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By J. R. Thoenen

THE consensus of opinion in the published literature on. Grecian magnesite is that it has been formed by alteration of the serpentine, which in turn was itself a product, of metamorphism from the original olivine intrusion. The general opinion seems to be that the magnesite was formed by descending waters heavily charged with CO2. Inasmuch as this opinion is held by engineers far better qualified than I to speak authoritatively on this subject, I hesitate to dispute that theory. However, certain occurrences coming under my observation do not, to me at least, seem to-entirely substantiate this theory. LOCATION Most of the Grecian magnesite comes from the Island of Euboea, although more recently some deposits have been opened on the mainland near the City of Saloniki, which prior to the war was Turkish. The island, comprising a state or province in the Greek political structure, is roughly 110 miles long and varies from 10 to 30 miles in width. It lies off the east coast of the Greek peninsula in the AEgean Sea with its long axis extending in a northwest-southeast direction. It is separated from the mainland by a long narrow arm of the sea known as the Atalanti Canal. Chalkis (Halkis), the capital on the west coast of the island, is the northern terminus of a branch of the state-owned railway and is connected with the mainland by a single-span, movable, highway bridge, roughly 150 ft. long.

Jan 1, 1928

By I. L. Nichols, D. C. Seidel, D. E. Traut

A fluidized countercurrent ion-exchange system was developed, operated, and evaluated by the Bureau of Mines. The system consisted of integrated multiple-compartment absorption and elution columns in which the solution flows are continuous except for short periods when resin increments are withdrawn. The exchange of uranyl sulfate between a simulated acid leach uranium solution and a strong-base, ion-exchange resin together with the subsequent elution with an acidified sodium chloride solution was studied. The effects of the number of sections, section heights, amount of resin withdrawal, and solution flow rates were investigated. Also examined were the kinetic and equilibrium relationships for the absorption step. The experimental data indicate a strong interdependence between variables. Solution retention time appears to be a major limiting variable. The column was efficient over a range of conditions, but close control was needed for optimum operation.

Jan 1, 1977

By H. A. Dierks

PENNSYLVANIA's anthracite region lies in the heart of the richest and most densely populated area of the U. S. Nearly 70 million people live within a radius of 500 miles, in which 130,000 manufacturing plants employ more than 8 million workers. The region comprises some 3000 sq miles and contains 484 sq miles of coal measures, which folding and erosion have divided into four separate and distinct fields, known as the Northern, Eastern Middle, Western Middle, and Southern.

Jan 10, 1957

By G. W. Cullen

Niobium-tin has been prepared on insulating suhstrates hby simultaneous hydrogen reduction of gaseous niobium and tin halides. Stoichiometric material is greater than 98.8pct theoretical density, appears to he single-phase, and has a total impirity level less than 0.3 at. pct. Transition temperatures and lattice constants may he related to composition. Typical current densities in various fields and orientations are given. IT is known that Nb3Sn carries large current densities in high fields, 1 and exhibits an unusually high transition temperature2 and critical field.3 For these reasons high-field solenoids have been constructed of this material.4 Because of the emphasis on solenoid fabrication, much of the materials research has been directed toward development of wire geometries wherein the brittle Nb3Sn is supported by a more malleable metal or alloy. There are, however, basic studies and applications that can be carried out only on Nb3Sn supported by an insulator. Insulating substrates are desirable for a number of reasons: the substrate does not interact with applied or induced currents and fields; diffusion of metallic species into the de- posit is avoided, both during the preparation and during subsequent heat treatment; irradiated samples are not more active than the deposit itself. Unsupported Nb3Sn geometries may also be prepared by preferential chemical dissolution of the insulating substrate. This report describes the preparation and properties of Nb3Sn deposits on ceramic substrates. Experiments currently utilizing material prepared in the manner described in this report include the following: dependence of current-carrying properties on field strength and orientation 5,6 radiation damage,7,8 tunneling,9 thermal conductivity (substrate removed),1° microwave surface impedance," tube magnetization,6,12 resistivity as a function of temperature,13 and current density and transition temperature as a function of annealing.14 Possible practical applications include magnetic shielding, superconductor generators, and frictionless bearings. PREPARATION Methods for the deposition of elemental niobium and tin by hydrogen reduction of the gaseous metal halides have been known for some time,15,18 but only recently a procedure was developed in this laboratory17 for the codeposition of these two metals on a hotwire as the intermetallic compound, Nb3Sn. This method of simultaneous hydrogen reduction of the gaseous niobium and tin chlorides is used for the preparation of Nb3Sn On ceramic substrates. The procedure differs from that employed on a hot wire in that insulating substrates cannot conveniently be heated to temperatures greater than their surround-

Jan 1, 1964

By John W. Rushton

What role does maintenance play in the design of a new mineral processing facility? Consider the fact that most new plants never reach design capacity the first year-or the second, third, or fourth years. The fact is, according to data collected from several plants which have started up in the last ten years, mill throughput and equipment availability doesn't peak, on the average, until the fifth year.

