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By Allan Clark

(San Francisco Meeting, September, 1915) IT is nearly three years since the metallurgy of the Homestake ore was discussed with considerable thoroughness, in a paper' read before the Institution of Mining and Metallurgy. Certain changes have been made in this period which are perhaps of sufficient interest to justify a brief description, and it is chiefly with such details and miscellanies that this paper will deal. In the circumstances, a certain amount of repetition is inevitable, but matter treated of in the former paper will be referred to here only when it is necessary for the sake of coherency. For full descriptions of equipment and technique, the former paper should be consulted. The mineralized slates and schists which constitute the ore vary considerably in composition, but the unoxidized ore, perhaps constituting the major part of the reserves, contains either chlorite or hornblende (cummingtonite), with quartz, carbonates of lime, magnesia and iron, and arsenopyrite, pyrite, and pyrrhotite. Ferrous minerals predominate, and this fact has been an important factor in determining the metallurgical treatment. With one or two exceptions the minerals noted are of relatively high specific gravity, and the ore as a whole is exceptionally heavy, many determinations giving an average specific gravity of 3.00. This high specific gravity presents one decided advantage, when the' cost of treatment is compared with operations elsewhere, in that the ton, almost universally the basic unit, represents a volume probably less by 10 per cent. than that of many gold ores. On the other hand, this high gravity renders more difficult the discharge of pulp from mortars, its distribution on amalgam tables, and its transportation in launders.

Jan 7, 1915

By Raymond D. Daniels, Frank E. Rizzo, James D. Gerber

ThIS discussion describes a method for the addition of small amounts of oxygen to columbium (niobium) in an accurate and reproducible manner. The method is based on the complete reduction by columbium of a carefully weighed amount of another metal oxide. The equilibrium Pq associated with Cb-CbO mixtures is extremely low, e.g., 10"25 atm at 100O°C, and the pressures over Cb-0 solutions are even lower. The equilibrium Pq associated with a given metal-metal oxide mixture can be easily obtained, with the aid of a Richardson-Jeffes chart.' Although columbium should effectively reduce almost any metal-metal oxide combination, the proper choice of a metal-metal oxide system is complicated by the low rate of oxygen transport in the gas phase at low oxygen pressures and the difficulty in reducing any columbium suboxide formed during the reduction of the oxygen source material. Thermodynamically, oxide formation on columbium will be avoided so long as the oxygen partial pressure over the columbium is below the equilibrium pressure associated with the mixture Cb-CbO. The logical choice of a source for oxygen would appear to be a mixture of Cb-CbO, since oxide formation would be precluded by nucleation difficulty. But calculations using the kinetic theory of gasses indicate that, for a temperature of 900°C, the reaction would proceed too JAMES D. GERBER, formerly Research Assistant, University of Oklahoma, Norman, Okla., is Research Metallurgist, Air Force Weapons Test Laboratory, Kirtland Air Force Base, N. Mex. FRANK E. RIZZO, Junior Member AIME, formerly Assistant Professor of Metallurgy, University of Oklahoma, is Associate Professor of Metallurgy, University of Texas at El Paso, El Paso, Tex. RAYMOND D. DANIELS, Member AIME, Professor of Metallurgical Engineering, University of Oklahoma, is an NSF Fellow, Institute de MBtallurgie Structurale, Universite de euch:tel, Neuchitel, Switzerland. Manuscript submitted October 28, 1968. IMD

Jan 1, 1970

By LEWIS F. THOMAS

MINING geologists and mining engineer, rarely give due thought to the geography of mining deposits. They realize, it is true that what may be ore in one place would be only worthless rock in another because f the in accessibility of a smelter r a market; and they may consider the lack of a supply of labor, or water, or power to carry on operations. But they do not think (of these things in terms of geography. Geography may be defined as the science of relationships between earth and man, so geographers are vitally interested in the how and why of mining as it is carried on at different place, having entirely different environment-. Such environments are geographic complexes or composites of natural and cultural elements, which are listed and briefly discussed in the following paragraphs.

