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By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Walter Morley

This paper is a record of the first of a series of tests on sulfide minerals to be made by the metallurgical department f the University of California. The purpose of the tests here recorded is to determine the action of standard oils, oil mixtures, and addition agents on the flotation of pyrites. The question of the commercial value of pyrite was not considered. Of the many factors affecting flotation, only two-the oil and the other agent used-were made variable. The flotation agents used are given in the accompanying table. PENSACOLA TAR AND TURPENTINE CO. (PENTARCO) NON-POL., SP. Dis. REF. PER No. KIND GR. POINTS INDEX ?VISC. CENT. 200 Refined wood creosote oil 0.965 105-275 1.5096 1.7 7-8 350 Crude pine wood oil 1.019 70-345 1.525 2.9 4 75 Crude wood turpentine 0.887 65-217 1.456 0.9 10-12 80 Crude pine oil 0.911 70-232 1.4894 1.1 8 750 Heavy pine tar oil 1.063 165-350 1.557 41.0 400 Wood creosote oil 1.025 190-360 1.4977 2.9

Jan 7, 1921

By H. M. Beatty, T. L. Joseph, Gust Bitsianes

SUCCESSFUL blast-furnace operation depends upon securing an optimum balance between a number of important variables. This balance will vary somewhat from furnace to furnace in the same plant and with raw materials available in different plants. It is difficult to isolate the effect of any one variable unless it has a rather pronounced effect upon the efficiency of operation. The physical properties of iron ore and coke are known to affect the process, yet it is difficult to set up any definite yardstick by which these differences can be appraised. In recent years, whenever practicable, operators have taken steps to obtain better control over the absolute size and uniformity of size of the ore and coke. The size and physical character of the stone, however, have received comparatively little attention, emphasis being placed upon chemical composition, fluxing efficiency, and action as a desulphurizing agent. Since the stone occupies only about 10 per cent of the volume of the stock column, its influence upon permeability is less than that of the ore and the coke. The large pieces now used have a tendency to roll to the center and thus increase the permeability of this part of the stock column. Smaller pieces would be more effective in promoting the permeability of denser portions of the stock. The size and physical properties of blast- furnace stone are important also for reasons best understood by considering the results obtained by the crushing and the sizing of iron ore. Crushing ore to about 2 in. at Provo, Utah, and to about I in. in Alabama produced material somewhat less permeable to gases, even though sized. In spite of some sacrifice in permeability, the efficiency of the process was improved by crushing and sizing the ore, as indicated by a substantial saving in fuel and increased output. This saving in fuel is due in large measure to more thorough reduction of ore in the upper part of the furnace and to a corresponding decrease in the amount of carbon consumed prematurely above the tuyeres by the reaction CO2 + C = 2CO ? 70,080 B.t.u. [I] The physical properties of stone, its size and rate of calcination are important because they influence the rate at which C02 is released and the completeness of calcination before reaching a level in the furnace where the temperature does not exceed 1050°C. (1920°F.). Briefly, carbon dioxide from the limestone or from the reduction of ore may cause premature com- bustion of carbon above the tuyeres. Assuming that 1000 lb. of limestone is used per ton of pig iron, about 435 lb. of C02 will be liberated during calcination of a good grade of stone. If all this CO2 from the stone were to oxidize carbon prematurely, about 120 lb. would be consumed above the tuyeres in a heat-absorbing reaction. The amount of carbon thus consumed when a

Jan 1, 1942

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By H. Margolin, A. Coucoulas

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKcll radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuAl2, and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band.1,4 Europium in EuAl2 appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref. 1. One of the other phases was identified as Co5Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acia Cryst., 1959, vol. 12, p. '162. A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently hiher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1 week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By Erminio Ferraris

The development of the mining industry in Sardinia dates from the application of the mining law of 1859, which, following the example of the French mining law of 1810, declared prospecting to be free, and suppressed the liens which had previously attached the mine to surface ownership. The first ore-dressing plants were installed by German engineers upon the classic models of the Harz and of Freiberg; but in 1880 Sardinia commenced to open a new path in that industry, utilizing the refuse from the mining of rich, selected minerals, of poor deposits, and of mixed ores. The first experiments were attempte to adapt the existing apparatus to local conditions, but progress was rapid, as was demonstrated already in 1887 by the calamine-dressing mill of Monte-poni, which exhibited a large plant designed in accordance with the experience gained, and constructed entirely in the machine-shops of the country, after new models and designs.' This example was followed two years later by the Sociékté Malfidano, with a large plant of the same sort, and with the reconstruction of the old-fashioned dressing-mill, built in 1880 by the Austro-Belgian Company. In 1900, almost all the mines of Sardinia had adopted the new designs, and the island contained 32 concen-trating-works, employing 2,000 h.p. and 1,924 workmen. Since that time, there have been added a large dressing-mill for blende at Gennamari, and two for calamine, at San Giovanni and at Masua, while the establishments at other mines have been enlarged and perfected. For the treatment of intimately mixed ores, a large establishment has been built upon the new