Jan 3, 1978

By O. S. True, C. H. Herty

It is well known that manganese will desulfurize molten iron through the formation of manganese sulfide, which, being only slightly soluble in the metal, rises to and enters the slag where it remains as such (mixer slag) or is converted partly or wholly to calcium sulfide (basic open-hearth slag). The reaction by which manganese sulfide is formed is Mn + FeS = MnS + Fe. This reaction is generally considered to be reversible, although McCancel states that such is not the case. The experimental work was carried out to confirm the results of Roh12 as to the reversibility of the reaction. Six trials are herein considered. In each 200 gm. of electrolytic iron free from manganese and sulfur were melted in a pure zirconia crucible in a carbon resistance electric furnace. To the melted iron in runs 2, 3 and 4 metallic manganese and manganese sulfide were added to give 1, 2 and 4 per cent. manganese respectively, with 0.50 per cent, of sulfur in each. In runs 5, 6 and 7, metallic manganese and iron sulfide to give the same proportions of. manganese and sulphur as in runs 2, 3 and 4, were added. The melts were held molten in the furnace for an hour and then cast into small ingots. The results of these melts are as follows: Ingredients of Charge Analysis or InRot ManOaneBe, SulfUR, ManOaneBe. SULFUR, Run Material Charged PeR Cent. PeR Cent. Per Cent. PeR Cent. 2 MnS + Mn............... 1.0 0.452 0.636 0.367 3 MnS + Mn............... 2.0 0.50 1.57 0.310 4 MnS + Mn............... 4.0 0.50 2.81 0.230 5 FeS + Mn................ 1.0 0.50 0.647 0.397 6 FeS + Mn................ 2.0 0.50 1.45 0.374 7 FeS + Mn................ 4.0 0.50 2.73 0.195

Jan 1, 1925

By A. H. Geisler

INTRODUCTION THE correlation of property changes during precipitation with structure has progressed, sometimes rapidly but other times more slowly, since the fundamental discovery of Merica, Waltenberg and Scott.1 The predominent factor that hampered the progress has been limitations imposed by the various detection methods. Refinements in X ray diffraction techniques and in metallographic methods, which have been extended by the electron microscope, have contributed new information within the last few years. These permit an extension of the theory as proposed by Mehl and fetter in 1940.2 Now that a suffcient number of alloys has been investigated to establish a general mechanism of the precipitation process, a correlation of the facts into a generally applicable theory of age-hardening is both warranted and desirable. 'I he purpose of the paper is to provide an orderly correlation of the phenomenological facts of precipitation hardening. Speculation on mechanism of hardening will be confined to that consistent with existing theories of hardening. Age-hardening accompanies the formation of a new structure, the precipitate, as provided by an alloy system in which solid solubility decreases with decreasing temperature. Upon this premise alone all such systems would be expected to include age-hardenable alloys. Alas, this is not always the case. Few attempts have been made to explain the variable degree of age-hardening among different alloys or to explain the influence of small alloying additions upon the hardening. Dispersion hardening as originally postulated3 is not adequate.* Coherency hardening-the term that will be used to distinguish the properties of a two-phase mixture in the unique and unstable transition state at which the phases are strained into precise atomic registry (continuity or coherency) in planes

