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By A. S. Odeh

This paper analyzes the effect of limited entry to flow at the wellbore on the steady-state productivity of a well. Wells that have been opened to flow along a fraction of their productive interval are termed wells with limited entry. Previous work treated the cases of a partially penetrating well, a well producing from the central portion of the productive interval and a well in which several intervals equally spaced were open to flow. In this paper the open interval can be located anywhere within the productive interval. Thus, in a sense, it generalizes previous work. The finite cosine transform was used to arrive at a solution for steady-state flow of a slightly compressible fluid. The solution was programmed for a CDC 1604 computer. Numerical vaIues for rd = 660 ft, r, = 1/4 ft, and range of sand thickness of 20 to 200 ft are presented in graphical form. The effect of rd and r, values on the result is shown in a table. The correct calculation of skin and damage ratio in the presence of limited entry to flow is explained and illustrated by examples. Moreover, the paper shows how to calculate the net decrease in productivity due to the combined effect of limited entry and perforations. INTRODUCTION In some wells only a fraction of the productive interval is open to flow. Location of this fraction is usually dictated by formation characteristics and reservoir behavior. For instance, if a gas cap exists, the open interval is located away from the gas-oil contact to prevent any possible gas coning. Wells that intentionally have been opened to flow along a fraction of their productive formation are tened wells with limited entry. Obviously, unintentional completions of this type also exist. Limited entry to flow decreases well productivity. Magnitude of the loss depends on the fraction of the formation open to flow, on the thickness of the sand, on the location of the open interval and on the ratio of rd /r, where r , is well radius and rd is the drainage radius of the well. The use of pressure buildup data on producing wells to calculate the condition of the formation around the wellbore is an accepted practice. van Everdingenl and Hurst2 introduced the concept of she skin factor s considered to be due to a thin layer of different permeability immediately around the wellbore. These authors dealt with the case of a well of complete radial geometry, i.e., a well with open-hole completion that completely penetrates the formation. The presence of a low-permeability skin results in a loss of productivity, as does limited entry. Therefore, if pressure buildup data obtained on a well with limited entry are used to establish the presence or absence of skin (i.e., formation damage), and a correction is not made for this loss of productivity, the calculations would result in an erroneous skin value. They might indicate the presence of formation damage when in reality there is none, or they might indicate a value larger than the true value. This could lead to an incorrect basis for planning remedial measures. Muskat3 studied the problem of partially penetrating wells for the case of incompressible flow. He presented equations and figures which allow estimation of loss in productivity. Brons and Marting,4 using equations based on Nisle's work,5 studied the loss of productivity for three cases. The first was for a partially penetrating well; the second was for a well producing from only the central portion of a productive interval; and the third was for a well in which several intervals equally spaced were open to flow. Their work was for steady-state depletion-type reservoirs wherein the well radius of drainage is established and the fluid is considered to be slightly compressible. Considered in this paper is the problem of wells with limited entry in which the open intervals are located anywhere within the productive sand. The finite cosine transform is used to arrive at a

Jan 1, 1969

[Year of Election to Honorary Membership 1876. PROF. RICHARD AKERMAN Stockholm, Sweden. 1913. DR. FRANK DAWSON ADAMS Montreal, Canada. 1920. HENRY STURGIS DRINKER Bethlehem, Pa. 1888. PROF. HATON DE LA GOUPILLIERE Paris, France. 1906. SIR ROBERT A. HADFIELD London, England. 1917. HERBERT HOOVER Stanford University, Cal. 1919. ROBERT W. HUNT Chicago, 111. 1915. JAMES FURMAN KEMP New York, N. Y. 1905. PROF. HENRI Louis LE CHATELIER Paris, France. 1913. EZEQUIEL ORDOENEZ Mexico City, Mexico. 1909. ALEXANDRE POURCEL Paris, France. 1911. ROBERT H. RICHARDS Boston, Mass. 1906. JOHN E. STEAD Middlesbrough, England. 1902. PROF. DIMITRY CONSTANTIN TSCHERNOFF Petrograd, Russia. 1907. CHARLES D. WALCOTT Washington, D. C.] [ ]

Jan 1, 1925

New York Meets first Wednesday after first Tuesday of each month. DAVID H. BROWNE, Chairman, JOHN H. JANEWAY, Vice-Chairman. F. E. PIERCE. Secretary, 35 Nassau St., New York, N. Y. P. A. MOSMAN, Treasurer. LEWIS W. FRANCIS. Boston Meets first Monday of each winter month. HENRY L. SMYTH, Chairman. ALFRED C. LANE, Vice-Chairman. HENRY A. WENTWORTH, Secretary-Treasurer, 60 India St., Boston, Mass. ROBERT H. RICHARDS, ALBERT SAUVEUR. Columbia Holds four sessions during year. Annual meeting in September or October. FRANK A. ROSS, Chairman. RUSH J. WHITE, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. FREDERIC KEFFER, FRANCIS A. THOMSON.

