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By T. A. Rickard

A severely technical article, however well written, can not be an agreeable form of literature. It suffers from the defects of its qualities. One defect is a congestion of language, due to a multiplicity of adjectival nouns. The sentences are packed with words of unpleasing sound, charged with complex ideas, crowding one another so closely that the phraseology moves like an ice-pack in Bering Sea or a log-drive in a river; the undercurrent of meaning may continue to move, but the surface is obstructed. This verbal congestion is made evident by ugly compoundings, many of which are adopted by the technical writer in the mistaken belief that they give directness to his statements. For example: A unanimously approved scheme "A scheme unanimously approved" The continuous temperature record "The continuous record of temperature" To stimulate interest in synthetic plant construction "To stimulate interest in the construction of synthetic plants " In smelters reverberatory-furnace firing with powdered coal has been practised for a decade. "In smelting, the firing of reverberatory furnaces with powdered coal has been practised for a decade. " A tar consumption of one pound per ton "A consumption of tar at the rate of one pound per ton'

Jan 1, 1931

By V. H. Gottschalk

SEVERAL years ago a group in the metallurgical division of the U. S. Bureau of Mines began a study of the application of new developments in physics to metallurgical problems'. Among these developments were the extensions of what may be termed by analogy the "sound spectrum." Electromagnetic waves, from X-rays to radio waves, have been quite thoroughly explored for metallurgical use, but the sound spectrum, extending from low-frequency vibrations involved in certain types of metal failure by fatigue through the range of audible sound to inaudible vibrations having frequencies of many kilocycles, has had only meager consideration from metallurgists. Because of the general interest in the process recently demonstrated by St. Clair3 for flocculating smoke by means of sound waves, this article is written to point out possible applications of sound and supersonic (ultrasonic) waves in the metallurgical industry.

Jan 1, 1937

By James T. Waber, Allen C. Larson, Karl Gschneidner, Margaret Y. Prince

The original graphical method proposed by Darken and Gurry for predicting which elements are soluble in a given element was slightly modified and was used to predict terminal solubilities in 1455 known binary combinations. it was found that the modified Darken and Gurry method had a reliability of 61.7 pct in predicting extensive solid solubility (greater than 5 at. pct) and of 84.8pct in predicting limited solid solubility (less than 5 at. pct), an over-all reliability percentage of 76.6. Using the same experimental data, it was found that using only the simple Hume-Rothery size-effect criterion was 50.1 pct reliable in predicting extensive solid solubility, only slightly better than a purely random choice. and 90.3 pct reliable for predicting limited solid solubility, an over-all reliability percentage of 67.6. THE first rational rules for determining a priori whether two metals are not freely soluble in the solid state were announced by Hume-Rothery and coworkers.1,2 These well-known rules have been accorded a special place in metallurgical literature. Since the "electronegative" and "relative valence effect" rules of Hume-Rothery were only qualitative in nature it was difficult to use them in a quantitative analysis. The next major step was made by Darken and gurry3 and apparently went unexplored for a number of years. They prepared graphs illustrating the influence of both electronegativity and size difference on the solubility of elements in silver, magnesium, and aluminum, and they drew elliptical figures, whose maximum width was ±15 pct of the solvent radius and the maximum height was ±0.4 electronegativity units. The purpose of the present paper is to assess and compare the effectiveness of using the simple size-factor and the Darken-Gurry criteria to predict which elements will be soluble and insoluble in a given solute. In 1957, waber4 prepared Darken-Gurry plots for determining the solutes that were likely to be soluble in 6 and plutonium and introduced an inner ellipse as an aid to determining which elements should be soluble to a considerable extent. As illustrated in Fig. 1, the major axis of the outer ellipse corresponded to ±0.4 electronegativity units (OD) while the minor axis corresponded to ±15 pct of the radius of the solvent phase (OB). This simultaneous "action" of the two Hume-Rothery criteria was used to indicate which elements would have little or no solubility in the host lattice, namely those elements whose points lay outside this ellipse. An inner ellipse, "centered" over the same point of the solvent was drawn with ±0.2 electronegativity units (OC) and ±8 pct (OA) as the major and minor axes. Solutes with points lying within the inner ellipse were expected to be capable of forming extensive solid solutions with the host element. Use of this method of applying the earlier Hume-Rothery criteria was moderately successful for plutonium. For 6-phase plutonium, only one element out of the eight predicted to be extensively soluble was known to be almost insoluble, and of the sixteen elements predicted to have more restricted solubility, five were known to be essentially insoluble. The success of discerning solubility in the E phase by this method was comparable. One prediction made on the basis of this analysis was that the heavier rare earth metals, such as holmium, erbium, and thulium, should be soluble in the 6 phase, whereas the lighter rare earth elements, such as lanthanum or

