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By Alden B. Greninger

That metallographic structures analogous to the martensite of steel may be found in certain copper-aluminum and copper-tin alloys has been known for many years; similar structures recently were found in certain copper-zinc a1loys.l In all three of these alloy systems the martensite structures result from transformation of the metastable fi phase when the speed of cooling from the B range is sufficiently high to suppress decomposition into equilibrium phases. In the normal decomposition of solid solutions into equilibrium phases, diffusion is needed to bring about the necessary changes in concentration, and the rate of reaction falls almost to zero at temperatures slightly above room temperature. The rates of reaction for martensite processes, however, are not dependent upon temperature; the transformation does not require rendjustments of concentration. For example, the martensite transformation in 60:40 (B) copper-zinc does not begin until the temperature has dropped to about minus 30" C., and then continues down to minus 130" C. and probably even at lower temperatures.' Furthermore, martensite processes apparently proceed only while the tempcrature is falling, within the proper range, and cease completely while the temperature is held constant ;$ and they cannot be suppressed by extremely rapid cooling although the rate of cooling for some alloys may be increased to over 10,000 times the critical cooling velocity. Isaitschew, Kaminsky and Kurdjumow2 account for these observed behaviors of rnartensite processes by postulating that the mechanism 6I... consists in a regular rearrangement of the lattice in such a way

Jan 1, 1939

By Alden B. Greninger

That metallographic structures analogous to the martensite of steel may be found in certain copper-aluminum and copper-tin alloys has been known for many years; similar structures recently were found in certain copper-zinc a1loys.l In all three of these alloy systems the martensite structures result from transformation of the metastable fi phase when the speed of cooling from the B range is sufficiently high to suppress decomposition into equilibrium phases. In the normal decomposition of solid solutions into equilibrium phases, diffusion is needed to bring about the necessary changes in concentration, and the rate of reaction falls almost to zero at temperatures slightly above room temperature. The rates of reaction for martensite processes, however, are not dependent upon temperature; the transformation does not require rendjustments of concentration. For example, the martensite transformation in 60:40 (B) copper-zinc does not begin until the temperature has dropped to about minus 30" C., and then continues down to minus 130" C. and probably even at lower temperatures.' Furthermore, martensite processes apparently proceed only while the tempcrature is falling, within the proper range, and cease completely while the temperature is held constant ;$ and they cannot be suppressed by extremely rapid cooling although the rate of cooling for some alloys may be increased to over 10,000 times the critical cooling velocity. Isaitschew, Kaminsky and Kurdjumow2 account for these observed behaviors of rnartensite processes by postulating that the mechanism 6I... consists in a regular rearrangement of the lattice in such a way

Jan 1, 1939

By Clifford S. Wilson

ScReened pipe is designed with the view of restraining the fine, free-running sands of the production zone from entering oil wells. Its successful use is dependent on a number of factors. The nature and effects of some of these factors can be determined through experiment and observation, but some of the elements that have a distinct bearing on the use of screened pipe can be evaluated only by estimate. The important subsurface conditions which affect the use of screened pipe are: 1. Depth of production zone. 2. Extent of production zone. 3. Reservoir pressure. 4. Character and relative quantity of oil and gas. 5. Character of sediments: a. Cossolidation of beds. b. Variation in beds. c. Grain-size gradation of sands. d. Free-running characteristics of sand from different levels. Aside from the use of mechanical equipment and tools, the measures to be taken in the installation of screened pipe involve: 1. Size of liner. 2. Length of liner. 3. Design and mesh of screen. 4. Portion of liner to be screened. 5. Manner of setting liner. 6. Preparation of or washing of the well before or during the setting of the screen. 7. Manner of bringing in the well. 8. Manner of flowing the well. Values applicable to the actual subsurface conditions that exist at any well can only be approximated. The accuracy of the estimate will be measured by the amount and quality of the evidence at hand and the personal factor of ability to interpret the evidence fairly, whether

