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By L. G. Austin

If S (x) is the specific rate of breakage of size x and B (x, y) (see Table 1 for Nomenclature) is the cumulative breakage distribution function, the Herbst Fuerstenau2 assumption is that Inserting this assumption into first-order grinding equations it has been shown" that there are then simple analytical solutions to the grinding equations, as shown in Table 2. In this context "plug flow" is defined as all material passing through the mill in the same length of time, the residence time t. The term "n fully-mixed" means that the mill has a residence time distribution" which can be treated as if the mill were n equal fully mixed sections in series. In addition it has been shown that the assumption of Eq. 1 also leads to simple analytical solutions for closed-circuit, steady-state grinding with an ideal classifier at the mill exit returning oversize to the mill feed. The solutions are also given in Table 2, with µ as the ideal classifier cut size, C the circulation ratio, and Q (x) the size distribution of the circuit product. The specific surface area of these size distributions is where the density-shape factor k. is assumed to be constant with size. In practice, most methods of size analysis or area [ ] measurement have a finite lower limit, so that the integration is really performed from xm, to xm, For a realistic degree of grinding the value of So is dominated by the fine sizes because of the 1/x factor. Consider batch grinding of a feed of size y to y + dy. The batch grinding solution given in Table 2 is then [ ] The fresh surface area produced is the area of the fines plus the area of the original material remaining minus the area of the original material, [ ] Little error is introduced by neglecting the last term on the right-hand side since at t = 0 it is zero, and when t is significant the first term dominates because of the fine sizes produced. In addition, the form of P (x, t) for [ ] realistic values of S (x) 2t ax° is such that the major fraction of fresh surface produced is contained within the bottom 10% of weight of broken material, that is, for sizes for which P(x, t) < 0.1 (providing y is not near x.,). Thus for surface area purposes Eq. 3 can be approximated by [ ] becomes providing again that the feed sizes are coarse relative to xmi. Then the fresh area production is and W is the mass in the mill. The rate of surface production is WK, and the specific surface is Kt. From Table 2, the specific energy is mt/W so surface production per unit energy is [ ] Surface produced per unit energy input = KW/m (8) where m is the energy input of the mill. Clearly, identical reasoning applies to open-cycle, plug-flow grinding, with t replacing t, and Eq. 8 is obtained again. Considering open-cycle, fully mixed grinding, similar reasoning gives P(x) - t S(x) for surface area purposes, and

Jan 1, 1974

By Yeatman, Pope

FOR many years geologists have felt that mining companies should adopt a more liberal policy in the publication of their reports. The increasing usefulness of the geologist to the mining profession in recent years demands that consideration be given to this question. Prior to 1900, the call for geologists of high reputation by mining companies was probably mainly in connection with lawsuits arising from the interpretation of rights or ownership as defined by the "Law of the Apex," and from problems such as finding the continuation of the vein or whether the vein followed was the main one or a branch. Later, outside of legal questions, the most intensive and general use of their services arose from the search for oil. Geologists to determine the position of the formations

Jan 1, 1938

THE CHAIRMAN.- This meeting is under the auspices of the American Institute of Mining and Metallurgical Engineers, and I think the germ of the idea originated in the steel business. Last year there was a meeting of prominent people in the steel industry with the idea of getting together and discussing practical phases of their business, so that everybody could contribute and from that there might be benefit derived for the industry. Several months ago when Mr. Bain was in Salt Lake City, he and Mr. Oldright asked me what I, as an individual, thought of it. From that originated this idea of having the copper people come together to discuss reverberatory smelting and all its phases. In starting out, it seemed the best plan to ask members what particular subjects they wished to discuss first; that is, the ones that would be considered more important. We asked Mr. Oldright, or suggested sometime ago that the meeting be postponed until May because May is a lovely month in Salt Lake. There are a number of attractive features around the city. We have a number of smelters here and I think that probably the most of the benefit will be derived from talking in an informal way and visiting the various plants around. the valley. At any rate, speaking as a resident of Salt Lake, I am glad to see all of you gentlemen here, and hope you have an interesting and instructive time. The tentative list of subjects for discussion at this conference is as follows: Construction Walls, etc. Walls, proper design and thickness of brick for various types of charging. Bottoms, construction of. Binding steel, correct weight and arrangement, where thrust of arch should be taken. Refractory materials, feasibility of using different material in various parts of the furnace. Water jackets, where applicable. Should bricks be used inside of same. Gas space, proper design for, height of roof above bath, etc. Roof Shape of Roof, in hot zone and elsewhere, longitudinally. Construction of roof, in various zones, around openings.

