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By Paul D. Merica, O. B. J. Fraser

PROBABLY the first metallic objects used by man were nickel alloys. In search for flints suitable for the fashioning of their rude tools, our paleolithic ancestors, some 25,000 years ago, quite likely may have come upon some of those heavy, metallic fragments that we now know as meteorites, which consist of an alloy of nickel and iron containing usually from 5 to 15 pct of nickel. Whether paleolithic man ever did discover and use meteoritic fragments, his sketchy records do not actually disclose. We do know, however, that such fragments have been found and used by peoples, particularly the North American Eskimos, for weapons and implements in just the same manner as stones, and prior to any knowledge by those peoples of the reduction of metals from ores. Meteoritic showers were recorded frequently in earliest times and the meteorites often were found and fashioned into useful objects. The ancient Arabic and other myths of "invincible swords fallen from heaven" seem thus to have had a very definite basis in fact, and such weapons, of meteoritic material, have actually been re- covered from archeological excavations. It thus seems probable that meteoric nickel-iron was found and used long before iron was recovered by smelting iron ores (perhaps about 1200 B.C.) and probably even before there was knowledge and use of bronze and gold. Although many centuries were to pass before nickel was first isolated, in 1751, from Swedish ores and recognized as an elemental

Jan 1, 1953

By J. E. Rowland

NIOCALITE is a new mineral species which has been identified in rock from the Oka district, Quebec. It occurs as prismatic crystals up to l 0 mm. in length and I mm. in width, in coarse, white, crystalline calcite with associated apatite, diopside, biotite, pyrochlore, and niobian perovskite. The crystals of niocalite are light yellow in col-our and have a vitreous lustre. The optical properties of niocalite (I) are as follows: Biaxial negative -2V = 56° a = 1.700, [ ] = 1.730 Birefringence y -a = 0.030 Optic orientation: X = b, Z/\c 12°, Y , /\a = 32° The specific gravity is 3.32 and the hardness is approximately 6 (Mohs scale). A detailed analysis performed on 2.4 gm. of hand-picked material reveals that niocalite is essentially a calcium niobium silicate. Table I gives the result of the analysis. Crystals of niocalite, apparently suitable for X-ray diffraction work, were selected, and single crystal photographs were obtained using both Weissenberg and Precession cameras. Initial difficulties were encountered in interpreting these films, and in correlating the crystal data with the optical data. The in-consistencies were explained by the fact that every grain examined was twinned to some extent.

Jan 1, 1957

Discussion of the paper of W. A. Forbes, presented at the New York Meeting, October, 1913, and printed in Bulletin No. 82, October, 1913, pp. 2477 to 2514.. SAMUEL K. VARNES,* Steelton, Pa.:-We have a gas-cleaning plant consisting of a, centrifugal dry dust catcher, and two rain-type wet scrubbing towers, 25 by 60 ft. each, for rough cleaning of blast-furnace gas. This plant was put in early in 1910, with the intention of cleaning gas for use in hot blast stoves and under boilers, and was so used for several months. Soon after it went into service, the blast-furnace men complained that they could not get as high blast temperatures as they had obtained when using dirty gas. It was decided to run a series of careful tests to determine if this were true and to what degree the apparent results might be affected by other conditions. About 60 tests were run, covering a period of five months, and at the end we came to the conclusion that it did not pay us to scrub the gas for stoves and boilers. The tests were all run upon a single stove, no boiler tests being made, but the conclusions of the stove tests being applied to the boilers. The furnace burden was practically the same for all the tests and averaged: Per Cent. Daquari and other hard ores 57 Nodules 13 Raw Mayari ore 25 Mill cinder and scale 5