Jan 1, 1941

By A. T. Goldbeck

THE use of stone as a building material in relatively large blocks is recorded in ancient historical records but only within the past 200 years has broken stone in small sizes begun to have extensive use, principally in highway construction. Tresaguet, in 1764, describing his method for highway construction in France, required the top surface to be built of stone about the size of a walnut, broken by the use of a hammer. It is said that the Romans, in the top layer of their rather massive roads, used large stones bonded together with lime mortar and bedded in small stones mixed with mortar. Much of the early macadam as built by McAdam around 1815 in England was made with hand-sledged broken stone. In 1858, the use of crushed or broken stone received a great impetus from the invention in that year by Eli Whitney Blake of what is said to be the world's first stone crusher. As a consequence of that invention, stone could be crushed to small sizes with considerable ease and, as a natural result, the use of crushed stone in macadam roads and as railroad ballast increased at a great rate. Also, as portland cement came into use, machine-produced crushed stone furnished readily available aggregate. Rapidly, other uses developed, such as for fluxstone in the production of pig iron and for other metallurgical operations and chemical utilizations. These utilizations made for the rapid growth of the crushed-stone industry and this growth is still proceeding with the growth of population and the development of new uses, notably the employment of limestone for the improvement of soils for agricultural purposes. The industries of which the production of crushed stone is a part have a tonnage second only to that of mineral fuel in the mineral industries of this country.

Jan 1, 1949

By Richard F. Link, George S. Koch

Advantages and disadvantages of deflecting (wedging) diamond-drill holes to obtain sampling data are compared with the alternative of drilling additional holes. The discussion is based on a statistical analysis of a large set of deflection data from exploratory boreholes in South African gold mines. Representative cost comparisons show the conditions under which deflections are likely to be desirable.

Jan 1, 1969

E. E. Olcott, New York City: Prof. Kemp's valuable description of the Lancaster Gap mine is in line with many other able contributions on the origin of mineral deposits that the Institute has lately brought forward. The splendid contribution that Prof.

Jan 1, 1895

By J. E. Elliott, K. O. Miller

Solubility studies were carried out to establish the phase distributions for various Fe-Ni-Pb-C alloys at temperatures where the metallic components exist as liquid solutions. Temperature us composition diagrams for the Ni-Pb, Fe-Pb, Fe-Ni-Pb, and Ni-Pb-C systems are derived by employing various approximations in conjunction with the data. Results are summarized for 1550°C in a quaternary phase diagram of the Fe-Ni-Pb-C system. BECAUSE surprisingly little information has been published on the phase diagrams of the Ni-Pb, Fe-Pb, Fe-Pb-Ni, and Fe-Ni-Pb-C systems, a study of these systems was undertaken to ascertain the important phase relationships in the temperature range of 1300" to 1550°C. Measurements were also made on the carbon-saturated systems in the hope that they would assist in the interpretation of the systems without carbon. This paper reports the results obtained from the simple equilibration of the various liquid and solid phases. EXPERIMENTAL PROCEDURE The experimental technique involved holding appropriati quantities of the metals in an alumina crucible, or in a graphite crucible when saturation of the melt with carbon was desired, for sufficient time at the desired temperature to ensure equilibrium. Then a sample of each liquid phase presen was drawn into a small-bore silica tube. This sample was withdrawn quickly from the furnace, cooled, and sent to the chemical laboratory for analysis. The cell assembly used is shown in Fig. 1. Durin the work on the Fe-Pb-Ni system, it was placed in a furnace wound with 20 pct Rh-80 pct Pt wire. This furnace eventually failed and subsequent studies were carried out between 1350" and 1475°C in a tube furnace heated by silicon-carbide resistance elements. A protective atmosphere of argon with approximately 10 pct hydrogen was supplied to the cell assembly at a gage pressure of 1 in. of water. Hydrogen was passed over palladized alumina and then anhydrous calcium chloride for purification. Argon was purified of oxygen and water vapor by passing it over copper gauze at 550°C and then through a calcium chloride drying column. The gases were mixed and redried before they entered the equilibration cell. Temperature was measured by calibrated Pt/Pt-10 pct Rh thermocouples and a Rubicon Type B potentiometer. The thermocouples were standardized against the melting points of pure nickel

