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By R. Lagneborg

WhEN mechanical twins initiate cracking it has been proposed1 that the friction stress for dislocation motion, in the Cottrell criterion for brittle fracture2 should be replaced by the stress required to propagate a twin, ttp. TF is the fracture stress, d the grain diameter, ß a geometric constant, u shear modulus, and y the effective surface energy. Since TTp is likely to vary with grain size, it cannot be substituted by a constant in Eq. [I]. If an expression for the energy change caused by a twin in a stressed material could be obtained, it is in principle possible to compute the critical size of the twin, i.e., the size at which the system can decrease its energy spontaneously, as a function of applied stress, thus giving the stress required to just barely propagate the twin, i.e., TTP. Consider a circular twin disc with a radius r and having a lenticular cross section, Fig. 1. Twin dislocations3 of strength b exist in the twin boundary parallel to the twin plane, one loop on each atomic plane. Assume that the total numbers of loops, n, can be replaced by one circular loop of a multiple dislocation, nb with a radius r. The energy change of the system, AW, due to such a twin in an applied stress field can then be calculated: The first term is the total twin surface energy, the second the elastic energy due to the twin dislocations, and the third the energy released by the twin in the applied stress field. yt is the twin boundary energy, r, the radius of the dislocation core, and T the applied

Jan 1, 1968

The use of the verb in this mood is not as common as formerly: at the time, for example, when the Bible was translated and the plays of Shakespeare were written. Nevertheless it is an essential part of literary English. In editing the 'Mining and Scientific Press' I do not insist upon the use of the subjunctive in articles that are contributed from the outside, but it is deemed proper in all our editorial writing. To speak plainly, the subjunctive is a mark of scholarship; it is ignored by those that are not particular in such matters, and unfortunately it is a source of perplexity to many that are entirely unfamiliar with the use of it. Therefore, as an editor, I think it well to allow the indicative mood to be used by contributors in sentences in which, to be strictly correct, the verbs should be in the subjunctive mood. The fact that most subjunctives are indistinguishable in form from indicatives is another cause of trouble to the uninitiated.* For example, the verbs in such phrases as "Suffice it to say", '(So help me God ", and "God save the King" are in the subjunctive. One reason why the subjunctive is becoming uncommon is the growing habit of expressing the subjunctive meaning by aid of auxiliary verbs that are coupled with the infinitive; thus: "It will sate to say" and "May God save the King". The subjunctive is common in subordinate clauses, and that is how it obtained its name, 'subjunctive', meaning

Jan 1, 1931

By William E. Harris

Time and experience have demonstrated that by means of the Waelz process zinc, lead, cadmium, arsenic, antimony, bismuth and tin can be volatilized satisfactorily. In this way difficult gold ores are being treated to allow for the recovery of the precious metal. Iron ore containing zinc is being treated to remove the zinc and recover the iron. In Germany, thallium is being recovered in commercial quantities from the zinc oxide fume; indium, germanium and gallium are also concentrated to a degree warranting recovery, even though these rare metals are only recognizable in the ore by means of the spectroscope. The physical, chemical or mineralogical condition of the raw material affects very little the applicability of the process. The name Waelz is derived from the German word Waelzen, meaning a "trundling motion," which very aptly describes the movement of the charge through the slowly rotating kiln. The recovery of zinc and lead by volatilization in a rotary kiln has its origin in a process patented in 1910 by Edward Dedolph, of British Columbia. The Dedolph patent was taken over by the Metallgesell-schaft of Frankfurt-on-Main, Germany, which in cooperation with the Griesheim-Elektron, now a part of a large industrial combine, introduced certain improvements (Ohlmer, Specketer patents), but without bringing the process to a state suitable for large-scale operations. The war temporarily stopped all work on the process, and it was not until after the war that the Krupp Grusonwerk, of Magdeburg-Buckau, Germany, quite independently of the Metallgesellschaft, instituted research work in this field of metallurgy, which in 1923 led to the Waelz process proper. The Krupp Grusonwerk and the Metallgesellschaft A.G. later on collaborated, and by their joint efforts further developed and perfected the Waelz process, which they are marketing together as "Waelz-Gemeinschaft." The process is capable of treating a varied type of material; for instance, oxidized and sulphide zinc ores, calamine (zinc carbonate ore) waste dumps, jig tailings, jig slimes, table concentrate slimes, brass ashes, zinc-bearing iron ores (where the iron sinter is the real objective and the zinc oxide a by-product), electrolytic-zinc leach residues, zinc muffle residues and works sweepings, lead-furnace slags, tin ores and slags, anti-