Jan 12, 1913

By F. A. Emmerton

I have used for about two years, in the laboratory of the Joliet Steel Company, a rapid method for the determination of phosphorus in iron, steel, and ores, which possesses one or two features sufficiently novel to warrant description. In general, it is the method described by Mr. Benjamin B. Wright (Transactions, vol. x., p. 197), involving the precipitation of the phosphorus by means of molybdate solution, and its estimation in the yellow precipitate by reduction of the molybdic acid, and titration of the resulting oxide with a standardized permanganate solution, according to the principles laid down by Werncke (Fres, Zeit., vol. xiv., p. 1). In the use of this method, I had difficulty at first in obtaining a yellow precipitate of reasonably uniform composition. It is a well-known fact that, to secure this result, the conditions of precipitation must not vary. The principal condition is temperature; and acidity, concentration, proportion of nitrates and chlorides, and time, are important elements. I am aware that uniformity in these conditions has been obtained to a reasonable extent by many chemists,. so that they are enabled to use with success, methods based on the

Jan 1, 1887

Jan 1, 1911

By James R. Arnold, John G. Mansanti

BACKGROUND Gold Fields Mining Corporation started their Chimney Creek operation in late 1987. The dump leaching operations commenced in October and the mill startup took place during the last half of November. The milling process at Chimney Creek is almost a conventional CIP plant with the major exception being the installation of a second thickener as a washing stage prior to CIP12 ' A simplified flow sheet is shown in FIGURE 1. Most of the gold in the mill is liberated by grinding in cyanide. After grinding in a conventional SAGball sill circuit, the cyclone overflow reports to the thickeners. The thickener overflow from the first thickener is pumped through 5 stages of carbon columns for gold adsorption. Slurry from the thickener underflow is leached, washed, re-thickened and pumped to CIP. After approximately 6 hours of retention time in CIP, the slurry is pumped to tailings for final deposition. The carbon from CIP is transferred to the third stage of carbon adsorption and then advanced as normal through the columns and strip circuit. Loaded carbon is stripped at approximately 1500C (3000 F) and 55 kPa (80 psi). After 4-5 hours of stripping, the grade of four tons of carbon is reduced from 5,140-6,860 g/t (150¬200 oz/ton) to typically 17 g/t (0.5 oz/ton). Zinc precipitation is used to recover the gold from the pregnant solution. After a water wash, the stripped carbon is transferred to acid wash or to the kiln feed tank for reactivation. All strip lots are acid washed in 3.0% HC1 and all stripped carbon passes through the kiln for thermal reactivation. Then the carbon is quenched, sized and stored in tanks or bins for transferral to CIP or to the carbon columns. Loaded carbon from the dump leach circuit is treated in a circuit consisting of five carbon columns which are parallel to the mill circuit. No distinction is made between the mill or dump leach carbon once the gold has been stripped from them. CARBON FINES HANDLING Once the carbon has been transferred from the carbon columns, every effort is made to minimize carbon attrition and to recover the carbon fines that have been generated in the process. Wemco Hidrostall pumps are used for transferring all carbon in

