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By Charles Hart

The art of electric smelting came with the turn of the present century and owes its existence to the introduction of alternating current, which found its first wide use in the establishment of the great power plants at Niagara Falls, N. Y. Prior to that time current was largely direct. The furnaces were electrolytic in nature and found their first metallurgical use in the production of aluminum, and this process still prevails. The normal production of pig iron up to that time was carried on in blast furnaces in which charcoal, coke and anthracite were used as the fuel. This new electric process called for sufficient carbonaceous material to reduce the oxides and impregnate the pig iron with sufficient carbon, but the remainder of the energy was to be supplied by electric power. The chemical reactions are essentially the same in electric smelting as obtains in the older blast furnace. All of these data are so well known in both methods as to need no discussion at this time, for they can be found in scientific : publications and books written during the first two decades of this century. Types of Furnaces The 40 years devoted to the practice of electric smelting may be divided into two . periods of 20 years each. The first was devoted to experimentation with furnace types and with many publications on theories and processes. The second half of this term was devoted to perfecting the types of furnaces and their active commercial operation. The arc furnace may be found in three types: (1) the direct-heating arc furnace with the positive electrode included in the bottom and the other electrode suspended above; (2) the independent arc furnace with its electrodes entirely above the charge, which of necessity depends upon heat reflected from the roof; (3) the direct-heating series arc furnace equipped with two or more electrodes suspended from the roof. Of these three types, only the last is used in electric smelting of iron ore at the present time. The elimination of the other types automatically removed many of the early designs, to the end that there are now only two general types in operation: (I) the " Electrometalls" or high-shaft furnace of Sweden, and (2) the low-shaft or pit-type furnace as offered by Tysland-Hole and Siemens-Halske. The "Electrometalls" furnace takes its name from the corporation formed by the engineers that had undertaken its perfection. After trying several designs they brought forward the furnace shown in Fig. I, which by the way is the highest development of this type of furnace as of today.l Note the trend in the lines, which have kept pace with modern blast-furnace design. The high-shaft furnace lends itself to skip filling and is fitted with tuyeres immediately under the crucible roof, whereby the gases are recycled and the roof preserved. The failure of the Electrometalls furnace in Norway, because of its inability to meet

Jan 1, 1941

By R. C. Edwards, T. G. Kirkland, Will Mitchell

A scrubber of new design has been invented for the beneficiation of glass and chemical sands. The machine is described and its capacity and metallurgical efficiency compared with the performance of other sand cleaning devices. THREE years ago, when the Process Research Laboratory at Allis-Chalmers Manufacturing Co. sought a remedy for the increasing cost of disposing of great quantities of spent sands from foundries, R. C. Edwards developed a continuous inclined paddle scrubber which removed a substantial amount of the charred coatings from the grains with a surprisingly small amount of degradation of the sand itself.' The satisfactory results obtained on foundry sand, using this piece of equipment in conjunction with classification, suggested that a similar procedure could probably be applied to the cleaning of other sands, such as those required by the glass and chemical industries. This paper describes the flowsheet and the results of tests performed on impure natural sands. The four materials tested were silica sands obtained from widely separated geographical areas. Three of the sands tested contained various amounts of iron oxide and the fourth an excessive amount of calcareous bonding material. The iron oxide was present predominantly in the form of grain coatings, which were scuffed by the paddle scrubber, and in all cases a product was manufactured which would meet one of the sets of specifications imposed by the glass industry.' The Edwards paddle scrubber used in these tests consists of a rubber-lined steel cylinder 18 in. in diam and 48 in. long, mounted on a frame so that its slope can be varied 5" to 35" from horizontal. This variable slope permits controlled flow of material through the machine. Rubber paddles rotate inside the cylinder and are secured to a center shaft 2 in. square, which extends through the entire length and is turned at both ends so that it can be supported by sleeve bearings centrally fixed in the end plates of the shell. At the upper or feed end it extends through the bearing on the end plate into a sheave, to which the motor drive is connected by means of Texrope transmission. The four sets of paddles mounted on the shaft, two in each set, are made of rubber belting, 1/4 in. thick, 9 in. wide, and 16 in. long. The two paddles in each set are secured on opposite sides of the square shaft, but in the same longitudinal position along the shaft axis. In other words, the two paddles in the set operate 180" apart. Each successive set is mounted 90" from the preceding one. One end of each paddle is bolted to the square shaft and the other weighted by a steel bar, lx1 1hx9 in. long, which is attached about Yz in. from the outer tip of the paddle. By centrifugal force at proper shaft speed, these weights force the paddle surface to rub smoothly against the rubber lining of the cylinder. During operation, the sand forces its way between the paddle face and the surface of the cylinder, providing the necessary abrading action as the pulp flows by gravity down the length of the cylinder. The capacity of the machine is limited by the amount and the hardness of the coating material and by the quality of product desired. The degree of scrubbing is governed by the retention time in the scrubber, which in turn may be changed by varying the feed rate, water content of the feed, and

