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By R. E. Morgan, D. L. Douglass

The determination of phase relationships and solid-solubility limits can be performed by quantitative metallography in addition to the usual X-ray and metallographic techniques. For example, Beck and smith1 redetermined the ß/ß + ?, ß + ?/?, a/a + ß and a + ß/ß boundaries in the Cu-Zn system by measuring the volume fraction of second phase of several alloys and extrapolating the volume fraction-composition curves to 0 and 100 pct. A modification of this technique is suggested for certain alloy systems, in which it is not necessary to use several alloy compositions but merely one. A single two-phase alloy may be used to determine terminal solubilities in the following manner. The method consists of equilibrating samples of the alloy in a two-phase region adjacent to the desired solid solution, at three or more temperatures, quenching, measuring the volume fraction of second phase present, and applying an analytical treatment to calculate the unknown solid solution. However, two restrictions are inherent in this technique. They are: 1) only certain types of alloy systems are amenable to it, and 2) the general features of the system must be known. The first drawback to the new technique, i.e., that only certain types of systems may be studied, necessitates that the composition at one end of the tieline must either be constant with temperature or well established as a function of temperature. Either a pure metal or some intermetallic compounds fulfill the former. If it is assumed that the volume per gram-atom of a dilute solution is unchanged by the addition of element B to element A, the composition of the solid solution in equilibrium with the second phase may be determined by a material balance and is given by where X, = volume fraction of B in a solid solution Xc = volume fraction of B in compound c X = volume fraction of B in alloy f = volume fraction of second phase The composition by weight may then be determined by the use of tables in the Metals Handbook2 when the density ratio of the solid solution constituents is known. A possible alternative treatment involving the use of the lever rule is less precise than the above tech- nique. This may be used when the density of the solid solution is either known or may be calculated from X-ray data for several compositions. The following analysis is then made. The ratio of compound to solid solution (by weight) may be expressed as follows: x0 - x wc = xr-x = x0 - x r2i Xc -X where Wc = weight of compound w = weight of solid solution x, - alloy composition, weight percent x = unknown composition Xe = compound composition but where V, = volume of compound VA = volume of solid solution pc = density of compound p, = density of solid solution fc = volume fraction of compound fB = volume fraction of solid solution and fs = l -fc then If pc and xc are known, and f, is measured, then pB is the only unknown on the right side of Eq. [4]. The known densities of the solid solution can be plotted for various compositions and can then be expressed mathematically as a function of composition. The use of an expression of pB = f(x)reduces the equation to one unknown—the desired solubility. In the event that the densities are unknown, they may be calculated for various compositions from Vegard&apos;s law. The calculated values are then plotted and expressed analytically. The most accurate results are obtained for Eq. [4] when fc<< 1, i.c., when (x, -x,) - 0, &/l-f, - m; but as fc/l -fc - 0, (xl-x,)- (x, - x), and x - x,,. However, the accuracy with which fc can be measured decreases as f, decreases.3 Alloys for investigation must be selected by a compromise, which is based upon an error analysis of Eq. [4] and knowledge of the accuracy of volume fraction measurements. An examination of phase diagrams in the literature showed many which were amenable to the technique described here. The zirconium-copper system was selected in order to determine the solubility of copper in beta zirconium. Pieces of an alloy which was arc-melted three times were wrapped in tantalum foil and sealed under an argon atmosphere in Vycor tubes. The sealed samples were equilibrated at temperatures from 850" to 960°C for 3 weeks and quenched to room temperature by smashing the capsule in water. Several planes of polish were examined, and

Jan 1, 1960

By F. C. Noyes

DAME Nature was in a generous mood when she distributed widely over the face of the globe numerous deposits of phosphate rock from which man can make phosphatic festiIizer to replace the phosphate re- moved from the soil by crops. The principal deposits are readily accessible to the world&apos;s greatest consuming areas and most of them are such that mining operations can be carried on at relatively low cost. The world&apos;s known reserves shown in Table 1 are sufficient to last well over 2000 gears at the present rate of consumption. Before giving a brief outline of the phosphate rock industry of foreign countries let us try to get a picture of the movement of phosphate rock throughout the world in 1938, the last full normal calendar year where it came from and where it was consumed. Table 2 shows the origin and finial destination of world shipments in 1938 by grand divisions. Table 3 (p. 499) shows shipment9 of phosphte rock to each country in Europe. Europe is seen to be by far the world&apos;s greatest market and the French North African mines the world&apos;s most important producers outside of the U. S. A.

