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By G. Sachs, S. I. Liu

Introduction In a previous investigation on the effects of repeated strains of large magnitude on the aluminum alloy 24 ST, it was found that the reduction in ductility by straining in tension was partially restored by a subsequent compression.&apos; As illustrated by the dashed line in Fig I,$ the ductility (e~) retained after prestraining in tension by a certain amount (el) and measured in a subsequent tension test is represented by a straight line sloping down under 4s°. If a compression of the same magnitude as the first tension is inserted (€2 = — €1) between prestraining and final testing in tension, such a "balanced" tension-compression cycle yields a ductility considerably higher than that present after prestraining in tension only. The results of these tests can be correlated with those of an investigation on the effects of prestraining in compression.~ As also shown in Fig I, the ductility in subsequent tensile tests decreased with com- pression, at a rate considerably slower than that after prestraining in tension. The above discussed testing conditions can be considered as special cases of a general straining cycle, consisting of first, straining in tension by an amount el, subsequently straining in compression by an amount e2, and finally determining the retained &apos;ductility, e,, in a tensile test. Prestraining in tension is then represented by el > o and e2 = o. Prestraining in compression is given by e~ = o and e~ < o. Balanced cyclic straining is defined by the condition el > o and cz = — 61. In order to obtain further information on the effects of straining cycles consisting of tension and subsequent compression, further tests were made, varying both the tension strain, el, and the compression strain, e2, within extreme limits; el varied between 0.06 and 0.28 and e2 between — 0.008 and —0.h approximately. Apparently, such tests have not been previously performed. They revealed phenomena which have not been recognized to date, The results of the investigation are herewith reported, without attempting to correlate them with internal processes within the metal structure. However, in order to assist in an analysis of this type, the results have been represented in various manners. In addition, further test data on the effects of prestraining by compression were provided by using specimens of various contours (notched specimens) in the sub-

Jan 1, 1949

By Edmund J. Pryor

DURING the war years restrictions on travel, pressure of work, and the irregular arrival of technical literature from abroad combined to severely isolate Great Britain in a period of intense war expansion of the art and practice of mineral dressing. Many British technicians were fully occupied with the day-to-day problems of improvising substitutes as regular sources of supply failed. and with mastering the strange demands and working conditions of wartime. After a long day spent between ones laboratory and production work, the rest of the waking hours were often filled with fire watching or home guard patrol activities, substituting for a night-shift manager, or "resting" in a dugout while the bombs came down. There was no time for serious study of such technical literature as survived the Atlantic crossing.

Jan 1, 1947

By C. A. Fisher

THE discovery of petroleum in Pennsylvania in 1859 marked the birth of an industry of paramount importance. Spreading from - Oil Creek, this remarkable industry may be said to have embraced the earth in a little more than half a century. Those who made the discovery little realized its deep significance or far reaching influence on our national life. For over sixty years, during which time this nation has created and developed the oil industry to a high state of efficiency and&apos; carried its activities to all parts of the world, we have&apos; at all times been the leaders in the production of crude oil and in the development of its technology. During the unprecedented growth and expanse of the oil industry there has been an increasing dependency of our basic industries on, petroleum, until at present it has become essential to our national existence. To meet the ever increasing demand for petroleum and its products, we have explored, at one time or another, for their oil possibilities, practically all parts of the sedimentary rock area in the United States. Furthermore, detailed surface and, in many places, subsurface studies have been made of all the promising regions; over 640,000 jewells have &apos;been drilled for. oil since the beginning of the industry; $12,000,000,000 have been spent in this work; seventeen major fields exceeding 100,000 bbl. daily production and more than a thousand minor pools have been opened up, and 8,000,000,000 bbl. &apos;of oil have been produced, or an amount nearly equal to the estimated future reserves of the United States made in 1921.