Jan 8, 1915

By A. U. Seybol

Eight binary iron alloys were examined after ion nitriding experiments to determine the behavior of the following elements: Al, Mo, Mn, Si, Ti, V,Cr, and C. Only Al, Cr, Ti, and V additions caused hardening in binary iron alloys. A few steels were examined to see the effect of Cr, Cr + Al, Cr + Ti, and Cr + V. It is suggested that a useful new class of ni-triding grade steels might be those containing about I pct V. The nitriding of steel, first described by Fry1 about 45 years ago, rapidly attained commercial application with very little knowledge of the fundamentals involved. While Fry,' in describing the status of nitriding in 1932, apparently correctly postulated hardening by precipitated nitrides, the details of the nitriding process were not understood, nor has the situation changed much since that time. It is also interesting to note that the compositions of some typical nitriding steels given by Fry at that time have changed little in the intervening years. Currently used nitriding steels owe their surface hardening to either chromium (as in 4340 steel) or aluminum plus chromium as in the Nitralloy grades, where both CrN and AlN appear to contribute to harden ing. Titanium additions have been studied experimentally, but thus far titanium steels have not won wide commercial acceptance. This subject will be expanded later. The orthodox ammonia nitriding process has been reviewed very adequately many times as in Jenkins3 and Case and VanHorn,4 and their is no need to outline the process here. Ion nitriding is not as well-known, although there have been several descriptions5-9 of the process given, sometimes with comparisons with the ammonia process. Most of these papers are primarily concerned with a description of the equipment, or of the physics or electrical engineering aspects of ion nitriding, but Noren and Kindbom9 gave the results of a metallurgical investigation using both processes. In brief, ion nitriding is carried out in a vacuum chamber from which the air is exhausted and replaced by a N2-H2 mixture, typically containing 10 to 20 pct N2, at about 5 to 10 torr pressure. While ammonia gas has also been used in ion nitriding, there is no evidence that ammonia makes any improvement in the ion nitriding process. A few hundred volts dc is applied between the grounded container wall (positive) and an insulated center post supporting the work (negative) to be nitrided. A glow discharge is created in the ionized gas, accelerating positive nitrogen ions to the work. These ions contain enough energy to form the normally unstable Fe4N "white layer", thus establish- ing surface nitrogen solubility characteristic of the a Fe/Fe4N equilibrium. This creates a substantial concentration gradient, driving dissolved nitrogen into the steel. The temperature employed is in the same range (around 500" to 550°C) as in ammonia nitriding, but because of factors which are not understood at present the nitriding time is ordinarily considerably reduced in ion nitriding. Other advantages have been cited,9 but it is not the purpose of the present work to contrast the two processes. The present objective was to examine the behavior of binary iron alloys during ion nitriding with respect to the microstructure, hardness level, and depth, and to examine some of these factors in steels as well. In this way it was hoped to be able to find out something about the individual role of these elements in steels. While all the work was done by ion nitriding, there seems to be no reason why any conclusions reached would not equally apply to ammonia nitriding, excepting only the kinetic aspects of the process. Another objective was an exploration of the critical-ity of the ion nitriding variables: gas composition, pressure, temperature, and time. EQUIPMENT AND MATERIALS The equipment used was substantially as described by Jones and Martin.8 The vacuum tank was about 12 in. in diam by about 18 in. high, and consisted of water-cooled stainless steel, with a single small window at the top for viewing inside. This sat on a heavy mild steel base equipped with the main pumping port, pressure control port, and vacuum gaging. A series of variable resistances was interposed between the glow discharge and a large-capacity -40 amp variable primary transformer feeding a 1000-v transformer, but 600 v were about the maximum ordinarily used. With the small l-in.-round, 4-in.-thick discs used for nitriding, the electrical load was usually about 500 v at 0.8 amp. The specimen temperature was controlled by a stainless-steel sheathed chromel-alumel couple, whose junction was in the steel stool upon which the flat discs were placed. These were ground through 400 Sic paper. Cycling of the temperature controller caused -0.2 amp variation in ion current, providing an ample control band. The binary iron alloys were made from vacuum-melted hydrogen-deoxidized electrolytic iron and alloys of 99.9 pct purity. Cast ll-lb-square tapered ingots were forged and hot-rolled to about 11/4-in.-diam rounds. Discs of 1/4 in. thickness by about 1 in. diam were machined from the rods for nitriding specimens. The following alloys were prepared: 1 pct each of Mn, Mo, Cr, Ti, Al, V, Si, and an Fe-0.8 pct C alloy. EXPERIMENTAL VARIABLES Of the variables total gas pressure, nitrogen partial pressure, temperature, and time, only nitrogen partial pressure was found to be critical to the operation. A critical nitrogen partial pressure was found corre-

