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By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By F. L. Fayers, J. W. Sheldon

It has been a matter of concern to the petroleum industry to determine what effect the capillary term has on saturation profiles, since these profiles determine ultimate economic oil recovery. In their original solution of the non-capillary two-phase flow problem, Buckley and Leverett&apos; showed that solutions of the two-phase flow equations became multiple-valued in saturation. Since it is physically unrealistic for saturation to have more than one value at a given position, Buckley and Leverett resolved this difficulty by introducing a saturation discontinuity or "shock". They evaluated the strength and position of the shock from material balance considerations. Recently Sheldon, Zondek and Cardwell&apos; have demonstrated that the method of characteristics can be used to solve this and related problems. Owing to capillarity it is physically unlikely that saturation shocks occur in an oil reservoir. Buckley and Leverett suggested that the effects of interfacial tensions should be included in the fluid flow equations, if the solutions are to give continuous single-valued saturation distributions. An analogy to this problem is encountered in the theory of wpersonic compressible flow where the introduction of the viscous term eliminates shock behavior. However, the mathematical form of the capillary term in the porous medium fluid flow equations differs from the viscosity term in the Navier-Stokes equation. This paper demons~rates that capillarity does eliminate the triple-valued behavior and indicates the magnitude of capillary and gravity effects on the saturation profile for a variety of systems. DERIVATION OF LAGRANGIAN AND EULERIAN FORMS OF THE DISPLACEMENT EQUATION The equations representing capillary, two-phase flow are given by applying Darcy&apos;s law and a material balance condition for each phase. The familiar Darcy and material balance equations are as follows. ^U*^0......<3, ^^r=°......c« S is the saturation of the water phase, and B the inclination of the porous medium. Pressures in the oil and water phases differ by the capillary pressure associated with the interfacial tensions, P.-P.=pAS)..........(5) where p, is determined experimentally. The porous medium is said to be oil-wet if P, > Po and water-wet if P, < Po. If the fluids are incompressible and the total volumetric flow rate, q, is constant, then v, f v,, = q...........(6) By eliminating P.. /»,, and v, from Eqs. 1, 2, 5 and 6 it follows that It is convenient to normalize the variables in the problem after the manner of Handy and Hadley% so that Eqs. 3 and 7 become where j,, = —, the fractional flow of water; (F, is a capillary pressure normalizing constant.) Substitution of Eq. 9 into Eq. 8 gives In this partial differential equation for an initial value

By B. S. Butler, H. D. McCaskey

The New London copper mine, about 8 1/2 miles east of Frederick, Md., was visited by the writers for a few hours in the spring of 1909 and the following brief notes on ore specimens collected are presented as a contribution to studies in chalcocite ores. For certain data on the structural and areal geology of this portion of Maryland the writers are under obligation to the unpublished notes and maps of Arthur Keith. The detailed study of the ores is the work of B. S. Butler. The deposit here discussed has many similarities to those of the Virginia district of Virginia and North Carolina, which have been described by Gratonl and Laney,2 except that in the deposits of the New London mine chalcocite is by far the most important ore mineral, while in the Virginia deposits bornite is commonly the most important sulphide. In the New London occurrence calcite is the most important gangue mineral. Field relations The -town of Frederick lies in the center of a narrow belt of limestone ranging in age from Ordovician on the east to Cambrian on the west. This belt is about + mile wide at Noland&apos;s Ferry, on the Potomac, and broadens to a width of 3 miles at Frederick. The general direction is east of north. The eastern boundary is, in places, a fault plane along which a series of metamorphic rocks of presumptive pre-Cambrian age have been thrust up. These ancient rocks, for several miles east and west of New London, are phyllites in the main, but closely inter-folded near the New London mine are long, narrow lenses of epidote

Jan 1, 1915

By F. B. Richards

For the last five years the furnace-men drawing their oresupply from the Lake Superior districts have had to solve the problem of using the very fine Mesabi ores as part of their oremixture. It is not my purpope to dwell on the early experiences and the progressive development in the use of these ores up to this time, but to lay before the members of the Institute one prominent feature concerning them, namely, the frequent and sometimes very disastrous slips (?) or explosions (?) occurring at furnaces where these ores are used. The Transactions of the Institute contain very little on this subject. Mr. F. E. Bachman, in his discussion of Mr. 0. 0. Laudig&apos;s paper (Trans., xxvi., 1061), advances a theory as to the cause of these occurrences; but this is the only reference to the subject in the Transactions up to this time, so far as I can recall. Probably all the furnace-men running the harddriven coke-furnaces in the central West have had more or less experience with this trouble; and I believe the majority of