Jan 1, 1925

By Rush Greenslade

THE oil and gas lease is the basic contract of the oil and gas industry; it is the foundation stone upon which the producing industry, particularly, is based. As the industry is precarious and highly speculative, the foundation contract should be of the utmost integrity and certainty. But right there an anomaly exists; the oil and gas lease is the most obscure, most uncertain, doubtful contract in the realm of law today. That is a condition that must be considered when taking oil and gas leases, and when buying, selling, and holding them. It may fairly be asked why should this industry rest upon so insecure a foundation. Why should not the oil industry rest upon the contract that is the basis of all industry, the warranty deed? There are many contributing reasons, but the principal one is business expediency. The Anglo-Saxon idea of ownership of land is that every land owner owns from the center of the earth to the sky all that is above and all that is below-consequently the oil and gas are owned by the person who owns the surface. That idea is not exactly true with reference to oil and gas, for many states have adopted the doctrine that oil and gas are like wild animals; they are fugacious and migratory and belong to the man that traps them. But, except for that doctrine, we believe that oil and gas are owned by the owner of the surface, wherein we differ from the Latin-American countries where the mineral rights are owned by the government. The United States was settled largely by homesteading. The owners of land were, in the main, farmers, who did not have the means or the faith to drill for oil or gas. The operators or speculators did not want to buy the land on the mere possibility of finding oil; hence a compromise resulted by which the land owner gave the speculator or the operator what he called an oil and gas lease, or a right to go upon his land and drill for oil and gas. What is supposed to be the first oil lease placed on record reads as follows: Agreed this 4th day of July, A.D. 1853, with J. D. Angier of Cherrytree township in the county of Venango Pennsylvania that he shall repair up and keep in order the old oil springs on land in said Cherrytree township, or dig and make new springs, and the expense to be deducted out of the proceeds of the oil, and the balance, if any, to be

Jan 8, 1924

By Games Slayter

NO reasonably well-informed person believes that the role of minerals, both metallic and nonmetallic, will be any less important in the future than it has been in the past. The contrary is true. Industrialization is based on mineral resources and man&apos;s ability to make use of them. A nation&apos;s standard of living, its political and military power, will continue to depend largely upon the extent to which it is industrialized-and minerals are the raw materials both of the machine and the power to run the machine. Minerals are also the raw materials of human health and stamina. The world&apos;s healthiest, most vigorous, and most long-lived peoples have always been those that have lived in regions of the globe where the earth is rich, and kept rich, in the phosphates and other minerals required for the production of the so-called growth foods. Only a small proportion of the land surface of the globe is suitable under any circumstances for large-scale production of these and other essential foods. As things stand, only a part of this land is capable of such production either because the soil minerals have been exhausted by cultivation, or because they never existed in the soil in sufficient quantities.

Jan 1, 1943

By A. B. Parsons

AN often repeated criticism of the profession of engineering is that it is as a whole it lacks solidarity. organization, co-ordination, and leadership. Significantly, the critic, are all engineers. Other members of the body politic either do not know about the absence of organization or they do not care. If engineers have no organization they have a plethora of organizations. There exist in the United State, today some 350 societies. institutes. clubs, associations, and councils of engineers and engineering technologists and this number excludes several hundred local chapters of national societies. trade associations, and local engineers&apos; clubs of purely social character- Successful engineers must be proficient in analyzing, planning, and co-ordinating. but it is generally admitted that for their profession as a whole their success in this respect has been indifferent.

Jan 1, 1943

THOSE MARKED THUS * ARE MEMBERS, MARKED THUS t ARE ASSOCIATES THESE SIGNS DOUBLED INDICATE LIFE MEMBERS AND ASSOCIATES RESPECTIVELY THE FIGURES AT THE END OF THE ADDRESS INDICATE THE YEAR OF ELECTION HEAVY FACED TYPE SIGNIFIES HONORARY MEMBERSHIP ` *AARONS, JULIAN B , Mine Supt, The Boulder Deep Levels, Ltd , Boulder, Western Australia, &apos;05 *ABADIE, EMILE R, Cons and Min Engr, 1004 James Flood Bldg, San Francisco, Cal &apos;76 *ABBE, CLEVELAND, JR, GeOl Aid, U S Geological Survey, Washington, D C &apos;00 *ABBOTT, AI ARTHUR, Cerro de Pasco Mining CO , Cerro de Pasco, Peru, So America &apos;95 *ABBOTT, ARTHUR V , Electrical Engr , Westinghouse, Church, Kerr & CO , 8 Bridge St, New York, N Y &apos;82 *ABBOTT, CLARENCE E, Chief Min Engr, Care Fayal Mine, Eveleth, Minn &apos;04