Jan 1, 1948

By L. D. Anderson

WHEN, after years of troublous experiences in roasting sulfide ores with heavy dust and fume losses resulting from the equipment and methods first available, there appeared on the, scene of metallurgy that revolutionary process known as sintering, it was felt that at last there had been found the ideal method for preparing sulfide ores for blast-furnace reduction. Not only were the sulfides roasted but also the fine oxidized ores were bound together with them in strong porous cellular masses which were in the best possible condition for reduction. With the experiences gained in the manipulation of the Huntington-Heberlein, Carmichael-Bradford, and Dwight & Lloyd processes there developed a refinement of detail which brought the whole plan of roasting by sintering to a high plane of perfection. But that metallurgy is never stationary is revealed by the fact that changes in milling practice, particularly the development of flotation, have introduced a new set of problems in sintering itself. Inasmuch as it is felt that these problems have not yet been solved in an entirely satisfactory manner this paper is written to record the present practice of the Salt Lake Valley smelters with the hope that there will be brought forth such discussion as may perhaps lead to still better practice. By far the greater proportion of the sulfides smelted today are flotation concentrates. Usually they are high grade, sometimes as high as 70 per cent. and more in lead. They are extremely fine, many mills grinding the ore so that from 60 to 80 per cent. will pass through screens of 200 mesh. The physical condition in which many of these concentrates reach the smelters is disconcerting to the metallurgists. Some are of about the consistency of putty. Others are of a sticky, slimy nature. Others again, dried to the limit, are veritable powders. Remembering that the down-draft sintering charge for the best results must be porous enough to let air be drawn through it reasonably well, must be thoroughly mixed, and must have some coarse material in it to segregate out and form a layer on the grates, it will be understood that the advent of this extremely fine material has made necessary still further elaboration in the equipment and processes of preparing sulfides for the blast furnaces, all of which is expensive. The high metal contents of the concentrates

Jan 1, 1929

By H. J. Engell, W. Frank, A. Seeger

SWISHER and ~urkdogan' have determined the solubility of oxygen in a iron. They found it to lie between 7 and 10.5 at.-ppm at 881°C. Using earlier work on the permeability of oxygen in bcc iron,' they arrived at the following expression for the diffusion coefficient of oxygen in bcc iron (k = Boltzmann's constant, T = absolute temperature): where The present authors3 have estimated the activation energy QD for the diffusion of oxygen in bcc iron in two different ways from various experimental data.2'4"6 In the first method QD + QS (QS = heat of solution for oxygen in bcc iron in thermodynamic equilibrium with solid FeO) was determined either from data on the reduction of FeO with hydrogen4 or from measurements of the internal oxidation of silicon in a iron.5 Using an estimate of QS from investigations of the oxygen solubility in 6 iron2 (in thermodynamic equilibrium with molten FeO) Q = 0.97 ev or Q~ = 1.06 ev were obtained. From the magnitude of these values it was concluded that oxygen migrates interstitially in bcc iron and that consequently the activation energy QD for diffusion of oxygen has to be identified with the migration energy E~ of the oxygen atoms. Therefore, for a second estimate of QD from the diffusion coefficient of oxygen in 6 iron at 1450" ~,~ we used the theoretical expression:3 (a = length of elementary cube edge, m = mass of interstitially diffusing atom, sM = migration entropy), applicable to diffusion via the octahedral interstices in bcc lattices. Taking sM = 3.8 k (migration entropy of carbon in a iron), one gets Q = 0.90 ev. Hence, in Ref. 3 Q = (0.98 *0.1) ev was proposed as a plausible value for the diffusion energy of oxygen in bcc iron. sM + 9 (9 = solution entropy for oxygen in bcc iron) can be determined from permeability measurements.4 Using the above-mentioned estimate for QS , the following expression for the solubility c (atomic concentration) of oxygen (in thermodynamic equilibrium with solid FeO) in bcc iron was derived: From [4] the solubility of oxygen at 881°C in a iron is calculated to lie between 0.6 and 12 at.-ppm. We see that the solubility determined by Swisher and

Jan 1, 1969

By R. E. Anderson, R. S. Busk

The mechanical properties of many nonferrous alloys can be modified by heat-treatment. This is almost always effected by controlling the amount of alloy in solid solution and the amount and distribution of second-phase material. The latter often is accomplished through precipitation or age-hardening treatments. The procedure is to solution-heat-treat the metal to provide a supersaturated solid solution and then cause precipitation of the dissolved material at some temperature below the solvus for the alloy. The generally used magnesium sand-casting alloys arc based on the ternary alloy system Mg-Al-Zn. Solid diffusion reactions in the system are slow enough so that a substantially completely supersaturated solulion is maintained even though the metal is relatively slowly cooled from heat-treating temperatures. Consequently, it is general practice to air-cool magnesium-alloy castings from the heat-treatment temperature prior to aging at an elevated temperature. Since it is necessary with many other alloys to cool quite rapidly before aging if optimum benefit from the aging is to be obtained, this study was undertaken to determine the effects of quenching on magnesium alloys. The] alloys used are shown in Table I, being selected as typical of the presently used magnesium alloys. Cooling Rates Since quenching is a means of rapidly extracting heat, there are two factors of interest in its study: (I) the rates of cooling that can be obtained and (2) the effect of various rates on the as-cooled as well as subsequently aged metal. The cooling rates were measured by drilling a hole 1/16- in diameter longitudi~lally in the center of a cylinder % in. in diameter and 3 in. long. The drilling was stopped to place the end of the hole at the center of the long axis of the cylinder. An iron-constantan thermocouple was inserted in this hole and wedged in place. The temperature drop during rapid quenching was recorded by a special1y built General Electric potentiometer recorder capab1e of measuring ' 500°F. temperature drop in 1/10 sec. For the slower cooling rates in air or oil, the temperature drop was measured by a Leeds and Northrup potentiometer recorder with the chart speed increased to One inch per minute' The cylinder was heated to the desired temperature, quenched as desired, and the temperature-time curve recorded. The cooling rates in still air, in oil at 350°F., in water at 180°F. and in a cold, high-pressure water spray were determined in this manner. The results of this study are presented in Fig. I. There is a great difference between water quenching and either air or oil quenching. There is little difference between the hot water quench and the cold water spray. Cooling rates were also