Jan 1, 1937

By J. M. Clark

For some years past, those interested in the development of the increasingly important mining industry of Canada, havc urged the adoptioi~ by the Dominion Parliament of a federal mining-law, which would have the force and stability of statutory enactment. At present, placer-mining in the Yukon Territory is governed by the Yukon Placer Mining Act. All other mining under federal jurisdiction is governed by Orders in Council and Ministerial Iiegulations. In the earlier stages of development, it is perhaps a matter of neces~ity that these important matters should be so dealt with; but it is now felt that the time has come when mining-rights in the extensive regions under federal control should be put on a permanent basis, and that any changes required from timc to time should be made only after full and open discu~sioii in Parliament. A short sketch will suffice to indicate how vast and varied the interests affected really are. When the Dominion of Canada mas constituted by the Inlperial Statute known as the British North America Act of 1867 (which into force by proclamation on July 1 of that year), it comprised only the present Provinces of Ontario, Quebec, Nora Scotia, and New Brunswick; but provision was made for the inclusion of Newfoundland, Prince Edward Island, British Columbia, Rupert's Land, and the North West Territories. Subsequently Rupert's Land and the North West Territories were acquired, the Crown Colonies of British Columbia and

Jan 1, 1912

By R. B. Sosman, J. C. Hostetter

It is well known that ferric oxide, Fe2O3, is paramagnetic, while magnetite, Fe3o4, is classed among the highly ferromagnetic substances. But magnetic data on oxides intermediate in composition between Fe2o3 and Fe3O4 have been almost completely lacking. Fe2O3 and Fe3O4 form a solid-solution series, according to present evidence.' In this series the properties change continuously from Fe2O3 toward Fe3O4, as the percentage of FeO increases from zero toward 31.03, which is the percentage in magnetite. It is possible that there is a break in the series near Fe3O4, but it has not yet been possible to establish the existence of such a break experimentally. The occurrence of solid solution in this series is shown by the dissociation pressure, or oxygen pressure in equilibrium with the oxides, which falls continuously over the range from Fe2O3 to Fe3O4. The oxygen-pressure curves at 1100" and 1200" are shown in Fig. 1. The existence of solid solution is also demonstrated by the continuous change in optical properties from Fe2O3 over to a composition containing about 18 per cent. FeO, at which point the opacity of the oxide becomes so great that it is impossible to obtain measurements at higher percentages of ferrous iron. Natural oxides of iron intermediate in composition between Fe2O3 and Fe3O4 are much more common than is generally supposed. If a mineral oxide is not strongly attracted by a small hand magnet and if it gives a red streak, it is usually labeled "hematite." If it is strongly attracted by the hand magnet it is usually labeled "magnetite" without further tests. As we shall show later, oxides containing from 1 up to 31 per cent. FeO can be thus erroneously lumped together as "magnetite." It is a fact, nevertheless, that the great bulk of natural oxides of iron lie fairly near either Fe2O3 or Fe3O4 in composition. The reason will be