Jan 1, 1990

By L. C. Kern

This paper presents information on the use of a new propping agent (malleable aluminum particles) which has been used successfully for producing high-conductivity fractures. The conductivity of a packed fracture depends on the width of the fracture as well as the permeability of the propping material. It is significant that the flow capacity of a propped crack is often increased many fold by propping the crack with a sparse distribution of particles. However, the flow capacity of a sparsely propped crack can be limited by two phenomena: (I) crushing of the propping particles, and (2) embedment of the propping particles in the formation walls. Malleable aluminum particles exhibit interesting properties which tend to overcome these limitations. As high loads are applied to the particles they will deform slightly, rather than shattering. The deformation results in a greater bearing area against the formation wall. This reduces the stress on the particle and reduces particle penetration into the formation. The behavior of aluminum particles under load and the bearing capacities of serveral formation rocks have been measured in the laboratory. By properly using these data, as explained in this paper, the flow capacities of aluminum-propped cracks can be calculated for a variety of conditions. Aluminum particles have been used successfully in the field to prop fractures. Where high-conductivity fractures were needed, the aluminum-propped fractures have given greater well stimulation than could have been expected for conventional fracturing processes. INTRODUCTION The purpose of a hydraulic fracture treatment is to create a conductive channel from the wellbore out into the oil or gas formation. The word conductive is emphasized because we believe that the fracture conductivity (flow capacity) is one of the most important factors influencing fracturing results. Previous papers have pointed out the additional well stimulation that can sometimes be achieved by increasing fracture conductivity. Several years ago, we investigated in some detail the effect of fracture conductivity on productivity increases to be expeced from vertical fractures. Both electrical analog and theoretical studies of unsteady-state flow behavior were made. A discussion of the electrical analog equipment and some of the results of the study were given in a previous paper' by Dyes, Kemp and Caudle. Further details were given recently by McGuire and Sikora.5 Fig. 1 shows the remarkable influence of relative fracture flow capacity and length on well stimulation. Briefly, the study indicates the following. 1. High-permeability formations require high-conductivity cracks for best results. 2. The longer the crack, the higher the fracture conductivity required for best results. 3. If the conductivity of the crack is very large compared to the formation (i.e., flow is not being limited by crack conductivity), then the longer the fracture, the better will be the results. Judging from recently published articles,1,314 there is current interest in methods for obtaining high fracture conductivities. Hence, we would like to present in this paper a discussion of a new fracture propping process (use of aluminum particle) which we have used successfully to obtain highly conductive fractures. There are several factors which influence the conductivity of a propped crack. Conventional fracturing techniques frequently result in a crack completely packed with fracturing sand. For such conditions, the crack conductivity is the product of the width of the packed fracture and the permeability of the propping material. It is significant that a large increase in conductivity sometimes can be obtained by propping with particles which are distributed sparsely (less than a

By W. E. (Bill) Stanley

Introduction This is an exciting day. It isn't often that you can find the best minds in a particular business gathered together in one place. But that is what we have here. You are the best and the brightest people there are in the business of gold mining. What we discuss at this conference confirms the major issues facing us and sets out the issues governing how our mines and mining companies will be run in the next few years. In looking over the list of papers to be given, I have noticed something. It is something that I have noticed at almost every mining convention I have ever attended. Almost every paper at this conference concerns itself with the technical side of mining. Most of us in this roan are professionals; we are either engineers, geologists, accountants or representatives of some other profession. In getting where we are today, we have had to work hard to acquire the technical skills needed for our individual professions. We are all proud of our knowledge and work hard to claim the right to be considered an expert in a particular technical field or subject area.

Jan 1, 1987

G. A. Burr, Parral, Chihuahua, Mexico (communication to the Secretaryt): I regret that Mr. Norris did not give more attention to the hoisting of water in inclined shafts or slopes: the only slope mentioned being Hickory Ridge Slope, No. 4, of the Union Coal Co. The surface arrangement, illustrated in Fig. 12 of his paper, if not unpractical, is at least unscientific and cumbersome. It is my opinion that the back- and sideguides shown in Fig. 12 are not only unnecessary where rails are used as a track, but are unsafe, excepting in the case of a very firm hanging-wall, or roof, and sides of vein-matter, having absolutely no tendency, either to settle from the back, or to squeeze from the sides, an effect which would inevitably force the guides out of alignment. The accompanying illustration, Fig. 1, shows what I consider a better method of hoisting water than that described by Mr. Norris. This method is based on the general practice in metalliferous mines of the West, where skips are used in slopes; and, while it is not original with me, I have frequently used it with very satisfactory results for dumping both ore and water.

