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By C. A. Fothergill

An improved blotter model is described which makes use of a plastic sheet as base for the blotter field and pins to represent the input wells. The model is simple to construct and adapt and is particularly useful for demonstration purposes. Operational details are given. INTRODUCTION The blotter model was first applied to the investigation of oilfield problems by Wyckoff, Botset and Mus-kat,' primarily in order to demonstrate the flood patterns which could be expected from various arrangements of input and output wells in waterflooding projects. In recent years the model has been largely superseded for analog studies by the potentiometric and electric analog models which are more refined and versatile, since they can simulate the form, and, in certain cases, permeability variations which it is not possible to do with the blotter model. However, the latter is still used for analog studies where the reservoir can be represented as being uniform in thickness and permeability, and where a visual record of the flood advance is required. Ramey andNabor,2 for example, have applied the model to the investigation of areal sweeps in oil recovery by in-situ combustion. Because of its limitations, the blotter model can be used in general for only very simple arrangements of input and output wells, but within these limitations it has a definite advantage over all other types, in that it provides a picture of the advancing flood using the simplest and most easily constructed apparatus, by contrast with the gelatin model, for example, which requires more elaborate equipment. Moreover, the experiments can be quickly repeated and modified if necessary, whereas considerable time is required to prepare a gel field, compared with that required for the preparation of sheets of conducting blotting paper. For these reasons the blotter model can be very useful for demonstration and teaching purposes, enabling the student to experiment for himself with different arrangements of input and output wells. A model has been constructed for this purpose which is simple to operate and adapt. The model (Fig. 1) consists of a base platform or box, approximately 12-in. square, on top of which are screwed three lathes of 1/2 -in. square section to form three sides of a square 6 in. in length. This forms the support for a sheet of Cobex, transparent plastic, thickness .003 in., on which is carried the blotting paper representing the field. The plastic is flexible and relatively soft, and can be attached to the support by cellulose tape so that it can be easily removed when required. The input wells are represented by brass drawing pins pressed through the plastic sheet from the underside until the points are just projecting through the top; these are connected in the circuit as shown in Fig. 2. The sheet of blotting paper of required shape and size is saturated with a solution of 0.2 n-potassium sulfate to which has been added a saturated alcohol solution of phenol-phthalein at a strength of 10 cc/liter of stock solution. The surplus water is removed and the blotting paper placed in position on the plastic sheet making contact with the drawing pins and the sheet (which is an insulator). The anode consists of a second sheet of blotting paper cut as shown and saturated with the same solution. This is suspended from a laboratory stand, being connected to the conducting wire by means of a crocodile clip and making contact with the horizontal blotting paper at the projecting point. This is the method used by Ramey and Nabor and which permits the hydroxyl ions or colored front to reach the anode. As shown in Fig. 2, the electrical voltage used is 220-v DC and a shunt is placed across the terminals to step down the voltage as required. Further adjustment can be made as necessary using a lamp board in series with the shunt to obtain the

Jan 1, 1958

By Anson Hayes

FOR the purpose of the following discussion the word "research" is interpreted as including all phases of development work on methods of manufacture, metallurgical characteristics, and uses of iron and steel. Research in the iron and steel industry then includes both plant re- search and laboratory research. Since iron and steel came into being, the steel consumer's plant and the steel producer's plant have been important factors in the development of the steel industry. Good minds have always been associated with both consumer and producer plants, so marked progress was made in the industry even when these were the only types of research and development groups in action.