Jan 1, 1918

By A. D. Dorenfeld

Factorial design is a mathematical method of drawing valid conclusions from a series of tests made in a predetermined pattern. It is applied to flotation ore testing using, in this case, five variables, each varied twice, requiring a total of 32 tests. Representative conclusions are checked by repeat testing. THE factorial design method of testing is particu-J- larly applicable to mill-scale plant tests because 1—the conclusions take into consideration all variabilities of the plant, 2—there are no subjective guesses as to the conclusions, 3—the number of tests necessary to check large numbers of variables are at a minimum, and 4—interactions between variables can be discerned. It is equally applicable to laboratory testing because once the variables to be investigated have been decided upon, as well as the number of levels for each variable, a well-trained assistant can run the tests, since the test work follows a predetermined mathematical pattern, leaving the conclusions to be found by the person in charge. The conclusion takes into consideration all errors of the tests. To illustrate the use of factorial design, a sample of copper porphyry ore was tested, the copper content of the batches not being uniform. Five variables were investigated, each at two levels, requiring only 32 tests. After suitable arithmetical analysis, conclusions for copper recovery and concentrate grade are arrived at. Four cases of these conclusions are checked by repeat testing. Testing Methods Reproducibility of flotation tests varies widely, depending on the experimenter, the process, the equipment, and probably a host of unknown and perhaps interacting variables. If the reproducibility of tests is good, let us say to 0.2 pct recovery of a certain metal, and the minimum difference between tests upon the variation of the interested variables is, say 1 pct, then simple averaging and inspection is ample in interpreting results. However, often such a happy situation is not the case. This is particularly true in mill-scale operations where the ores are variable, and a host of minor operating fluctuations common to most milling, and familiar to all mill operators, is the normal state of affairs. Yet, mill scale tests are run, the results averaged, and conclusions drawn therefrom. The trustworthiness of such results should be measured by comparison to the experimental error—the measure of the degree of reproducibility of the results. This comparison is a test of significance. Thus, if daily results of recoveries average 80.0 pct, and a spread of 78.0 pct to 82.0 pct, is recorded, then, clearly, on changing mill operations, an 81 pct recovery cannot be construed as significant by using averages, since it is well within the previous test limits. By using rigorous statistical tests of significance, conclusions arrived at by inspection or simple averaging may be shown to be based on inadequate evidence or even wrong. In any event, a plant super-

Jan 1, 1952

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

Taking the Long View THE present international situation has serious implications for this nation. The possibility of total war is no more appalling than the threat of making the United States permanently into an armed camp. A period of ten years under such conditions could mean a Communist victory without firing a shot-if the present trend toward statism is allowed to continue. As individual citizens and as members of the mining profession we have the power to oppose the march toward socialism. We must not adopt shortsighted policies dictated by self-interest, but must endeavor to size up the situation as a whole and act according to what will be best in the national interest. The economic picture for the metal mining industry under present emergency conditions is apparently bright. Demand for metals exceeds supply. But there is danger that fluctuating prices will bring Government regulation. Care must be exercised in our pricing policies, or the calamity of Government intervention will be inevitable. President Truman's "loophole" reference to percentage depletion early in the year caused a brief flurry of excitement, but now that the immediate threat is over the industry has lapsed into sommolence on this subject. Special tax privileges accorded the mining industry because of inherent risks should be guarded by a continuing propaganda campaign to educate Congress and the public. If this is not done we may find ourselves losing the necessary tax protection which we now possess by a capricious act of legislation. Stockpiling minerals from abroad certainly lengthens the life of our own mineral resources. The present consumer demand for the base metals indicates foreign sources of supply for stockpiling. However, this is only one facet of the problem. For strategic military reasons it is necessary that the United States have quick sources of all minerals within our national boundaries. Undeveloped mineral deposits do not meet this need so that where it is possible to encourage our own mineral development by stockpile purchases, it should be done. A need exists for an overall controlling agency that would make purchases for the stockpile according to military necessity, current metal market conditions, and so as to strengthen the mining industry. In the course of the history of the United States we have been engulfed in several wars by the necessity of protecting our economic rights abroad trading privileges-and also because of moral obligations. Disregarding the moral side, it is difficult to reconcile fighting wars to protect world freedom of trade when in peacetime we attempt to restrain such trade by tariff barriers. When it comes to accepting subsidies from the Government in one form or another it is difficult to overlook the immediate personal gains and see in the future that where the Government lays out capital it becomes a partner in the business and not a silent one. It is apparent that hope for the traditional American way of life cannot be bought without some self-sacrifice; and we cannot wait for the other fellow to start it because it is the responsibility of each individual citizen. By taking the long view our course should be apparent and not diverge sharply from our own personal benefit.