Jan 1, 1963

By K. L. Young

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection case. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. INTRODUCTION When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressures. The two methods are Cullender and Smith1-" (numerical integration), and average temperature and com-pressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correcton. The average temperature and compressibility method, in addition to neglecting kinetic energy change, asumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. l or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. where 111.1 qeC2/d p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation,

By E. P. Haqyes, J. K. Butler

011, and gas development has continued unabated on the Texas Gulf Coast during 1937. Although the number of important new discoveries has not been great, the extensions in older fields, owing to discovery of new sands and the lateral extension of known sands, has been extensive. Twenty-four new producing fields were added during the year, and many of these areas give promise of developing into important producing districts in the future. Alta Mesa, Amelia, Aransas, Clara Driscoll, Five Corners, Hamman, Heyser, Old Ocean, Premont, Seabreeae, Segno and West Columbia have all had major extensions during 1937. The 1937 production for the Texas Gulf Coast was 120,141,429 bbl., or 32f per cent increase over the 1936 production of 90,865,293 bb1. t The total number of producing wells has increased from 6727 to 8968. Well abandonments have becn few and indications are that they will continue to be so. Rigid proration has been and continues to be in effect, and, as a result, wells in the Gulf Coast will have prolonged life. New Fields Tables 1 and 2 contain general information on all fields in this district. The following named fields were discovered in 1937: Aransas County.—Barnsdall Oil Company's No. 1-A Edwards was the discovery well for the Lamar field. It was drilled to a total depth of 9785 ft., plugged back and completed at 7530 ft. in the Frio as a gas and distillate well. Present indications are not very promising for a major field. Bee County.—The McMurray (Strauch) field was discovered by Dirks Bros. No. 1 Strauch at a total depth of 4577 ft. This is a Yegua producer, and had an initial production of 230 bbl. on a 3/16-in. choke. Brazoria County.—The Sandy Point field was discovered by Henry DeArmanls No. 1 Fite, which was completed as a producer at 6501 ft. in the Marginulina-Frio series. Galveston County.—Although the Hitchcock field was discovered in 1936, the first commercial oil producer was completed in 1937 when

Jan 1, 1938

Application of Kutter's Formula to Gases Discussion of paper by F. ERNEST BRACKETT, presented at the Pittsburgh Meeting and issued, as Pamphlet No. 1578-A-F, with MINING AND METALLURGY, June. 1926. C. S. WITHERELL, New York, N. Y. (written discussion).-There is no reason to doubt that the relationship between the rate of flow and the impelling force of all fluids can be expressed by a general typical equation . that takes cognizance of all relevant factors such as density, viscosity (or its reciprocal mobility) and nature of channel-walls. Most fluids that are commonly conveyed by flow in confined channels are so highly mobile that they may be considered non-viscous, hence for these fluids the factor of viscosity does not need to appear in the equation. Water is the outstanding example of this class of fluids and its dynamic behavior has been so thoroughly investigated that proven formulas pertaining thereto, be they rational or empirical, would naturally serve as prototypes for the other non-viscous fluids. As non-viscous fluids can be classed all gases and vapors, most unsaturated aqueous solutions, gasoline, alcohol, etc. Viscous fluids comprise those that have a sluggish flow such as most. oils, tar, molasses, etc., the high viscosity of which is due to shearing resistance between molecules; a force that must be taken into account in figuring the flow of fluids of this class.

Jan 10, 1926

By LIONEL E. BOOTH

ORE tests are made for the purpose of determining the correct methods of treatment for any particular ore. They should be conducted so as to insure that the results obtained in actual mill practice, on ore of similar grade and physical nature, will duplicate the results obtained in the test work. As the expenditure of many thousand of dollars may be involved in the building of the necessary mill, the testing of ores calls for extreme care and skill in handling laboratory machines, and a knowledge of actual practice to guard against the danger of obtaining results in test work that would be impractical to duplicate on a commercial scale. The importance of a correct sample of the ore is at once apparent. No matter with what degree of care the test 4rk is done, it loses its value when made on an unrepresentative sample. It is the first safeguard against future disappointments in the loss of capital and time. A number of failures in the past have been traced directly to faulty or lax methods in obtaining the ore sample.

