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By Harrison Everett Ashley

Prof. Hofman's diagrams, Figs. 5 and 7 of his paper, which are reproduced as Figs. 1 and 2 of the present contribution, confessedly fail to show comprehensively the properties of the silicates investigated. Each curve is carefully discussed, and the author has evidently drawn all the conclusions that can be thus reached; but he says :* "The curves do not show, as was hoped, any simple connection between silicate-degree, percentage of lime, and minimum of formation-temperature." There is, therefore, in this case, an excellent opportunity of

Jan 1, 1902

By Pol Duwez, Paul Pietrokowsky

The crystal structure of the compound TisGeS has been determined from X-ray powder diffraction data. Related silicon and tin compounds have been found to be isomorphous. Unit cell dimensions, axial ratios, and parameters for equivalent atomic positions are given. THERE is, at present, only meager information pertaining to the solid state reactions of titanium with the elements in group 4B of the periodic table (silicon, germanium, tin, and lead). The only two compounds whose crystal structure has been established are TiSi² and TiGe² (references 1 and 2 respectively). These two compounds are isomor-phous and have an orthorhombic symmetry D242h— Fddd. The titanium-rich regions of the constitution diagrams of titanium-silicon, titanium-tin, and titanium-lead have been investigated by Craighead et al.³ While valuable information concerning the alpha solid solubility of these three elements in titanium was obtained, no light was shed on the existence or nature of the titanium-rich compound in these systems. The present study is concerned with the crystal structure of the intermediate phases Ti5Si ?, Ti³Ge³, and Ti5Sn³, which were found to be isostructural. The alloys were prepared by mixing the pure metal powders in the desired proportions, pressing the mixture into pellets, and melting them in an electric arc furnace in the presence of a helium atmosphere.& After melting, the specimens, weighing approximately 5 g, were sealed in evacuated quartz vials, homogenized at 1038°C for three days, and quenched from that temperature. Powder diffraction patterns were made with a 143.2 mm diam Debye-Scherrer X-ray camera in which the Ievins and Straumanis film arrangement was utilized. Filtered copper radiation was used throughout the entire investigation. A study of the powder patterns of a series of alloys of various compositions indicated the presence of a compound around a composition corresponding approximately to a ratio of 3 titanium to 2 silicon, germanium, or tin. From a visual examination of the diffraction patterns, it was evident that the silicon and germanium alloys were iso- morphous. For small angle reflections, the powder pattern of the tin compound was analogous to that of the silicon and germanium compounds, but after the first ten reflections, the similarity was no longer clear. The powder pattern of the germanium compound was selected for indexing, since it exhibited a weak small angle reflection and clearly resolved doublets in the back-reflection range. Good agreement between observed and calculated values of (1/d)² was found by indexing the pattern on the basis of hexagonal symmetry. For the hexagonal system:

Jan 1, 1952

By J. B. Cohen

In an investigation of the microstructure of shock-loaded metal specimens1 C. S. Smith found that there was little distortion of grain boundaries or change in external dimensions, although the hardness corresponded to that produced by severe rolling. Furthermore, the hardness of individual grains was independent of the deformation structures present; grains with no markings were as hard as those heavily populated with markings. These markings which resemble twins do not appear in copper until high shock-loads of the order of 200 kb are applied. It appears that due to the high velocity of a shock wave and its sharp front, heavy deformation takes place on a submicroscopic scale. In this work an attempt was made to examine this deformation, particularly at a load below which macroecopic markings appear. The broadening of 200 and 400 diffraction peaks was examined from the face of a poly crystalline sample normal to the direction of the shock wave. These peaks were chosen because the elastic constants in copper are such that residual strains would be greatest in the <100> directions; hence, the strain-broadening contribution to these peaks would be large in comparison to other sets. Also the broadening due to stacking faults and microtwins would be greatest with this set.2 A complete Fourier analysis of these peaks was made, as described by warren,&apos; using the Stokes correction with peaks from an annealed sample.3 With the aid of the U. S. Army Ordnance Corps EDVAC computer and a curve matching program, sixty sine and sixty cosine coefficients were obtained for each peak. The last of these was about 1.5 pct or less of the largest coefficient, indicating good representation. Transverse sections from a 1.5 in. rod of as-drawn electrolytic tough-pitch copper were reduced in cross-sectional area about 50 pct by cross rolling. Disks 1.5 in. in diam were recrystallized at 275 °C for 30 min and then at 300°C for the same time. The faces were polished and deeply etched in nitric acid to remove 25 mils. The grain size was 0.02 mm. Laue back-reflection patterns indicated the sample was well recrystallized. The two diffraction peaks from this sample were recorded on a Norelco diffractometer using filtered copper radiation. Peak intensities were kept less than 600 cps to assure linearity of the counter and circuitry. This sample was then placed between two rods of the same material and diameter. The top rod was 2.25 in. long and the bottom rod 1 in. long. (In

Jan 1, 1961

By George Hulst

PRIOR to 1914, there was little demand for antimony in this country; its use was limited almost entirely to the manufacture of type and bearing metals. Practically no antimony ore was mined here, the market being supplied principally from China, and the alloy was produced by a direct mixing of lead and antimony. The great world war, with its demand for shrapnel in hitherto undreamed of quantities, precipitated a great boom in the price of antimony. Nominally quoted at 6 c. to 7 c. in 1914, the price increased by leaps and bounds to 45 c. in March, 1916. Under the stimulus of high prices many shall mines were opened, for it became profitable to work ores containing as low as 20 percent. antimony. High-grade sulfide ores (stibnite), containing 55 per cent. to 60 per cent. antimony, were received from Bolivia, China, and Alaska. Low-grade sulfide ores, running from 20 per cent. to 45 per cent., were produced in Nevada, California, Idaho, Utah, and Mexico; much of this ore was fairly rich in silver. The principal oxide ores came from Mexico and Oregon. The following analyses are representative of various types of antimony ore: Se Pn Cu Ao Au SIC), Fe S CAO ZN As Oxide Ore 25.09 46.02 0.95 0.40 10.98 0.30 0.22 Sulfide ore 5.5.20. 15.12 1.05 19.87 ? 0.40 0.25 Sulfide Ore 37.16 11.30 0.10 34.0 7.60 0.50 17.05 7.40 0.36 0.10 Sulfide Ore 41.55 15.00 0.20 76.0 0.04 5.60 0.25 18.17 0.85 0.25 0.10 The International Lead Refining Co. fortunately was equipped to handle these ores through residue and blast furnaces. The charge consisted of a variety of sulfide ores containing Sb 20 to 60 per cent. and Si02 6 to 45 per cent., oxide ores containing Sb 20 to 40 per cent. and SiO2 10 to 45 per cent. Secondary materials, such as battery plates, battery mud, lead oxide, paint, etc., together with refinery skims, softener skims, and other refinery byproducts, were treated along with the antimony ore to furnish the lead required. All silver-bearing antimony ores were treated in the residue furnace, the sulfur, iron, and copper forming matte that carried part of the silver, the balance going into lead bullion. The

Jan 9, 1919

A recent study estimates that a 10% improvement in the performance of wire rope used on draglines could save the US coal industry $2 million annually in rope costs. In addition, such an improvement could boost annual coal production by allowing the industry&apos;s draglines to remove an extra 1.5 million m3 (2 million cu yd) of solid overburden each year. These findings, although admittedly preliminary, suggest the magnitude of benefits that can be derived from a well-planned wire rope maintenance program.

Jan 3, 1978

By Akira Yazawa, Alžbeta Gubcova

RECENT lead-smelting techniques have tended toward use of high-grade concentrates with minimum amounts of flu, accompanied by profitable employment of roast reaction.1-5 In order to better understand these smelting processes, thermodynamical calculations have been carried out on the Pb-S-0 system, and the results obtained have been presented in isothermal reaction diagrams in which log Ps, and logPo, were the axes. The diagram thus constructed seems to be more convenient to grasp the equilibrium aspect than those published hitherto.6-8