Jan 1, 1961

By J. C. Jaeger

It frequently happens in engineering and mining situations that "bad" rock is encountered which consists of rock broken up into blocks a few inches or less in diameter by a network of intersecting joints. These joints may be open, or filled by veins of solid material, or covered with weathering products. Essentially, the material consists of an aggregate of small interlocking blocks. In such circumstances, major joint systems usually can be recognised and studied, but there are probably many minor planes of weakness which may cause the blocks to be of almost random shape. It is extremely difficult to determine the properties of such materials. Measurements on small specimens give the properties of the constituent rock and not the jointed material. At the other extreme, the material has occasionally been tested as loose aggregate in large triaxial pots, but this gives no information about the strengthening effect of the interlocking of the small blocks of rock. One simple approach, which has been much used, is to regard the rock as randomly jointed on a small scale and to apply soil mechanics theory to it. In this case, the normal and shear stress at failure are related by [ ] where the coefficient of friction p and the cohesion c will be those of the individual joints. Even in very bad rock, it is usually possible to drill core in small diameters of 1 to 2 in. which will contain a number of joints, both open and filled. The testing of such joints provides one simple method of determining some of the properties of closely jointed rock and will be discussed in detail in the next section. Calculations based on Eg. 1 with values of c and µ obtained in this way may be expected to give a lower limit for the strength of structures in rock.

Jan 1, 1970

By Blamey Stevens

(San Francisco Meeting, October, 1911.) My previous paper is entitled, The Laws of Igneous Emanation Pressure. The present paper lays no claim to the exactitude and completeness of a law, since it is of a provisional nature and may be disregarded when experiments have established a basis for more exact reasoning. The general physical states in which aqueous emanations may occur are first considered. The possible physical conditions under which the mineral elements may occur in emanations are then discussed, and a classification of deposits, dependent on emanation, is proposed. A system of scientific experimental investigation is outlined, and it is shown that the physical and chemical properties of emanation may be exactly determined thereby. The investigation is urged as feasible and simple, and not necessarily requiring large and costly apparatus. It is the only step necessary to make possible the formulation of a complete set of laws of igneous emanation. Process of Emanation. In a rising column, magma ranges in temperature from 900° to 1,200°C. Exhalation must begin at some fairly great depth. What this depth may be we can only surmise, since no experimental evidence is available. Exhalation, however, continues as the magma flows upward, until at another level the occluded gases have all escaped. This depth is probably upward of 5,000 ft. (See Fig. 1.) All exhalations must come from between these two levels. As the whole emanation is the sum of the exhalations and residues, the residues must come from below the uppermost level. They will be most abundant when coming, from those parts of the intrusion which have solidified below the lower level.

Apr 1, 1912

By F. P. Schwarz, A. J. Erickson, S. M. Weber

The Mount Hope stockwork molybdenum deposit, Eureka County, Nevada, occurs In a small igneous cauldron complex 32 to 38 mybp in age. The deposit is characterized by alteration zones and mineralized shells symmetrically distributed around multiple intrusive. For samples from the 25000 meters of 1981-82 drilling, an appraisal of error in in-house sample preparation and in commercial assaying has been made. After splitting, drill core is crushed and reduced in volume (8: 1 at 10-mesh, 8: 1 at 70-mesh, 6: 1 at 200-mesh) to supply 25 grams of 200-mesh pulp for replicate analyses. A 0.5 g portion of the pulp 1s used for dissolution and atomic absorption analyses. Factors which initially generated unacceptable data variances have been minimized by planning, repeat analyses, introduction of standards, and routine monitoring. Assuming that error between replicate assays defines a Gaussian distribution with its average ideally equal to zero, precision (from preparation including core splitting and analysis of 8400 pairs of molybdenum samples) is on the order of ± 25%. The error distribution is not based. Accuracy is approximately 4% lower than absolute as determined by replicate assays of commercially prepared samples.

Jan 1, 1984

By Martin A. Moyers

THE nation's effort to win the war speedily is reflected in current trends in coal utilization, as in all other fields of our lives. In all industries, wherever coal is used for the production of heat and power the emphasis is on getting the most useful result with the least expenditure of matt.ria1. In addition to carrying its own share of the load, increased as it is by the demands of war industry, coal has had to fill in for the other fuels, mainly petroleum products, whose distribution from their more distant sources has been crippled by lack of shipping. Thus, the outstanding note in the utilization of coal this year is not the development of new methods of burning or handling coal but the extraordinary job that the industry has done in producing enough coal to serve all needs.