Jan 1, 1899

By J. W. Mills

The strike and dip of bedded formations is readily determined by trigonometry if some marker horizon is intercepted by three holes. If no marker can be identified and if orientation of the cores is unknown, as is the usual case in diamond drilling, the determination still can be made readily by the use of a stereonet if the bearing, inclination, and angle the bedding makes with the core axis is known for each of the three holes. Such determination, valid only if the bedding orientation is fairly uniform within the area drilled, is considered simpler, faster, and more effective than any solution previously published. Method: The steps of this procedure are as follows: 1) Mark north and south poles on tracing paper placed over stereonet. 2) Plot the three diamond drillholes by drawing a line from the center of the net in the direction of the bearings of the holes. Then rotate the paper until each line, in turn, lies along the equatorial diameter of the net; the end of each line is determined by the inclination of the hole measured in degrees from the periphery toward the center of the net along the equatorial diameter. Fig. 1 illustrates a vertical hole and a hole inclined at -23° due east.

Aug 1, 1955

By B. Bryan

The tank car price of gasoline today is controlled by oil in the ground, rather than by stocks of gasoline or methods of refining. Previous to the commercial cracking of fuel oil, there was a normal and continuous relation between gasoline stocks, consumption and prices. From the beginning of the new cracking era in 1923 to the summer of 1926 there was a changing relationship, growing toward a correlation between the potential gasoline in storage and the price of gasoline. Since the development of large reserves of shutin production in Wyoming, California, Seminole, West Texas and Venezuela, the relationship between stocks of gasoline and gasoline prices has disappeared. The extreme depression of the Group 3 price can only be accounted for by oil which is not being produced but which we fear may be produced at any time. In Fig. 1, the curve of gasoline stocks is simply stocks of finished gasoline. The curve of potential gasoline is made by taking 40 per cent. of all stocks except gasoline, kerosene and lubricants, adding to that stocks of finished gasoline and dividing the sum by total gasoline con-sumption to get the months&apos; supply of gasoline at the current rate of consumption. The price curve is the lower figure given by the National Petroleum News for the first quoted date of each month, with the price scale reversed. Stocks of potential gasoline have decrrased from 17 months&apos; supply at the peak of 1924 to a low of 7 months&apos; supply during the past summer, yet the low immediately precedes the lowest price for gasoline since it was a waste product. The tendency of the price curve to parallel the curve of potential supply is quite pronounced until the summer of 1926, since which time they have abruptly separated. The curve of gasolinct stocks is equally remarkable in relation to price when it is considered that total consumption for the year 1927 is almost exactly twice that of 1924. Clearly a new factor has been introduced. There is no possible factor to account for this distortion except known reserves of oil in ground storage, and therefore, until such time as the Bureau of Mines or the

Jan 1, 1928

By A. J. Lanza

IN view of the immense amount of attention that silicosis has received in this country in the past few years, it is timely to review the status of the silicosis problem at present. Who gets silicosis? The individual exposed to the inhalation of free silica dust. The effects upon the individual depend upon the amount of silica inhaled or, in other words, the severity of exposure, rather than upon any special variation or susceptibility among those exposed. A considerable amount of study has been given to determine what may be the role of predisposing causes in the development of silicosis. To men-tion one instance, at the Picher Clinic careful records were kept of all previous illnesses of the men examined as well as abnormalities present at the time of examination. Examinations of over 27,000 miners were made during the years the clinic was conducted under governmental auspices-a very fair sized sample. The general conclusions from all this work were that the incidence of silicosis is not appreciably influenced by racial, structural, or other inherent qualities; it is influenced by acquired defects-particularly as these affect the lungs. That is to say, the average run of human beings respond similarly to similar exposures to silica dust and those whose lungs are already impaired by tuberculosis or other pulmonary disease acquire silicosis more readily than those with healthy lungs. It may well be, and there is some clinical evidence in support, that negroes acquire silicosis more readily than do whites, but the infection factor has not been so carefully studied among negroes exposed to silica as it has among whites. We know that tubercle infection is more prev-alent among negroes than among whites. There may be other factors concerned in the development of silicosis in negroes as compared to whites, but there is not available information upon which to base posi-tive statements.