Jan 1, 1924

By Charles R. Austin, Carl H. Samans

In an earlier serics of studies on 18-8 stainless steel at 600º, 700º, and 800ºC.l one pretreatment was used throughout; viz., 15 min. in hydrogen at 950°C., followed by an air quench. Several manufacturers of this alloy since have expressed doubt as to the suitability of the temperature employed, recommending instead the more customary Strauss treatment as promising superior results. In this subsequent investigation on the effects of the temperature of pretreatment several interesting points have arisen, which are described in this paper. Previous work on our equipment had shown a marked difference between alloys of "similar chemical composition" that had been manufactured by different companies. Accordingly, one mill-bar length was selected from which to prepare all specimens. It could then be assumed that any marked differences in creep characteristics would be due to effects resulting from variations in the pretreatment of the alloy. The material was furnished by the Allegheny-Ludlum Steel Co. in the form of 5/16-in. dia. rod, finished by air cooling from a mill anneal at 1950°F. (1066°C.). It was analyzed only for the elements shown: carbon, 0.07 per cent; chromium, 18.73; nickel, 9.46; manganese, 0.40. Three pretreating temperatures were chosen, the specimens being held for 15 min. in hydrogen at either: (1) 1150°C., to conform to the recommended Strauss treatment; (2) 950°C., to compare with the results of previous tests; or (3) 75Q°C., to initiate precipitation of carbides in the material before testing. As the test cross sections were only 1/8-in. dia., air cooling followed the annealing treatment. These treatments permitted two direct comparisons: (1) between the 1150" and 950°C. treatments to indicate the effect of grain size when all carbides were probably in solution at the start of the test; and (2) between the 950" and 750°C. treatments to indicate the effect of carbide "nucleation" for similar grain sizes.

Jan 1, 1940

By Carl H. Samans, Charles R. Austin

In an earlier serics of studies on 18-8 stainless steel at 600º, 700º, and 800ºC.l one pretreatment was used throughout; viz., 15 min. in hydrogen at 950°C., followed by an air quench. Several manufacturers of this alloy since have expressed doubt as to the suitability of the temperature employed, recommending instead the more customary Strauss treatment as promising superior results. In this subsequent investigation on the effects of the temperature of pretreatment several interesting points have arisen, which are described in this paper. Previous work on our equipment had shown a marked difference between alloys of "similar chemical composition" that had been manufactured by different companies. Accordingly, one mill-bar length was selected from which to prepare all specimens. It could then be assumed that any marked differences in creep characteristics would be due to effects resulting from variations in the pretreatment of the alloy. The material was furnished by the Allegheny-Ludlum Steel Co. in the form of 5/16-in. dia. rod, finished by air cooling from a mill anneal at 1950°F. (1066°C.). It was analyzed only for the elements shown: carbon, 0.07 per cent; chromium, 18.73; nickel, 9.46; manganese, 0.40. Three pretreating temperatures were chosen, the specimens being held for 15 min. in hydrogen at either: (1) 1150°C., to conform to the recommended Strauss treatment; (2) 950°C., to compare with the results of previous tests; or (3) 75Q°C., to initiate precipitation of carbides in the material before testing. As the test cross sections were only 1/8-in. dia., air cooling followed the annealing treatment. These treatments permitted two direct comparisons: (1) between the 1150" and 950°C. treatments to indicate the effect of grain size when all carbides were probably in solution at the start of the test; and (2) between the 950" and 750°C. treatments to indicate the effect of carbide "nucleation" for similar grain sizes.