Jan 1, 1943

By Kenneth B. Barnes, George H. Fancher

With the advent of water-flooding into active commercial usage in half a dozen areas in the Mid-Continent, the process passes the experimental stage and joins other methods and processes now in use which have been found suitable in one oil field or another in securing a more profitable production than has existed heretofore. The use of the air-gas lift, acidization, pressure maintenance and repressuring have presented their problems in economics and engineering during their introduction and extended application. When a new field is discovered or attention is turned to an old producing area in which these methods have not been considered, it is to be expected that these problems again arise. While some information is available as to the results obtained by water-flooding in a few localities in the Mid-Continent, the extrapolation of the sand data on which the results are based, for even generalized use in other areas and fields in the region, is hazardous. It is precarious to assume that the same physical condition will obtain in a sand over more than small, special areas. This paper is concerned with a brief presentation of such data as are available to the authors on existing operations, a survey of the region and extent to which application of the method seems most likely to be made, an estimation of the crude reserve existing for such operations, suggestions as to the importance of core analysis in guarding against uncontrolled floods and its usefulness in predicting ultimate recoveries, and comment on some of the economic phases involved. These subjects, as concerned with water-flooding in the East (notably Bradford, Pennsylvania), have been discussed in detail in the literature and are generally well known. Especially is this true of discussions of the mechanical equipment and various lease layouts and development patterns for water-flooding.

Jan 1, 1936

By Kenneth B. Barnes, George H. Fancher

With the advent of water-flooding into active commercial usage in half a dozen areas in the Mid-Continent, the process passes the experimental stage and joins other methods and processes now in use which have been found suitable in one oil field or another in securing a more profitable production than has existed heretofore. The use of the air-gas lift, acidization, pressure maintenance and repressuring have presented their problems in economics and engineering during their introduction and extended application. When a new field is discovered or attention is turned to an old producing area in which these methods have not been considered, it is to be expected that these problems again arise. While some information is available as to the results obtained by water-flooding in a few localities in the Mid-Continent, the extrapolation of the sand data on which the results are based, for even generalized use in other areas and fields in the region, is hazardous. It is precarious to assume that the same physical condition will obtain in a sand over more than small, special areas. This paper is concerned with a brief presentation of such data as are available to the authors on existing operations, a survey of the region and extent to which application of the method seems most likely to be made, an estimation of the crude reserve existing for such operations, suggestions as to the importance of core analysis in guarding against uncontrolled floods and its usefulness in predicting ultimate recoveries, and comment on some of the economic phases involved. These subjects, as concerned with water-flooding in the East (notably Bradford, Pennsylvania), have been discussed in detail in the literature and are generally well known. Especially is this true of discussions of the mechanical equipment and various lease layouts and development patterns for water-flooding.

Jan 1, 1936

By Frank Tolonen

IRON-ORE beneficiation is becoming of vital importance to the Lake Superior region, since only a few decades will be needed to exhaust the direct shipping ores even if generous allowances are made for discoveries of new orebodies. If the region is to continue as the chief source of ore to the steel industry of the United States, it must concentrate or otherwise beneficiate the enormous tonnages of available iron formations. A beginning along this line has already been made. About one-fifth of the total shipment, even now, is the product of some sort of concentrating process, while another fifth is improved in physical structure by crushing, screening, drying, sintering, or some other similar method. The amount of material amenable to these processes is limited, however; and, in order to be able to utilize the billions of tons of iron formations that cannot be so beneficiated, an intensive study of their nature and concentration possi-bilities is necessary. As long as high-grade ores are available in ample quantities, ore dressing is economically impossible, but as soon, as the supply nears exhaustion it becomes necessary. At first the products of ore dressing must meet as nearly as possible the same specifications as the rich ores in order to be adapted to the reduction processes already established. The future requirements as to quality will depend on the one hand upon the ability of the ore dresser to eliminate undesired constituents and charac-teristics in the material, and on the other upon the adaptation of the reduction processes to the product that can be economically supplied. A better understanding of the blast furnace and other reduction reactions, and improvements in the preparation of raw materials, should enable the Michigan districts to continue to supply ore for a long time to come. The study and testing of the iron formations necessary to bring a utilization of the low-grade ores, though requiring time and effort on the part of all concerned, should not be postponed, especially since the economic situation forces the use of the highest grade ore in preference to the leaner material.