Jan 1, 1909

By Thomas O. Ziebold, Robert E. Ogilvie

Experimental analysis of diffusion samples covering the entire Cu-Ag-Au system at 725°C has been carried out. Experimental coefficients are computed at twenty-eight points in the lermary system. It is found that the direct coefficienl for copper is nearly independent of the silver, content for 1ow-silver alloys and that the cross coefficient for silver correlates with the ther-nzodynatnic properlies. This lalter observalion leads to the conclusion that the mobililies of copper and gold are nearly equal. Thermodynarmic actiuilies for Cu-Ag-Au were computed from binary data and adjusted to be consistent with neasured tie lines across the two-phase region which extends into the ternary diagram at 725°C. Application of these therknodynarnic calculaliorls to the dijftcsion data terifies the Onsager reciprocal relations to the extent that experimental uncertainlies will allow. It is jound that diffusion neav the critical point of the 1200-phase field in the isothermal section at 725°C causes the composition gradients for copper and silver to approach infinity while the direct and cross coeficients become equal. From the standpoint of experimental Procedures, it has been shown that microanalysis of ternary samples may be carried out using a simple expression for the conversion of X-ray zntensily to composilion. The accuracy of' this method has been demonstrated by the analysis of standard alloys and by the reproducibility of composition determinations using differed X-ray lines. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. When only two elements are present there is just one independent composition variable, and the diffusion profile of composition vs distance across a sample must change monotonically through all solid solutions bracketed by the terminal alloys. If two-phase regions are stable for compositions between the terminal values, these must appear as planar interfaces in the diffused sample, with the composition profile exhibiting sharp discontinuities. Adding a third element may alter this picture completely. Because of the additional degree of freedom in the composition, we may see composition profiles which do not change monotonically through solid-solution ranges, and stable, nonplanar phase interfaces. Even though two-phase regions may lie between the terminal compositions of a diffusion sample on the constitution diagram, they will not necessarily appear in the diffusion profiles. In binary diffusion only one coefficient is needed to describe the interdiffusion process. From Fick's law this coefficient relates the diffusive flux of one component to its own composition gradient. In ternary diffusion we must allow for cross interaction between the two independent species. By a linear extension of Fick's law we introduce "cross" or "off-diagonal" diffusion coefficients which relate the flux of one component to the composition gradient of the other independent constituent. Thus, we require four interdiffusion coefficients to describe the transport process in a ternary system. In its most general form,1,2 the rate equation for mass transport by isothermal diffusion in a system of s components states that the diffusive flux of component i, Ji, is a linear summation of all driving forces, Xk, each force being multiplied by an appropriate compliance coefficient:

Jan 1, 1968

By S. A. Bradford

Internal-oxide precipitates in decarburized a iron alloys were studied by microscopic and X-ray methods. Diffusion of oxygen is primarily trans-granular, although large amounts of manganese or PhosPhorus cause preferred grain boundary dimsion at temperatures below 1450OF. Transgvanular internal oxidation follows the parabolic rate law with an apparent activation energy of 60 kcal per g-atom for decarburized rimmed steel and around 50 kcal per g-atom for higher alloy contents. The internal oxide is (Fe,Mn)0. Evidence was found for a miscibility gap in the FeO-MnO system. UNTIL very recently, the internal oxidation of metals was studied primarily as a scientific curiosity or, in a few cases, as a means of strengthening alloys by precipitation hardening. However, with the recent development of low-carbon enameling sheet steel, internal oxidation has become a problem of practical importance to the steel industry. For example, in 1961 it was reported1 that internal oxidation of steel can occur during decar-burization by open-coil annealing and will reduce the notch ductility of the sheet unless the process is carefully controlled. The present study was therefore undertaken to learn more about the rates and mechanism of oxygen diffusion and oxide formation in iron alloys. BACKGROUND The process of internal oxidation has been well-defined in the literature:',' oxygen dissolves in an alloy, diffuses inward from the surface of the metal, and reacts to form a precipitate with the alloying element that will provide the most stable oxide. he growth of the finely divided so-called subscale, i.e., the internal-oxidation zone, depends on the diffusion rates of both the oxygen and the reactive element.4 Investigators have generally found that increasing the temperature increases the size of the oxide particles, the rate of subscale growth, and the tendency to transgranular diffusion. With very few exceptions, the square of the thickness of the internal oxide layer is directly proportional to the reaction time. Given two conditions easily satisfied for iron systems— a) an oxygen solubility much less than the concentration of the alloying metal and b) an oxygen-diffusion rate to the oxide boundary much faster than that of the alloying element—then the general expression developed by Rhines and co-workers5 for the parabolic growth rate of the internal-oxide zone can be simplified to the following form: where Co and CM are, respectively, the solubility of oxygen and the concentration of the alloying element, DO is the diffusion coefficient of oxygen, O/M is the weight ratio of oxygen to metal in the precipitated oxide, and x is the thickness of the internal-oxide zone after an annealing time t. Both the oxygen solubility and diffusion coefficient can be approximately expressed as functions of temperature by Arrhenius-type equations: in which H and Q are, respectively, the heat of solution and the activation energy of diffusion. Consequently, the apparent activation energies calculated from Arrhenius plots are the sum of the heat of solution of oxygen in iron and the activation energy for diffusion of oxygen. The data, if not the interpretation, of Schenck et al.8 bear out the fact that oxygen diffuses in the atomic form. The general rate law for atomic diffusion is: the reaction rate being proportional to the square root of the pressure at low pressures. Benard and Moreau8 studied both the surface oxidation of Fe-Ni alloys and the gradual penetration of oxygen into the metal. They observed that oxide particles first form along grain boundaries and then grow to form continuous films that eventually envelop the grains. The parabolic rate law does not usually apply in these cases, especially at the higher temperatures. The oxide formed is wustite which gradually transforms into Fe3O4 and finally into Kennedy and coauthors8 examined Fe-Ni alloys with 26, 75, and 84 pct Ni oxidized at 800°C and

Jan 1, 1964

By J. C. Swartz

New measurements of graphite and cementite solubilities in ferrite have been obtained to resolve disagreements among previous data. To measure graphite solubility, specimens of iron were equilibrated with rarious carburizing atmospheres at temperatures be-twee~z 480" and 1435°C. The carbon activity of each atmosphere relative to graphite was taken from published data. After quenching from each equilibration treatment the concentration of carbon (typically 10 pprn by wt) was determined from the height of the Snoek peak in the internal friction spectrum. A few inclividual analyses by combustion support the reszdts of Smith on the solubility of graphite near the eutectoid temperature. Combination of these combustion and internal friction analyses determines In a, (at 0.01 wt pct) = 24,000/RT - 12.72, where a, is the activtity relative to graphite in ferrite at fixed cornposition. The same specimens were used to determine the solubility of self-stressed cementite precipitates. The results indicate solubilities of 6.3, 23.2, and 68 pprn carbon by wt at respectively 400°, 500". and 600°C. The once large discrepancy between the cementite solubility determined by internal frictiori and that calculated from flee energy data has been almost completely resolved. A recent study1 (hereafter designated I) on the solubility of cementite in a iron did not fully resolve the disagreement among previous data. The remaining disagreement is illustrated by the phase diagram in Fig. L The data of I are represented by the line labeled "stress-free" cementite. They determine a heat of solution of cementite of (14.8 * 0.2) kcal per mole which contrasts with the (20 * 1) kcal per mole derived from Smith's graphite solubility2 and the formation energy of cementite.3 Toward resolving this disagreement we have obtained new data on the solubilities of graphite and cementite. METHODS As in I the Snoek peak in the internal friction spectrum was used to measure the concentration of carbon dissolved in ferrite. This method relies on the relation C=kQ-1 [1] in which C is the concentration of dissolved carbon, Q-I is the Snoek peak height, and k is a proportionality factor which is a function of the peak temperature, polycrystalline texture, and other parameters characteristic of the ferrite lattice. To determine true heats of solution via Eq. [1], it is necessary to establish that k is independent of the temperature from which the specimen is quenched. Some evidence on this point is contained in a separate report.* Additional evidence is shown by the data points in Fig. 1. These represent the Snoek peaks of two specimens carburized to about 10 ppm C, copper plated, and quenched first from 888º then from 588°C. The copper plate was removed before each Snoek peak measurement. These data show that there is no detectable dependence of k on quenching temperature. The solubility of graphite was determined by repeatedly carburizing various specimens of iron wire with gas mixtures of known carbon activity relative to graphite. To cover a wide temperature range within the a phase boundaries it is desirable to use as low a carbon concentration as is compatible with reasonable precision. With the present internal friction apparatus the best compromise of these desires is a concentration near 10 wt ppm. The dashed line in Fig. 1 was used to approximate the activity of carbon* for

