in from some previous state at which higher pressures prevailed. These two sources may both operate and they generally cannot be distinguished easily in the field. There are other complicating sources of stress such as temperature gradients and chemical alteration. Nevertheless, some bodies of rock, by exfoliating, show evidence of high internal stress even though they are practically unweathered and so isolated topographically that the presence in them of significant stress due to exterior loads or active tectonic forces seems unlikely (Fig. 1). Moreover, completely isolated rocks are known to change density, shape, or size 1,2 to expand under constant compressive stress;3 and even to disintegrate 4,5 without the intervention of weathering processes. The stresses involved here must be truly residual in the sense long used by metallurgists; that is, residual stresses in a body are those that remain.

Jan 1, 1970

The re-development of the Mount Charlotte gold mine in Kalgoorlie was carried out piece- meal as funds became available. Optimisation of productivity to offset the high risk which is a function of an indefinite gold price, has been the principal objective of the management.

Jan 1, 1980

By J. S. Kirkaldy, D. G. Fedak

The extra degree of freedonz introduced by a second independetzt concentration in a tenzary system gives rise to the possibility of unstable planar phase interfaces in semi-infinite diffision layer couples. Diffusion paths which pass continuously in and out of too-phase regions of the phase diagram but which are not coincident with tie-lines give rise to super saturated zones which may be either adjacent to or isolated from planar phase interfaces, with corresponding nonisolated or isolated precipitates. Nonisolated precipitates are equivalent to morphological development of the interface. Selected couples in the ternary systems Fe-Ni-Cr and Cu-Zn-Sn have been examined nzetallographically and ifz the latter case both isolated and uo~zisolated precipitates have been observed. The diffusion path in one of the couples showing interface morphological developtnent has been examitled using electron probe microanalysis. IGNORING the spurious effects of preferential grain boundary diffusion and anisotropic crystal growth7 it can be unequivocally stated that it is impossible for a binary isothermal diffusion couple constructed of two unsaturated phases to sustain a nonplanar phase interface. Consider for demonstrative purposes the schematic phase diagram of Fig. l(a). Given an initial flat phase interface, semi-infinite boundary conditions and the internal boundary condition fixed by the constitution diagram, xB = xB(T), the unique solution of the diffusion equation requires a persistent flat interface. No other solution is possible. If, however, we anticipate the involvement of surface tension, then the internal boundary condition must be written xB = xB (T,Y) where r is the radius of curvature of a hypothetical nonplanar interface. The introduction of a new parameter such as r can be equivalent to the release of an internal constraint, so that a stable nonplanar interface may be possible after all. Consider a perturbation to the interface as indicated in Fig. 1(b). According to the Ostwald-Freundlich equation: which is applicable to a system of this constitution, the solubility of A in the matrix ß ,xB (Y), at a point of curvature r is given by where Va is the molar volume of the a-phase, R is the gas constant, and a is the interfacial tension. Since the right hand side is positive, xB(r) >xB cm, as indicated in Figs. 1(a) and 1(c). Accordingly, the perturbation will carry the interface concentration in a direction which is opposite to that which would sustain local equilibrium. Such a perturbation is necessarily moderated and the system is returned to its initial condition. This result is general for all binary couples since we can regard an interfacial perturbation as an attempt to precipitate within un-

Jan 1, 1962

By George H. K. Schenck

The North American-based mining engineer needs to understand the differences that exist between mechanical mining or boring machines built on this continent and those built in Europe. The differences Ere most clearly seen when machines for large-sized openings--about 15 feet high-are considered. This report will focus on the innovations of European origin. The rock-breaking tool, drag bit, or roller cone that is efficient for a particular project is related directly to the strength of the rock involved. This strength is generally stated in reference to the rock's unconfined compressivee strength in pounds per square inch (psi) although it is well recognized that a rock's shear strength is also important. Compressive strength has been adopted because it is simple to test for and provides a convenient comparison. Table 1 relates cutter type to compressive strength and indicates the general nature of the machine innovation devel¬oped in Europe.

