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DEPENDENCY on foreign sources for many mineral raw materials is a characteristic of our economy which is becoming painfully evident. Although investment in foreign mining projects has increased, it has not kept up with the growing demand for foreign minerals. The sphere of American investment capital in mining ventures abroad has been severely limited by the rise of nationalism in many underdeveloped countries. Consequently, we can look back over half a century in which mining investment, exclusive of petroleum, has increased by 50 pct whereas other American investments abroad have multiplied by better than 300 pct. Investment in foreign mining or petroleum encounters different problems than capital investment for other industries. It is rarely invested in industrialized nations. Most of it goes to countries with expanding frontiers, like Canada, or to underdeveloped nations like Liberia. It must be used for building communities, recruiting and training labor, and establishing lines of communication and transportation. These complications are an accepted part of the mining game. However, the most complex problem is in those countries which consider mineral exploitation a usurpation of the people's natural heritage. This is a characteristic of the young government existing by a tenuous balance of power in an underdeveloped nation. American mining capital understandably has shunned these nations as being poor investment risks. However, they possess minerals which are needed by industry. Our government has attempted to stimulate mineral supplies beyond those provided from abroad by private capital. ECA, now under DMPA, makes loans to foreign mining companies. Since the ECA program cannot be expected to continue indefinitely, Point IV seems to be the logical next step to encourage foreign countries to fill our shortages. However, only 1 pct of the $35 million budget provided in the first year for Point IV was alloted for mining programs. Considering the need for minerals and the difficulties of procuring them by private investment, a larger share is needed and justifiable. Those who have been engaged in foreign mining can vouch for the fact that it takes many decades to teach the complex technology and economics of mining to the natives of under-developed countries. For this reason Point IV must be considered a long range program. Mineral requirements for the present must be met by more direct measures. Encouragement of private investment in foreign mining by such incentives as tax relief on profits from foreign sources, international bank-borrowing facilities for private capital, and diplomatic assistance in encouraging foreign countries to cooperate are imperative for our future mineral security.

Jan 1, 1952

By Luke L. Y. Chang, Bert Phillips

ThE tendency toward further oxidation of the intermediate oxides and the high volatilization rates of the higher oxides have prevented direct attainment of equilibrium data for the system tungsten-oxygen. As a result, St. Pierre et al.1 have proposed a phase diagram (to 800°C) based on thermody-namic data to 1200°C for the known tungsten oxides (WO2z, W18O49, W20O58, and WO3) and a report on a tungsten suboxide W3O.2 Recent modification of a technique previously described3 5 now permits adequate preservation of compositions of mixtures of metallic tungsten and metal oxides (e.g., of tungsten, cobalt, calcium, samarium, titanium) in order that condensed phase relations may be established to 1700 This method has been applied to study the high-temperature stability of tungsten oxides. In the method used, the desired compositions were sealed in nonreactive containers such that only a small gas volume remained. Each sample then established its own equilibrium atmosphere at temperature. This method has advantages in the study of systems of the W-0 type where knowledge of the condensed phases is desirable but for which composition and pressure of the gas phase are not readily attainable because of oxide volatility. Mixtures of 99.99 pct tungsten metal powder and purified tungsten anhydride (WO3) or in some cases W18O49* were equilibrated in pellet form in sealed

