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By Raymond M. Howe

Additional data have been secured on the disintegration of furnace linings and the spalling of stove brick. The first article on the disintegration of furnace linings appears to have been written by John Pattinson in 1876.l The furnace involved was 85 ft. (25.0 m.) higher and 27 ft. (8.2 m.) in diameter at the boshes; after being in blast five years, the top brick became contaminated with carbon and disintegrated. An examination of the lining showed that the discolored, disintegrated brick were in a zone found from 35 to 67 ft. (10.6 to 20.4 m.) above the hearth; immediately below, in a zone extending from 22 to 40 ft. (6.7 to 12.1 m.) above the hearth, the brick were hard and porcelain-like in appearance. Analyses of samples taken from the different sections are given in Table I. The water-soluble portion found in the sample taken 39 ft. (11.8 m.) above the hearth had a composition approximately as follows: silica, 0.50 per cent.; lime, 0.04 per cent.; potash, 0.78 per cent.; soda, 0.20 per cent.; potassium chloride, 6.19 per cent.; moisture, 1.03 per cent.; total, 8.74 per cent. The carbon Table 1.—-Analyses of Samples Taken from Diferent Sections of Furnace . I ii In Iv v Section 67 Section 45 Seotion 39 Section of Original ft Above ft above ft above vitrified Lining Hearth Hearth Hearth Portion Per Cent. per Cent per Cent per cent. per Cent Silica........................... 55.70 55.60 55.67 47.60 37.07, Alumina........................ 35.50 35.40 30.00 26.47 23.18 Ferric oxide..................... 3.00 1.32 0.96 Lime........................... 0.23 0.06 0.17 Magnesia....................... 1.22 0.95 0.86 0.00 Potash......................... 2.60 2.10 5.30 7.54 21.59 Soda.........,.................. 0.45 0.42 1.67 0-76 6.28 Ca1bon ......................... 2.05 3.24 5.97 Carbon dioxide.................................. 2.. 17 Water...................................... 7.70 Water-soluble........................... 8.74

Jan 1, 1920

By J. R. Lucas, R. L. Frantz

Mine sealing programs for the alleviation of acid mine drainage were begun by the Federal Government in the '30's. As part of an acid mine research project to The Ohio State University, a field test was undertaken to determine the effectiveness of mine seals for reducing mine acid. Details of the tests made at the McDaniels mine show the feasibility of air-sealing and flooding an acid-producing drift coal mine. Work by the University continues. The Federal Government undertook in the early thirties an extensive mine sealing program for the alleviation of acid mine drainage. In the states of West Virginia, Ohio, and Pennsylvania many general summaries have been made on this program but no critical evaluation with supporting data has been found on the effectiveness of mine seals for reducing mine acid. Because of this it was decided to undertake a field testing program as part of an acid mine research project of the Engineering Experiment Station, The Ohio State University. The objective of this phase of the project was to develop and install a field research laboratory for acid mine drainage studies. Specifications for such a mine laboratory were developed and resulted from the following considerations: 1) Size and preservation—the test mine shou1d be of limited size to permit frequent and detailed examinations; it should be in a reasonably sound condition to permit safe entry. 2) Isolation—the mine should be physically separated from all other mines. 3) Openings—a minimum number would be desirable to reduce the sealing problem. 4) Structure—the mine especially near the openings should be structurally sound. 5) Acid production—the mine should be producing significant quantities of acid. After considerable searching, the McDaniels mine was selected in the Hocking coal field in Vinton County just above Lake Hope State Park in southeastern Ohio. The small drift mine in the middle Kittaning coal consisted of two small rooms with one mine opening about 6 ft above a seasonal stream bed. Before it was finally decided to seal the mine, a short study was made of the acid drainage over several months. Fig. 1 shows a plot of acidity (milligrams per liter), flow (gallons per minute), and acid production (pounds per day) vs time over the sampling period. Because the coal was overlain with a porous sandstone, the mine drainage was consistent the year around even though the mine was