Jan 10, 1950

IT has been discovered by skilled bell founders, more through experience than from geometrical calculation (although calculation does enter), that a certain relationship of dimensions in both large and small bells makes the tone and the weight almost certainly what is desired. This is in addition to the customary shape which is, according to the historians, perhaps that found by the first discoverers of bells. Among themselves bell founders have made a rule of these measurements and have called it the bell scale. Beginning with the small ones weighing ten pounds, it increases by degrees to a point where, as I have seen, they are able to make them even twenty-five and thirty thousand pounds. This scale is of great enlightenment if one does not have a bell already made for comparison.

Jan 1, 1942

By L. J. Klinkenberg

It is pointed out that the current concept of pore size distribution is not unequivocally defined and that different methods aiming at a determination of such a distribution therefore do not lead to the same results. A pore size distribution should not be based on the idea that a core should, under all circumstances, behave as a bundle of straight non-interconnected capillaries of the same pore size distribution. This is illustrated by calculations and experiments on the displacement of miscible liquids. INTRODUCTION The introduction of the concept of pore size distribution has been an attempt to characterize the intricate geometry of the flow channels in porous media. As pores in a porous medium are interconnected it is impossible to describe exactly what is meant by a "pore" and, therefore, the term pore size distribution requires further amplification. In the visual method for the determination of pore size distribution "the pore" is considered to be the hole between the grains as observed on thin sections or on a polished surface of the rock under a microscope. In all other presently known methods,1,2 a displacement process is studied and it is ascertained what as- semblaae of straight cylindrical capillaries would show the same behavior. The distribution of the capillary diameters of this assemblage is said to represent the size distribution of the pores of the actual porous medium. From the foregoing it is already apparent that it is useless to try to decide which process or which method of investigation leads to a "correct" pore size distribution. To illustrate this further a displacement process in which a fluid is displaced by another miscible with it will be discussed and the results will be interpreted in terms of a pore size distribution. DISPLACEMENT EXPERIMENTS WITH MISCIBLE LIQUIDS OF NEARLY IDENTICAL VISCOSITY AND DENSITY Interpretation in the Form of a Pore Size Distribution If distilled water is displaced from a homogeneous unconsolidated sand pack by, for instance, a dilute solution of NaCI, the breakthrough recovery i.e., the amount of distilled water produced at the moment the first trace of NaCl can be detected in the effluent water, is between 95 and 100 per cent of the pore volume of the pack. This result can be understood by following in imagination the course of one particle of the liquid. Imagine a length, ?l, at the end of which a liquid particle has an independent chance of a renewed choice of pores of different diameters. In other words, the particle has a choice of traveling time, at, for any length ?l; instead

Jan 1, 1958

By Norbert R. Morgenstern

INTRODUCTION An understanding of the role of water in controlling the stability of rock masses is central for a rational approach to the subject. The presence of water can hinder mining opera- tions in two ways: 1. excessive discharge 2. excessive pressure It should be noted that if the rock mass is very tight, excessive pressures can exist without large discharges. Alternatively, if abundant water is available and the rock mass is open, then substantial discharges can occur under quite small pressures. The problems associated with excessive discharge are usually well understood by the mining engineer. Vehicle mobility is inhibited, some areas are flooded and hence become inaccessible; at best, a costly nuisance exists. The methods of solving these problems are also well-known to mining engineers. They generally involve tapping the source of the excessive discharge and channeling it away in such a manner that any hindrance to the mining operation is minimized. The effects of water pressure on the stability of rock masses are less obvious and the following will be devoted solely to this aspect of the problem. The manner in which water pressures enter into the consideration of stability is made clear by an understanding of the concept of effective stress. THE CONCEPT OF EFFECTIVE STRESS The simplest mechanical model for the problem of rock slope stability consists of a rough, rigid block sliding down an inclined plane under the influence of gravity. This is illustrated in [Fig. 1]. The down-slope component of the weight of the block tends to produce movement which is resisted by the shearing force generated by friction along the base of the block. The shear stress per unit area inducing movement is

