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By E. Hornbogen

The deformation mechanisms of a iron-phosphorus alloys were compared at 20oand —196°C. Alloying with phosphorus increases the resistance to slip, but has little effect on the resistance to twinning. The stress for onset of twinning is nearly independent of temperature, but there is an increasing tendency for cleavage along (112) twin boundaries with decreasing temperature and increasing phosphorus content. FIVE iron-phosphorus alloys and one high-purity iron (0.004 pct C, 0.004 pct N, 0.05 pct O) were vacuum melted and cast, then homogenized for 6 hr at 1100oC and water-quenched. Single crystals were cleaved from the coarse grains produced in this manner. The hardness was measured* on polished (100) surfaces of the crystals at 20" and -196°C. Laue back-reflection patterns indicated a deviation of not more than 3 deg from coincidence of the {100} plane with the surface. The deformation mechanisms were studied by relief effects on the polished surfaces. Yield points in compression (0.5 pct offset) were measured with polycrystalline material. At 20°C the addition of phosphorus to a iron leads to a change from slip to twinning as the main deformation mechanism, Figs. 1(a), (b). Between 2 and 4 at. pct P slip and twinning occur simultaneously. In alloys with more than 4 at. pct P twinning is the main deformation mechanism and slip was observed only in the neighborhood of twin intersections. All cracks at 20oC were on (100) planes, some initiated by twins.' From measurements made at-196oC, hardness and yield points of all the alloys were nearly constant and the same as the hardness of high phosphorus alloys that deformed by twinning at 20°C, Figs. 2 and 3. In the high-purity iron, plastic deformation at -196°C occurred by both slip and twinning, but deformation in the iron-phosphorus alloys appeared to be entirely by twinning. In the high phosphorus alloys a large number of cracks formed along the (112) twin boundaries and at intersections of twins, in addition to the (100) cleavage, Fig. 1(c). DISCUSSION In , iron, plastic deformation can occur either by slip or by twinning, depending upon composition,

Jan 1, 1961

By Lewis Carroll

AS he contemplates the numerous good things the hard-working committees have evolved for the 140th Meeting of the Institute, the Editor knows just how the walrus felt when he uttered his memorable, if somewhat lugubrious lines. For there are the Annual Reception and Dinner at the Commodore, 'the Gold Supply Symposium, the luncheons, general and special, and the Annual Institute of Metals Lecture, a Round Table on Iron Ore and a wonderful Informal Dance at the Grand Central Art, Gallery, substantial general sessions, a Smoker-and many other things. -Old, friends and new, reminiscences and confidential chats, horizons pushed back by new information and adjusted perspectives, courage revived and ambitions stimulated-one with a flair for the modernistic might make something-or nothing-of the kaleidoscopic preview 'of the coming Annual Meeting.

Jan 1, 1931

Jan 1, 1886

By P. Somasundaran, D. W. Fuerstenau

This article presents the results of an analysis of grinding of 1:1 mixtures of 4x8-mesh quartz and limestone in laboratory ball and rod mills. From these experiments, the amount of energy consumed in grinding each component of the mixture was determined. In the ball mill, limestone consumes slightly more energy than quartz in the initial stages of grinding, but as the grinding proceeds quartz begins to consume a slightly greater fraction of the energy. The postulate that the fraction of energy consumed by any material in a ball mill is proportional to its volume fraction has been shown to be approximately true. On the other hand, in a rod mill energy consumption by quartz and limestone is equal only in the initial stages of grinding, with energy consumption by quartz greatly exceeding that by limestone as rod milling proceeds. Preferential energy consumption in tumbling mills has been discussed in a number of papers. For example, from an analysis of the kinetics of comminu- tion in ball mills, Arbiter and Bhrany' obtained rate equations based on the postulate that only coarse particles are ground, indicating that fine particles are protected from the action of the balls by coarser particles. In rod mills this protective action is much more pronounced than in ball mills. Recent studies on the rod milling of limestone-quartz mixtures have shown that this protective action causes the mineral with the lowest grindability (quartz in this instance) to consume the greater fraction of energy. 2 However, in the ball milling of mixtures it has been postulated that the consumption of energy by one of the constituents is determined by its volume fraction within the mill. 3 Possibly this hypothesis may be a simplification of the ball milling of mixtures since the protective action suggested by Arbiter and Bhrany may result in some preferential energy consumption by one of the constituents of a mixture. The objective of this study has been to determine preferential energy consumption in laboratory ball and rod mills by analyzing size distributions of each material in the products obtained from grinding 1:l mixtures of quartz and limestone. MATERIALS AND METHOD The procedure for carrying out the tests on wet grinding quartz-limestone mixtures has already been described.'r3 In the present investigation, 1:l mix-