Jan 1, 1964

By Bernard Kopelman

THE particle size of tungsten metal powder used to make tungsten wire for use in radio tubes and incandescent lamps must be closely controlled if the highly desirable feature of nonsagging is to be achieved. Our knowledge of factors affecting the particle size of tungsten powder has been limited by lack of any extensive literature on the subject. There are no publications in the English language discussing this problem in any but the most general terms. In this paper the published experimental information on this subject is reviewed. Based on the published data and some experimental data obtained by the author, a general theory of factors affecting the particle size of tungsten metal powder obtained by reduction of the oxides in hydrogen is offered. The various forms of the tungsten oxides and tungsten metal used in the experiments described were those prepared by com¬mercial processes, so that the experimental results obtained on a laboratory scale would be more directly applicable to actual commercial reduction conditions. The effects of time of reduction, temperature, and concentration of water vapor in the hydrogen were observed by counting microscopically the particle distribution obtained. Such a method is very time-consuming, but the data obtained by this method are more reliable and more fundamental than those obtained by any of the several instruments available for measurement of particle size. REVIEW OF THE LITERATURE Until the year 1912, tungsten powder was prepared commercially by reducing tungstic oxide in the presence of carbon or one of its compounds (such as glycerin or ethylene glycol), usually by firing the mixture in a closed fire-clay crucible. The resultant powder contained about 95 per cent tungsten.1 When reduction of tungsten oxides by H2 was introduced commercially, 2.1 several investigators became concerned with the equilibria between tungsten metal and its several oxides in an atmosphere of hydrogen and water vapor.4-13 While these many investigations were in fair agreement on the equilibria there arose considerable controversy as to the chemical composition of the oxide between W03 and W02, because of very poor agreement on the equilibrium constant of this intermediate oxide reduction reaction. The controversy on this intermediate oxide has been in progress for more than 10o years. Thus Malguti,14 in 1835, decided it was W02.56. In 1857, Riche" proposed the formula W308. Usler,16 in 1865, confirmed the existence of W308 and further proposed W4O11. In 1897, Desi17 agreed upon W308 but also found W5014.

Jan 1, 1946

By J. F. Lewis

BELIEVING that one of the essential points in mining, as in all other business, is to know the expense incurred in each particular department, I have carefully kept an account with each department for the past three years; and, as it may be of interest to some of our members, I herewith present it to the Institute, reduced to percentages of the total yearly expense, showing the cost for materials, repairs, expenses, tools, team accounts, powder, oil, and fuel, also for labor under its several heads :

Jan 1, 1878

By Rudolf Gahl

SOME time ago the Detroit Copper Mining Co. had to decide the question whether it would pay to re-treat slime-tailings, and several machines were tested in order to ascertain the type of construction which would give the greatest saving. In previous tests on the ore of this company, several tables proved far inferior to the Frue vanner, and for this reason they did not receive any serious consideration. In the late tests, however, one table was found to surpass the vanner in the percentage of saving made. The Frue vanner used in these tests had been adjusted approximately to the slope which the slime-vanuers in the concentrator of the Detroit Copper Co. had at that time, about 2 in. between the inside of the wooden posts, or 0.272 in. per ft. It had not been determined, however, if this slope was the most economical one for treating the slime-feed in the mill, or for re-treating the tailings from the slime-vanners, and I was instructed to ascertain by test-runs, under different conditions, the best adjustments for the work to. be done. In order to determine if a change in the adjustments of the machines would improve the results, it seemed sufficient to continue running the tests between the vanner and the table before mentioned, keeping the feed and all other conditions the same, but. varying the adjustments of the vanner .from run to run. I employed a vanner-man of long experience to operate these machines, who expressed the opinion that a slope between 2 3/8 and 2.5 in. between the posts (0.323 and 0.340 in. per ft.) would give the best results. Some runs made this way gave a considerable improvement. While for a slope of 2 in. (0.272 in. per ft.) the saving had been only 40.5 per cent. of that of the table, it .was 49.2 per cent. for 2.5 in. (0.340 in. per ft.) slope. A decrease of

Sep 1, 1909

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

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of' virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law'), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.' Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor's original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*'8 showed that Taylor's least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen' obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