Jan 1, 1970

By R. J. Tailleur, M. Rosenberg

Oil well drilling muds prepared with lubricating aids such as oil, graphite or mica will not produce a sufficiently strong protective lubricant film for the bit bearing surfaces under high load conditions encountered in drilling operations. Consequently, the damage to the bearing surfaces resulting from the absence of such a film frequently results in a shortening of the drill bit life. Several different types of extreme pressure lubricating additives for use in muds have been developed. These arlrlitives are capable of providing a protective lubricating film for bearing surfaces subjected to high load pressures. A modified version of the Timken lubricant tester, an instrument commonly used for testing the extreme pressure lubricating properties of oils, is used for measuring and controlling the lubricating qualities of the mud. Comparison tests made in the laboratory with 55/8-in. tricone bits drilling on steel plates immersed in extreme pressure lubricating muds and conventional muds showed that the bearing life of those bits tested in the lrrbricating mud was three to four times greater than obtained with conventional muds. Drilling tests made with extreme pressure lubricating muds in West Texas increased over-all bit life three to fourfold, reduced drilling torque and wear on drill pipe and drill collars. INTRODUCTION Roller bit cones contain roller, ball and journal-type bearings that are subjected to very heavy loading during drilling operations in which the only lubricant available for these bearings is either water or drilling mud. These bearings must be able to operate satisfac- torily in order for the cutting structures on the surface of the cones to be fully utilized. Frequently, the bearings wear to the point that the cones freeze and the bit must be pulled before the cutting structures on the cones become worn. In some instances the bearings continue to turn with severe wear but the cones, which are held on the bit by the bearings, drop off; and this causes an expensive fishing job. In other instances the bearings wear to the point that the cones pinch in causing an undergauge hole and delays to ream the hole. The advantage of increasing bit bearing life is self-evident. Because of inability to control the internal wear of bits while drilling, it was felt that improvement of the lubricating qualities of the circulating mud would be helpful. However, the often-discussed lubricating property attributed to muds has been a rather vague and intangible one. The literature has implied that the oil-emulsion muds are more effective lubricants than non-emulsion muds. Actually, there has been no direct method of measuring the lubricating property of muds which would indicate that one mud was better than another; there has been no way to determine whether the lubricating property of any mud was adequate. Furthermore, in comparing lubricating properties of muds, two qualities should be considered—the coefficient of friction and the extreme pressure lubricating qualities. For example, graphite can reduce the coefficient of friction, but does not provide a strong enough lubricating film to protect bit bearings subjected to high loads. The primary object of the investigation reported herein was to find a method for prolonging the bearing life of drill bits; and considering the heavy loads used in drilling, it was felt necessary to find both a method of measuring lubricating properties under high load conditions and methods of establishing effective lubrication under these conditions. Extreme pressure lubrication deals with that realm of lubrication where metal surfaces are in rubbing contact with each other under very high pressures. These pressures may be quite high, as for example,

By F. C. Blake

THE test of the English cupellation furnace should be so supported that the cupeller can change readily the elevation of the test, and at the same time watch the litharge channel. It is also important to raise or lower either side, independently of the other, in me of uneven wear of the side walls or of the breast. If the refined silver is poured from the test, it is much better to control the lowering of the test from the front than to raise the back by screws or a lever. In order to enable the cupeller to manipulate the test with one hand, when the litharge is running, and to pour the refined silver from the test without aid, I have altered the common support to the test, as shown in the accompanying drawing. The common method of supporting the test is by four screws, working in cross-bar nuts beneath the test. The points of the screws set, into the test plate upon which the test rests. These screws are usually worked by pounding or pulling upon the heads, which may be either small pulleys or straight bars, as shown on the back screws in the drawing. The screws are also worked by turning a crank, which is

Jan 1, 1882

By F. C. Blake

THE test of the English Cupellation furnace should be so supported that the cupeller can change readily the elevation of the test, and at the same time watch the litharge channel. It is also important to raise or lower either side, independently of the other, in case of uneven wear of the side walls or of the breast. If the refined silver is poured from the test, it is much better to control the lowering of the test from the front than to raise the back by screws or a lever. In order to. enable the cupeller to manipulate the test with one hand, when the litharge is running, and to pour the refined silver from the test without aid, I have altered the common support to the .test, as shown in the accompanying drawing. The common method of supporting the test is by four screws, working in cross-bar nuts beneath the test. The points of the screws set into the test plate upon which the test rests. These screws are usually worked by pounding or pulling upon the heads, which may be either small pulleys or straight bars, as shown on the back screws in the drawing. The screws are also worked by turning a crank, which is