Jan 1, 1953

By R. C. Edwards, T. G. Kirkland, Will Mitchell

A scrubber of new design has been invented for the beneficiation of glass and chemical sands. The machine is described and its capacity and metallurgical efficiency compared with the performance of other sand cleaning devices. THREE years ago, when the Process Research Laboratory at Allis-Chalmers Manufacturing Co. sought a remedy for the increasing cost of disposing of great quantities of spent sands from foundries, R. C. Edwards developed a continuous inclined paddle scrubber which removed a substantial amount of the charred coatings from the grains with a surprisingly small amount of degradation of the sand itself.' The satisfactory results obtained on foundry sand, using this piece of equipment in conjunction with classification, suggested that a similar procedure could probably be applied to the cleaning of other sands, such as those required by the glass and chemical industries. This paper describes the flowsheet and the results of tests performed on impure natural sands. The four materials tested were silica sands obtained from widely separated geographical areas. Three of the sands tested contained various amounts of iron oxide and the fourth an excessive amount of calcareous bonding material. The iron oxide was present predominantly in the form of grain coatings, which were scuffed by the paddle scrubber, and in all cases a product was manufactured which would meet one of the sets of specifications imposed by the glass industry.' The Edwards paddle scrubber used in these tests consists of a rubber-lined steel cylinder 18 in. in diam and 48 in. long, mounted on a frame so that its slope can be varied 5" to 35" from horizontal. This variable slope permits controlled flow of material through the machine. Rubber paddles rotate inside the cylinder and are secured to a center shaft 2 in. square, which extends through the entire length and is turned at both ends so that it can be supported by sleeve bearings centrally fixed in the end plates of the shell. At the upper or feed end it extends through the bearing on the end plate into a sheave, to which the motor drive is connected by means of Texrope transmission. The four sets of paddles mounted on the shaft, two in each set, are made of rubber belting, 1/4 in. thick, 9 in. wide, and 16 in. long. The two paddles in each set are secured on opposite sides of the square shaft, but in the same longitudinal position along the shaft axis. In other words, the two paddles in the set operate 180" apart. Each successive set is mounted 90" from the preceding one. One end of each paddle is bolted to the square shaft and the other weighted by a steel bar, lx1 1hx9 in. long, which is attached about Yz in. from the outer tip of the paddle. By centrifugal force at proper shaft speed, these weights force the paddle surface to rub smoothly against the rubber lining of the cylinder. During operation, the sand forces its way between the paddle face and the surface of the cylinder, providing the necessary abrading action as the pulp flows by gravity down the length of the cylinder. The capacity of the machine is limited by the amount and the hardness of the coating material and by the quality of product desired. The degree of scrubbing is governed by the retention time in the scrubber, which in turn may be changed by varying the feed rate, water content of the feed, and

Jan 1, 1953

By M. G. Arthur

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~

Jan 1, 1944

By R. Hastings Keller, Ralph E. Esarey

Oil and gas activities in Indiana during 1943 continued to decline at about the same rate as in 1942. New development, production, and prospecting, all showed the results of Federal regulation, low price for crude oil and shortages of labor and materials. Several local stripper-well operations were shut down, but no large-scale abandonment has occurred as yet. During the year, 277 holes were drilled for oil and/or gas, of which 99 were completed as oil wells, 19 as gas wells and 159 as dry holes. This record was a decline of 21 per cent over last year in the total number of completed tests, 20 per cent in the number of oil wells and 9.5 per cent in the number of gas wells. As in the previous year, most of the drilling (82 per cent) was in the southwestern part of the state, Gibson County ranking first, with 77 completions and 49 oil wells. Posey County was second, with 59 completions and 20 oil wells. The remaining 18 per cent of the drilling was in the old Trenton oil and gas area. The total footage drilled during the year was 482,799 ft., a decline of 18 per cent from the previous year. Of this, 146,559 ft. was wildcat footage. The total initial production of the oil wells completed was 6362 bbl. and of the gas wells was 2,562,000 cu. feet. Three tests in the old Trenton area were drilled into the Cambrian and reported nothing more than tar residue. A Devonian test was to be made in the Griffin field in the Wabash River but owing to the delay caused by Federal restrictions this test did not get started in 1943. It is expected to spud in March 1944. The new discoveries in 1943 were virtually all in the southwestern part of the state, and all, so far, one-well pools, except the North Owensville pool, in Gibson County. The latter was brought in during the month of February and by the end of the year nine wells were producing in the pool, with a reported initial yield of 1260 bbl. per day. By the end of the year it had a daily average production of 401 bbl. and an accumulated production of 39,129 bbl. The average gravity of the oil is reported to be 35.6. On the Ohio-Indiana state line, early in 1943, a new pool was opened up in the old Trenton area. The discovery well was on the Ohio side of the line. An offset well was completed on the Indiana side, with an initial yield of 64 bbl., and settled down to 5 bbl. per day. This well produced 1154 bbl. up to Dec. 31, 1943. There was no further development here, because of the Federal Conservation Order M-68, restricting drilling to one well on 40 acres. The development pattern usually followed in this area is one well to 5 acres. The E. Rogers field was extended by one pool (Table 4). Most of the development in the oil-field pools during the year took place in the Kirksville pool, in Gibson County, and the Caborn pool, in Posey County. The crude-oil production in 1943 was approximately 5,273,000 bbl., a decline of 29 per cent from the previous year. The Griffin field, of Gibson and Posey Counties,