Jan 1, 1968

By B. W. Gonser, C. M. Heath

The importance of grain size and its control in wrought brass needs no lengthy discussion, since specifications so often make exact control imperative. Aids to this control are therefore of interest. The effect of a number of different elements on the grain growth of brass under various conditions of annealing has been reported in the technical literature. In particular, a paper by Cook and Miller1 a few years ago, with the discussion that followed, gave valuable information on the effects of iron, phosphorus, manganese, aluminum, aluminum plus nickel, and aluminum plus silicon. Price12 in his discussion of that paper, added a description of some commercial brasses that exhibited a grain-refining effect owing to the presence of 2 per cent A1 and 1 per cent Ni. Gibson and Doss3 have recently given data on the effect of iron on annealing high brass. No comprehensive study, however, has been given to the effect of additions of chromium. It has been the purpose of this investigation to determine the effect of adding various amounts of chromium to a plain cartridge brass, particularly in regard to the effect on grain growth in various annealing treatments after cold-working. Prepakation of Alloys Alloys of high-purity brass of 68.5 Cu, 31.5 Zn composition were made containing from 0 to 0.17 per cent Cr. These were produced in induction furnaces, using unlined graphite crucibles to hold the charge. The melts were cast into rectangular chill molds giving ingots about % by 3 by 10 in. in size.

Jan 1, 1938

By C. M. Heath, B. W. Gonser

The importance of grain size and its control in wrought brass needs no lengthy discussion, since specifications so often make exact control imperative. Aids to this control are therefore of interest. The effect of a number of different elements on the grain growth of brass under various conditions of annealing has been reported in the technical literature. In particular, a paper by Cook and Miller1 a few years ago, with the discussion that followed, gave valuable information on the effects of iron, phosphorus, manganese, aluminum, aluminum plus nickel, and aluminum plus silicon. Price12 in his discussion of that paper, added a description of some commercial brasses that exhibited a grain-refining effect owing to the presence of 2 per cent A1 and 1 per cent Ni. Gibson and Doss3 have recently given data on the effect of iron on annealing high brass. No comprehensive study, however, has been given to the effect of additions of chromium. It has been the purpose of this investigation to determine the effect of adding various amounts of chromium to a plain cartridge brass, particularly in regard to the effect on grain growth in various annealing treatments after cold-working. Prepakation of Alloys Alloys of high-purity brass of 68.5 Cu, 31.5 Zn composition were made containing from 0 to 0.17 per cent Cr. These were produced in induction furnaces, using unlined graphite crucibles to hold the charge. The melts were cast into rectangular chill molds giving ingots about % by 3 by 10 in. in size.

Jan 1, 1938

By D. Gupta, S. Weinig

This investigation comprises the study of dislocation-oxygen interactions in a! titanium and its effect on the ductile to brittle transition in titanium. Internal friction techniques using a low-frequency lorsion pendulum were used to study the oxygen atom interactions with dislocations in "superpurity" titanium. A calculation of the interaction energy between an oxygen atom and a dislocation, based on the "breakaway" strain resulted in a value of 0.015 ev as compared to theoretical values of 0.022 and 0.035 ev for edge and screw dislocations, respectively. Both the saturation of the room temperature decrement and the transition from ductile to brittle behavior occurred at 1.5 at. pct 0. It was proposed that the embrittlement was due to oxygen atoms immobilizing the dislocations. It was possible to increase the ductility of the Ti-0 binary alloys by decreasing the oxygen pinning. The increase in uniform elongation was 30 pct for an increase in the preanneal temperature of 300°C. ThE room-temperature ductility of a titanium is significantly affected by interstitial solutes. Although oxygen has a solid solubility of 15.5 pct by weight, the room-temperature ductility extends only to 0.6 pct.&apos; The ductility precipitously falls at this concentration and the fracture characteristics change from ductile to brittle.2 The small effective bulk composition of solute required to destroy the room-temperature ductility of the titanium must be indicative of an in-homogeneous distribution of solute atoms. Internal friction techniques were used in this investigation to