Jan 1, 1944

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

By L. A. Creglow

IN common with many other companies engaged in the mining and processing of ores, research has always been an important activity of the United States Smelting Refining and Mining Company. Much of this research has been carried on at the various plants of the Company by the operating staffs, and over the years has been an essential factor in developing new methods and improving existing methods of operation. In 1917 arrangements were made with the Massachusetts Institute of Technology under which the Company had the exclusive use of one or two small laboratories in the then newly constructed MIT buildings and the use of the metallurgical laboratories, subject of course to the Institute&apos;s needs. After about two years this work was temporarily discontinued but was resumed in 1920 under the direction of G. H. Clevenger, consulting metallurgist for the Company, who recently retired. Becoming cramped for space, the laboratory was moved to a location near MIT on Amherst Street, Cambridge, in 1924. Establishment of a general research laboratory in metropolitan Boston naturally followed from the fact that the head office of the Company was located there and that the library facilities available for all types of research were, and are, unsurpassed. The disadvantages in carrying on research at great distances from the operating units of the Company were always apparent, but with widely scattered plants this disadvantage could not he overcome. With

Jan 1, 1948

By L. B. Davidson

The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made.1 -5 Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigations are dissimilar. Edmondsonl found that in Berea sandstone a temperature-dependent effect was present, while Shilobod,2 using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A&M U.3-5 found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75OF to 540°F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study. It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system. Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75OF to 500°F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effect6 to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated7). Evidence for a similar source of temperature dependence in superheated steam-white oil experiments

Jan 1, 1970

By E. H. Rose

IN the realm of ore dressing the most pregnant feat of all time was announced in 1945: the winning of the mineral raw materials which made the harnessing of atomic energy possible. Lost in the stupendous implications of the end result, in the two billion dollar hugeness of the project, and in the famous names attached thereto, the fact that crude uranium ores had to be concentrated received relatively little notice in the press. Only the final link in the concentrating chain was publicized-ether extraction of uranyl nitrate, developed by Hoffman and carried on by the Mallinckrodt Chemical Works, or methods developed by the Ames group under Spedding. Some of the earlier links represented less glamorous but equally difficult and exacting research. One may only speak a word of admiration for those who worked hard, accomplished much, and said nothing. The universal lament for most of the year was "man shortage." A group of Canadian engineers expressed it as "being so short of labor that no labor was available to develop laborsaving devices." . Despite this, an outstanding amount of mineral-dressing progress was made in 1945. Necessity allowed no alternative. The insatiable demand of war for minerals forced the exploitation of lower and lower grade ores, and of others not before considered of commercial character or use, requiring the mineral dresser to fight for and win new bridgeheads on the home front.

