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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 Ivan E. Goodner, Charles H. Fulton

THE subject of the constitution of copper-iron mattes has received considerable attention in recent years by Keller,1 Bolles,2 Hofman,3 and Gibb and Philp.4 Still more recently Friedrich, Röntgen, Wiedmann, Heyn and Bauer, and Leroux have published, in some instances, elaborate researches on the various systems of the sulphides, and the sulphides and their respective metals, which enter into the constitution of mattes, and have added very greatly to the knowledge of the subject. The work of Friedrich has been especially fruitful. But to date no effort has been made to correlate the data obtained in the latter researches and apply then to the study of the product called " matte," which is made in such large quantities by copper and lead-smelters. In this paper we propose to determine, by metallographic and chemical means, the constitution of copper-iron and copper-lead mattes in the light of the recent data above mentioned. We do not discuss copper-nickel mattes or speisses (artificial arsenides). The paper is divided into three sections I. A review and discussion of the various binary systems of the metallic, sulphides, and the binary systems of various metals and their respective sulphides entering into the constitution of mattes; also a discussion of the physical and chemical properties of these sulphides. II. A description of the results obtained from the chemical and metallographic examinations of the samples of copper-iron and copper-lead-iron matte obtained from various plants.

Nov 1, 1908

By Marius R. Campbell

Does mine-sampling show the commercial value of a coal, and if so, how should it be done? This question is often asked, but seldom answered. During the past summer, while engaged in securing coal for the Government coal-testing plant at St. Louis, I had an excellent opportunity to obtain information on this subject, and the results seem to furnish an answer to the questions propounded above. Sampling for the Geological Survey Coal-Testing Plant. In organizing the work of the testing-plant, it was decided that coal in car-load lots only would be accepted for testing, also that this coal should be loaded under the immediate supervision of a representative of the plant, so as to be certain that the car-load sample would be representative. As an additional check on the work, two mine-samples were to be collected from each mine visited, and these samples, as well as the sam¬ple from the car when it was received at the testing-plant, were to be carefully analyzed at the chemical laboratory, which was established in connection with the plant and operated under the direction of Prof. N. W. Lord, of the Ohio State University, Columbus, Ohio. Mine-Sanmhling:-Mine-samples were collected with great care by me and my assistants, Messrs. J. Shober Burrows, John W. Groves and Frank W. De Wolf. The dominant idea in the regulations which were adopted for mine-sampling was that it should be done in such a manner that the sample would have the same composition as the commercial output of the mine. .

Sep 1, 1905

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent papers on interface energies in metals¹,² the concept of an equilibrium of forces has been used in the measurement of interfacial tensions. Mathematically the equilibrium of three forces is given by the relations: where the 2&apos;s are the interfacial tensions (interface energies per unit area of interface) of three phases or grains meeting at angles 21 22 and 23 (212 relates to the 1-2 boundary formed by grains 1 and 2;223 to the 2-3 boundary, etc.). If these relationships are valid, one can calculate relative values of the interface energies from measured boundary angles on specimens which have been brought to equilibrium. Since Eq 1 may be derived through a mathematical process of minimizing the grain boundary energy under the restriction that the ?&apos;s be independent of boundary orientation: the concepts of surface tensions and equilibrium of forces are not particularly essential. To deal with the general case involving dependence of boundary energy on boundary orientation, it becomes desirable to drop certain concepts formerly held (namely that energy per unit area is identical with force per unit length or surface tension) and to use the energy concept alone. It is appropriate, therefore, to use E in place of ? in deriving and using the more general equations that express the anisotropic nature of the grain boundary energy. Herring3# &apos; recently has derived the required general equations using the principle of minimization of energy. Specifying the boundary orientations in terms of angles (4) measured with reference to crystal axes within the grains, Herring&apos;s equations take the form E23 + E21 cos?8 + E12 cos?2 — sin ?12 + sin?2-?E12/?12 =O [2] where the partial derivatives are measured in the direction of counterclockwise rotation of the boundaries. Eq 2 implies that an infinitesimal displacement of the triple point along the 2-3 boundary produces no change in the boundary energy. Similar equations apply for infinitesimal displacements along each of the other two boundaries. From such equations Herring obtains the following general relationship (1 + E1 E2) sin?8 + (E2 — E1) cos?3 ________ E38______________ = (1+ E2 E8) sin ?1+ (E3— E2) cos ?1 __________^5____________[3] (1 + E sin ?2, + (E1 — E8,) COS ?2 1 E28 where E1 = 1/E23- E25 and PC and c8 have similar expressions. It is apparent that Eq 3 reduces to Eq 1 when the c&apos;s vanish. Eq 3 also reduces to Eq 1 when the E&apos;S are all equal. Shockley and Read&apos; have pointed out one limitation to these equations. When E plotted versus 4 appears as an energy cusp, as their theory requires, for example, for the energy near a twin boundary position, then Eq 3 (and therefore Eq 1 also) no longer applies if one boundary is in the minimum energy position. One of the equations of form Eq 2, however, applies if the infinitesimal displacement is along the boundary associated with the energy cusp. From the foregoing treatment it will be apparent that equilibrium angles alone are not sufficient in general for calculating relative interface energies.