Jan 1, 1904

By Ralph H. Phelps

WHAT information do you have on precision investment casting? Please send me all available information on the removal of paraffin from oil wells and pipe lines. How can I find out how to remove magnesium oxide from lime? I want a good book on the pickling of steel. Can liquid oxygen be used as an explosive in a mine? Where can I get a bibliography on the plasticity of metals? These questions, selected from the scores of questions asked the Engineering Societies Library staff every day, indicate some of the diversity of the requests received. The samples chosen relate to interests of AIME members but the questions that come to the Library by mail, telephone, telegraph, and in person cover all fields of engineering, science, and technology. Some questions can be answered quickly; others require extensive searching. Those that can be answered in a few minutes or ten, twenty, or even thirty minutes are usually done without charge. For the more difficult questions a charge is made. In this way those requiring considerable service pay for it and the Library finds it possible to serve more persons.

Jan 1, 1948

By A. E. Michon

My comments today are directed toward western coal and its impact on Burlington Northern. I will be discussing three major topics. These are: location and extent of mining activities, the flows of this coal traffic into the various market territories, and finally the interaction of this western coal with coals found in the balance of the United States. When we at BN speak of western coal, we refer to those substantial deposits lying in southeastern Montana and north-eastern Wyoming. This territory covers many different coal formations. For the sake of simplicity, I will be referring to this general area as the Powder River Basin (or the "western" coal fields). This slide highlights the area overlayed by a map of the BN rail system. The U.S. Bureau of Mines estimates the demonstrated reserve base of Montana and Wyoming to be approximately 176 billion tons. Of this figure, about 73 billion tons is minable by surface methods. This is roughly 72% of the total strippable reserves in the western united states, BN does not have sole access to this coal for there are deposits in southern Wyoming near the union pacific railroad. I will say more about this later.

Jan 1, 1978

By Charles T. Holland

IN connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter [ ] into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. STRENGTH OF COAL It is generally agreed that one of the necessary conditions for bumps is a strong [ ] coal.1 Therefore, since the strength of coal is an important factor, a study of this property should be made. Several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines8 and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semibituminous (Pocahontas No. 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the same coal.

Jan 1, 1942

By Charles Catlett

Much has been done of late years to facilitate preliminary stratigraphical investigations, and for examination at considerable depths and in a certain character of material the diamonddrill, in its general forms, certainly stands pre-eminent among the tools for such work. But there are large classes of deposits —indeed, I may say the larger proportion in which ordinary. prospecting is done—which lie near the surface and are interbedded with soft and fine material. The method usually employed for prospecting these is by means of small shafts. These are sunk with considerable slowness and at considerable expense, depending largely upon the character of the material encountered, and are greatly interfered with by water. In this region the smallest are 3 by 4 feet, but they are usually considerably larger. Having had occasion during the past year to do a large amount of prospecting work, I have found the use of a hand-auger and drill of immense value in this respect, and in my practice it has largely superseded, and always preceded, the other forms of investigation. I believe that the information desired mas

Jan 1, 1898

By Dougla McDonald, Richard Poulin

"Most mine managers in Canada today will agree that one of the keys to mining efficiency and productivity is their human resources. A5 a result, many mines develop some sort of incentive designed to tap their employees' capabilities to the fullest extent. Historically, the most common plans used have been ""piece-rate"" plans, where individual or small groups of miners are paid a financial bonus based on some measure of their productivity. Recently, however, incentive plans that take a more team-based approach have been developed in some Canadian mines. One such plan will be defined in this paper, and its popularity in the industry today discussed.Gainsharing PlansThere are two primary components to a gainsharing plan. The first is a cash incentive, which is paid to all employees and based on factors that are highly correlated with employee productivity, and key to the profitability of the mine. For example, the typical gainsharing cash incentive is based on the cost/unit of metal produced. Management (in consultation with employees in some cases) will establish the budgeted cost per tonne, and any savings in this amount is shared between the company and the employees. The second is a management philosophy and associated communication network, which is designed to foster an environment that encourages information exchanges, communication, participation, and trust between employees and management. The typical gainsharing communication network consists of two tiers of committees. The first, operational committees, include all employees working in the same department or departments which frequently interact. The employees meet monthly with management personnel to discuss problems encountered and brainstorm for solutions. In most cases, these committees will nominate a person in the group to structure the meeting to maximize its efficiency. The second, the screening committee, is a single group consisting of representatives from the various operational groups, whose primary job is to ensure that the plan is effective, and the objectives and results generated by the plan remain consistent with the mine objectives. In short, gainsharing plans tell employees that their bonus depends upon performance and then gives them the opportunity and incentive to affect that performance. The opportunity is provided by a communication network and positive management practices, and the incentive comes in the form of ""intrinsic"" rewards of participation and the ""extrinsic"" rewards of the bonus payments. Figure I will clarify the relationship between the intrinsic and extrinsic rewards."