Jan 1, 1940

By A. E. Wells

In this paper are described various comparative tests made on cracked and straight run gasolines. The results of these tests may be briefly summarized as follows: Samples of 54 to 55° Bé. gravity cracked gasolines, with end point of about 442° F., and with a somewhat larger proportion of the less volatile fractions than conformable to government specifications, were used in a single cylinder variable compression engine under the same conditions as were samples of straight run gasoline of 58 to 59° Bé. gravity, and of which one had a greater proportion of the more volatile fractions than called for in government specifications. The cracked gasolines showed decidedly less tendency to knock, hence could be used at higher compression ratios and thereby developed from 10 to 20 per cent. more power than did the straight run gasolines. These figures may be taken as one measure of the superiority of the cracked gasolines under test with the straight run gasolines. It is not claimed that all cracked gasolines are superior to all straight run gasolines to the extent indicated by the above tests; cracked gasolines vary as do the straight run products. Cross's work and that of others have indicated that certain cracked products may have a much greater superiority over straight run than that determined above. From various sources and by different methods of testing data are being obtained to show the definite and generally quite considerable superiority, as an anti-Cetonating fuel of cracked gasolines over straight run gasolines. It is now becoming generally recognized that by increasing the production of cracked gasoline motor fuel from those heavier petroleum fractions, which otherwise would be used for burning purposes, the petroleum industry is not only working in the interest of the conservation of the world's supply of petroleum, but is at the same time making available to the gasoline-consuming public a product distinctly superior to the straight run gasolines.

Jan 1, 1927

By James Hyslop

MECHANIZATION of American coal mining continues to make rapid progress. Economic pressure will compel abandonment of manual methods wherever possible and will also provide the incentive needed for the improvement of machines and mining systems. However, rapid progress may be made along strictly technological lines and at the same time much slower progress in approaching maximum productivly and efficiency. One can well ask, just how efficient are mechanized mines, and to what extent is productivity affected by the mental attitude of management and workers?

Jan 1, 1946

By R. H. Coats

MINING occupies a position of less importance than manufacturing or agriculture in Canada, but its relative contribution has increased greatly during the post- war period. Mineral production was only 5.14 per cent of the net value I of production of all kinds of commodities in 1919, but by 1936 the pro- portion had risen steadily to 12.76 per cent. Mining felt the depression, hut unlike agriculture, which is still ' sorely stricken, it has passed from early convalescence to complete recovery. For each of the last two years new high records were established for the industry as a whole and for the quantity of most metals produced. Mining has had a notable effect on - the growth of the power industry in Canada. Water power has been developed in the same or adjacent areas wherever mining camps have been 1 established, with few exceptions. Consumption of electrical energy by the mining industry gained 72 per cent within a decade, rising from 1604 million kw.-hr. in 1926 to 2754 in 1935. In. 1935 alone the mining industry purchased electric power

Jan 1, 1937

By L. C. Graton

At the Tenth International Geological Congress, Mexico, 1906, Waldemar Lindgren presented "The Relation of Ore Deposition to Physical Conditions." Retrospect ranks it as the outstanding offering at that Session and as the most fundamental contribution up to that date on the philosophy of ore deposition. Elaborating thereon in his text-book "Mineral Deposits," Lindgren analyzed ore-forming processes under conditions prevailing from great depth up to surface; explained the nature of deposition in each environment; and developed a comprehensive genetic ore classification, which brought wide acceptance and enriching contributions by many. Since Lindgren's latest edition (1933), have come wealths of material relevant to ore genesis, particularly through amazing renaissance and proliferation throughout science. Current publication regarding ores now emanates largely from a generation caught in pressures of the breathless modern tempo, which tempts scant reflection upon earlier truths. Consequently, today's thrilling output contains not a few offerings that need challenge because supplanting interrelationship and system by what seems, collectively, an assemblage of strange, ad hoc and often self-contradictory concepts. From these latter some merit may eventuate but at the probable cost of present confusion and delayed progress. The following pages, naming numerous post-Lindgren advances, record the conviction, held by many, that Lindgren's philosophy, progressively improved, remains the soundest approach to understanding ore genesis.