Jan 1, 1951

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By H. A. Domian, H. Biloni, G. F. Bolling

Jan 1, 1965

By AIME AIME

MICA is perhaps our No. 1. strategic mineral problem because of its large requirements in a variety of equipment for use in the military services, and because the principal source of this material has heretofore been British India, a source now threatened partly because of distance and lack of ships. [Block mica and bauxite were added to the "most critical" list published by the W.P.B. on Nov. 6.] No satisfactory substitute has yet been found for most of the uses of mica, which largely involve electrical insulation. Brazil is now our nearest and best major source of this material. No splitting plants have yet been established there but in 1941 we imported about a million pounds of block mica from that country and in 1942 that quantity will be considerably exceeded. In Brazil, mica is found almost exclusively in the pegmatite dikes along the mountain range bordering the eastern part of Minas Gerais. A belt, roughly 180 miles long by 100 miles wide, extends from Theophilo Ottoni to Carangolo. The principal mica-mining districts in this belt are the Governador Valladares area to the north and the Espera Feliz district to the south. The dikes are usually 10 to 50 meters wide and a mile or two long and intrude the old metamorphic schist formation. They are weathered and easily mined.

Jan 1, 1942

By AIME AIME

LOCAL COMMITTEES. GENERAL RECEPTION COMMITTEE.-Mr. and Mrs. H. S. Chamberlain, Mr. and Mrs. J. T. Lupton, Mr. and Mrs. T. H Lasley, Mr. and Mrs. R. S. Faxon, Mr. and Mrs. H. Clay Evans, Mr. and Mrs. C. E. James, Mr. and Mrs. B. F. Thomas, Air. and Mrs. H. S. Probasco, Mr. and Mrs. W. M. Lasley, Mr. and Mrs. L. W. Llewellyn, Mr. and Airs. T. G. Montague, Mr. and Mrs. E. B. Thomasson, Mr. and Mrs. C. F. Milburn, Mr. and Mrs. C. A. Raht, Mr. and Mrs. C. C. Notting¬ham, Mr. and Airs. Z. C. Patten, Mr. and Mrs. Willard Warner, Mr. and Mrs. S. R. Read, Mr. and Mrs. Carl White, Mr. and Mrs. M. M. Allison, Air. and Mrs. C. E. Buck, Mr. and Airs. H. F. Temple, Air. and Mrs. M. M. Hedges, Mr. and Airs. X. Wheeler, Mr. and Airs. John A. Patten, Air. and Airs. N. T. Montague, Mr. and Mrs. R. H. Williams, Mr. and Mrs. T. R. Preston, Mr. and Airs. Morrow Chamberlain, Mr. and Airs. T. C. Thompson, Mr. and Airs. T. L. Montague, Mr. and Mrs. O. L. Hurlbut, Air. and Mrs. C. A. Lyerly, Mr. and Mrs. Garnett Andrews, Air. and Mrs. M. B. Ochs, Mr. and Airs. Webster James, Mr. and Mrs. D. P. Montague, Mr. and Mrs. Z. C. Patten, Jr., Mr. and Mrs. W. A. Sadd, Mr. and Mrs. J. B. Pound, Air. and Mrs. George D. Lancaster, Air. and Airs. J. F. Johnston, Mr. and Mrs. R. W. Barr, Air. acrd Mrs. W. B. Davis, Mr. and Airs. Douglas Baxter, Air. and Mrs. W. R. Crabtree, Mr. and Mrs. Lewis M. Coleman, Mr. and Mrs. Newell Sanders, Mr. and Mrs. E. Y. Chapin, Mr. and Mrs. W: B. Riddell,. Mr. and Mrs. J. B. Frazier, Mr. and Mrs. John A. Moon, Mr. and Mrs. C. D. Mitchell, Dr. and Airs. J. H. Race, Mr. and Airs. A. W. Chambliss, Mr. and Mrs. J. P. Smartt, Mr. and Mrs. J. F. Tarwater, Mr. and Mrs. L. D. Drewry, Capt. and Mrs. A. B. Putnam, Mrs. Minnie C. Ewing, Mr. G. F. Meehan, Mr. Sam S. Gerstle, Mr. P. A. Brawner, Mr. C. M. Preston, Air. George M. Guild, Mr. L. M. Mansfield, Dr. J. W. Johnson, Dr. J. AI. Hogshead. EXECUTIVE COMMITTEE.-H. S. Chamberlain, Chairman; H. S. Probasco, C. M. Preston, H. Clay Evans, J. T. Lupton, M. B. Ochs, C. C. Nottingham, Al. Al. Alli¬son, R. S. Faxon, C. E. James, C. A. Raht. EXCURSION TO CHICKAMAUGA PARK.-T. C. Thompson, Chairman; B. F. Thomas, G. F. Meehan, Morrow Chamberlain, W. J. Bass, J. K. McGoodwin. EXCURSION TO HALES BAR LOCK AND DAM.-R. H. Williams, Chairman; John A. Patten, Newell Sanders, George M. Guild, Capt. A. B. Putnam. EXCURSION TO ROCK-WOOD.-F. H. Clymer, Chairman; T. L. Brown, T. A. Wright, J. P. Tarwater, T. L. Peterman. INSTITUTE HEADQUARTERS.-The Hotel Patten. THE first session, held Thursday evening, Oct. 1, in the Banquet Hall of the Hotel Patten, was called to order by Capt. H. S. Chamberlain, Chairman of the Local Committee, who, in behalf of the city of Chattanooga, extended a hearty welcome to the members and guests of the Institute.

Nov 1, 1908

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969

By R. E. Hummel, J. W. Koger

IT is generally accepted that the martensitic start temperature (Ms) can be determined by resistivity measurements and is that temperature where the resistivity vs temperature curve on cooling first deviates from a straight line.1-4 Both Titchener and ever&apos; and pops5 have used resistivity measurements to follow the martensitic transformation in b1 Cu-Zn and ternary Cu-Zn-based b-phase alloys, respectively. Actually because of the nature of their measurements the temperature of minimum resistivity (M) was used by these authors to determine "Ms" . Also, due to experimental difficulties in detecting M, with resistivity measurements, Pops and Massalski 8 determined M, by optical microscopy. The present communication is concerned with high-precision, low-temperature resistivity measurements which reveal a definite M, temperature which differs from the temperature of minimum resistivity (M). It is also shown that M is merely the result of the geometry of the percent-transformation curve and the temperature coefficient of resistivity of the alloy. In other words, it will be demonstrated that M has no apparent significance (except that it denotes a temperature at which some percent of martensite can be detected in a given alloy). Alloy specimens were made by melting 99.999 pct Cu and 99.9999 pct Zn in sealed and evacuated quartz tubes and homogenizing them at 601PC for 300 hr. After the alloy was cold-rolled into foils suitable for resistivity measurements, it was quenched in ice water from 871PC. The chemical analysis showed a zinc content of 38.8 wt pct. The cooling rate during the martensite transformation was 1°C per min and was controlled with a thermistor. Electrical resistivity measurements were made using a K-3 type potentiometer; the reproducibility of the resistivity values was better than 0.03 pct. Temperatures were measured with a thermocouple to an accuracy of better than 0.2° C. Fig. 1 shows the resistivity vs temperature curves of the martensitic transformation in B1 Cu-Zn for both cooling and heating. The starting point of the martensitic transformation (M,) was taken as that