Jan 1, 1945

By John Garcia

IN some districts of the bituminous coal field the problem of construct-ing bulkheads to seal off water under pressure is becoming increasingly important. Recently this matter has been brought very much to the front by the loss of a large Illinois mine due to failure of a bulkhead that separated it from several old, flooded mines. As this great misfortune has provoked much inquiry about proper bulkhead design, it-is felt that a description, of the successful and extensive water-sealing practice at three mines that have different natural conditions will be of considerable interest to those connected with properties having a present or future water problem and to engineers that may have to design safe bulkheads of economical construction. These three mines are the Saxton and Dresser, near Terre Haute, Ind., and the Hegeler, near Danville, Ill. All three have water conditions that make it necessary to regularly seal off all worked-out sections of the mine, and there are considerably over a hundred bulkheads in each. As far as the writers know, these three mines are the only ones in the bitu-minous coal fields of the United States with anything like so large number of water seals and experience, although a number of other mines are known to have a few bulkheads. More detail will be included herein on the Saxton mine than on the others, as the writers are more familiar with it.

Jan 1, 1937

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. Temperatures and Underground Waters Surface Temperatures.—The average surface dry-bulb temperature at Superior is 72.4°; wet-bulb, 57.4°; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the downcast shafts; however, the variation between winter and summer causes a difference of only 2" to 3" in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.—Rock temperatures on the deeper levels of the mine are as follows:

Jan 1, 1940

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. Temperatures and Underground Waters Surface Temperatures.—The average surface dry-bulb temperature at Superior is 72.4°; wet-bulb, 57.4°; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the downcast shafts; however, the variation between winter and summer causes a difference of only 2" to 3" in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.—Rock temperatures on the deeper levels of the mine are as follows:

Jan 1, 1940

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contarnination could be reduced about 80 pct. The water company's supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters. and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West Penn Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs supplying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical'" Coal Measures"' rocks, the principal source being pyrite (and marcasite) in Pittsburgh and Rooster coals. Springs and seeps on hillsides issue from sandstone and limestone formations intersecting shale or clay land surfaces, or from perched water tables. The two reservoirs create an artificial permanent water table. Soap-hardness tests on three seepage samples taken in a dry summer ranged from 150 to 500 ppm. Water sampled came from aquifers above Pittsburgh and Rooster coals, obviating the possibility of contact with pyrite-containing coal. Since acid contamination of mine waters is the result of chemical reactions of oxygen and water with pyrite, it will be reduced by the exclusion of either air or water. The Sunnyhill Coal Co. has applied this principle in its "contouring" method of strip mining by burying contaminated coal-waste material under a compact, smoothed-up surface of top-soil, gravel, clay, and sand at a cost