Jan 1, 1946

By D. K. Deardorff, Haruo Kato

D. K. Deardorff and Haruo Kato (U. S. Bureau of Mines)—We wish to refute the 1875" 20°C value that Giessen, et al., report as the transformation temperature of hafnium. Although these authors state that their work along this line will be reported later, we can&apos;t leave their value undiscussed, for we believe it to be 125°C too high. Our value of 1750° 20°C, which the authors mention, has been substantiated in our laboratories by the use of three other methods. The first method of substantiation was by heating and cooling curves using a hafnium/tungsten thermocouple, the couple having first been calibrated against a t/Pt-10 pct Rh couple. The second method was by quenching and metallography of dilute Hf-Ta alloys. The third cussion, it may be pointed out that the observations of Rogers referred to large unidirectional strains where the internal cracks or voids appeared only after a strain of 32 pct or more. On the contrary the internal fissures observed, as a result of fatigue cycling, occurred for a total extension of some 5 pct and furthermore followed the directions of the slip zones. Finally, it is not our contention, as implied in Dr. Alden&apos;s last paragraph, that the tensile stress is an important factor in crack propagation. Indeed, in connection with the reference to the companion report, special note is made of the fact that "Deformation was apparently concentrated in grains which have a slip plane nearly perpendicular to the specimen axis and thus near the plane of maximum applied shear." This dependence of the growth of fissures on the orientation of the slip planes with respect to the direction of maximum applied shear is clearly shown in work on the torsional cycling of single crystals which has been submitted for publication. method was by heating and cooling curves with W/W-26 pct Re thermocouple. Counting the original resistometric method, four different methods have yielded 1750" 20°C as the transformation temperature of hafnium. All our work on determination of the hafnium transformation temperature has shown that the specimen under test must be quickly heated to and through the transformation temperature if the lowest possible transformation value is to be determined; otherwise a higher value not representative of pure hafnium will result. Speed was emphasized in all methods. In our resistometric work the corresponding voltage, amperage, and temperature readings were taken quickly and the transformation temperature was usually reached within 5 min total heating time. In the thermal analysis work involving Hf/W or W/W-26 pct Re thermocouples the transformation temperature was attained within three minutes total heating time, this time being less because the two variables were

Jan 1, 1963

Organization Place Date 1919 American Electrochemical Society New York, N. Y. Apr. 3-5 American Chemical Society Buffalo, N. Y. Apr. 8-11 National Foreign Trade Council : Chicago, Ill. Apr. 24-26 American Iron and Steel Institute New York, N. Y: May American Institute of Electrical Engineers Lake Placid, N. Y. June 23-27 American Society for Testing Materials..: Atlantic City, N. J. June 24-27 American Railway Bridge and Building Association Cleveland, O. Oct. 21-23

Jan 4, 1919

Discussions of the paper of Mr. Gayley read by title at the Lake Superior hieeting, but first presented at the New York meeting of the Iron and Steel Institute, October, 1904 (see p. 746). With the exception of Mr. Pourcel&apos;s discussion (p. 1038), these papers are here published under a mutual agreement between the Councils of the two Institutes, and will also be found, with others, in the Journal of the Iron and Steel In-slitute for the pear 1904, Mr. E. Windsor Richards, Past-President,&apos; said that in 1799 Mr. Dawson, of Low Moor, read a paper before a scientific society in York pointing out the great diff&apos;erence in the moisture of the air going into the blast-furnace in the hot months of the year and in the winter months. A cold blast-furnace was a very sensitive instrument, and showed this very clearly, for in June, July and August the furnace did not drive so well; it did not make the quality of iron and required more fuel; so that Mr. Gayley was on the right road to effect an enormous improvement in this direction. He considered that Mr. Gayley was on the way to great success, and hoped that the apparatus would not be a very expensive one. He supposed it mas too early for Mr. Gayley to let them know what the saviug was

Jan 1, 1905

By W. H. Bassett, C. H. Davis

In the commercial annealing of cartridge brass there are four points regarding which definite data are essential. They have to do with the correct interpretation of grain count in its relation to annealing temperature and, incidentally, to Brinell hardness. These points are: 1. The comparison of the grain sizes of two cartridge-brass mixtures: 69 copper, 31 zinc, 0.376-in. (9.5-mm.) gage; and 68 copper, 32 zinc, 0.130-in. (3.3-mm.) gage 2. The comparison of the grain sizes of annealed metal that had previously been reduced by rolling varying amounts; for instance, 20.0, 36.6, 50.9, and 59.1 per cent. 3. The determination of standards for grain sizes on annealed brass of the composition 68 per cent. copper, 32 per cent. zinc and 69 copper, 31 zinc. 4. The comparison of grain size with Brinell hardness on identical samples of annealed metal. In their comprehensive and thorough investigation of the recrystal-lization of cold-worked alpha brass on annealing,l Mathewson and Phillips have discussed the relations between temperature of anneal, degree of deformation, and structural alteration in alpha brass. They have also shown certain comparisons between the ordinary physical properties and the grain size of annealed brass. The purpose of the present investigation is mainly concerned with the grain size of cartridge brass, its relation to Brinell hardness, and the publication of sufficient data to enable those engaged in the inspection of such material to have a correct foundation upon which to work. The first alloy was taken from regular mill stock that had been rolled from 0.580 in. to 0.376 in. (14.7 mm. to 9.5 mm.) gage, a reduction of 35.1 per cent. This bar (No. 1) had the following composition: Copper, 69.20 per cent.; zinc, 30.76 per cent.; lead, 0.02 per cent.; iron, 0.02 per cent. The second alloy was also taken from mill stock of 0.325 in. (8.25 mm.) gage and was rolled as shown in Table 1, in order to get four bars reduced two, four, six, and eight B. & 5. numbers respectively. This second alloy

Jan 1, 1919

By Albert J. Phillips

SEVERAL important changes have been&apos; made during 1933 in the compilation and distribution of technical literature to those interested in nonferrous physical metallurgy. The Institute of Metals, of Great Britain, announced that preprints of all its papers would be distributed monthly to all members in combination with their bulletin of abstracts. The A.I.M.E. has announced that it will distribute to all members of the Institute of Metals and Iron and Steel Divisions a monthly bulletin entitled Metals, which will carry preprints of all publications of interest to the members of these two divisions. The American Society for Steel Treating has declared its intention to change its name to the American Society for Metals in order to indicate the broader scope of its activities. The abstract service of Metals and Alloys has been improved and expanded, covering practically the entire field of metallurgical literature. These changes and innovations now provide unparalleled reference service entirely in the English language.

