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By AIME AIME

M ODERN metallurgy properly belongs to this century. The great advance made in this science is directly attributable to the discovery of the Roentgen rays. Application of the results of this discovery, together with the more recent corroborating studies in electronic diffraction have definitely and for all time established this science. Metallurgists today speak with familiarity of the atoms of the different metals in terms of their orientation, atomic volumes, lattice structures, dimensional lattice constants distance of nearest approach, and the like. One matter of profound interest, which is quite staggering to the imagination of the human mind, is the enormity of the number of atoms even in a small particle of metal. As an illustration, let us compute the number of atoms in the volume of one cubic centimeter in a single grain of absolutely pure copper. Eighteen and a fraction cubic centimeters equal the volume of one cubic inch.

Jan 1, 1940

By T. A. Rickard

The writing that is effective is woven with a fine 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 'Itreatise, 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 trans¬mitting 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, ouvaeis (suntaxis), is derived the Greek name for an editor,

Jan 1, 1931

By G. C. Waterman, W. E. Hawes

Mr. Grieves' paper on "Shaft Sinking Today --A Boring Business Tomorrow" in the Dec. 1981 issue of MINING ENGINEERING is an excellent description of recent improvements in speed and costs of shaft sinking. However, shaft boring techniques are not a recent development. In 1935-36, the Idaho Maryland Co. (gold), Grass Valley, CA, bored the vertical 1.5-m-diam Idaho No. 2 ventilation and supply shaft to a depth of 346 m. The equipment was designed and perfected by Branner Newsome and was, I believe, described in "Transactions." Pickands Mather later bored a 1.8-m-diam shaft to a depth of about 305 m using Newsome's design. The Idaho No. 2 shaft cut through hard gabbro, diabase dikes, soft serpentine, very incompetent ankeritized serpentine and a strong fault zone. The completed shaft did not require timber support; the fault zone was cemented. Equipment consisted of a rotating 1.5-m or 3-m core barrel with a slotted bottom which cut a 76-mm kerf. The cutting agent was chilled steel shot introduced into the slot as needed. The driving mechanism and core barrel were lowered into the shaft, the former secured to the wall and the inshaft "engineer" operated the motors which controlled core barrel rpm and advance. After an advance of 1.5-3 m the equipment was lifted out of the shaft, a half(?) stick of powder cut off the drilled core, and it was hoisted to the surface with a cable attached to an eye bolt at the tope of the core. A "shift" consisted of three men: hoistman, equipment operator (down the shaft), and a surface laborer. Advance was variable as equipment and techniques were perfected. Near the end of the job advance was, as I remember, 1.5-3 m per shift. Costs were, as I recall, about $115/m. Up to 4 m cores were lifted out in one piece and swung to the dump by a stiff leg derrick. The Newsome equipment was relatively inexpensive to build and operate and his method should be (more than?) competetive with the methods described by Grieves.

Jan 1, 1983

By James H. Taylor

"Titanium is a widely distributed, dark grey metal1ic element found in small quantities in many minerals. It has no important uses." Happily, this early quotation proved to be wrung; titanium has, on the contrary, found a large number of very important uses. The error in the 1926 quotation illustrates the problems associated with forecasting the future development of any metal. 'The paper will nevertheless attempt to estimate what will happen to the European titanium industry over the coming decade with slightly more accuracy. It was not until 1955 that anything other than pilot plant facilities were installed in Europe. In 1955 IMI's plant in England, two plants in Germany, one in France and one in Sweden came into operation. All the companies associated with titanium installed melting furnaces but only IMI Titanium has forging and rolling facilities devoted solely to the production of titanium. The other firms rely on the use of equipment of their parent steel companies for processing the me1 ted titanium ingots.

Jan 1, 1982

Jan 1, 1925

By Douglas R. Piteau

Douglas R. Piteau (Engineering Geologist, De Beers Corp., Kimberley, South Africa; Presently Consulting Specialist at Nchanga Mine Open Pit, Chingola, Zambia)-Mr. Lutton is to be commeneded on his analyses and presentation of such practical data which can be used for predicting a preliminary optimum slope angle in rock. It appears that he assumes all slopes analyzed to be straight. Although there are overriding factors which affect the general slope configuration, such as structural discontinuities, ground water, and other environmental factors such as weathering conditions, regional stress, etc.,8 the affects of plan geometry under certain conditions also can be of outstanding importance. In investigation of natural slopes, for example, the effects of plan geometry are not entirely appreciated and it is in this respect that discussion is given. Experience in southern Africa has shown that the overall geometry of surface openings in rock, particularly those with dimensions of the order of 1500 ft or less, i.e., where radii of curvature of the slopes are less than, say, 700± ft, must be considered in rational slope-stability analyses. That is, the slope angle is not only a function of slope height, strength of the mass, and geometry of structural discontinuities, but also is dependent upon the plan geometry of the local slopes and the plan shape of opening. Technically speaking, adequate analysis of the slope must be three-dimensional, the third dimension being that of overall plan configuration and the analysis must incorporate its subsequent effects. However, current theories of slope stability all deal with the slope as a two-dimensional problem, i.e., a slice of unit length of an infinitely long slope is considered for a condition of plane strain. In this the tacit assumption is made that the plan radii of the crest and toe of the slope are infinite and no attention is given to the plan geometry of the slope. Clearly this is not the condition encountered in practice, particularly in open pit mining where excavations, relatively speaking, can be small and where these radii of curvature accordingly can have important affects on the slope stability. This is illustrated by the analyses of Piteau and Jennings 9 of the natural slopes which had developed around pipes of four diamond mines in the semiarid Kimberley area of South Africa. Although these slopes consist of dolerite overlying shale, the values of the slope angles of all the pits were corrected for a height of slope of 320 ft assuming that no dolerite occurred. This brought the data onto a comparable basis. These data were analyzed statistically and a clear empirical relationship, as is shown [in Fig. 4], is seen to have formed between angle of slope and curvature of slope, i.e., the angles of slope are greatest where the radii of curvature are least. Also, it can be seen that the slope of each line is different, indicating that the plan shape of the open pits also are significant, the curve being steepest for the open pits which are more circular in shape in contrast to those which are more elongated. The effect of slope curvature on the average angle of slope for the two extreme radii of 200 ft and 1000 ft for all four open pits is 39.5° and 27.3°, respectively. Hence, the concave curvature effect represents an average increase in slope angle of 12.2° from the essentially straight slope. In quantitative terms in Mr. Lutton's Fig. 2, this represents displacing the curve for a 320-ft pit from the second curve from the bottom (i.e., shale in subtropical climate) to that of the third from the bottom (i.e., quartzite in temperate environment).

Jan 1, 1972

By W. T. lsbell

HERCULANEUM, MO., about thirty miles south of St. Louis on the Mississippi River, is the site of the lead smelter of the St. Joseph Lead Co. The lead concentrates come by rail from the Flat River district and from three properties in Madison County, Missouri; from the Balmat division in St. Lawrence County, New York; a small tonnage from the Tri-State district; and occasionally from the Aguilar property in Argentina. The average grade is 67 to 68 percent lead and 1 to 3 oz of silver. The bulk of the material is flotation concentrate, with some gravity or table concentrate. No secondary metals, outside drosses, or any materials high in bismuth, arsenic, or antimony are treated. All concentrate is received in box-caps and is unloaded directly from a trestle into the concentrate bins at the roaster plant. Flux, coke, and any miscellaneous lead-bearing material is either unloaded directly into bins or unloaded with a locomotive crane. All moving and switching of cars is done with two thirty-ton steam locomotives. Shipping facilities for the plant are provided by the Missouri-Illinois Railroad. Water for the plant and for fire protection is obtained from a dam built in a near-by creek. Drinking water both for plant and town is obtained from

