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By Edgar S. Cook

The Warwick furnace at Pottstown, Pa., constructed for anthracite fuel, is, as may be remembered, 554 feet high, with 15; feet bosh. The actual working height from stock-line to bottom is only 474 feet, the bell-and-hopper taking up 8 feet. During the year 1886 we used mixed fuel, in the proportion of three-fourths anthracite and one-fourth coke. The total product of iron was 30,6299 tons of 2280 lbs., being a weekly average of 589 tons, including all ordinary and extraordinary stoppages. Deducting the latter, the weekly average would be about 600 tons. The fuel-consumption for the year was 1.2 tons per ton of iron, while the ore-mixture yielded 52 per cent. of iron. For about two months during the summer of 1887 we were obliged to run on anthracite exclusively, owing to the Connellsville coke strike. In the fall of 1885, in relining the furnace, the crucible had been built 8 feet 9 inches in diameter, with the view of using regularly one-quarter of coke (the largest previous diameter having been 7 feet 5 inches), and we felt somewhat apprehensive of the results when compelled to use anthracite only. The average of seven weeks' run on coal, as compared with the average of the seven corresponding weeks of 1886 (using one-quarter coke), was as follows:

Jan 1, 1889

The Nominating Committee desire to submit the following nominations. President and Director: SIDNEY J. JENNINGS District 0 Vice-President and Director: H. S. DRINKER District 2 R. M. RAYMOND District 0 Directors: G. C. STONE District 0 HENNEN JENNINGS District 9 S. A. TAYLOR District 2 F. G. COTTRELL District 6 ARTHUR THACHER District 3 These nominations were unanimous. By order of the Committee J. V. N. DORR, Chairman. Oct. 10. 1917.

Jan 12, 1917

DAVID THOMAS 1871 R. W. RAYMOND 1872-1874 A. L. HOLLEY 1875 ABRAM S. HEWITT 1876 T. STERRY HUNT 1877 ECKLEY B. COXE 1878-1879 WILLIAM P. SHINN 1880 WILLIAM METCALF 1881 RICHARD P. ROTHWELL 1852 ROBERT W. HUNT 1883 JAMES C. BAYLES 1884-1855 ROBERT H. RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B. POTTER 1888 RICHARD PEARCE 1889 ABRAM S. HEWITT 1890 JOHN BIRKINBINE 1891-1892 H. D4. HOWE 1893 JOHN FRITZ 1894 J. D. WEEKS 1895 E. O. SPILSBURY 1896 THOMAS M. DROWN 1897 CHARLES KIRCHHOFF 189S

Jan 1, 1939

By T. P. Oxford, G. Y. Onoda, E. D. Whitney

Disposal of phosphatic clay waste slurry has been a problem since the advent of hydraulic processing of phosphate rock in Florida. Alternatives to the present practice of storing slimes behind earthen dikes have been earnestly sought for more than a quarter of a century. Seepage dewatering is a promising technique intended to increase waste clay solids content to a level sufficiently high to permit clay disposal in mine cuts, in lieu of above-grade impoundment. An experimental array of vertical seepage columns containing mine tailings sand was constructed. Significant improvement in waste clay dewatering relative to that occurring in a control test was observed when approximately 1800 m3 of waste clay was disposed of in the presence of the seepage aids.

Jan 1, 1983

I-institute of Metals Division S. SKOWRONSKI, Chairman ZAY JEFFRIES, Vice-chairman WILLIAM M CORSE, Secretary Executive Committee J. R. FREEMAN, JR, Local Section G E JOHNSON R S ARCHER, Non-ferrous Data Sheets P. D. MERICA EDGAR C BAIN, Journal Committee L W SPRING SAM TOUR, Papers Committee F. L. WOLI H. C. JENNISON, Membership Committee Local Section Committee J. R. FREEMAN, JR., Chairman R. J. ANDERSON, Cincinnati R L. DOWDELL. Minneapolis R. S WILLIAMS, BostoI G. H. CLAMER, Philadelphia W. A SCHEUCH, Chicago R. F. WOOD, New York