Jan 1, 1937

By W. M. Courtis

SINCE many accounts of Silver Islet Mine, in Lake Superior, have already been published, it is supposed that the members of the Institute are familiar with the location and character of the mine. To many, however, a more detailed account of the ore and manner of treatment will, perhaps, not be without interest. The extraordinary richness of Silver Islet ores, and the difficulty of obtaining correct assays, induced the company to erect smelting works of its own. Accordingly, ground was broken at Wyandotte, Mich., early in the spring of 1871, and the work was pressed on with indomitable energy by Captain E. B. Ward of Detroit, as president, and Mr. Thomas MacFarlane, the discoverer of Silver Islet, as superintendent of the works, so that by July 1st the works were so far completed that smelting could be commenced. The intention was to work Western ores with those from Lake Superior, since the latter contain but a small amount of lead. Hence the capacity of the works is much larger than is needed for the present yield of the mine. The planned process for treatment was smelt-

Jan 1, 1874

By K. D. Jacob

ALL types of commercial phosphate rock produced throughout the world contain fluorine in quantities ranging from approximately 0.4 to 1.3 per cent in the Curacao and Christmas Island phosphates to 3.1 to 4.2 per cent in the phosphates of the United States and North Africa1. For a given type of rock, the fluorine content is usually roughly propor-tional to the phosphorus content. SIGNIFICANCE OF FLUORINE IN PHOSPHATE ROCK On the basis of chemical and X-ray diffraction studies, Hendricks and co-workers2 concluded that fluorapatite, Ca10F2(P04)6, is the essential phosphatic constituent of the commercial types of domestic phosphate rock. On the other hand, Bredig and co-workers3 have recently advanced the opinion, also based on X-ray diffraction studies, that the mineral phosphates usually contain carbon dioxide in the apatite lattice, and that the phosphate rocks of. the United States are really fluorcarbonate apatites. However, the domestic types of phosphate rock do not seem to differ greatly from coarsely crystalline fluorapatite in their behavior toward chemical reagents in general, and for the purpose of this paper it will suffice to consider fluorapatite as being the essential phosphatic constituent of these types of rock.

Jan 1, 1936

By W. D. Douglas, M. J. Hampshire, G. J. C. Young

This paper describes the replacement of a conventional filtration, clarification, and zinc precipitation plant by a carbon-in-pulp (CIP) electrowinning plant, with the objective of improving the recovery of gold from cyanide leached, acid plant calcines. The discussion covers early laboratory studies to the design and erection of the full-scale plant. Particular emphasis is placed on the problems encountered with commissioning and the strategies employed to solve them.

Jan 1, 1985

By Charles Will Wright

Brief descriptions of the occurrence of the various deposits of strategic minerals then known in South America are published in "The Mineral Deposits of South America," by B. L. Miller and J. T. Singewald, 1919; in "Ores and Industry in South America," by H. F. Bain and T. T. Read, 1934; and in many publications on the individual countries. To give a gen.era1 idea of the situation today and possibilities for future output of strategic minerals in several of the countries, the following notes are offered. All tonnages are in metric units.

Jan 1, 1940

By G. E. Agar, A. L. Mular

G. E. Agar (Manager, Minerals Processing Research, International Minerals & Chemical Corp., Skokie, III.) — The author notes a discrepancy between the parameters a and ß which are the slopes of the size distribution and energy-size modulus plots respectively. The reason for the discrepancy and the systematic decrease in the magnitude of a with grinding time is abundantly clear from the work of Fuerstenau8 on dry grinding. Fuerstenau shows very clearly in his Fig. 5 that at short retention times the parameter a is the same as that obtained by sizing over the complete size range. From this figure, it is obvious that sizing to only 400 mesh gave distribution curves similar to Mular's - that is, the slope apparently decreased systematically with increased grinding. As a consequence of the improper determination of a, the magnitude of ß given by Mular must be larger than the true value. In order to demonstrate this, the following Fig. 6 was taken from Mular's paper (his Fig. 1). Fuer-stenau's results show that we can approximate the correct value of K by drawing lines parallel to the short retention time curves through the 400-mesh