Jan 1, 1970

By Charles Fettke

The deposits described occur in a belt starting 1 ½ miles east of Juncos and extending 6 miles in a southeasterly direction. They are of the contact metamorphic type, being associated with a limestone and calcareous tuff that is interbedded with andesite tuffs and andesites which have been invaded by a quartz diorite intrusion. Of the fire occurrences examined, the largest can be traced for a horizontal distance of 2000 ft. No mining has, been done, but some of the outcrops lead to the belief that deposits of commercial size are present. IN CONNECTION with the gathering of data for a report on the geology of the Humacao district of southeastern Porto Rico during the summer of 1916, under the auspices of the Scientific Survey of Porto Rico and the Virgin Islands, conducted by the New York Academy of Sciences, the writer had an opportunity to make a brief examination of the magnetite deposits of the eastern portion of the island. Inasmuch as these deposits have attracted some attention as possible future sources of iron ore, and as there is only scanty reference made to them in literature,1 a short description based on this reconnaissance survey was deemed to be worthy of record. The magnetite deposits of eastern Porto Rico occur in association with a belt of limestone, trending approximately S 53° E, which begins 1 ½ miles east of Juncos and can be traced for about 6 miles toward the coast. Four outcrops of magnetite were observed, which are designated

Jan 2, 1924

By W. L. Honnold

(San Francisco Meeting, September, 1915) OWING to a unique labor situation and other unusual circumstances, the mining methods of the Rand are hardly comparable with practice elsewhere. They are' of considerable interest, however, and their impor-tance is increased by the magnitude of the industry with which they are identified, gold of $166,186,000 value, say 40 per cent. of the world's production, having been recovered from 25,701,954 tons of ore milled in 1914. In the sketchy remarks to follow, attention will first be drawn to some influential factors of general bearing, after which certain features at two mines of the writer's group will be referred to. It is hoped that engineers associated with similar or different conditions and practice will contribute to broaden the discussion. Before proceeding, recognition is due the generous assistance of C. E. Knecht and F. A. Unger. GENERAL OBSERVATIONS The principal mines are situated along the northern limit of an irregularly shaped geological basin, and extend in almost unbroken continuity over a distance of about 60 miles. As the boundaries are defined by vertical planes there are both "outcrop" and "deep-level" properties, all differing in size and in technical features. So much has been written in regard to the geology of the Rand that only a few pertinent features need here be recalled. Briefly, the ore deposits are profitably enriched portions of certain conglomerate beds or "reefs," rarely more than three, which are interposed between quartzite, or quartzite and slate, and lie so closely together that where more than one are mined they are dealt with as a work-ing unit, although they may lie stoped separately. Their collective extension is locally referred to as "the Reef."

Jan 8, 1915

PROF RICHARD ÅKERMAN Stockholm, Sweden DR. FRANK DAWSON ADAMS Montreal, Canada PROF RICHARD BECK Friberg, Germany ANDREW CARNEGIR New York, N.Y. DR. JAMES DOUGLAS New York, N.Y. PROF HATON DE LA GOUPILLIERE Paris, France SIR ROBERT A. HADFEILD London, England PROF HANS HOFFER Leoben, Austria PROF HENRI LOUIS LE CHATELIER Paris France EZEQUIEL ORDONEZ Mexico City, Mexico ALEXANDRE POURCEL Paris, France DR. ROSSITTER W. RAYMOND New York, N.Y. DR. ING H. C. EMIL SCHROEDTER Dusseldorf, Germany JOHN E. STEAD Middlesborugh, England JAMES M. SWANK (Associate) Philadelphia, Pa. PROF DIMITRY CONSTANTIN TSCHERNOFF St Petersburg, Russia PROF TSUNASHIRO WADA Tokyo, Japan CHARLES D WALCOT Washingtion D.C.