Jan 1, 1950

By Zay Jeffries

Jan 1, 1930

By D. C. Hilty, W. Crafts

Determination of the solubility of oxygen in iron containing silicon, or manganese, or both, has confirmed the earlier work on silicon, shown that manganese is more effective than expected, and has demonstrated that the combination of silicon and manganese is a much stronger deoxidizer than might have been inferred from their individual effects. SILICON and manganese are of primary impor-tance in the deoxidation of steel, and a study has been made at the Union Carbide and Carbon Research Laboratories, Inc. of the solubility of oxygen in iron in the presence of silicon and manganese, singly and in combination, as a basis for more effective control of inclusion formation. The investigation was carried out with the same equipment and experimental procedure that were used in the determination of the oxygen solubility of iron containing aluminum'. The heats were melted in a rotating crucible furnace under an argon atmosphere. Bath temperatures were controlled by platinum/platinum +10 pct rhodium thermocouples to attain equilibrium at 1550°, 1600°, and 1650°C, so that oxygen solubility isotherms were determined directly without requiring calculation from a temperature coefficient. A detailed description of the furnace and procedure is given in the paper on aluminum deoxidation1. Oxygen solubility in the presence of more than 0.10 pct silicon was found to approximate earlier determinations closely, but some deviation was observed at lower silicon contents. Manganese appeared to be more effective than had been anticipated. The combination of silicon and manganese lowered the solubility for oxygen markedy as compared with either silicon or manganese alone. Although the solubility for oxygen in the presence of both silicon and manganese represents only a part of the information needed to control inclusion formation, it suggests a partial explanation of the benefits of this combination that have been observed in practice. Manganese and Oxygen in Liquid Iron: The study of oxygen in iron in the presence of manganese was carried out in magnesia crucibles of the type furnished commercially for laboratory induction furnaces. Alumina crucibles were unsatisfactory, because the work on the aluminum-oxygen equilibria in iron' had shown that merely melting iron in an alumina crucible limited the solubility of oxygen to a level considerably below that anticipated for moderate concentrations of manganese. Silica crucibles appeared unsuitable because of the dangers of excessive fluxing by the melt. Moreover, as will be shown later, melting iron in a silica crucible also limits the oxygen content below that in equilibrium with

Jan 1, 1951

By E. F. Young

The Porter Tunnel will open up 10 million tons of coal for Philadelphia & Reading which can be taken without hoists or pumps.

Jan 3, 1951

By F. G. Loper

Simulation as a mathematical technique is not new. However, recent increases in digital computer speeds and the ease of programming with languages such as Fortran have centered a good deal of attention around simulation in the last few years. By ignoring all but the relevant characteristics of a process, a mathematical simulator may be constructed which, when fed operating data, should react as the process would. The output becomes numbers, instead of tons, however. Thus, a trial-and-error operation of such a simulator will permit management to study a major system change at little cost.

Jan 1, 1967

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore-guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. THE following question has been suggested for discussion: ? "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein. ? Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line?

Jan 1, 1939

By J. W. Marx

A method is given for predicting the complete gravity drainage characteristics of arbitrarily long columns from centrifuge drainage measurements on reconstituted core samples. Oil residuals corresponding to hundreds of years of normal gravity depletion can be obtained in a few hours on the centrifuge. The gravity flow rate at any stage of the depletion process may be determined from the time correlation derived, and experimentally checked, in this study. INTRODUCTION Apart from the original observations of Muskat et al1, research publications2,3,4 on the subject of gravity drainage have been largely concerned with establishing in detail the saturation, S as a function of the height, z, in a draining column at any given time, t. Some form of numerical integration must be employed to obtain production rates and cumulative production even when S(z, t) is known. Furthermore, the relevant experimental work has been concentrated on drainage of a single wetting liquid from unconsolidated media. Since oil production usually concerns the drainage of a partially wetting liquid from consolidated media, in the presence of connate water, and since it is unlikely that sufficient information exists to establish S(z, t) in detail for any natural reservoir, the published research work appears to be, at best, only qualitatively applicable to production problems. With this in mind, the present study was undertaken by the writer. Experiments were planned whose results would have two advantages over existing measurements: 1. Observations were to be made on specific reservoir rock, reconstituted with formation water and formation oil. This would reduce their generality, from the research viewpoint, but increase their utility for production purposes. 2. The measurements were to be self-integrating, i.e., the phenomena were to be described and interpreted in terms of cumulative results. THEORETICAL DEVELOPMENT It was commonly known that centrifuging a liquid bearing porous medium increases the drainage rates and minimizes capillary end effects. The specific problem lay in selecting an acceleration, a, such that the mean residual saturation of a model cylinder was equal to the residual saturation of an arbitrarily long prototype column when the latter was drained by earth gravity alone. The physical conditions required to permit a valid scaling of model drainage time, tm with prototype drainage time, t, may be stated as follows: (a) At t = tm = O, So = Smo; (b) At t = tm? 8 Sr. = Smr.; (c) For all intermediate values of t and dS/dt=dsm/dtm whenever S = Sm; (d) S(z) = Sm(z) = a constant when t = tm = 0. 1 Here S = T I S(z)dz, where h is the length of the « Jo cylindrical column being drained and the subscripts S,Sm, and refer to model, initial, and residual systems, respectively. The first three conditions mean, simply, that an 3 vs t plot will be numerically identical with an S, vs t, plot,

Jan 1, 1957