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By A. M. Beebee

IN the present century the coal and manufactured gas industries have been eclipsed in public interest by oil, natural gas, and hydro- electric energy, which have had the benefit of rapid development and novelty. I sometimes wish that our social- order were such that hydro power had been developed first, that the use of gas from coal had never been seriously considered, and that our domestic energy requirements were supplied by other fuels. Sup- pose the manufacture of gas from coal should then come on the scene at the present time with the current plight of the railroads, coal regions, and labor generally, presenting the fact that it could increase the amount of coal mined and shipped by the railroads by some 16,000,000 tons, and increase the coal used at existing u plants five times. Imagine the great public interest that would be manifested; it would supply the cooking and water-heating requirements of a community with a superior character of service at a cost to the customer approximately half that which had obtained previously. Would not such a situation be heralded as the salvation of our country and all help be given it?

Jan 1, 1940

By Charles S. Barrett

NUMEROUS determinations1-7 of the tex-ture of cold-rolled polycrystalline iron, steel, and ferritic alloys have been made with good agreement among the various observers as to the principal features of the texture common to all, but there has been no adequate explanation of the texture in terms of the behavior of individual grains. This study presents an explanation of the texture based on the observed rotation of single crystals when deformed in a manner similar to a grain in the aggregate, a method we have found useful in leading to a better understanding of compression and tension textures;8,9,10 in particular, the aim has been to determine experimentally the end orientations of rolled single crystals of iron. These are discussed in connection with the point of view of Wever1 and of Boas and Schmid2 that the rolling texture is a simple compression texture (compression normal to the rolling plane) superimposed on a simple tension texture (tension in the roll-ing direction), and the point of view of Kurdjumow and Sachs3 that three ideal end orientations exist.

Jan 1, 1940

By M. K. Foster

Ten horizontal retort zinc blocks of a modified Hegeler design are in operation at Nueva Rosita, Coahuila, Mexico, and produce approximately 170 t of spelter daily, or 62 000 t/year. A block consists of two furnaces of 448 retorts each, making 8960 retorts as the plant complement. Each furnace block is fired with natural gas and air maintaining the combustion mixture in the furnace always slightly reducing. No attempt to recover energy through waste heat boilers is made. The spelter moves to market by rail and truck either in palletized bundles weighing approximately 1060 kg, as loose slabs weighing 26.5 kg each, or as 1088 kg ingots. At present 46% of the metal is exported and 54% is consumed domestically in Mexico. The present day trend toward equalized or alloyed spelter, as well as special shaped castings results in sales of 35% of the entire plant's production. Sulfuric acid is also produced by the Contact Process using vanadium pentoxide as the catalyst. The plant is basically a Monsanto contact system, producing approximately 68 t of 100% sulfuric acid daily. Both 98.5% sulfuric acid and 20% oleum are available. All of the acid made is consumed in Mexico. Shipments are made in 26,900 dm3 tank cars.