Jan 1, 1947

By Carl Zapffe

THE object of the Bradley process is to free manganese oxide from its associated gangue and separate the contained iron oxide by dissolving the manganese and precipitating it from the solution. 'The fundamental features of the process are : making. both 1 a manganese ore and an iron ore; effecting a separation of manganese .and. iron by means of selective roasting; leaching- the manganese from the roasted ore by using ' ammonium sulfate; precipitating the manganese by using the ammonia gas generated during leaching; fixing the precipitate by oxidizing with air; breaking down and reforming the ammonium sulfate, so that daily very little additional ammonium sulfate beyond that originally charged into the system is required; washing the manganese precipitate and the iron-silica residue and evaporating the liquor to conserve the dissolved salts in the moistures of these two products and 'to reduce the sulfur content,; drying the precipitates; magnetic wet-concentration of the iron-silica residue; sinteriny the manganese-and .the' iron-concentrates.

Jan 1, 1929

On the following pages are abstracts of papers published by the Institute during the year 1934 as TECHNICAL PWLICATIONB, CONTRIBUTIONS, m bound volumes and in MINING AND METALLURGY. For abstracts of papers that appear In bound volumes in 1934 but that were published as TECHNICAL PWLICATIONS m 1932 or 1933, see the TRANSACTIONS for 1932 and the YEAR BOOK dated January, 1934. Many of the TECHNICAL PWLICATIONS have been reprinted In bound volumes Information regarding this disposition, and number of pages in each paper, may be found m the list beginning on page 92 Volume numbers are given as listed at the beginning of the index, page 99 The abstracts are grouped as follows:

Jan 1, 1935

Henry LOUIS, London, England (communication to the Secretary) : Prof. Richards's paper has impressed me as highly valuable. Without entering upon any discussion of it as careful and thorough as it deserves, I venture to mention one or two points which a perusal of it has recalled to my mind in connection with my own study and practice of ore-dressing. I always mentally divide jigging into two phases: 1. A particle at rest on the jig-bed is lifted and carried upwards by the rising current of water, at an increasing velocity, which tends to a maximum. When the upward current is stopped, the particle continues to rise with rapidly diminishing velocity until it comes to rest. This completes the first phase. 2. In the second phase, the particle falls from its position of rest with an increasing velocity which tends again to a maximum, and continues to fall until the rising current of water has reduced its velocity to zero. This completes the second phase. The second phase will evidently be greatly modified by the effect of suction, as Prof. Richards shows; but I do not see that his experiments very clearly imitate the action of the second phase. And the brief intervals at the end of each phase, when the mineral particle, by reason of its acquired velocity, is still moving, though in opposition to the water-current, yet remain to be investigated. I feel especially, in Prof. Richards's paper, a difficulty which I have felt with regard to all similar previous investigations, namely, that the experiments deal with particles falling a long distance, when the velocity becomes uniform. I question whether this uniform maximum velocity is attained in actual jigging-practice. If so, it is certainly for a comparatively very small proportion only of each stroke. It seems to me that an investigation like that of Prof. Richards, but confined to the first 6 or 8 inches of fall only, and carried out with suitably delicate recording-apparatus, is what we

Jan 1, 1895

By Frank Milliken

IN September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1007 to 1019. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was dissemi-nated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was prob-ably less than 6o per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a com-plete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof com-prised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. 1, which gives percentages of tonnage and copper content.

Jan 1, 1940

By W. F. Flanagan, K. R. Evans

The strong temperature dependence of the flow stress of bcc metals has prompted considerable interest and controversy concerning the rate-controlling influence of the Peierls' mechanism upon deformation in metals.18"21 Dorn and Rajnak" recently offered a criterion for Peierls' deformation utilizing a line-energy model of a dislocation to estimate the saddle-point activation energy, for the nucleation of a pair of kinks as a function of applied stress and the height and shape of the peierls9- barrier. It was found that Un/2Uk, where 2Uk is the excess energy of a kink pair, was a unique function of where is the effective stress and 7p is the Peierls' stress as defined in Fig. 20. The relationship found by Dorn and Rajnak between is given by the solid line of Fig. 21. may be expressed in terms of the temperature of test, T, and the athermal temperature, T,, defined in Fig. 20. Considering the strain-rate, 9, of deformation for a thermally activated process to be given by where fo is nearly a constant, it is seen that and the theoretical relationship of Fig. 21 may be examined with readily obtainable experimental parameters. Dorn and Coworkers analyzed a large amount of experimental data in this manner for materials sus-