Jan 1, 1963

By Eugene McAuliffe

In the year 1581, the counselors of King Philip of Spain suggested to that monarch that a canal across the Isthmus of Darien would open the west coast of the South American continent to Spanish miners and explorers, enlarging and expanding the flow of precious metals then just beginning to trickle across the path cut by Spanish Conquistadors, from old Panama to Puerto Bello on the east coast. The King sent out a party of surveyors and explorers under the command of a young engineer, Savadaerro, who returned after two years, reporting upon a location for a canal which was virtually adopted by the French engineers employed by De Lesseps, who in 1877 commenced the work of constructing the Panama Canal-296 years after Sava- daerro's first survey was begun. The suggestion for an Isthmian canal, made to the king at a time when Spain was a proud, virile nation and when that country was contending with England in the fields of discovery and conquest, represents a measure of vision that has never failed to intrigue the imagination. That the young Spanish engineer recommended an undertaking so gigantic in conception that it took three and one-third centuries for its completion from the time it was first visioned matters little. In the day of Philip of Spain,

Jan 1, 1932

By J. Spotts McDowell

Ackowledgments........................... 5 Introduction............................. 5 The Silica Minerals. Stability Relations......................... 6 Optical Properties........................ 9 Density.............................. 10 Melting Points....;..................... 10 Thermal Expansion..................,..... 10 Solubilities............................ 12 Identification of Cristobalite and Tridymite.............. 12. The Silica Refractories. Raw Materia1........................... 13 American Deposits....................... 13 Properties Determining Usability................ 15 Expansion on Heating..................... 16 Texture........................... 17 Silica Brick............................ 17 Manufacture........................... 18 Properties of Silica Brick .................... 19 Analysis ......................... 19 Density......................... 19 Porosity......................... 20 Strength....................... 21 Melting Point....................... 22 Specific Heat....................... 22 Thermal Conductivity................... 23 Expansion........................ 24 Effect of Rapid Temperature Change.........:... 26 Constitution......................... 26

Jan 1, 1918

By AIME AIME

It is with the deepest personal sorrow, and with the regrets of the Steel Company of Canada, that I report to you the death of one of our most valued associates, the late Frank B. McKune, superintendent of the Open-Hearth Department of our company. Many of you will remember Mr. McKune for his long attendance at these meetings, for the intelligent interest he took ill them, as well as for his innovations in steel-production practices.

Jan 1, 1940

By Murray F. Hawkins

One problem of reservoir engineering is the early estimation of the size of newly discovered reservoirs. Often these reservoirs are the expansion type in which sizeable pressure drops occur incident to the production of small fractions of the oil reserve, above the bubble point, and a material balance equation may be solved to find the reserve. The early form of this equation' considered only the compressibility of the oil. Later Hall2 showed that the compressible nature of the formation rock is a significant factor in production above the bubble point, and he presented a new equation which includes a formation (rock) compressibility term. This note presents a further extension of the material balance equation as applied to volumetric, unsat-urated reservoirs above the bubble point by including a term for the presence and compressible nature of the interstitial water. DERIVATION OF EQUATION During a decline in average reservoir pressure, ?p ?p, — p1 the initial reservoir volume V,, will decrease to some value V, due to the reduction in pore volume as a result of a decline in the hydrostatic pressure within the formation, and v, = V,, [l — cr ?p]......(1) The formation compressibility c, is expressed in terms of change in pore volume per unit pore volume per psi. Simultaneously the connate water within the formation expands from an original volume V,, = S,V,, to a new volume V,, V, = s,v,, [I + c,npl.....(2) The difference [Vp — V,] is the hydrocarbon pore volume at pressure p and may be equated to the volume of the remaining oil, or [N — N,] B, = V,,, [I - C~A;] - S,.Vpi [l + cwnjl.........(3) But the initial oil in place in terms of the initial reservoir volume, connate water, and formation volume factor is Ilividing Equation 3 by Equation 4 eliminates V,, to give,

Jan 1, 1956

By Clinton M. Young

(Pittsburg Meeting, March, 1910.) I. INTRODUCTION. THE experiments herein. described were carried on in 1908-9 . by the State Geological Survey of Kansas. Some months before taking up work on black powder the Survey had resumed work on an interrupted investigation of explosions in coal-mines, a subject which is engaging the attention. of numerous investigators. An unusual number of serious disasters has directed to. the subject a study which discloses the disquieting fact that, in the. United States, the ratio of lives lost per ton of coal mined has been on the increase. Methods of coal-mining have changed to some extent with the great increase of output, attained in, comparatively recent years. These changes involve the working of very extensive mines, with increased difficulty of ventilation, increased accumulation of coal-dust, and. a very great increase in the amount of explosive used.. . This last point assumes truly startling proportions when it is carefully observed. In the fields of the Middle. West it is not now uncommon for a miner to use six ,kegs (150 lb.) of black powder in a "pay" of two weeks, while within the memory. of men still active, one keg (25 .lb.) would last two men for a " pay." So. great has . the use of explosives become in some fields that the skilled coal-miner is hard to find, and the coal is not mined, but blasted. A preliminary study of the subject. of explosions in coal-mines has. led to the belief . that the use of, large -quantities of explosives, in some cases by slightly-trained men, had not been * Associate Professor- of Mining Engineering, University of Kansas, Lawrence, Ran.

Aug 1, 1910

By W. M. Peirce

COAL'S importance in the metallurgy of zinc may be gauged by the fact that approximately a million and a half tons is so employed annually in the United States. This brief paper will show in what way the various steps in the treatment of zinc ores utilize this fuel, either in its primary form or as coke or gas, and to what extent. The first step in zinc metallurgy that requires the use of fuel is roasting the sulphide ore, which is the type of ore in which zinc commonly occurs. Since the roasting is nearly or completely autogenous, however, this use of fuel is too minor to warrant further attention. Concentration of zinc ores is usually carried out by conventional milling methods, but a pyrometallurgical method, the Waelz process, is used to concentrate certain low-grade ores, and to recover the zinc content of certain residues in concentrate form. The Waelz process uses a continuous rotary kiln in which a mixture of coal and zinc-bearing material is heated to a

Jan 1, 1948

By W. L. Saunders

(Wilkes-Barre Meeting, June, 1911.) I. INTRODUCTION. IT is now generally admitted by experts that at least so far as rapid progress is concerned the Alpine system of tunnel-driving is superior to any other. This is perhaps natural in view of the record of experience in driving tunnels through the Alps. These great mountain-chains cannot be treated in the ordinary way by shaft-sinking and driving headings, thus multiplying the points of attack. The work must be done from the ends only, hence speed in driving is of the utmost importance; and, as necessity is the mother of invention, the concentration of effort to make progress has resulted in an organization and in mechanical appliances that have produced results so much in excess of the usual practice, even in America, that a discussion of the subject in detail should be of much value to the engineer and contractor. The first Alpine tunnel was the Mont Cenis, length 7.5 miles, driven with a progress that averaged about 7.75 ft. per day. Next came the Saint Gothard, 9.5 miles long, 18 ft. per day; Arlberg, 6.5 miles long, 27.25 ft. per day; Simplon, 12.25 miles long, 36 ft. per day. The figures represent progress when driving from two headings, so that by dividing them in two we get the daily single-heading progress. The latest of the Alpine tunnels is the Loetschberg, now being driven. In this work the world's record has been beaten by a single day's record in one heading of 36 ft. and by an average daily record in. one heading of 29.5 feet. The Alpine range forms a natural barrier between a large section of northern and southern Europe. This range extends from the southeast of France to the frontier of Hungary, between Italy and the plains of southern Germany. The contour

Jul 1, 1911

By A. W. Asman

The problem of balanced design in a belt conveyor has been under constant study. Increased use of this method of transport in recent years has stimulated investigations. Conveyor belt, power transmission and other machinery should be adequate to perform the required service. All components of the belt conveyor should work as an efficient unit moving its load continuously between terminals. As part of a long term research project on belt conveyors, Hewitt-Robins established in 1954 a 2-year grant at Pennsylvania State University. Under terms of the grant, certain fundamental phenomena were to be studied. This work evolved a new concept in belt conveyor power determination based on the principle of belt tension. The Penn State contract furnished the foundation for later more detailed studies. From these most recent investigations, more specific factors were defined. In the final analysis, all of the data collected has been worthwhile in belt conveyor design. Units now operate over long distances at speeds of over 800 fpm. Long high lifts are commonplace. Where vertical or inclined shafts were the rule, belt conveyors receive first consideration. Although belt conveyors have moved forward rapidly, the future will see a tremendous gain in their use. The ideal test belt conveyor would be several thousand feet in length and have a maximum tension of at least 70,000 lb., Also, this conveyor should be horizontai and have a variable feed rate of more than one material. Data from such a field belt conveyor combined with laboratory information would permit accurate analysis. Since this type of conveyor was not available, many field locations were visited: An alternate would have been to erect a closed circuit system in the laboratory. Either method had limitations and the first was selected as having the best possibilities. Manufacturers of conveyor belting and machinery basically have been using the same horsepower formula. As more information became available from field installations, factors in the basic formula were modified. Practically all conveyors are designed today by adding together the horsepowers required to move the empty belt, move the load horizontally, and elevate the load. In selecting size of drive motor, the first two elements are relatively unimportant if the last is large. However, it is the combination of

Jan 1, 1961

By John S. Alexander

By P. Nicholls

Though the burning of fuels extends far back into antiquity, and though fuel beds are the most common and widely distributed example of chemical actions and engineering practice, there has been little attempt to group fuel beds by types or to define the principles associated with them. This paper does not profess to cover completely the subject of fuel beds. It suggests some of the over-all principles of the two more common types. No new investigational data are included, but the deductions are largely based on a recent publication of the U.S. Bureau of Mines'. Definition of Types There are three primary types of fuel beds: (I) Underfeed, in which the fuel and the air move in the same direction; (2) overfeed, in which the fuel and the air move in opposite directions; (3) crossfeed, in which the fuel and the air move at right angles to each other. The principle that fixes the type is the relation between directions of the flow of fuel and of air. Fig. 1 shows the three types diagrammatically. All other types are compounded of these three in a simple or more or less complex manner. It does not follow that these three type designations are limited to the methods used in representing them in Fig. 1; they may be turned in any direction, and as long as the relative directions of the fuel and air are the same the type is not changed. For example, A as shown .resembles a pot-type stoker, but the air and fuel can move downward as in the so-called smokeless heating boiler furnace. Also, C can be placed horizontal, as in chain-grate stokers. For this reason, the terms used to designate the three types are not all that could be desired; more logical ones could be coined, but those used probably are satisfactory until the discussion of fuel-bed types becomes more common.

Jan 1, 1936

By P. Nicholls

Though the burning of fuels extends far back into antiquity, and though fuel beds are the most common and widely distributed example of chemical actions and engineering practice, there has been little attempt to group fuel beds by types or to define the principles associated with them. This paper does not profess to cover completely the subject of fuel beds. It suggests some of the over-all principles of the two more common types. No new investigational data are included, but the deductions are largely based on a recent publication of the U.S. Bureau of Mines'. Definition of Types There are three primary types of fuel beds: (I) Underfeed, in which the fuel and the air move in the same direction; (2) overfeed, in which the fuel and the air move in opposite directions; (3) crossfeed, in which the fuel and the air move at right angles to each other. The principle that fixes the type is the relation between directions of the flow of fuel and of air. Fig. 1 shows the three types diagrammatically. All other types are compounded of these three in a simple or more or less complex manner. It does not follow that these three type designations are limited to the methods used in representing them in Fig. 1; they may be turned in any direction, and as long as the relative directions of the fuel and air are the same the type is not changed. For example, A as shown .resembles a pot-type stoker, but the air and fuel can move downward as in the so-called smokeless heating boiler furnace. Also, C can be placed horizontal, as in chain-grate stokers. For this reason, the terms used to designate the three types are not all that could be desired; more logical ones could be coined, but those used probably are satisfactory until the discussion of fuel-bed types becomes more common.

Jan 1, 1936

By AIME AIME

QUALITY and size do not ordinarily go hand in hand, but there is good evidence that both these attributes reached a new peak at the Annual Meeting of the Institute in New York just concluded. Certainly, the total attendance of 2500 was far above any yet attained, as might be expected with the recent rapid growth of Institute member- ship. General comment indicates that the quality of the papers also was notable, though not measurable by so definite a yardstick as attendance. During the meeting 49 technical sessions were held, at which more than 250 formal papers were presented. In addition, there were some thirty special meetings of committees, Divisions, and other Institute groups. In reporting the Annual Meeting eleven years ago the statement was made that "unless the Engineering Societies should build for themselves a new building it is probable that no meeting can be larger," and "the fifth floor, where a buffet lunch is served each day, has reached its full capacity and it seems quite evident that any future development of Institute meetings must be along the lines of quality, not size." Unfortunately the angel to succeed Andrew Carnegie, who financed the building of the present home of the Institute 35 years ago, has not yet ' appeared. Even if some one would merely build another elevator or two in the present building it would help. Fortunately, the modern auditorium of the American Radiator & Standard

Jan 1, 1940

By R. M. Kuralt

CONCESSION from the Chilean government granting the company use of the Rio Salado water stipulates that a minimum of 35,000 metric tons of such salty water must be diverted from the Salado daily, and be disposed of in a manner not to contaminate the Rio Loa to the east of its confluence with the Rio San Salvador at Chacance, Fig. 1. Consequently, the selection of a suitable site for the sulphide plant tailing disposal had the additional problem of the disposal of excess brackish waters. Studies of the terrain in the area directly to the south of the plant indicated that construction of tailing ponds would be costly, and generally unsatisfactory due to excessive slope of the ground, lack of flanking hills, danger of raising the groundwater level thus causing springs along the Antofagasta-Bolivia railroad; and the possibility of creating a dust nuisance at the plant site or at Calama due to blowing sands. Further to the southwest the San Salvador river canyon offered some possibilities and surveys were made at sites A to D, inclusive, Fig. 1. Here again costly dams would have been necessary to impound the tremendous quantity of tailing produced by the new plant, and provision would have to be made to handle a considerable flow of water through the disposal area to the west of the Rio Opache. Additional surveys were made in the area to the southeast of the plant which brought to light the existence of a natural basin of about 14 1/2 square miles, flanked by low-lying hills, and requiring only the most rudimentary dams to close the outlets at the western end. It has been estimated that the Salar de Talabre, as this basin is called, has the ultimate storage capacity of 1 billion tons of tailing with dam heights of only 60 ft. Pipe Line Layout After the decision had been reached to use the Salar de Talabre for the main disposal area various methods were considered for transporting the tailing from the 300 ft diam thickeners to the disposal site, 17.7 miles away. The first plan was to construct a. concrete launder on a 11 pct grade but a survey of this grade line indicated it would not lead directly into the Salar but would terminate somewhat to the north, and from that point on the slope would be considerably less than 1 pct along a natural watercourse. A slope of 2 pct or even 2 ¼ pct in such a rough watercourse or ditch is the ideal, judging from the success of operations at Cananea. Since a simple ditch is the most economical vehicle for the transportation of tailing, it was decided to use one with a 2 ¼ pct grade for as much of the distance as was possible with the existing terrain and to construct a concrete headbox, or forebay, at the terminus of the ditch to supply a steel pipe line leading the rest of the way into the Salar. Referring to the maps of the Chuquicamata area outlining the tailing disposal system, Figs. 1 and 2, one can trace the flow of the tailing from the thickeners to the Salar as follows: The 8-in. spigot pipes from the thickeners (1) discharge into a concrete sump feeding a concrete launder with a 2 pct slope. The launder carries the tailing into a concrete junction box (2) located south of the sulphide plant. The purpose of the junction box is to provide emergency facilities for diverting the tailing flow from the main disposal area to the emergency area. It also provides a junction point for the launder from the sulphide plant's future east extension. The box is fitted with a pair of radial gates controlling flow into the main tailing ditch (6) or the emergency ditch (3) which terminates on the pampa. All ditches are of the same cross section, namely 4 ft wide at the bottom with 1 : 1 side slopes and with a minimum depth of 21/2 ft. Where the nature of the ground demands it, the ditches are lined with stone rubble. The overflow from the plant's 10 million gal reservoir (4) is led into the main tailing ditch by way of a spillway ditch (5). The main ditch terminates in a trashscreen fitted, concrete forebay (7) which serves as a headbox for a 24 in. O.D. x 3/8 in. wall, Dresser coupled, steel pipe (10) and a 12 in. x 8-gage spiral welded, wedge-lock coupled, steel pipe (8). The forebay is fitted with two compartments, one for each pipe, and flow into each is controlled by radial gates. Each compartment is fitted with a 6-in. drain pipe controlled by a rubber pinch valve. To protect the forebay from the abrasive effects of the tailing, the sides of the compartments will be lined with old