Jan 1, 1970

By J. M. Uys, T. B. King

WalSH, Chipman, King, and rant' have measured the water content (as hydrogen) of actual steel-making slags. An average water content of 290 ppm was found for basic open-hearth tapping slags and 114 ppm for acid open-hearth slags. Upon equilibration of these slags at 1550°C with a 25 pct H20-75 pct Nz atmosphere, the water content increased to about 410 and 300 ppm for the basic and acid slags, respectively. Walsh et al. concluded that an acid slag was thus relatively far removed from equilibrium, and that basic slags showed a closer approach to equilibrium, with the water vapor in the furnace atmosphere. Herasymenko2 contended that these conclusions were unjustified, as the oxygen pressure used in the equilibration experiments, ;bout 5 x X atm, was quite different from that found in the furnace. Consequently, during the experiments the slag composition would have changed due to oxidation of ferrous iron. As an extension of Walsh's work and to attempt to clarify this matter, the solubility of water in a basic open-hearth slag was measured as a function of oxygen pressure. Similar measurements were also made on synthetic silicates in the "Fe0"-Fe203-SiO, system. The experimental technique has been described previously by Walsh et a1.l and Uys and King.3 Samples of the basic open-hearth finishing slag, contained in 10-cc platinum crucibles, were equilibrated at 1550°C with atmospheres of different oxygen pressure but constant water-vapor pressure, Ph~o = 0.192 atm. Calculations, as well as measurements, indicate that this figure approximates the water pressure of the combustion gases in a steam-atomized, oil-fired open hearth. Oxygen pressures in the open hearth can vary from 10"2 atm in the combustion gases to between l0-' and 10" atm in the steel bath. The former figure depends on the combustion practice and the latter on the carbon content and temperature of the bath. The oxygen pressure of the slag should lie somewhere between these extremes and is expected to be closer to that of the steel bath than that of the combustion gases. Oxygen pressures were therefore varied between 10" and 6 x l0 atm. At the lowest pressure the slag "puffed up" when quenched (indicating possible loss of water) so experiments were not conducted at lower oxygen pressures. The results are shown in Fig. 1, which includes the water content of the slag "as sampled". The results show that the water content of the slag increased appreciably on equilibration with water vapor at 0.192 atm pressure and that the water solubility apparently decreases with increased oxygen pressure. The solubilities found are comparable to those of the Li20-Ca0-Si02 system.3 Work with synthetic slags in the "Fe0"-Fe203-SiOz system was performed at 1500" C, with Ph20 = 0.192 atrn and for oxygen pressures varying between 10"2 and 10-lo atm. Samples for chemical analysis were prepared as described by Larson.4 The results are shown in Fig. 2. Some low-silica melts tested at low oxygen pressures "puffed up" when quenched and analyzed less than 100 ppm water; these results are not included in Fig. 2. The melts containing 40 mol pct silica also showed a tendency to "puff up" during the quench, when they were tested at the lowest oxygen pressure. These results indicate that, at constant silica content, the solubility of water decreases somewhat with increased oxygen pressure. The effect is, however, small considering the wide range of oxygen pressures studied. Also, at constant oxygen pressure (above about lom5 atm) the solubility increases

Jan 1, 1963

By D. F. Hewett

CONTENTS PAGE Introduction 1 Geologic features of eastern Oregon 2 Geology of the Sumpter quadrangle 2 Rocks older than the ore deposits 3 Rocks younger than the ore deposits 8 Lodes of the Sumpter quadrangle 8 Areal distribution 8 Geologic distribution 9 Major features of the veins 9 Mineralogy and texture of the veins 13 Ore deposits zonally disposed around the Bald Mountain batholith . . . . 13 Summary of mineralogy and texture 32 Zonal relations 33 Ore deposits zonally disposed around Greenhorn Mountain batholith . . . 36 Zonal relations 37 Relation of textural features to zonal arrangement of veins 37 Summary of zonal relations 38 Comparison with similar districts 39 Outlook for the district 40 INTRODUCTION IN an earlier report on the Sumpter quadrangle1 it was briefly stated that the quartz lodes of that region might be separated into several groups or belts on the basis of the kind and abundance of the minerals of which they are composed, and that these belts were disposed as areal zones around the principal intrusive mass of the region. When the opportunity to revisit the region was offered in 1929, as a result of a cooperative agreement between the State Mining Board of Oregon and the United States Geological Survey, it seemed advisable to pay particular attention to this feature of the lodes, in the hope that if the idea of zonal relations was confirmed it might serve as a guide in exploitation.