Jan 1, 1970

By David Hill

The Australian underground coal mining industry is increasingly operating in an environment that challenges traditional concepts of coal pillar design, against a background of heightened expectations and demands from other stakeholders with regard to the protection of both natural surface features and burgeoning civil infrastructure. The result is greater possibility of conflict between mine operators, developers and regulatory bodies, with potential for unnecessary sterilisation of Australia?s coal resources and/or escalating surface development / infrastructure protection costs. On the positive side some significant advances have occurred in the general level of understanding of pillar behaviour and stability, both in Australia and overseas. This paper examines some current issues in coal pillar design, focussing particularly on the application and limitations of analytical models of pillar loading. Established methodologies are reviewed and alternative approaches explored, including examples of key geometrical, geological and probabilistic concepts. Practical experiences from the Southern Coalfield of New South Wales (NSW) are examined for the purpose of highlighting critical variables. Finally, some suggestions are made with regard to the direction and opportunities for future research, with particular regard to coal pillar loading, in the interests of all stakeholders.

Jan 1, 2008

Arrangements have been completed in New York whereby the re- sources of The Engineering Foundation, under the auspices of the four principal national engineering societies, are placed at the disposal of the National Research Council, which was appointed by the National Academy of Sciences* at the request of President Wilson. The object of the Council is to coordinate the scientific research work of the country in order to secure efficiency in the solution of the problems of war and peace. The Council was without funds until The Engineering Foundation, established to further scientific and engineering research, offered to place its resources at the Council's disposal, including the services of its secretary, Dr. Cary T. Hutchinson, to act as-secretary of the Council. The offer was accepted and plans for immediate activities have been placed in the hands of an executive committee. In indicating how thoroughly, every branch bf science and engineering is represented, Dr. George E. Hale, Director of the Mt. Wilson Solar Observatory, and Chairman of the Council, when he was in New York attending to the details of the arrangement, called attention to the personnel of the body, saying that it is the purpose to enlist the cooperation, in the solution of our industrial and military problems of a scientific character, of every possible established agency. Medicine, for example, is represented on the Council by Dr. William H. Welch, President of the National Academy of Sciences, Brigadier General William C. Gorgas, , Surgeon Crenera.1 of the United States Army, Dr. Simon Flexner, Director of the Rockefeller Medical Institute, and Dr. Victor C. Vaughan, Past President of the American Medical Society; biological science by Dr. Edwin G. Conklin, Professor of Zoology, Princeton University; chemistry by Dr. A. A. Noyes of Massachusetts Institute of Technology and Dr. L. H. Baekeland; physics by Dr. A. A. Michelson of the University of Chicago; and electricity by Professor M. I. Pupin, of Columbia University.

Jan 10, 1916

The objective of this study was two-fold: 1. To perform a world literature search pertinent to the analysis, selection and design of hoisting systems and their components and to codify the search into a literature compendium. The search resulted in a technical data file of over 1500 hard copy items. The compendium index was also suitable for establishing a comprehensive computer-loaded data base on the subject. 2. To develop a comprehensive system of guidelines to cover salient aspects of analysis, selection and design of electrical, mechanical and structural components of a hoisting system with a view to establish parameters for maximum safety and efficiency of operation, installation and revision of the system. 3. (a) In-shaft equipment design and specification criteria are considered as they influence guideline preparation. (b) A comprehensive review of hoist electric drives and controls as applied to mine hoists is set forth with special reference to duty cycle calculations and their effect on electrical component selection.