Jan 1, 1933

By R. F. Lee, G. Purcell

Tests carried out in the Department of Mining and Metallurgy at the New Mexico Institute of Mining and Technology indicate that high density rigid foams may, with the addition of suitable fillers, have structural properties comparable with concrete. Since polyurethanes have other useful properties that are unique to the foams, they have great potential value for both mining and civil engineering applications. Polyurethane, a generic term for a wide variety of closely related foam compounds, suggests rather misleadingly that foams are simple polymers of the urethane monomer ethyl carbamate (H,NCOOC,H,) . Polyurethane foams certainly do contain urethane groups, but these need not necessarily preponderate. Other reactive groups may be, and usually are, present so that the final polyurethane product will most likely contain, in addition to urethane groups, aliphatic and aromatic hydrocarbon, ester, ether, amide and urea groups.

Jan 9, 1963

By C. F. Wang

Manchuria in General Manchuria, called the "Three Eastern Provinces" in Chinese, forms the northeastern corner of China and is bordered by Siberia on the north and northeast, and by Korea on the east. It is a land famous in Chinese annals as the place of origin of the Ching dynasty, and in more recent times it has been an arena for diplomatic maneuvering and commercial competition between the Russians, advancing from the north, and the' Japanese from the southeast. It derives its name of "three eastern provinces" from the fact that it is divided into three provinces; Hei-

Jan 2, 1918

By Richard S. McCaffery

A Research on iron blast-furnace slags has been in progress since 1922 in the metallurgical department of the University of Wisconsin, supplemented by observations, tests and critical examination of operating records at 10 furnaces. From the data thus collected information has been put into forms suitable for use by furnace operators and is given in this report and the three accompanying papers.' In the viscosity results reported, it is estimated that temperatures were measured within 5" C. and that the viscosity determination of the particular slag investigated is accurate within ± 4 per cent. In the viscosity diagrams in the various papers, the equal viscosity lines were drawn in such a manner that in all cases they are located correctly with respect to the actual experimental results, but when determining a viscosity for a particular composition from the diagrams, the viscosity may. be slightly less accurate than the experimentally determined viscosity for the same slag, for the reason that the iso-vis lines interpolated between the experimental results may be shifted slightly without violation of the experimental data. The viscosity diagrams represent our judgment of their position under the above conditions, and we believe the relative accuracy of viscosity data taken from the diagrams is more than sufficient for any use to which the data may be put. Hundreds of samples of slags synthetically produced in the laboratory and of actual furnace slags have been studied in various ways. The ranges of compositions of slags used for viscosity measurements are: silica 25 to 55 per cent.; alumina 0 to 35 per cent.; lime 25 to 55 per cent.; magnesia 0 to 20 per cent. These measurements were made at temperatures of 1250°, 1300°, 1350°, 1400°, 1450°, 1500°, 1550°, 1600" and 1650" Centigrade. Descriptions of apparatus, methods used and statements of the problems investigated have been published in the papers listed in the bibliography beginning on page 120.

Jan 1, 1932

By Jerome Strauss, Carl L. Shapiro

THIS is a critical examination of the theory that the amount of carbon necessary to form the iron-carbon (carbide) eutectoid is lowered by the addition of any carbide-forming element. Although this theory has been built up over a long period of years,, it appears, in the light of recent published investigations upon the ternary constitutional diagrams of iron with carbon and other alloying elements, to be no longer tenable. A survey of these new results, summarized below, shows that (as is known) some metals lower the carbon content of the iron-carbon (carbide) eutectoid, whereas others raise it, but (as not heretofore clearly set forth) some first move the eutectoid in one direction and then, at higher concentrations, shift it in the opposite direction. Moreover, these differences in behavior exist even among the common alloying metals classed as carbide formers. PART I INFLUENCE OF BODY-CENTERED CUBIC ELEMENTS The effects of the various body-centered cubic metals (chromium, tungsten, molybdenum, vanadium, columbium and tantalum) are reviewed individually. Iron-carbon-chromium System.-In the monograph on Alloys of Iron and Chromium, Kinzel and Crafts' concluded that the carbon content of the eutectoid is lowered by increasing the chromium content. The quantitative influence of chromium on the eutectoid point of iron-carbon alloys was shown by Monypenny2 (Fig. I) and no data have been forthcoming to refute his findings. Iron-carbon-tungsten System.-Gregg,3 in the monograph on Alloys of Iron and Tungsten, accepted the data showing that tungsten decreases the amount of carbon required to form the eutectoid. The influence of tungsten on the eutectoid percentage of carbon as determined by Oberhoffer and Daeves4 is shown in Fig. a; these results have received general approval. Iron-carbon-molybdenum System.-In the monograph on Alloys of Iron and Molybdenum, Gregg5 reviewed the work of Guillet,6 Swinden,7 and Reed,8 all showing that molybdenum lowered the carbon content of the eutectoid, whereas Takei9 contradicted this conclusion. Svetchnikoff and Alferova,10 a little later, showed that large additions of molybdenum shift the eutectoid to the right. These last-named investigators found that molybdenum, up to 1.2 per cent, shifts the pearlite point and the point of maximum solubility of cementite in the gamma phase only slightly in the direction of lower carbon content; on the other hand, increasing amounts of molyb-