Jan 1, 1931

By S. G. Gibbs, A. B. Neely

Jan 1, 1967

By Y. C. Liu

Both the habit plane of martensite and the orientation relationship between the matrix and martensite platelets of different habit planes have been investigated in binary titanium alloys with molybdenum, chromium, and iron. The effect of the mode of deformation on the martensite habit plane was studied. A micrograph of an exposed mar-tensite platelet is presented. IN the study of martensitic transformation in Ti-Mn alloys,' two martensite habit planes—{334), and {344)8—were reported. The {334), habit was also observed in unalloyed titanium upon transformation,' although there is disagreement with respect to the exact indices. The other habit plane, {344),, has not been reported in martensitic transformation in any other alloys. The present investigation was made to determine whether other binary titanium alloys with P-stabil-izing elements would exhibit a crystallography of transformation similar to that of Ti-Mn alloys. Furthermore, since martensite platelets can be induced by deformation under certain conditions, it was of interest to investigate whether the mode of deformation, compressive or tensile, would influence the formation of martensite platelets on a specific plane in an alloy system which possesses two martensite habit planes. Experimental Procedure The material used for the preparation of the binary alloys of iodide titanium with molybdenum, chromium, and iron had the following purities: 99.99 pct iodide titanium, 99.9 pct molybdenum, 99.423 pct chromium, and 99.9 pct iron. The compositions of alloys listed in this paper are in nominal weight percentage. All specimens used were prepared and treated according to the procedure described in reference 1, unless stated. For the subzero temperature treat,ment the following experimental schedule was followed. After specimens had undergone the grain-growth treatment, they were quenched into an ice-water bath and were then metallographically examined. In specimens of higher alloy content, no martensitic transformation was observed. In those in which mar-tensitic transformation did occur, only specimens in which the martensite platelets existed as fine needles in localized regions were used. All specimens were reannealed 17 hr at 1200°C, quenched into ice water. and the capsule was broken. They were held in the ice water for from 5 to 10 sec, then transferred to a liquid-argon bath. This stepped quenching procedure was found to be more efficient than direct quenching into liquid argon. In the latter case, as soon as the hot specimen was immersed in the liquid argon, a protective, insulating layer of argon gas formed, and the specimen continued to glow vividly in the bath for some time. In the study of the habit behavior of martensite produced by deformation, specimens were deformed at room temperature either by compression, tension, or rolling. Martensite habit planes were determined by the two-surface analysis procedure described in reference 1. A stereographic net of 153/4 in. diam was used throughout the investigation. The method for determining the orlentation relationship between martensite and the matrix follows that used by Greninger and Troiano.' A diamond-polishing table with its auxiliaries was used in order

Jan 1, 1957

By Philip B. Bucky

CONTENTS [PACEPACE r. What Is a Rock Burst?2 4. How Can Rock Bursts Be Predicted? . 35 Jack Spalding2Jack Spalding35 A. F. Robertson 2, 5A. F. Robertson35 W. R. Crane 2A. B. Yates and P. J. Shenon. . . . 35 G. S. Rice 2W. R. Crane 35 P. J. Shenon 2G. S. Rice 35 L. C. Graton 2B. F. Tillson 36 2. What Are the Causes of Rock Bursts? 6 5. How Can Rock Bursts Be Controlled?. 36 Jack Spalding6Jack Spalding36 A. B. Yates and P. J. Shenon . 7, 12, 29A. F. Robertson 36 A. F. Robertson 12, 28W. R. Crane37 W. R. Crane 15A. B. Yates and P. J. Shenon. . . . 37 G. S. Rice 15Oscar Weiss38 Oscar Weiss15G. S. Rice37, 42 P. B. Bucky21R. D. Hoffman42, 43 P. H. Bird 21, 26, 28R. D. Hall 42 M. K. Hubbert26R. H. Cromwell42 G. Wheeler 26. J. Shenon 42 B. F. Tillson26, 28P. B. Bucky42, 44 T. T. Read 27B. F. Tillson 42, 44 A. B. Yates 43, 44 3. How Can Rock Bursts Be Prevented? . 30P. H. Bird 43 Jack Spalding. . . . • . • • • • . 306. General Discussion . A. B. Yates and P. J. Shenon. . . . 31Jack Spalding44 A. F. Robertson32R. D. Parker49 W. R. Crane 35C. Baring Horwood 51 G. S. Rice 35P. B. Bucky 52] FOREWORD THIS symposium brings together points of view, experiences and ideas on rock bursts from a goodly portion of the globe. Some conceptions, particularly those regarding the necessity of depth, have been fairly well shattered, as we find that they are present in the water tunnels of New York, on the surface at marble quarries in Vermont, and in the coal mines of the United States, as well as in the deep mines of the South African and Kolar gold fields, and in the nickel, copper and gold mines of Canada. Their occurrence under such a variety of conditions is, therefore, a challenge,