Jan 1, 1968

By James C. M. Li, J. Weertman

James C. M. Li (United States Steel Covp.)—The author has discovered a single analytical relation between the minimum, or the steady-state, creep rate and the applied stress confirming a statement made earlier by orn" that such relation should exist and should reduce to the power law at low-stress levels and to the exponential law at high-stress levels. However, as pointed out by the author, all the available theories of creep are not adequate to explain such a single relation. Inspired by such a statement, I have made a suggestion concerning a possible explanation13 of the new relation. This is based on the concept that the rate-controlling step is the cooperative motion of a short dislocation segment. The nature of and the reason for the cooperation have been discussed13 as well as the reason why the motion of the dislocation could be controlled by the mobility of the short segments. A natural short segment has been proposed13 to be the node formed at the intersection of two dislocations. The reason why the node may contain only a few atoms has not been discussed and the application of the proposed model to all the metals and alloys reported in this paper has not been attempted. It seems appropriate to include these in this discussion. The model was partly inspired by the substructure recently observed in the electron microscope on creep specimens. One such example is shown in Fig. 48 in Darken&apos;s Campbell Memorial Lecture. The substructure is a collection of dislocation intersections and irregular networks. No pileups have ever been observed in such specimens. A closer look at the network indicates that one set of dislocations is more straight than the other set sug- gesting that the other set may be mobile in the plane of the net. Since, for the network to survive the creep deformation, some dislocation reaction has to take place at the intersection of the two sets of dislocations, the mobile dislocation, even if it can slip in the plane of the net, will have difficulty in moving at these intersections. To illustrate, an idealized network is shown in Fig. 9. The thin lines represent the set of dislocations which are mobile and can slip in the plane of the net except at the nodes which are formed at the intersection of the two sets of dislocations. The other set of dislocations, represented by the thick lines, may have a Burgers vector which is not parallel to the plane of the net, and therefore may be immobile. Because of this nonparallel Burgers vector, the Burgers vector of the node, which is avectorial sum of the Burgers vectors of the two sets of dislocations, will also be nonparallel to the plane of the net. Therefore, the node cannot slip in the plane of the net and the set of mobile dislocations will have to drag the node along as indicated in Fig. 9. Now the problem is how many atoms could be involved in the nodes. Exact calculation of the length of the node is a difficult task especially since the length should be a steady-state length and not an equilibrium length. An estimate of the equilibrium length can be made by balancing the line tension of all the dislocations. The results would be a small fraction of the length 1 between nodes as shown in Fig. 10. In some instances such a calculation shows that the node will not be formed. But, since the calculation is only approximate, it does not rule out the possibility of the formation of a short node. In other instances the equilibrium length of the node is an appreciable fraction of I. Such a node would

