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By B. F. Tillson

ALTHOUGH most accidents occur through the A carelessness or misfortune of the workmen; that is no reason why we should not take all physical precautions practicable. The best way to approach the problem of mine safety is to acquire a personal feeling of responsibility for the accident and then plan how it might have been prevented had we known that it was to occur. A statistical analysis of the physical conditions contributory to accidents will give an indication of some of the methods or mechanisms that should be revised or safeguarded. The handling of rock or ore is a common source of minor injuries. Freedom from accident when mucking largely depends on the skill and care of the workman; this also is true, to a certain degree, to loading cars from chutes, but much can be done in the layout of chutes and their equipment to provide equal safety with less skill. Permanent stagings, or rigid units that may be easily assembled, should be provided so that the men handling the chute boards or gates and barring the jammed chunks will have a convenient safe footing for their operations. A stance to the side of the chute mouth is to one in front, because a man will not be liable to be struck by flying lumps or his bar, should it he caught in the mass, yet in many mines the workmen face the chute when loading a car. Fig. 1 shows the operation of a plank chute having special latches which support the chute boards in such manner that they may be conveniently dropped into place to stop the flow of ore.

Jan 1, 1926

By William Campbell

(Cleveland Meeting, October, 1912.) THE structure of iron and steel, though the object of so much study and research for the past 25 years, is by no means thoroughly understood. In the first place, we have three or more distinct iron-carbon thermal diagrams, each with its own supporters, and each representing a theory of the structure and constitution of cast-iron. In the second place, by reason of the fact that austenite, the solid solution of carbon in iron, decomposes in the solid state into ferrite, or pure iron, and cementite (Fe3C), and that quenching from above this transition-range, no matter how rapid, cannot entirely prevent the change and thus preserve the austenite by itself at ordinary temperatures, it happens that under the microscope we find, in addition to the ferrite, Fe3C, and austenite, which the thermal diagram of steel requires, it series of transition-products with distinctive structures, to which have ,been given the names martensite, troostite, sorbite, etc. Now these transition-products, in addition to the solid solution, austenite, have been the source of much controversy, at times very bitter. One side would insist that, say, troostite was an entity, which the other side would deny, pointing out that it must be a transition-mixture, with a particular structure. That austenite was a solid solution of carbon in iron has been denied by one school ; we have been told that Fe24C dissolved both Fe3C and Fe, and thus gave rise to a whole series of quenching-products-all this in spite of the fact that no matter how the thermal diagrams differ in regard to cast-iron, they all agree in regard to the solid solution, austenite, for Fe24C finds no place on the diagram. Thus it happens that while the authorities fight both in regard to the iron-carbon diagram and the structures met with in hard- * Associate Professor of Metallurgy, Columbia University in the City of New York.

Dec 1, 1912

By R. W. Harper, M. C. Fuerstenau, J. D. Miller

Data were obtained with hematite with octyl hydroxamate and oleate as collectors to determine the mechanism of collector adsorption and also to establish the roles that conditioning time and temperature assume in this system. The presence of hydroxy complexes of iron are apparently necessary for chemisorption of collector to occur, and it appears as if extended conditioning times and elevated temperature promote greater dissolution of the mineral and hence greater concentrations of hydroxy complexes. Data were also collected with two natural hematitic ores. With one ore that was ground to 70% - 15u, an addition of 0.4 lb per ton hydrox-amate resulted in a final concentrate recovery of 86% at a grade of 64% iron. Satisfactory concentrate grade could not be obtained with fatty acid under these conditions. The effect of conditioning time prior to the addition of collector was also examined with another ore. When the ore was conditioned for 3 min, 19% of the iron was recovered in the concentrate at a grade of 67% Fe. With a conditioning time of 7 min, 73% of the iron reported to the concentrate at a grade of 62% Fe. These products were obtained with an addition of 0.2 lb per ton hydroxamate. This ore also responded well to flotation with fatty acid. The use of potassium octyl hydroxamate as a collector for iron oxide has been the subject of an earlier study.1 From this initial study, it was suspected that hydrolysis of surface ferric iron was involved in collector adsorption. More recent work in other systems has shown that slight mineral dissolution, followed by hydrolysis of cations common to the mineral lattice, is apparently necessary, and that adsorption of these hydroxy com- plexes probably occurs prior to the adsorption of collector. In view of these facts, work has been continued on the hydroxamate-hematite and oleate-hematite systems to gain better insight into the mechanisms of collector adsorption on iron oxide. Microflotation experiments in conjunction with infrared analysis were used in this regard. In addition it was felt necessary to establish more clearly the responses that can be obtained from natural ores when hydroxamate is used as collector as compared to those obtained when fatty acid is used. Experimental Materials and Techniques Pure potassium oleate, potassium octyl hydroxamate, synthesized from hydroxylamine hydrochloride and methyl octanoate, and a distilled Tall Oil were employed as collectors. Conductivity water was used in the