Jan 1, 1968

COUNCIL OF ECONOMICS, AIME Formerly Mineral Economics Division Established as a Division December 15, 1948 Established as a Council February 26, 1957 Sheldon P Wimpfen, Chairman John D Ridge, Vice-Chairman (Mining) A J Philips, Vice-Chairman (Metals) Warren B Davis, Vice-Chairman (Petroleum) COUNCIL OF EDUCATION, AIME Formerly Mineral Industry Education Division Established as a Division January 15, 1932 Established as a Council February 26, 1957 James D Forrester, Chairman Charles V Kirkpatrick, Vice Chairman (and Chairman-elect) Lysle E Shaffer, Past Chairman Truman H Kuhn, Secretary-Treasurer Colorado School of Mines Golden, Colorado John S Bell, Contact AIME Director

Jan 1, 1960

By R. H. Smith, A. C. Polk

The physical properties of the materials are listed, together with a short explanation of how this material binds the sand grains together without materially reducing the effective permeability of the sand. The chemical can be used in wells with bottom-hole temperatures ranging from 105°F to more than 350°F A description of the equipment required and the techniques used for applying these plastics to the wells is included. Introduction Recovering oil and gas from unconsoli-dated sand formations offers one of the most troublesome of all production problems. These sands generally present no particular trouble while drilling is in progress, but after the well has been completed and a pressure differential has been established across the face of the producing zone, the formation begins to L'slough," resulting in "sanding up" of the well. The term "sanding up" means that sufficient volumes of sand have moved into the well bore or casing to cause a serious reduction or complete halt of all flow of oil, water or gas. In rare cases a well may produce only a small amount of sand and still continue to flow or pump, the sand being carried to the surface in the fluid stream. However, in such instances, the result may be a costly repair bill due to the effect of the sand on surface and pumping equipment. The difficulty of producing petroleum from sands that are loosely cemented has long been recognized by petroleum engineers but only within the last few years has any new approach to the problem been undertaken. This involves the use of plastics that are capable of bonding the individual sand grains in place without materially reducing the effective permeability of a formation. The successful application of plastics for the consolidation of poorly cemented sands is relatively recent but now it is widely used in many of the more difficult areas on the Gulf Coast of Texas and Louisiana. This relatively new use of plastics1 in the oil fields has been preceded by much laboratory and field research on the use of various chemicals2,3 for solving numerous well-completion and work-over problems. Plastics now are being used successfully to control gas-oil and water-oil ratios,4'6 in zone isolation, the repair of casing leaks, the elimination of caving in cable-tool drilling wells6'7 and in the setting of linerss and casing.9 Sand-consolidating plastics, however, are basically different from all others in that they must not form an impervious seal. Field Practices The approach to the sanding-up problem usually has been the mechanical obstruction of the movement of the sand grains.

Jan 1, 1947

By A. C. Polk, R. H. Smith

The physical properties of the materials are listed, together with a short explanation of how this material binds the sand grains together without materially reducing the effective permeability of the sand. The chemical can be used in wells with bottom-hole temperatures ranging from 105°F to more than 350°F A description of the equipment required and the techniques used for applying these plastics to the wells is included. Introduction Recovering oil and gas from unconsoli-dated sand formations offers one of the most troublesome of all production problems. These sands generally present no particular trouble while drilling is in progress, but after the well has been completed and a pressure differential has been established across the face of the producing zone, the formation begins to L'slough," resulting in "sanding up" of the well. The term "sanding up" means that sufficient volumes of sand have moved into the well bore or casing to cause a serious reduction or complete halt of all flow of oil, water or gas. In rare cases a well may produce only a small amount of sand and still continue to flow or pump, the sand being carried to the surface in the fluid stream. However, in such instances, the result may be a costly repair bill due to the effect of the sand on surface and pumping equipment. The difficulty of producing petroleum from sands that are loosely cemented has long been recognized by petroleum engineers but only within the last few years has any new approach to the problem been undertaken. This involves the use of plastics that are capable of bonding the individual sand grains in place without materially reducing the effective permeability of a formation. The successful application of plastics for the consolidation of poorly cemented sands is relatively recent but now it is widely used in many of the more difficult areas on the Gulf Coast of Texas and Louisiana. This relatively new use of plastics1 in the oil fields has been preceded by much laboratory and field research on the use of various chemicals2,3 for solving numerous well-completion and work-over problems. Plastics now are being used successfully to control gas-oil and water-oil ratios,4'6 in zone isolation, the repair of casing leaks, the elimination of caving in cable-tool drilling wells6'7 and in the setting of linerss and casing.9 Sand-consolidating plastics, however, are basically different from all others in that they must not form an impervious seal. Field Practices The approach to the sanding-up problem usually has been the mechanical obstruction of the movement of the sand grains.

