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By Chas. B. Dudley

A Discussion of the papers of Mr. James Gayley, on "The Application of the Dry-Air Blast to the Manufacture of Iron," and of Mr. J. E. Johnson, Jr., on "The Physical Action of the Blast-Furnace," by Messrs. Charles B. Dudley, R. W. Raymond, J. E. Johnson, Jr., William F. Mattes, James Gayley, David Baker, John Birkinbine and F. E. Bachman. (Washington Meeting, May, 1905.) CHAS. B. DUDLEY, Altoona, Pa.:-Pam not a blast-furnace man, and this always puts me it a disadvantage because I cannot go into the details of the making of iron and steel. I have not the experience, and have to take the statements of other people, so what I say regarding the subject of this paper is not in the sense of an expert. When I first heard of Mr. Gayley's experiments, I said to myself, " I fear they will result in failure, since, apparently, Mr. Gayley has forgotten one chemical fact, namely, that carbon does not combine with oxygen in the absence of water-vapor." This fact which was so astonishing when it was first brought out some years ago, and which those who are interested may find in the Journal of the Chemical Society of London, for 18S5, page 349, and 1894, page 611, led me to think that the drying of the air would be a mistake. The general subject of the influence of water-vapor on chemical action is a large one; but the special point in which we are for the moment interested, namely, the influence of water-vapor on the combustion of carbon, was especially treated by Mr. H. B. Baker, in the papers referred to. Apparently, however, as the result of Mr. Gayley's experiments, we are to learn that the amount of moisture still left in the desiccated air is sufficient to secure perfectly satis¬factory combustion. In thinking over Mr. Gayley's paper, it occurred to me that there were two alternatives, either of which might be chosen, namely, we might dry the air as Mr. Gayley does, or possibly we might, in a very much simpler way, simply saturate the air at a constant temperature, and thus get uniform working and

Sep 1, 1905

STANDING COMMITTEES Executive--HORACE V. WINCHELL, chairman. Membership-KARL EILERS, chairman. Finance-J. V. N. Dorr, chairman. Library-E. GYBBON SPILSBURY, chairman. Papers and Publications-BRADLEY STOUGHTON, chairman.

Jan 3, 1919

By L. D. Clark, S. S. Saluja

A physical law, governing the rupture of rock by confined explosive charge correspondent to current expressions for determining weight of charge to rupture rock burden, W, was developed in the form Q = cVw3 by two early investigators performing unique experiments with ice. The coefficient C, is found by trial blast. Recent physical tests conducted with rock, synthetic materials and ice to establish the validity of the theory on which it and other related formulae are based indicated: (a) that failure under hydrodynamic impact pressure is by tension rather than shear as was assumed; (b) that the fundamental law of mechanics, enabling the determination of Q = cvw3, modified to the form P = R x Sa x Wb is valid when low velocity explosives are used; (c) that rock breakage under the action of low velocity explosives is entirely due to explosion gas pressure, as was believed; (d) that under the action of high velocity explosive it is due to the joint effects of scabbing and gas pressure; and that further possible modification could make the above equation also applicable to these joint mechanisms. shape could be easily frozen and because large loads would not be required. They found: (a) that the not unfamiliar shearing equation for metals was applicable to ice where P = load in lb; S = periphery of pressure surface, in.; W = burden, in.; K = modulus of rupture by shear in lb per in.2; and (b) that "the form of cavity produced by the application of gradual pressure is similar to that obtained by blasting in rock under similar conditions of free face and pressure surface!" This similarity in crater shapes leads to the conclusion that rock would rupture by shear, as did ice, and its behavior under the force of a blast could be governed by such a relationship as P = S x W x K. Three important interrelated empirical expressions were derived and rock, charging and spacing coefficients C,, C, and e were established and substantiated by trial blasts. In checking the accuracy of the main assumptions, duplication of the ice tests, substituting rock, suggested that K is not constant and that P = K x W x S, though valid for ice, does not necessarily hold for homogeneous limestone.' Conclusions from this later work raised questions making continued investigation desirable because such conclusions do not destroy the practical value of the empirical equations or theory. Further study for the establishment of the relationship between load, burden and periphery of the pressure surface and possible application of these to the mechanism of rock blasting was undertaken by the authors of this paper. MECHANICAL TESTING - EXPERIMENTAL PROCEDURE Certain inconsistencies in the results of the aforementioned tests repeated on three types of limestone suggested these inconsistencies be attributed to rock inhomogeneity. It was also suspected that the loading speed, which could not be held uniform, may have contributed. The earlier work with both rock and ice