Jan 1, 1930

By Paul W. Zimmer, Carl E. Dutton

Iron ore in the Menominee district is mined from two iron-formations of middle Precambrian age. The older formation is present in the northeastern part; is composed mainly of hematite, magnetite, quartz, and minor silicates; and contains about 34 per cent iron. The rock has been so coarsened by meta- morphism that concentration of magnetite and hematite is feasib!e, and pellets containing more than 60 per cent iron are being produced. The older formation is also present in the southeastern part where it has 1:een only slightly metamorphosed. Ore containing more than 50 per cent iron was formerly mined from local residual concentrations of iron oxides from which silica had been sufficiently leached, or replaced by iron oxide, or affected by combinations of these processes. The younger iron-formation occurs in the western part of the district and, if unaltered, is interlayered siderite and chert. The ore in this area also contains more than 50 per cent iron and formed as local residual concentrations but in two stages. The siderite was converted to iron oxides (hematite and "limonite"), and silica was contemporaneously or subsequently removed by leaching, or replacement, or combinations of these processes.

Jan 1, 1968

By J. M. Sands

THE state of Kansas had a daily average crude-oil production of about 87,000 bbl. at the beginning of the year. This showed a steady but consistent decline during the 12 months, so that the daily average production at the end of the year was slightly over 68,000 barrels. GREENWOOD COUNTY THE most active development in Kansas during the year was in Greenwood County, in a line from near Sallyards in T 25-R 9 to east of Madison in T 22-R 11. The main part of this development has been in a succession of pools beginning at the south with the Polhamus pool in 34-24-9 and 3 and 4-25-9; Thrall pool in 28, 29, 32 and 33-23-10; Burkett pool in 13, 23, 24 and 26-23-10; Seeley and Wick pool in 22, 27, 28,. 32 and 33-22-11 and 5, 6, 7, and 8-23-11; Frohm pool in 11, 14 and 15-22-11; Madison pool in 31 and 32-21-12 and 6, 22, 12 and 1-22-11. Some of these pools have two or more sands, locally called Bartlesville and Burgess Sands. They range in depth from 1850 ft. near Madison to 2450 ft. near Sallyards, the general dip being to&apos; the west. The thickness of these sands run from 20 to 100 ft., the initial production of the wells being 50 to 1000 bbl of 40-gravity oil or better.

Jan 3, 1924

There were present twelve- Directors, the Secretary and the Assistant Secretary of the Institute, and fifteen guests. A committee of three was appointed to draft a suitable resolution of memorial of the services of Joseph Esrey Johnson, Jr. The committee consists of Joseph W. Richards, Chairman, J. V. N. Dorr and Allen H. Rogers. William R. Walker was elected a Director in place of J. E. Johnson, Jr., and Edwin Ludlow was elected a member of the Executive Committee in his stead. George C. Stone was appointed Chairman of the Committee on Membership in place of Mr. Johnson. The following resolutions were then adopted: RESOLVED, That a special business meeting of the Institute be and the same hereby is appointed to be, held at the office of the Institute, No. 29 West 39th Street, Borough of Manhattan, City of New York, on the 27th day of June, 1919, it 8.30 o&apos;clock in the P. M. to consider and take action upon the proposal to change the name of the Institute to "American Institute of Mining and Metallurgical Engineers, Incor-porated," and the further proposal to extend the corporate purposes of the Institute so that it shall, in addition to its other powers, be empowered to promote the arts and sciences connected with the economic production of the useful minerals and metals, and the welfare of, those employed in these industries, by all lawful means.