Jan 1, 1952

By H. Kazemi, G. W. Thomas, M. S. Seth

The double-porosity model of Warren and Root7 for examining pressure drawdown and buildup phenomena in naturally fractured reservoirs has been extended to intetpret interference test results. Both analytical and numerical solutions are presented. The practicality of some of the assumptions in the Warren-Root model was also investigated. The standard procedure for interpreting interference tests in naturally fractured reservoirs beretofore employed an equivalent homogeneous reservoir model. A comparison of our results with the equivalent homogeneous model indicates the latter is inadequate for early time responses. For late time responses, however, the simpler equivalent homogeneous model yields favorable results. Finally, the effects of well spacing and the magnitude of the interporosity flow parameter are briefly cited. INTRODUCTION Interference tests can be used to provide reservoir information not obtainable from conventional pressure drawdown and buildup tests. The technique involves measuring the response in one or more wells arising from a pressure perturbation introduced into another well. It has been. successfully applied to single-layer, homogeneous, unfractured, isotropic and anisotropic formations to arrive at values of well storage capacity and a measure of directional permeability.l The techniques of interference testing usually can be extended to heterogeneous systems, provided the permeability contrast between any existing rock layers is not excessive.9 In such cases, the practical interference effects in an observation well of an interconnecting heterogeneous reservoir can be predicted using an equivalent homogeneous model. The calculated properties are then average values. Russell and Prats2 have demonstrated the utility of this approach for a single-phase, two-layer system. For naturally fractured reservoirs, some different approaches usually are necessary. The major departure from homogeneous or nearly homogeneous reservoir treatment is to characterize the fractured system as an entity having "double-porosity"; namely, we suppose the existence of both primary and secondary porosity, where the former is contained within a systematic array of identical rectangular matrix blocks and the latter is contained within an orthogonal system of continuous, uniform fractures (see Fig. 1). It is sufficient to assume that the permeability of the rock matrix is so small that movement of reservoir fluids to the producing wells is entirely through the fracture network. This assumption has been validated by Barenblatt3 and .employed by others?-7 Warren and Root7 used the double-porosity model to develop an interpretation of pressure drawdown and pressure buildup tests in naturally fractured