Jan 1, 1923

Jan 1, 1902

By George C. Lipsey

FOR many years the mining of coal and other minerals occurring in sedimentary formation has been planned according to information obtained by diamond drilling. Placer mines have used churn drills for sampling and estimating deposits, and some metal mines have used the method either wholly or in part. The diamond drill method, therefore, although not entirely new, has come into more prominence in the last few years. Several large-scale developments now being planned or in the production stage have used this method in varying degree. This paper will describe the operations of the Howe Sound Exploration Co., Ltd. at Snow Lake, Manitoba, where a gold mine was developed and equipped for mining and milling wholly on the basis of diamond drilling results. The property has been in operation nearly 3 years, so that results can be compared with the estimates and assumptions made from the diamond drilling. In developing the subject it is necessary to outline as briefly as possible the normal method of mining, from discovery to production stage. Table I sets forth these various stages, the methods of financing, the percentage of total cost, and the relative time interval required for each section of the work. The plan presented in this table cannot be applied to all mining developments, but it gives a basis on which to work. In Stages 2 and 3 the investment is moderate, and if the property does not respond favorably the options or interests can be terminated. Stage 4 represents a sizeable investment, and it is more difficult to drop the property after this part of the operation is completed. Stages 2, 3, and 4 may be repeated several times by different groups or companies before Stage 5 is reached, but when Stage 5 has been started the total capital investment must be provided and there can be no turning back. It will be noted that there is a total of 116 units of investment in the overall cost if one company proceeds with Stages 2, 3, 4, and 5 in order. Stage 4, however, consumes time which is important when markets are being considered. Bringing a property into production when metal prices are low is much more difficult than when the prices are high, and if this stage can be set aside production is attained more quickly. When Stage 4 is eliminated the total becomes 86 units of cost for Stages 2, 3, and 5, but an adjustment of 14 units must be added to Stage 5. These 14 units represent the useable value of Stage 4. Thus Stage 4 represents an investment of 30 units if carried on before Stage 5, but 14 units if included with Stage 5. This is accounted for by the fact that development work can be accomplished more cheaply under Stage 5, since everything that is done is planned on a production basis with permanent services. Stage 4 must of necessity be governed by expenditures, and a great many temporary services, including housing and power plants, must be provided. The prospect shaft is a small one, and drifts,

Jan 1, 1952

Jan 1, 1901

By T. A. Rickard

The mountains of the picturesque Dauphine, in southeastern France, have long been known to collectors as the source of many minerals of rare occurrence; but. they contain also several mines, which, though less known, date from the time of the Saracens, many centuries back, to that of the graduate from the Ecole des Mines. In the department of the Isere, upon the cliffs of Villard Ey-