Jan 1, 1964

By Vincent P. Gi. ccnella

GOLD was discovered in Gold Canyon on May 15, 1849. Following this discovery placer miners worked the gravels in the canyon for-ten years, finally discovering the outcrop of the Comstock lode at Gold Hill in May, 1859, and in Ophir ravine on June 12 of the same year. Before long large quantities of gold and silver, were taken from the lode and one of the West's most spectacular mining booms drew thousands of fortune seekers to Nevada. After a long period of production activity waned and in late years little mining was done. The recent reopening of the old mines and the discovery of ore in other parts of the vein, and in other veins of the district, has led to a revival of interest in the Comstock. Virginia City, Gold Hill, and Silver City, situated along the great vein system, are enjoying a period of prosperity and a large influx of people.

Jan 1, 1934

By C. P. Sandberg

Notwithstanding the growing importance of this subject, no work specially devoted to it has hitherto been published. Having had to inspect during the last twenty years nearly a million tons of iron and steel rails for various countries, I have obtained experience of what rail manufacturers can practically execute, as well as of what railway engineers practically require. Bearing these two points in mind, I have from time to time published observations with a view to unite both interests,—that of the producer and that of the consumer,—and to reduce the specifications and the forms of sections to standards, or types, in order to facilitate the execution of the works and to improve the construction of permanent way. The Swedish government railways, as well as private companies owning railways in Sweden, Norway, and Denmark,.have during the time above mentioned consulted with me and intrusted to me their rail inspection. I therefore owe to these countries much of the opportunity which I have enjoyed of gaining experience and position. Next to Sweden, America is the country which has most liberally favored me with its confidence in placing these matters in my hands. Through circumstances not under my control there has been little exportation to, and less work done by Europe for, America during the last six years; but the recent revival of the rail trade has been the more gratifying to mo, seeing that almost all the importers of American rails are still specifying for the Sandberg rail sections and inspection. It is therefore with feelings of gratitude that I now beg to lay before the American Institute of Mining Engineers, and I hope, through that body, before the American railway world, the results of some experience which I have gained in the execution of work for their country, and which therefore belongs rightfully to

Jan 1, 1881

By C. P. Sandberg

INTRODUCTION. NOTWITHSTANDING the growing importance of this subject, no work specially devoted to it has hitherto been published. Having had to inspect during the last twenty years nearly a million tons of iron and steel rails for various countries, I have obtained experience of what rail manufacturers can practically execute, as well as of what railway engineers practically require. Bearing these two points in mind, I have from time to time published observations with a view to unite both interests, -that of the producer and that of the consumer,-and to reduce the specifications and the forms of sections to standards, or types, in order to facilitate the execution of the works and to improve the construction of permanent way. The Swedish government railways, as well as private companies owning railways in Sweden, Norway, and Denmark, have during the time above mentioned consulted with me and intrusted to me their rail inspection. I therefore owe to these countries much of the opportunity which I have enjoyed of gaining experience and position. Next to Sweden, America is the country which has most liberally favored me with its confidence in placing these matters in my hands. Through circumstances not under my control there has been little exportation to, and less work done by Europe for, America during the last six years ; but the recent revival of the rail trade has been the more gratifying to me, seeing that almost all the importers of American rails are still specifying for the Sandberg rail sections and inspection. It is therefore with .feelings of gratitude that I now beg to lay before the American Institute of Mining Engineers, and I hope, through that body, before the American railway world, the results of some experience which I have gained in the execution of work for their country, and which therefore belongs rightfully to

Jan 1, 1881

Willet G. Miller, Toronto, Canada (communication to the Secretary): In his interesting paper Mr. Lindgren says: " As to ultimate results, it would seem as if we should be justified in concluding, with Prof. Suess, that the gold-supply of the world will gradually decrease if no further important improvements are made in the processes for the extraction of this metal; but regarding events so far distant no predictions may safely be made." It seems to the writer that no very important improvements require to be made in order at least to keep up the present production for many years to come. In many parts of the world there are large deposits of auriferous material which can be worked if present conditions are slightly changed. In the territory occupied by the Archean protaxis of the Province of