Jan 1, 1944

By E. R. Morgan, J. C. Shyne, V. F. Zackay

NITROGEN used as an alloying element in steel has received increased attention in recent years. Its merit as an austenite stabilizer and hot strengthener has long been recojinized, particularly by European investigators.' Recent work' indicates that nitrogen contents of 1/2 pet or more allow the addition of several percent of ferrite-forming hot strengtheners, such as molybdenum, without subsequent austenite decomposition at elevated temperatures. The room temperature properties of such alloys are characterized by high yield and tensile strengths with excellent ductility, even after cold working, as shown in Tables I and 11. The 1350°F creep-rupture properties of Cr-Mn-Mo-N steels are comparable to those of commercial alloys such as Timken's 16-25-6, containing 16 pct Cr, 25 pct Ni, and 6 pct Mo, as shown in Table 111. Cr-Mn steel containing 1/2 pet N must be made under pressure if ingot gassing is to be avoided. However, there are difficulties attendant to this practice. Pressure melting restricts the ingot size, and the equipment required is costlier and more complicated than comparable air melting facilities. An effort was made, therefore, to determine more economical methods of adding nitrogen. The pressures generated in centrifugal casting usually range from 5 to 10 atm and are sufficient to prevent the gassing of high nitrogen Cr-Mn steels. A centrifugal casting was made of an alloy containing 16 pct Cr, 18 pct Mn, 2 pct Mo, and 0.73 pct N. A risk, 8 in. diam and 11/2 in. thick, was cast at 1000 rpm. It has been calculated that a pressure of 9 atm was developed at the periphery of the disk at this speed. Metallographic inspection of specimens taken from the disk revealed no gas holes or other defects. The elevated temperature properties of radial and circumferential specimens taken from this casting are given in Table IV. The creep-rupture life of this cast nickel-free austenitic steel was equivalent to that of the wrought Cr-Mn-Mo-N steels. Although centrifugal casting appears to lend itself to the manufacture of high nitrogen austenitic steels, its applicability is limited to relatively small sizes. A process applicable to the production of large ingots of high nitrogen steels is suggested by low carbon rimming steel practice. Gas holes formed during ingot solidification are not detrimental so long as they weld shut during hot rolling. An economic advantage of gassing ingots is the increased ingot-to-slab yield, especially if the ingots are mechanically capped. Also, it is probable that higher nitrogen levels can be achieved with mechanically capped ingots than with hot-topped ingots. A series of gassy heats was made under both atmospheric and higher pressures, as indicated in Table V. Several of the air melted ingots were mechanically capped by chilling the molten ingot tops with a steel plate. The ingots were allowed to freeze in steel molds without hot-tops unless otherwise indicated. A comparison of Table 111 with Table V shows no significant difference in the creep-rupture properties of the gassy and the nongassy ingots after hot work- ing nor between the gassy ingots produced under different conditions. References 1 F. Rapatz: Application of Stainless and Heat Resisting Steels Alloyed with Nitrogen. Sinhl and Eisen ( 1941) 61, pp. 1073-1078. 'V. I?. Zackay, J. F. Carlson, and P. L. Jackson: High Nitrogen Austenltlc Cr-Mn Steels. Trans. ASM 119551 48, PP. 509-523.

Jan 1, 1957

By R. J. Hopkins, L. B. Haney

On the basis of limited experimental work conducted at the Port Pirie smelter, it would appear that, by increasing the specific surface of sinter, and possibly that of coke as well, a marked increase in the rate and degree of sinter reduction in the furnace shaft can be achieved. Fusion-point tests have shown that this increased reduction means a much higher sinter fusion point and narrower plastic zone, while the more efficient utilization of coke in the furnace is inherent in the intensification of reduction by the provision of a more reactive sinter surface. Investigations aimed at increasing the ability to operate the blast furnace with a higher lead tenor of sinter reducing fuel cost proportionately, and at eliminating the loss in reduction potential in coke entering the furnace, as shown by the presence of appreciable proportions of CO in the top gases, are reported. Several lines for future investigations that could result in improved smelting methods are proposed. A SOMEWHAT informal presentation of ideas on lead blast-furnace smelting will be given in this paper. These ideas have been developed during observations of furnace behavior at Port Pirie and earlier at Mt. Isa, and have been guided by the results of laboratory experiments at Port Pirie. The authors do not intend to propound any particularly new theories, but present their ideas as a basis for discussion which may help toward a better understanding and improved control of blast-furnace operation. Performance variations of considerable magnitude occur from time to time at most lead blast-furnace plants. While Port Pirie is fortunate in having a very regular supply of high grade concentrates, it is no exception in this respect. Such irregularities are of considerable economic importance and they constitute a challenge to present-day metallurgists in their efforts to obtain an ever greater degree of control over furnace operation. In operating as Port Pirie does with a relatively high lead charge, it has been recognized for a long time that shaft conditions are ,of the greatest importance. A practical, or engineering, attack on the problem of accretions consisted of changes in furnace design, e.g., by widening the shaft to 10 ft above the bottom row of tuyeres, and by the provision of curved ends and vertical walls.' That this attack has had a great measure of success is shown by the fact that barring down of these wide furnaces is rarely necessary, shaft conditions have greatly improved, and sensitivity to charge variations has been markedly reduced. These modifications, followed by some metallurgical changes (chiefly the incorporation of pig iron into the furnace charge in 1948), have brought furnace operation to a point where some variables which were previously masked can now be studied. Accordingly, over different periods of time during the last five years, such variables as could be given numerical values have been recorded and subjected to statistical examination. The objectives of this work were: 1—to reveal the true importance of the different variables and 2—to show the proportion of total furnace variation which is unexplained and therefore referable to causes not measured at present? e.g., shaft accretions, sinter structure, coke structure, and others. Statistical Study of Variables In this work factors relating to furnace speed and lead reduction have been examined: 1—slag com-