Jan 1, 1937

By N. V. Hansell

The last few years have shown an increasing interest in the subject of beneficiating iron-ores in all iron-producing countries. In the United States, this movement has been slower than in certain parts of Europe, for the obvious reason that the abundance and relative cheapness of the Lake Superior irou-ores has hindered the development of enterprises for the preparation of low-grade ores. Gradually, however, conditions have changed. The world&apos;s consumption of iron is increasing enormously. Being in 1900 about 40,000,000 tons, in 1910 it was already 60,000,000; and there is no reason to doubt that for the near future the increase in iron-cousumption mill continue at the same rapid rate, especially with the development of China, certain parts of Africa, and other regions which have hardly been touched as yet by modern industrialism. It is, therefore, not surprising that apprehension is felt that the known available iron-ore resources of the world are gradually being depleted. Signs of this feeling are the recent iuvestigation, under the direction of the U. S. Geological Survey, of the iron-ore resources of the United States, and the estimate presented to the last International Geological Congress, at Stockholm, Sweden, of the iron-ore resources of the world. These investigations have emphasized the fact that the known high-grade ore-deposits are limited in extent, and will, at a not distant future, be exhausted, compelling the iron industry to depend for raw material on the enormous deposits of low-gratle ores which are distributed over almost all the world. The discovery of new deposits of high-grade ore, in countries not yet thoroughly explored, will not materially change this prospect. Of course, the part which such new deposits will play in the future cannot be forecast. The difficulty and cost of transportation will probably exclude many of them from use at the present centers of the iron industry.

Jan 1, 1913

By F. T. Lee

Directional dependence of strength and deformation properties of the Mount Waldo granite pluton in southeastern Maine is controlled by joints and microfractures whose orientations are linked to flow- induced alignment of microcline crystals. Longitudinal and cross joints which formed during cooling of the mass, as well as much younger sheeting fractures, are commonly associated with subparallel, discontinuous microfractures. The orthogonality of microfractures (open, closed; filled, unfilled; bubble planes) establishes the ease of splitting of the granite. The easiest splitting direction (rift) is subhorizontal, the second easiest direction (grain) is parallel to the cross joints, while the direction of least easy splitting (hardway) is parallel to the longitudinal joints. Static and dynamic measurements made in the field and laboratory established that structural features are responsible for the marked stiffness anisotropy of the granite. In the central part of the pluton the static Young&apos;s modulus in the north-south direction averages 31.1 GPa, and 20.9 GPa in the east-west direction; the stiffer direction being parallel to the long C-axes of microcline phenocrysts and microfractures as identified in outcrop, core samples, and thin sections. Vertical downhole sonic measurements of dynamic moduli ranging from 2.5 to 16.2 GPa appeared to be anomalously low when compared to the static horizontal values. However, the field sonic values were confirmed by laboratory sonic pulse testing of oriented cores. The field results reflected closely spaced layers of open horizontal microfractures. Those deformation and strength properties that are closely tied to bubble planes, filled microfractures, and microcline orientation could be extrapolated to greater depths with good hope of success.

Jan 1, 1984

By J. E. Hilliard, J. W. Cahn

In this paper it is suggested that the degree of contiguity (or contact) between adjacent grains be described by three parameters which can be rigorously determined from measurements on a random plane of polish. An expression is also derived for the number of contacts per unit volume and it is shown that this quantity can-not, in general, be estintated from measurements on a random plane. IN a recent contribution1 Gurland has proposed various parameters for describing the degree of contiguity (or contact) between grains of the same phase in an alloy. To relate these parameters to measurements on a random two-dimensional section, it was necessary in most cases to make some assumption about the form of the structure. Since Gurland was specifically interested in sintered carbide structures, he chose, quite reasonably, to assume that the grains were constant-size spheres and that all the intersections were flat areas of constant radius. Since, as we will show, the relationships between the parameters and the measurements are strongly dependent on the grain shape and size distribution, it is evident that these assump tions will not be satisfactory approximations for a

Jan 1, 1960

By G. A. Vissac

The drying of fine coal involves special techniques, which are discussed and analyzed. Types of dryers employing these techniques are described. Calculations are presented for new methods of deal ing with the entrained dust that is always present in fine coal drying operations.