Jan 1, 1933

By R. J. Wasilewski

Axial expansion has been determined by X-ray diffraction up to 600° to 760°C in a titanium and four high-oxygen alloys. Expansion data cannot be fitted to the usual quadratic expression and anomalies observed are believed indicative of the changes in the bonding configuration of the valence electrons. Furthermore, there is significant disagreement between data obtained on poly crystalline and single crystal powder specimens. The major disagreement occurs within the temperature range (-470°C) where both mechanical and electrical properties also show markedly anomalous behavior. X. HIS work forms part of an investigation of physical properties of pure titanium and its osolid solutiono alloys with oxygen and nitrogen. In view of the anomalies observed in both the electrical resistivity' and the susceptibility behavior it was decided accurately to determine the thermal expansion behavior of the pure and alloyed a titanium. PREVIOUS WORK The axial expansion coefficients reported for pure titanium are listed below. As can be seen, there is a marked discrepancy between the axial expansion and the experimentally determined coefficients on poly crystal line material. Thus, if we take the most recently reported axial expansivities3,4 we obtain perature interval of 25o to 700°C. The experimental value reported for polycrystalline metal is, however, of the order of 9.7 x 10o6 per OC. EXPERIMENTAL I) Pure Titanium. High purity titanium powder of -325 mesh was used throughout most of this work. The only significant impurities present were the interstitials, oxygen and nitrogen, which analyzed respectively 650 and 80 ppm. The purity of the ma-

Jan 1, 1962

By R. I. Jaffee, H. R. Ogden, D. J. Maykuth

IN THE past year, Jaffee and Campbell&apos; and Finlay and Snyder2 reported on the mechanical properties of titanium-base alloys, some of which were in the same ranges of composition as are covered in this paper. In this paper, evidence confirming that given by Finlay and Snyder on the effects of carbon, oxygen, and nitrogen on titanium will be presented; and, in addition, new data will be given on the effects of these elements on the flow properties and phase transformation of titanium. Materials and Preparation of Alloys The preparation and general properties of iodide titanium have been adequately described elsewhere.&apos; , As-deposited iodide titanium rod, prepared at Battelle, of Vickers hardness less than 90 was employed as the base metal in the present work. This was the same material as that used by Finlay and Snyder.2 The probable analysis reported by them for standard quality metal holds here also: N 0.005 pct, 0 0.01 pct, C 0.03 pct, Fe <0.04 pct, A1 <0.05 pct, Si <0.03 pct, and Ti 99.85 pct. Carbon was added in the form of flake graphite supplied by the Joseph Dixon Crucible Co. Oxygen was added in the form of c.p. grade TiO, powder, produced by J. T. Baker Chemical Co. Nitrogen was added in Ti3N4 powder, supplied by the Remington Arms Co. Individual ingots weighed 7 or 8 g. Carbon, oxygen, or nitrogen was added by placing the corresponding powder in a capsule made from as-deposited iodide titanium rods and melting the capsule with the balance of the charge. The charge was are-melted with a tungsten electrode on a water-cooled copper hearth under a partial vacuum of very pure argon (99.92 pct minimum). Melting was practically contamination free. Vick-ers hardness increases of less than 10 points were normal for unalloyed iodide titanium control melts. Nitrogen analyses of are-melted iodide titanium showed a nitrogen content of 0.005 pct, about the same as is present in the as-deposited rod. No tungsten pickup was found in a melt of iodide titanium analyzed for tungsten. Weight losses in melting nitrogen-free alloys were very small and varied consistently from nil to 0.015 g (0 to 0.2 pct). This permitted the use of nominal composition for these alloys. Chemical analyses made for carbon, which can be analyzed conveniently by combustion methods, justified this procedure. Where nitrogen was added, considerable splattering took place. Here it was necessary to analyze for nitrogen by the Kjeldahl method. The ingots were hot rolled at 850°C to about 0.045 in. thick. After hot rolling, the strips were descaled by mechanical grinding, and then given a cold reduction of 5 to 10 pct to insure a uniform thickness throughout the length of the specimen. The edge strips and the tensile strips were annealed in a vacuum of 1x10-4 mm Hg pressure for 3 1/2 hr at 850°C and furnace cooled. Methods of Investigation Hardness Measurements: At least five Vickers hardness measurements were taken using a 10-kg load on each sample in the following conditions: (1) top and bottom of each ingot, (2) top and bottom surface of as-rolled and annealed sheet, and (3) on cross-section of annealed sheet and all quenched specimens. Tensile Tests: Tensile tests were conducted on Baldwin-Southwark testing machines having load ranges of 600 or 2000 lb. Tests were made on 1-in. gauge-length specimens, 3 1/4-in. overall length, 1/2 in. wide, 0.040 in. thick, with a reduced section 1 1/4 in. long and 0.250 in. wide. Two SR-4, A-7 strain gauges, one mounted on each side of the specimen, were used to measure the strain over a limited range to determine the modulus of elasticity. After the modulus of elasticity readings had been taken, load vs. strain readings were taken, using only one strain gauge, at increments of 0.0001 in. until the yield points were passed and then at 0.001-in. increments to the limit of the strain-gauge indicator (0.02 in.). Strain readings above 0.02 in. per in. were taken every 0.01 in., using dividers to measure the strain between the 1-in. gauge marks until the maximum load had been reached. Crosshead speed, when using the SR-4 gauges, was 0.005 in. per min, and, when using dividers, 0.01 in. per min. Flow Curves: Flow curves were determined using the true stress-true strain data obtained during the tension test. The usefulness of this type of information has been dealt with very adequately elsewhere by L. R. Jackson,&apos; J. H. Hollomon,6 and many others. Flow curves of true stress vs. true strain could be converted to the more conventional cold-work curve of 0.2 pct offset yield strength vs. percentage of cold reduction by means of the transformation, 1/1 = 1/1-R, where R is the fraction reduction in cold working. Thus, the true strains corresponding to percentage reduction can be calculated, and the 0.2 pct offset yield strengths scaled off the — 6 curve by taking the true stresses corresponding to the values of 6 + 0.002 strain. Heat Treatment: For the transformation studies, the alloys were heat treated in a horizontal-tube furnace using a dried 99.92 pct argon atmosphere, and quenched into water. Essentially no contamination was found after several hours of heat treatment at temperatures up to 1050°C. Metallography: Specimens were prepared in the