Jan 1, 1910

NEW MEMBERS The following list comprises the names of those persons who became members during the period Mar. 10 to Apr. 10, 1914. Members ADAMS, DANIEL T., Mining 1416 Westminster Bldg., Chicago, Ill. BLICKENSDERFER, FRANK CLEVELAND, Sampler Morenci, Ariz. CAVERS, THOMAS WILLARD, Met Copperhill, Tenn. CLAPP, CHARLES H., Geol Univ. of Arizona, Tucson, Ariz. CLARK, PATRICK T., Pres Bullwhacker Mine, Spokane, Wash. COMSTOCK, HARRY, Mining Mineville, Essex Co., New York. COOKE, JOSEPH H., Gen. Mgr Mono Dev. Co., Gisborn, Tooele Co., Utah. COOPER, DEXTER P., Civ. and Hyd. Engr 101 Park Ave., New York, N. Y. DEGOLYER, E. L., Geol Apartado 269, Tampico, Mexico. DESHAYES, ERNEST F., Mine Foreman Baldy, N. M. DOUGLASS, WILLIAM CRAWFORD, Min. Engr 107 Leonard Hotel, Butte, Mont.

Jan 5, 1914

By J. S. Wakeman

The techniques of testing the physical properties of green pellets produced in a batch balling test are described. It has been found that these physical properties, i.e. drop resistance, wet compressive strength, and plastic deformation under load, are generally related to the moisture content of the wet balls. A "criterion" method of analyzing data from a series of batch tests is discussed. This method facilitates the comparison of results of various test series. A time-sharing computer program, which correlates the test data from a batch series, generates the "criterion" values for subsequent comparison and analysis, and produces X, Y plots of the various moisture-strength relationships, is presented. Examples of computer output and use of the "criterion" evaluation method are given.

Jan 1, 1973

By AIME AIME

THOUGH Frank Wardlaw was born in the East- at Schroon Lake, N. Y., on July 14, 1887-and was educated in New York City-Columbia, E.M., 1916 he has spent his entire professional life in the West, and is still there, as assistant general manager of the Inspiration Consolidated Copper Co., in Arizona. His first jobs were as miner and surveyor for the Utah Consolidated Mining Co., at Bingham, where he worked under A. S. Winther, now general manager of Inspiration&apos;s adjoining big neighbor, the Miami Copper Co. After rising to the position of chief engineer and geologist, Mr. Ward- law left Utah Consolidated to go to Chile for two years with the Braden Copper Co. Then he returned to his

Jan 1, 1940

By W. C. Phalen

E. G. SPILSBURY; New York, N. Y.-I would like to emphasize what Mr. Phalen says in his paper regarding the possible utilization of the waste acids in the West for the acid concentration of phosphate rock, and to call attention to the fact that this is already being done by Mr. Laist at Anaconda, who is producing concentrated phosphoric acid from these low-grade rocks. During the last year, he has not been able to carry this along to the extent he, had expected, owing to the tremendous demand which they have had for all the acid they can produce, so instead of having a. surplus of acid, as was expected, they are really short of this material for their electrolytic copper and zinc work.

Jan 4, 1917

John Langton, New York, N. Y. (communication to the Secretary*):—In Mr. Firmstone&apos;s discussion (Trans., xli., 912) the formula he gives for the periodical payment—his equation (2)—may be simplified in form. The expression given by Mr. Firmstone is : q=S(l+ r) 1-(1+r)-(1+r) r which is a simpler form to use in calculations. Where S= principal to bc extinguished. Q = periodical payment or charge for sinking-fund, r = rate of interest per period (i. e., interest on $1 per period). n = number of payments or periods. Kent&apos;s Mechanical Enyineer&apos;s Pocket Book, under the heading Annuities, equation No. 5, gives : " The annuity which $1 will purchase for any number of ytlars n is * Received Jiily 16, 1911.