Jan 1, 1971

By Joseph A. Holmes

I. INTRODUCTORY. THE plans for the investigation of fuels and structural materials now being conducted by the Technologic Branch of the United States Geological Survey were, before being decided upon by the Director of the Survey, submitted for consideration to the National Advisory Board, upon which there are nine representatives from the membership of the American Institute of Mining Engineers, viz.: Messrs. John Hays Hammond, Robert W. Hunt, B. F. Bush, and E. V. d'Invilliers (representing the Institute); Messrs. Julian Kennedy and C. S. Robinson (representing the Iron and Steel Institute); Dr. Charles B. Dudley (representing the American Society for Testing Materials); Mr. F. H. Newell (representing the U. S. Reclamation Service); and Dr. Richard Moldenke (representing the American Foundrymen's Association). It seems fitting, therefore, that a report of these investigations of the past three years should be submitted to the Institute for publication in its Transactions. The above, together with other representatives of the national engineering societies and allied organizations, were invited by President Roosevelt to serve, along with the Chiefs of the several Government Bureaus who have charge of public works and large. fuel purchases, on the National Advisory Board to give advice concerning these investigations. The appointment of this National Board grew out of a wish on the part of the President, the Secretary of the Interior, and the Director of the Geological Survey not only that the appropriations for these investigations be expended in a manner most beneficial to the several branches of the government

Jan 7, 1908

Jan 1, 1893

By W. M. Peirce

FOR many years it was considered quite the proper introduction to any discussion of zinc metallurgy to remark that the methods of extracting zinc from its ores were archaic. Often there was an added implication that the industry in every phase savored of the days of alchemy. On rare occasions comments of this sort may still he heard. Fortunately, not only for the zinc industry but for the world at large, there is today no longer a basis for considering zinc metallurgy unprogressive. Progress in any industry is possible along three distinct lines. The methods of production may be improved, thereby reducing costs. In the case of basic materials, this may also have the important effect of increasing potential supply. Second, quality may be improved. Finally, the product may be made more valuable to consumers through increased knowledge of its utilization, thus holding old markets or opening new.

Jan 1, 1931

By L. H. E. Weyher

As a result of past developments, mainly at universities, the coal industry has had access for a decade or more to a number of computer programs for coal mine planning. Using some of these programs Bethlehem Steel's Research Department in 1969 launched jointly with Bethlehem Mines Corporation an extensive research and development program aimed at: (1) testing the capabilities of these programs through trial applications as the need and opportunity existed, (2) defining what additional capabilities were required to make mine planning computer systems fully useful in the hands of Bethlehem's mine-planning engineers in the field, and (3) developing and implementing in the field the mine-planning systems agreed on. This program is now nearing completion, and several of Bethlehem's operations routinely use the planning tools that were developed. The progress of this research program is discussed in terms of our initial trial applications of computer methods to mine planning and the incorporation of several innovative features into our new set of computer programs, in particular, the use of time sharing, data base management systems, and general-purpose simulation languages.