Jan 1, 1955

By B. Ehgartner, M. Karmis, C. Haycocks

INTRODUCTION Interaction effects between mining operations developed on different levels of contiguously placed bedded deposits are a major problem in many parts of the United States. Efficient design criteria, derived from careful analysis of field studies as well as theoretical and model analysis, have shown that many problems that may result from seam interaction can be avoided, minimized, or on occasion used with beneficial results. Selection of seam mining sequence is rarely based only on ground control considerations, but rather on factors such as seam ownership, characteristics and accessibility. Therefore all possible mining sequences and methods must be considered in the development of multi-seam design criteria. Increased utilization of the longwall method of mining creates special problems in multi-seam mining due to the inevitability of caving and, therefore, subsidence. Considerable valuable experience has been gained in this direction from British mining operations where interaction problems are extremely common and the longwall method is the primary method used. However, limitations persist in the application of much of this information to U.S. conditions due to variation in layouts between advancing and retreating longwall systems and the inherent difference in the geologic environment. Considerable field data is available for U.S. room and pillar operations, and where successful pillaring operations have been carried out close parallels may be drawn with ground control mechanisms in longwall operations. VARIABLES AFFECTING INTERACTION Analysis of ground control multi-seam problems shows that factors contributing to interaction may be classified into variables that are fixed by the geo- logic environment and those that depend on engineering design. These may be described as follows (Haycocks et al, 1982): Fixed: (i) Depth*, (ii) Innerburden thickness*, (iii) Innerburden physical characteristics*, (iv) Stress field, (v) Seam thickness, (vi) Coal characteristics, (vii) Completed mining operations either above or below the seam to ve mined, and (viii) Age of workings. Mining: (i) Height, (ii) Dimensions and geometry*, (iii) Method*, and (iv) Spatial location of entries* *These variables are regarded as being critical effects. Few attempts have been made to quantify the variables controlling interaction. Dunham's (1978) linear regression analysis, combined with the National Coal Board's MRDE Roadway Monogram, is probably the most noteworthy. This study involved eighteen multi- seam longwall mines in the United Kingdom. The following variables were taken into account: seam depth, pillar width, opening shape, floor and roof conditions, rate of face advance, vertical seam interval, and age and geometry of overlying workings. A multi-linear regression analysis of these variables fitted by appropriate field values developed a prediction equation for lower seam stability. Although the study included many variables, it neglected the nature or geology of the innerburden. The prediction equation was found unreliable, but it did show the significance of geometry as a factor controlling lower seam stability. MINING SEQUENCES Irrespective of the type of mining method selected only four possible mining sequences are possible for two seams. Finlay and Winstanley wrote in 1934. .. "Experience has shown that whether the upper or lower seam was worked first, the subsequent working of the other seam in the same area seriously affected the roads in the seam first worked." Those effects depended upon the four basic mining sequences: 1) The upper seam is mined out prior to mining the underlying seam; i.e., the seams are mined sequentially downward and mining of the underlying seam is not commenced until operations above are completed and have ceased.

Jan 1, 1982

By Dr. O’Neil Thomas J., Donald W. Gentry

Pure gold was hidden in the quartz, they said, 'Twas proved by dreams and signs, and rods divining, By chemic tests, and spirits of the dead, In fact by everything-except by mining. " from R.E. White, "The Mining Town," Alta California, August 18,1873 Textbooks in mining engineering have traditionally covered ore reserve estimation and mine valuation in a single volume. Indeed, Examination and Valuation of Mineral Property by R. D. Parks (1957), having been the standard of the profession for over 20 years, is a classic example. However, the state of knowledge in these two fields has grown tremendously. Most mining engineering curricula now cover these topics in separate courses, and in practice, these tasks are usually performed by different individuals. Thus, this trend now suggests the need for separate, specialized publications rather than a single volume for both topics. Because of the separate development of the science of ore reserve estimation, it is important to state at the beginning what this chapter does not cover. It does not address in detail the design of sampling programs, sampling methods, or the processing of samples or sample data compilation. There are a number of suitable references available on these topics, including Peters (1978), Gy (1979), as well as the previously cited book by Parks. Furthermore, this chapter does not cover in any substantial detail either the traditional methods for using sample data to calculate ore reserves or the more recently developed geostatistical methods. The traditional methods are thoroughly covered by Popoff (1966) and more concisely by Barnes (1980). Among the more useful references for statistical applications in ore reserve estimation are Barnes (1980), David (1977), and Clark (1979). A thoughtful review of the entire science and art of ore reserve estimation is provided by King, McMahon, and Bujtor (1982). In spite of the fact that expansion of knowledge now calls for separate books on ore reserve estimation and financial evaluation, neither publication can ignore the important interrelationships between the two fields. In regard to this text, the unique and crucial role of ore reserves can not be omitted entirely; however, the field is now simply too extensive to treat here in any comprehensive manner.