Jan 1, 1961

Pulverized Fuel Combustion The apparatus shown in the illustration is a complete equipment f r supplying coal to boiler and metallurgical furnaces, cement and lime kilns, dryers, and to all furnaces requiring a temperature and quality of fame under prompt and easy control. It is claimed that the Aero Pulverizer makes practicable the highest efficiency obtainable from burning coal. It makes coal burn like a gas, a flame, the physical and chemical character of which is regulable- a flame that may be elongated or shortened, thus placing the zone of highest temperature where needed- a flame that may be made oxidizing, reducing, or neutral, as occasion may require. The coal is burned as pulverized, and there is no storage of the powder with its attendant hazard. Artificial drying before pulverizing is not necessary if the coal supply be sheltered from rain and snow. Where the Aero is used, it is wholly a furnace question whether a dryer should be installed; it is not at all a pulverizing or storage question. Labor is reduced to a minimum. Slack coal at low cost yields its last B.T.U.

Jan 11, 1915

By L. L. Wyman

THE exact nature of the changes that take place in the iron-nickel alloys, giving rise to the interesting and useful expansion alloys in the Invar range, has yet to be fully understood. Similarly, the ternary iron-nickel-cobalt alloys, which also possess such commercially useful expansion characteristics, 1,2 are concerned with transformations that appear to be identical with those found in the parent iron-nickel alloys. The investigations on iron-nickel alloys in the range 26 to 29 per cent Ni have been reported by several authors" wherein it is shown that there are factors other than temperature, such as stress and grain size, which play an important part in determining the temperature at which the low-temperature transformation takes place. It will be shown in this paper that the ternary iron-nickel-cobalt alloys having nickel contents comparable to the alloys mentioned above behave in a parallel manner. The alloys in the range of 26 to 31 per cent Ni and 16 to 21 per cent Co have a coefficient of expansion of about 4.0 X 10-1 per degree Centi-grade, and the alloys in this range of composition find considerable application in making glass-to-metal seals, because these expansion properties so well match commercial glasses. The behavior of these alloys is not a simple matter, for it has been observed in alloys of 28.5 per cent Ni and 18.5 Co that severe working can cause the appearance of a second phase having a needlelike structure similar to the martensite structure in carbon steels. Fig. 1 shows the change brought about in an alloy of this composition when a strip of this material was cut with tin shears. This second phase has been identified as the body-centered cubic alpha phase, and it is the purpose of this paper to describe the results of some of the preliminary investigations in the study of the changes involved in these alloys.

Jan 1, 1939

Jan 1, 1967

By L. F. Elkins

Water coming into wells with bottom water present in the Fosterton field, when their oil recovery was only 0.1 to 1.5 per cent of oil in place below the lowest perforation, confirms lack of shale barriers to vertical flow which also are not apparent in cores and electric logy. Low contrast of vertical and horizontal permeability, high mobility ratio betweerz oil and water zone and pos.rible rate effects due to gravity Combine to prevent easy analysis of water invasion pattern and efficiency by analogy or intuition. Theoretical analysis of performance including these factors using a new direct nurnerical .solution of potential distribution in a network led to unanticapted indications that water would under-run the entire oil reservoir with low volumetric coverage if supplied through natural influx or peripheral water injecfion below the oil-water contact. An unusual pattern of water injection is to he adopted in this recently unitized pool to provide more uniform water flooding in that two-thirds of the oil reservoir not underlain by bottom wafer. INTRODUCTION The Fosterton field, Southwestern Saskatchewan, Canada, was discovered in Jan., 1952. It produces at a depth of 3,100 ft from a pinch-out of the Roseray sand at the Lower Cretaceous-Jurassic unconformity. The field, covering 2,500 acres, contains 54 wells on 40-acre spacing. Development was essentially complete in June, 1954, but significant production did not start until May, 1955, when a pipeline outlet became available. Within one year rapid in- creases in gas-oil ratio and early encroachment of water created operating problems in the down-structure eastern half of the field and raised serious questions about reservoir performance and ultimate recovery. This paper describes the unusual behavior of water encroachment—on both well and reservoir bases—and the analyses made to interpret it. The field was unitized July 1, 1958, for water flooding. A somewhat unconventional