Jan 1, 1943

To the Members It has been, and is the endeavor of the A. I. M. E. to serve each and every member. One of the means of letting the membership know what is going on in the mining; metallurgical and chemical fields, and by far the most important, has been our monthly Bulletin. To publish this costs money, and to partly defray the costs, it was decided to accept such advertising as could be secured. The A. I. M. E. is the only one of the American National engineering societies whose dues are as low as $10 per year, and it actually spends more upon the Bulletin and Transactions than the sun total it receives for clues. Hence the need of advertising revenues. We are planning even greater improvements for your Bulletin-improvements that will help you in your work. It will mean a better publication, with more information than ever before. To successfully carry out our plans, we must have your co-operation. We are not asking you for financial, but for your moral support. With that we shall accomplish a great deal. What we ask of you, brother member, is to give evidence to those patronizing our advertising pages, that you not only read the editorial pages, but the advertising section as well, and that you have in mind the welfare of your Institute by consulting the advertising pages when in the market for equipment. Do you realize that if you mention your Bulletin when writing advertisers or purchasing supplies, that not only would your publication secure more advertising, but better satisfy present advertisers. We have reason to know that our advertisers secure business as a result of our publication, but they demand some evidence that you see their advertisement. Unfortunately, our members do not as a rule mention where they saw the advertisement, and as a consequence advertisers have no means of knowing whether their investment in the Bulletin is paying. The A. I. M. E. Bulletin can be made the best advertising medium in the mining, metallurgical and chemical fields, simply by each member doing his bit. It is very little to ask of you, and the returns to the mining industry will be enormous.

Jan 9, 1915

By W. T. Cardwell

This paper presents a theory for estimating the rate of gravity drainage of a liquid out of a sand column. Account is taken of the variation in permeability to the liquid as the saturation in the upper part of the sand becomes less than 100 pct. The theory is confirmed by previously published experimental data. Introduction Petroleum engineers have expressed the need for 4 theory of gravity drainage. Brunner,' in particular, has pointed out that some type of mathematical theory is necessary to begin the application of laboratory data to field problems. Muskat and his associates2'3-4 have recently made contributions to the theory of gas-drive behavior and have indicated an intention to apply their methods to water-drive systems. No theory of gravity drainage rates has been developed, however, and it seems desirable to formulate one at this time. Differential Equations of Capillary Flow The flow of liquids in partially saturated porous media has been studied by many investigators.6-10 Richards6 presented derivations of fundamental differential equa- tions governing two-phase capillary flow; and used simplified forms of those equations in solving a steady-state problem. Muskat and Meres6 presented and used equations different from those of Richards. Their equations did not explicitly involve capillary pressure gradients; but included, on the other hand, terms expressing the effects of the evolution of gas from the liquid phase during flow. Leverett8 stated in 1940 that "previous work on the flow of fluid mixtures in porous solids [had] failed adequately to account for all of the three influences that cause motion of the fluids: capillarity, gravity, and impressed external pressure differentials." Leverett's basic equations, however, were specialized forms of the general equations of Richards,5 which had actually taken account of the three influences mentioned by Leverett, but had not been used in a problem involving all three. The fact is that our knowledge of capillary flow and our ability to express this knowledge in differential equations exceed our ability to solve the equations except in a few cases. General differential equations have usually been of little more than formal value. In solving practical problems, it has been necessary to develop specific equations, preserving terms that involved the factors important in those problems, and purposefully neglecting other terms that were not of predominating influence. This is the method followed here. It is believed that the solution of the particular problem and the scheme of the solution itself are new.

Jan 1, 1949