Jan 1, 1912

By C. H. Samans, G. F. Tisinai, J. K. Stanley

The addition of nitrogen (0.10 to 0.20 pct) to Fe-Cr-Ni alloys of simulated commercial purity results in a real displacement of the u phase boundaries to higher chromium contents. The effect is small for the (Y + s)? boundary, but is pronounced for the (y + a +s)/(y + a) boundary. Although there is an indication of an exceptionally large shift of the n boundaries to higher chromium contents, especially in steels with nitrogen over 0.2 pct, the major portion of this apparent shift results from the fact that carbide and nitride precipitation cause "chromium impoverishment" of the matrices. The effect of combined additions of nitrogen and silicon to the Fe-Cr-Ni phase diagram is demonstrated also. Nitrogen can nullify the effect of about 1 pct Si in shifting the (y + o)/? phase boundary to lower values of chromium at all nickel levels from 8 to 20 pct. NItrogen can nullify this U-forming effect of about 2 pct Si at the 8 pct Ni level, but not at the 20 pct Ni level. The alloys studied were in both the cast and the wrought conditions. There are indications that the u phase forms more slowly in the cast alloys than in the wrought alloys if both are in the completely austenitic state. The presence of 6 ferrite in the cast alloys accelerates the formation of U. Cold working increases the rate of o formation in both cast and wrought alloys. THE major improvement in Fe-Cr-Ni austenitic alloys in recent years has been in the addition or removal of minor alloying elements to facilitate better control of corrosion resistance, sensitization, and heat resistance. One shortcoming of the austenitic Fe-Cr-Ni alloys, which never has been completely circumvented, is their propensity toward u formation. In the AISI-type 310 (25 pct Cr-20 pct Ni) and type 309 (25 pct Cr-12 pct Ni) steels, sufficient amounts of u phase can form, if service or treatment is in a suitable temperature range, to cause severe embrittlement. Also, there is a growing conviction that this phase may be contributory to some unexpected decreases in the corrosion resistance of certain of the 18 pct Cr-8 pct Ni-type steels. The present paper discusses the effect of nitrogen additions on the location of the (r+u)/d and the (y+a+u)/(y+a) phase boundaries in the ternary Fe-Cr-Ni system, for cast and wrought alloys of simulated commercial purity, and in similar alloys containing up to about 2.5 pct Si. The objective is to define compositional limits for alloys which will not be susceptible to u formation when used near 1200°F (650°C). An excellent review of the early studies of the u phase in the Fe-Cr-Ni system has been compiled by Foley.1 Rees, Burns, and Cook2 have determined a high purity phase diagram for the ternary system, whereas Nicholson, Samans, and Shortsleeve3 are- stricted themselves to a portion of the simulated commercial-purity phase diagram. Both groups of investigators show almost an identical position for the commercially significant (y+u)/y phase boundary. Further comparison of the work of the two groups indicates that, below the 8 pct Ni level, the commercial alloys have a decidedly greater propensity toward u formation than the high purity alloys. The two groups of workers agreed that both the AISI-type 310 (25 pct Cr-20 pct Ni) and the type 309 (25 pct Cr-12 pct Ni) steels are well within the (y+~) region and that the 18 pct Cr-8 pct Ni-type alloys straddle the U-forming phase boundaries. Nicholson et al.3 showed, in addition, that these boundaries shift toward lower chromium contents if greater than nominal amounts of silicon or molybdenum are added. The effect of nitrogen on the location of the s phase boundaries in the Fe-Cr-Ni system has not been known with any certainty. In 1942, an approach to this problem was made by Krainer and Leoville-Nowak,&apos; but at that time they apparently were unaware of the slow rate of s formation in strain-free samples and aged their samples for insufficient times, e.g., 100 hr at 650°C (1200°F) and 800°C (1470°F). For this reason, it would be expected that their (y+ u) /y boundary would be shifted toward lower chromium contents (restricted ?-field) when equilibrium conditions were approximated more closely. Procedure for Studying the Alloys The alloys used were prepared in the following way: Heats of 200 lb each were melted in an induction furnace. A 5 lb portion of each heat was poured into a ladle containing an aluminum slug for de-