Jan 1, 1970

By L. Adler

The proper transfer of roof loads from props and bolts to ribs and pillars can result in appreciable savings. The author shows how to plan such load reduction in underground mines. For openings in bedded rocks, analyzed by simple beam theory, it has been shown that roof loads can be shifted from one support to another.&apos; This transfer is effected by controlling the relative deflection of adjacent supports. If this action is used to reduce loads in the props or bolts and increase them in the ribs or pillars, it could be productive of economies averaging 30 pct. Such savings can be realized by: 1) using smaller artifical supports such as props and bolts, and 2) increasing loads in the rib to induce eventual failure for longwall caving. Since the rib is relatively load-insensitive, it provides a natural load sink. However, caution must be used in applying such permissive deflections, for while the supports are being handled properly, the stresses in the roof itself are very sensitive to such manipulations.1 An underground opening overlain by a relatively thin immediate roof, and a thick main roof, is usually laid out as shown in Fig. 1. The total open span (T) between pillars or ribs is calculated on the basis of the main roof, and the secondary spans (L) on the basis of the immediate roof, so that a complete accounting of the existing loads is made. For this purpose the immediate roof is treated as a uniformly loaded continous beam, which is an indeterminate structure as shown in Fig. 2(A). The term systematic supports places the following two restrictions on the continuous beam: 1) Spans between all supports are equal: uniformity of spans. 2) Loads on all supports (excepting ribs) are equal: uniformity of supports. The usual mode of analysis of such a structure by beam theory is to divide it up into a series of simply supported beams with end moments as shown in Fig. 2(B)2 The problem now is to transfer a maximum roof load to the rib from the span immediately adjacent to it by permitting its support to deflect, and yet not fail the roof. Once this has been done, the load can be equalized on all other supports by permitting further degrees of relative deflection. It is necessary, therefore, to determine an expression for the constant load on each support, and the required deflections, in terms of properties of the roof. From Fig. 1: T/L0 = No and T/L = N [1] Where: T = allowable span of main roof, ft. (Calculated from S = Mc/l) S is allowable modulus of rupture, psi. M is maximum moment, lb-ft (in this case wT2/12). c is distance from neutral axis to extreme fiber, ft. I is moment of inertia with respect to the neutral axis, ft4. L,, = allowable span of immediate roof, ft (calculated as was T). L = actual span of immediate roof, ft. N0 and N are pure numbers where No < N and N is the integer just higher than Nu. For example: If T =100 ft and L0 - 15 ft 100 N0 =100/15= 6.667 . . .N= 7 L = T/N = 100/7 = 14.28 ft Consequently N = No + n where n is a positive fraction i.e.: 0< n < 1 Since from Eq. 1, T = NL = N0L0 Lo /L = N/No = N/N-n

Jan 1, 1961

By CHARLES R. KETES

I. INTRODUCTORY. INDUSTRIALLY, the most important service that geological science can now render to mining in the Upper Mississippi leadand zinc-fields is to devise some practical scheme whereby the productive ore-belts may be located with greater certainty than they have been in the past. Up to the present time there has been little service of this kind, and in spite of all that has been worked out concerning the geologic features of the region, and notwithstanding all that has been written about these ore-deposits, this particular phase of the subject has been, for some reason or other, the very one that has received the least consideration. The neglect by geologists in this respect has been all but complete. The following notes are suggestive of some practical solutions to the problems presented. As here suggested, the geologic relationships of the ore-bodies were surmised some years ago, though somewhat vaguely perhaps. No opportunity for securing critical data appeared until recent investigations of a private character were undertaken, which bad in view the extensive prospecting of undeveloped areas. Fresh from rather wide experiences of a decade in the principal mining-regions of four continents, and after a lenstrum&apos;s residence among the chief mining-camps of the West and of Mexico, under conditions which measured geologic hypotheses in meters and rigidly tested their values in, terms of dollars, the recent return to the Joplin field and a new survey of its ore-conditions were fraught with somewhat unexpected results. Aspects of the ore-deposition were presented of which previously there was no hint. Ten years&apos; absence from the district had tended greatly to clarify former hazy impressions. It enabled many features, then only dimly outlined, to be considered more nearly in their true perspective and in their real relationships to their surroundings. It permitted a great mass of details collected a dozen years before in connection with the work of the Missouri Geological Survey to be viewed under new light and to

Feb 1, 1909