Jan 1, 1893

By Arnulf Muan, W. C. Hahn

Activities of "FeO" in "FeO"-MgO solid solutions have been determined in the temperature interval 1100" to 1300"C by equilibrating oxide samples with pure metallic iron in atmospheres of known oxygen partial pressures. The end members "FeO" and MgO form a complete solid solution series. The system shoztls a considerable positive deviation from Raoult's law. A large amount of data has been accumulated during the past 50 years on stability relations existing among various crystalline and liquid phases in oxide systems of importance in metallurgical processes. By comparison, very little is known about the thermodynamic properties within the various homogeneous phases present in the systems, particularly the crystalline phases. The present paper deals with determination of activities as a function of composition in solid solutions of wüstite ("FeO") and periclase (MgO). Such solid solutions ("Magnesiowustites") have simple sodium chloride structure and are known to be continuous between the end members at elevated temperatures (> 1000°C) and strongly reducing conditions such as prevail in contact with metallic iron. Wiistite has a defect structure in which the ratio of oxygen to iron varies and never has as low a value as 1:1 corresponding to the simplified formula FeO. Within the range of stability of this phase, the composition changes between a maximum oxygen content of approximately 25.6 wt pct (corresponding to the formula FeO.83O) and a minimum oxygen content of approximately 23.2 wt pct (corresponding to the formula Fe0-96O). The activity data to be reported in the present paper are based on using as standard state the wüstite which is in equilibrium with metallic iron at a particular temperature, i.e., "FeO" of minimum oxygen content at each temperature. For sake of simplicity, the formula FeO will be used to represent the wustite phase in the remainder of this paper. Consider the reaction 2 FeO solid solution = 2 Femeta1 + Ozgas in which FeO dissolved in another oxide dissociates to metal and gas. The activity of FeO in the solid solution, relative to "pure FeO" in equilibrium with metallic iron as a standard state, is then expressed as Here Po, and po2 * are the partial pressures of oxygen of the gas phase in equilibrium with metallic iron and the oxide solid solution or "pure FeO", respectively. The equation holds only if the metal phase is essentially pure Fe. The oxide combinations used in the present investigation fulfill this requirement. Magnesia is so much more stable than FeO that for all practical purposes aFe = 1 in the metal phase present in all mixtures used in this investigation. I. EXPERIMENTAL METHOD 1. General Procedure. The experimental method used was analogous to that developed by Foster and Welch1 and used recently by Hahn and Muan.2 It consisted of four steps: a) Determination of the equilibrium between FeO and Fe. b) Determination of d-spacing change with composition in oxide solid solutions (FeO-WO). c) Equilibration of various members of the solid solution series with a metal phase and a gas phase of known oxygen partial pressure. d) Determination of compositions of solid solutions resulting from step (c) by means of data obtained in step (b). 2. Starting Materials. General Aniline and Film Corp. carbonyl iron powder, type HP, was used as the source of metallic iron. A representative analysis was as follows: Fe, 99.6 pct; C, 0.01 to 0.04 pct; 0, 0.1 to 0.3 pct; N, 0.00 to 0.05 pct. Other elements were present as traces only. Wiistite was prepared from "Baker Analyzed" Reagent grade Fe2O3 of reported analysis as follows: Assay (Fe2O3), 98.8 pct; insoluble in HC1, 0.02 pct; not precipitated by NH,OH, 0.02 pct; Zn, 0.003 pct. Production of wüstite was achieved by a two-step

Jan 1, 1962

By J. W. Harshbarger, E. L. Montgomery

The region of metallic ore deposits in northern Chile, southern Peru, western Bolivia, and northwestern Argentina occurs in arid zones at altitudes as high as 6 km (19,700 ft). Because surface water supplies are meager, new mines require unexploited sources of water. Prolific ground water aquifers occur in salar basins in this region of the Andean Highlands. Exploration water wells have been constructed and aquifer characteristics have been tested in eight salar basins. Results indicate ground water quality is good. Aquifer transmissivity and storage computed from results of pumping tests indicate maximum capacities of more than 170 L/sec (2700 gpm) for individual production water wells. Results of investigations conducted by the authors demonstrate that ground water reservoirs in the Andean Highlands comprise a source of large quantities of water for the mineral industry.

Jan 1, 1986

By Derek C. Shelton

This chapter covers the preparation of specifications for a dry crushing and wet grinding comminution circuit.