Jan 1, 1963

By John W. Pack

At present the manufacture of metallic zinc, or spelter, in Missouri, is carried on only at the establishments located at Carondelet, or South St. Louis. Although the development of the industry has not yet reached that fulness which it has attained elsewhere in the United States, still the commanding advantages of position of these establishments are so evident that the prospective importance and magnitude of spelter manufacture in this State, and especially at this locality, can hardly be doubted. A study of the chemical and technical aspects of the business of these points cannot be without interest to the metallurgist as well as to the capitalist. I have endeavored to investigate, as far as was practicable, within the limits of a paper of this character, some of the problems connected with this industry, at the same time making a few comparisons of the results attained at some of the Carondelet works with those of other establishments with regard to which information could be obtained. In the prosecution of these studies I have been kindly aided by the managers of Carondelet establishments, and by Prof. Charles P. Williams, Director of Rolla School of Mines. To the latter I am especially indebted for assistance in regard to methods of analysis. To all these gentlemen I return my thanks for their valuable aid. Other sources of information will be duly credited in their proper places.

By William M. Courtis

Since many accounts of Silver Islet Mine, in Lake Superior, have already been published, it is supposed that the members of the Institute are familiar with the location and character of the mine. To many, however, a more detailed account of the ore and manner of treatment will, perhaps, not be without interest. The extraordinary richness of Silver Islet ores, and the difficulty of obtaining correct assays, induced the company to erect smelting works of its own. Accordingly, ground was broken at Wyandotte; Mich., early in the spring of 1871, and the work was pressed on with indomitable energy by Captain E. B. Ward of Detroit, as president, and Mr. Thomas MacFarlane, the discoverer of Silver Islet, as superintendent of the works, so that by July 1st the works were so far completed that smelting could be commenced. The intention was to work Western ores with those from Lake Superior, since the latter contain but a small amount of lead. Hence the capacity of the works is much larger than is needed for the present yield of the mine. The planned process for treatment was smelt-

GENTLEMEN : Herewith are submitted reports for the calendar year 1933 of your Treasurer and the Chairmen of the following standing committees: Finance, Admissions, Membership, Papers and Publications, Library, and MINING AND METALLURGY. TO these reports you are referred for additional details of the year's activity. Finances.-Income for 1933 from all sources totaled $121,690 com- pared with $138,331 in 1932. Incidentally, this exceeded the income as estimated in the budget by $7,190; the largest item being a "surplus" of $3,316 over the budget expectancy as to member dues. As compared with 1932 the most important items of shrinkage in income were $9,000 from dues and initiation fees; $5,500 from the magazine, MINING AND METALLURGY; and $2,500 from sales of publications other than the magazine.

Jan 1, 1934

By John R. Spencer

A capillary tube variable volume cell is described, which has operated satisfactorily over a range of 100°F and 3,500 psi to 550°F and 1,500 psi. The cell contents are entirely visible over the length of the capillary with the exception of a space at the top amounting to three per cent of the total volume. Observations on the critical behavior of simple systems have been greatly facilitated by the apparatus, it being possible to establish the critical conditions for a particular mixture in the course of a day's run. INTRODUCTION Many types of apparatus have been designed for obtaining data on the phase relationships of hydrocarbon systems. Such apparatus can in general be subdivided into two classifications; (l), indirect measurement of phase volume, and (2), direct visual observation of phase volume, each of which has outstanding advantages and disadvantages. Indirect measurement of phase volume requires the use of rather elaborate apparatus including internal probes in which are located the device for determining the locus of the interface between phases. Such equipment is by its very nature costly, and is complex from the standpoint of operating technique. Probing techniques can be used, however, over wide ranges of temperature and pressure with a high degree of reproducibility. Apparatus for visual observation of phase behavior obviously has the advantage of enabling the experimenter to see exactly what takes place, but because the material to be tested is contained in a cell constructed of both metal and glass, is limited severely as to the temperature range of operation. Furthermore. the maximum pressure usually is limited by the choice of material used for sealing the glass to the metal, and by the strength of the glass itself. In the interest of increased efficiency of observation, as much of the cell as possible should be visible to the eye. Glass capillary tubes have been used successfully but have always given difficulty at the metal-to-glass seal. An apparatus has been devised to overcome the problems of sealing and resistance to temperature effects that have heretofore been the limiting factor with glass apparatus in the observation of phase volumes at elevated temperature and pressure. APPARATUS The objective which dictated the general arrangement of the apparatus (Figs. 1 and 2) was simplicity of operation. The air bath, A, was constructed of an iron framework to which was attached approximately one inch of glass wool bats which were covered on the outside with "Masonite." A roughly octagonal center piece was installed to provide forced circulation of the air by the fan, B, past the heaters, D, cell, F, and thermoregulator, C, respectively. The entire top of the box is removable to facilitate charging of the cell and to permit easy maintenance. Two windows are provided before and behind the cell to allow the operator to observe the contents against the background fluorescent light, E. The heaters,