Jan 10, 1953

NEW MEMBERS The following list comprises the names of those persons who became members during the period Jan. 10, 1919, to Feb. 10, 1919. ADAMS, FRANCIS SPEARMAN, Supt., Power Dept., Anaconda Copper Min. Co.; Anaconda Mont. ALDERSON, G. E., Min. & Met. Engr 1317 Sloane Ave., Lakewood, Ohio. BENJOVSKY, T. D., Min. Engr., Cons. & Constr 2045 Vine St., Denver, Colo. BROPHY, OSCAR, Met 1523 S. Broad St., Philadelphia, Pa. BUTTRAM, FRANK, Chief Geol., Fortuna Oil Co., 424 Liberty National Bank Bldg., Oklahoma City, Okla. COCHRAN, R. B., Mine Supt., The Teziutlan Copper Co., Aire Libre Puebla., Mexico. CONNAR, T. C., Civ. & Min. Engr. & Geol.; Chief Engr., Zanesville Coal Co., Zanesville, Ohio. DAVE, E. O Capt., Co. A, 212th Engineers, Camp Devens, Mass. FOLEY, CHARLES B., Electro-Met., Martin Rockwell Corpn., 347 Madison Ave., New York,. N. Y. HOSFORD, WILLIAM F., Asst. Tech. Supt., Western Electric Co., Inc., Hawthorne Station, Chicago, Ill. HOSTER, M. T., Supt., French Creek Mines, E. & G. Brooke Iron Co., St. Peters, Pa. KAWASAKI, SHIGETARO, Chief Geol., Geological Survey of Chosen, Government General of Chosen, Keijo. Korea.

Jan 3, 1919

By Magnus Troilius

The importance of having methods for the rapid and accurate determination of manganese in modern steel manufacture cannot be overestimated. The method adopted in the laboratory of the Midvale Steel Works is very satisfactory, and I think it will be of interest to some of the members to give a description of it. Before giving the more detailed account of the manipulations, a review of some well-known methods and chemical facts may not be out of place. The " bromine and ammonia" process, as fully described in the tenth volume of the Transactions of this Institute, was certainly an improvement on the methods in which fixed alkaline salts were used, as these gave invariably too high resnlts, as generally carried out. But the separation of all the iron before the manganese was, in both methods, a source of great inconvenience and delay.

Jan 1, 1884

Jan 1, 1968

By Robert E. Tally

CHAUNCEY L. BERRIEN, Butte, Mont. (written discussion).-Having had much actual experience with mine fires which have occurred or have been active in the mines of the Anaconda Copper Mining Co. during the past 4 years and having lately visited the fire zone of the United Verde mine with Mr. Tally, I wish to congratulate him for the success which he has had in controlling this fire and making the mine perfectly safe .for his miners. By this work he is not only keeping the property in operation but is reclaiming many lost orebodies. The ventilation system as described by him is practically the same as that used under my direction at the Mountain View mine fire in Butte in 1913 and at the Pennsylvania fire in 1916. This same system is at present being followed at the Leonard mine to extinguish a fire which has been active for 10 years although bulkheaded. The mining system in the Butte mine, at the origination of these fires was the same as that at the United Verde, namely, square setting .accompanied by the use of much timber bulkheading in the stopes owing to heavy ground. The pyritic content of the ore in Butte is not as high, but on the whole conditions have been the same, with the exception of actual location of the fire in the mine. I agree with Mr. Tally that flooding, the use of C02 or any gas, and the use of steam are all impracticable unless the fire zone can be absolutely sealed. His system of upcast escapement shafts in the fire zone, the use of bulkheads and fans to keep the gases away from the firemen, must be resorted to. By the method lie describes actual stoping may be carried on safely if started from the bottom of the fire and if the fire zone extends to the surface. In other words, the fire zone must be isolated from the rest of the mine by bulkheads and solid ground, with no ground above which can be damaged by spread of fire or caving. The serious fires in Butte have .occurred on or between levels in the mines where it was necessary to prevent their .extension upward, downward and laterally while the work of actually extinguishing them was in progress. This necessitated proper bulkheading should we lose control of the fire, the installation of ventilation similar to Mr. Tally&apos;s and the systematic drilling of holes with diamond drills for distributing water on the fire and around it.