Jan 1, 1982

By John Randall

It is a fair assumption that the main purpose of any diagram is to present facts to the eye in more convenient form than they could be tabulated in figures, and this implies that a screen diagram should set forth in a convenient and familiar form certain facts as to the character of the material screened regardless of the screen standards used, and it seems particularly desirable on account of the well-known differences in the size of openings of different laboratory screens having the same nominal mesh. In making screen-sizing tests it has been customary first to consider the largest size, going progressively to the smallest, and this seems to have led to the practice of placing the smallest size .at the right-hand side of the diagram and measuring toward the left. This is not altogether convenient and might be changed to advantage, but for illustration I have preserved that feature and present the method just as I have used it for over 2 years. Direct plotting in which the intervals on the diagram are proportional to the sizes of the openings, or to the arithmetical difference between them, seems at first sight more natural and is extremely useful for certain purposes, but it makes the diagram very crowded in the smaller screen sizes while the larger ones occupy unnecessary space, making it less convenient for most purposes, and for that reason the method here discussed is the well-known one based on the ratio between openings, and is plotted in logarithms instead of the direct values of the screen opening. Metric coordinate paper is convenient, although not necessary; it is recommended, as the use of the metric scale gives a diagram of convenient size, but any scale of equal parts may be used. In order to make any screen diagram translatable in terms of any standard screen size, it is necessary to have noted on the size scale of the diagram all points corresponding to the openings of the various screens in question, instead of a single series of points as with a single screen. In drawing the diagram assume 0.001 in. (corresponding approximately to 0.025 mm.) to be the smallest size to be considered and fix this as the zero point at the lower right-hand corner of the diagram. This value is selected because the values are to be plotted in logarithms, and the logarithm of 1 is zero. Then lay off to the left for the position of each screen

Jan 1, 1918

By K. Verghese, R. W. Rousseau, R. P. Gardner

A radioactive tracer method and a size-discretized, mass balance model are formulated and demonstrated in a feasibility experiment for the determination of crystal growth rates in MSMPR crystallizers. The system studied is aqueous KN03 with K-42 as the radioactive tracer. The results indicate that the method should prove to be very valuable for this application, particularly when systems exhibiting size-dependent growth rates are of interest. An indicated refinement to the tracer method is the simultaneous use of an additional tracer in the liquid to determine the amount of radioactivity from the liquid that is adsorbed on the samples of filtered crystals.

Jan 1, 1980

Jan 1, 1957

By Edward E. Hicke, Charles A. Stickels

The dihedral angle of liquid-lead inclusions in solid nickel has been measured as a function of temperature from 371 to 816 C at zero pressure. and as a function of pressure up to 50,000 psi at 317 and 593 C. Thermodynamic expressions are derived for the temperature and pressure coefficients of interfacial tensions in this system. A method is presented for obtaining relative tempmature and pressure coefficients from dihedral-angle data, and the resulting values are used in conjunction with the thermodynamic relations to calculate excess properties of the solid-liquid interface. Defining the position of the solid-liquid interface by the condition that the excess concentration of lead is zero, the excess concentration of nickel and the excess entropy at the solid-liquid interface are: where y(593) is the interfacial tension of the nickel grain boundary saturated with lead at 593C and zero pressure. These values are considered reliable to within a factor of two. While similar calculations are not possible for the nickel grain boundary, it is shown that the expwimental results imply that the excess concentration of nickel at the boundary and the excess entropy of the boundary are negative. THE temperature and composition dependencies of interfacial tensions in metal systems have been reported by several authors in the last 15 years.'-' No measurements of the effect of pressure on inter- facial tensions in metals have been reported, although measurements made on nonmetallic gas/liquid and liquid/liquid systems suggest that a measurable effect should exist.6-l2 The purpose of these experiments was to determine the influence of temperature and hydrostatic pressure on dihedral angles in the Pb-Ni system. The equilibrium dihedral angle is expressed as a ratio of interfacial tensions by2: where 8 is the dihedral angle, yGB is the Ni-Ni grain boundary tension, and SL is the solid Ni-liquid Pb interfacial tension. Three sets of ex- periments were run to determine: a) the effect of temperature from 371" to 816°C on the dihedral angle at zero pressure; b) the effect of pressure up to 50,000 psi on the dihedral angle at 371° and 593°C. THERMODYNAMICS The properties of interfaces of most direct concern are the interfacial tension, excess concentrations of various components at the interface and the excess entropy of the interface, S°. These quantities are defined following Gibbs. Consider an interface separating phases a and 0. Construct two surfaces C, and C such that all properties of phase a remain uniform up to C, and all properties of phase 0 remain uniform up to C. The region between C, and Cp is the interfacial region. Let a "dividing surface", D, be constructed in the interfacial region such that it passes through all points "similarly situated with respect to the condition of the adjacent matter."l3 Surface D divides the interfacial region into a portion a' adjacent to phase adjacent to phase . Let a closed curve, C, enclose an area A in D. Erect normal lines to D along C; these lines and the surfaces C,, Cp, and D then enclose volumes V and V' in the two halves of the portion of the