Jan 1, 1951

By John R. Spencer

A capillary tube variable volume cell is described, which has operated satisfactorily over a range of 100°F and 3,500 psi to 550°F and 1,500 psi. The cell contents are entirely visible over the length of the capillary with the exception of a space at the top amounting to three per cent of the total volume. Observations on the critical behavior of simple systems have been greatly facilitated by the apparatus, it being possible to establish the critical conditions for a particular mixture in the course of a day's run. INTRODUCTION Many types of apparatus have been designed for obtaining data on the phase relationships of hydrocarbon systems. Such apparatus can in general be subdivided into two classifications; (l), indirect measurement of phase volume, and (2), direct visual observation of phase volume, each of which has outstanding advantages and disadvantages. Indirect measurement of phase volume requires the use of rather elaborate apparatus including internal probes in which are located the device for determining the locus of the interface between phases. Such equipment is by its very nature costly, and is complex from the standpoint of operating technique. Probing techniques can be used, however, over wide ranges of temperature and pressure with a high degree of reproducibility. Apparatus for visual observation of phase behavior obviously has the advantage of enabling the experimenter to see exactly what takes place, but because the material to be tested is contained in a cell constructed of both metal and glass, is limited severely as to the temperature range of operation. Furthermore. the maximum pressure usually is limited by the choice of material used for sealing the glass to the metal, and by the strength of the glass itself. In the interest of increased efficiency of observation, as much of the cell as possible should be visible to the eye. Glass capillary tubes have been used successfully but have always given difficulty at the metal-to-glass seal. An apparatus has been devised to overcome the problems of sealing and resistance to temperature effects that have heretofore been the limiting factor with glass apparatus in the observation of phase volumes at elevated temperature and pressure. APPARATUS The objective which dictated the general arrangement of the apparatus (Figs. 1 and 2) was simplicity of operation. The air bath, A, was constructed of an iron framework to which was attached approximately one inch of glass wool bats which were covered on the outside with "Masonite." A roughly octagonal center piece was installed to provide forced circulation of the air by the fan, B, past the heaters, D, cell, F, and thermoregulator, C, respectively. The entire top of the box is removable to facilitate charging of the cell and to permit easy maintenance. Two windows are provided before and behind the cell to allow the operator to observe the contents against the background fluorescent light, E. The heaters,

Jan 1, 1951

William Clinton Brown, Brooklyn, N. Y.: The demand for an apparatus for cooling water for condensers, refrigeratingmachinery and air-compressors, as well as water-jacketed furnaces, has led manufacturers to put such an apparatus on the market, so that it is now possible to purchase a cooling-tower, properly designed and constructed, by simply stating the amount of water to be cooled and the temperatures of the hot and the cold water. The principle is similar to that described by Mr. Henrich, but wood is not used in the best apparatus. There are two great objections to wood: First, it cannot last long under the very trying conditions to which it is subjected; and second, it absorbs the organic matter with which water in constant use becomes impregnated, and the resulting odor is very disagreeable. A few days ago I saw a cooling-tower and condenser, built by the Henry R. Worthington Co., in operation at the Edison electric-lighting station in Brooklyn, N. Y., cooling the water for a 700 horse-power condenser. It consisted of a large stack of iron, about 15 feet in diameter by about 30 feet high. This stack was filled with tiling through which the water falls. A whirligig distributes the water evenly over the top, and a large fan, about 6 feet in diameter, driven by a 10 horse-power electric motor, blows air into the bottom, thus giving a positive circulation. The water, in running down the sides of the tiling, is met by the blast of air, and enough is evaporated to cool the rest. The vacuum-gauge on the condenser showed 26 inches; so the condenser was undoubtedly getting sufficient cool water.