Jan 1, 1988

By R. L. Fullman

IN the investigation of metallurgical transformations and the relationships between microstructure and properties of metals, it frequently is desirable to obtain a measurement of the relative amounts of the various phases present and of the mean size of particles into which each phase is dispersed. The relative amounts of the phases can be measured by the classical methods of area, lineal, and point analysis,1-5 in accordance with the principle that the volume fraction of a phase, the fraction of a polished cross section occupied by the phase, the fraction of a random line occupied by the phase, and the fraction of randomly arrayed points occupied by the phase are all equal. The validity of this relationship depends only on the attainment of a truly random sample of area, length, or points, and not on the size, shape, or distribution of the particles constituting the phase. Smith and Guttman8 have derived a relationship between the interface area per unit volume S, and the measurable quantities L., the interface length per unit area on a cross section, and NL, the number of interfaces per unit length intersected by a random line. Their equation, Sv = — L8 = 2NL is also valid regardless of the distribution of particle sizes and shapes. In contrast to the situation concerning measurement of relative fractions of phases and of interface area, the measurement of particle sizes in opaque samples has not been subjected to a complete analysis. It has been common to measure some lineal or area dimension of particles on a polished cross section and to use the mean value as a qualitative measure of particle size. In the present paper, quantitative relationships are established among the various mean dimensions on a polished cross section and the actual dimensions of the particles present. Particles of Uniform Size Spheres: If a metal sample contains particles of a phase a dispersed in the form of spheres of uniform size, a polished cross section through the sample will reveal circular areas of phase a with radii from 0 to ?, the radius of the spheres. Consider a cube of unit dimensions to be cut from the sample. If a cross section parallel to one of the cube faces is examined, the average number of particles per unit area (N,) equals the number of particles per unit volume (Nv) times the probability p1 that the plane would intersect a single sphere positioned at random within the unit cube. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length 2r would lead to the plane intersecting the sphere, the probability of intersecting a single sphere is just 2r. N8= Nvp1 = Nd-2r [1] Applying the equality of area and volume fractions, the relationship is found between sphere size and average area s of uniform spheres intersected by a random cross section, 4 - f = NV V = Nr . — pra = N s = Nd . 2rs S = —pr2 [2] A similar analysis reveals the average traverse length across spheres of uniform size when random lines are passed through the sample. If a randomly oriented unit cube is cut from the sample and a randomly positioned line is passed through the cube parallel to a cube edge, the number of spheres intersected by the line (Nl) equals the number of spheres per unit volume times the probability p1 of the line hitting a single randomly placed sphere in the cube. Since possible positions of the line occupy unit area, and possible positions for which it will pass through the sphere occupy an area of pr2, the probability of the line hitting a randomly placed single sphere is pr2. NL = Nv p1 = Nvpr2 [3] Combining this relationship with the equality of volume and lineal fraction, the desired relationship is obtained between radius and mean lineal traverse length -i, for spheres of uniform size. 4 - - 3 l=4/3r [4] Circular Plates: Consider a sample containing particles of a phase a in the form of circular plates of uniform radius r and thickness t, where r >> t. If the plates are randomly oriented, as in a sufficiently large sample of a fine grained polycrystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the plates are not randomly oriented, it is necessary to randomize the orientation of the cross-sectional planes and traverse directions. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of plates cut by the cross-sectional plane per unit area is equal to the number of plates per unit volume times the probability of a plate intersecting a single randomly positioned and randomly oriented plate in the cube. If J is the component of the plate diameter in the direction normal to the cross-sectional planes, the probability of a plane cutting a single randomly oriented plate is equal to J, the mean value of J for all possible orientations of the plate. Let 4 be the dihedral angle between a plate and the cross-sectional plane, and let p?, d? be the probability that a plate makes an angle between 4 and ? + d? with the cross-sectional plane. Then for ran-

Jan 1, 1954

By J. P. Harrison, R. Roostaei

"In this paper we investigate the consequences of using conventional triaxial peak strength criteria in the polyaxial stress conditions that occur around the end of a long circular underground opening. A series of 3d boundary element analyses were performed using Examine3D to determine the stresses induced around the tunnel in different in-situ stress conditions. To discuss the applicability of a triaxial strength criterion in failure prediction, strength factors were computed for both the Ottosen polyaxial strength criterion and the triaxial Hoek-Brown criterion. Assuming that the Ottosen criterion is an accurate indicator of strength factor, the discrepancy from this value due to the Hoek-Brown criterion is the error in prediction.In order to simultaneously show the error in prediction and actual strength factor, a quantitative bivariate colour scheme is used to visualize the results. This allows rapid identification of regions with large error, and where either unsafe or overly conservative conditions occur. We show how the inappropriate use of triaxial criteria rather than polyaxial criteria leads to an under- or over-estimation of strength factor, and can result in uneconomic or unsafe design. Extending the analysis to different in situ stress regimes shows how the in situ stress conditions affect the assessment."