By H. D. Mellom

The direction of the optic or "C" axis of a uniaxial metal crystal can be found with the metallurgical polarizing microscope by examining two planes of section on the crystal. Complete orientation of the crystal can be determined if a twin crystal is common to both surfaces of section. Examination of Uniaxial Metals in Polarized Light-Rotation of a uniaxial crystal surface, properly prepared,' shows four extinction positions 90 deg apart, provided that the surface is not close to a basal section. One of these two extinction directions corresponds with the projection of the optic axis on the surface of section. This direction can be found if the 'sign of the rotationr2 for the metal is known. To find the direction of the optic axis, the crystal is rotated on the stage 45 deg from an extinction position. With a crystal of negative sign, to produce extinction the analyser must be rotated towards the optic axial direction and vice versa. All sections, other than basal, of a uniaxial crystal have the same sign of rotation and, since there is no change in sign with wave length, white light can be used for these measurements. U the sign of the rotation is not known the presumed direction of the optic axis can be determined assuming a positive sign. A third section cut normal to the presumed optic axis will show basal extinction if the assumption is correct. It is convenient to use the edge between the two planes of section as a fiducial direction common to both surfaces. The optic axis can be related to this direction. If the above measurements are repeated on the other plane of section and the angle between the two section planes measured, stereographic projection can be used to determine the orientation of the crystal optic axis. Determination of Complete Orientation—The complete orientation of a uniaxial crystal can be determined provided that a twin crystal is common to both surfaces of section, and the twin law is known. The orientation of the twin crystal optic axis can be determined in the same way as for the main crystal

Jan 1, 1962

By A. L. Sweetser

Experience has shown how difficult it is to obtain information regarding laboratory-tests in connection with the chlorina-tion-process for the extraction of gold from its ores, and I therefore present the following method, somewhat in detail, for the benefit of those who may desire to pursue research work in this field. The ore chosen was a partly-decomposed porphyry, extremely siliceous and comparatively soft, and of an average value per ton of from $25 to $26 in gold and $0.68 in silver. The chemical analysis gave: Fe,O,, 3.35; FeS, 1.5; MnO,, 0.75; ZuCO,, 4; A1,0,, 3.20; H,O, 0.7 ; SiO, and insol., 83.50 per cent. The ore, first crushed to pass a 5-mesh screen, was coned and quartered until a 45-lb. sample was obtained. Samples for assay and analysis, taken from this lot by means of riffles, were crushed to pass a 100-mesh screen. The original sample was divided into 10-lb. lots, of which one was crushed to pass a 10-mesh screen; another through a 12-; the third through a 20-, and the last through a 30-mesh screen. Because of the production of an excessive quantity of fine material it was deemed inexpedient to crush finer than 30-mesh size—a decision the wisdom of which is proved by the data in Table I., showing the increasing ratio of slimes, in proportion as the ore is crushed finer. In order to determine the percentage of fines in the sizes of mesh selected, a weighed sample of ore was taken from each mesh, and a sample from the 10-mesh lot was passed successively through 20-, 40- and 100-mesh screens, and the percentage remaining on each screen determined. This process was repeated with the 12-, 20- and 30-mesh lots, with the results given in Table I.