Jan 1, 1951

By E. T. Dumble

In the Bosquejo Geoldgico de Mexico, published in 1897 by the Secretaria de Fomento as Nos. 4, 5 and 6 of the Boletin del Institute Geologico de Mexico, the Director, Jose C. Aguilera, after a detailed account of the geological observations made by himself and his assistants on their several trips through the various districts of the Republic, gives in Part 2 a synopsis of the geology of Mexico, describing . al1 the formations recognized, the rocks comprised in them, their geographical distribution, disturbances, principal eruptions and economic features, as explanatory of the Geological Map of Mexico. In Part 3 Prof. Ordonez describes many of the interesting eruptive rocks of Mexico." This work brings together in a very satisfactory way about all of the published results of geological investigations in Mexico; and although the determinations of the authors with reference to some of the sedimentary deposits are very different from those of other writers, they seem to be based upon good paleontological grounds in each instance. From the map and the text of this paper it appears that the condition of knowledge in regard to the geology of the State of Sonora, at the time of its publication, was about as follows: The western portion of the State, lying between the coast line of the Gulf of California and the foot-hills of the Sierra Madre mountains, is largely Quaternary, interrupted by areas of Azoic rocks and of later eruptives, with two or three limited exposures of limestones of the Cretaceous; while the eastern or