By Dr. O’Neil Thomas J., Donald W. Gentry

The greatest of all gifts is the power to estimate things at their true worth. LaRockefoucauld INTRODUCTION The primary reason for performing a feasibility study on a proposed mining venture is to investigate all phases of the proposal in as much detail as necessary to justify either dropping the project or continuing expenditures through the next stage. The economic evaluation component of the feasibility study, therefore, must ultimately be based on information which provides an answer to the question, "What is it going to cost?" Unfortunately engineers preparing feasibility studies never have all the engineering or economic information they would like or need. Consequently, the economic portion of the analysis can only be performed if estimates of the various costs associated with the project are made. Project cost estimates, in turn, require estimates of all the physical factors affecting cost components, including anticipated performance of plant and equipment as well as all pertinent geologic, mineralogic, and metallurgical variables. Before useful cost estimating procedures can be applied considerable data must be collected, compiled, and organized. Preparatory work typically includes organization of cost data available for estimating purposes, development of techniques for updating historical costs, and establishing methods of forecasting prices and costs over the duration of the project. Cost estimates for mining and mineral processing projects involve so many features and variables that it is absolutely essential to have some means by which the vast amount of detail can be organized. It is very important to identify, in as much detail as possible, all the cost data available (historical and developed) to the estimator. These costs, after being properly identified in detail, should be com- piled, stored, updated regularly, and made readily available for use in developing new cost estimates Accessing files of current cost information requires a standardized numerical system of classifying cost data. When uniform definitions and procedures are used, every project record contributes to the common store of estimating data.

Jan 1, 1984

By Cyril Stanley Smith

Jan 1, 1949

By Cyril Stanley Smith

Jan 1, 1949

By S. G. Lasky

Abraham Lincoln is reputed to have said that if you want to chart a course to some destination, you have to know where you are starting from. In this instance we have to define our starting point in a double manner: 1) What was the theoretical basis of the Paley predictions? 2) What actually did the Commission predict, so that we can see how the predictions have worked out up to now as a basis for considering how they may have to be changed.

Jan 3, 1960

By S. E. Hasko

It is the purpose of this note to report the crystal-lographic data for nine new B5A compounds* having the Cu5Ca structure, with A a rare earth and B a transition element, Co, Ni or Cu. In previous papers, some magnetic data1 and preparation and crystallo-graphic data2 for other B5A compounds having the same structure have been reported. Crystallographic data for these compounds are shown in Tables I and 11. These results are in agreement with others of this series reported previously by Wernick and ~eller.' The abnormally large atomic volume of Yb metal3 is not manifested in Ni,Yb, when one compares it with the compounds reported here and the data of reference 2. This is not true for the compound YbAl,, having the cubic Laves structure (MgCuz), to be discussed in other papers.4'5 Thus, it appears that Yb has a valence of 3; i.e., the 2 s and Id electrons are lost to the conduction band.4'5 Lattice constants for four of these compounds prepared by levitation melting have been reported by Nassau, Cherry, and wallace.' The lattice constants

Jan 1, 1961

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By Harry Seltz

INTERMETALLIC compounds are formed in many binary metal systems. Some compounds are stable to their melting points, and others decompose at lower transition temperatures. Even those of the first class are dis-sociated in the liquid state, as indicated by the continuous for in of their solubility curves at their melting points1. While the lattice structures of some of these compounds have been determined, their thermodynamic properties have not been investigated. In this paper is described the determination of the free energy and heat of formation of the compound CdSb, which is of the first class mentioned above, melting congruently at 455° C. This compound shows a rhombic structure, and the lengths of the edges of the elementary cell containing four molecules are: a =6.52, b = 8.60, c = 4.16 A.2 There are three possible methods of determining the free energy of formation of a compound of this type. The first method, applying the third law of thermodynamics, requires the measurement of its heat capacity preferably to liquid hydrogen temperatures, and a calorimetric determination of its heat of formation. The second method involves the study of the equilibrium of the compound in some gas reaction, such as: CdSb + CO2 = CdO + CO + Sb From the known free energies of formation of CdO, CO2 and CO the free energy of formation of CdSb could be calculated. The third method measures the electromotive force of a galvanic cell in which the cell

