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By H. E. Doerr

The writer has been unable to find much information relative to tests made to determine the effect of forging on the specific density of steel. The opinion, however, among men engaged in the business, seems to be that forging greatly compresses or consolidates the steel. While such is doubtless the case with spongy or porous steel, the following experiments indicate that there can be little or no change in the density with steel initially free from cavities. Ten ingots of basic open-hearth steel cast as shown in Fig. 1 were used in the experiments. All the specimens were 0.53 carbon with all other elements the same, the analysis being determined from drillings taken midway between the center and outside of the upper end, as shown in Fig. 2. The specimens were selected from over one thousand ingots so that the tests could be comparative for the work done in forging only, but no two of the ingots were cast in the same heat. Each ingot remained in the mold approximately 30 min., when it was removed and sir-cooled. About 12 hr. later, when the temperature had been reduced to approximately that of the surrounding atmosphere, the head was discarded and the ingot heated in an oil furnace to approximately 2250" F. (1235" C). Approximately 1 min. was required to forge under the steam hammer to 1 1/4 in. (31.75 mm.), rough diameter, as shown by the dotted lines in Fig. 2. All ingots were allowed to air-cool after forging. Cylinders 1/2 in. (17.7 mm.) in diameter and 1/2 in. high were then turned from the forged and unforged parts of the ingots and numbered. The ten pairs of specimens were submitted to Louis E. Endsley, Professor of Railway Mechanical Engineering, University of Pittsburgh; A. N. Talbot, Professor of Applied Mechanics, University of Illinois; L. Z. Slater, chief chemist, Scullin Steel Co., St. Louis, Mo. NO information was furnished as to which specimens were forged or unforged and each laboratory used the same specimens, submitting the average of three independent determinations, a tabulation of which is shown in the accompanying table in which the laboratories are designated by the letters A, B, and C. While there is considerable difference in the individual determinations for a number of the specimens, the averages

Jan 1, 1920

By R. F. Campbell, R. F. Miller

SIXTEEN steels containing different combinations of chromium and molybdenum, in amounts up to 5 per cent of each element, were examined for microstructure and hardness after air cooling and after furnace cooling from suitable austenitizing temper- [ ] atures. Diagrams summarizing the structures and hardness resulting from these two cooling rates are presented (Figs. 3, 4, 7).† Data were also obtained on the influence of these two elements, individually and in combination, on the depth 0f decarburization observed after furnace cooling (Fig. 8). COMPOSITION OF MATERIAL The chemical composition of the steels investigated is given in Table I. The plain carbon steel was made in a 25-ton Heroult electric-arc furnace, while the alloy steels were made in a 4.5-ton Ajax-Northrup elec- [ ] tric induction furnace. The cast ingots were hot-rolled to I.75-in. bars. AIR-COOLED SERIES The I.75-in. bars were forged to flat plates, 0.25 in. thick, from which specimens 0.5 in. wide by 2 in. long were cut. The specimens were pretreated to improve their homogeneity by heating to I830°F. (1000°C.) for 20 min. and oil quenching. They were then reheated to I740°F. (950°C.) for one hour and air-cooled, after

Jan 1, 1941

By Sherwin F. Kelly

LITERALLY from the four corners of the earth, from Jerusalem and China, from Mysore and Uganda, as well as from geophysicists in the United States, came contributions from workers in magnetic and electrical geo-physical methods, most of them unfortunately unable to be present themselves. The most lively discussion centered on the phenomena of natural potentials in the earth, dealt with in M. B. R. Rao's paper from Mysore, and in Parke Dickey's contribution, which he presented in person. In the oil fields, the weak potentials observed in sedimentary strata traversed by bore holes have traditionally been ascribed to phenomena of electro-filtration and electro-capillarity. Research tending to refute this theory was presented by Dickey, who reported the existence of natural potentials in core samples, and between strata exposed in underground workings. This precipitated a lively discussion as to the possible role of electro-filtration, selective adsorption of ions by mineral particles, and electrolytic potentials, in the production of this phenomenon.