Jan 1, 1917

PROF RICHARD ÅKERMAN Stockholm, Sweden PROF RICHARD BECK Friberg, Germany ANDREW CARNEGIR New York, N.Y. DR. JAMES DOUGLAS New York, N.Y. PROF HATON DE LA GOUPILLIERE Paris, France SIR ROBERT A. HADFEILD London, England PROF HANS HOFFER Leoben, Austria PROF HENRI LOUIS LE CHATELIER Paris France M FLORIS OSMOND Paris, France ALEXANDRE POURCEL Paris, France DR. ROSSITER W. RAYMOND New York, N.Y. PROF ROBERT W. RICHARDS Boston Mass. DR. ING H. C. EMIL SCHROEDTER Dusseldorf, Germany JOHN E. STEAD Middlesborugh, England JAMES M. SWANK (Associate) Philadelphia, Pa. PROF DIMITRY CONSTANTIN TSCHERNOFF St Petersburg, Russia PROF TSUNASHIRO WADA Tokyo, Japan CHARLES D WALCOT Washingtion D.C.

Jan 1, 1917

By T. M. Howell

JET piercing is a licensed process developed by Linde Air Products Co. Experiments with this method lapsed during World War II, but in the decade that followed the process was expedited. Two types of drills mount the jet piercing equipment for blastholes. The turntable of one machine rotates the complete stem system as well as the blowpipe, which emits three individual flames at different levels. Depth penetrated is limited by length of the blowpipe mounted in the rotary mechanism. This machine has successfully drilled blast- holes in Minnesota taconite.

Jan 6, 1957

By P. M. Budge, William L. Fink, Kent R. Van Horn

The investigation of the phase relations of high-purity aluminum-base alloys is a part of the fundamental research program of the laboratories of the Aluminum Company of America. The results of a number of binary and ternary systems have previously been published in the Transactions of this society. The aluminum end of the binary aluminum-titanium system has been studied. This system has received relatively little attention. To the authors' knowledge, there are two previous papers on this subject. E. van Erckelensl determined the constitutional diagram reproduced in Fig. 1. According to this diagram, the liquidus represents the separation of TiA14, (Ti = 30.7 per cent.). He concluded that this is the composition of the compound, because in his work the eutectic horizontal terminated at 30.7 per cent. titanium and the metallographic examinalion of a sample of this composition revealed only one phase. According to the constitutional diagram developed by W. Manchot and A. Leber,² reproduced in Fig. 2 from data given in their article, the liquidus represents the separation of the compound TiA13 (Ti = 37.2 per cent. ). The composition of the compound was derived in a manner similar to that utilized by van Erckelens. Moreover, Manchot and Leber confirmed the composition of the compound by analysis of the constituent left as a residue after dissolving the alloys in weak sodium hydroxide solution. Although these are the only publications describing the constitution of the system, other investigators have studied the composition of the titanium compound. L. WÖhler3 says that there is a compound TiA13 which was later confirmed by W. Manchot and P. Richter4 and by

Jan 1, 1931

By William Fink

THE investigation of the phase relations of high-purity aluminum-base alloys is a part of the fundamental research program of the laboratories of the Aluminum Company of America. The results of a number of binary and ternary systems have previously been published in the transactions of this society. The aluminum end of the binary aluminum-titanium system has been studied. This system has received relatively little attention. To the authors' knowledge, there are two previous papers on this subject. E. van Erckelens1 determined the constitutional diagram reproduced in Fig. 1. .According, to this diagram, the liquids represents the separation of TiAl4 (Ti = 30.7 per cent.). He concluded that this is the composition of the compound, because in his work the eutectic horizontal terminated at 30.7 per cent. titanium and the metallographic examination of a sample of this composition revealed only one phase. According to the constitutional diagram developed by W. Manchot and A. Leber,2 reproduced in Fig. 2 from data given in their article, the liquidus represents the separation of the compound TiAl3 (Ti = 37.2 per cent. ). The composition of the compound was derived in a manner similar to that utilized by van Erckelens. Moreover, Manchot and Leber confirmed the composition of the compound by analysis of the constituent left as a residue after dissolving the alloys in weak sodium hydroxide solution. Although these are the only publications describing the constitution of the system, other investigators have studied the composition of the titanium compound. L. Wöhler3 says that there is a compound TiAl3 which was later confirmed by W. Manchot and P. Richter4 and by