Jan 1, 1900

By John Peperakis, James Quigley

IN 1950 Kaiser Steel Corp. acquired control of the Utah Fuel Co., a pioneer Utah coal concern owning large reserves of high volatile coking coal near Sunnyside, Utah, and large reserves of coal elsewhere in Utah and Colorado. Kaiser Steel later disposed of the noncoking quality reserves included in the property and over the past six years has developed a group of three fully modernized mines and a central preparation plant at Sunnyside. This plant is geared to furnish 1.6 million tons per year of low ash coking coal to the byproduct coke ovens at its steel plant at Fontana, Calif., and to its beehive oven coking plant at Sunnyside. General Problems: Topographic and physical conditions under which Utah coals are found differ from those in most bituminous coal districts of the eastern and central states. Utah coal seams lie under deeper cover, generally at steeper pitches; consider- able distances are burned along the outcrop and back from the surface of the outcrop. Usually the coal seams lie high up on escarpments, accessible only through deep narrow canyons or long rock tunnels and tramways. The topography at Sunnyside is particularly rough, with great changes in cover over the coal in relatively short horizontal distances. This is due to the cliff-making sandstones of the cretaceous Mesa Verde group, the coal-bearing measures being in the Blackhawk formation. The thick massive Castle Gate sandstone of the Prince River formation overlies the coal-bearing rocks and is suspected to be the chief cause of roof control problems.

Jan 10, 1957

By E. C. Dominguez, H. B. Scharf

The Sparrows Point plant of Bethlehem Steel Co., southeast of Baltimore, is the largest Bethlehem plant, with an annual rated capacity of 6.2 million ingot tons. There is considerable diversity of product, but a high percentage is sheet, tin plate, galvanized sheets, and rod and wire. The large amount of light-weight end product requires a number of pickling installations that necessarily consume large quantities of sulfuric acid. In the coking operations sulfuric acid is also consumed in recovery of ammonia as ammonium sulfate and in treatment of recovered light oil derivatives. Total sulfuric acid consumption in the plant is currently approaching 10,000 tons per month, of which 55 to 60 pct is required for pickling. In 1951 the acute sulfur shortage caused grave concern as to future sulfuric acid supply for the Sparrows Point plant. Raw materials for acid making were already at hand in the form of hydrogen sulfide and pyrites sufficient to produce nearly half the sulfuric acid required at that time. It was also known that the Bethlehem mining activities would produce additional pyrites in the future. Late in 1951 Bethlehem management decided to build a 250-ton sulfuric acid plant at Sparrows Point to utilize these raw materials. The plant was built and put in operation in May 1953. The steel plant has expanded considerably since 1951, and it is now necessary to operate the acid plant far over rated capacity in order to supply plant demand. Production of acid in 1954 amounted to 93,000 tons.

May 1, 1956

By Allan D. Taylor

INTRODUCTION From the designer&apos;s view, the installation starts with the first definition of the orebody, and progresses through a long and complex development. The design is affected not only by the characteristics of the ore, but by all of the personalities and events of the project during its development. The following discussion attempts to touch on the most important aspects which define the context in which the designer must work in apply the do&apos;s and don&apos;ts. That context is the basis of the viewpoint. WHAT CAN GO WRONG The Project Is Going Over Budget This is a common and serious concern to the plant designer. The Project Falls Behind Schedule Another common and disturbing condition with which the plant designer must cope. Some Equipment Fails to Perform This can be due to either faulty equipment or operating deficiencies. It can be the result of a wide variety of causes, but the designer will be an interested party in the search for the cause and the cure. The Plant Isn&apos;t Flexible Enough Sometimes a plant will handle some or even most of the ore satisfactorily but is unable to treat another type properly. This can be a significant problem. An example might be a case where low capacity of a cyclone feed pump makes it impossible to accompany an increase in grinding mill throughput with a corresponding increase in dilution water. This could lead to an increase in cyclone feed density, and a loss in product grade or a limit on the plant capacity. Spillage And Cleanup Are Excessive This is one of the most common and annoying defects in metallurgical plants, and one for which the designer can rarely delegate blame. Maintenance Is Excessive Another common complaint in new plants, and also one for which the dedesigner must accept most of the responsibility.