Jan 6, 1919

By Robert T. Gdagher, Allison Butts

EDUCATIONAL trends as reflected in curricular changes are of interest and importance in engineering educa¬tion both as matters of record and as considerations for the future. The data on which the evidence of this report is based were obtained by sending questionnaires to all schools in the United States granting the undergraduate degree in mining engineering, metallurgy, or metallurgical engineering. The questionnaire had two parts, one inquiring as to the general nature of revisions made or planned, and the other asking for information on specific courses added to or dropped from the curriculum, or given more or less time than formerly. The frequency with which curricular changes are made, even in normal times, is notable. Although it was expected that the period since 1939-40 would show numerous revisions, it was somewhat surprising to find that of 62 mining or metallurgical curricula in existence in 1939-40 and reported in the present survey, 58 had been revised or are shortly to be revised, 52 having already been changed during this period. Moreover, approximately half of the mining schools that have already revised their curricula, and probably a similar proportion of the metallurgical schools, are about to make further important changes.

Jan 1, 1948

By J. C. Bradley

The relation of annealing temperature to conductivity of copper wire has been determined. Conductivity hard was 98.26 per cent. After a 10-min. heat,ing at 200" C. it was 98.69. By annealing 10 min. at 300" C. a large increase, to 100.93, occurred. Maximum conductivity, 101.15, was attained after a 500" C. anneal; thereafter it decreased to 100.53 after a 950" C. anneal. If copper is gassed the decrease is much more than this. Material and Method The work was done on high grade electrolytic copper, 99.942 per cent, copper plus silver, silver 0.0008 per cent. It was hot-rolled to 1/4 in., then cold drawn to 0.080 in. The wire was cut into 25 5-ft. lengths and numbered 1 to 25 as cut. Four samples were tested hard. The others were wound into 5-in. diameter coils. For the 100" C. heating a coil was put into water, the water brought to . boiling, and the wire kept at this temperature for 10 min. For the higher temperatures the coils were placed in envelopes of sheet copper, a little water added, and the envelopes sealed by folding over the edges twice, and hammering them together. This kept the air out very well. The envelope and wire were brought to the desired temperature; this was maintained for 10 min., then the whole was water-quenched. Results Data from the tests are shown in the table and plot (see Fig. 1); conductivity is referred to the International Annealed Copper Standard at 20" C. Conductivity hard is considerably less than conductivity soft.1 The increase is sharp when the wire anneals. The maximum, 101.15 per cent, in the particular material used, comes at 500º C.; thereafter the conductivity falls to 100.53 per cent. after 950" C. annealing, a drop of 0.62 per cent.