Jan 1, 1896

By William P. Shinn

It is almost exactly seven years since the last previous meeting of the Institute in this city. In a paper on " Pittsburgh, its Resources and Sorroundings," read at that meeting, I showed that Allegheny County had produced in 1878, " one-twelfth of all the pig-iron,.... two-ninths of all the rolled iron (except rails), over one-eighth of all the Bessemer and open-hearth steel, two-thirds of all the crucible blister and puddled steel, one-fourth of all the glass, one-eighth of all the coal, and one-sixth of all the pig-lead produced in the United States;" and the object of this paper is to show that, great as the record then was, it has been greatly surpassed since.* Population. In my former paper I expressed the opinion that the census of 1880 would show the population of Allegheny County to be in excess of 300,000. The census report made it 355,869. The following shows the growth of the county in population from 1790 to 1880: 1790,...........10,309 1800,........... 15,087 1810,...........25,317 1820,...........34,921 1830,...........50,552 1840.............81,235 1850............138,290 1860............178,881 1870,...........262,204 1880,...........355,869 This makes Allegheny County, in 1880, rank sixth in population of the counties of the United States, whereas in 1870 its rank was ninth. The population of Pittsburgh in 1880 was 156,359, being twelfth

Jan 1, 1886

By W. A. James

NATURE endowed the Niagara Frontier with great resources but it was the molding of these resources by the early pioneers that assured its future development. This great industrial district of New York stretches along about fifty miles of shore line on the eastern end of Lake Erie and the Niagara River, embracing the two counties of Erie and Niagara, with the city of Buffalo about in the center. This location at the junction of the eastern end of the Great Lakes and the western boundary of the State, a great focal point of land and water, transportation, guaranteed the development of the Frontier. Although the first white settlers came to this section in 1784, it was not until after the turn of the nineteenth century that real development started. Perhaps the most significant influence in the early days was the completion of the Erie Canal between Buffalo and Albany in 1825. This then monumental achievement gave Buffalo an advantage in the race for the best trade route to the Western

Jan 1, 1938

By AIME AIME

THE growth of the spirit of progress and mutual aid which motivated the founders of the Institute sixty years ago in Wilkes-Barre was vigorously demonstrated at the sixtieth anniversary meeting held there on May 22. Committees headed by Cadwallader Evans, "resident director" of the Institute, and Paul Sterling, chairman of the local section, had arranged for a full-day tour of the northern anthracite field, so that the hundred and fifty members and guests who had come for the celebration of the anniversary might see the changes and progress made in that field in recent years. More than forty automobiles were in line in the cavalcade which left the Westmoreland Club at nine- thirty. Operations visited were fully described in the May issue of MINING AND METALLURGY, so it is enough to say that after a seventy-five mile drive through the beautiful Susquehanna Valley and over the rolling green hills of northern Pennsylvania a stop was made for lunch at Forest City. Carey, Baxter and Kennedy, contractors at the stripping operations there, had provided, in the shelter of tents, a well-prepared luncheon and other refreshments. The return trip was made by way of Scranton, arriving at Wilkes-Barre at five- thirty.