Jan 1, 1960

By Clyde Wyman

THERE has always been a question as to the extent to which oxidizable alloys might he recovered from charged scrap in the, acid electric furnace. While qualitative information was not lacking, the quantities that might be recovered and the conditions best suited for such recovery were not clearly defined. The present investigation was carried out to determine the efficiency of alloy recovery from residuals contained in the bath, especially in regard to the recovery of vanadium. A series of 24 heats was produced at the Burnside Steel Foundry Co., including medium manganese-molybdenum-vanadium, manganese-chromium, and grade B steels, in which vanadium recoveries from the residual vanadium were investigated. Recoveries of other alloys were also studied from the accumulated data. These heats were produced in a 5-ton acid-lined electric furnace. The analysis of metal and slag samples and the micrographs were prepared by the Research Laboratories of the Vanadium Corporation of America. In addition to the vanadium contained in the scrap charge, ferrovanadium was added to the charge and to the molten bath to bring the residuals up to the desired level. Vanadium pentoxide (V2O5) in one series of heats was added to the bath after meltdown, for the same reason. In addition to the general furnace practice, the slags of these various heats were treated with coke breeze, Ferrocarbo-S (silicon carbide), and aluminum dross to determine the effects of different reducing agents upon the alloy recoveries and upon the final product.

Jan 1, 1947

By Clifford S. Wilson

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

Jan 1, 1933

By Ira Joralemon

THE sampling of disseminated copper deposits has been described often but the method of combining assays, to give the true shape and value of the orebody as it will be mined has received less attention. As the ore mined during five or ten years at several of the great disseminated properties has averaged materially lower in grade than the published estimates, the question of the sampling and estimating of these orebodies seems timely. In this paper, attention is given particularly to factors that may cause errors in the final estimate. Sampling of diamond-drill holes, churn-drill holes, and underground workings is briefly described in the first part of the paper; then the method of combining assays to give the average grade and tonnage that will be mined is taken up in some detail. The necessity of study of the geology of the deposit and of probable costs is emphasized. Finally, the methods of calculating tonnages are outlined. DIAMOND-DRILL SAMPLING There are three main requisites for accurate diamond-drill sampling. First, the core should be removed and the hole cleaned out at the beginning of every sampling interval, usually 5 ft. (1.5 m.). After the rods are let down, water should be run through them until it becomes clear. The water must be clear before drilling starts. In this way the material knocked down from the sides of the hole by the descending rods is washed away, instead of being left to salt the sludge, sample.

Jan 2, 1922

By H. Rush Spedden

R. T. Hukki has extended his study of ball mill grinding at supercritical speeds with an excellent mathematical analysis of tumbling mill grinding. When he speaks of supercritical speeds he is referring to the original Fahrenwald critical-speed formula. He said that, as an example of the use of supercritical speeds, if a fine grinding mill of any type is wet-grinding ore of 3.5 sp gr with steel balls at a certain conventional subcritical speed, the same power input and capacity should be obtainable with autogenous medium of 3.5 sp gr at a speed 100 to 120 pct of the critical in a grate- type mill of the same effective size. In addition, he introduced what he calls the base mill concept which, he stated, makes it possible to compare performances of mills of different sizes grinding with a metallic medium or with an autogenous medium of any specific gravity and at any speed. He showed the use of this concept and explained how it makes possible the evaluation of mill sizes and motors for any grinding purpose at any accuracy well within the conventional standards of design in milling practice. He further stated that the maximum capacity in pilot plant mills with various media, either metallic or autogenous, has always been found to be within the supercritical speed range. In his discussion of this paper he substantiated these findings with statements showing the increased capacity obtained in a milling plant in Finland which followed his principles.

Jan 7, 1960

By Samuel Lasky

THE writer has been interested in determining the mineralogic dis-tribution of silver in the base-metal ore of the Ground Hog mine of the Asarco Mining Co. in the Central mining district of New Mexico.1 This ore consists of a varitextured mixture of sphalerite, chalcopyrite, galena and pyrite in a quartz gangue. The average ore contains 14 per, cent of zinc, 9.5 per cent of lead, 5 per cent of copper, and 10 oz. of silver per ton. Generally it is accepted that the silver in ores of this type, in which no definite silver minerals can be recognized, is contained in the base-metal minerals. Published assays of pure mineral specimens from many dis-tricts show that each of the base-metal minerals contributes in some degree to the total silver content of the ores, and to determine the pro-portionate amount contributed by each mineral in any specific ore it has been the practice to assay selected specimens of each mineral, the purity of which has been determined microscopically. There being no such assays available for the Ground Hog ore, and it being impract cable to have enough of them made to give average results, the writer resorted to a mathematical attack upon composite assays of large quantities of ore and concentrates. Surprising results were obtained, and it is the threefold purpose of this paper to present these results, to describe the mathe-matical method used, and to point out the value of using this method even when assays of pure specimens are available.