Jan 1, 1984

By M. G. Arthur

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~

Jan 1, 1944

By William B. Senseman

For reasons well known to mining engineers, wet grinding is quite universal in plants having to do with the extraction of metallic values from crude ores. In the processing of the nonmetallic and industrial minerals, dry grinding is the more common method. The crude materials usually contain less moisture than is required for wet grinding and the products usually are marketed in dry form; most of them as powders. To grind wet, therefore, would entail the addition of water and an expense for drying the product, which is not justified. Furthermore, the material would be a dried cake that would still have to be pulverized or disintegrated before use. For producing fine products, air separators have largely replaced the earlier practice of sizing with screens and bolting reels. Mills in which the air-separating feature is an integral part of the design are now commonplace. Mill designs are many and air systems have developed along various lines, but for the purpose of this discussion, only the fundamental idea need be emphasized— the idea of using air for sizing and removing pulverized material from a grinding mill. About 20 years ago, when the use of mills equipped with air separation had become common practice, heated air or gas was introduced to such a system for the removal of moisture. The purpose of this discussion is to outline the developments and trends that have followed this experiment. It is an important development, for mills equipped with air separation are now universally used for pulverizing not only nonmetallic and industrial minerals, but a great variety of other materials. All such mills are essentially the same. Dried material is pulverized, removed by an air stream, trapped in a cyclone collector, and relatively clean air from the cyclone is returned through a fan to the mill. There is no theoretical need for a vent from the system. The practical need is to vent the air that leaks into the system, and, since the cyclone is not 100 per cent efficient as a dust collector, this vented air carries some dust with it. The initial attempt at drying was made on a system like that described, by the addition of a furnace. The minus pressure within the mill draws hot gas from the furnace. Infiltration air, along with the drying gases and evaporated moisture, is vented as before. The first application was made to a mill used for pulverizing coal. The coal contained very little moisture, so very little drying effect was needed for the success of this experiment. Actually, some calculated efficiencies of over 100 per cent were obtained before due allowance was made for the conversion of mill power into useful heat. When moisture is low, the heat obtained from the conversion of mill power is an appreciable part of that required. That drying can be effected in the short time interval available in a grinding mill of this type is better understood by visual-

Jan 1, 1947

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By F. R. Brotzen, A. R. Troiano, E. L. Harmon

Precipitation processes leading to drastic property changes are a frequent occurrence in titanium alloys containing large amounts of the retained high temperature P phase. In order to establish the kinetics and nature of these precipitation processes, a series of Ti-V alloys was studied. Time-temperature-transformation diqgrams were obtained for 12.5 and 15 pct V-Ti alloys. These diagrams consisted of two intersecting C-shaped curves: one in the high temperature region for the euilibrium transformation P +u+P, and another at lower temperatures depicting the formation of the meta-stable transition phase, o. Presence of the transition phase retarded the precipitation of the equilibrium a phase. Deformation of retained P resulted in the formation of the o phase. Reversion and retrogression phenomena of the transition phase were observed. A negative temperature coefficient of resistance was found in quenched alloys containing from 15 to 20 pct V. CERTAIN titanium-base alloys can be heat treated to produce appreciable changes in properties. For example, remarkably high hardness values may be obtained by aging or isothermal quenching treatments. Most of the information available to date on the hardening of titanium-base alloys has been systematized recently in an article by L. D. Jaffe.' It was pointed out by that author that the hardening was the result of the decomposition of the retained j3 phase to the equilibrium constituents, a and p, and that this decomposition had many of the characteristics of an age-hardening reaction. Recent work by Frost et al.' 3 has contributed much to the fundamental understanding of the hardening mechanism in titanium-base systems. These authors established the presence of a transition phase in the transformation from j3 to a + j3, which they designated o. The transition phase, in their opinion, was at least partially responsible for the hardening and embrittling effects which accompanied low temperature aging. The present investigation of the mechanism and kinetics of the hardening reaction was carried out for the Ti-V system. Ti-V alloys were ideally suited for a study of the decomposition of j3, since age hardening was known to occur readily in this system." Moreover, no intermetallic compounds occur in this system, Fig. 1, thus simplifying the interpretation of the results. Material and Procedure Alloys containing 12.5 and 15 pct V were prepared by Battelle Memorial Institute from iodide titanium furnished by Watertown Arsenal and vanadium of 99.8 pct purity. Ingots of 8 Ib each were prepared by arc melting in an inert atmosphere with a tungsten electrode and water-cooled copper crucible. Each of the ingots was melted once, forged at 1600°, and rolled at 1400°F. Following this, the ingots were remelted, forged, and then rolled to % in. sq bars, which were subsequently grit blasted, pickled, and wire brushed. Another set of alloys containing nominally 17.5 and 20 pct V was produced by the Research Div., New York University. These alloys were arc melted in an inert atmosphere in lots of 20 g each. Heat-Treating Procedure: Whenever feasible, specimens were heat treated in high vacuum resistance furnaces at pressures below 5x10." mm of Hg. Aging and isothermal quenching treatments were generally carried out in salt baths. Specimens were not attacked by the salt, provided the tempera-