Jan 1, 1943

By Zay Jeffries

EACH generation accepts the developments of the preceding generations without full appreciation of the difficulties that had to be overcome or of the effect of any given development on society. Today, the production of pig iron is the yardstick with which general industrial health and progress are measured. So natural and logical does this seem to us, that it is difficult to picture conditions prior to the fourteenth century when pig iron was unknown. Not only was pig iron unknown but iron or steel could not be melted and poured into castings; all iron and steel articles were forged from sponge iron. All castings, as well as many worked articles, were made of non-ferrous metals or alloys. In many parts of the world, over long periods of time, not only was the annual exchange value of non-ferrous metals greater than that of iron and steel, but their combined tonnage was greater. At present, the value of the pig iron produced in a year is of the same order of magnitude as that of all non-ferrous metals combined; the tonnage of pig iron is, however, about twenty times that of all non-ferrous metals combined. Owing to lack of records, we will probably never know the relative importance of the various metals at all periods in historic times. A certain conclusion is that the iron and steel industry, since the discovery of pig iron and the cheap methods of converting it into steel, has grown at a much more rapid rate than the non-ferrous metal industries. Notwith-standing their fundamental fitness for man's needs, iron and steel owe their importance in no small degree to the low cost of production. The low cost was a result of increased knowledge of the production appliances and of the metallurgical processes. This increased knowledge is the key to our modern industrial civilization.

Jan 5, 1924

By Edmund C. Pechin

THE writer approaches this subject with a great deal of diffidence —first, because it is utterly impossible to treat it satisfactorily within the limits of a paper, and, secondly, because the larger development is of so comparatively a recent date as to make authoritative data on some interesting points unavailable. For over one hundred years small charcoal-fnrnaces have been in existence, at widely scattered points, making a few tons of iron daily, and then gradually increasing to a daily output of, say 10 to 12 tons, as the market widened. With the exhaustion of local supplies of wood, inaccessibility to market, and sharp competition, bringing lower prices, many were compelled from time to time to make temporary stops, and finally to cease altogether. During the first half of the century there were at different times in operation between 75 and 90 charcoal furnaces. The last Directory of the Iron and Steel Works of the United States (1890) gives 19 as the number of charcoal-stacks in Virginia. Of these several are cold, and, it is

Jan 1, 1891

By Everette Lee DeGolyer

FIFTEEN thousand barrels of oil daily, the production of the United States 75 years ago, amounted to more than 90 per cent of world supply. Russia and Romania, neither of which produced as much as one thousand barrels daily, were the only other suppliers in substantial quantity. The adolescent oil industry of the United States, a dozen years old in 1871, was still confined to the Appalachian region. Wells were drilled by cable tools; many of them were "kicked down" by manpower with a spring pole; and depths were measured in hundreds rather than thousands of feet-a 1000-foot well was a deep well. Casing was an innovation, come into general use only a few years previously and still so new as to be subject to bitter patent litigation. Crude oil was packaged in wooden barrels and shipped by flat boat and barge on the creeks and rivers and by railroad. Such pipe lines as existed were only a few miles long. There were many refineries. Pittsburgh, Cleveland and the Atlantic seaboard were refining centers. Refineries were very small, however, and their operations consisted essentially in simple fractionation by distillation and treating for quality. The products in demand were burning oil or kerosene and lubricating oils. Oil was not yet used as fuel and gasoline was a nuisance to the refiner.