Jan 1, 1934

By I. R. Kramer, L. J. Demer

Aluminum single crystals were pulled in an electrolytic cell allowing surface removal during the deformation. The extent of Stages I and 11 of the stress-st-aitz curve was increased and the slope decreased as the rate of metal removed from the surface was increased. An increase of the strain rate caused a decrease in the effectiveness of the metal removal. The data indicate that the work-hardening coefficient in Stage I is determined primarily by the conditions which exist on the surface of the crystal. In Stages 11 and 111, both surface effects and internal barriers are important. ALTHOUGH numerous investigations have been conducted on the plastic flow characteristics of metals in an attempt to explain the mechanism of work-hardening, relatively few studies have taken into account the influence of the surface. In all current theories of work-hardening it is assumed that the impediments to the movement of dislocations are within the crystal. The barriers due to the surface and the existence of solid and liquid films have been neglected even though it has been demonstrated that the surface exerts a large effect. A number of investigators1-l8 have shown that solid films on the surface of single crystals markedly affect their mechanical behavior. In general, the presence of a solid film tends to increase the yield stress and increase the work-hardening rate. Often, on single crystals, Stage I and, at times, Stage II regions are completely suppressed. Various mechanisms have been offered for the effects of oxide and metal films as well as the influence of electrolytes. Of these, concepts concerned with the locking of surface dislocation sources and the blocking of dislocations at the surface resulting in pileups appear to be actively considered at present. Barrett,11 Takamura,6 Gilman,19 Lipsett and King,20 Shapiro and Read,10 and Weiner and Gensamer21 are among those who have interpreted their results in terms of piled-up dislocations at the surface, while Adams.22 and Chalmers and Davis23 have explained their experimental observations in terms of locking of surface dislocation sources. In general, the change in plastic flow properties due to electrolytes has been explained in terms of the unblocking or unlocking of dislocations by the removal of the oxide films. In considering the two proposed mechanisms, it appears that the locking of sources of surface dislocations by a solid film should exert a primary influence only on the critical resolved shear stress for flow and not on the slopes of Stages I and 11. However, the blocking at the surface of dislocations from internal sources may also affect the critical resolved stress and furthermore exert an influence throughout the whole plastic range. In certain cases it does not seem feasible to explain the results of experimental observations in terms of locking of surface dislocation sources. The abnormal aftereffects found by Barrettll,12 by removing the oxide by an acid treatment are excellent evidence of the blocking of dislocations at the surface. Additional evidence in favor of a blocking due to a pileup of dislocations at the surface may be found from the observations that the critical resolved shear strength continues to increase with the thickness of the oxide layer until very heavy oxide layers are formed. If the locking of surface dislocations sources were the dominant factor, the critical resolved shear stress would not be expected to increase after all of the surface sources were locked by the formation of the oxide. This may be expected to happen after a few atomic layers of the oxide are formed. In spite of the above evidence on the strong influence of the surface on the plastic flow characteristic, this has been ignored in current theories of work-hardening. Seeger24,25 suggested that most of the dislocations may slip out of the crystal only when the specimen axis is within certain areas of the orientation triangle. In other areas the resolved shear stress in other glide systems is large enough to generate dislocations which can form Lomer-Cottrell locks, thereby decreasing the average slip distance in some directions and causing a larger hardening rate. Friede126 assumed that at the beginning of Stage 11, a large number of Lomer-Cottrell dislocations are formed by a catastrophic process which used up all the Frank-Read sources on the secondary slip-planes. In this manner a fixed number of Lomer-Cottrell locks is formed which act as barriers against which the dislocations can pile up. In Stage 111, Seeger24 and Diehl, Mader, and Seeger25 proposed that Lomer-Cottrell barriers are circumvented by the cross slip of extended screw dislocations. Cottrell and Stokes,27 Friedel,26 Cottrell,26 and stroh29 suggest that the Lomer-Cottrell dislocations collapse under the stress field of the dislocation pileup. It is the purpose of this paper to report the changes in Stages I, II,and III of the deformation process in

Jan 1, 1962

By J. R. Lucas, R. L. Frantz

Mine sealing programs for the alleviation of acid mine drainage were begun by the Federal Government in the &apos;30&apos;s. As part of an acid mine research project to The Ohio State University, a field test was undertaken to determine the effectiveness of mine seals for reducing mine acid. Details of the tests made at the McDaniels mine show the feasibility of air-sealing and flooding an acid-producing drift coal mine. Work by the University continues. The Federal Government undertook in the early thirties an extensive mine sealing program for the alleviation of acid mine drainage. In the states of West Virginia, Ohio, and Pennsylvania many general summaries have been made on this program but no critical evaluation with supporting data has been found on the effectiveness of mine seals for reducing mine acid. Because of this it was decided to undertake a field testing program as part of an acid mine research project of the Engineering Experiment Station, The Ohio State University. The objective of this phase of the project was to develop and install a field research laboratory for acid mine drainage studies. Specifications for such a mine laboratory were developed and resulted from the following considerations: 1) Size and preservation—the test mine shou1d be of limited size to permit frequent and detailed examinations; it should be in a reasonably sound condition to permit safe entry. 2) Isolation—the mine should be physically separated from all other mines. 3) Openings—a minimum number would be desirable to reduce the sealing problem. 4) Structure—the mine especially near the openings should be structurally sound. 5) Acid production—the mine should be producing significant quantities of acid. After considerable searching, the McDaniels mine was selected in the Hocking coal field in Vinton County just above Lake Hope State Park in southeastern Ohio. The small drift mine in the middle Kittaning coal consisted of two small rooms with one mine opening about 6 ft above a seasonal stream bed. Before it was finally decided to seal the mine, a short study was made of the acid drainage over several months. Fig. 1 shows a plot of acidity (milligrams per liter), flow (gallons per minute), and acid production (pounds per day) vs time over the sampling period. Because the coal was overlain with a porous sandstone, the mine drainage was consistent the year around even though the mine was