Jan 1, 1977

By MARK H. LAMB

(Canal Zone Meeting, November, 1910.) THE recent growth of a sentiment among cyanide-plant designers against the use of gravity-stamps for the crushing preliminary to cyanidation may be said to date from the almost simultaneous perfection of the ribbed tube-mill liner and of the tall, air-agitation tank. The first step in the resulting change of practice was the universal adoption of the tube-mill for fine-grinding and the use of coarse screening oil the battery. This was the beginning of the surrender of supremacy by the gravity-stamp ; since merely the single fact that it was a more economical machine for crushing fine had retained it in favor as compared with ball-mills, rolls, or steam-stamps. The surrender, however, is not yet complete. It is the universal practice to use rolls where a relatively small tonnage is to be crushed coarse, as, for example, when coarse concentration is included in the plan of treatment. Power, attendance, repairs, and first-cost are smaller for the rolls, under such circumstances, than for stamps; and it is becoming daily more apparent that, with no concentration to provide for, the use of rolls and tube-mills, without the complication of trommels and elevators required by concentration, is rapidly gaining favor in the eyes of the leading designers. The next step was the use of the rapid-running Chilean mill between the gravity-stamps and the tube-mill, which again narrowed the field of operation of the gravity-stamp while radically widening its screen-aperture. Such a combination of stamps and Chilean mill offers advantages when fine concentration is necessary, since the reduction in the Chilean mill call be adjusted easily and governed by varying the screen-mesh. But even concentration is now looked at askance. One of the leaders of this metallurgy has abandoned the separation and

Jul 1, 1910

By Cyril Stanley Smith

Jan 1, 1949

By Cyril Stanley Smith

Jan 1, 1949

By Thomas T., Read

T HE preceding chapter has recorded the initiation of mineral industry education during the period 1890-1910 in numerous institutions that had not previously offered it. It should also be emphasized that in many institutions where instruction had begun before 1890, as recorded in earlier chapters, but had not yet become firmly established,, this period was one of marked growth and development. This was not universally true, however, for at the Universities of Pennsylvania, Michigan, Illinois, Wisconsin, Washington (St. Louis), Iowa, Vanderbilt and Tennessee, and at the Polytechnic College of Pennsylvania, mineral industry instruction was being dropped during this period, instead of gaining in strength. It is necessary to emphasize this, because writers on the subject have not infrequently , attempted to make a much too simple correlation between mineral -discovery or production and the intensity of student interest in mineral industry curricula. It would naturally be true that periods of large mineral production would, in general, coincide with cycles of business prosperity, and the latter are conducive to starting new ventures, educational as well as business. It should be equally evident that opportunities for business and professional success might, in such periods, appear to increase at a more rapid rate in industries other than mineral, or in the utilization of minerals rather than in their production. The author has not been able to perceive any simple and clear relation between interest in mineral industry education and mineral discovery, production, and utilization, or general business prosperity. On the contrary, the more the problem is studied the more complex the factors involved in it appear to be. In a later chapter an attempt will be made to analyze them in more detail.