Jan 1, 1903

By J. C. Purcupile, R. L. Morris

Present methods of roof support require that first a hole must be drilled, and then a toggle belt or grouted resin bolt be set. Automating this system is very difficult. Therefore, we decided to develop a system which would insert pins into the roof in one step. We think that this type of system can be automated much easier. It would then speed up the roof bolting operation and eliminate the need for a man to work under unsupported roof, making roof bolting a much safer job. There are two ways that a pin can be inserted in a mine roof without drilling a hole. It can either be pushed in, using a very high, constant axial force; or it can be hammered in like a nail. The former method involves very high compressive stresses in the pin, and requires complicated machinery to prevent buckling. Since hammering the pin does not require high axial forces buckling is not as likely. Also, experiments have shown that there are no problems associated with getting the pin to go in straight. We chose to develop the second method. While investigating methods for hammering a pin into a mine roof, we learned that piles were being driven 10 times faster than by conventional methods with a method called "orboresonance." We decided to turn the pile driver upside down, and drive pins up into the mine roof. Sonic Pin Setting Machine The machine consists of a steel bar supported at the nodal points of its first mode of transverse vibration (Fig. 1). A mechanical oscillator, driven by a hydraulic motor, is attached to one end of the bar. This provides the forcing function for the vibrations in the bar. The hydraulic power is supplied by a portable unit. When the forcing function is near the natural frequency of the bar, large amplitudes of vibration occur and require little power input. An anvil is attached to the bar at a point of maximum deflection, providing a means for striking the pin. Since the bar is being driven near its natural frequency, it takes little energy to accelerate the bar back and forth between each hit. This means that most of the power being put into the bar is going into driving the pin. This is unlike conventional pile drivers which use most of their power to accelerate the hammer back and forth between hits. The resonant frequency of the bar we used is about 250 Hz, which is in the audible range, hence the term "sonic pin setting machine." The system benefits are: (1) elimination of the two-step drilling and pin-setting roof bolt operation, (2) increased speed, (3) more intimate contact between the formation and bolts, (4) less expensive roof bolts, (5) higher integrity, (6) potential for automatic operation. Modifications During the months from Oct. to Dec. 12, 1974, under U.S. Bureau of Mines grant No. 00144104, "Projects on Coal Extraction," six members of the senior class at Carnegie Mellon University designed and built the experimental machine. They drove three pins into the Safety Research coal mine at Bruceton, Pa., and determined that the project was worth continuing. In January 1975 we began making modifications and repairs in preparation for a more extensive program of testing at Bruceton. The major items were: 1) Design and build a collapsible pin guide to keep the pin parallel with the line of travel of the lift table. 2) Move the anvil to the center of the bar. 3) Refinish the nodal holes and install new node pins and bushings. 4) Realign the bar in its frame. 5) Install a relief valve on the lift unit to control the upward force. The upward force that we exert on the pin is relatively small, so there is no tendency for it to buckle. This means that all we need to do is hold the pin straight during its initial penetration. This allows the bushing to travel up and down in a straight line. At the beginning of penetration, the bushing

Jan 1, 1977

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By W. A. Tiller, W. C. Johnston