Jan 1, 1931

By V. V. Clark

WHEN a district is more or less primitive, and a trained mining engineer attempts single- handed to prospect it according to old standards, he generally fails. He has not the ability to live out in the open alone for months at a time and carry on with enthusiasm and determination like the old-time prospector. But the same engineer, placed in an organized group where modern prospecting methods are employed, is immediately put on his mettle and his chances of winning are greatly increased. Marsman Investments, Ltd., with headquarters in Manila, has at the present time, Sept. 4, 1937, six prospecting parties in the Netherland East Indies. Three of these groups are combing their assignments for lode mines, studying structures, developing and reaching out into veins and zones with diamond drills. The other three are searching for placer mines with pans, pits, and Empire drills. I am in charge of one group seeking commercial gold placers on the Island of

Jan 1, 1937

By John Chipman

The concentration of a solute in a dilute ),zetallic solution may be measured by any of several parame- ters including weight percent, atom fraction, atom ratio, and lattice ratio. The ratio of filled to unfilled interstitial sites is useful for interstitial solutes. A variable 2 proportional to this ratio is used as a measuve of concentration. For component 2 irz a bitzary solution z2 = n2/Ym - nz/b) where b is the numberber of interstitial sites per lattice atom. For a t~lul-ticortzporzent solution this becomes zz = n2/(nl + Cvjnj) in which Vj = - l/b for an interstial solute and +1 for a substitulional solute. In the infinitely dilute solution the activity of an interstitial solute 2 is proportional lo z2. At finile concentration the departure from this limiting law is expressed us an activity coefficient, his coefficient is a function of concentra1io)z expressed as tevactiolz coeffcient 8; is analogous to the jark~iliar e£ bul is found to be independent of concentvation in certain solutions for which data are available. It is found that the same equations may be used to express the activity of a nonmetallic solute, sulfur, in liquid solutions of iron containing other solutes, both metallic and nonmetallic. For a nonmetallic solute or for one which strongly increases the actiuity of sulfur, it is convenient to assign arbitvarily a value vj = — 1. When this is done the derivative is found to be constant in each of the ternary solutions studied. The activity coefficient of sulfur in a complex liquid iron solution may be expressed as where nk is a second-order cross product determined in the quaternary solution Fe-S-j-k. The equation is used to calculate tlze activity of sulfur i)z three sevetl- component solutions. IN thermodynamic calculations concerning dilute solutions it is unnecessary to invoke laws and relations which extend across the concentration range to include concentrated solutions. In most binary metallic systems, as arkeen&apos; has recently pointed out, there exist two terminal composition regions of relatively simple behavior, connected by a central region of much greater complexity. When the solute is a nonmetal there is only one such region and in many systems the concentration range is extremely limited. It is the purpose of this paper to suggest a method for the calculation of activities in such a terminal region in which one or more solutes are dissolved in a single solvent of predominantly high concentration. HENRY&apos;S LAW In the usual textbook statement of Henry&apos;s law, concentration is stated in mole fraction. This has the advantage that it makes Henry&apos;s law thermodynamically consistent with Raoult&apos;s law. Since all measures of concentration at infinite dilution are related by simple proportion it follows that mole fraction, molality, atom ratio, weight percent, or any other unit of concentration can be used with the appropriate constant. At finite concentrations, however, calculations based on the law depend upon the unit employed. Deviations from Henry&apos;s law at finite concentrations depend upon the composition variable employed. They are evaluated in terms of activity and interaction coefficients2 which have become familiar features of metallurgical thermodynamics. It is the purpose of this paper to propose a measure of concentration for metallic solutions containing interstitial or nonmetallic solutes by means of which the calculation of activities in complex solutions may be simplified. The discussion will be restricted to free-energy interaction coefficients3 typified by Wagner&apos;s c|a BINARY SOLUTIONS The several measures of concentration which are to be considered are shown in line a of Table I. The corresponding activity coefficients are in line b and the deviation coefficients, sometimes called self-interaction coefficients, are in line c. Henry&apos;s law simply states that the activity coefficient approaches a constant value at infinite dilution. By adoptihg the infinitely dilute solution as the reference state and defining the "Henrian" activity as equal to the concentration in this state, the activity coefficient is always unity at infinite dilution. This convention is far sim~ler and more useful in dilute solution than emploiment of the &apos;Raoultian" activities and it will be used in the following discussion. The several definitions and equations of Table I will be referred to by means of their coordinates in the table. Early observations of deviations from Henry&apos;s law in metallic solutions were shown graphically4 rather than analytically. For the case of sulfur in liquid iron5 the slope of a plot of logfs vs (%S) was constant in the range 0 to 4.8 pct S, indicating constancy of eh2&apos; in Ic. He was proposed by wagnerz and has been widely adopted. The a function of IIIc recently employed by ~arkenl was designed specifically for dilute solutions. Darken has shown that the value of a12 remains essentially constant for many binary solutions within a substantial range of compositions. The atom ratio is directly proportional to the molalitv.<, a conventional measure of concentration. IVb and C served as the basis for smith&apos;s6 classic studies of