Jan 1, 1927

By F. B. Sherman, Keros Cartwright

Sanitary land filling has become one of the most widely used methods of disposing of solid refuse. A principal concern of regulatory agencies and the public itself is that landfill operations do not degrade the physical environment, including water resources, and the ground-water reservoir in particular. Knowledge of ground-water and engineering geology can guide landfill operations into suitable terranes or develop measures to compensate for natural limitations at a particular site. Experience and research in Illinois suggest four activities relating to landfill disposal that warrant attention by geologists and engineers: (1) regional delineation of favorable and unfavorable hydrogeologic conditions to facilitate planning and preliminary screening of potential landfill sites; (2) site evaluations, with considerations of geologic materials, topography, water levels, flow systems, and local occurrence and use of water resources; (3) research on aspects of the hydrogeologic environment that control effects of, or are modified by, landfills; and (4) formulation of practices in the siting, construction, and operation of landfills that prevent, mitigate, or isolate deleterious effects. The first two activities are basically in the domain of earth science, requiring the application of fundamental concepts of geology and hydrology and conventional site-exploration methods. The third activity, research, requires contributions from geology as well as other disciplines, including soil physics, sanitary engineering, and chemistry. The fourth calls for policy decisions by regulatory agencies and elected officials, using the contributions of scientists and engineers. Throughout history, man has disposed of unwanted materials by dumping. As urbanization has increased, haphazard dumping practices have given way to disposal under more controlled conditions because of increasing congestion of population and production of waste and greater concern for public health and environmental amenities. Many states and communities have already outlawed open dumping and open burning of refuse. The only practical methods of disposal of large volumes of refuse, therefore, are contained, high-temperature incineration, or burial in a sanitary landfill. In Illinois, regulation of solid waste disposal has been delegated to the Environmental Protection Agency. Each session of the legislature since 1965 has passed increasingly strict laws regulating waste diposal. As a result, the work of evaluating sanitary landfill sites has increased significantly for both the Department of Public Health, now the Environmental Protection Agency, and the Illinois State Geological Survey, which advises the Agency on matters of ground-water geology and pollution. In fact, our ground-water staff spends as much time on studies relating to waste disposal, primarily sanitary landfills, as on ground-water resource studies. Many other geological agencies are experiencing similar demands for increased assistance in solving waste-disposal problems. This paper summarizes some of the salient features of the sanitary landfill concept, describes activities of the Illinois Geological Survey in ground-water and engineering geology relating to landfills, and suggests policies that need consideration. A sanitary landfill is located and operated in such a way that vermin and pests, nuisances, and degradation of air and water are kept at acceptable levels. Some of the physical requirements of a sanitary landfill are all-weather roads for year-round access, fences to retain blowing paper, a daily cover of at least six inches of suitable earth material, and a final cover of at least 2 ft of earth material. Dumping into or adjacent to standing water generally is not allowed. Two common operating techniques are used. In the first, trenches are dug, the refuse is placed in them, and the earth removed from the trenches is used to cover the waste. In the second method, area fill, refuse is placed in low ground and covered with earth from adjacent high areas. The hydrology of the site is a prime consideration in locating sanitary landfills. Putrescible refuse, if saturated above field capacity, produces a leachate that usually has a high concentration of dissolved solids.2 As the leachate also acts as an agent for transporting bacterial pollutants, it constitutes a potential pollution hazard. To reduce the production of leachates, the topography of the landfill area should be such that surface water will not flow into or through the fill. Operations that will result in refuse disposal below or near the highest known water-table elevation may be required to take corrective or preventive measures to protect the ground water. In practice, under humid conditions such as prevail in Illinois, locations where disposal can take place above the water table are relatively few because surficial materials are commonly fine-grained, which permits slow gravity drainage and results in high degrees of saturation (100% moisture content) near the surface. At some sites, although disposal has taken place above the water table, ground-water mounds have developed, resulting in permanent saturation of the refuse. Permeability barriers usually are required to protect the ground-water reservoir from degradation by leachates. The convention in Illinois is to have a minimum of

Jan 1, 1972

R. F. MCELVENNY.- Over 20 years ago I went back East on a little tour of copper companies to see how copper was handled and fabricated, and I met a Mr. Bassett who took me through the Waterbury branche of the American Brass Co. I have not seen this gentleman for 20 years, but I have a letter from him that I would like to read to you. &apos;The American Brass Co. Waterbury, Conn. May 19, 1930. To the-Salt Lake City Conference on Reverberatory Smelting Practice: Through the courtesy of Mr. Scott Turner, Director of the U. S. Bureau of Mines, Mr. G. L. Oldright has been temporarily released from his regular duties to act as your secretary. We have asked him and Mr. McElvenny to make the necessary preliminary arrangements and to present to you at the opening session the greetings of the officers and&apos; directors of the Institute. I am very glad that it has been possible for you to come together under the auspices of the Institute and that the acceptance of our invitation has been so very unanimous. Such an acceptance of the invitation to this meeting indicates your interest in getting together for an exchange of technical data and ideas. We anticipate that this meeting will be of real service to the smelting industry through your open discussion and exchange of ideas, and we sincerely hope that you will form an organization which will arrange for future meetings of a similar nature. While it probably may not be desirable to. distribute the minutes of this conference except to the members who take part in it, we hope that later the Institute publications may be enriched by such matter as you think it desirable to have published; and also, that some of you may be able to offer technical papers for the Institute publications. I hope that you will find a permanent organization desirable and trust that it will be possible for you to form such an organization so that conferences may be regularly called. We hope that you can make use of the Institute organization and that we can be of real service to your industry. With best wishes for your success in this undertaking, I am Most cordially yours, W. H. Bassett, President.