Jan 1, 1956

By G. S. Hume

During the war years the drilling activity in Canada has been steadily increasing and still further increase is expected in 1945. The production of oil, which in the past has come largely from the Turner Valley field in Alberta, shows a decline since 1942, the peak year. New discoveries made in 1944, however, give promise of replacing the decrease from Turner Valley where the crude-oil production in 1944 was nearly 1,800,000 bbl. less than in 1942, but with an increase of 145,000 bbl. in natural gasoline, a product of great value to the war effort. A very considerable part of the decline in Alberta has been offset by new production of more than a million barrels in 1944 from the Norman Wells field, in the Mackenzie River area of the Northwest Territories. It should not be forgotten, however, that this is largely due to the Canol development, a war project, the future of which is dependent on many factors not connected with an ordinary commercial operation. The year 1944 has been the best in new discoveries in Alberta for all time. The discovery of a new deep field at Jumping-pound, 20 miles west of Calgary, with the hopc of a type of product similar to that of Turner Valley is the culmination of many years of effort to interpret the subsurface structures in relation to the complicated surface foothills faulting and folding. In this case the subsurface structure on the Paleozoic limestone was inferred from geological investigations but precisely defined by seismograph. In addition to Jumpingpound the discovery of oil of 34.5 gravity at a depth of less than 5000 ft, in the Devonian of the Plains at Princess, 125 miles east of Calgary, is of great significance since this is the first substantial production from the Devonian in Alberta, although previously some oil had been obtained at two places from the Devonian in the foothills. The effect of this discovery is already apparent in the number of wells now drilling to the Devonian in the southern Plains. In southern Alberta a new producing area has been found in a Lower Cretaceous sand at Barnwell, a few miles west of Taber. Also, at Conrad, 20 miles southeast of Taber, an important new discovery has been made at a depth of about 3000 ft. in a sand in Jurassic shales, in a strali-graphic trap on the northeast flank of the Sweetgrass arch. In northeast Central Alberta an important extension has been found in the Lloydminster area, where only a few wells have so far been drilled. A new well 3 1/2 miles south of the previous producers found a coarser sand at the productive horizon and as a result will have an increased daily yield. At Blackfoot, 9 miles west of Lloydrninster, a new producing area in the Lower Cretaceous may have been discovered at a depth of 2004 ft. At the end of 1944 the well was being tested. Forty-four unsuccessful wildcat wells were drilled in Alberta in 1944. The decline of Turner Valley, the major producing field, was anticipated at the beginning of the war and in an effort to offset this and encourage new development the Dominion Government put into force tax concessions and other measures that,

Jan 1, 1945

By W. M. Johns

The geological mapping of Lincoln and Flathead Counties was a five-year project undertaken by the Montana Bureau of Mines and Geology. This paper, written by the Project Geologist of the survey, is primarily concerned with the stratigraphy of the Belt rocks encountered in mapping. Lincoln and Flathead Counties of northwestern Montana are underlain by sedimentary rocks of the Belt Series of Precambrian age. In only a very small part of the area, near Libby and Troy, have economic mineral deposits been worked with any success. Most of the area has been inadequately mapped as to geology. The region is crossed by the Great Northern Railway and served by the Pacific Power and Light Co.; officials of these two companies believed that with better geologic maps, prospecting might be stimulated and lead to the discovery of mineral resources that would contribute to new economic development within the area. A cooperative mapping agreement was proposed jointly by the two companies to the Montana Bureau of Mines and Geology in May 1958, and thus was born the Kootenai-Flathead five-year project. The dual objectives of this project are: 1) the possible location of mineral deposits of economic value, and 2) the ''stimulation of prospecting exploration" by others. This was to be achieved by geologic mapping of some 6800 sq miles and by establishing a field office in Kalispell where prospectors could come to have their rocks and minerals identified and receive geological advice on their problems. This writer has finished four field seasons as Project Geologist and thus became familiar with the Belt section in the Libby, Yaak River, Ural, Thompson Lakes, Pleasant Valley, and Stryker quadrangles (see Fig. 1). Progress on the project is given in annual reports issued by the Bureau.* This *Montana Bureau of Mines and Geology, Bulletins 12 (1959), 17 (1960), and 23 (1961). paper is concerned essentially with the stratigraphy of the Belt rocks so far encountered in mapping. PREVIOUS WORK IN THE AREA Willis28 made the first study of the stratigraphy and structure in the Lewis and Livingston Ranges of Glacier Park just east of the project area. In 1904, Daly made a study of the Belt rocks of the 49th parallel, using the names from bottom up, Creston, Kitchener, Moyie, and Gateway, for rocks ranging in age from that of Prichard to that of basal Missoula group. Walcott26 studied the Belt rocks exposed in the Mission Range (see Fig. 1) and other areas to the south of the area under discussion. Calkins and McDonald made a reconnaissance of northern Idaho and northwestern Montana in 1905. Calkins was the first to use Walcott's term 'Ravalli' as a group name for the strata equivalent to the Burke, Revett, and St. Regis formations (see Table I). Clapp worked on the Belt of western Montana (including Lincoln and Flathead Counties) throughout his lifetime. The Fentons9 studied the Belt of Glacier Park and