Jan 1, 1941

By Charles White Merrill

Mankind's progress is measured in minerals. Man's emergence from prehistory is marked by passage through a Stone Age and a Bronze Age and into the present era, sometimes called the Iron Age or the Age of Metals. With the evolution of civilization and the development of a modem industrial economy, minerals become more and more important. Structures, roads, and machines are built largely of minerals; the energy to heat the structures and to drive the machines is mostly mineral; agricultural fertility is maintained by mineral fertilizers and water; and military strength is provided by fortresses, armaments, and munitions, largely of mineral origin. Thus in the material world, in the productivity of the economy, access to minerals has paramount importance. Every evidence indicates increasing dependence on minerals in the modem economy, particularly on the mineral fuels as energy sources to provide the power base for advancing industrialization. Both the total and the per capita consumption of almost every mineral is increasing in the industrialized nations. Moreover, nations with predominantly agrarian economies call themselves underdeveloped and universally strive to industrialize. Most mineral consumption trends in the more advanced economies have been greatly exceeding population growth-which itself has been advancing at an accelerating rate-and sometimes have surpassed the growth in real income. Some minerals have only recently been adopted or grown to importance in use. Titanium metal did not appear as a commercial product until 1948, and even coal seriously displaced wood as a source of heat less than two centuries ago. On the other hand, minerals have always played an important role in construction. The prehistoric megaliths that form the dolmens of Salisbury Plain are stone; the pyramids are andesite faced with limestone; and many other ancient structures are built of mineral materials. In modem times the whole course of architecture has been redirected by new building materials, mostly mineral. Most conspicuous is the sky-

Jan 1, 1964

By Allen Garrison

A PREVIOUS paper1 reviewed some of the properties of clays and shales and presented some data on the nature of the gelling phenomenon. It included a brief discussion of origin of clays and shales, their com-position, structure, retention of water, ionization, base exchange, and the nature of the gelling of water suspensions, Other publications of the Institute2-8 have discussed the properties of clays and their relations to drilling-fluid behavior and control. It is the purpose of this article to present some new data obtained and arranged in a different manner and making possible a better understanding of the chemical reactions involved in the control of drilling-fluid characteristics during the normal drilling operations. EXPERIMENTAL PROCEDURE The difficulties involved in the measurements of the flow character-istics of plastic fluids are too familiar to recite, The possible applications of some of the well-known instruments to this problem have been ade-quately discussed by Hobson9 and he has given an excellent bibliography. Although there are many viscosimeters of varied design, none of them appear to fulfill the most obvious demands of accuracy in the measure-ment of clay or shale suspensions, Since the fluid characteristics are dependent on the rate of flow of the fluid, and the viscosity usually falls off very rapidly as the rate is increased, it is clear that the first require-ment is that the instrument shall be capable of a wide variety of speeds. The viscosity of the fluid at any fixed and constant rate of flow is also a function of time, so that the second demand is that the instrument shall be capable of a constant and continuous motion for a prolonged period of time.

Jan 1, 1939

By G. Sachs, S. I. Liu

Introduction In a previous investigation on the effects of repeated strains of large magnitude on the aluminum alloy 24 ST, it was found that the reduction in ductility by straining in tension was partially restored by a subsequent compression.&apos; As illustrated by the dashed line in Fig I,$ the ductility (e~) retained after prestraining in tension by a certain amount (el) and measured in a subsequent tension test is represented by a straight line sloping down under 4s°. If a compression of the same magnitude as the first tension is inserted (€2 = — €1) between prestraining and final testing in tension, such a "balanced" tension-compression cycle yields a ductility considerably higher than that present after prestraining in tension only. The results of these tests can be correlated with those of an investigation on the effects of prestraining in compression.~ As also shown in Fig I, the ductility in subsequent tensile tests decreased with com- pression, at a rate considerably slower than that after prestraining in tension. The above discussed testing conditions can be considered as special cases of a general straining cycle, consisting of first, straining in tension by an amount el, subsequently straining in compression by an amount e2, and finally determining the retained &apos;ductility, e,, in a tensile test. Prestraining in tension is then represented by el > o and e2 = o. Prestraining in compression is given by e~ = o and e~ < o. Balanced cyclic straining is defined by the condition el > o and cz = — 61. In order to obtain further information on the effects of straining cycles consisting of tension and subsequent compression, further tests were made, varying both the tension strain, el, and the compression strain, e2, within extreme limits; el varied between 0.06 and 0.28 and e2 between — 0.008 and —0.h approximately. Apparently, such tests have not been previously performed. They revealed phenomena which have not been recognized to date, The results of the investigation are herewith reported, without attempting to correlate them with internal processes within the metal structure. However, in order to assist in an analysis of this type, the results have been represented in various manners. In addition, further test data on the effects of prestraining by compression were provided by using specimens of various contours (notched specimens) in the sub-