Jan 1, 1931

By S. Weissmann, P. R. Swann, D. F. Wriedt

The sizes and density of precipitates in an intemally oxidized 0.19 wt pct Al-Ag single crystal have been determined by low-angle X-ray scattering and by transmission electron microscopy . The correlation in particle sizes measured by the two techniques is reasonably good. For an oxidizing temperature of 800°C the particles were found to INTERNAL oxidation of dilute alloys of aluminum in silver produces an oxide which has an excess of oxygen compared to Al2O3.' It is believed that the excess oxygen is an indication of the small sizes of the oxide particles. Depending upon the particular model chosen for the oxide structure, the size of the o-A1 particles can be calculated as a function of the oxygen-to-aluminum ratio. These calculations pre- have diameters in the range 30 to 140A, with a mean size of about 50.4 as observed by electron microscopy. At lower oxidizing temperatures, less than 600°C, no clearly resolved particles are formed, and it is suspected that if A1-0 clusters exist they must be exceedingly small, i.e., 10A or less in diameter. dicto that the particles would vary in size from 15 to 100A. This range of sizes is amenable to detection by both small-angle X-ray scattering and transmission electron microscopy. This paper compares the cluster sizes in such internally oxidized A1-Ag alloys determined by transmission electron microscopy and small-angle X-ray scattering. SPECIMEN PREPARATION Single crystals were prepared from 99.9999 pct Ag, obtained from Cominco Products, and 99.99 pct Al, obtained from Aluminum Co. of America. All melting operations were carried out in graphite molds under flowing purified hydrogen in a horizontal zone refiner. The silver was first degassed,

Jan 1, 1964

By THOMAS J. CLIFFORD

IN 1926, finer grinding began to be a feature of the milling practice of the Southeast Missouri lead district. Nothing since the adoption of flotation has caused greater changes and greater improvement in results. The trend toward finer grinding, with the consequent discarding of tailing at finer sizes, and consequent lower assays in lead, continued to progress until 1931, when the abnormally low price of lead brought a halt: that is, the better metallurgical results obtained would not offset the increased costs due to higher power and necessary maintenance. Since 1931 a slight tendency toward the discard of coarser tailing has taken place. , In 1926, larger rod mills i.12 ft. 1 in. by 6 ft. 6 in.) than any previously used in the district were installed in cue plant, and a new primary crushing plant, of greater capacity was built. This combination demonstrated immediately the better metallurgical results obtainable by finer grinding and all the mills now running have adopted the practice.

Jan 1, 1934

By W. M. Tuddenham, R. J. P. Lyon

In many areas surrounding the orebodies in mining districts rocks have been bleached and altered by the ore-forming solutions and have been oxidized during later weathering processes. A number of the rock-forming silic-ates have been broken down to clay, sericitic micas and chlorites have been developed, and pyrite may be found hundreds of feet outside the economic limits of the orebody. These halos of altered ground are prime targets used by geologists in many districts to delineate promising sites for drilling. Both in the field and in the laboratory it is often difficult to map these mineralogical changes in the halos in detail without numerous petrologic examinations. The secondary minerals are generally fine-grained, and since conversion of one mineral to another is often progressive, many alteration processes have not proceeded to completion (feldspars to clay to sericite mica). Qualitative detection of these minerals is difficult; quantitative determination is frequently impossible.

Jan 1, 1960

By A. L. Titchener, M. B. Bever

The stored energy of cold work was investigated in drawn gold-silver wires by tin-solution calorimetry as a function of strain, strain rate, initial grain size, and temperature of defornation. The energy expended in the deformation process was measured. Hardness was also measured and was correlated with the stored energy as a function of strain and strain rate. Mechanisms of energy storage are discussed. THE variables which determine the amount of energy stored in a metal during cold work are of two kinds: those involving the metal and its condition and those involving the process of deformation. For example, the stored energy differs between one metal and another and between different degrees of purity of a single metal. It also depends on the nature of the deformation process and particularly the extent, rate, and temperature of deformation. Most investigators have reported the stored energy as a function of strain (or some similar geometric parameter) or of the energy expended during deformation. In general the stored energy increases with strain, rapidly at first, but more slowly at large strains until a saturation level is reached. Information about the effects of other variables, however, is limited. Some data are available on the dependence of the stored energy on the purity of a metal1 and on the composition of