Jan 1, 1882

By R. J. Lloyd

INTRODUCTION The Mount Isa Mine is a large modern underground mine located in North-Western Queensland, Australia. Two ore types are mined and treated separately. Currently silver-lead-zinc ore is mined at the rate of 2.6 million tonnes per annum and copper ore at the rate of 4.6 million tonnes per annum. The silver-lead-zinc orebodies are mined by sub level open stoping and cut and fill methods whilst all copper ore is extracted by various forms of sub level open stoping. The mining operations are highly mechanised and utilise diesel powered load-haul-dump units of various sizes, two and three boom face drilling jumbos, electric-hydraulic rotary-percussive ring drills, in-the-hole hammer drills, rotary blasthole drills, raiseborers, battery/trolley locomotives, a large fleet of rubber tyred service and supply vehicles plus light rockdrills mounted on airlegs, rail mounted overshot shovels and battery and diesel powered locomotives. All stoping production ore is extracted with diesel powered load-haul-dump units. The ore is tipped into orepasses which connect to the main rail haulage levels. On the haulage levels electric battery/trolley locomotives are used to pull rakes of bottom dump or side dump trucks which feed the ore into primary crushers. Following two stage crushing the ore is conveyed to the shaft and hoistod to surface in bottom dump skips. Each ore stream has its own rail transport system, crushing stations and hoisting shaft feeding separate concentrators. This paper will consider some aspects of the role of equipment and machinery in the growth of the mine, will discuss in some detail the machinery and equipment in use today and will conclude with a look at some possible developments in mining equipment for the future, with particular reference to the Mount Isa Mine. A summary of mining equipment in use at Mount Isa is given in the Appendix. THE PAST Silver-lead-zinc ore was discovered at Mount Isa in 1923 and within a very short time many small mines were being developed. However the rich surface ore traces did not continue and by 1928 Mount Isa Mines Limited had acquired sufficient leases to plan for a large scale mine to exploit the low grade orebodies. At this early stage it was recognised that the mine would need to adopt the most mechanised mining techniques then available in order to overcome its twin disadvantages of low graaes and extreme remoteness. The Company introduced bar mounted drifters and overshot shovels to replace hammer and tap and hand shovelling in development work and by 1930 headings were advancing at the rate of 30 metres per week. In keeping with the concept of mechanisation the early engineers designed the Man and Supply shaft with a very large, for those days, cage compartment measuring 3.8 m x 3.4 m. This shaft was the main means of access into the mine for 36 years until the K57 shaft (now R62 shaft) was commissioned in 1966. Man and Supply is still in regular use. Production commenced in 1931 at an annual rate of approximately 660 000 tonnes of silver-lead-zinc ore. The mine was mechanised to an extent which was previously unknown in Australia; whilst the concentrator, smelter and power house utilised the most modern and efficient equipment available. Even so, the mine was very near to closure on several occasions and did not return a dividend to its shareholders for many years. Production levels remained at or slightly below 660 000 tonnes until a separate copper ore streani and mill was commissioned in 1953, doubling the existing production levels. The first underground crushers were installed at this time. Production rates expanded in the years between 1953 and 1973. By 1960 production reached 2740 000 tonnes of ore. In 1965-66 total production was 3650 000 tonnes and in 1973 the production rate plateaued at the current level.