Jan 1, 1962

By H. C. Vacher, C. J. Newton

EXTENSIVE investigations in the field of residual strain measurement by X-ray diffraction have been made by Bollenrath, Hauk, and Osswald,1 by Smith and Wood,2'3 by Greenough; by Rosenthal and Norton." and many others. Since X-ray strain measuremeits apply only to those crystals of the test body which are of the proper condition and orientation to diffract and since the residual strains revealed may be accompanied by either body or tex-tural stresses, there has been considerable disagreement among investigators with respect to the validity of conclusions in this field. Although the experi-mentors have employed a variety of loading schemes, surface preparations, and X-ray wave lengths, the observations almost invariably have been made only on the outer surfaces of the specimens. The present note is not to be construed as an exposition of a new method of stress analysis by X-ray strain measurements on sections but as a presentation of some results which point to interesting possibilities for further experiments with sections. The two test rods used in this study were of ingot iron annealed at 910°C. The initial length of the gage section was 2 in. and the diameter was 0.415 in. Cross-sections were cut from the ends of the annealed rods to provide strain-free material. The tensile rod was axially loaded the desired amount in a commercial testing machine. A 1 in. portion of the gage length was cut from the other rod and was subjected to compression in the same machine. Details of this plastic straining of each rod are given in the upper half of Table I. A half-cylinder piece about 1/4 in. long was obtained by making a short longitudinal plane cut containing the axis of the rod near the center of the gage length. From adjacent material a disk about 1/8 in. thick was cut to provide the cross-section specimen. Later another section was cut from this same region with an angle of 30" between the normal to its surface and the axis of the test rod. A cross-section and a longitudinal section were cut from the compression rod in a similar manner. All of these as well as the strain-free cross-sections were mounted in Bakelite and used as specimens for the following X-ray strain measurements. During the course of the study, it became apparent that the condition of the surface of a specimen was a highly critical factor. One of the annealed strain-free specimens as a control was subjected to about 24 hr of polishing with fine alumina, interrupted about every 2 hr for etching with 1 pct nital. Its lattice parameter was determined at intervals from measurements on back-reflection X-ray diffraction patterns, which were calibrated with diffraction from tungsten powder. The parameter gradually approached the value found in the literature for strain-free iron and remained there, within the limits of the experimental error. This determined a long polishing and etching procedure which was adopted for all the specimens and which gave X-ray results from the surfaces believed to be representative of each specimen as a whole. A large number of back-reflection patterns were made with cobalt and chromium radiation, all at normal incidence. Except for some preliminary stationary exposures made to monitor the removal of cold work from the surfaces, each exposure was made with the specimen slowly translating and the film slowly rotating. In appropriate cases a thin layer of a standard metal powder, tungsten with cobalt radiation and silver with chromium, was dusted over a film of vaseline on the surface of the specimen to serve to calibrate the X-ray patterns. After the preliminary work, four films were made,

Jan 1, 1956

By Ralph E. Hartline, Wilfred Tapper

The Strataflow process for locating water entry in producing, wells is now available. This method as now practiced utilizes the fact that fluids of different salinities have different electrical resistivities. By introducing into the well a fluid of a markedly different salinity than that of the fluid being produced, a pronounced resistivity change will occur at the point of entry. By running a Strataflow survey the points of major and minor water entry may be interpreted from changes in the resistivity of fluid in the hole. Strataflow results are obtained with the well operating under almost normal producing conditions, and are a logical primary step in any workover program, having as its purpose shutting off of the water. INTRODUCTION Water production is a serious problem in many producing oil wells. It certainly increases lifting costs and in some cases presents a disposal problem. It often aggravates corrosion problems and can even endanger oil production. With accurate information to guide an effective workover program, many marginal wells could be restored to Profitable Production. The shortcomings of previous meth- ods of water entry location were recognized. The Strataflow process is the result of several years of development and field testing directed toward overcoming these limitations. It represents the continued development of a process reported by Silverman and Brown. The earlier work established the basic soundness of fresh-to-salt water resistivity contrast in delineating zones of water entry, but its application was limited by the difficulty of maintaining static balance of the well during preparation for the test. A more serious deterrent to its use, however. was its unadaptability to existing well logging service equipment and field operating methods. STRATAFLOW PRINCIPLE The general principle of the new method involves, first, conditioning the well by displacing the fluid in the bore of the well adjacent to the zone to be tested by a conditioning fluid which is miscible with the formation fluid. This displacement is carried out without interruption of the well production. The conditioning fluid must have some measurable physical, chemical, nuclear, or electrical property which is distinctive from that of the formation fluid. As the well continues to produce. formation liquid entering the well bore dilutes the conditioning fluid so that zones of entry may be determined by making a log of the property undergoing change. This general principle may be applied to indicate zones of either water or oil entry by suitable selection of conditioning fluid and proper logging equipment. The Strataflow process, as it is currently practiced for water entry location, uses fresh water as the conditioning fluid and depends for its operation upon the marked difference of electrical resistivity between this fresh water and the salty water produced by the formations. If possible. any necessary modifications of the well equipment are made a week or so before the test. The well is then returned to normal production. On the day the test is to be carried out. the conditioning water is landed at the bottom of the well and the test is made without interrupting production except for a brief period required for the conditioning water to consolidate into a continuous column extending to a point well above the test section. With this general description of the process in mind, a more detailed step-by-step description of the process will be clearer. PRELIMINARY PREPARATION OF WELL The Strataflow survey, as it is currently practiced for water entry location, is applicable only to pumping wells. Since the required electrical measurements are made by a special