Jan 1, 1908

By E. J. Roberts

Hydrometallurgical operations and many processes in the chemical industry require the separation of dissolved material from solids. One of the decisions which has to be made in designing a plant for such an operation is how this separation shall be accomplished. It is the purpose of this paper to set forth the general principles involved in such separations in order that the optimum flowsheet and equipment may be selected. Countercurrent Decantation with thickeners, or C.C.D. as it is generally known, is, of course, only one way of separating dissolved material from undis-solved. Other unit operations such as Countercurrent Filtration (C.C.F.) and Countercurrent Classification (C.C.C.) are widely used. The same principles may also be applied to centrifugally assisted decantation, as with nozzle or solid bowl type centrifugals, and to separations using screens, either gravity or centrifugal type. Another form of countercurrent washing applicable to granular materials is practiced in continuous ion exchange operations. All of these operations depend on two basic principles, or combinations of these principles. In C.C.D. type operations the solids are concentrated into the smallest possible volume of liquor in each step and the resulting pulp then mixed with a more dilute liquor and recon cen trated, the liquors separated from the more dilute stages being advanced to dilute the more concentrated liquor in a previous solids concentrate, as is shown in Fig. I. This will be termed the solids concentration-solution dilution principle, or, for short, solution dilution. countercurrent decantation- type circuits. The second principle used in washing solubles from solids is that of solids concentration-solution displacement. Here the solids are restrained from movement while wash solution is forced through the interstices in a counter-current fashion, as in Fig. 2. In the simplest application of this principle, once the "cake" has been formed, it is not disturbed until the operation is completed. In continuous filters, the cake is merely moved under the successive washes and the displaced filtrates removed as in Fig. 4. Often, however, after one or two displacement washes, a repulping step is introduced, the cake reformed and washed again. This procedure brings the solution dilution principle into play as well as the solution displacement principle. Merely thickening ahead of filtration, which is often operationally advantageous, does not hybridize he circuit. It still can be a pure solution displacement operation from the washing

Jan 1, 1961

By . M. Muskat

A THEORETICAL consideration of the mechanics of various water-flooding systems with the viewpoint of comparing their relative merits involves the study of two fundamental properties of such systems. On the one hand, it is important to determine the efficiency of the flood as measured by the percentage of the total area that is swept out by the encroaching water before water actually reaches the output wells. This is really a measure of the regional tendency of the water to "bypass" the oil. On the other hand, the various systems must be compared from the viewpoint of their resistances which determine the rate of fluid production obtainable for given pressures maintained at the water input wells. The first of these questions has been studied and very definite answers have been obtained by means of simple electrolytic models.1 These models showed that, in an ideal system, the percentages of the areas flooded out before water reaches the output wells are about 57 per cent for the direct line-drive flood (the input and output wells being equally spaced and placed in alternate parallel lines), 74 per cent for the regular five-spot network, and 79 per cent for the seven-spot network. With respect to the efficiency of the usual flooding arrangements, they are, therefore, given quite accurately by the above numbers. With regard to the resistances of the flooding networks, electrical conduction models have also been used successfully2 and are well adapted to the problem of determining experimentally the pressure distribution and streamlines, or over-all resistances of specific flooding networks. However, such models do not permit readily a study of the effect of changing dimensions or configuration within a network, since a new model must be made up for each set of dimensions considered.