Jan 1, 1971

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Will H. Coghill, Fred D. DeVaney, R. G. O’Meara

The size of ball mills in the ore-dressing industry has increased from about 4 ft. in each dimension to 10.5 ft. in diameter by 8 ft. in length. In the cement industry they are as long as 45 ft. Plainly the trend has been toward larger mills. The common belief is that the big mills economize in floor space and first cost, but the advantage with respect to friction has not been clearly defined. In the ball-mill studies at Rolla, Mo., laboratory mills as small as 2 by 2 ft. have been found as efficient in terms of the amount of grinding per unit of net power as mills 6 by 4 or 6 by 12 ft. Therefore, if supremacy can be claimed for the big mills, advantage must come from other sources. The advantage to be considered here is reduced loss by friction or dead load. In the study to determine whether big mills have relatively less loss by friction the commercial catalogs were used for fundamental figures. The dimensions and weights of Table 1 are taken from the catalogs (the last line gives data on a Rolla laboratory mill). The net power—that is, the power expended within the mill for grinding—is calculated by a new formula.' The assumed speeds are each at 70 per cent of their theoretical critical speeds, and the mills are loaded to the center with balls. In other words, they are assumed to be working under analogous conditions and are set for good grinding. In the last column the ratio B: A shows that the larger commercial mills are lighter per unit of net power than the smaller mills, and more of the motor output should therefore go into grinding. The laboratory mill seems to have some advantage over the larger mills; it would be expected to be light because it has no liners.

Jan 1, 1935

By G. L. Oldright, F. S. Wartman, H. E. Keyes

The economic manufacture of sulfuric acid by the ordinary chamber process usually involves production on a large scale and a plant that is costly to construct. The nature of sulfuric acid makes it costly to transport any great distance. For these reasons, the metallurgist has not found it feasible, at times, to beneficiate ores amenable to leaching, and a need exists for a local process that will produce acid cheaply on a small or large scale. To leach ores containing residual sulfides, an oxidizer, such as ferric sulfate, is needed in solution. Precipitation with scrap iron is one of the cheapest methods of removing some metals from solution, giving a plant of low first cost and supplying a source of cheap ferrous sulfate. The other ingredient needed for the process is SO2 roaster gas, the addition of which, as described below, will give both ferric sulfate and sulfuric acid. Where roaster gas is a waste or obnoxious product, the expense for materials is still further lessened. The use of ferric sulfate and sulfuric acid as a solvent lends itself well to the utilization of scrap iron as a precipitant, and the stages of the process fit in well together as an economic whole. Applications The hydrometallurgist usually thinks of ferric sulfate as a partial solvent for some of the sulfides of copper alone, as most work has been done on this metal. The processes of Hannay and Christensen, for leaching unroasted galena with ferric chloride made by anodic oxidation, show the added solvent action given by "ic" salts when added to brine solutions. It was found by R. D. Bradford (in some work to be published soon by the University of Utah) that, by the addition of a ferric salt to a brine solution, the silver as well as the lead in an unroasted semi-oxidized ore could be largely dissolved. The "ic" salt in the case of silver has evidently the same effect as the case of cupric sulfate when