Jan 1, 1930

By P. A. Beck, M. V. Nevitt

All binary and a number of ternary u alloys formed by first long period transition elements were examined and found to be ferromagnetic at low temperatures. The Curie temperatures for these alloys were measured. It was found that the correlation of the Curie temperature with composition may be described qualitatively in terms of the contributions of the various component atomic moments to the saturation moment of the alloy. Ternary Fe-Cr-Mo u phase alloys were also found to be ferromagnetic, with a Curie temperature dependent on the iron content and largely independent of the unit cell dimensions. Similar relations were found for the Co-Fe-Cr and the Co-Cr-Mo a alloys, where the Co + Fe content appears to determine the Curie temperature. RECENTLY, it has become increasingly evident that the u phase is some kind of an "electron compound." Several papers1-&apos; discussed the empirical correlation between the composition of the various u phases in alloys of the transition elements and the distribution of electrons in the partially filled d-levels of the component atoms. However, a picture of the latter can be formed only in a more or less intuitive manner, as in the Pauling theory," and the rigorous treatment of these problems is at present prevented by lack of adequate knowledge of the electronic structure of the transition elements in the metallic state. It appeared reasonable to expect that investigation of the magnetic properties, which are related to d-shell electrons, may help in clarifying the physical nature of the foregoing empirical correlation. Qualitative tests of samples of various compositions have shown that certain u alloys become ferromagnetic at liquid nitrogen temperature." The present investigation was undertaken to determine whether or not low temperature ferromagnetism is characteristic of a large variety of u alloys and to establish how the Curie temperatures of ferromagnetic u alloys are influenced by changes in composition and in lattice parameter. In the first portion of the in- vestigation, Curie temperatures were measured for a series of u alloys containing either vanadium or chromium with one or two of the elements manganese, iron, cobalt, or nickel. In the second phase of the work, data were obtained on the Curie temperature of ternary (Fe, Co, Cr)a, (Fe, Cr, Mo)a, and (Co, Cr, MO)U alloys, as a function of composition and of interatomic spacing. Experimental Procedures High frequency vacuum melting in high purity re-crystallized alumina crucibles was employed in the preparation of the u alloys, using metals whose lot analyses are given in Table I. Approximately two-thirds of the alloys were analyzed chemically, the analytical results being in acceptable agreement with the intended compositions, as seen in Tables I1 and 111. The specimens were annealed for homogen-ization in an atmosphere of purified 92 pct He and 8 pct H, mixture or in evacuated and sealed Vycor tubes at temperatures from 780" to 1300°C, depending on the temperature range of the u phase field for the particular composition. The annealing temwerature and time for kach alloy are given in Tables 11 and 111. Curie points were determined by an induction method; the change with temperature of mutual inductance between two coils was observed when the i-u specimen was inserted into the flux path between the coils. The transformer consisted of three coils each containing 1200 turns of 0.0050 in. diam enameled copper wire. The center coil, P in Fig. 1, served as the primary coil, and was linked magnetically with each of the two secondary coils, S, and S? which were connected in series opposition. The primary coil, P, was energized by an audio-oscillator, set at a frequency of 500 cycles per sec, while the signal from the transformer secondary circuit,