Jan 1, 1995

H. A. BUEHLER, Rolla, Mo. -I consider the lead .and zinc deposits of the Mississippi Valley to be the result of descending waters. There are many features that we have not determined and yet when you see the general field relations, it seems to me that the cause and effect can be well explained by descending circulation. In the Joplin-Miami district, for instance, the ore deposits are connected with openings or with old cavity fillings which have a direct connection downward from the surface to practically 300 ft. In the Miami camp, in the western part of the field, some of the deepest orebodies are directly connected with water, channels; the same condition has been obvious and always present with the shallower ores. I speak of one deposit that I have examined more thoroughly than any other in that district, the Admiralty property, which contains large openings or caves at the deepest levels. It seems to me that waters which would pass upward through 1800 ft. of dolomite would be saturated with lime and magnesia so far as the carbon dioxide of those waters would dissolve them, and therefore, on

Jan 1, 1918

The writing that is effective is woven with a he texture into an agreeable pattern; it is free from knots, loose threads, and stray fluff. The instrument that weaves this literary fabric, whether it produce a homely sock or a lordly tapestry, a simple story or a learned treatise, is a disciplined intelligence, as sure as a steel needle, as precise as a swift loom. The simile breaks down at this point, for the product of the pen is instinct with the human spirit and therefore transcends in beauty anything made by a mere machine. If words are to be woven into eloquent meaning, they must be well knit. Upon the relation of words to each other and of groups of words to other groups, known as phrases, clauses, and sentences, depends the success of writing as a means of transmitting thought from man to man. To be understood beyond question, you should know not only what your words denote' but how to build your sentences; you must not only choose your words aright but construct your sentences properly. A sentence is a combination of words that makes complete sense; it says something about something. A clause is a subordinate sentence or a sentence within a sentence. A phrase is a group of words without a predicate; it makes sense, but not complete sense. For example: I shall wait for a few minutes before I go home. The whole statement is a sentence; "I shall wait" and "before I go home" are clauses; "for a few minutes" is an adverbial phrase. The orderly arranging of words and of combinations of words is called 'syntax'; and from the original Greek form, [s?ta???] (suntaxis), is derived the Greek name for an editor,

Jan 1, 1931

BLASPA is the name for a computer code which can assist in the rapid optimisation of blasting procedures in an open-pit mine. BLASPA is based on a mathematical model of the blasting process, a model which has been developing since 1963 as a result of blasting research carried out at the College Militaire Royal de Saint-Jean under sponsorship of the Defence Research Board, and in co-operation with the mining and explosives industry. The model presently includes the following aspects: (1) Geometry, i.e. spacing, burden, bench height, collar, sub-grade drilling; (2) Explosives, i.e. types and grades of explosives, distribution into bottom and top load or decking, size of hole and coupling; (3) Hookup, i.e. parallel or angled firing, delays, location of primers. Computer costs are very small, by comparison with purely spherical AEC codes, so that any number of simulations can be carried out very efficiently. The system has already been used to carry out thousands of simulations for over 40 mines in Canada and abroad. It will be explained how such simulations become a useful guide for a mine's blasting engineer who wishes to optimize his blasting and drilling costs.