Jan 1, 1952

By Renato G. Bautista, Theodore D. Tiemann

A kinetic study of the hydrogen reduction of taconite from the Wisconsin Gogebic range was made over the temperature range from 500° to 1000°C on eleven size fractions from 4 to 150 mesh. Two stages of reduction were observed, a rapid initial reaction followed by a slower reaction presumably taking place at an internal receding FexO-Fe interface. Calculated mean activation energies for the two reactions were 7800 and 14,600 cal per mole respectively. In recent years there has been an increased interest in the direct reduction of iron oxide ores to metallic iron by means of gaseous reducing agents such as hydrogen and carbon monoxide.1,2 These investigations have been motivated by the desire to develop a process that will by-pass the blast furnace in the production of steel. The majority of these processes have been developed to produce metallic iron by direct reduction from high-grade iron oxide ores.3"5 Very little work has been done on the low-grade siliceous iron oxide ores.6"8 The work reported here is directed principally towards the fundamental aspect of the reduction reactions of siliceous iron oxide ores, since the practical aspects of the gaseous reductant process were discussed previously. The ore used in the investigation was obtained originally from the United States Bureau of Mines10 trench sample of the Yale member of the Wisconsin Gogebic range iron formation. The Yale taconite has an average analysis of 28.2 pct Fe and approximately 50 pct SiO2. Chemically, these nonmagnetic taconites contain on the average about 53 pct silica and 30 pct Fe. An average analysis calculated fron the USBM10 figures for a composite of the five members (Norrie, Plymouth, Pence, Pabst, and ale) of the iron formation is given in Table I. Mineralogically, based on previous X-ray diffraction and other studies, the principal minerals are hematite (Fe2O3), geothite (Fe2O3.H2O), and quartz (SiO2). Minor amounts of iron containing silicates, siderite (FeCO3) and magnetite (FeO. Fe2O3) are present.10,11 The iron minerals and the quartz are finely disseminated requiring extremely fine grinding for liberation. For the experimental work, the ore sample was screened into a number of size fractions, the analyses and densities of which are given in Table II. EXPERIMENTAL PROCEDURE The reduction experiments were carried out in a 24 in. by 2 in. ID nichrome-wound vertical-tube furnace mounted on a stand. A 1 1/2 in. OD zirconium-oxide combustion tube was used inside the furnace to contain the atmosphere. To the top of this combustion tube was joined a pyrex ground-glass joint to which was attached a glass bulb with a small (1.0 mm) opening at the center, and with two outlets controlled with a stopcock on each side. A pyrex-glass joint with connections to three stopcock joints for introducing hydrogen, nitrogen, and mixtures of hydrogen and nitrogen gas was joined to the tapered bottom of the combustion tube. The sized ore fractions were contained in a 1 in. diameter by 1 1/2 in. 150-mesh nickel screen basket. The basket was suspended in the furnace from a balance by means of a supporting nickel wire which hung freely inside the combustion tube. The furnace temperature was controlled by a Leeds and Northrup Speedomax Type G controller, connected to a chromel-alumel thermocouple placed

Jan 1, 1962

By S. F. Reiter, W. R. Hibbard

A survey of the effect of heat treatment on the room temperature hardness of Fe-Mo alloys has been made. Constant strain rate tensile tests were performed between room temperature and 1800°F. These data were analyzed to determine the effect of temperature and composition on the strain hardening coefficient and strain rate sensitivity. Constant load creep-rupture tests were made on these alloys and the results related to composition and structure. A relation between the high temperature strength of the precipitation hardened alloys and the volume of precipitate has been observed. IN view of the extensive use of ferritic materials at elevated temperatures, it is surprising to note the limited amount of information relating the variables of plastic deformation, i.e., composition, structure, temperature, stress, strain, and strain rate. Hollomon and Lubahn' showed how the several variables of plastic flow might be treated analytically. No data were available on carbon-free iron and its alloys in a form suitable for this analysis. Several German investigations2-" constitute most of the experimental work relating high temperature properties to the constitution of these types of materials. In order to obtain new data, the iron-rich alloys of the Fe-Mo system were selected for detailed investigation for the following reasons: 1—Some of the important effects of molybdenum on the mechanical properties of iron have already been studied.' , 821 2—By suitable heat treatment of selected alloys, it is possible to study strengthening effects of four types: AT -a transformation, B—substitutional, C—precipitation, and D—dispersion of hard inter-metallic compound. Materials and Treatment Four-pound ingots were vacuum cast, employing the same melting schedule previously used.? The raw materials were electrolytic iron and lamp-grade molybdenum. The ingots were forged to l/z in. sq. rod and one portion swaged to 0.350 in. diam rod for the production of 1 15/16 in. long button-head specimens. The button-head specimen blanks were solution treated for 16 hr at 2100°F in hydrogen of —70°C dewpoint and then water quenched. They were subsequently plunge ground to the standard 0.160 in. diam test bar. Micrographs of the solution treated alloys are given in Figs. la through Id. The higher molybdenum alloys contained large equiaxed ferrite crystals similar to those in Fig. Id. A portion of the % in. rod was hot rolled to 0.100 in., sandblasted, and cold rolled to 0.020 in. Strip tensile specimens having a 0.020x0.200 in. cross-section and a 2.25 in. gage length were machined from the sheet. The alloys containing molybdenum were subsequently annealed 1 hr at 1560°F. The iron strip was annealed 4 hr at 1300°F in wet hydrogen. The resultant structures are shown in Fig. 2a through h. The ASTM grain sizes were 1 to 3 as solution heat treated or 3 to 4 as annealed. The chemical analyses of the alloys are given in Table I. Carbon contents were obtained after the heat treatments in hydrogen. Alloy 15.9 pct Mo was tested as a cast alloy.'

Jan 1, 1956

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949