A high-temperature electromagnetic stirrer is described in which heating and stirring are accomplished by independently controlled power sources. The appavatus is suitable lor use at temperatures up to 1700°C in a variety of ambient atmospheres. Some typical examples of the homogenizatimz capabilities of the system are given. THERE are few processes in solidification that are not markedly affected by motion in the melt during freezing. In many instances, the mechanisms are diffusion-controlled, and the transport in the melt may be greatly accelerated by deliberately stirring the melt. In zone-refining, stirring1 assists the removal of rejected impurities from the interface, so the process proceeds at a faster rate. The transition from a planar to a cellular interface is caused by constitutional undercooling in the melt ahead of the interface: and stirring delays its onset. Stirring is valuable for homogenization of melts: and chemical reaction with sluggish kinetics may be accelerated. Finally, it has been observed that grain refinement is related to motion in the melt. Fine grain castings are usually produced by the addition of catalysts to the -melt,' catalysts which are thought to act simply as hetereogeneous nucleation centers. Even here motion is important. Richards and Rostoker 5 applied ultrasonic vibration to a solidifying A1-Cu alloy which had been innoculated with a catalyst and found that the grain diameter fell linearly with the amplitude, the peak acceleration and the power input to the melt from the transducer. Finally, mechanical and electrical stirring alone have been used to generate a fine-grained structure.6,7 Johnston ef a1.' have carried out a series of systematic investigations of grain refinement by electromagnetic stirring in a number of low melting point alloys. They found, for example, that the number of grains per unit volume in Pb-Sn alloys could be increased several orders of magnitude by stirring an undercooled melt at the moment of recalescence. In general, a relation AT .H = constant prevailed for a given grain size, where AT was the undercooling of the melt and H the field strength. In more recent work, deliberate homogeneous nucleation of slightly undercooled melts established that the mechanism of refinement must be one involving crystal fragmentation and subsequent multiplication, rather than a "shower" of nuclei effect.9 It is the purpose of this note to describe a stirring device suitable for use up to 1700°C. At low temperatures mechanical stirring and direct-current methods are feasible, but at high temperatures the problem of a protective atmosphere and of electrode corrosion rules out such procedures. The most convenient method for high temperatures is to use externally generated ac fields for both stirring and heating. With rf induction heating alone, considerable stirring and agitation can be achieved, but in general the penetration of field into the melt is small, and the stirring cannot be controlled independently of the heating. In the present experiments, separate power sources of different frequencies for heating and for stirring were used. A susceptor design was chosen so that the 450 kc rf heating field was completely absorbed in the susceptor. The stirring frequency, 400 cps, hereafter called the af field, was chosen so that a high penetration of the melt proper was achieved. EXPERIMENTAL APPARATUS The apparatus, Fig. 1, consists of a quartz tube and end plates, surrounded by an rf induction coil and six equally spaced af stirring coils, four of which are shown in full and a fifth in section. Each af stirring coil is a transformer of which the secondary is a single-turn water-cooled copper loop and the primary is composed of two 10 amp-117 v Variac cores as shown. These cores are cooled by forced air, as each of the six pairs will carry maximum currents of 15 amp for short periods. Each set of Variac windings are connected in series, but opposite sets are connected in parallel with a three-phase 400 cps 400-v source. By properly phasing the coils in this way, a rotating field is produced. Capacitors C1, C2, and C3 in Fig. 2 are used to match this inductive load to the generator. Fig. 3 shows a cutaway view of the quartz tube. The sample (1 in. diam by 1 in. high) is placed in a tapered alumina crucible. An axial W-26 pct Re thermocouple, enclosed by a protection tube, is provided. The cruci-

Jan 1, 1968

The high-grade orebody at Miami was mined successively by top-slicing, shrinkage, stoping and under caving. The method described in this paper was developed to enable the low-grade orebody (36,000,000 tons assaying 1.06 per cent copper) to be mined at a low cost without further dilution of the grade. The method is clearly described and illustrated by drawings and photographs, and the original paper should be consulted as it is impracticable to abstract it, beyond noting that the mining cost is just under 40 cents per ton and the average grade of ore now being produced yields less copper than the mill tailing of 1915, the tons mined per day having increased from 4000 to 18,000 in the same period. Vertical and Incline Shaft Sinking at North Star Mine By Arthur B. Foote, Grass Valley, Calif. (Tech. Pub. No. 324: Class A. Metal Mining, No. 36) THE main shaft of the North Star mine is an inclined one following the main vein at an average dip of 26 deg., a vertical shaft intersects it at the 4000-ft. (incline) level, the incline continuing to the 6300-ft. level. At this point the vein was found to give out and a new vein, called the No. 1, was found to dip in exactly the opposite direction.

Jan 1, 1930

Executive Committee, Board of Directors H D Smith, Chairman, C E Reistle, Jr, Vice-Chairman, T B Counselman, J S Smart, Jr, L F Remartz Finance Committee, Board of Directors A B Kinzel, Chairman, Philip Kraft, P D Wilson Investments Erle V Daveler, '57, Chairman, Henry Krumb, '56, Andrew Fletcher, '58, G F Moulton, ex officio as Treasurer, A B KInzel, ex officio as chairman of the Finance Committee Endowment W W Mein, Jr, Chairman, D H McLaughlin, J V N Dorr, J B Haffner, J R Suman, Henry Krumb, E V Daveler, D C Jackling, Wilfred Sykes, N G Alford, W J Coulter, C E Weed, 0 H Johnson, L F Reinartz, J B Morrow, R McMillan Endowment Fund "X" G F Moulton, Chairman (RIME Treasurer), Erle V Daveler, '58, G I Brigden, '57, Philip Kraft, '56