Jan 1, 1955

Organization Place Date 1919 American Chemical Society Philadelphia, Pa. Sept. 2-6 National Assn. of Stationary Engineers Huntington, W. Va. Sept. 8 American Peat Society Minneapolis, Minn. Sept. 22-24 American Iron, Steel Electrical Engineers St. Louis, Mo. Sept. 22-26 American Institute of Min. and Met. Engineers. Chicago, Ill. Sept. 22-27 American Steel Treaters&apos; Society, First Annual Convention Chicago, 111. Sept. 22-27 National Exposition of Chemical Industries.... Chicago, Ill. Sept. 22-27 National Safety Council Cleveland, O. Sept. 29-Oct: 2 American Foundrymen&apos;s Association Philadelphia, Pa. Sept. 29-Oct. 4

Jan 9, 1919

By Spencer S. Shannon

This chapter is concerned with the uses, geology, exploration, evaluation, preparation for markets, and future of 90thorium and 39yttrium, along with 14 rare-earth elements. The rare-earth metals or lanthanides were divided into three categories by Berzelius. The cerium subgroup is comprised of 57lanthanum, 58cerium, 59praseodymium, 60neodymium, and 62samarium. 61Promethium does not occur naturally. The terbium subgroup includes 63europium, 64gadolinium, and 65terbium. The remaining lanthanides are placed in the yttrium subgroup. Strictly speaking, yttrium is not a rare earth. Because the properties of yttrium resemble those of heavy rare earths, its name has been used as a designating adjective. The yttrium subgroup includes 66dysprosium, 67holmium, 68erbium, 69thulium, 70ytterbium, and 67lutetium. Rare-earth elements, especially those of the same subgroup, tend to occur together rather than in discrete minerals.

Jan 1, 1975

By Brian F. Osborne

A continuous on-line particle-size analysis system for solid/liquid suspensions is described. The basic sensor utilizes a centrifugal principle to separate particles according to size, the resultant separation being measured by means of beta-ray attenuation. Results obtained when analyzing a variety of materials at sizes from 65 mesh (210 µ) to 20 w are discussed in detail. Accuracies better than 2% are demonstrated. The effects of particle specific gravity, and mixtures of materials of diverse specific gravities, are discussed from both a practical and a theoretical viewpoint. It is demonstrated that particle specific gravity has a minimal effect on the size reading obtained. This renders the instrument suitable for handling materials where the ratio of light to heavy component may change. The design of the first commercial installation of this instrument is described in detail. This installation will be capable of analyzing three streams in sequence, measurement at three particle sizes being effected on each stream.

Jan 1, 1975

By R. Moldenke

The presence of nickel-chromium in pig iron made fro111 Cuban oles is so well known that the word "Mayari" is unconsciously associated with it. Since 1904, when exploration of the Mayari deposits of iron ore in northeastern Cuba was undertaken, there llas been increasing interest in these ores. Tlie Transactions contain numerous references to t1ieln.l This iron ore, which is shipped to the Tinited States in the nodulizecl state, has been thoroughly tested and found very valuable; the deposit covers over 25,000 acres and there is in sight over 500,000,000 tons of ore that, by systematic mining, runs practically constant in composition. With nickel and chromium present, also titanium in sufficient quantities to attract attention, as well as extremely low phosphorus and sulfur contents, the iron founder is naturally interested in the utilization of RInpari ore for pig iron for the better grades of finishrtl iron products. The present point of coilsn~iil)tion ol ILlapri ore is at Sparrow&apos;s Poi111, where hlayari pig iron of ally desiretl coml>osition is made. The composition of the dried ore is about as follows: Iron -29 per cent., silica 3 pc.r cent., nickel 1 per cciit., chroiniun~ 1.5 per cent., alumina 11 per cent., ant1 coinbined water 13 per cent. When nodulized, the iron runs up to nearly 56 per cent., the silic:~, :tlumi~i:i, nickel, and c~llromiurn are slightly highr than the arno~l~its just given. Practically all the, combined wntcr is driven off aild the iiodulizccl ore carries only a few- tenths per cent. of 1 C. M. Weld: Residual Rrolvn Iron Ores of Cuba. Tmns, (1909) 40, 299. C. K. Leitll nnd If&apos;. J. Mcncl: Origin of Iron Ores of Central and Northeostr~n rlbn. Trans (1911) 42, 00. C. W. Hayes: May:~ri and Mos Iron-ore Deposits in Cuba. Idem, 109. J. E. Little: Maynri lron Mincs, as Developed by the Spanish-American Iron (&apos;0. Idem, 152. J. F. Iie~np: M&apos;ryari Iron-ore Dcposi(s. Trans. (1915) 61, 3. C. K. Leith 2nd N. J. Mead: Additional Data on Origin of Lateritic Iron 01cs or Eastern Cubn. Tmns. (1916) 63, 75.