Jan 12, 1916

By Norman B. Pilling, George P. Halliwell

The effects of lead and tin up to maximum contents of about 0.1 per cent. each, in the presence of oxygen between 0.04 and 0.30 per cent., have been studied. Tin is retained efficiently in the oxidized condition, whereas lead is not. An approximate relation between the lead-oxygen and tin-oxygen contents is deduced which, if observed, permits the presence of these elements without detrimental effect. Excess of lead beyond this limit affects ductility and rolling properties adversely and an excess of tin correspondingly diminishes the conductivity. It is shown that copper carrying a combined lead and tin content of several hundredths per cent., yet fully equal in quality to electrolytic wirebar, may be produced under commercial conditions. Tin is not normally found in more than bare traces in current grades of American electrolytic copper, and lead is rarely found to more than a few thousandths per cent. In the electrolytic refining of copper these metals do not present great difficulty in separation and their presence in any considerable amount in copper that has been refined by this method need not be tolerated. On the other hand, the effect of these elements is not entirely academic, as a considerable tonnage of scrap copper liberally contaminated with them has been reclaimed by the fire-refining process into metal with a residual lead and tin content of several hundredths per cent., yet having excellent working properties and fully equal in quality to current grades of electrolytic wirebar. Such copper has been found entirely suitable for use in the manufacture of electrical apparatus. In the absence of oxygen, tin is known to depress the conductivity rapidly, and lead to impair ductility and the rolling properties, yet the effects of these metals on commercial grades of copper—i. e., copper containing from 0.03 to 0.10 per cent. of oxygen—apparently has not received systematic attention. Occasional reference is made to the fact that in the presence of oxygen lead may be tolerated, yet Addicks says,1 in regard to overpoling: "The unstable condition can be controlled by adding certain substances, notably lead, in small quantities, but as mere

Jan 1, 1926

By D. G. Brubaker

IN the history of geophysical exploration by the electromagnetic method many procedures and types of equipment have been used. Source arrangements for surveying on the ground have included long wires grounded at both ends, large loops laid on the ground, small horizontal loops, and vertical loops of moderate to small sizes. Receivers have ranged from simple direction-finding coils to combinations of coils and a bridge circuit to measure quantities related to both amplitude and phase of the received signal. Primary considerations in choosing a survey method are effectiveness, speed, and economy. In work on the ground in which locating and out- lining conducting bodies is the objective, methods using a vertical coil and a simple direction-finder have been found the most satisfactory. Mason1 and his associates applied such a method by setting up a vertical source loop, fed with low frequency alternating current by an engine-generator set. With a direction-finding receiver they surveyed lines along the ground in the plane of the loop, taking measurements at each station of the azimuth and inclination of the magnetic field direction. Deviations of this direction from the normal direction, that is, from horizontal and perpendicular to the traverse line, indicated a conducting body. Recent advances in design of light-weight generating equipment have encouraged using this and similar methods.

Jan 7, 1957

By G. J. Benard

In the 1970’s, several plants have been built and others are in the design stage which use solvent extraction for recovery of copper from acid leach solutions. Other plants are presently being built for the recovery of nickel and cobalt from laterite ores by prereduction and ammonia leaching. A review will be given on the materials of construction for these leaching and solvent extraction processes. Many plants have factors in common which permit selection with a greater degree of accuracy. Based on pilot plant corrosion data, effective use of materials of construction includes proper selection of materials, substitution of lower cost plastics for alloys, and selection of materials resistant against chloride stress corrosion cracking.