Jan 1, 1942

By C. W. Davis, L. R. Messer

THE name fuller's earth, which was derived from its early use in "fulling" or removing grease from woolen goods, is a term that is generally considered to designate mineral matter, containing hydrous aluminum silicates of the clay group, which has a high capacity for removing colors from oils, whether of animal, vegetable, or mineral origin. Fuller's earths are usually dried and may be "tempered" by heating or may be treated with water or reagents to improve their efficiency. For our purpose the term "acid-treated earths" will include those products from the partial decomposition of mineral water by acid which are equal to or more efficient than an untreated fuller's earth from Quincy, Fla., when used in bleaching mineral oil by the "contact" process. In general, the contact process for treating oils consists of heating and agitating a mixture of oil and finely divided adsorbent, the latter being subsequently removed by filtration. The term "adsorbent" is used because, although there has been a great deal of controversy over the mechanism of removal of impurities from oils by mineral matter, there is no doubt that adsorption, which involves the surface of the solid, plays a major part.' The properties that make fuller's earth useful in the treatment of petroleum products by "percolation1' and in the purification of edible oils by the contact process have long been studied, but the comparatively recent adaptation of the contact process to the bleaching of petroleum products has made desirable the further investigation of fuller's earth and other adsorbent earths.

Jan 1, 1929

By Sallie McCabe Johnson

LIFE IN RUSSIA for the foreign woman is hard. It is up to her whether her days are spent in tearful longing for ironic or whether she :hakes the real effort to ferret out the interesting or amusing side of such exasperating conditions as ooh a Russian can conjure. So to begin Discard all promises.. This is perhaps the most difficult thins- to learn but promises in Russia are nut what they are at home. There are many reasons for ibis, sonic good and some bad but whatever the reason. the fact remains that they are usually worthless- as each of us must slowly learn In, disappointment after disappointment. Also we must learn that we cannot expect to get or to do a certain thing just because someone else has done so. What we did yesterday perhaps cannot be dune today. What we purchased air hour ago, oxen ten minutes ago- we cannot purchase now. What our neighbor did this morning we cannot do this afternoon. Changes arc continuous. Every person's experience is different from that of another aid this in a great measure accounts for the conflicting stories brought horns. In a land of chaos we live only from hour to hour and this is one of the exceedingly exasperating conditions to face. When I wished to visit Leningrad, an overnight nip from Moscow, more than a week's lime w as required to obtain a ticket, vi en through the efficiency of lntourist: alone I might have spent a month at it. Each day

Jan 1, 1932

By C. A. Fisher

THE discovery of petroleum in Pennsylvania in 1859 marked the birth of an industry of paramount importance. Spreading from - Oil Creek, this remarkable industry may be said to have embraced the earth in a little more than half a century. Those who made the discovery little realized its deep significance or far reaching influence on our national life. For over sixty years, during which time this nation has created and developed the oil industry to a high state of efficiency and' carried its activities to all parts of the world, we have' at all times been the leaders in the production of crude oil and in the development of its technology. During the unprecedented growth and expanse of the oil industry there has been an increasing dependency of our basic industries on, petroleum, until at present it has become essential to our national existence. To meet the ever increasing demand for petroleum and its products, we have explored, at one time or another, for their oil possibilities, practically all parts of the sedimentary rock area in the United States. Furthermore, detailed surface and, in many places, subsurface studies have been made of all the promising regions; over 640,000 jewells have 'been drilled for. oil since the beginning of the industry; $12,000,000,000 have been spent in this work; seventeen major fields exceeding 100,000 bbl. daily production and more than a thousand minor pools have been opened up, and 8,000,000,000 bbl. 'of oil have been produced, or an amount nearly equal to the estimated future reserves of the United States made in 1921.