Jan 1, 1949

By E. P. JENNINQS

(Cleveland meeting, October, 1912.) LARGE deposits of titaniferous iron-ore occur at Caribou, an old silver-mining camp in Boulder county, Colo., 17 miles west by south of Boulder, and a few miles northwest of the tungsten-mines. Professor Regis Chauvenet 1 published a part analysis of the ore many years ago, but gave no description of the wall-rock. Caribou hill, which contains both the silver-bearing veins and the iron-ore deposits, is a low dome of gabbro surrounded by the Archaean schists and gneisses of the Front range of the Rocky mountains, the peaks of which, a few miles west of Caribou, attain an elevation exceeding 12,000 ft. The gabbro stock is roughly elliptical in outline, with approximate diameters of 1 and 3 miles. The crest of the dome is 10,500 ft. above sea-level, and the town and ore-deposits are 500 ft. lower. Outcrops of the iron-ore occur in the town and extend NW. for 2,000 ft., where they disappear under the swampy meadows of Caribou park. Portions of the deposit are covered by drift, but one continuous outcrop is 900 ft. long and from 200 to 250 ft. wide. A second deposit is 0.25 mile south of the town along the eastern slope of the hill. It is not as well defined as the north bed, but is approximately 1,000 ft. long and from 100 to 200 ft. wide. The easily disintegrated ore does not form prominent outcrops, but the outlines of the deposits are readily traced by the large amount of ore fragments that cover the ground. Trenches and pits sunk on the outcrop expose a roughly banded magnetic iron-ore, with pyroxene as the principal gangue-mineral. The Gabbro. This rock was classified in the field as a gabbro from the presence of pyroxene and striated feldspars, and for convenience the field-name will be retained. 1 Chauvenet, Regis, Biennial Report of State School of Mines, Golden, Colo., p. 16 (1886).

Oct 1, 1912

By J. E. Hilliard

Isobaric sections of the eutectoid region of the iron-carbon phase diagram have been exgerimentally determined at 35, 50, and 65 kb. The phase boundaries were located by metallographic analysis of specimens quenched after equilibriatwn at known temperatures and pressures. With increasing pres -sure a pronounced decrease in the solubility of FesC in austenite was observed together with a depression of the eutectoid temperature. These two effects resulted in a shift of the eutectoid composition toward a lower carbon content; at 65 kb the eutectoid was at less than 0.2 wt pct C. These results are in qualitative agreement with thermodynamic calculations. It has also been shown by calculations that Fe3C in contact with saturated austenite will be stable with respect to both graphite and diamond formation at all pressures above -3.5 kb. 1 HE investigation described in this article was part of a more general study of the effect of high pressure on transformations in Fe-C alloys. Thermodynamic calculations and exploratory runs made in 1959 at the start of the program indicated an appreciable change with pressure in the phase equilibria of Fe-C alloys. However, the calculations were not considered reliable enought to provide the quantitative information required for the interpretation of the effect of pressure on the kinetics of transformations. An experimental investigation was therefore made to determine a series of isobaric sections of the eutectoid region of the phase diagram at pressures up to 65 kb. EXPERIMENTAL PROCEDURE Materials. Seven alloys with analyzed carbon contents of 0.10, 0.20, 0.38, 0.60, 0.77, 0.93, and 1.20 wt pct C were prepared from Ferrovac" iron and high-purity graphite induction melted in magnesia crucibles under argon. The ingots were hot worked and swaged down to 0.19-in.-diam rod which was then centerless ground to a final diameter of 0.125 in. Samples for chemical and spectrographic analyses were taken from each end of the rods. The prin- cipal impurities were found to be Ni, Al, Co, and Si which were present in amounts up to 0.03, 0.02, 0.01, and 0.01 wt pct, respectively. Specimens were prepared by slicing the ground rods into pills 0.06-in. thick which were silver plated to reduce decarburization during the equilibration. Silver was chosen for this purpose because of its very low solubility for carbon and its mutual immisicibility with iron. High-Pressure Apparatus. The high-pressure runs were carried out in the "Belt" apparatus.&apos; As shown in Fig. 1, this consisted of a cylindrical cell compressed between two Carboloy punches loaded by a uniaxle press. Radial support to the cell was given by the "belt" which was a Carboloy die heavily prestressed by a series of steel binding rings. Laminated gaskets of lava and metal separated the punches from the inner surface of the "belt". A cross-section of the high-pressure cell is shown in Fig. 2. Two specimen pills were located inside a resistance heater of 0.20-in.-diam Nichrome tubing. The ends of the tube were sealed with alumina and lava pills tamped in place after the