Jan 1, 1956

By F. C. Canney

Geochemical prospecting seeks hidden mineral deposits by sampling for variations in the chemical composition of naturally occurring materials. Usually the samples are of soils and other products of weathering and erosion—surface materials extremely susceptible to contamination by human activities. Except when a survey is conducted well away from populated areas, contamination is an ever-present hazard. The program&apos;s success is particularly endangered when the contaminants are the elements sought; if these occur erratically throughout an area, spurious anomalies completely unrelated to mineralized areas can be formed. Evenly distributed contamination can be dangerous too, if it raises the background to such a level that true anomalies can no longer be easily detected. Suppose, for example, that in an area where the lead background is 20 parts per million the soil over a lead vein contains 1000 ppm of lead. Here the contrast would be 50 to 1, which is very satisfactory for geochemical surveying. Now if 1000 ppm of lead from some source were added evenly to the soil in this area, the contrast would be reduced to about 2 to 1, and the anomaly would no longer be readily detectable because a threshold of significance twice the value of the background is the minimum generally used for interpreting geochemical data. Of the many possible sources of contamination, probably most important are smelter fumes, which may distribute large quantities of metal contaminants over many square miles of ground. For several reasons, the investigation reported here was begun in the Coeur d&apos;Alene district in northern Idaho: 1) a lead smelter has been operated in this district since 1917 and an electrolytic zinc plant since 1928, and presumably the contamination patterns are strongly developed; 2) to evaluate the usefulness of certain geochemical techniques, V. C. Kennedy and S. W. Hobbs of the USGS had already studied the distribution of copper, lead, and zinc in the soils (both in background areas and other veins) and in the water and plants, providing a criterion for measuring the magnitude and effect of soil contamination; 3) one of the economically important parts of the district lies south of the South Fork of Coeur d&apos;Alene River and within a radius of five miles of the reduction plants near Smelterville (Fig. 1). In this area, and in the entire district, conventional methods of prospecting are hindered by heavy vegetation and thick soil cover, and the possibility of contamination by smelter fumes has discouraged geochemical prospecting. Should data reveal that geochemical prospecting could be done successfully in such an area, a particularly useful tool would be available to mining companies and prospectors searching for concealed orebodies in this economically important part of the district. The field work on which this report is based was done from July 28 to 31, 1955. It should be emphasized that this was reconnaissance study only, and therefore far from exhaustive. Previous Investigations in U. S. : The first geochemical survey known to have been affected by contamination was conducted in 1940—a geobotan-ical reconnaissance made in the Michigan copper district by a private company. Geologists found striking variations in the copper content of oak and maple leaves, but unfortunately the high copper isograds of the study seemed to be related more to the Calumet and Hecla copper smelter fall-out than to mineralized ground.&apos; The leaves of one oak tree near the smelter contained 0.4 pct Cu. Similar contamination was reported by Clarke (Ref. 2, p. 41), who conducted experimental geochemical soil and botanical surveys at Ray, Ariz. He found that the leaves of oak trees growing in unmineralized ground near Superior, Ariz., contained more copper than the leaves of oak trees growing on the capping of the Ray orebody and attributed this fact to contamination from the fumes of the Magma smelter at Superior. According to H. E. Hawkes,3 soils and stream sediments in the Superior area are also severely contaminated. Hawkes&apos; work there has shown a copper content averaging 0.5 pct in the surface horizons of soils within one mile of the smelter stack. Samples taken only a few inches below the anomalous surface samples showed only background copper values. In 1950 L. C. Huff&apos; of the USGS made a geochemical survey in an area near Jerome, Ariz., and found considerable zinc and copper in the soils over unmineralized basalt close to Clarkedale, Ariz., and over limestone close to Jerome. As the amounts were notably greater than could reasonably be expected to be derived from the underlying rocks, Huff suspected airborne contamination from the smelter at Clarkedale. Description of Area: The area sampled in detail (Fig. 1) for the study presented here is one of strong relief. The dominant watercourse is the westward-flowing South Fork of the Coeur d&apos;Alene River. East of Kellogg the South Fork flows in a rather narrow canyon, but its valley floor widens considerably to the west where much of the flood plain is covered by an extensive veneer of mining, milling, and smelting debris. South of the South Fork and between Big Creek and Pine Creek is a mountainous area where

Jan 1, 1960

By Franz Posepny

CONTENTS. Introduction. Part I. General Facts And Theories. [ ]

Jan 1, 1902

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

Eight members of the Board, the Secretary of the Institute, and eleven guests were present. Vice-president Henry S. Drinker presided. The President was authorized to appoint delegates to a meeting, on May 16, of the League to Enforce Peace. The Joint Conference Committee reported that the American Institute of Metals had accepted the invitation to form the Institute of Metals Division of this Institute. The Committee on Publications of the Institute of Metals was added to the Committee on Publications of the A. I. M. E. Exchange of one volume of Transactions of the A. I. M. E. at reduced price to members of the British Institute of Metals was authorized, in return for the reduced price given to our Institute of Metals Division on the annual proceedings of the British Institute.