Jan 1, 1935

By R. S. Lewis

IN a recent study1 of the evolution of engineering education 1870 was taken as the initial point, as it is said to mark the transition from the poineer era in American engineering education to an era of rapid growth and consistent development. Prior to the founding of Rensselaer Polytechnic Institute in 1824, West Point Military Academy was the principal source of formal engineering training. In 1849 Rensselaer revised its program on the model of the leading French technical schools. Lawrence Scientific School was estab-lished at Harvard and Sheffield Scientific School at Yale in 1847. The University of Michigan pioneered in en-gineering instruction in the West, offering its first course in 1853 and awarding its first degree in 1860. Other important steps in -the progress of engineering education were the founding of Columbia School of' Mines in 1864, the opening of Massachusetts Institute of Technology in 1865, and the founding of Cornell Uni-versity and the Thayer School of Civil Engineering at Dartmouth in 1867. From its organization in 1852 until 1871 the Ameri-can Society of Civil Engineers was virtually the only national society of engineers. In 1871 the American Institute of-Mining and Metallurgical Engineers was founded, to be followed later by the Mechanical En-gineers in 1880 and the Electrical Engineers in 1884. This expansion and diversification of the engineering profession was paralleled in the colleges, and by 1885 the plan of different curricula in the major branches of engineering was soundly established.

Jan 7, 1927

By H. W. Mead, C. E. Birchenall

The rates of growth of graphite nodules in cast irons are calculated for a model of a growing graphite sphere surrounded by a shell of austenite through which carbon and iron are diffusing. The carbon is supplied by a cementite-austenite mixture at the outer edge of the shell. The calculated rates from carbon diffusion agree fairly well with the measured values, but the rates based on iron self-diffusion are much too low. Because the iron must be removed for the process to continue, o plastic deformation mechanism is suggested. THERE has been an unfortunate tendency in the literature of growth and dissolution reactions to identify the slope of a plot of the logarithm of the growth or dissolution rate vs reciprocal of temperature with the activation energies determined by diffusion measurements in chemically similar systems. If the solubility limits at the growing or dissolving phase interfaces change appreciably with temperature, such procedures may lead to serious errors in specifying the mechanisms controlling the rates of these processes. A reaction involving the simultaneous growth of graphite from and dissolution of cementite in austenite will be discussed here to show that substantial oversimplifications have been made in earlier studies of this process. From a dilatometric study of the overall y-range graphitization process, Bunin and Danil'chenko' found an apparent activation energy of 90 kcal per g-atom. They concluded that, since this value was much nearer the approximately 68 kcal per g-atom observed for self-diffusion in pure iron than it was to 32 kcal per g-atom for diffusion of carbon in iron, the rate-controlling process must be the diffusion of iron away from the growth interface to provide space for graphite to grow. Bunin and Salli' bolstered this agreement with the observation that graphite forms preferentially at surfaces, cracks, and pores where free volume is present initially. Ziegler, Meinhart, and DeaconQ ad found an apparent activation energy for graphitization of 98 kcal per g-atom. This value, like that of Bunin and Danil'chenko, applies to nucleation and growth occurring simultaneously. It is not generally assumed that nucleation is entirely diffusion-controlled. Treatments such as prior cold-working and prequenching, which strongly affect the rate of graphitization, would be expected to have little effect on diffusion processes occurring at the graphitization temperature. In any case 90 kcal per g-atom is not particularly close to the 54 kcal or lower to be expected for diffusion of iron which is carbon-saturated.' The presence of silicon in iron is said to reduce the activation energy for diffusion,' so its presence in cast irons would be expected to have a similar effect. The growth rates of nearly spherical graphite nodules have been studied by Brown and Hawkes." The initial rate of growth before impingement of adjacent carbon-depleted areas was found to be parabolic, and rate constants were measured at several temperatures. Their apparent activation energy for the growth process only was roughly 45 kcal per mol. Burke and Owen' made growth-rate measurements on several alloys, recording appreciable induction periods, initial nucleation rates, and average radial growth rates based on an assumed linear rate of radial growth. They found that increased silicon content increases the ovel-all reaction rate and the initial rate of nucleation, and decreases the induction period. Assuming 1) spherical nodules. 2) constant volume rate of nucleation, 3) austenite in equilibrium with cementite at positions where the cementite is not depleted, and 4) a constant diffusion distance during the growth of a nodule, they calculated an apparent overall activation energy of 68 kcal per mol, which was related to an activation energy for nucleation of 79 kcal per mol and activation energy