Jan 1, 1933

By A. Lawley S. Schuster

The tensile behavior of copper foils prepared from rolled bulk material has been studied over the thickness range 2 to 53 , and for a range of pain sizes. For foils of comparable grain size, having the cube texture and tested along (100), yield strength increases with decreasing foil thickness t below -26p, with a corresponding decrease in ductility. Deformation occurs in the form of localized slip clusters distributed throughout the gage section. To the extent that the tensile strength (10 to 18 kg mm-) is unaffected by foil thickness, and that the foils possess fair ductility, the stress-strain behavior resembles that of bulk material rather than that of whiskers or evaporated films of comparable dimensions. The dependence of yield strength o on foil thickness t below -26p is of the form: oy = oo + kt-1/2. Possible explanations for the stress increase are considered based on 1) the dependence of active dislocation source length on foil dimensions, 2) the locking of surface sources, or the blocking of mobile sources at the surface due to surface film. It is now well-established that filamentary whiskers of many materials show exceptionally high strength compared with bulk crystals.'-11 As the diameter of the whiskers decreases to -1, the observed fracture strength approaches, and in certain cases exceeds, the calculated shear stress for the nucleation of slip in a perfect crystal.' In general, the stress-strain curve is entirely elastic, with strains at fracture approaching 1 pct. Similarly, thin films12-24 of evaporated or electrodeposi-ted material have been shown to possess tensile strengths three to seven times that of bulk material, with total strains at fracture -1 to 2 pct. In the present study, attention has been directed to the room-temperature tensile behavior of thin foils of copper over the thickness range 2 to 53, prepared from rolled bulk material. Yield stress, ultimate tensile strength, elongation to fracture, and work-hardening behavior are measured as a function of grain size and foil thickness. Structurally such foils are superior to either evaporated or electrodeposited films, and in the recrystallized condition exhibit considerable ductility. Apart from preliminary work by Sumino and Yamamoto25 on the work-hardening behavior of rolled and recrystallized copper foils, no systematic tensile studies have been carried out on material of this form. EXPERIMENTAL PROCEDURE Tensile specimens were prepared from 99.995 pct purity rolled copper foils of thickness 2, 6, 12, 26, and 53, obtained from the Hamilton Watch Co., Lancaster, Pa. Irrespective of specimen shape, it is necessary to use tensile foils with edges free from notches or tears. To this end, any form of cutting operation was excluded, and the tensile foils prepared using a photoengraving process, the details of which are described elsewhere.26 Since tensile data are required under conditions of uni-axial stress, the specimen shape is extremely important. Ideally, the foil should be infinitely long, allowing a gradual taper from the grip area to the gage section; however, from a practical standpoint, long foils are easily damaged during testing. A modified tensile specimen was therefore selected having a parallel gage section 1.25 by 0.20 in. with a tapered shoulder section increasing to 0.5 in. at the grips, and an over-all length between grips of 4 in., Fig. 1. In practically all tests, these foils fractured within the parallel gage section. By approximating the foil contour (Fig. 1) to a hyperbola it is possible to analyze the stress distribution in the tensile foil using two-dimensional elasticity

Jan 1, 1964

By R. W. Stahl

Employees and dollars are necessary to all enterprises and any force, such as fire, which destroys either, can bring very serious consequences, including business failure. Since everyone acknowledges the necessity of conserving human life, we will devote most of our paper to the economic factors involved. A coal-mine fire is considerably more difficult to combat than a fire in a surface building because of the combustible surroundings in the mine, the explosive gases emitted from the coal, the suspension of explosive dust when mine timbers burn and the unsupported roof falls, the limited space in which approach to the fire can be made, and the limited avenues of escape. A survey of coal-mine-fire protection indicated that a rather low value was being placed on property and equipment. This prompted comparison with other industries. The comments made in this comparison are not intended as an indictment of the coal industry, since we do have mines that are well protected against fire, but the comments on conditions at the mines visited are factual and may help others to improve similar conditions. SURVEY PROCEDURES Plants of the steel, aluminum, rubber, chemical, and petroleum industries were surveyed, and all facets of the fire-protection scheme were covered. The industrial plant invariably had four times as much water readily available for instant use than the mine. In many mines where water is available, no equipment for applying it is provided, such as hose, nozzles, and adapters, so that time is lost in collecting this equipment. (See Table I.) EXTINGUISHERS Many more and generally larger portable extinpishers are available at the plant as compared to the mine. The extinguishers are generally placed nearer to sources of danger. In addition, respiratory protective equipment is always available at strategic points in plants but only in a few mines. (See Figs. 1 and Table 11) INSPECTING AND TESTING EQUIPMENT Plant water facilities are checked weekly and flushed at 6-month intervals, and hose is pressure-tested at least yearly; some mines check water yearly, but hose is not tested unless used. Fire extinguishers are inspected weekly in plants and completely overhauled yearly; one mine had monthly checks and overhauls only after use. FIRE BRIGADES AND TRAINING Every plant had designated fire-fighters and some complete full-time brigades; at one mine a chief mechanic was designated as being in charge of fires, and other depended entirely upon officials who might not be familiar with the equipment. COST OF FIRES AND PERCENTAGE OF CAPITAL INVESTMENT IN FIRE PROTECTION The direct cost of recent mine fires ranged from $128,000 to $240,000; indirect costs, such as lost tonnage, idled equipment, lost orders, and the like might run the cost to over $500,000. (See Figs. 2 and 3).