Jan 1, 1963

By H. M. St. John

THE melting department is the heart of the foundry. From it clean metal flows to the molding floor, in the right quantity, at the right time and at a sufficiently low cost-or, if not, the foundry fails to thrive. Since it is our purpose here to discuss present-day melting practice in the foundry, it may be well at the start to emphasize the wide differences in foundries and the conditions under which they must operate in order to reach the goal stated in the first paragraph. In every foundry, large or small, jobbing or captive, the same factors must be dealt with but they are of varying consequence and must be dealt with in varying ways in different foundries. Particularly in the nonferrous industry, there is so wide a variation in the composition of alloys used and in the character of castings made that no one type of furnace, nor any one method of operation, can be expected to produce the best results at all times. The present discussion will not attempt to include all nonferrous metals. It is intended to cover only the copper-base alloys in which copper is the dominant element, most of which are commonly known as brass or bronze. The discussion is further limited to the melting of these copper-base alloys for use in sand-casting foundries. Die-casting plants, the brass-rolling mills and certain other metal industries have melting problems peculiar to those industries, which will not be considered here. The following considerations are elemental in all foundries and are listed in what is believed to be the relative order of their present-day importance: I. The melting department must meet the foundry&apos;s requirement for dean, fluid metal, of specified composition and purity, at a temperature suitable for the work the foundry has in hand. This is the prime consideration in any foundry, at any time, anywhere. 2. Working conditions surrounding the melting furnaces and attending their use must be good. 3. The cost of molten metal at the mold must be as low as possible. 4. The operating characteristics of the furnaces must be sufficiently flexible, to meet normal variations in foundry requirements. 5. The operation and maintenance of the melting equipment must not require more skill and experience than is available in the particular foundry in question. METAL QUALITY It is not a function of the melting furnace to refine or improve the quality of the metal but simply to melt it without impairing its quality. Good practice requires, therefore, that care must be taken to supply the melting department with metal of inherently good quality, assured by specification or otherwise, having all the properties necessary to produce the castings desired. An alloy contains a number of primary elements, which must be present in definite proportions if the castings made from it are to have the desired properties. If the castings are made to a customer&apos;s specification, this will state the range within which these principal elements (for example, copper, tin, lead and zinc) are permitted to vary.