Jan 1, 1964

By C. J. Wilhem, J. M. Devine

A corrosion-testing apparatus which operates in the field and which will determine the comparative resistance of various ferrous materials to corrosion by gaseous hydrogen sulfide at ordinary temperatures is described. The principle of the uniform method of testing is to allow natural gas containing hydrogen sulfide, direct from its source in the field, to flow over the group of specimens for a given period of time, and subsequently to estimate the corrosion sustained by each specimen by determining its loss in weight. The comparative results obtained when specimens of 47 representative ferrous materials of described typical composition \\ere tested at ordinary temperatures with natural gas containing hydrogen sulfide are given in tables showing average penetration of metal, Inches per year. The primary purpose of the work Mas to determine the possible utllity to the petroleum and natural gas industries of ferrous materials that are commercially available, and no attempt is made to discuss the results of the tests from the metallurgical standpoint. The following is a summary of the results obtained: 1. Steels containing 12 to 27 per cent of chromium showed the highest resistance to corrosion. The presence of nickel In these high-chromium steels did not affect their resistance. 2. Steels containing approximately 5 per cent of chromium showed comparatively high resistance, but somewhat less than that of the high-chromium steels.

Jan 1, 1934

By Kiyoshi Azuma, Hiroshi Kametani

The variation of the dissolution behavior of a ferric oxide with calcining temperature has been investigated. Samples were prepared by thermal decomposition of ferric hydroxide, nitrate, oxalate, and sulfate at low temperature, followed by the calcination in the temperature range between 600" and 1200°C. The samples of eight series and a fine crystalline sample of hematite were dissolved in 1 N hydrochloric acid at 55.2°C and the results are represented on double-log graphs for convenience. It is confirmed that all dissolution courses follouj either the accelerated process or the parabolic process except in the special case of the crystalline hematite which dissolced in accordance with the uniform dissolution of a particle. Examinations of the physical properties of the oxide powders revealed that the surface area measured by the permeability method is strikingly relevant to the dissolution behavior of the oxide. In the previous paper,' detailed data were presented on the effect of the kind of acid, the solution temperature, and the concentration of acid on the dissolution of two ferric oxides. It was also shown that these sam ples dissolved in strikingly different ways. The present investigation was carried out on the dissolution of various calcined samples prepared from various ferri salts by various methods to ascertain the course of dissolution. Pryor and Evans2 pointed out a change of the dissolution rate at around 700°C for a series of calcined ferric oxides prepared from the hydroxide. Several papers374 reported also the dissolution of ferric oxide samples. It seems, however, that a systematic account of the relationship between the dissolution behavior and physical properties of the oxide has not yet been given. This paper presents the variation of the dissolution of the oxide in relation to the calcining temperature and the change of physical properties of the calcines. EXPERIMENTAL Raw materials were prepared by precalcination of ferric hydroxide, thermal decomposition of ferric nitrate, oxalate, and sulfate, and aerial oxidation of ferric chloride vapor, at as low a temperature as possible. The products were crushed, ground, if necessary, and sieved with a 100-mesh Tylor screen prior to calcination, after which the specimens were dissolved in acid solution. The following is a detailed description of the preparation of the samples. Sample H. About 500 g of ferric chloride (guaranteed reagent) were dissolved in 5 liters of deionized water and filtered. Ferric hydroxide was precipitated by addition of the minimum amount of ammonium hydroxide solution, and the precipitate was washed continuously till chloride ion