Jan 1, 2015

By Donald Barton

THE theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A = K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America; most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec.2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. In most cases, it is very nearly, but not quite, perpendicular to the earth's surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth's surface it commonly is very nearly, but not quite, a straight line.

Jan 1, 1928

By Donald Barton

THE theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A =KRM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical dis¬cussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America, most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec.2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. . In most cases, it is very nearly, but not quite, per¬pendicular to the earth's surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth's surface it com¬monly is very nearly, but not quite, a straight line.

Jan 1, 1928

By M. M. Gadde

Recent regulatory changes in the United States make it mandatory to conduct structural analysis of coal mine seals used to isolate abandoned workings from active mining areas. Different loading criteria are available for seal design depending on whether gob composition is actively monitored and maintained or not and whether the gob conditions lead to deflagration or detonation type loading. Since the loads involved in seal designs are dynamic in nature, the structural analysis must be made using dynamic stress analysis techniques. However, because of the significant complexities involved in conducting dynamic analyses, some designers use approximate simplified techniques to address the design problem. In this paper two such simplified methods are critically evaluated for their suitability to design coal mine seals. The benefits and limitations of the simplified methods are also outlined. Some comparisons are made to show the differences between sophisticated three dimensional dynamic analyses and the simplified methods and to delineate the problems associated with the latter approaches.

Jan 1, 2009

By Richard D. Hagni

The techniques of reflected light microscopy and cathodoluminescence microscopy are uniquely suited to the study of the products from many important industrial problems. Ref1 ected 1 ight microscopy provides the means to rapidly identify the mineralogy of an industrial sample, determine the abundance of each phase, and examine the mineral intergrowths or textures. Cathodoluminescence microscopy is a relatively new instrument that provides the means to cause many minerals to cathodoluminescence under the microscopy. The cathodoluminescence of a mineral allows it to be readily distinguished from other phases that differ in cathodoluminescence but are similar in optical properties. Cathodoluminescence microscopy is especially useful to detect cathodoluminescence minerals that are present in only small quantities. Reflected 1ight microscopy and cathodoluminescence microscopy have been successfully applied in studies of beneficiation products, prediction of beneficiation and leaching problems, phosphatic iron ores and mill products, pyrometallurgical products, roasted refractory gold-bearing sulfides, ceramic build-ups, electric arc furnace and smelter dusts, and other industrial products.

Jan 1, 1993

By Norman B. Pilling, George P. Halliwell

The effects of lead and tin up to maximum contents of about 0.1 per cent. each, in the presence of oxygen between 0.04 and 0.30 per cent., have been studied. Tin is retained efficiently in the oxidized condition, whereas lead is not. An approximate relation between the lead-oxygen and tin-oxygen contents is deduced which, if observed, permits the presence of these elements without detrimental effect. Excess of lead beyond this limit affects ductility and rolling properties adversely and an excess of tin correspondingly diminishes the conductivity. It is shown that copper carrying a combined lead and tin content of several hundredths per cent., yet fully equal in quality to electrolytic wirebar, may be produced under commercial conditions. Tin is not normally found in more than bare traces in current grades of American electrolytic copper, and lead is rarely found to more than a few thousandths per cent. In the electrolytic refining of copper these metals do not present great difficulty in separation and their presence in any considerable amount in copper that has been refined by this method need not be tolerated. On the other hand, the effect of these elements is not entirely academic, as a considerable tonnage of scrap copper liberally contaminated with them has been reclaimed by the fire-refining process into metal with a residual lead and tin content of several hundredths per cent., yet having excellent working properties and fully equal in quality to current grades of electrolytic wirebar. Such copper has been found entirely suitable for use in the manufacture of electrical apparatus. In the absence of oxygen, tin is known to depress the conductivity rapidly, and lead to impair ductility and the rolling properties, yet the effects of these metals on commercial grades of copper—i. e., copper containing from 0.03 to 0.10 per cent. of oxygen—apparently has not received systematic attention. Occasional reference is made to the fact that in the presence of oxygen lead may be tolerated, yet Addicks says,1 in regard to overpoling: "The unstable condition can be controlled by adding certain substances, notably lead, in small quantities, but as mere