Jan 1, 1961

By B. M. Burchfiel

CALIFORNIA possesses such an abundance of ceramic materials other than clays, that she is quite independent of other states and foreign countries so far as these materials are concerned. Certain users import some feldspar, silica, and allied minerals, but they do so from choice and not necessity. Production is largely for home consumption, so the total volume of ceramic materials produced is comparatively small. Many small deposits of the materials here under discussion are worked by individuals, and their output sold to individual grinding companies or users. The data given here shall be confined to the larger deposits and developments because they give a truer picture of typical deposits, operations, and materials.

Jan 1, 1936

Pulverized Fuel Combustion The apparatus shown in the illustration is a complete equipment f r supplying coal to boiler and metallurgical furnaces, cement and lime kilns, dryers, and to all furnaces requiring a temperature and quality of fame under prompt and easy control. It is claimed that the Aero Pulverizer makes practicable the highest efficiency obtainable from burning coal. It makes coal burn like a gas, a flame, the physical and chemical character of which is regulable- a flame that may be elongated or shortened, thus placing the zone of highest temperature where needed- a flame that may be made oxidizing, reducing, or neutral, as occasion may require. The coal is burned as pulverized, and there is no storage of the powder with its attendant hazard. Artificial drying before pulverizing is not necessary if the coal supply be sheltered from rain and snow. Where the Aero is used, it is wholly a furnace question whether a dryer should be installed; it is not at all a pulverizing or storage question. Labor is reduced to a minimum. Slack coal at low cost yields its last B.T.U.

Jan 11, 1915

By J. Armanet

THREE MINING colleges are maintained in France; the École Nationale Supérieure des Mines, of Paris; École Nationale Supérieure des Mines, of Saint Etienne; and the École Supérieure de la Metallurgie et des Mines at Nancy. Besides graduates of these schools, a few graduates of the École Centrale des Arts et MIanufactures and of the École Polytechnique are employed as ]nine managers or engineers; however, most of the latter have taken a graduate course at one of the mining schools.

Jan 1, 1939

The National Mine Health and Safety Academy near Beckley, W. Va., is dedicated to reducing accidents and improving health conditions in the mining industry through education and training. Though this basic mission remains unchanged, the Academy now serves a much broader mining community than it did when established in the late 1960s. From its original emphasis on training federal coal, metal, and nonmetal mine safety inspectors, the Academy has expanded its programs to reach mining industry and labor representatives, state agency employees, and university students taking mining-related courses. The Academy&apos;s resident programs, short courses, seminars, and continuing education courses cover a wide range of subjects and various experience levels, but all have been developed with one idea in mind - to reduce accidents and health hazards through education and training of the widest possible audience.

Jan 11, 1979

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

Jan 1, 1967

By Scott Tzcrner

WITHIN recent years people have begun to realize the importance and significance of the mining and allied industries. The leading part the engineer plays in civilization is becoming recognized. However accurate quantitative knowledge of the industrial importance of mining is still seldom possessed except by those close to this business. It is true that there are a few who go to the extreme and represent the whole progress of civilization as a reflection of man&apos;s gradual mastery of mineral utilization, but on the whole, the magnitude of the-industry is underestimated. In this paper I shall call attention briefly to the importance of mining in the United States, in Canada, and in the world. Ordinarily, the annual primary mineral production of the United States is about $5,500,000,000. The average for the last 5 years has been a little over that, but last year, sadly enough, it was less than 31/4 billion. Just now, we are on the decline, and have been for the last two years. In Canada, the 5-year average was about $268,000,000, and last year it was 227 million. Due in part to gold mines (in 1930, for the first time, Canada&apos;s gold production exceeded that of the United States), the Canadian average is holding up better than ours. Average world mineral production over the last -5 years has been estimated at about $12,000,000;000 whereas in 1931 it was less than than 8 billion.

Jan 1, 1932