Jan 1, 1957

By Theo B. Comstock

TO the large majority of visitors the unique features of the National Park are interesting chiefly on account of their novelty. Scientists of all schools may find here food for reflection, and much that is rare and marvelous; but the real, practical uses of the reservation, aside from its pleasure-giving adaptations, are not as yet fully appreciated. Since 1873, the writer has on frequent occasions expressed freely his own views upon the proper means of utilizing the Park for the best interests of science.* Some of the recommendations made have been adopted by the authorities. At the suggestion of friends I present here a brief statement of facts concerning matters which may be of advantage for visiting engineers to know, hoping that the very limited stay of the Institute may thereby be rendered a little more profitable, and that our common profession may possibly receive some benefit. First, then, it should be understood that, as in many other cases in. the West, the present routes to the Park from the south are not the most direct. The expedition of Captain (now Major) Jones in 1873 discovered a practicable route for a, wagon or railroad via the head of Wind River, through To-gwo-tee Pass and Two-Ocean Pass, by which the distance from Point of Rocks, Wyoming, on the Union Pacific R.R., to the Yellowstone Lake, is only 290 miles. Eventually, it is probable that a railway line from Cheyenne or some other point in Wyoming will be constructed, which, taking advantage of

Jan 1, 1888

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using

The thirty-second annual meeting of the Montana Society of Engineers was held at Great Falls, Mont., on Apr. 10-12. The first day was given to the reception of visitors and the second day to the inspection of points of engineering interest. On Saturday, at the business meeting, the following officers were elected: President, Samuel Barker, Jr.; first vice-president, Charles A. Lemmon; second vice-president, George T. McGee; secretary and librarian, Clinton H. Moore; treasurer, Harry H. Cochrane; trustee for three years, Theodore Simons.

Jan 6, 1919

A. M. Strong, Bishop, Cal. (communication to the Secretary*) :—The paper of Mr. Eeyes gives us the most complete account of the geology of the borax-deposits in the Death Valley region that has yet been published, and is a valuable addition to the geological literature of a very interesting though little-known territory. During the past ten years I have been over much of the northern part of the country described by Mr. Eeyes and the region immediately north of it.

Jan 1, 1910

By L. G. Huntley

Points out differences between the new, more liberal, law passed by the Colombian Congress and the law passed in 1919, gives a few facts about the pipe-line concession granted to a Canadian company, and tells of new drilling developments. PROBABLY the most important development in the Colombian oil situation during the past year was the passage by Congress of a new petroleum law, which went into effect Jan. 31, 1923. The principal points of interest in which this new law changes or improves the previous one are as follows: Law 120 of 1919 provided that one person or corporation could not acquire more than three exploitation zones. of 5000 ha. each, and royalties were based on a sliding scale, to wit: 6 per cent. royalty on lands 400 km., or more, from the ocean; 8 per cent. on lands 200 but not over 400 km. from the ocean, and 10 per cent. royalty on lands located less than 200 km. from the ocean. Rentals were fixed at 10 centavos per hectare for the first year; 20 centavos for the second year; 50 centavos, third year, and $1 (one peso) yearly thereafter. Under this law the term of the lease was fixed at 20 years and, at the discretion of the government, could be extended for 10 years additional. After the expiration of the lease and its corresponding extension, the machinery and other material placed upon the property would vest in the government. A bond of 20,000 pesos was also required of the lessee to guarantee faithful performance of his contract.

Jan 3, 1924