Jan 1, 1926

By G. Howell Clevenger

FORMERLY great divergence of opinion existed in regard to the influence of copper in steel, as affecting its various physical properties. More recently the investigations of Stead,1 Breuil,2 Wigham,3 Burgess and Aston,4 Ball and Wingham,5 Miiller,6 Dillner,7 and others have shown fairly good agreement in the major points. Copper steel has been shown by these investigators to possess special properties which make it valuable for certain uses. The general range of composition of the useful alloys of copper and iron, and of copper, iron, and carbon, has been quite definitely established, for the former by Burgess and Aston,8 and for the latter by Breuil 9 and Stead.10 Stead 11 has removed one difficulty in reconciling certain of the earlier data by calling particular attention to the influence of carbon in copper steels. Another point which caused confusion in the earlier investigations, particularly in regard to " red-shortness," was the presence of sulphur. Failure to note the presence of sulphur often led to attributing " red-shortness " to the presence of small amounts of copper. Turner 12 has called attention to the fact that where copper exists in an iron ore it often occurs as the sulphide, so that the presence of copper in steel made from such ores might also, necessarily, mean the presence of sulphur. It is evident that the effect in this case might be quite different than where pure copper was added.

Jan 10, 1913

CONTENTS PAGE PEIRCE, CARL-Making Rimmed Steel. Discussed by L. F. Reinartz. H. D. Hibbard, C. L. Kinney, Jr., A. H. Woodward, V. B. Buck, A. L. Feild, J. V. W. Reynders 1 SCHROEDER, F. W., and LARSEN, B. M.-Progress Report of the Effect of the Open-hearth Process on Refractories. Discussed by D. A. Lyon 12 KEATS, J. L., and HERTY, C. H.-Elimination of Metalloids in the Basic Open-hearth Process. Discussed by J. V. W. Reynders 14 Making Rimmed Steel Discussion of paper by CARL PEIRCE, presented at the New York fleeting and issued, as Paper No. 1563-C, with MINING AND METALLURGY, March, 1926. L. F. REINARTZ, Middletown, Ohio.-Mr. Carl Peirce has presented a valuable paper on a subject that has been very widely discussed in recent years, especially since the demand for high finish, deep drawing and other grades of sheet steel in the lower carbon ranges has become an important factor in the steel business. Steel of this analysis has been produced for many years, but the product for which it was made did not require the extra care in the steel plant that it does today. It must now be worked down into thin sheets for special purposes and undergo many severe finishing processes both in the steel mill and in the fabricating plants. Mr. Peirce's paper has outlined in a concise and logical manner the steps which must be taken in manufacturing such steels. The secret of successs is attention to details of well known steel practices. I agree with him that quality steels of this class cannot normally be made out of inferior raw materials. Scrap should be clean and if possible not too variable in analysis. Galvanized scrap or babbit are particularly objectionable. Scrap should be in such physical condition that undue delays are not encountered in charging the furnace. Limestone should preferably contain over 95 per cent. available calcium carbonate, and be free from clay or other foreign substances. Almost universal practice shows that 10 per cent. limestone is required for proper slag volumes to protect the metal from over oxidation. The use of 8 per cent. limestone makes the operation less fool-proof.

Jan 4, 1926

Integrated chemical thermodynamic software and computerised databank systems have evolved over the last 15 years. The extent to which these systems have automated thermodynamic calculations relevant to extractive metallurgy is examined. The scope for further automation and the role of the expert consultant is discussed.