Jan 1, 1926

By Albert Hill Fay

In giving a sketch of the geology and mining of the tin-deposits of Cape Prince of Wales, a short description of the geographic and climatic conditions may be of special interest on account of this being a part of the world of which very little is known, even by the reading public. As shown in Fig. 1, the location of the Cape is lat. N 65° 35' and long. W. 168o. It is bounded on the north by the Arctic ocean ; on the west by Bering strait and on the south by Bering sea. It is the Westernmost point of the mainland of North America, and to the west, across the strait, one can see East Cape, Siberia, which consists of a rugged, steep coast of granite cliffs. The climatic conditions arc of interest because of the part they have had in the surface geology, and also because they affect mining from an economic standpoint. In connection with the climate and geography, it does not seem out of place here to quote a few lines from the prologue of The Wandering Jew, written by Eugene Sue, under the caption " The Land's End of Two Worlds." "The Arctic Ocean encircles with a belt of eternal ice, the desert confines of Siberia and North America—the uttermost limits of the Old and New World, separated by the narrow channel known as Bering's Straits. " To the north, this desert is bounded by a ragged const, bristling with huge black rocks. At the base of this Titanic mass lies enchained the petrified ocean (Bering sea) whose spell-bound waves appear fixed as vast ranges of ice mountains, their blue peaks fading away in the far-off frost-smoke, or snow-vapor. " Between the twin peak* of East Cape, the termination of Siberia, the sullen sea is Been to drive tall icebergs across a stream of dead green. There lies Bering's Strait. Opposite, and towering over the channel, rise the granite masses of Cape Prince of Wales, the headland of North America. "These lonely latitudes do not belong to the habitable world."

Jan 1, 1908

By R. W. Raymond

THE question, what is the best proportion among weight, fall, and speed of stamps, is one which has not yet received thorough and systematic examination. In considering the economical application of stamping machinery, we meet, at the beginning, with serious difficulties in obtaining accurate data for comparison. The weight and fall of stamps vary as the shoes and dies wear out; and this may lead to a change of speed also. Moreover, defects in engines, boilers, or machinery for the transmission of power, may occasion serious losses, which cannot fairly be charged to the arrangements of the stamps proper. Again, the capacity of stamp-mills is directly dependent, in some degree, upon the nature and extent of discharge, fineness of screens, and other peculiarities of the battery. Finally, the hardness and tenacity of the rock crushed varies so much that comparisons between different localities cannot be implicitly trusted. The safest experiments are those made in the same mill, by changing first one and then another condition of working; but this is seldom possible for such conditions as weight and lift of stamps, and only within narrow limits for their speed. We may eliminate of friction, transmission, and generation of power, in the case of stamps, by measuring the power actually developed by their fall. Thus, the weight, multiplied into the fall in feet, and the number of drops per minute, gives us exactly the number of foot-pounds exerted by each stamp. Dividing by 33,000, the number of foot-pounds per minute in one-horse power, we have the horse-power per stamp, from which the effective power of the whole mill may be obtained. Dividing the amount of rock crushed daily by the effective horse-power, gives us the daily amount per horse-power ; and this is the best measure that can be obtained for the effectiveness of the stamps. A complete discussion of the subject would require us to determine the exact influence of the discharge, etc., and the exact resistance offered by different classes of rocks, for both of which points the data are wanting. Professor J. D. Hague, in the third volume of the United States Geological Exploration of the Fortieth Parallel, gives a valuable