Jan 1, 1934

By R. T. Mishler

Silver-gold. mine, in northern Mexico, with arrow veins in rhyolite. One fourth area developed has been ore. Deposits average 20 in. wide and 73 oz. silver per ton; diluted in mining to 40 oz. per ton. Developed by drifts and raises at 100-ft. intervals. Samples cut every 5 ft. Ore and waste sampled separately to make combined stoping width 3 or 3 1/2 ft. Ore reserves figured to sloping width; high assays not modified. Tonnage and assay of ore extracted higher than estimates. Ore stoped principally by cut and fill method. Cars from each stope counted and sampled. Cars check tonnage to concen¬trator within 1 per cent.; silver assay 9 per cent. high. Tonnage and assay from scopes corrected to agree with feed to concentrator. Profit or loss for each slope estimated monthly. THE Lucky-Tiger mine is a silver-gold property, situated at El Tigre, in the northeastern part of Sonora, Mexico, at, an elevation of 6000 ft. in the Sierra Madre Mountains. It is 30 miles by wagon road from the Esqueda station on the Nacozari railroad. Since its discovery in 1903, the mine has produced forty million ounces of silver. The ore has averaged 40 oz. silver and 0.25 oz. gold per ton. Copper, lead and zinc have been of minor importance, having averaged 0.4 per cent., 1.1 per cent., and 1.5 per cent., respectively. The richness of the ore,, combined with its occurrence in narrow veins, required the use of the more expensive methods of mining.

Jan 2, 1925

By R. J. Borg, C. E. Birchenall

The self-diffusion coefficients for a iron have been deternzined between 980° and 1167° K using Fe55 as the tracer. With decreasing temperature the diffusivity was found to decrease more rapidly than predicted by the Arrhenius equation in the region of the Curie temperature. The diffusion coefficients obtained well above the temperature of the magnetic transformation are more precise ard differ substantially from all the previously reported values. In the temperature region beginning at least 50" above T,, the diffusion coefficient is given by D = 118 (±2) exp 1 HE self-diffusion coefficients for a iron have been reported previously as the result of four independent investigations The general lack of agreement and the poor precision of most of the previous work prompted the redetermination by the present authors. The possible effect of the onset of ferromagnetism upon the diffusivity5 provided an additional impetus for this investigation. The earlier measurements of Birchenall and Mehl1 gave low values for the diffusion coefficient at temperatures below the Curie temperature, Tc. However, the precision of these measurements is not sufficient to establish an indisputable correlation between the low values and the magnetic transformation. The results of this investigation along with all the previous ones are shown in Fig. 1. EXPERIMENTAL Small rectangular samples, approximately 1 by 0.5 by 0.3 cm, of high-purity iron (Vacuum Metals Corp., "Ferrovac") are first heated in hydrogen at 900°C for24hr in order to remove possible trace amounts of dissolved carbon and oxygen. The small

Jan 1, 1961

By F. A. Hill

Coal mining in the State of Washington offers many interesting problems for the mining engineer, due to the varied physical conditions occurring in different fields, and often in, the same mine. The different coal seams worked in the same mine commonly require different mining and transportation methods for economical operation. The coal measures have inclinations ranging from 5° to vertical, and in the same mine the dip of the coal may vary from 30° to 50°. In all fields, the seams are extensively faulted, folded, and sheared. The quality of the coal produced ranges from brown lignite to bituminous- coking coal, the following being typical analyses: Lignite Sub Coking Coal bituminous Moisture 23.5 14.30 0.57 Volatile hydrocarbon 31.0 33.03 23.57 Fixed carbon 37.4 41.30 65.55 Ash 8.1 11.37 10.31 100.0. 100.00 100.00 Very little of the coal contains as much as 0.75 per cent. sulphur. The brown lignites occur mostly in Lewis and Thurston Counties, and, as a rule are very cheaply mined. This coal has been successfully used in locomotives of the Oregon & Washington Railroad, after equipping them with specially designed fireboxes. The sub-bituminous coals occur in all the coal-mining counties. Their cost of production varies widely, according to the character of the formations, the pitch, and the wall conditions. This makes a fairly good steam coal, but the lump is used mostly for domestic trade, after grading into lump, nut, and pea.