Jan 1, 1955

By A. M. Beebee

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

Jan 1, 1940

By A. G. Guy

IN the course of a research on steady-state diffusion it became necessary to make diffusion calculations for a finite solid. This problem was found to be sufficiently different from the corresponding problem for the semi-infinite solid for an entirely new approach to be necessary in obtaining a useful solution. The assumption of an exponential variation of the diffusion coefficient with concentration' was no longer a practical necessity, so that the new solution offered the possibility of handling diffusion in semi-infinite solids for arbitrary variations of the diffusion coefficient with concentration. In discussing the principle on which this method of calculation is based, it is convenient to consider the relatively simple problem of one dimensional diffusion into a matrix that initially contains none of the diffusing substance. The solution of the set- ond Fick Law,?C/?t=D0?2C/?x2, for diffusion into a semi-infinite solid is3 C/C=1-F(x/2vD0t [1] where C is the concentration of the diffusing substance at a depth x cm below the surface after dif- A. G. GUY, Member AIME, and M. GOLOMB are Professor of Metollurgicol Engineering and Professor of Mathematics, respectively, Purdue University, Lafayette, Ind., A. S. YUE, formerly with Purdue University, is now with the Research Laboratory, Dow Chemical Co., Midland, Mich. TP 4505E. Manuscript, July 18,1956. fusion has occurred for t seconds; C, is the concentration of the diffusing substance at the surface of the matrix; Do is the diffusion constant, expressed in sq cm per sec; and + represents the Gauss error function. The corresponding solution for diffusion into a finite solid of thickness, 1, is conveniently written for the change in concentration, C+, at a point midway through the matrix and for times, t, great enough for the following equation to be used4 c1/2/C1=(1/2-2/?e-?2D0t/l2) [2] In Eqs. 1 and 2 the diffusion coefficient is represented by the symbol Do (rather than by D) to emphasize that these equations are valid only for constant values of D. To understand how these equations can be modified to take account of actual variations of D, such as that shown in Fig. 1, first consider the fact that for a given time of diffusion theconcentration at a given point is determined, not by the D value alone, but by the ratio x/vD0 in Eq. 1 and by a similar ratio, l2/D0 in Eq. 2. Even though in fact D varies, it is possible to keep this ratio constant by using a special coordinate system, x,, that varies with D in the appropriate manner. The necessary character of this special coordinate system can be easily visualized by imagining that

Jan 1, 1958

By L. D. Jaffe, H. C. Mann, E. L. Reed

The authors have recently published1 evidence that brittle transgranular fracture of polycrystalline metals does not originate at a point and propagate continuously across the material, but rather develops at numerous related points, leading to a series of micro-cracks which subsequently link up. Series of related microcracks were observed in steel specimens broken in fatigue—specifically, at the central portions which broke during the final sudden fracture. Microcracks of the type mentioned have also been reported by Baeyertz, Craig and Bumps'2 in steel broken under impact. % Some micrographs published by Irwin3 may possibly be interpreted as showing discontinuous brittle cracks. This paper presents additional observations of the authors on discontinuous crack propagation under various conditions. Impact Test Specimens The impact test specimens were cut longitudinally from a steel forging containing: The heat treatment consisted of oil quenching in a heavy section from 1600°F and tempering at 1260°F. The resulting yield strength was 78,000 psi, tensile strength 100,000 psi, elongation 20.0 pet in 2 in., and reduction of area 55.0 pet. Standard V-notch Charpy specimens were broken in a 217 ft-lb machine at a striking velocity of 16.8 fps. Energy absorption and fracture appearance of this material in the V-notch Charpy test are plotted as functions of temperature in Fig 1. After test, fractured halves of specimens appearing 0, 40, 80, and 100 pet fibrous (to the unaided eye) were electroplated with nickel, sectioned longitudinally (perpendicular to the notch at its midpoint), polished and etched with Cohen-Hurlich-Jacobson (C-H-J) reagent (picric acid plus Zephiran chloride in ethyl ether)4 or with Vilella reagent (1 pet picric plus 5 pct hydrochloric acid in ethyl alcohol).5 Fig 2 and 3 show cracks near the path of final fracture in the specimen rated 0 pct fibrous. Many of the cracks terminate at the boundaries of ferrite grains, some at boundaries of pre- existing austenite gzains. * A crack often starts near the end of another. Cracks within the same ferrite grains are parallel or approximately parallel in several cases. A large percentage of the cracks are branched. Fig 4 illustrated a group of cracks in the 40 pct fibrous specimen. Branching and parallelism are well marked. No more than three directions of crack have been observed on the polished surface in one ferrite grain. This is consistent with the evidence6 that brittle fracture of ferrite takes place on the cube face crystallographic planes: the {100} planes. The appearance of some cracks suggests that they have passed around a projecting corner of a second ferrite grain by going outside the plane of polish. In Fig 5 cracks in the 80 pet fibrous specimen may be observed. Some of