By M. P. Boss

Of the two methods of mechanical reduction—that of percussion and that of abrasion—it is not easy to say which was first employed by primeval man. The stone hammer and the flat or hollowed stone used for grinding are found together in the remains of prehistoric periods. But the use of the maray, or bucking-stone, developed from the hammer, was probably introduced later than that of crude millstones. Diodorus Siculus, the Roman historian of the first century B. c., mentions such millstones as used in the mines of Egypt to pulverize material which had been previously broken in a mortar. The invention of the arrastra for fine grinding is declared by some authorities to have been made by Bartolomeo de Medina, at Pachuca, Mexico, about A. D. 1557—which is quite probable. Being the first to amalgamate silver on anything like a business scale, he must have felt the necessity for oregrinding apparatus of greater capacity than the old primitive millstones; and the arrastra was thus the natural successor of the millstone. It is very unfortunate that the archives of Pachuca, which has made so much history in ore-treatment, were destroyed in some one of the many insurrections for which, also, the place is renowned. The first application of the stamp to the crushing of rock is asserted by some writers to have been the invention of a Saxon nobleman named Von Maltitz, about the year 1505. Better authenticated reference, however, is made to one Paul Gronstetter, a native of Schwarz, and called an ingenious worker, who, in the year 1519, established at Joachimsthal a process of wet stamping and sifting. Two years later, a larger plant was established at the came place. It is said that he had previously introduced the same device at Schneeberg. How much of the invention was due to Gronstetter is not certain;

Jan 1, 1902

The negative charges on diaphragms of quartz, tungstic oxides, stannic acid, acid dyestuffs, soaps, and glass have for a number of years been explained on the basis of chemical equilibria—a hydrogen ion or light metal ion passes into solution leaving the solid complex ion negatively charged. While there are a number of observations which indicate a proportionality between the ( potential and the streaming potential it should be recognized that all the experimental evidence thus far presented shows that if hydrogen ion concentration is kept at a constant value, electrokinetic phenomena are influenced by salts. The multivalent ions exert the greatest effect on the reduction of osmotic flow. In the interpretation of all electrokinetic data the assumption is made that the potential of the solid remains constant. That this is not true is evidenced by the values of [ potential for quartz in contact with conductivity water as reported by the several investigators and by the authors of this paper. It is apparent that the nonreproducibility of surfaces will always prevent the obtaining of exactly comparable data. At best the experimental technique described depends on a theory which is capable only of showing a trend—another quartz surface should exhibit similar but not identical potential curves. It seems entirely reasonable to assume that the negatively charged laurate ions should have little or no attraction for a negatively charged quartz surface. The weight of previous experience in selection of flotation activators points unerringly to the usefulness of the multivalent metallic ions. The primary reason why the divalent barium ion is not available to two negative charges on the quartz surface might easily be that of distance between such adjacent negative charges. Otherwise activation could not occur, and the quartz could not assume the remaining unit positive charge of the barium ion. For this case no electrical double layer theory seems necessary. Clearly this is, at the negatively charged quartz surface, a case of partial chemisorption of the cationically divalent barium ion followed by the anionic neutralization of the remaining cationic charge by the freely moving laurate ion. It is hoped that the authors will continue with this interesting technique and that their results will continue to indicate trendwise what is known about the

Jan 1, 1957

By Yap Chu-Phay

IN the previous paper, the writer showed how, on the basis of thermodynamic reasoning, it seems probable that when true equilibrium conditions obtain, carbon exists as Fe3C in the liquid state and as elementary carbon in the solid state (7 Fe), in which case the solidus would be a straight line from 0.18 to 1.70 per cent. carbon (Fig. 1). In the same paper he concluded that the solidus obtained by Honda 'and his co-workers1 probably does not represent the same conditions, insuring a complete equilibrium. Except for a downward temperature displacement, the solidus obtained by Gutowsky,2 using the Heycock and Neville method, practically coincides with Honda's solidus as shown in Fig. 1. The writer at first thought that perhaps in some way Gutowsky's thermocouple was improperly calibrated for high-temperature measurements, as his liquidus was also much lower than those obtained by Carpenter and Keeling3 and by Ruer and Goerens.4 However, the eutectic temperature obtained by Gutowsky agrees with the generally accepted value of 1130° C., so that the validity of the inference regarding improper temperature calibrations is to be strongly doubted. In Fig. 1, Gutowsky's solidus is shown both in the original and in the corrected form. In the latter, a correction of 29.2° C. is made for all temperatures above 1416° C. in accordance with-

Jan 1, 1931