Jan 1, 1947

By W. L. Fink, R. S. Archer

This paper describes results obtained on aluminum-beryllium alloys and aluminum-beryllium-copper alloys in the preparation of which aluminum of 99.95 per cent. purity was used. The constitution and structure of the high purity binary alloys are given. The aluminum-beryllium eutectic occurs at 0.87 per cent. beryllium and 645° C. The solid solubility of beryllium in aluminum at 631° C. is 0.05 per cent, beryllium, and at room temperature is less than 0.013 per cent. beryllium. The densities of the alloys are substantially the same as the values calculated on the assumption that the densities of the elements are not changed by alloying. All of the alloys age-harden at room temperature after a solution heat treatment, and the chill cast aluminum-beryllium-copper alloys age-harden at room temperature without a prior solution heat treatment. Hardness and tensile properties are given. Salt spray corrosion tests on sheet specimens are described. It is shown that beryllium docs not lower the corrosion resistance of aluminum to salt spray provided the alloy has received a solution heat treatment. Commercial Possibilities of Beryllium Alloys Beryllium has certain properties such as low density, high hardness, good corrosion resistance, low thermal expansion and fairly good electrical conductivity, which would indicate that it is worthy of consideration as an ingredient of light alloys. It was not until recently, however, that beryllium could be produced with sufficient ease to encourage research along this line. The production of beryllium by electrolysis from a fluoride bath has now developed to the stage where it could be used commercially if there were sufficient demand for the element. Claims made in certain newspapers and technical articles in regard to thc strength and corrosion resistance of thc aluminum-beryllium alloys are not justified by experimental results. Moreover, beryllium is an expensive metal ($200 a pound at the time this work was done) and, on account of the nature of its ore and the consequent difficulty of its extraction, it will in all probability continue to be a relatively expensive metal, although the cost would undoubtedly be a great deal less than $200 a

By B. E. Thompson, H. B. Fuqua

For a very brief description of the North Texas area, and the general geological features with which it is associated, the reader is referred to the opening paragraph of last year's summary1. A more complete discussion of the structure of the area, together with other interesting data concerning it, has been published recently by the Bureau of Economic Geology at the University of Texas2. It has been impossible for the authors to isolate the statistics for production for each of the many small pools of this district, as such statistics are not kept by operators except by counties or arbitrary divisions of counties. The total number of wells drilled in Archer, Wichita and Clay counties also has been subject to some estimate, as many of the shallower holes are not reported. While both routine development in proven or semiproven areas and exploratory drilling during 1935 showed an increase over the year 1934, the discovery of new producing areas of importance did not show improvement over that period. Several extremely local productive spots within semiproven areas were found in Archer, Cooke and Wilbarger counties; and extensions to older producing areas were developed in Archer, Baylor, Cooke, Montague, Wichita and Wilbarger counties. In Archer County, the Grace and Woods No. 1 Archer County (Fee), 4 miles northwest of Archer City, in the Thomas Glass survey, encountered a sand from 2836 to 2845 ft. of Pennsylvanian (lower Canyon) age, which showed an initial yield of 75 bbl. daily. While its production is of negligible importance, it is given special mention in this review because of the fact that it is producing from a new and deeper horizon than has been previously exploited in the county. Little deep development occurred in the district during the year. The Walter Gant No. 2 C. M. Worsham in J. M. Swisher survey, about 14 miles east of Henrietta, in Clay County, was abandoned at 5127 ft. in

Jan 1, 1936

By H. B. Fuqua, B. E. Thompson

For a very brief description of the North Texas area, and the general geological features with which it is associated, the reader is referred to the opening paragraph of last year's summary1. A more complete discussion of the structure of the area, together with other interesting data concerning it, has been published recently by the Bureau of Economic Geology at the University of Texas2. It has been impossible for the authors to isolate the statistics for production for each of the many small pools of this district, as such statistics are not kept by operators except by counties or arbitrary divisions of counties. The total number of wells drilled in Archer, Wichita and Clay counties also has been subject to some estimate, as many of the shallower holes are not reported. While both routine development in proven or semiproven areas and exploratory drilling during 1935 showed an increase over the year 1934, the discovery of new producing areas of importance did not show improvement over that period. Several extremely local productive spots within semiproven areas were found in Archer, Cooke and Wilbarger counties; and extensions to older producing areas were developed in Archer, Baylor, Cooke, Montague, Wichita and Wilbarger counties. In Archer County, the Grace and Woods No. 1 Archer County (Fee), 4 miles northwest of Archer City, in the Thomas Glass survey, encountered a sand from 2836 to 2845 ft. of Pennsylvanian (lower Canyon) age, which showed an initial yield of 75 bbl. daily. While its production is of negligible importance, it is given special mention in this review because of the fact that it is producing from a new and deeper horizon than has been previously exploited in the county. Little deep development occurred in the district during the year. The Walter Gant No. 2 C. M. Worsham in J. M. Swisher survey, about 14 miles east of Henrietta, in Clay County, was abandoned at 5127 ft. in

Jan 1, 1936

By A. Patton, F. N. Speller

The use of roll scale in the Bessemer process dates back, to the best of our knowledge, at least 20 years. It was first used by the Ohio Steel Go., Youngstown, Ohio (now the Ohio Works of the Carnegie Steel Co.) under the direction of Sam McDonald, Superintendent of the Bessemer Department at these works. Two 10-ton vessels and one blowing engine capable of blowing one heat at a time were employed. The object of using the scale was to shorten the length of the blow, or in other words, to increase the production with the same equipment. Various means were tried out for introducing the roll scale into the bath of molten iron: It was shoveled into the vessel before the heat was charged, so that the metal would flow over the scale; it was shoveled into the bath after the vessel was turned up; it was dumped into the empty iron ladle by the wheelbarrow-load, and at times was dumped on top of the molten metal in the iron ladle. But the practice of introducing the scale into the iron ladle had to be abandoned on account of danger from explosions and of skulling the ladles. It was soon learned that the proper place to charge the scale was in the empty vessel, so that when the molten iron was poured into the vessel it flowed over the scale, causing a considerabIe reaction to take place before the heat was turned up. Eventually, cylindrical chutes similar to those now in use were installed. Into these chutes the scale is dumped and carried into the empty vessel. Before this convenient means of introducing the scale was adopted, the Ohio Works had satisfactorily demonstrated that roll scale would increase production, by blowing 107 heats in one 12-hr. turn (1,087 tons) with one blowing engine, blowing one heat at a time; whereas, prior to the use of scale, the best practice at these works was about 80 heats under the same conditions. In using roll scale and other oxides of iron to facilitate and control the refining of pig iron in the converter, the Bessemer plant has borrowed one of the most active agencies used in the open-hearth process with, as would be expected, much the same results. The effect of such additions to the Bessemer charge may be discussed as to the influence of this practice on quality, production and cost.

Jan 1, 1917

Andes Copper has an old camp and a new camp, both isolated until recent road improvements. The old camp is at Potrerillos and the new one at El Salvador, 25 road ,miles away. The company was incorporated in 1916 and the first mine, concentrator, leaching plant, smelter and town were built in the succeeding twelve years. The first blister copper was poured on January 24, 1927. Economic conditions determined the long development period but the end result was the design and construction of a mining complex that was all of a piece, unlike the piecemeal additions to El Teniente and Chuqui. The mining episode at Potrerillos came to an end in 1960 when the ore at La Mina became exhausted and the new mine, El Salvador was brought in. Both of these ore deposits come within four hpundred feet of the surface and had they been developed within the last five years might reasonably have been brought in as open pit mines. However, that is conjecture, and as it stands the operation at La Mina was so ideal for the mining method selected, blockcaving, it became a classic for the textbooks. On the other hand, El Salvador has turned out to be a blockcaving mine to test an engineer's skill. In mining the copper deposit at Indio Muerto mountain, there are ground conditions of every conceivable type. Tunneling in one section, the back can cave like sized pea gravel and only spiling can hold it; in another heading only the lifters are shot but often the rest of the round will sit down in one piece; elsewhere the bottom squeezes up and closes the drifts; and contrary to all other locations, there are sections where the block can be undercut without support. Today the scope of operations at Andes extends from mining to electrolytic copper. Ore is mined at El Salvador and the concentrator is also situated there. Concentrates pipelined 14 miles to Llanth, the water decanted, and then it is hauled by rail 40 miles and 5500 ft higher to the Potrerillos smelter and refinery. Potrerillos and El Salvador are respectively 90 and 70 miles from the port of

Jan 11, 1969

By J. A. Collins

THE process of plastic extension of face-centered cubic single crystal-line rods is so well understood, since the notable studies of Taylor and Elam,1 that the change in orientation of any crystal by slip and rotation may be predicted from the measured elongation. It is customary to assume a very homogeneous deformation, wherein gliding lamellae are free to rotate so that their slip direction continually approaches the axis of the rod, until a second slip system comes into operation; whereupon conjugate slip proceeds quantitatively to an end adjustment with the [112] direction in the axis of the rod. This process has been checked in many face-centered cubic materials and readily permits the preparation of specimens that have been sub-jected to various determinable amounts of shearing action. It is clearly of interest to study in such measurably strained specimens the development of a recrystallized structure on annealing and if possible detect the source of nuclei from which the new crystals grow. Strain-annealing experiments of this character have been performed by others but not in detail sufficient to permit a study, for example, of the number of recrystallized grains vs, the amount of shear. In the experiments now reported, this was done with a wide variety of orientations covering nearly the entire range of slip on a single system and corresponding to amounts of shear (ratio of shearing distance to distance between lamellae) at the conclusion of a test of from 0.08 to 0.57. A particular point was made of determining the crystallite rotation, or small angular range assumed by the octahedral slip plane after these various amounts of shear. The mechanism of recrystallization and the magnitude and effect of recovery on the recrystallization process was investigated.

Jan 1, 1940

By AIME AIME

POSSIBILITY of a greatly increased manganese production from domestic source; is indicated by news that the Bureau of Mines has been successful in producing concentrates with high manganese content from the low-grade deposit, in the Las Vegas, Nev.) area. The first unit of the comprehensive group of pilot plants built by the Bureau of Mines at Boulder City, Nev., under a defense appropriation has started operations, demonstrating definitely the applicability of a process developed in the Bureau laboratories. About 12 1/2 lb. of manganese is needed for the production of every ton of steel, and substitution is difficult. The United States produces only about 3 per cent of its total needs of this ore. Only high-grade ore, such as the Russian ore, containing 18 per cent or more manganese, is generally used by American producers in making ferro¬manganese the form in which manganese is usually added in steel manu-

Jan 1, 1941

By Frank Firmstone

When in charge of the Glen don Iron Works, the importance of good methods of filling was forcibly brought to my attention, and it occurred to me that the first step toward the discovery of the best plans was the accumulation of exact information as to the distribution actually effected by various chargers; also, that something could be done in this direction by careful measurements in the furnace, to be afterwards recorded for comparison on drawings. The figures shown herewith have been prepared from such measurements, and nearly all of them refer to Glendon, where the fuel used was anthracite and the ore-mixture about threequarters of New Jersey magnetic ores and one-quarter of brown-ores from the vicinity of the works. Every occasion furnished by the blowing-in of furnaces was utilized, but the data accumulated rather slowly in this way; and, opportunity oEering to make special trials at no great expense, the figures from 2 to 7 were thus obtained. The trials were made by dumping a hopperful (6 barrows) of material at once into the furnace, and, when all the fuel of a round (12 barrows) had been put in, the profile of the upper surface was obtained by stretching a steel tape across the top on a diameter and at a known height. By measuring down from this with a graduated rod, the profile was easily obtained with sufficient accuracy, especial pains being taken to get correctly the crests of the ridges and the bottoms of the hollows, as many intermediate points being included as seemed necessary. This was repeated on another diameter when there was occasion. The same course was followed for the limestone and ore.

Jan 1, 1899

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,000. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation,' the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service.

Jan 1, 1946

FRIENDS of the late Charles F. Rand presented in 1930 a sum of money from which. the income is available to support various phases of the work of the Institute in which Mr. Rand was so deeply interested. At present the fund amounts to $10,000. The specific terms of the deed of gift are as follows: "The fund collected to establish a memorial to the late Charles F. Rand shall be placed in the custody of the Board of Directors of the American Institute of Mining and Metallurgical Engineers, to be set up as a trust to be known as the `Charles F. Rand Foundation', the income of which shall each year be applied to a distinct purpose to be decided upon in that year by vote of the Board of Directors. This purpose shall be such as to promote the general welfare of the Institute and to constitute a permanent memorial of the usefulness of Mr. Rand, who for many years gave unstintingly of his time and talents in its service.

Jan 1, 1952

By Richard Hamburger

The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new & do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951

By AIME AIME

FOUK fields of activity are now recognized by the A.I.M.E. in its award of medals for conspicuous achievement: the Saunders medal for mining, the Douglas medal for non- ferrous metallurgy the Lucai medal for petroleum, and the Rand medal for distinguished achievement in the broad field of mining administration including the organization and development of enterprises in all branches of the mineral industry. This last is known officially as the Charles F. Rand Memorial Medal, and it award is made possible through funds supplied by the Charles F. Rand Foundation. Until this year money thus available was used for other special projects, so that the forthcoming presentation of the Rand medal to Robert C. Stanley is notable as being the first time that achievement in mining administration has been thus recognized.

Jan 1, 1940

By R. M. Brick, F. L. Vogel

THE elementary mechanism of deformation in the body-centered cubic metals has been a subject of dispute for many years. If the problem were merely that of designating the crystallographic plane or planes of slip, the solution would have appeared long ago. However, there must be greater differences in the deformation behaviors of the body-centered and face-centered types than the differences in their lattices would suggest. The lines of slip formed on the polished surface of a strained face-centered cubic metal conform to glide over a single plane of the crystal. Slip in body-centered cubic iron, however, is frequently observed as curved and forked lines which could not possibly define a single plane of atoms. This alone is sufficient reason to expect different modes of deformation to operate in the two lattice types. The literature in this field now has generally accepted the proposition that {110), {112), or (1231 planes will act as slip planes in iron. It is essential that the experimental evidence supposedly supporting this proposition be critically examined. Taylor and Elam1 in 1926, using relatively small single crystals, determined the operative slip systems by measurements of the distortion of a grid engraved on the specimens prior to deformation. Their results indicated that shearing had taken place in the close-packed direction on a plane adjacent to or coinciding with the plane of maximum shear which contained the slip direction. This led the authors to propose a theory of noncrystallographic or banal slip. The authors considered an alternate rationalization of banal glide. Slip on two (1101 planes or possibly two {112} planes containing the same <1ll> direction could produce the wavy slip lines. By employing plane segments of varying widths, the integrated plane could take any position in the <111> zone. They rejected this explanation, however, feeling that the preponderance of evidence was against it. Taylor&apos; continued the investigation of the plasticity of the body-centered cubic lattice on ß brass. He reasoned that the resistance to shearing of a given plane in the zone of the slip direction was a function of the angle between the glide plane and the closest (110),: P F=—cose sine cos(X —?) [1] where F is the resistance to shear; P, the axial load at yielding; A, the cross sectional area; e, the angle between slip direction and load axis; x, the angle between plane of maximum shear containing the slip direction and the (101) pole; and ?, the angle between observed glide plane and the (101) pole. Differentiating Eq. 1 and rearranging, dF — = tan(x-?) d? [2] F which expresses the variation of the shear resistance with the angle $. Integrating this equation between the limits 0 and ? yields In F/F0 = ?0?tan(x— ?) d? [3] Here, F, is the resistance to shear of the (110) plane and F is the resistance to shear of a plane $ degrees from the (110). Thus, the variation of shear resistance with $ can be calculated from an experimentally measured x vs $ relationship. Fahrenhorst and Schmid8 sed several methods, none of them involving direct observation, to determine the glide system in ferrite. They determined the variation of critical resolved shear stress with

Jan 1, 1954

By Richard Hamburger

(1) Introduction: The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new,&apos;,2 do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951