Jan 1, 1981

By U. N. Bhrany, N. Arbiter

F. C. Bond (Consulting Engineer, Processing Machin-Dept., AllisChalmers Manufacturing Co., Milwaukee) This is a very comprehensive paper. It deals with 1) size distribution functions, 2) energy-particle size relationships, and 3) criteria for grinding efficiency. The method of analysis used consists of tracing the increase and decrease of successive Tyler scale screen fractions as grinding progresses. The treatment is based upon the assumption that the work done in grinding is concentrated entirely upon the coarse size fractions in the mill. It is postulated that when a feed consisting entirely of particles of one size fraction is batch ground that finer fractions increase at a constant rate as grinding progresses, until finally each in turn begins to be ground and to decrease in amount. It is shown that under these conditions the empirical Gates-Gaudin-Schuhmann log-log size distribution plot can be logically explained. It is difficult to imagine any condition of ball mill operation, or any probability analysis, which would result in no grinding contacts on the finer particles present. However, the authors' postulate must be accepted if their conclusions are to be sustained. They conclude that the equation expressing the for mation rate of each size fraction can be resolved into the G.-G.-S. size distribution equation, and that the curvilinear portion of the log-logsize distribution line represents the only particle sizes which are being ground as well as produced. The author's statement that the G.-G.-S. Eq. 4 applies only to the finer portion of the size distribution while the Rosin-Rammler Eq. 6 applies over the whole size distribution range certainly supports the view that an exponential equation of the Rosin-Rammler type corresponds more closely to actual size distribution than does the power law G.-G.-S. equation. However, the G.-G.-S. equation is used to derive Eq. 8 and Eq. 9, which state that the energy required to grind a ton through a particular mesh varies inversely as the particle size to the exponent -a , whic h is the slope of the extended G.-G.-S straight line. This is stated to apply to both batch and continuous grinding. The G.-G.-S. slope exponent thus becomes very important in all crushing and grinding analyses by this method. The authors include some data which can be used to test their conclusions, as described below: We will consider grinding a feed composed of 14 mesh (1190u) to -200 mesh (74u). The average of 17 Allis-Chalmers grindability tests on quartz gives a work index (Wi) of 12.77. The -200 mesh product should have 80 pct passing 41.6u or P = 41.6. The equivalent 80 pct passing size of the 14 mesh feed particles is considered to be the particle diameter, as is true for spherical particles. Thus F is 1190u. In the work index equation 10 wi 10 wi 127.7 127.7 P f 41.6 1190 = 16.1 kw-hrperton. In Table I the ball mill exponent for quartz is 1.0 and from Eqs. 9 and 10: w=kw-hr/ton =Constan/(do/di) = 16.1 ton so that (1190) Constant/ Constant and the Constant equals 259. The tons per horsepower-hour value is 0.0464, in agreement with Table IV. The exponents for other minerals are listed in Tabl e 11. In Table IIA, the kilowatt hours per ton required to grind these minerals between the same sizes as the quartz, both by the authors' method and the work index equation, are listed. According to the authors kw-hrperton = 259/(16.1)".

Jan 1, 1961

By Louis A. Panek

THE purpose of this paper is to present a method of designing safe and economical arch structures that are to be constructed of concrete or directly of original earth materials. The experimental data used to illustrate the design method are taken from Bucky and Fentress,1,2 and the application of the ideas presented by them is extended by obtaining an additional set of curves from which arch structures may be designed. This design method is based upon the following principles of similitude: A scalar model made of the same material as that of the full sized structure will behave similarly to its prototype if the density of the model is increased in the same proportion as its linear scale is decreased. Let R represent the scale or model ratio, namely, the ratio of a prototype linear dimension to the corresponding model linear dimension. The effect of increased density may be obtained by rotating the model in a centrifuge at a speed such that the centrifugal field exerts on the model an accelerative force R times the accelerative force of gravity. Under these conditions; (I) model unit stresses are equal to corresponding prototype unit stresses, (2) the ratio of the prototype deformation at a given point to the model deformation at a similar point is equal to the scale ratio, R, and (3) the model and the prototype will behave similarly within and beyond the elastic limits of strain. According to the above relations, such models can be used to solve the following problems: I. The dimensions of the most economical safe arch structure for a given load. 2. The maximum safe roof span underground for given geologic conditions. The procedure is described briefly as follows. Tests are made by rotating in a centrifuge a number of models that repIesent a variety of prototype loads and dimensions. From the experimental data, curves are plotted to show the relations between these loads and dimensions. The curves are used to solve directly the problems stated above. Structural design is based upon the working (safe) stress of the material of construction, which is established by applying a factor of safety to the experimentally determined ultimate strength of the material. In conformity with this principle, each model is gradually loaded until failure occurs. A safety factor is then applied to the results. If a safety factor of 4 is used, a given model at failure represents a safe prototype, the linear dimensions of which are equal to one-fourth the model ratio at failure times the corresponding model dimensions. The safe model ratio is computed from the following formula: [Safe R = (rl 47r2n2r _ 7r2n2r~r~ \4/ gg in which: n = centrifuge revolutions per second at model failure; r = radius of rotation of the model in feet; g = 32.2 ft/sect.]