Jan 1, 1980

By Roderic A. Ellman

The new Woodrow Wilson Bridge (WWB) will replace the existing bridge over the Potomac River to connect Alexandria, Virginia to Prince Georges County, Maryland. The new WWB will extend approximately 1.1 miles across the river, with a 367-ft long bascule span in the main river channel where the water depth is about 36 ft. The bridge is primarily comprised of fixed spans in relatively shallow water and a bascule span over the navigation channel. The subsurface soil profile was quite variable along the bridge alignment. In Virginia, there was fill over soft Alluvial deposits underlain by dense Terrace deposits, as well as remnant foundations from a former ship yard. At the bascule span, there was up to 50 ft of a soft organic silty clay layer underlain by a deep deposit of stiff Cretaceous clay. Along the Maryland approach, there were Alluvial deposits over dense Terrace deposits over stiff Cretaceous clays and dense Cretaceous sands. The variation in subsurface conditions led to the selection of alternative deep foundations that suited the specific conditions and were based on the design phase testing program, from which ultimate design capacities were determined. During construction, there were instances of unexpected pile performance, notably different than that experienced during the design phase testing, requiring changes to the contract installation criteria and re-design. This paper will present the types of deep foundations used for the project, the performance criteria assumed during the design, the measured performance and difficulties encountered during construction, and the resulting remedial actions, i.e., changes to contract installation criteria and/or re-design due to the unanticipated field conditions.

Jan 1, 2009

By J. B. Morgan

The mechanical behavior of MgCu2 from 20 o to 725°C has been determined by "brittle-ring" tensite-test techniques, axial compression, and bending experiments. Compressive ductility begins at 450°C (0.65 T/Tm) and slowly increases with increasing temperature white the tensile ductility is characterized by an abrupt brittle-ductile transition at 600°C (0.8T/Tm). The compressive strength increases eightfold from room temperature to 400°C with a "normal" decrease as the temperature is further increased. The tensile strength goes through a rather abrupt threefold increase above 600°C with a subsequent decrease at higher temperatures. The slip system is (111)[110] and the twinning system is (111)[112]. At high temperatures MgCu2 is quite rate-sensitive, and dynamic yield points are observed that are extremely orientation-dependent. The high-temperature creep behavior under constant load is characterized by an increasing strain-rate with time. The general characteristics of the mechanical behavior make it possible to classify MgCu2 with those materials in which initial mobile dislocation density and the dislocation velocity-stress dependence are significant in determining mechanical response. Mgcu2 is the C15 prototype of the cubic Laves phase. Its range of homogeneity extends from 32.8 to 35.5 at. pct Mg at 500°C and narrows at lower temperatures. The lattice parameter is reported to vary from 7.02 to 7.05A,1 and the compound is completely ordered to the melting point of 819°C. MgCu2 has a brassy metallic appearance, is extremely brittle, and many of its physical properties are intermediate between those of the constituent elements: the electrical resistivity is 3.5 x 10-6 ohm-cm, Young's modulus is 10x 106 psi, the shear modulus is 6 x l06 psi, and the thermal coefficient of expansion is 18.7 x 10-6 cm per cm per "C from 20" to 250°C. Usually, properties of intermetallic compounds as functions of temperature have been determined by hardness, compression, or impact behavior, and almost all of these experiments have been performed on polycrystalline materials. Tammann and Dahl,2 for instance, determined the onset of ductility in a series of binary intermetallics by ball-hardness measurements and found the onset to range between 0.71 and 0.96 T/T,. Lowrie's3 investigations included some tensile properties, and he found ductility beginning around 0.65 T/Tm for most materials examined. His work did include some data on polycrystalline, nonstoichiometric MgCu2, however. The present work is an attempt to extend the examination of the particular compound MgCu2 in single-crystal form in order to aid the formation of general concepts about mechanical be-

Jan 1, 1965

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962