Jan 1, 1991

By A. Goulsbra, S. McAllister, R. Dunne

Since 1992, a tailings gravity re-treatment plant has been in operation at the New Celebration Gold Mine to recover aurifer­ous pyrite (Martins, Dunne and Gelfi 1991; Martins, Dunne and Delahey 1993). The gravity pyrite concentrate is ground in a Tower mill to liberate gold (average particle size around 25µm) prior to cyanide leaching. Although the re-treatment plant has met the predicted gold recovery, based on original laborat01y testwork, there is still room for improved gold recovery. This requires enhanced pyrite recovery, especially in the finer size ranges. The application of centrifugal gravity separators would seem to be an ideal means to achieve this criterion. In particular, the Falcon continuous centrifugal separator (Series C machines) would appear to be ideal for this particular duty. A testwork program to evaluate the application of the contin­uous Falcon to recover pyrite from New Celebration ores was unde1iaken over a six month period during the later part of 1997. The work involved laboratory batch testwork, followed by con­tinuous testing of the Falcon Cl0 (2tph to 3tph) and Falcon C40 (l00tph) units. A summary of the results from this evaluation program are provided in this paper.

Jan 1, 1998

WITH the economic situation of the world what it is, we may expect important events in every month of 1922, and January showed us some-what of the nature of things that will happen. The Germans announced their inability to meet in full the reparation payments that were due Jan. 15. The Su-preme Council arranged a plan for them to pay some thing on account every 10 days, and called a conference at Cannes to talk things over. While this conference was in progress Premier Briand resigned and was suc-ceeded by Poincaré. This emphasized the growing differences between British and French policies and interests. The French want to exact the utmost from the Germans; so do the British. The latter think, however, that the French aims will so cripple the Germans that they can not work properly and hence can not trade. Great Britain, with a huge unemploy-ment problem, must have trade. The French thought that Briand was unduly deferring to the British and withdrew their support of him. The other important political developments of the month in Europe were the establishment of the Irish Free State, relieving the British of the vexatious Irish question; and the growing tendency to recognize the Soviet government of Russia and admit its representa-tives into international conferences. In the United States the great political event was the establishment of the dominance of the agricultural bloc in the Senate, which implies the passage of agrarian legislation that will probably be unwise. Economically, there was no progress in the United States. If anything there was probably some reces-sion in the physical volume of business. There were some further reductions of wages, but these were irregular, geographically, and moderate in amount. The great unionized trades maintained the jam. Events of great importance were the formal demand of the anthracite coal miners for increased wages on April 1 and the declaration of the bituminous coal miners that they would resist a reduction at that time. The attitude of these groups is believed to presage labor troubles in the spring. In the metal markets affairs were dull during Janu-ary, but prices were generally firm, save for a little further weakening in iron and steel. In the matter of production, however, there was some quickening of activity, especially in copper, zinc and iron.

Jan 2, 1922

By R. N. Stevens

GRAIN boundary sliding plays a part in the high-temperature deformation of polycrystalline solids, and many investigations1-11 have been carried out to determine the deformation contributed by this mechanism. The principal method employed has been to measure one of the components of the grain boundary displacement, see Fig. 1, at a large number of boundaries, and from the mean value so obtained to calculate the elongation contributed by sliding. A formula connecting these mean values and the elongation contributed is evidently required, and many have been derived. They are usually of the form where Egh is the tensile elongation contributed by sliding, is the mean value of the component, x, N is the mean number of grain boundaries intersecting a line of unit length, and K is a dimensionless parameter known as the averaging factor. Table I summarizes the equations used by various investigators. Examination of these shows that their derivations usually involve doubtful assumptions, and are often in serious error. The purpose of this note is to point out that rigorous solutions to the problem of calculating Egb from x have been available in the literature for some years.' Since this is so little known, and also the original derivations do not make some important points clear, it is proposed to rederive the basic equations. These will be extended further, and the conditions in which the extended equations may be applied will be indicated. The mean values of the components of the sliding vector (I, d, and I:, Fig. 1) will depend on the method by which boundaries are sampled in order to make measurements.3,11 Boundaries are usually sampled by marker lines parallel to the stress axis, or lines perpendicular to the stress axis, the measurement being made at the point where the marker line intercepts the boundary. We will denote the mean values determined by these various sampling methods as follows. lT, dT and vT are mean values obtained by making measurements at pointswhere a transverse line intercepts the boundary while lL, dL, and vl, are the mean values from a longitudinal line. The number of boundaries per unit length also may depend on the direction of measurement, and so we define NT and Nl to be the number of boundaries per unit length, after creep, in the transverse and longitudinal directions, respectively.

Jan 1, 1967