Jan 1, 1947

By B. G. Reisdorf

This paper describes the microstructural changes that occur when quenched ultrahigh-strength steels containing OA pet C and various amounts of nickel, silicon, and cobalt are tempered. The changes that occur in hardness, yield strength, and martensite diffraction-peak widths when these steels are tempered are related to the precipitation of the carbide phases. An unea$ectedly high silicon content (about 30 pct) was found in the E -carbide phase in a steel containing only 1.5 pct Si. TEMPERED martensitic steels have such wide-spread utility that they have been the subject of numerous investigations, and a sizable amount of literature has developed on this subject.M This investigation, which is a part of a larger program to correlate microstructure with mechanical properties at a variety of strength levels, is limited to the microstructural changes that occur when a quenched 0.40 pct carbon steel (USS Airsteel X-200 steel) is tempered, and to the effects of the alloying elements—nickel, cobalt, and silicon—on these microstructures. Used in this investigation were electron microscopy, electron-diffraction identification of the carbide phases, electron-probe micro-analysis of the carbides, X-ray determinations of retained austenite, and measurements of martensite X-ray diffract ion-peak widths. MATERIALS AND METHODS The chemical analyses of the eight heats examined eats No. 30 through 37) are shown in Table L Heat No. 30 has the chemical com~osition of Airsteel X-200, and the remaining seven heats contain various amounts of nickel, chromium, cobalt, and silicon. The heats were air-melted in an induction furnace and cast into 8 by 8 in. ingots that were subsequently heated to 2300 and rolled to 1-in.-thick plate. Oversize 0.505-in.-diam tensile specimens were rough-machined from the plates and austenitized in air at 1700° F for half an hour and oil-quenched. The specimens were then tempered in air at temperatures of 400° to 1000 for tempering times of 1, 4, and 16 hr, and finish-machined to 0.505-in.-diam tensile specimens. Electron micrographs were prepared from Formvar replicas of the midthickness of tensile-specimen shanks that had been electrolytically polished and etched in nital. Electron-diffraction patterns were obtained from carbon-extraction replicas. The replicas were prepared by etching the sample surface in the same manner as for microscopy, evaporating carbon on the etched surface, and re-etching the sample to free the carbon film and the precipitate particles. Electron-probe microanalysis was performed on some of the extraction replicas. To obtain adequate fluorescent X-ray intensities, several thicknesses of replica were exposed to the electron beam so that the results represent an average composition of the extracted particles rather than an analysis of single precipitate particles. The retained austenite contents of the specimens were determined by an empirical X-ray diffraction

Jan 1, 1963

By M. J. Pool, P. J. Spencer, R. V. Miner

The partial molar heat of solution of rhodiunz in liquid lin and Rh-Sn alloys has been measured as a function of rhodium concentration at 700" , 725" , 750" , and 775°K. The values at infinite dilution are very exo thermic, ranging from -29,950 to -28,260 cal per g-atom Rh at 700" and 775"K, respectively. At the solubility limit the heat of solution becomes sharply nzore exothermic and has permitted the liquidus boundary to be accurately established at each temperature. From the measurements in the two-phase region of liquid Plus RhSn, the heat of formation of RhSn,has been determined. A large increase in the heat of formation between 725" and 750°K suggests the possibility of a phase transformation in this compound. V ERY few measurements have been made of the heats of solution of transition metals in liquid tin; yet those values that are available are of great interest because of their very large exothermic nature. For example, the heat of solution at infinite dilution of palladium in tin has been measured as about -26,000 cal per g-atom (625" to 800°~),' while the heat of solution at infinite dilution of platinum is even more exothermic at -28,591 cal per g-atom (914°K).' These values are of the same order of magnitude as the heat of formation of many intermetallic compounds and as such clearly indicate that very strong bonding must exist between the solute and tin atoms in the liquid solutions. Rhodium might be expected to display similar solution characteristics in tin in view of its close electronic resemblance to palladium and platinum. Since no thermodynamic data are available for Rh-Sn alloys, rhodium was chosen as an appropriate solute for further investigation of transition-metal systems with highly exothermic heats of solution at infinite dilution. EXPERIMENTAL The heat of solution of rhodium in dilute Rh-Sn liquid solutions was measured as a functlon of rhodium concentration at 700°, 725", 750°, and 775°K. The liquid-metal solution calorimeter used in this work has been fully described elsewhere. At the start of each series of measurements, the solvent bath consisted of about 0.5 g-atoms of 99.9+ pct pure tin. To this was made a number of small rhodium additions, about 0.0005 g-atoms each, and the heat of solution was measured for each. Rhodium of 99.9+ pct purity in powder form was used in order to promote rapid dissolution in the liquid tin. The powder specimens were contained in tin foil stated to be purified (lead-free). This foil was found to have no measurable heat of solution in pure tin so the effect of any impurities could be neglected. The energy equivalent of the calorimeter was experi- mentally determined by dropping tungsten and/or tin specimens at intervals during each series of rhodium drops. The tungsten and tin used were 99.95 and 99.999+ pct pure, respectively. The only heat effect due to a tungsten drop, or a tin drop at low rhodium concentrations in the bath, is the sensible heat of the specimen. The heat content of these materials is well-established and is presented in the compilation of Hultgren et al. 4 As the rhodium concentration in the tin bath increases a small heat effect arises from the reaction: Sn (liquid, T) — & (soln, T) where T is the temperature of the tin bath. Where necessary, this heat of solution of tin was determined by Gibbs-Duhem integration, and corrections were made to the heat effect of the tin calibration specimens and the tin foil containing the rhodium specimens. RESULTS AND DISCUSSION The calculated values of the heat of solution of rhodium in dilute Rh-Sn alloys as a function of composition are shown graphically in Fig. 1. The values have been corrected for the sensible heat of the specimens, initially at 273"K, and apply to the reaction:

Jan 1, 1969

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'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 ?'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# ' 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'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's vanish. Eq 3 also reduces to Eq 1 when the E'S are all equal. Shockley and Read' 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 F. Gordon Smith

ALTHOUGH several geological indicators of the critical type are known, including quartz inversions and decomposition of hydrous minerals such as serpentine, there are very few of the general type. Solid solutions are excepted, but the limitations of use are very restricted and interpretations are sometimes ambiguous. General methods for determining temperature and pressure conditions during the crystallization of minerals would have considerable scientific and economic value. It is not the purpose of this paper .to, discuss the various methods of geological thermometry and barometry, but to present one general method, applicable to all minerals, and to describe what progress has been made in the methods of measurement. The general method, in. brief, is a study of the stress conditions in and around various types of foreign inclusions which are trapped in minerals during growth. The method depends upon the fact that any homogeneous gas, liquid, or solid will in general have coefficients of thermal expansion and volume compressibility different from those of any given mineral. Therefore stress must develop in and around all types of inclusions in minerals if the temperature or the pressure, or both, are changed from the conditions which prevailed during the growth of the mineral. The methods of measurement consist of determinations of the temperature-pressure conditions of fit of the inclusions in the host mineral. The types of inclusions in minerals are: 1-gas, or liquid plus vapor, when observed at room temperature, due to crystallization under pneumatolytic conditions; 2-liquid, or liquid plus vapor when observed at room temperature, due to crystallization under hydrothermal conditions; 3-glassy solid, or devitrified glass, due to crystallization under magmatic or high temperature metamorphic conditions, in a siliceous liquid; and 4-crystals, due to overgrowth of other minerals crystallizing simultaneously or of other minerals which crystallized previously. A survey of the literature shows that much valuable earlier work on inclusions, especially that carried out in England in the last century, has dropped out of current knowledge. The following is a brief summary of the significant, contributions to the problem up to the present day. Davy in 1822 asserted that fluid inclusions in minerals consist of an aqueous solution of salts and a gas bubble, the whole being either at lower or higher pressure than atmospheric.1 At intervals from 1823 to 1862, Brewster contributed information concerning other types of inclusion consisting of 1-aqueous solution, a much more expansible liquid, and a gas; 2-aqueous solution, salt crystals, and a gas; and 3-the very expansible liquid and a gas. The very expansible liquid fills the gas space between 20° and 30°C. Compression strain effects were seen around inclusions in diamond, topaz, and other minerals.2-6 Sorby in 1858 and 1869 further advanced the study begun by Davy, stating that fluid inclusions represent a sample of the mother liquor of crystallization and that the degree of filling of aqueous inclusions at room temperature defines the temperature-pressure relations during formation of the host. The degree of filling may be measured by determining the minimum temperature of filling of the inclusion by the liquid phase. The very expansible liquid in some fluid inclusions is liquid. carbon dioxide. The temperature at which salt crystals in fluid inclusions completely dissolve in the fluid is the minimum temperature of formation. Inclusions of glass or devitrified glass indicate crystallization from a melt. Inclusions of crystals in minerals are often centers of strain, which may be seen by optical effects or by radial tension cracks. Sorby realized that an analysis of stress-strain relations about inclusions could be used to provide precise data on the temperature of crystallization, but the matter was never pursued.7,8 Hartley (1876, 1877),9,10 Hawes (1881),11 Wright (1881),12 Johnsen (1920),13 and Holden (1925)14

Jan 1, 1952