Jan 1, 1967

By G. Y. Chin, W. L. Mammel

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of' virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law'), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.' Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor's original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*'8 showed that Taylor's least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen' obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

By S. W. Miller

MOST of the steel welding done at the present time is in material containing not over 0.3 per cent. carbon, and the tests here described were in similar material. These tests are not as yet completed but it is hoped that more results and more reasons for the conclusions may be presented at the meeting in February. From the time the author found the peculiar structure in electric welds referred to in a previous paper,1 that is, needles or plates in the grains and similar material, in larger spots, at the grain boundaries, he has felt that these plates which may be iron nitride and probably contain some carbon, were at least partly responsible for the brittleness of electric welds. He has found but few traces of similar lines in oxyacetylene welds until the last 2 mo., when he has found them in large numbers under certain conditions. In the top of these welds, they are quite numerous. In the body of heavy oxyacetylene welds, they appear at times, but not nearly to the extent that they do in electric welds; the author has never seen them in the body of welds in material less than ;3/4 in. (19 mm.) thick. They are shown in Fig. 82. The reason they were not noticed before is undoubtedly due to the fact that in making tests of welded pieces the weld was always ground off level with the plate, and as this structure only appears in the top ;1/16 in. (1.5 mm.) of the weld, they were removed by the grinding or machining; also, welds ¾ in. thick had not been examined. It did not appear, in making bending tests, that this structure had much influence on the strength of oxyacetylene welds; while electric welds are noticeably brittle. Further, oxyacetylene welds made with certain special materials were exceedingly brittle even after the tops of the welds were removed; this was true in cases where there was no sign of the plates whatever and where the welds were remarkably free from oxide and the other usual defects. It appeared, therefore, that this brittleness did not depend on any variable that had been noticed so far, and it was

Jan 2, 1919

By S. W. Miller

MOST of the steel welding done at the present time is in material containing not over 0.3 per cent. carbon, and the tests here described were in similar material. These tests are not as yet completed but it is hoped that more results and more reasons for the conclusions may be presented at the meeting in February. From the time the author found the peculiar structure in electric welds referred to in a previous paper,1 that is, needles or plates in the grains and similar material, in larger spots, at the grain boundaries, he has felt that these plates which may be iron nitride and probably contain some carbon, were at least partly responsible for the brittleness of electric welds. He has found but few traces of similar lines in oxyacetylene welds until the last 2 mo., when he has found them in large numbers under certain conditions. In the top of these welds, they are quite numerous. In the body of heavy oxyacetylene welds, they appear at times, but not nearly to the extent that they do in electric welds; the author has never seen them in the body of welds in material less than ;3/4 in. (19 mm.) thick. They are shown in Fig. 82. The reason they were not noticed before is undoubtedly due to the fact that in making tests of welded pieces the weld was always ground off level with the plate, and as this structure only appears in the top ;1/16 in. (1.5 mm.) of the weld, they were removed by the grinding or machining; also, welds ¾ in. thick had not been examined. It did not appear, in making bending tests, that this structure had much influence on the strength of oxyacetylene welds; while electric welds are noticeably brittle. Further, oxyacetylene welds made with certain special materials were exceedingly brittle even after the tops of the welds were removed; this was true in cases where there was no sign -of the plates whatever and where the welds were remarkably free from oxide and the other usual defects. It appeared, therefore, that this brittleness did not depend on any variable that had been noticed so far, and it was