Jan 1, 1982

By R. R. Hartman, W. B. Agocs

In the course of a return flight from Olympia, Wash., to Laramie, Wyo., an airborne magnetometer profile was recorded continuously. The level of flight was controlled at barometric levels along segments of the flight. Barometric altitude was changed from 3000 ft to a maximum of 12,000 ft above mean sea level to take care of topographic variations. Terrain clearance varied from 800 to 7300 ft. Horizontal positions were obtained by recording and tying to cities, towns, airports, river crossings, and other landmarks in the course of the flight. Figs. 1-6 show the course of the flight and the general geologic and tectonic features traversed. The flight line begins south of Olympia, Wash., and proceeds south across the Puget-Willemette depression to the Columbia River. Thence it proceeds eastward along the Washington-Oregon border across the Cascade Mts. and lava flows and the Umatilla basin to Pendleton, Ore. From Pendleton it traverses the Blue Mts. uplift of Oregon in a southeasterly direction, and then to the Boise basin of southwestern Idaho. The flight line swings in an easterly direction as it passes over the Snake River downwarp to the south of the Idaho batholith. It then passes over the northern portion of the Great Basin and the heavily overthrust area at the intersection of the Utah, Idaho, and Wyoming borders. The flight then assumes an easterly course to cross the series of basins and uplifts of southern Wyoming and terminates near the western flank of the Laramie uplift.

Dec 1, 1956

By Eric Jette

THE results of an investigation of the ternary system iron-chromium-ilicon were reported in 1936 by the present authors.1 Partly for the sake of theoretical interest, and partly because of the possible commercial importance of these alloys, the present investigation was undertaken to determine the effect of some of the commoner elements likely to occur, deliberately or otherwise, in such alloys if made on a commercial scale. The elements thus added were carbon, nickel or manganese. The alloys studied were, therefore, parts of quaternary systems. This investigation was concerned primarily with the effect of these additional elements on .the alpha-iron phase and the boundary between this phase region and the alpha plus sigma two-phase region. The sigma phase is a ternary solid solution based upon the compound FeCr. The work was performed mainly by X-ray methods, but a number of microscopic examinations were also made and are reported. While isolated alloys in the composition ranges studied may have been discussed in metallurgical publications, no systematic investigation of any assistance to us was found. Of the earlier work, the investigations on the iron-chromium-carbon system and on the chromium carbides by Westgren and his coworkers,2,3 enabled us to identify the carbide phase. Several articles appeared after the present experimental work had been completed. Lucas and Wintrup4 determined the solubility of carbon ill molten iron-chromium-silicon alloys. Tofaute and his coworkers5,6 have made detailed studies of the iron-chromium-carbon system, which will he referred to later.

Jan 1, 1937

SEC 1 The membership of the Institute shall comprise seven classes, namely 1 Members, 2 Honorary Members, 3 Senior Members, 4 Associates, 5 Junior Members, 6 Rocky Mountain Members, 7 Junior Foreign Affiliates All shall be equally entitled to the privileges of membership, excepting that no member of any class whose residence shall be outside of the United States of America, except those residing in Mexico and Canada, shall be entitled to vote SEC 2 Members A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years&apos; employment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields This shall not apply to Rocky Mountain Members SEC 3 Honorary Members Each candidate for Honorary Membership must be recommended by the Committee on Honorary Memberships and must be elected by ballot at a meeting of the Board of Directors by the unanimous vote of the Directors present, provided, however, that the number of Honorary Members shall at no time exceed twenty Such election shall automatically act as a transfer of such member from any other class of membership to which he may belong SEC 4 Senior Members The Directors may, at the special request of any Member or Associate who has reached the age of seventy years and who has paid

Jan 1, 1952

By AIME AIME

A JOINT meeting of the Canadian Institute of Mining and Metallurgy and the American Institute of Mining and Metallurgical Engineers was held at Spokane, Wash., and Cranbrook and Kimberley, B. C., on Oct. 13 to 16, 1926, with a total attendance at one or another or all of the meetings of about 300 members, ladies and guests. At the opening meeting, on Oct. 13, in the Davenport Hotel, Spokane, about 175 were present. The morning was occupied with addresses of welcome by M. H. Sullivan for the Columbia Section, who called on Mayor Charles A. Fleming, President John F. Davies for the Chamber of Commerce, and E. R. Hannibal, president of the Associated Engineers, each of whom heartily welcomed the visitors. Philip N. Moore, former president, and special representative of President Samuel A. Taylor, replied for the A.I.M.E., and Lewis Stockett, president, and Charles A. Banks, chairman, British Columbia Division, Canadian Institute of Mining and Metallurgy, and Henry M. Parks for the visiting A.I.M.E. sections, made appropriate responses on behalf of those they represented. The members and ladies had luncheon with the Associated Engineers. Philip N. Moore addressed the assembly on "The Opportunity of the Engineer"; an excerpt from his address appears on another page. At the afternoon meeting, with Lewis Stockett in the chair, Frank M. Smith was asked to make a brief statement of the proceedings of the Silver Producers Association in Denver. Supplementing his talk by placing a well-prepared statement on "Silver and the Plan of the Royal Commission on Indian Currency and Finance" in the hands of those present, he narrated what had been undertaken by the Silver Producers Association and what they hoped to accomplish.