Jan 1, 1963

By U. N. Bhrany, N. Arbiter

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and

Jan 1, 1961

Jan 1, 1966

By R. C. Neavel

One of the most important requirements to be met by any coal producer is delivery of size consists tailored to specific applications. Generally these specifications include a minimum as well as a maximum size limit. The customers of a major Indiana coal producer noticed that some shipments of sized coal contained a large proportion of undersize pieces. Also, in these shipments, the pieces which remained within the specified limits were cracked and, when handled, crumbled readily. The producer, certain that these shipments had been properly sized at the tipple, suspected that degradation had occurred in transit. The Indiana Geological Survey was requested to examine the coal from one of these shipments to attempt to determine the cause of breakage. Two basic facts about coal and coal seams led to the employment of petrographic techniques in this investigation. First, all coal seams consist of accumulations of diverse organic and inorganic constituents; and second, most coal breakage, either desirable or undesirable, can be attributed to the inherent weakness of some of these constituents or to poor adhesion between certain constituents. Analyses of degraded coal Sampling: Samples were secured from 2 stock piles of 2-by 4-inch coal in a dealer&apos;s yard. The coal in both piles had received the same treatment from mining to storage, although it had been mined and shipped on two different days. The size consist of one pile, however, appeared smaller than that of the other. The sample from the degraded pile is referred to as the slack sample, and the other is called the unslack sample. Size analyses: In order to determine the actual size consist, the samples were screened, with a minimum of rough handling, on square 2-inch, 1-inch, 1/2-inch, and 12-mesh screens. It is assumed that 100 percent of the 2-by 4-inch coal is retained on a 2-inch round screen at the tipple. Analyses of several loads at the tipple indicate that approximately 26 percent of the 2- by 4-inch coal, 100 percent of which was assumed held on a 2-inch round screen, passed through a 2-inch square screen. Twenty-six percent may be taken as the normal difference between round and square screens. Results of the analyses of stockpile coal are shown in Table 1. Cumulative percent versus size are plotted on a Rosin-Rammler chart as Figure 1. Both samples approximately follow normal size distribution; this indicates that breakage is not size preferential and also that the samples are representative of the stockpiles. Although both samples exhibit the same general size distribution, the median size of the slack sample is considerably smaller than that of the unslack sample. Fifty-five percent of the unslack sample was undersize (29 percent greater than the normal 26 percent difference), and 83 percent of the slack sample was undersize (57 percent greater than the normal 26 percent difference). Both piles contained a greater percentage than normal of undersize coal; this indicates that they were both affected by degradation, but to a different degree. Bedding-plane analyses: Coal, because of its laminated nature, will break preferentially along bedding planes, especially where adjacent constituents are poorly cemented to each other. Subsequent breakage perpendicular to the

Jan 1, 1961

Established as a Division March 13, 1935 R H Feierabend, Chairman T E Gillingham, Jr, Northeast Vice-Chairman W A Riggs, Southeast Vice-Chairman C F Clausen, Mid-Continent Vice-Chairman R H Wilpolt, Rocky Mountain Vice-Chairman J K Brooke, Pacific Southwest Vice-Chairman Leslie C Richards, Pacific Northwest Chairman V A Haw, Canadian Vice-Chairman J S Holland, Sec&apos;y -Treas National Lead Company Mining Department 111 Broadway New York 6, New York

Jan 1, 1960

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,&apos; there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin&apos; in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin&apos;s Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier&apos; were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6&apos;Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

Thirty years ago a party of American Engineers, with members of their families, belonging to the four national engineering societies, sailed for Europe and visited England and the Paris Exposition of 1889 and received many courtesies, official, professional, and individual. Plans: have been made for a reunion dinner to be held in New York City, about May 26, at which it is hoped that all survivors, ladies as well as men, of that trip may meet again. It is, therefore, urgently requested that anyone who was of that party communicate immediately with the Secretary of the Committee, Jesse M. Smith, Engineers&apos; Club, 32 West 40th St., New York, N. Y. Announcement of the precise date and place, and full details, will he sent to every individual who can he reached.

Jan 5, 1919

By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

By JO. E. SHERID

THE Dawson coal-mines are owned and operated by the Stag Canon Fuel Co., of which Dr. James Douglas is President and E. L. Carpenter general manager. The property is situated in Colfax county, N. M., and the openings now in operation are in townships 28 and 29 N. R. 20 E., and township 28 N. R. 21 E., shown in Fig. 1. The mines are part of the southern end of the Raton coal-field, which extends north into Colorado and embraces many coal-camps of the Trinidad section. II. GEOLOGY. Geologically, the coal-measures, commonly known as the Laranmie series of the Cretaceous system, have a thickness of about 800 ft. in the vicinity of Dawson. The coal makes an excellent coke, and, according to some authorities, its coking properties are clue to the action of intruded sheets and sills of igneous rock, the sheets occasionally thickening into masses resembling laccoliths, at such places making nearer approach to the coal and sometimes producing small areas of natural coke. There are but few dikes through¬out the entire southern portion of the field and little or no faulting along the dikes. In some parts of this great coal-field the intrusive sheets are far removed in the green shales below the coal-measures, and are so much altered as to be difficult of identification. There is but little disturbance of the strata through¬out the Raton coal-field in as far as it extends into New Mexico. There are two workable seams in the coal-measures, and two or three smaller coal-seams, ranging from 1 to 2.5 ft. in thick-

Jun 1, 1909