Jan 6, 1918

By Frank G. Breyer

THE .following developments in the zinc field during 1935 are listed in the order of their importance. Each will he amplified in later paragraphs. In the field o f Metallic Zinc: (1) Construction of further continuous vertical retort smelting capacity in the United States and Germany. (2) Expansion of fractional distillation capacity in the United States. (3) Great expansion in the zinc-base die-casting industry in the United States and abroad. (4) Wide acceptance of heavy galvanizing by the steel industry. (5) Construction of the first commercial wire electroplating plant for putting on heavy coats of pure zinc. (6) Firm establishment and appreciable expansion of the practice of using zinc dust as a reducing agent in the organic chemical industry.

Jan 1, 1936

By L. E. Young

IT has been said the British Empire was built on British Coal. In all the postwar planning for Great Britain the necessity for producing cheap coal and the prosperity of the coal industry are given first consideration. On Jan. 23, 1945, there was released in London a "Report to the Colliery Owners" which had been awaited with great interest. This was entitled "A Plan for Coal" and was the recommendation of Robert Foot, chairman of The Mining Association (Colliery Owners), prepared at their request. Presentation of the "Plan" at this time is particularly significant as it is an answer to the demand for nationalization of the coal industry by the Labour Party and at the same time is a carefully considered program for postwar reconstruction, prosperity, and stability. In the words of Mr. Foot, If the coal industry for the first ten years after this war is to find itself in a situation similar to the one it occupied for the ten years following the last war, with its record of disputes, strikes, stoppages, short-time working, unemployment, and, with it all, a completely insufficient margin of profit, and all the insecurity and instability in our basic industry that was brought with them, it is goodbye to any real prospect of full employment, social security, and high standard of living. To present an elaborate review of the conditions which have brought to a crisis the unfortunate situation in the British coal industry is here unnecessary, but certain of the salient points

Jan 1, 1945

By T. F. Witheree

The Fletcherville Furnace was built in 1864 and 1865, making its first blast from August until October of the latter year, when it was blown out to prevent its " bunging-up." Repairs were made in time to enable it to be blown in again December 12th, 1865, the blast ending October 7th, 1866. Total product 1921.15 tons iron, an average of 6.8.2.5 tons per day, from ores yielding 44.8 per cent. Consumption of charcoal 223.2 bushels per ton of iron. The furnace journal up to this time shows no record of furnace dimensions, or temperature of the blast, but as near as can be ascertained, they were as follows, viz.: Height of stack, 42 feet. Diameter of bosh, 11 feet. Angle of bosh, 71/2 inches to 12 inches rise, about 58°. Diameter of open tunnel head, 42 inches. Number of tuyeres 3 ; each 3 inches in diameter. Dam 15 inches high. Tuyeres 24 inches high. Tymp 224 inches high. Diameter of steam cylinder, 20) inches. } Diameter of blast cylinder, 64 inches. } Stroke 5 feet. The engine is direct-acting horizontal non-condensing. December 26th, 1866, the furnace was again put in blast, having been considerably altered in the crucible; the height of stack, bosh, and tunnel head remaining as before. Six tuyeres were put in, three in each of the side arches. The hearth or crucible was rectangular in form, 3 feet wide x 31/2 feet long x 64 feet high. Inclination of bosh 58°. Height of tuyeres 26 inches; nozzles 21/4 inches diameter. Temperature of blast estimated to be about 500°.

THE twelfth annual meeting of the American Asso-ciation of Petroleum Geologists will be held in Tulsa, Okla., on March 24 to 26, at the Mayo Hotel. The per-sonnel of the committee on arrangements for this meet-ing is as follows : Chairman, M. M. Valerius ; finance, J. H. Gardner; program, Sidney Powers,; publicity, Luther H. White; reception, L. G. Welsh; registration, Frank A. Herald; exhibits, Frank C. Greene; entertain¬ment, Harry H. Nowlan ; ladies&apos; entertainment, T. E. Weirich; golf tournament, A. L. Beekly; hotels, G. C. Potter; transportation, A. W. Duston; banquet, R. Hughes; decoration, V. H. Hughes.

Jan 2, 1927