Jan 1, 1960

By T. L. Joseph

THE United States Bureau of Mines has been studying the blast-furnace process for, about ten years. An experimental furnace was developed by the bureau in cooperation with the Minnesota School of Mines Experiment Station, University of Minnesota. Many data have been obtained and published.1 Royster, Joseph and Kinney§(48) found that the particle size of ore had an important effect upon the blast-furnace, process. Kinney(28) stated: Economy in blast-furnace practice depends largely upon efficient gas-solid contact in the shaft of the furnace. If efficient work is not done in the shaft, the hearth and bosh will not function properly. A condition may be readily imagined where the particles of ore in the shaft are so large that the time entailed in the descent of these materials into the bosh is not sufficient to permit proper reduction and preparation prior to the time the ore enters the bosh of the furnace. Another condition may be pictured where the density of the stock column and the flow of stock is such that the ore will take one course and the gas another. Both of these examples will result in insufficient contact between the gas and the ore. Unreduced ore will reach the hearth, and the gas which has not been efficiently oxidized will reach the stock line. The result is the use of an excess of carbon in the smelting process. It is obvious that fine ore particles occurring in the ore as charged, or . formed in the furnace due to heat and mechanical action, place a definite limitation upon the efficiency of the operation. There is also an economic loss of fine material as dust.

Jan 1, 1930

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman' developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,' and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,' as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman's work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

By T. T. Read

FOR the second time the Mineral Industry Education Division opened the sessions at the Annual Meeting by gathering at the Engineering Woman's Club, Sunday at 3 p. in., and, in spite of the informality of the hour, with a good attendance of representative men in the educational field. The chairman of the Division, Thomas T. Read, after briefly reviewing some of the more significant events of the past year, introduced H. P. Hammond, professor of civil engineering, Brooklyn Polytechnic Institute, a leading figure in the project of the Engineers' Council for Professional Development for accrediting engineering schools. Prof. Hammond made it clear that the project is not to rate engineering schools but to accredit them; not to arrange them in order of excellence, but to segregate them into two groups, those that are entitled to recognition as genuine engineering schools, and those that are not. About thirty schools in the whole country will presumably fall into the latter class; they are typified by an unnamed institution where the teacher of mathematics bears the title of Professor of Civil Engineering and the man who teaches chemistry that of Professor of Chemical Engineering, and having no engineering instruction except some elementary surveying, but still claiming in its catalogue to be an engineering college. While everyone would like to avoid the necessity of accrediting engineering colleges, it cannot be avoided, since the University of the State of New York, and several other agencies, are already doing it. If it cannot be avoided it is best that it should be done by a qualified agency set up by the national engineering societies, so that the results may command respect and general acceptance. It is for this reason, and this alone, that the accrediting committee of the E. C. P. D. has been set up. It is now ready to begin its task, and during-the coming year it will accredit the schools in two of the seven geographical districts into which the country has been divided, beginning with New England and the Mid-Atlantic States.

Jan 1, 1935

By H. Evans, L. A. Hunt

In the pellet-producing industry it is sometimes claimed that "The pellets are made in the concentrator," or that "The key to good pellets is in the balling operation." However, one claim is generally agreed on: If you can put in, on, and through the indurating furnace a good green ball of Proper size and adequate strength to withstand the handling, load, dehydration, and thermal shock until it is properly heat-hardened, you will have the pellet product you desire-that is, a "competent" green ball. The strength requirements that enable a competent green ball to withstand the environment of the indurating furnace are usually less restrictive than those for transporting the green ball from its source of production to the furnace. Experience has shown that different types of material may have different balling characteristics which may impose limitations on the quality of the green ball that can easily be produced under normal conditions. Therefore, if a specific material will produce a green ball that meets the physical requirements for competency in the furnace, but not for handling or transportation, various practices must be instituted to overcome this deficiency. In other words, if a normal handling system is too rigorous for the green balls that can be produced under standard conditions, then "handling with care" should be tried.

Jan 5, 1967

By Vincent P. Gi. ccnella

GOLD was discovered in Gold Canyon on May 15, 1849. Following this discovery placer miners worked the gravels in the canyon for-ten years, finally discovering the outcrop of the Comstock lode at Gold Hill in May, 1859, and in Ophir ravine on June 12 of the same year. Before long large quantities of gold and silver, were taken from the lode and one of the West's most spectacular mining booms drew thousands of fortune seekers to Nevada. After a long period of production activity waned and in late years little mining was done. The recent reopening of the old mines and the discovery of ore in other parts of the vein, and in other veins of the district, has led to a revival of interest in the Comstock. Virginia City, Gold Hill, and Silver City, situated along the great vein system, are enjoying a period of prosperity and a large influx of people.

Jan 1, 1934