Jan 4, 1918

By R. S. Sandhu, L. E. Baker, W. Y. Shieh

The finite element method of analysis was introduced by Clough.1 Within a short period, it has developed into a powerful solution technique in structural and continuum mechanics. It has been used to solve boundary value problems in two and three-dimensional elasticity.2-5 Anisotropy and heterogeneity of materials were allowed for at the earliest stages. 1,4 Its application has been extended to allow for cracks,5 creep and viscoelasticity, 6,7 incremental construction,6-8 nonlinear elasticity3,9 effect of joints in rock,10 and to materials with different behavior in tension and compression.7 Because of its versatility, the finite element method has found increasing application in the field of rock mechanics. In fact, several of the more significant developments have been motivated by problems in this field. Elasto-plastic material behavior based on the incremental or rate-type theory of plasticity rather than the deformation theory was considered by Reyes and Deere11 A material law based on a generalization 12 of the Mohr-Coulomb criterion was used. In this chapter, the formulation of material laws developed by Reyes and Deere 11 is used. An efficient analysis procedure, incorporating recent developments in finite element analysis, is developed for plane-strain conditions. To demonstrate its effectiveness, the procedure is applied to three cases, one for which an exact solution is available, another for which field observations had been made, and a third one for which a parallel study was made, using an accepted limit-equilibrium method.

Jan 1, 1970

By R. P. Smith, L. S. Darken

FOR a high-purity iron-carbon alloy, the phases existing at equilibrium at temperatures slightly above the temperature of the metastable eutectoid are austenite and cementite (hyper-eutectoid) or austenite and ferrite (hypo-eutectoid) and those below the eutectoid temperature (carbdn content > 0.02 pct) are ferrite and cementite. Such an alloy, held in a carefully controlled and measured temperature gradient (about 1 cm per deg) which includes the eutectoid temperature, then quenched and examined metallographicall.y, provides a precise measure of the eutectoid temperature. The samples were hollow cylinders approximately 1.3 cm OD, 0.63 cm ID, and 2.5 cm long, which had been carburized to the desired carbon content at 1000°C with an appropriate hydrogen-methane mixture. In order to cool the samples to room temperature with a minimum change of carbon content and absence of cracks they were quenched in a Cerro Bend bath at 480°C, followed by a water quench to room temperature. Three cylinders were suspended in the furnace1 in a purified helium atmosphere, by a closed end, thin wall, silica tube which also served as a thermocouple well. The top and bottom cylinders served only as a means of making the temperature gradient along the center cylinder more uniform. The temperature was determined with a platinum-platinrhodium thermel calibrated by comparison with a thermel certified (* 0.5OC) by the National Bureau of Standards. After holding in the temperature gradient for 24 to 72 hr the samples were quenched in Cerro Bend at 480°C, followed by

Jan 1, 1960

By Teder R. I., M. M. Protodyakonov

In order to find an empirical relation between a quantity F and (m) independent variables or factors, each of which take (n) different values or levels, it is necessary to conduct nm different experiments (all possible combinations of the factors), each of which has to be repeated a few times (usually five) due to the scattering of the data. The total number of such experiments is very large, thus for example, when m = 4 and n = 5, it is equal to 5.54 = 3125; and very rarely is it possible to conduct such a number of experiments. Various possible methods of planning partial experiments are illustrated in Fig. 1. Each method shows a large combinative square consisting of five columns and five rows of middle squares, each of which, in turn, is further divided into five columns and five rows of cells. Such a partition corresponds to a plan of an experiment with four factors, each of which takes five different levels. The blackened cells indicate the combination of factors in a partial experiment. The total number of experiments is reduced on the basis of the following considerations: a) The effect of only a few levels of some factors is studied (Fig. la). Such an investigation gives no information on the effect of some factors, therefore it cannot be accepted as satisfactory; b) By reducing the number of levels of each factor; in such a case it is not possible to obtain an empirical relationship, but only whether some factors have an effect. This is evidently inadequate;

Jan 1, 1971