Jan 1, 1926

By H. J. Struth

AN unusual engineering achievement in the Gulf Coast last year was the drilling of a wildcat well in the swamps of Louisiana, using direct current. More unusual was the fact that it was necessary to house a diesel engine and generator on a barge in order to supply power. The remoteness of the well made it necessary to transport living quarters and drilling equipment to the location by means of barges, and involved the digging of a canal from a lake to the location, approximated one mile. The drilling equipment used on this well consisted of two generating units, each having one 210-hp. six-cylinder @$-in. bore type VDMA, 600 r.p.m. diesel engine, direct connected to a type CD-169, 125-kw., 250-volt direct current generator, which in turn is direct connected to a type CD-105, 15-kw. 250-volt exciter. One of these motors operates the draw works, one the mud pump, and one a duplicate spare. The generating equipment on the barge was approximately 250 ft. from the derrick, the control wires being brought from the derrick to the generator barge enclosed in a standard fire hose. This is an original idea for confining the con- 11.01 wires in one cable; obtaining minimum space and ample protection. Both control and power lines were suspended on poles. This well was at Lake Grande Ecaille Dome, which was located by seismograph in 1928. Fig. 1 shows the derrick, power barge and living quarters where direct G. E. current was used with rotary drilling equipment.

Jan 1, 1932

By J. A. Hutcheson

NO one questions that it is technically possible to achieve the controlled release of atomic energy in a form that can be converted into heat or electricity. However, before this is actually an accomplished fact a great amount of work must .be done. This work falls into two general classifications: research and engineering development. At present a research program is under way in this country, co-ordinated and directed by the Atomic Energy Commission, which, as time goes on, will uncover fundamental knowledge of this new science that is essential before industrial applications of atomic energy are practical. Undoubtedly therefore, as the store of available knowledge increases, a time will come when answers to the many questions relating to practicality of atomic energy in industry can be determined with reasonable certainty. That the application of atomic energy in industry will eventually be proved practical is assumed. What then are the engineering problems that must be solved before the first practical electric power generating station can be built?

Jan 1, 1948

President Howe: It is, of course, not easy to discuss off-hand the paper which Mr. Becker has presented with so much lucidity. I will only make one remark, which is outside of the line of his argument, and concerns merely a passing allusion in his paper. Mr. Becker speaks of the fact that glass breaks with a flat or conchoidal fracture, and that steel shows a rough or " cupped " surface of frac-

Jan 1, 1895

By R. H. Swallow, George Hess

Aerial photography was once a crude, uncertain tool. Today it is a precision mapping instrument which saves important time and money for strip mining and other industry. Aerial photography began in the boxkite days of aviation. The Army first used it for rough reconnaissance photographs. Then, in the early Twenties, industry began to use aerial photographs of their plants and facilities for advertising or annual reports. The quality of these pictures was not very good by today&apos;s standards, but this work began the development of better cameras, better lenses, better photographic techniques.

Jan 1, 1949

Edward A. UehliNg, New York City (communication to the Secretary*):—In adding my mite to the discussion, I wish to touch on a few points which bear emphasizing and perhaps a little further elucidation. Mr. Grammer says that he "found the electric pig-breaker at Duquesne, if used in connection with the iron-chill, less expensive and more satisfactory " thau the casting-machine. The cost of handling the iron over the Duquesne casting-niachine is about double the average cost of the other Uehling machines at the several Carnegie plants. It is nearly as expensive to run as the Hey1 & Patterson machines, and while Mr. Grammer&apos;s statement is, no doubt, true, as applied to that particular machine and breaker, it should be borne in mind that the machine at Duquesne had embodied in it several new features, which were not improvements; also that it was taxed beyond its economic capacity. The machine at the Lucy furnaces under the management of Mr. Scott handled the output of the two furnaces, and saved

Jan 1, 1905

By A. B. Young

T HE smelting industry in Utah is represented by four plants: The Midvale of the United States Smelting, Refining & Mini.ng Co., the Murray of the American Smelting and Refining Co., the Garfield of the same company and the Tooele of the Inter- na.tiona1 Smelting Co. The first two are lead smelters, the Garfield plant is a copper smelter while the last named embraces both a lead and copper smelter. A total daily smelting capacity of over 10,000 tons is represented, of which 4000 tons is lead smelting capacity. With the exception of Tooele, forty miles distant, all of these smelters are within twenty miles of Salt Lake City. Pyrometallurgical operations in this district are con- fined entirely to the production of unrefined bullion, which is shipped east to the various refineries of the respective companies. The smelting industry in this state had its beginning away back in the latter days of the Civil War, many years before the completion of the trans-continental railroad. Ox teams were still bringing their companies of better fixed Mormon emigrants across the plains to the valley of the Great Salt Lake and those in lesser circumstances were still pushing their hand- carts over the same roads to the temporary abode

Jan 1, 1925

By J. E. Hilliard

AS is well-known, the length per unit volume, Lv, of any lineal feature (such as grain edges in a polycrys-talline specimen) can be estimated from a count of the number of point intersections with a random plane of polish. Specifically:&apos; Lv = 2NA in which NA is the expected number of intersections per unit area of the plane. As with all other measurements in quantitative metallography, the estimation of Lv is subject to a sampling error, the magnitude of which will depend on the number of observations. The analysis is usually performed by counting the number of intersections falling within a closed test figure of known area applied to a succession of different areas on the plane of polish. The test figure can be drawn directly on the screen of a projection microscope or else superimposed on the image of the structure by means of a reticule in a focusing eyepiece of an ordinary microscope. The use of micrographs is very inefficient unless, as in the present study, these are also needed for some other purpose. Consider an analysis in which n applications are made of a test figure within which the expected number of intersections is N. The expected total number of intersections counted is then given by NT = nN If (N) is the standard deviation in N for one application of the figure and if the latter is applied to non-overlapping regions so that the N&apos;s are independent in the statistical sense, then the standard deviation in Nt is given by: a(NT) = a(N)vn Eliminating n from Eqs. [2] and [3] we obtain: Thus, k will be a constant for a given specimen and test figure. From Eqs. [ I] and [4] we find As is to be expected, therefore, the fractional error in the estimation of Lv is inversely proportional to the square root of the total number of intersections counted. It is very desirable to have at least a rough estimate of k before starting an analysis, since it will then be possible to decide in advance by use of Eq. [5J how many counts should be made in order to achieve the desired accuracy in Lv. Without such information the investigator, unless lucky, will either do needless (and tedious) work or else obtain a result with too large an error. It is very easy to calculate k for the limiting case of N — 0, i.e., when the test figure is vanishingly small. In this case there is a negligible probability of two or more intersections falling within the figure. There are therefore only two possible outcomes: a count of one with a probability of, say, p and a zero count with a probability of (I-p). Thus and Therefore: We might expect k to depend on N and therefore on the size of the test figure. Such a dependence was observed2 in the analogous case involving the estimation of grain-boundary area per unit volume by a count of the number of intersections of a test circle with traces of the boundaries on the plane of polish. In this case the theoretical value of k at the limit N — 0 was 1.41. It was also predicted that k would display an initial sharp decrease with increasing N. Experimentally, k was observed to decrease to a value of 0.62 at N - 6 and thereafter remain approximately constant. Furthermore, the value of k for N > 6 was found to be insensitive to the form of the structure provided no pronounced anisotropy or grain-size variation was present. In order to determinewhether k would exhibit a similar dependence on N in the estimation of grain-

Jan 1, 1967