Jan 1, 1947

By A. L. Bailey, B. A. Landry

W. W. ANDERSON and G. E. KELLER*—We want to compliment the authors on this very thorough paper. It gives information which the coal industry has needed for some time. We hope that the additional information which the authors are collecting will he available shortly. The mixing and riffling procedure that was followed for experimental purposes is obviously not practical in routine float-and-sink testing because of the particle size degradation which would result in handling the sample so many times. It is important to obtain our tloat-and-sink fractions with a minimum amount of handling of material. A statement is made in the paper (p. 80) that "the variable most likely to affect the size of sample required to meet a given preassigned accuracy would be the state or degree of mixing of the coal." We agree that this is a large factor, but do not believe it is the most important factor. Our own opinion is that the most important single factor governing the total gross weight of sample that must be collected is the percentage of the weight of material in the smallest fraction that results from the screening and float-and-\ink operations. In other words, size of sample is governed by the total number of fractionations that must he made, and the distribution of material within the fractions. We can imagine a coal with perfect mixing, but with such a small amount of material in some float-and-sink fraction in one of the coarse sizes that a much larger sample would have to be taken than would be the case with very poorly mixed material, but with a large percentage of coarse material more evenly distributed in all float-and-sink fractions. Our own observation of many float-and-sink tests that we have run in our own organization on many types of coal is that the size of sample that must be used on fine size float and sink is governed more by the requirements for weight of material to be used for analysis in the laboratory than by weight of material necessary to obtain accurate float and sink percentage of weight values. In other words, it is our opinion that very small samples can be used for float-and-sink fractionation in the fine sizes, but that accurate analysis of the fractions will depend on a larger weight of sample being pulverized for the laboratory than is necessary to establish the float-and-sink distribution with respect to weight. A. L. BAILEY and B. A. LANDRY (authors' reply)—The authors thank Messrs. Anderson and Keller for their comments based on long experience. It is agreed that the involved mixing and riming technique used may be disadvantageous from the standpoint of degradation. Fortunately, the paper does point out that the extended riming was unrewarding in causing further mixing. Two large unknowns remain, however: (1) how much of the mixing from the presumed highly unmixed state in the bed was achieved toward the random state during blasting, loading, transportation, screening, and further transportation to the point where the gross sample was taken, and (2) how much of the mixing took place during the preparation described preceding riming. As has been pointed out by one of the authors.6 the degree of mixing has a very large effect on the size of sample required and there are still too few experimental data to show at what stage of coal handling most of the mixing occurs. The discussion states that the weight of material in a screened fraction, or in a float-and-sink fraction, is more important than the mixing factor. We do not believe that these factors are comparable in this instance inasmuch as our purpose was to give minimum sampling requirements to achieve a preassigned accuracy in the percentages of float, middlings, or sink, and nothing more. The gross sample had already been screened and no further division by screening was made or contemplated; also, it was not intended that the middlings and sink fractions would necessarily be adequate for percentage ash or other determination. In other words, the sample obtained by the method outlined is not intended for washability studies but only for preparation plant control. Further experimental work has been done, since the paper was prepared, to investigate the effect of increasingly larger top and bottom sizes on the variability of float, etc., of a double-screened coal from Western Pennsylvania. Results will be published and eventually attention is to be given to the preparation of sampling specifications. E. H. M. BADGER*—I should like the authors to explain more fully the fundamental assumptions on which their Eq 4 is based. The equation is of the form s2 = p(l - p) which is the usual expression for the (standard deviation)2 when the chance of finding a particular kind of particle in the sample is proportional to the number fraetion, p. But instead of the number fraction, the authors have used the weight fraction, WF/W. The chance of finding a particular kind of particle in the sample can only be proportional to the weight fraction, if the average ?eig?ts of all kinds of particles, that is, float, midlings, or sink, are the same. Surely a much more justifiable assumption would be that the average volumes of the particles are the same, and, if this is so, Eq 4 would not be true. This may be demonstrated as follows: Let be the weight fraction of float, middlings, or sink, dl the density of this fraction, and d2 the density of the rest of the coal. Then assuming that the average volumes of the pieces in the three classes are the same, the number fraction, p, is given by ? P = d1/l-?/d2 + ?/d1 = ?d2/d1 + ?(d2-d1) The weight fraction, w, in terms of p is given by ? = pd1/(l-p)d2 + pd1 = pd1/d2 + p(d1-d2) _____ [61

Jan 1, 1950

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947