Jan 1, 1923

By R. Moldenke

The presence of nickel-chromium in pig iron made fro111 Cuban oles is so well known that the word "Mayari" is unconsciously associated with it. Since 1904, when exploration of the Mayari deposits of iron ore in northeastern Cuba was undertaken, there llas been increasing interest in these ores. Tlie Transactions contain numerous references to t1ieln.l This iron ore, which is shipped to the Tinited States in the nodulizecl state, has been thoroughly tested and found very valuable; the deposit covers over 25,000 acres and there is in sight over 500,000,000 tons of ore that, by systematic mining, runs practically constant in composition. With nickel and chromium present, also titanium in sufficient quantities to attract attention, as well as extremely low phosphorus and sulfur contents, the iron founder is naturally interested in the utilization of RInpari ore for pig iron for the better grades of finishrtl iron products. The present point of coilsn~iil)tion ol ILlapri ore is at Sparrow&apos;s Poi111, where hlayari pig iron of ally desiretl coml>osition is made. The composition of the dried ore is about as follows: Iron -29 per cent., silica 3 pc.r cent., nickel 1 per cciit., chroiniun~ 1.5 per cent., alumina 11 per cent., ant1 coinbined water 13 per cent. When nodulized, the iron runs up to nearly 56 per cent., the silic:~, :tlumi~i:i, nickel, and c~llromiurn are slightly highr than the arno~l~its just given. Practically all the, combined wntcr is driven off aild the iiodulizccl ore carries only a few- tenths per cent. of 1 C. M. Weld: Residual Rrolvn Iron Ores of Cuba. Tmns, (1909) 40, 299. C. K. Leitll nnd If&apos;. J. Mcncl: Origin of Iron Ores of Central and Northeostr~n rlbn. Trans (1911) 42, 00. C. W. Hayes: May:~ri and Mos Iron-ore Deposits in Cuba. Idem, 109. J. E. Little: Maynri lron Mincs, as Developed by the Spanish-American Iron (&apos;0. Idem, 152. J. F. Iie~np: M&apos;ryari Iron-ore Dcposi(s. Trans. (1915) 61, 3. C. K. Leith 2nd N. J. Mead: Additional Data on Origin of Lateritic Iron 01cs or Eastern Cubn. Tmns. (1916) 63, 75.

Jan 1, 1923

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith&apos;s data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy&apos;s obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:&apos;l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969

By Robert :H. . Lesemann

I recently gave a talk at a seminar on mine development in the Eighties. I had to present CRU&apos; s long-range market outlook for copper, lead, zinc, nickel, molybdenum and silver. In reviewing the recent history of each metal, and our projections, I tried to find some common pattern of behavior that could prove a guide in projecting future market behavior. When you sweep aside your input-output models and econometric equations, what you seem to be left with is this: "When a market goes through a prolonged period of price weakness, you can usually look forward to a period of considerable improvement. " "When a market goes through a prolonged period of price strength, you can always anticipate a prolonged period of price weakness." Stated another way, "The better things are, the worse they will get."

Jan 1, 1982