Jan 1, 1946

By Robert E. Green, T. Hinton

The velocities of the three possible modes of elastic-wave Propagation have been calculated for single-crystal aluminum at 1-deg intervals throughout the standard steveographic triangle. The results are presented as isospeed contours. The deviations between the direction of maximum energy propagation and specirzen axes are presented as arrows drawn within the standard triangle. The orientation factors associated with dislocation nzotion on the primary slip system only and also on all twelve slip systenzs have been calculated for all three elastic waves. The orientation factors associated with a longitudinal standing--7aue resonant specivnen hazle also been calculated. The relevance of these results to ultrasonic attenuation measurements is discussed. DUE to the widespread use of ultrasonics in the investigation of the properties of solids a number of authors15 have discussed in detail the theory of elastic-wave propagation in solids. In this paper the modes of wave propagation are evaluated according to the procedure suggested by reeen&apos; for the case of single-crystal aluminum at 1-deg intervals throughout the standard stereographic triangle. The wave speeds are presented in the form of contour diagrams within the standard triangle. The deviations between the direction of maximum energy propagation and the normals to the wave fronts are presented as arrows drawn within the standard triangle. The orientation-de pendent factors (orientation factors) associated with dislocation damping as derived in the preceding paper6 have been calculated for the case of aluminum at 1-deg intervals throughout the standard triangle. The orientation factors for dislocation motion on the primary slip system only and on all twelve slip systems are presented in the form of contour diagrams, for both the traveling- and the standing-wave conditions. The relevance of these results to ultrasonic attenuation measurements is discussed. ELASTIC-WAVE PROPAGATION Three waves can be propagated in a linear elastic homogeneous anisotropic medium. The velocity of propagation v of each of these waves in a medium of density p can be obtained from the determination of the eigenvalues and eigenvectors of the matrix equa- The A&apos;s are a series of moduli which are functions of the elastic constants cij and the direction cosines 1, m, and n of the specimen axis. In the case of cubic single crystals where there are only three nonzero elastic constants cll, c12, and C, the A&apos;s are, The solution of Eq. [I] will give the wave speeds (eigenvalues) and the direction cosines a, 0, and y of the particle displacements (eigenvectors). To obtain the direction of maximum energy flux requires the calculation of the energy-flux vector ET with com- w is the angular frequency, A, the amplitude, and v the velocity of the wave. The direction cosines a, b, and c of the energy flux vector are then given by

Jan 1, 1967

By N. Brown

IT has been observed that a hexagonal-close-packed crystal will undergo the same macroscopic displacements as an isotropic material if the basal plane is perpendicular to the axis of twist.&apos; Other orientations may produce both bending and twisting, but this analysis will be confined to pure torsion of a right circular cylinder. The z axis, the axis of twist, and the specimen axis are coincident. The displacements are given by Uq = rz, Ur = Uz = 0 [1] where 4 is the angle of twist per unit length. This requires rotational slip, as discussed by Frank&apos; and Wilman, which may be observed readily. The relative rotation of adjoining slip planes is simply produced by a movement of a planar grid of screw dislocations."." The screw dislocations are of the same sign and they move radially inward. For hexagonal-close-packed metals, the grid is hexagonal and the screw dislocations lie in the < 2110 > directions. The displacement of a point is the resultant of two displacements produced by intersecting screws sweeping over the point. The dislocations must pass over the point (r, o) in such a manner that its resultant displacement corresponds to the observed macroscopic displacement. If 6&apos; is measured from the [1010] direction, then for 0 < ? < ~/3, only the [1210] and 121101 type screw dislocations are needed to produce the required displacement. If n1 screws of type [1210] and n2 of type [2110] pass over a point, then, in order that Ur = 0 n, sin ? - n2 sin (/3 — 6&apos;) = 0. [2] If the tangential displacement is to be independent of 0, then n1 cos ? + n2cos (/3 —?) = N [3] where N is independent of ? and thus depends only on r. Nb is the tangential displacement where b is the Burgers vector. Since U? is a linear function of r, then N must be a linear function of r. If a2 is the outer radius and a, is the inner radius to which the plastic deformation has extended, then N = Nm2 r-a1 [4] This function meets the conditions that at

Jan 1, 1956

By A. W. Hale

IN a work published in 1838, De Morgan, the author of the article on "Probabilities,&apos; in the Encyclopedia Metropolitana, says " The method of least squares is not yet introduced into the affairs of common life,….that many things which are demonstrable only by the higher branches of mathematics are looked upon as useless." And he mentions an instance in which "a method was suggested for estimating the relative importance of boroughs, by considering their population and contributions to the revenue com-

Jan 1, 1881