Jan 2, 1919

By C. H. Benedict

Largest and most important of the milling plants under construction during the year is the Morenci plant of the Phelps Dodge Corp., in Arizona, where plans are being rushed for production in 1942. Grate mills will be used for fine-grinding, and in the pilot plant, classifiers of the spiral type have the preference for the closed- circuit work. The flotation units will be chiefly of the pneumatic type, with some mechanical units as auxiliaries. The Fagergren, Pan American, and Agitair machines were left in the competition as the year closed. If the absence of European markets for finished products has dislocated the mining industry, fortunately the lack of raw materials required in the beneficiation of ores has not been serious. except possibly as to the inability to import flint grinding pebbles. Some of the less important gold mines still use pebbles for grinding as is also the practice in the comminution of nonmetallics used in various industries. T the Calumet & Hecla in the Lake A Superior copper district pebbles have been used exclusively in open- circuit grinding in the Hardinge mills treating the

Jan 1, 1941

By E. J. Wasp, N. T. Cowper, R. A. Davis, W. F. McDermott

On October 26, 1967, the world's first long distance iron ore slurry line was put into service by Savage River Mines. The commissioning of this $5 million installation climaxed three years of development, testing, and construction. The mine and concentrator are located approximately 30 miles from the town of Waratah in a rugged semi-mountainous terrain. The open pit mine will produce approximately 5 million long tons a year of crude ore, which is ground in autogenous mills, separated magnetically, thickened and prepared for the pipeline. The 53-mile pipeline transports the 2,250,000 tons of concentrate north to Port Latta. The Port Latta facilities include the receiving, storage and thickening equipment for the slurry as well as filtering, balling and pelletizing equipment to produce the 2,250,000 tons of high grade iron ore pellets. Five vertical shaft furnaces are used for pelletizing.

Jan 1, 1969

By AIME

WE got our chance to talk with Arthur J. Blair at the Annual Meeting at the Pennsylvania Hotel. By two o'clock Wednesday afternoon things had quieted down enough so we had our interview in the foyer to the Ball Room. There were the usual questions. Where were you born? In La Salle County, Ill., on March 26, 1885. Where did you go to school? Northwestern University, B.S. degree in 1906. Where did you start work? For E. J. Longyear right after leaving school. One's ability as a geologist was measured by one's ability to wield a brush hook and ax. He stayed on the job as geologist for three years and then got to thinking about the advantages of a warmer climate. The advantages stacked up favorably, so off he went to Birmingham, Ala., just about the time U.S. Steel took over the Tennessee Coal, Iron and Railroad Co.

Jan 1, 1948

By AIME AIME

FOR the use of workmen and employees, the company should establish a dispensary and a -hospital where workmen who suffer accidents or professional diseases may be taken care of; and at suitable places in the mine or metallurgical plant it should install first-aid stations. Workmen have a right to receive 75 per cent of their wages while they are unable to perform their work as result of a professional disease; but some companies pay full wages and in the case of natural disease, with the exception of venereal, alcoholism, injuries from fights, and chronic illnesses, 50 per cent of their wages up to a period of two months. The number of diseases the Law considers as professional is large and increases almost daily. Among the professional diseases, the one which has caused greatest harm to the miners and expense to the companies is silicosis. To avoid its propagation, companies should take every possible precaution that the working atmosphere is free from dust, abating this by frequent sprinkling of the workings using, wet drills and furnishing the workmen adequate protective apparatus such as respirators.

Jan 1, 1937

By Leon Borgman, Michael P. Lipkewich

Orebodies at or near the surface are generally amenable to open pit mining. The development of a mining program involves designing an ultimate pit and a production schedule. This pit maximizes total profit while the production schedule maximize6 the present value of the property. Optimum pit limits can be approximated by two-and three-dimensional numerical techniques. These techniques presuppose that the mineralized area has been sufficiently sampled to allow a reasonably accurate prediction of grade at any spatial location.

Jan 1, 1969