Jan 1, 1925

By John Ward Smith

Dawsonite-bearing oil shale of Colorado's Green River formation offers a unique and vast (more than 5.9 Gt of A120 j) resource of easily extractable alumina. The processing methods required by the thermal reactions of dawsonite and its oil-shale carrier also require production of shale oil, soda ash, and nahcolite as marketable coproducts. These production methods are presented. The alumina production process is contrasted with the Bayer process to describe technical advantages of extraction of alumina from oil shale which may offset the problems associated with processing a relatively lean ore. While alumina production from oil shale requires development of new technology, the technical problems appear solvable. Only the political problems arising from the now onerous and completely unnecessary federal oil-shale withdrawal appear less solvable.

Jan 1, 1982

By Prince Lazarovich, Hrebelianovich

I WAS asked by the chairman of one of the Sessions on Employment Problems to talk about the viewpoint of the foreign workingman. I am not a workingman. I have never done what a work-hand might call an honest day's labor; that is, I have never been in a factory or manufacturing plant or in a mine, though in truth, hard work and I are well acquainted. I was a soldier, am an engineer, have long been actively interested in the most important waterway construction in the near East, have served politics and diplomacy, written books and lectured at universities. My knowledge of the foreign workingman in this country comes from the fact that my own compatriots here at various times came to me and appealed for advice and help, and last year I was asked by the employment manager of a corporation to undertake a welfare job at one of their plants. I went out, saw the plant, talked with the superintendent and outlined certain of my ideas which he personally heartily approved, but which did not find favor with those higher up. I approach the subject of the foreign workman's point of view with the understanding that the industrial employer's effort is for the maximum of efficiency. I am conversant with labor conditions abroad both in industry and agriculture. What I have learned of industrial conditions in America as they affect the foreign immigrant has been chiefly gathered from the cases referred to of foreign workmen who from time to time have come to me with their troubles. In the course of those investigations, in order to give whatever help or advice was possible, I have been impressed with the fact that the great United States industries evidently had- pot yet sufficiently recognized the value of studying the conditions of the workingman in the lands of his origin across the seas. A careful study of that which could be called the moral element in connection with its foreign labor would give industry a knowledge of the man's reason for coming, what' grievances he brings with him, his hopes for a future, and the peculiar character of his capacities. The employer would thereby be enabled to meet the man, to be helpful to him, to aid him and at the same time promote industrial efficiency, inasmuch as a workman who believes that he is being dealt with humanly and squarely is contented and satisfied and will give willingly, and even with pride, the best that is in him; justice and a fair deal is all the man wants.

Jan 4, 1918

By J. C. Borland, J. H. Rogerson

Jan 1, 1963

By AIME AIME

T HE appointment of Herbert Hoover to the portfolio of Commerce in the President's Cabinet is to engineers the fulfillment of a long deferred hope to have an engineer in high political office and is a matter of congratulation to us for three reasons; because he is a mining engineer who represents the highest type of idealistic engineering effort; because he is a past president of the Institute; and because he has probably a broader grasp of world problems than any other living engineer. Frank A. Vanderlip in the preface to his book "What Happened to Europe" tells of the many interviews he had with the most prominent men in Europe which were made possible for him by his eminence as a banker and by the courtesy of the American ambassadors. He cites by name such well known figures as Austin Chamberlain, Sir Auckland Geddes, Monsieur Delacroix, Monsieur Briand, Mr. Padkrewski, Mr. Venizelos, Colonel House, General Pershing, Mr. Baruch, and many others and says :

Jan 1, 1921

By J. P. Carson

The works of the Tula Iron Company are in the Republic of Mexico, State of Jalisco, twenty-eight leagues southwest of Guadalajara, ten leagues northwest of the town of Sayula, through which passes the projected line of the Mexican National Railroad. Its geographical position would be about: latitude, 20' 10' N., longitude, 40 35' w. of Mexico City. The surrounding country is a rolling plateau, 6000 feet above the sea, enjoying the most magnificent climate in the world, the average temperature being about '70'. The works were commenced in 1850 by a company with very small capital, having not the least idea of the undertaking. They soon fell into the hands of the money-lenders, and after changing