Jan 1, 1961

By W. R. Clark, W. W. Cotter

Jan 1, 1946

By W. W. Cotter, W. R. Clark

Jan 1, 1946

By L. W. Bahney

MANY methods for the determination of gold or silver, or both, in cyanide solutions have been published, which with care in manipulation, and modification in some cases, will give results that are satisfactory. It is possible to classify or group these methods as follows: 1. Evaporating the solution in a porcelain or agate-ware dish containing litharge,1 or in a "boat" made of lead foil. 2. Forming a lead sponge containing the precious metals by means of zinc shavings,2 zinc dust,3 or a piece of aluminum.4 3. Decomposing the cyanide solution with an acid and precipitating the precious metals by the use of one or a combination of some of the following: Copper sulphate,5 sodium sulphite,6 hydrogen sulphide,7 cement copper.8 4. Precipitating the silver by zinc dust held in a Hooch crucible and determination with a standard solution of sulphocyanate.9 5. Electrolysis.10 6. Colorimetry.11

Jan 2, 1915

Organization Place Date 1919 American Society of Civil Engineers..: Twin Cities, Minn. June 17-20 American Society of Mechanical Engineers Detroit, Mich. June 17-20 American Institute of Chemical Engineers Boston, Mass. June 18-21 American Drop. Forge Association Pittsburgh, Pa June 19-21 American Institute of Electrical Engineers Lake Placid, N. Y. June 24-27 American Society for Testing Materials Atlantic City, N. J. June 24-27 Society for Prom. of Engng. Education Baltimore, Md. June 25-28 American Chemical Society Philadelpia, 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

Jan 6, 1919

By Francis Foley

INTRODUCTION DURING the summer of 1919, the late Dr. Henry M. Howe, then Chairman of the Division of Engineering of the National Research Council, organized a committee to obtain a better insight into the behavior of carbon steels under the influence of various treatments by a proper control of the time and temperature factors. During part of 1919 and 1920, work in connection with this investigation was carried on at Dr: Howe's laboratory at Bedford Hills, N. Y. During 1921 there was an enforced hiatus in the work, occasioned by the illness which resulted in Dr. Howe's death in 1922. At that time one of the present authors compiled the results of the work which had been done and this was published in 1923.1 Following the publication of this work, it seemed desirable to carry on in the same manner an investigation of steel of C 0.75 per cent., which steel had not been as fully treated as had the other steels of C 0.34 and 0.52 per cent., used in the published work. Furthermore, certain unusual results have been obtained in the treatment of C 0.52 per cent. steel by quenching and drawing, and repetition of this part of the work seemed advisable. This has been done during the past year at the School of Mines and Metallurgy of the University of Missouri at Rolla, Mo., by a cooperative undertaking of the School and the Bureau of Mines, working in conjunction with the Committee on Heat Treatment of Carbon Steels of the National Research Council. The present paper is a report of the results obtained in this work.

Jan 2, 1926

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

Jan 1, 1959

Thirty years ago a party of American Engineers, with members of their families, belonging to the four national engineering societies, sailed for Europe and visited England and the Paris Exposition of 1889 and received many courtesies, official, professional, and individual. Plans: have been made for a reunion dinner to be held in New York City, about May 26, at which it is hoped that all survivors, ladies as well as men, of that trip may meet again. It is, therefore, urgently requested that anyone who was of that party communicate immediately with the Secretary of the Committee, Jesse M. Smith, Engineers&apos; Club, 32 West 40th St., New York, N. Y. Announcement of the precise date and place, and full details, will he sent to every individual who can he reached.

Jan 5, 1919