was not detected by silver nitrate solution, and then filtered. The filter cake was dried at 120°C for a week and ground, and the -100 mesh portion was used. Sample S. Ferric sulfate (guaranteed reagent) was pyrolytically decomposed in a crucible at 700°C for 24 hr and the product was sieved. In this case the following calcination was carried out at temperatures over 700°C. Sample B. Commercial ferric oxide (guaranteed reagent). About 15 kg of ferric nitrate were decomposed in a furnace maintained at 800°C for 2 hr. The actual temperature of the decomposition was not measured. The product was crushed and sieved, and the -100 mesh portion was used. Sample N. About 50 g of ferric nitrate (guaranteed reagent) were decomposed in a beaker in a sand bath until a red-brown dense solid was produced. This product was crushed and sieved, and subjected to complete decomposition at 500°C. The precalcined product was again sieved and used. Sample N2.5. Since the decomposition temperature was not controlled for sample AT, a different sample was prepared in a temperature-controlled furnace. The subscript represents the decomposition at 250°C. The product was treated in the same manner as sample N. Sample Nc. Under atmospheric pressure it is prac-tically inevitable that ferric nitrate hydrate melts to form a brown liquid at about 50°C before pyrolysis. For this reason, the salt was first slowly heated under reduced pressure (about 10-3 mm Hg measured in a trap refrigerated by dry ice-alcohol) to achieve dehydration without melting. About 5 hr were required for the dehydration and the partial decomposition. Then the temperature was elevated to 500° C in air for complete decomposition. The relatively porous product was sieved and used. Sample Ov. About 200 g of ferric oxalate hydrate (extra pure) were dehydrated under reduced pressure (as described above) followed by thermal decomposition at 500°C for 6 hr in air. The decomposition of this salt was accompanied by liberation of carbon monoxide, by which the ferric salt was initially reduced to a black powder. The powder changed in turn into brown ferric oxide as the gas liberation decreased and reoxidation predominated. The product consisted of sparkling fine particles passing through a 100-mesh screen. However it was ground and sieved as for the other samples. Sample D. Commercial fine powder for magnetic tape purposes. The preparation was as follows.5 Ferric chloride vapor and preheated excess air were mixed and passed into a reaction tube where oxidation took place at 450°C. The fine powder formed was collected in a cottrell chamber. The product was vacuum-degassed at 450°C for 1 hr and sieved.

Jan 1, 1969

S., at Niagara Falls, as an expert chemist. There he was engaged in perfect.ing the various kinds of gases, and while thus employed was gassed several times, which so affected his heart and lungs that he was unable to withstand an attack of the influenza which developed into pneumonia, from which he died at the end of 24 hours. He was a member of St. Luke's Episcopal Church, Lebanon, and belonged to the Ancient Accepted Scottish Rite of Freemasonry, Lebanon Lodge 121, I. 0. 0. F. and Camp 65, P. 0. S. of A. Lieutenant Bernhardt Edward Heine Bernhardt Edward Heine, a lieutenant in the Aviation Service of the U. S. Army, died as the result of a fa1I1 in an aeroplane at Fort Sill, Okla., on Aug. 10, 1918. The accident occurred on Aug. 2, when the machine in which he was flying with Lieutenant Carsons fell from a height of 1500 ft.; Lieutenant Carsons was instantly killed, but Lieutenant Heine died from his injuries a week later. Lieutenant Heine was born at Mount Clemens, Mich., in 1895. After attending the local High School he entered the Michigan College of Mines, and became a Junior Member of the Institute while still a student. He graduated in 1916, with the degree of B. S. In 1914 he served as a transitman for the engineering department of the City of Hancock, Mich. Lieutenant Heine had been in the army since 1916, having been with the 'troops at 'the Mexican border. He had been in the Aviation Section since August, 1917.

Jan 1, 1920

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields