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By L. F. Mashburn, T. J. Ferree

A Reichert cone concentrator was installed in an aggregate plant circuit to recover the extremely fine "flour gold" known to exist in the deposit. The gold content of the bank- run gravels averages about 0.1 g/t-about $1.29/t, based upon $12.86/g ($400 per oz) gold. The fineness of the gold averages between 950 and 960. The Reichert cone, in conjunction with a conventional shaking table, recovers in excess of 85% of the gold. A screen analysis of the gold particles shows 44.1 % is - 74pm (-200 mesh) in size. The plant operates with a two-man crew.

Jan 1, 1983

By J. E. Wilson, F. P. Lebar

TYPICAL of southwestern Wyoming are coal structures that dip from 4° to 17°. Those at the Reliance and Winton mines of the Union Pacific Coal Co. average 91/2 and 15°, respectively, and dip almost directly to the west. By using a hoist for main haulage, a method of mining has been developed whereby four places are driven on the pitch of the seam. Slightly upgrade from the strike at intervals of 300 ft. a two-entry system is driven to the north and to the south. In both fields, which are nongassy, an exhaust system of ventilation is used. Slope, manway, and lower or haulage entries are placed on the intake. Two air-courses and upper or breaking entries are placed on the return. A retreat system of mining is used exclusively. From the opening of its first coal mine, in the year 1868, until 1923, when the Joy loader was introduced into The Union Pacific Coal Company's operations, slopes, aircourses, and manways were driven by hand. Development work was conducted on the night shift or off shift, and the main hoist was used for haulage. The slope was driven down the pitch with crosscuts turned at intervals of 75 ft. and entries at 230 ft. Connections to the workings above were made by driving up the pitch 75 ft. Mule haulage was used to furnish cars to the hand loaders driving planes up the pitch. A sheave was placed at the upper end of the plane with a I¼-in. hemp rope dou- bling around it and having me end attached to the car and the other to the mule. The mulc, pulling downhill, raised to the working face a small wooden car of one-ton capacity. With the introduction of mechanical loading, mule haulage and small wooden cars disappeared and auxiliary hoists, electric locomotives, and steel cars with a capacity of 4 tons were substituted. Development work was done during two or three shifts of the 24-hr. period. Driving of haulage slopes down the pitch by hand continued. Crosscut intervals were changed to Ioo ft. and the crosscuts were driven with shaking conveyors. With the use of a 90° swivel, aircourses and manways were driven up the pitch. Entry intervals were changed from 230 ft. to 300 feet. Mobile loaders of the Joy type were first employed by this company in the year 1923 at Hanna, Wyo. In 1928, two 4-BU Joy loaders were transferred from Hanna to Winton No. I mine, where they were used in driving slopes and entries. At the time of transfer, the machines were about worn out and were not suited to the steep pitch, therefore frequent breakdowns occurred. However, experience justified the belief that the mobile loader was fitted for driving slopes in this field. During 1937 a unit was installed in Reliance No. 7 mine, and during 1939 one in Winton No. 7½ mine. With the introduction of this type of mobile loader, a new era of development began. Speed undreamed of in hand-loading days became a reality. The cost of development down the pitch has been reduced until it

Jan 1, 1942

By J. E. Wilson, F. P. Lebar

TYPICAL of southwestern Wyoming are coal structures that dip from 4° to 17°. Those at the Reliance and Winton mines of the Union Pacific Coal Co. average 91/2 and 15°, respectively, and dip almost directly to the west. By using a hoist for main haulage, a method of mining has been developed whereby four places are driven on the pitch of the seam. Slightly upgrade from the strike at intervals of 300 ft. a two-entry system is driven to the north and to the south. In both fields, which are nongassy, an exhaust system of ventilation is used. Slope, manway, and lower or haulage entries are placed on the intake. Two air-courses and upper or breaking entries are placed on the return. A retreat system of mining is used exclusively. From the opening of its first coal mine, in the year 1868, until 1923, when the Joy loader was introduced into The Union Pacific Coal Company's operations, slopes, aircourses, and manways were driven by hand. Development work was conducted on the night shift or off shift, and the main hoist was used for haulage. The slope was driven down the pitch with crosscuts turned at intervals of 75 ft. and entries at 230 ft. Connections to the workings above were made by driving up the pitch 75 ft. Mule haulage was used to furnish cars to the hand loaders driving planes up the pitch. A sheave was placed at the upper end of the plane with a I¼-in. hemp rope dou- bling around it and having me end attached to the car and the other to the mule. The mulc, pulling downhill, raised to the working face a small wooden car of one-ton capacity. With the introduction of mechanical loading, mule haulage and small wooden cars disappeared and auxiliary hoists, electric locomotives, and steel cars with a capacity of 4 tons were substituted. Development work was done during two or three shifts of the 24-hr. period. Driving of haulage slopes down the pitch by hand continued. Crosscut intervals were changed to Ioo ft. and the crosscuts were driven with shaking conveyors. With the use of a 90° swivel, aircourses and manways were driven up the pitch. Entry intervals were changed from 230 ft. to 300 feet. Mobile loaders of the Joy type were first employed by this company in the year 1923 at Hanna, Wyo. In 1928, two 4-BU Joy loaders were transferred from Hanna to Winton No. I mine, where they were used in driving slopes and entries. At the time of transfer, the machines were about worn out and were not suited to the steep pitch, therefore frequent breakdowns occurred. However, experience justified the belief that the mobile loader was fitted for driving slopes in this field. During 1937 a unit was installed in Reliance No. 7 mine, and during 1939 one in Winton No. 7½ mine. With the introduction of this type of mobile loader, a new era of development began. Speed undreamed of in hand-loading days became a reality. The cost of development down the pitch has been reduced until it

Jan 1, 1942

By Thomas M. Drown

THE method usually employed in accurate determinations of sulhur in pig-iron and steel is to treat a weighed sample of borings in a flask with muriatic acid, and to pass the gaseous products through an alkaline solution of lead or silver, which precipitates all the sulphur of the sulphuretted hydrogen in the form of sulphide of lead or silver. The sulphide thus formed is subsequently oxidized by aqua regia, bromine, or other oxidizing agent, and the sulphuric acid formed precipitated in the usual way by chloride of barium. I have substituted for the alkaline metallic solution, a solution of permanganate of potash in the strength of one gramme of permanganate to 200 cubic centimetres of water, and find that it gives results quite as accurate as those obtained by using an ammoniacal solution of silver. By the employment of the permanganate it will be readily seen that there is considerable saving of time and work. In order to test the accuracy of the method, six samples of pig-iron borings were weighed out (about six grammes each) and treated identically

Jan 1, 1874

By Thomas M. Brown

The method usually employed in accurate determinations of sulphur in pig-iron and steel is to treat a weighed sample of borings in a flask with muriatic acid, and to pass the gaseous products through an alkaline solution of lead or silver, which precipitates all the solphur of the sulphuretted hydrogen in the form of sulphide of lead or silver. The sulphide thus formed is subsequently oxidized by aqua regia, bromine, or other oxidizing agent, and the sulphuric acid formed precipitated in the usual way by chloride of barium. I have substituted for the alkaline metallic solution, a solution of permanganate of potash in the strength of one gramme of permanganate to 200 cubic centimetres of water, and find that it gives results quite as accurate as those obtained by using an ammoniacal solution of silver. By the employment of the permanganate it will be readily seen that there is considerable saving of time and work. In order to test the accuracy of the method, six samples of pig-iron borings were weighed out (about six grammes each) and treated identically

By J. T. Ryan

WITH J. T. Ryan, of Pittsburgh, in the chair, 40 men on Monday afternoon were attracted to the first meeting of the new Health and Safety in Mines Committee. The speakers were well received and the discussion was good and virile. The field and scope of the new Health and Safety in Mines Committee was reviewed briefly, yet concisely, by Scott Turner. This committee is to cover the whole mining industry, in which much progress in reducing accidents has been made in recent years. Members of the A.I.M.E. can considerably assist in this important problem.

Jan 1, 1933

Mr. Cottrell : I omitted to speak of the cost of installation. The precipitation-plant at the Balaklala smelter, up to the time of initial operation, including the construction of flues, installation of the apparatus, etc., cost $107,000, and subsequent modifications probably represented at least $15,000 more. Upon the information gained in this plant, the installation at the cement-mill, handling nearly twice as much gas, has been reduced in cost in a number of ways, but the overhead construction, carrying the precipitator at the top of the stacks, is naturally expensive, yet, even so, the total cost of construction will probably not greatly exceed $150,000. The mechanical details of the tubular form last shown have been worked out more recently than those of the plate form, and the tubular form promises to be still less expensive in construction, as you would naturally expect. The cost of operat-ing the plant varies somewhat with the character of the gases used. The amount of power consumed is not determined by the tonnage of the material collected, but by the volume of gas to be handled. It takes as much power to precipitate a thin cloud as a dense one. In the cement-plant they are getting a higher efficiency; i. e., a greater number of cubic feet treated per kilowatt than in the earlier plants. This is perhaps partly due to higher temperature of the gases, which here average about 450° C. The best figures on the cement-plant are between 3 kw. and 4 kw. Of

Jan 1, 1913

INTRODUCTION The regional characteristics of porphyry copper deposits in South America southward from Pantanos and Pegadorcito, Columbia, will be summarized. The age of formation of deposits spans the period from the Permian to the present. Where possible, the general characteristics and the individual structural features of the deposits are integrated into the plate tectonic model. Individual deposits cited in this chapter, located in Fig. 1, are the best known and most fully described, and form the Andean copper belt (Peterson, 1958). Smaller porphyry copper deposits fall both east and west of the line of large, high grade deposits (e.g., Chuquicamata and Toquepala) that make up the spine of this belt. Most of those smaller deposits (e.g., Mi Vida [Koukharsky and Mirre, 19761) are omitted from Fig. 1 and Tables 1 and 2, however. Neither the Andean orogen nor the individual deposits within it are as well de- scribed in the literature as are their counter- parts in the Cordilleran orogen of North America. Therefore, generalizations relying on regional geologic mapping, geophysics, and isotopic geochemistry lack details pertinent to this type of deposit in the Cordilleran orogen. The South American porphyry copper province has been described by Hollister ( 1974) to include most of the Andean orogen excepting the tin province of Bolivia. Porphyry copper deposits have not been commonly found within the tin belt, although copper-tin (e.g., San Rafael, Peru) and copper-tungsten (e.g., Llamuco, Chile) de- posits are known. James (1971) shows the depth to the Moho to be appreciably greater where the tin belt exists, but disclaims any genetic significance from the coincident appearance of the tin-tungsten province and the inhibition of porphyry copper development where the sialic crust thickens. Dates on tin mineralization in this belt (Clark and Farrar, 1973) are similar to some dates for porphyry copper mineralization known else- where in the Andean orogen. It seems that some mechanism is needed to explain the geographic separation of porphyry copper- molybdenum and simultaneous tin-tungsten- molybdenum metallization within the same tectonic system and appearing at similar distances from the trench. The thickened crust of the tin belt is one of the few known differences. Tables 1 and 2 list some of the most important porphyry copper deposits explored to date, but do not include Antaminas, Peru. or a number of other large skarn deposits

Jan 1, 1978

By C. E. Birchenall

DaVIES and Richardson1 have measured composition changes for Mn1-Owith variation in the equilibrium partial pressure of oxygen at 1500°, 1575°, and 1650°C, where 6 is the deviation from the simple stoichiometric ratio. No trend in this relationship with temperature was observed, so these remarks apply to the whole temperature range. The experimental values and their spread are shown by the bounded straight-line segments in the figure. Davies and Richardson assume that the stoichiometric oxide shows Frenkel disorder, given by the equation Mn2+Mn2+ + Mn" [1] where Mn2+ is a normal lattice ion which moves into an interstitial site (Mni2+) leaving a vacancy (Mn,"). The superscript dashes indicate that there is an excess charge on the anions surrounding the vacancy. Schottky disorder, in which a perfect crystal acquires equal numbers of cation and anion (Ov") vacancies according to leads to equations of exactly the same form in the analysis below. In view of the neutron diffraction results of Roth,2 which shows extensive Frenkel disorder in Fe1-o, Eq. [I] seems more appropriate. The deviations from stoichiometric composition, MnO, result from the addition of oxygen according to In effect Davies and Richardson ignore the variation of Mn3+in constructing equilibrium constants. This approximation might not appear to be very serious if the excess positive charges are really free posi- tive holes (P+) and if the intrinsic conductivity is high as a result of the reaction where e- is a conducting electron. However, the calculations of Buessem and Butler3 indicate that the partition functions of the free charges make a large contribution to the equilibrium constant, and this approximation would not be a desirable one. Furthermore, Morin4 shows that the positive holes are probably localized in MnO and therefore are described better by the mass action principle than by a degenerate gas model. Davies and Richardson's considerations require that activity corrections be applied beyond a 6 value of about 0.005. It is proposed to show here that the dissociation pressure curve can be calculated reasonably well over the whole composition range studied without activity corrections by choosing appropriate equilibrium constants for reactions 1 and 2. As stoichiometric composition The mass action constant, Ks, for reaction [I.] and the equilibrium constant, K,, for reaction [2] are given by where the concentrations which do not change significantly have been absorbed into the constants. The brackets denote concentrations. The deviation from stoichometric composition is given by gardless of [Mni2 ]. Substituting Eq. [7] in [6]

Jan 1, 1961

By William K. Callaway

Cominco American has operated the Magmont Mine for 16 years as a traditional open stope room and pillar mine. Diminishing ore reserves and the discovery of high grade ore zones over 90' in thickness caused consideration to be given to hydraulic sandfilling as a method of ground support to increase pillar extraction and mine life. This paper will review the results of sandfill testing. Plans for underground experiments, and operational plans for the future will also be discussed.

Jan 1, 1984

By W. C. Kerr

A BRIEF sketch only is here intended, with a few illustrations, in order to give a general notion of the character and structure of these veins. I have stated elsewhere, several years ago, that these veins were wrought on a large scale and for many ages by some ancient peoples, most probably the so-called Mound Builders; although they built no mounds here, and have left no signs of any permanent habitation. They opened and worked a great many veins down to or near water-level ; that is, as far as the action of atmospheric chemistry had softened the rock so that it was workable without metal tools, of the use of which no signs are apparent. Many of the largest and most profitable of the mines of the present day are simply the ancient Mound Builders' mines reopened and pushed into the hard undecomposed granite by powder and steel. Blocks of mica have often been found half imbedded in the face of the vein, with the tool-marks about it, showing the exact limit of the efficiency of those prehistoric mechanical appliances. As to the geological relations of these veins, they are found in the gneisses

Jan 1, 1880

By W. C. Kerr

A brief sketch only is here intended, with a few illustrations, in order to give a general notion of the character and structure of these veins. I have stated elsewhere, several years ago, that these veins were wrought on a large scale and for many ages by some ancient peoples, most probably the so-called Mound Builders; although they built no mounds here, and have left no signs of any permanent habitation. They opened and worked a great marly veins down to or near water-level; that is, as far as the action of atmospheric chemistry had softened the rock so that it was workable without metal tools, of the use of which no signs are apparent. Many of the ladgest and most profitable of the mines of the present day are simply the ancient Mound Builders' mines reopened and pushed into the hard undecomposed granite by powder and steel. Blocks of mica have often been found half imbedded in the face of the vein, with the tool-marks about it, showing the exact limit of the efficiency of those prehistoric mechanical appliances. As to the geological relations of these veins, they are found in the gneisses

Jan 1, 1880

By AIME AIME

A SYMPOSIUM on current. conditions in Mexico, particularly in the oil and mining industries, was a most successful feature of the May meeting of the New York Section of the A.I.M.E. Heath Steele, vice-president of The American Metal Co.. Ltd., with an intimate knowledge of Mexico gave the principal address, and asked that his analysis of the present situation he regarded neither as an endorsement of Mexico's policy nor as the criticism of a disgruntled operator. To explain the .attitude of the great mass of the Mexican people towards recent developments, he first described briefly the political, social, and religious beliefs and customs of tile Mexican Indian. In spite of their contact with foreigners these beliefs and customs have remained unchanged throughout many generations. The old communal spirit and the idea of common ownership of the land still persist especially in the rural districts and villages; the old custom of a council for local self-government is reflected in the present-day labor committee. Mr. Steele discussed in order land oil, and mines.

Jan 1, 1938

By C. V. Millikan, Herbert F. Beardmore

Declining Productivity Index, as considered herein, is a productivity index that has a substantially and consistently decreasing value when measured over a period of a few hours. If not recognized, it may be interpreted as representing an unsettled or unstable condition in a producing well. It forms the basis of a number of predictions as to future performance compared with the performance of wells in which the productivity index does not decline. The nost important of these are that: (I) the rate of oil production will decline more rapidly, (2) the gas-oil ratio will usually increase abnormally, (3) the amount of water ultimately produced will be negligible, if any, (4) stop-cocking will increase current production and decrease gas-oil ratio. When such relative well performance is indicated, it follows that certain reservoir performance and operating practices may be anticipated: (I) disappointing recovery, (2) longer natural flow, (3) no active water drive, (4) better evaluation of acidizing, shooting and reworking, (5) intermittent operation of wells, (6) smaller pumping equipment required. It is significant that the basis of these important predictions is bottom-hole pressure tests that can be made immediately after completion of the wells. Introduction "'Productivity index" is the number of barrels of oil produced per day per pound per square inch of differential pressure between the reservoir and the bottom of the well. "Declining Productivity Index," as considered herein, is a productivity index that has a substantially and consistently decreasing value when measured over a period of a few hours. Productivity index can be determined only when the rate of production can be stabilized. In most wells the rate of production and bottom-hole pressure are easily stabilized to give a constant productivity index for a period of many hours. A few produce so erratically as to preclude probability of an acceptable test in the usual sense. A satisfactory productivity index can be determined in some wells only by gauging the production accurately by hours, measuring the bottom-hole pressure continuously, and from these data calculating the productivity index for successive hours. Such figures frequently will have a decreasing value—that is, a declining productivity index—and when plotted on double. logarithmic cross-section paper with productivity index as ordinate and time as abscissa will be a straight-line curve. The angle between the curve and the abscissa is referred to as the rate of decline. Declining productivity index may appear to be the result of change in permeability to oil due to decreasing saturation of oil and increasing saturation of gas in the reservoir. It is possible that such is in fact the cause, but if so, more is involved than merely relative saturation of oil and gas. This seems evident because the rate of decline in productivity index is substantially the same regardless of the pro-

Jan 1, 1945

By Alfred F. Brainerd

HAVING had considerable practical experience in the management of colored mining labor in the South, I have thought a few observations upon its peculiarities might interest those not personally familiar with it. In mining, as in all other departments throughout the South, this class of labor is largely in excess of any other; and its characteristics need to be known and duly taken into consideration by those who may be charged with the conduct of southern enterprises. The colored laborers are fervently religious, intensely superstitious, improvident, and usually good natured and happy,—in a word, they are like children. That strong religious emotions do not involve necessarily a moral sense highly developed in the direction of ethics, is shown in the propensity of the colored population for chickenstealing, and in the brutal fights and other outbreaks of which they are not infrequeutly guilty, upon any slight provocation. It is only fair to say, however, that many individuals among them are in the highest degree steady and trustworthy. To one accustomed to seeing white miners at work in the middle, northern or western States, the colored miners seem somewhat slow and lazy. But their efficiency is greater than it appears to be. The almost tropical sun of midsummer beats upon their unprotected heads

Jan 1, 1886

By Frank Riddle

PRODUCTS made from the ores of the sillimanite group, and synthetic substitutes for them, have unique properties, and service tests prove that they are playing, and will continue to play, a major part in improvements in metallurgical processes. Also, they are examples of how comparatively useless, rare, or "museum" minerals have been made available in commercial quantities. Until research developed uses for them, the minerals had been observed only in small, scattered masses, or crystals. Improvements in ceramic processes and compositions have come about very gradually. In the last 10 or 15 years, several outstanding developments have been made. Of greatest interest to the mining and metallurgical engineers are those affecting the composition, necessitating the mining of new minerals, and improvements in ceramic products used in metallurgical processes.

Jan 1, 1932

By Stuart E. Buckley

The application of hydrocarbon equilibrium data to various problems encountered in refining and in natural gasoline recovery is an old and well established practice. Both generalized data and data on specific hydrocarbon systems have been made available by a number of investigators. More recently such data have been applied to the relations governing the separation of oil and gas both in the reservoir and at the surface. Most of the applications to production problems, however, have been based upon examinations of surface samples of oil and gas. This paper describes a technique that has been used satisfactorily in a number of cases to calculate directly from the hydrocarbon analysis of and auxiliary laboratory data on a subsurface sample of the reservoir fluid the behavior of the oil and gas during the various stages of separation at the surface incident to production. Types of Information Calculated The system of calculations is not designed to supplant field data, but rather to correlate with them laboratory data obtained under controlled conditions in order to obtain a more complete and exact picture than usually is possible through the use of field data alone. The chief advantage of the calculations is the possibility of their use at a minimum of both time and expense to determine completely the effect of any possible operating technique upon each of the following: (1) The gas-oil ratio resulting from liberation of the dissolved gas; (2) the composition and gasoline content of the liberated gas; (3) the composition and gravity of the residual oil; (4) the amount and composition of the gas liberated upon flashing the oil from the separator to the stock tank; (5) the shrinkage of the oil in passing from the reservoir to the stock tank. This information is frequently essential to the correct determination of the advisability of installing a natural gasoline plant, to design such a plant to take care of seasonal production, and to determine the optimum separator pressures to carry in various parts of a field.

Jan 1, 1938

By AIME AIME

THE Chairman of the Iron and Steel Division for 1945 is one of the most versatile and best-known men in this industry, with wide experience in research and operations and in handling both the men and the materials that are used in enormous quantities. Erle G. (Doe) Hill was born in Santa Ana, (alit, April 21, 1890 and graduated (Bachelor of Science) in mining and metallurgy from the University of California in 1913. For the next five years lie held a variety of jobs as miner, foreman, and null superintendent in gold, silver, copper, and quicksilver mines in the West and in Mexico. As Doe was an individual endowed with an exceptional amount of horse sense, he left the West in 1918, to become instructor of mining engineering and ore dressing at Carnegie Institute of Technology, and while in that post did considerable consulting work as a geologist and mining engineer. In 1920, still possessing the same common sense. he got out of mining engineering and geology and became associate professor of metallurgy at the University of Pittsburgh, a position he retained for nearly ten years.

Jan 1, 1945

By Jackson R. Pellett

INTRODUCTION The Friedensville mine is situated in Upper Saucon Township, Le- high County, Pennsylvania, in the southern central part of the Allentown quadrangle of the United States Geological Survey, approximately 5 miles southeast of the City of Allentown and 4 miles south of the City of Bethlehem. Zinc was first discovered in the Friedensville area early in the 19th century and several mines were operating during the latter part of the century. Zinc oxide was produced in 1853 and zinc metal in 1859. All mining in the area ceased in 1893 chiefly because of an unfavorable economic situation caused by a severe ground water problem and competition from the higher grade ores in New Jersey. Property acquisition by the New Jersey Zinc Company began in 1899 and periodic exploratory drilling was carried on until 1940 when sufficient reserves were proved for development of a mine. Shaft sinking was undertaken in 1947 and, due to severe hydrologic conditions, was not completed until 1952. Production began in 1958 and today the mine is producing about 64,000 tons of zinc concentrate per annum. The concentrates are trucked to the Company's smelter at Palmerton, Pennsylvania, approximately 30 miles north of Friedensville. The mine also produces from its mill tailings industrial and agricultural grades of limestone for commercial markets.

Jan 1, 1970

By R. A. Vandermeer

It is usually assumed that the rate-determining step in the migration of a grain boundary involves the thermally activated transfer of single atoms across the interface. Chemical reaction rate theory then gives a migration rate which is proportional to the driving force when this is small compared to kT.1 In their recrystallization studies on aluminum, Gordon and vandermeer2 obtained data which was capable of providing the first experimental test of this proportionality. They correlated stored energy (driving force) release measurements determined calorimetrically with fraction recrystal-lized kinetic (growth rate) data acquired metallo-graphically at a temperature where a significant amount of recovery takes place concurrently with recrystallization. Within experimental error, the results of Gordon and Vandermeer confirmed experimentally, at least over a limited range, the linear dependence of boundary migration (growth) rate on driving force in accordance with theory. In obtaining these results, however, an incorrect, implicit assumption was made in relating the average instantaneous growth rate of the recrystallized grains to the measured fraction recrystallized kinetic data. The purpose of this present note is to point out and correct this assumption. An alternate approach, whereby a more proper average growth rate can be calculated from the recrystallization kinetic data, is presented. The earlier data, reevaluated in terms of this new approach, show the same general trend as before so that the original conclusion of Gordon and vandermeer2 is still valid. As was shown in a detailed study3 of the geometrical features of recrystallization in aluminum, the colonies of recrystallized grains can be regarded as uniform cylinders embedded in a three-dimensional matrix, the number of such colonies being constant. Thus during the early stages of recrystallization the volume fraction recrystallized, Xv, can be written as Xv=ynvlr2 [l] where y is a shape factor and i and r are defined as the average length and radius of a recrystallized colony and are spatial averages over the specimen. -nv, is the number of such colonies in a unit of volume. The erroneous assumption made in the earlier paper2 was that r in Eq. [I] could be replaced by

Jan 1, 1965