Jan 1, 1879

By Robert H. Richards

(Pittsburg Meeting, March, 1910.) THIS is in part a review paper, indicating the various steps that have been taken in developing hindered-settling apparatus, some of the standard data that have been obtained, and some of the conclusions one is led to as to the effect of it in improving concentrating-methods and machinery, and in part it brings in some unpublished work. CAUSES OF LOSS IN ORE-CONCENTRATION. In making a study of the separation of valuable minerals from the waste gangue, particularly by water concentrators, it is necessary to define, first of all, what are the causes of-loss that are likely to interfere with the concentration. Having made this definition; we can then study to see in what way the machines make their losses, and plan remedies for them in an intelligent way. Losses may be stated to occur as included grains, as flat or long grains, as fine free mineral, and as absolute slime. We will take, these up one by one, as follows: Included Grains.-Fig. 1 shows by a set of diagrams how included grains may occur: first, where the heavy mineral grains attached to the quartz are of large size; secondly, where they are of small size ; and thirdly, where very fine particles of heavy mineral are included in the quartz. We have to decide in regard to included grains whether they are rich enough to go direct to, the furnace, or poor enough to throw away, or whether they lie between these two points and require recrushing as the only means of severing the values from the waste. This last case is the only one requiring special treatment at our hands. We will therefore consider that next. * By mutual consent, this paper has been presented also before the Colorado Scientific Society, and the Canadian Mining Institute, Montreal.

Feb 1, 1911

By D. E. Stephenson. Discussion by R. G. K. Morrison, L. Obert

R. G. K. Morrison (Chairman, Dept. of Mining Engineering and Applied Geophysics, McGill University, Montreal, Que., Canada) - The discing of drill core has been a recognized pressure phenomenon for many years but only recently has an interest been taken in the mechanism involved. The work of Jaeger and Cook is referred to in the text. The authors have now advanced the study to establish, within certain loading limitations, a direct relationship between axial and radial stress at failure. This is an important contribution. In mines generally, where pressure conditions result in the spalling of openings, the faces of drifts and crosscuts, on scaling, usually show a concavity with respect to the opening very similar to the face of the drill hole after the separation of the stub. The same holds for shaft sinks. This suggests a similarity between the mechanism of the discing of core and that of the spalling of an opening, under pressure, to develop a more stable outline. The latter, commonly regarded as shear, is the most conspicuous type of failure observed in

Jan 1, 1967

By C. C. Harris, A. Jowett, S. K. Ghosh

An equation derived from first-order kinetics and accounting for return from froth to pulp has correlated continuous flotation data. The concentration of floatable material in the pulp can be altered either by changing the feed concentration or the feed rate. The latter does not affect the flotation rate constant, the froth to pulp return constant, and the concentration of non-floatable material in both the pulp and concentrate. Both the return constant and the concentration of non-floatable material in the pulp are directly proportional to the feed concentration, while the concentration of non-floatable material in the concentrate is related to the feed concentration. The investigation of the froth flotation process by continuous test methods, previously used by Brown and smith,1 Jowett and Safvi2 and Jowett and West,3 is being continued. Recent tests, primarily concerned with flotation cell design, have yielded kinetic data suitable for testing an equation proposed by Arbiter and Harris4 which postulates that a flotation process is defined by two rate constants: 1) the rate constant for mass transfer from pulp to froth. Previous workers have regarded this as the flotation rate constant. 2) the rate constant for mass transfer from froth to pulp, which has previously been ignored. THEORY Under continuous flow conditions at the steady state in Fig. 1 the equation developed4 is Symbols are defined in Table I. The air-liquid ratio terms4 have been omitted, since they are substantially constant for a given set of conditions. Also, for a system operating at the steady state Vf and V, remain constant and Eq. 1 can be written: Cp/Cc=b'/a,+Qc/a' [2]

Jan 1, 1963

By R. G. Bentsen, D. A. T. Donohue

The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today.1-4 Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming. To use dynamic programming, we must be able to predict not only the production rate-time curve resulting from a given stimulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism. We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process. Oil Production Response Model The advantage of using a mathematical model is its generality and ease of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results. With this in mind, we kept our model as simple as possible, yet generally representative of the actual physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated. In

Jan 1, 1970