Jan 1, 1974

By C. Wagner

When an alloy solidifies and the composition of the solid differs from the composition of the liquid, atoms of the alloying elements rejected at the solid-liquid interface have to diffuse toward the bulk liquid. Diffusion may be supported by convection. Theoretical calculations have been made for a liquid without convection, for a liquid involving natural convection, and for solidification of a liquid alloy at the surface of a rotating disk as an example of forced convection. WHEN an alloy solidifies, the equilibrium composition of the originating solid phase differs in general from the composition of the liquid phase. Thus, segregation may take place, i.e., the composition of the solid phase formed at different times differs from the bulk composition. The degree of segregation depends on several factors such as the partition ratio of the alloying elements between the liquid and the solid phase, the rate of solidification, and convection. To clarify, a theoretical analysis has been worked out. The following presuppositions are made: 1—Calculations are confined to the solidification of binary alloys in which the concentration of component A (solvent) is much greater than that of component B (solute). 2—The equilibrium concentration of the alloying element B is assumed to be lower in the solid phase than in the coexisting liquid phase. 3—At the solid-liquid interface, partition equilibrium is assumed. 4—The dependence of the partition ratio of the solute between the liquid and the solid phase on concentration and temperature is disregarded since only small concentrations of the solute are considered. 5—The concentration of the alloying element B in the solid phase is supposed to be lower than the saturation concentration for the formation of a second solid phase. 6—diffusion in the solid phase is disregarded, since diffusion rates in the solid state are comparatively low. When the partition ratio of the solute between the liquid and the solid phase is greater than unity, a part of the solute is rejected at the solid-liquid inter- face and has to diffuse toward the bulk liquid. Thus there is necessarily a concentration difference in the liquid between the solid-liquid interface and the bulk liquid as has been pointed out by Hayes and Chipman,&apos; Rutter and Chalmers,&apos; Tiller, Jackson, Rutter, and Chalmers, and others (see Fig. 1). In view of the concentration gradient in the liquid phase, the ratio of the concentration of the solute in the solid phase to that in the bulk liquid differs from the equilibrium ratio, although at the solid-liquid interface, partition equilibrium is assumed. Under certain limiting conditions, the solid may even have virtually the composition of the bulk liquid as is shown below. General Equations Let u be the linear crystallization velocity in cm per sec, D the diffusion coefficient of component B in the liquid phase in cm2 sec-&apos;, c&apos;,, and c", the concentrations of component B in the liquid and the solid phase, respectively, in mol per cm", and s the distance from the solid-liquid interface toward the bulk liquid at a given time t. The partition ratio is assumed to be equal to a partition constant K. Thus. The difference in the specific volume between the liquid and the solid phase may be disregarded. In view of the discontinuity of the concentration of the solute at the interface according to Eq. 1, u(c&apos;, — c",), , , = tic&apos;, (S = 0)(1 — K) gram-atoms B per unit area per unit time are rejected at the interface and have to diffuse toward the bulk liquid. From Fick&apos;s first law it follows that uc&apos;,,(s = 0) (1 ~K) == - D(dc&apos;,,/?>s). _-„. [2] The concentration profile in the liquid near the interface depends on the interplay of diffusion and convection as is discussed in the following sections. A schematic concentration profile is shown in Fig. 1. The "effective thickness of the diffusion boundary

Jan 1, 1955

By Eugene A. Smith

Geological Relations. In his second report upon the Geology of Alabama, Prof. M. Tuomey calls attention to a rock occurring near Florence, in the Tennessee valley, the composition of which is as follows: Per cent. Carbonate of lime,.. .. .. ..16.41 Phosphate of lime,.. .. .. ..14.19 Peroxide of iron,.. .. .. .. .36 Quartz and other insoluble matters,. .. ..68.72 99.68 This rock was referred by Prof. Tuomey to the Carboniferous, because he found the Carboniferous limestones always resting conformably upon it, whilst both rest uncomformably upon the underlying Silurian or Devonian rocks. The recent discovery in Tennessee of phosphate-rock of this age (or approximately so) has stimulated the search in Alabama for similar rich material; but our search has been, up to this time, unrewarded by the finding in quantity of anything of better quality than the rock whose analysis is given above. It is, however, in high degree probable .that the rich phosphaterock of Tennessee will at some time be found to have its counterpart in Alabama. Materials of several kinds, containing a notable quantity of phosphoric acid, have been found in Alabama in both the Cretaceous and the Tertiary formations, and for our present purpose they may be most conveniently considered in their geological relations.

Jan 1, 1896