Jan 1, 1968

By Peter R. Morris, Alan J. Heckler

THREE angles are required to specify the orientation of a crystallite with respect to a physical reference frame. The distribution of crystallite orientations in a polycrystal is thus a function of three angular variables. The most widely used experimental techniques for studying orientation in polycrystals lead directly to the pole figure representation, i.e., the distribution of the poles of certain crystallographic planes in terms of two angular variables. In recent years1-5 methods have been developed which permit determination of the (three-angle) crystallite orientation distribution from several (two-angle) pole figure distributions. In this work Roe&apos;s method has been applied to the study of orientation in hcp materials. The method is illustrated for commercial purity titanium sheet (Ti-70) which was cold rolled (65 pct reduction), annealed at 1450°F for 3 min, and air cooled. The grain shape was observed to be equiaxed after this treatment. EFFECTS OF PHYSICAL, CRYSTALLOGRAPHIC SYMMETRY In Roe&apos;s method the crystallite orientation distribution, w(?,?,F), is expanded in a series of generalized spherical harmonics 11(?,?,F) = E E E W^Zirmtye-tote-in* [l] 1=o ,,,=-I ,,=-I where { = cos 8. The set of Euler angles employed here is illustrated in Fig. 1. The axis for each rotation is denoted by a double arrowhead. The positive sense of each rotation is that of a right-handed screw advancing in the direction of the double arrowhead. The X, Y, and Z directions correspond to the rolling direction, cross direction, and normal direction, respectively. In the initial orientation (10.O), (12.O), and (00 . 1) planes are perpendicular to the X, Y, and Z directions, respectively. The IC/ rotation about the Z axis is carried out first by rotating X into X&apos;, Y into Y&apos;, and leaving 2 unchanged, i.e., Z&apos; = Z. The 8 rotation about the Y&apos; axis is carried out second by rotating X&apos; into X", 2&apos; into Z", and leaving Y&apos; unchanged, i.e., Y" = Y&apos;. The I$ rotation about the Z" axis is carried out last by rotating X" into X"&apos;, Y into Y"&apos;, and leaving 2" unchanged, i.e., 2"&apos; = 2". Any specified orientation of the X&apos;", Y&apos;", and Z&apos;" crystal-fixed axis system relative to the X. Y, and Z physical axes (rolling direction, transverse direction, and sheet normal direction, respectively) can be obtained by appropriate IC/, 8, and (F rotations. The Zl,, of Eq. [l] are the Jacobi polynomials, augmented by the square root of the weight function. The Zl,, are symmetric in m,n, i.e., Zl,,= Zlnm. For orthotropic physical symmetry and hexagonal crystallographic symmetry, the coefficients, W!,,, of the series are all real, W!mn = Wzfi, = Wlm~ = Wlfi~, 1 and m are even and n is restricted to 6k, where k = ...,-2,-1, 0, 1, 2, .-.. The determination of the Wlmn from pole figure data has been previously described.&apos;~~ The Zl,, may be written in multiple angle form

Jan 1, 1970

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 27 Montreal, Canada Sept, ?79 8 28 New York, N.Y. Feb, ?80 9 29 Lake Superior, Mich Aug, ?80 9 30 Philadelphia, Pa. Feb, 81 9 31 Staunton, Va May, 81 10 32 Harrisburg, Pa Feb, 81 10

Jan 1, 1952