Jan 1, 1950

By William Rawles

THIS report is the first of a series planned by The Mineral Inquiry, organized by the American Institute of Mining and Metallurgical Engineers to make factual studies of the world's mineral resources in their political and international relations. The efforts of The Inquiry are directed toward filling certain notable gaps in available information, without duplication of many other investigations touching this field which" are being conducted by other organizations, public and private. Much of its work is indirect-suggesting topics for study by other individuals and organizations and aiding in their planning and correlation. The present report is designed to show the nationality of the commercial control of mineral resources, in addition to the geographic distribution of production by nation-in other words, the overlapping of political and commercial control. Detailed accuracy cannot be claimed for the figures presented. For some companies division of ownership by nationality has been very difficult to ascertain, as many companies are reluctant to dis-close the extent of their holdings in other corporations, and the impossi-bility of tracing all stock ownership is obvious. Also there are frequent changes in the distribution of stock control. The percentages given rep-resent only the participation that has been identified definitely, even though it is known in some cases with fair certainty that larger interests exist, as, for instance, American participation in foreign chromite companies. In bringing' together these figures we have had the cordial co-operation of the United States Bureau of Mines, the United States Geologi-cal Survey, the Mineral Division of the Bureau of Foreign and Domestic Commerce, the Brookings Institution, and of many specialists connected with the mineral industries covered. The report does not cover the entire list of minerals. Coal, although it is one of the most important minerals, was omitted because not more. than one or two per cent of the world's production comes from mines that are owned by companies foreign to the countries where the coal is produced. Others, such as gold, are omitted because sufficient data have not yet been accumulated. It is hoped that some of these may be covered in subsequent reports. It is not our purpose here to discuss the significance of the figures sub-mitted, but only to point out the general nature of the problems on which they have a bearing.

Jan 1, 1933

By Henderson, Robert

A GOOD idea of the magnitude of the underground operations at Climax can be gained from the following figures. A little more than 43,000,000 tons has been drawn from the mine and of this amount, 40,500,000 tons has been drawn in the past ten years and 12,000,000 tons was drawn in two of the war years. The maximum daily average output over a period of one month was slightly more than 20,000 tons but during this period, production on certain days was 24,000 tons, and 9000 tons was produced in a single eight-hour shift. This production came chiefly from 260 draw points although all of them were never in operation at one time. The haulage system for these draw points is made up of 7.5 miles of 36-in.-gauge track, and 131,000 ft. of subsidiary drifts and 44,000 ft. of raises have been driven to develop the necessary broken ore reserves for this high production. Power consumption is often considered an index of operating efficiency. In 1943, the year of maximum production, the mine power consumption was 19,223,000 kw.-hr. or 3 kw.-hr. per ton; in 1945 it was 3.5 kw.-hr. per ton. To handle this amount of power, there are four transformer stations and one switch station in the mine. Mr. Garrabrant, the chief electrician, describes the electrical installation in this issue.

Jan 1, 1946

By Jack C. Haptonstall

Abstract-Minas de San Luis, S.A. operates the old Tayoltita mine located in the Sierra Madre Occidental in Durango, Mexico. Yearly production is 55 000 kg (1.7 million troy ox) of silver and 1000 kg (31,000 troy ox) of gold from milling 165 000 t/y (181,900 stpy) obtained from fissure veins. A 4.4 km (2.75 miles) adit, to intersect the veins below existing workings, was completed in 1974. The adit and ancillary projects facilitated extensive mechanization of the mine, ramp development of it, integration of duplicate facilities and elimination of obsolete facilities. It provided a deep-level access for exploration and development of the veins, and resulted in a 25% increase in production with the same labor force. The cost of the in-house financed project was $3.4 million.

Jan 2, 1978

By Open-Hearth Steel

We have a very high-powered organization up here this morning, headed by Kenneth C. McCutcheon, general superintendent of the Ashland Division of the American Rolling Mill Company, and L. A. Lambing, superintendent of the open-hearth and Bessemer departments of Jones & Laughlin Steel .corporation of Aliquippa, Pa., representing the open-hearth men. Also, we have P. F. Dolan, assistant general manager of the Maryland plant of Bethlehem Steel Company, of Sparrows Point, and Harry E. McDonnell, superintendent of blast furnaces of Weirton Steel Company of Weirton, W. Va., representing the blast-furnace section.

Jan 1, 1940