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By J. D. MacKenzie

THE world production of copper for the first eight months of 1927 shows an increase of 3 per cent over the same period in 1926. Since February of this year, however, production has been considerably curtailed. The United States reduction in the last four months has been offset by the increased South Ameri-can and Belgian Congo production. The United States is now producing 58 per cent of the world production, Chile and Peru 17.3 per cent, Belgian Congo 5 per cent. In 1926 the United States produced 54 per cent, Chile and Peru 16.3 per cent, Belgian Congo 6.3 per cent. Production, Tons 1917-largest war year 1,580,000 1925 1,581,000 1926-increase 3 per cent 1,628,000 1927-increase 3 per cent 1,670,000 Copper Producing Countries, 8 mo., 1927: Tons Per Cent United States 644,000 58.0 Chile and Peru 192,000 17.3 Europe 90,000 8.1 Belgian Congo 56,000 5.0 Japan 46,000 4.1 Mexico 30,000 2.7 Canada 23,000 2.1 Figures are not available for Spain and Portugal, which would probably precede Mexico.

Jan 12, 1927

Geological Survey of Ohio, Columbus, Ohio. Wilbur Stout, State Geologist. A complete list of publications will be sent upon request The present Geological Survey of Ohio is the fourth organization of this kind in the state The first Survey issued two reports, dated 1838 (not now available), the second, from 1869 to 1888, issued two reports, 75 cents and $1, respectively, and five volumes on geology, $1.25 to $3 50. The third organization, 1890 to 1900, issued a report for 1890, $1, and vol. 7 (1893), $150 Since 1900 the present organization has issued a number of Bulletins, most of which deal with the geology of some part of the state, as follows: Bulletin 10, The Middle Devonian (1909), 25 cents, 14, Columbus Quadrangle (1911), 30 cents; 15, Devonian and Mississippian of northwestern Ohio (1912), $1; 17, Conemaugh Formation (1912), 60 cents, 22, The Dunkard Series (1920), 60 cents; 23, Camp Sherman Quadrangle (1921), 50 cents; 24, Wayne County (1921), 50 cents, 28, Columbiana County (1924), $1, 30, Delaware County (1926), 75 cents, 31, Vinton County (1927), $1; 35, Jefferson County (1930), $1. Other bulletins on Ohio geology and resources of most interest are.

Jan 1, 1933

By W. J. Maraman, D. R. Harbur, J. W. Anderson

A device for rapidly quenching liquid metals into thin platelets has been developed at the Los Alamos Scientific Laboratory. This rapid quenching equipment is built around the technique of catching a molten drop of metal between a rapidly closing plate and a stationary plate. The design and operation of this unit are described. The closing speed of the smasher plate at impact is 12.6 ft per sec. The quenching rate for this device is controlled by the interface resistance between the plates and the platelet, and is dependent upon the heat content and density of the material being quenched. The initial quenching rate down to the freezing point of the platelet material is lo5º to 106ºC per sec. After an isothermal delay, which is poportional to the heat of fusion of the platelet material, the final cooling rate down to the temperature of the smaslier plates is l04ºto 105cº per sec. RAPID heating of metals by capacitor discharge and other methods has provided the metallurgist with a useful tool for probing into the kinetics of phase changes and the many nonequilibrium phenomena which occur during rapid temperature changes. Equally interesting studies can also be made on metals and alloys which are rapidly cooled from the liquid state.' Studies in this field have been limited, however, because the rates at which metals could be cooled were many orders of magnitude slower than the rates possible for heating. In recent years many new laboratory methods have been developed to rapidly cool metals from the liquid state to ambient temperature and below.2"4 All of these methods involve spreading a liquid drop of metal into a thin foil in a very short time. The methods developed have varied from ejecting a drop of molten metal at the inside surface of a rotating cylinder or stationary curved plate to catching a falling drop of molten metal between rapidly closing plates. The equipment which has been developed at the Los Alamos Scientific Laboratory for rapidly cooling molten materials uses the latter of these two approaches. The basic design, operation, and initial results of this rapid quenching device are given in this report. APPARATUS The drop smasher, which is now being used to obtain rapidly cooled metal foils, is shown in Fig. 1. Basically the device consists of a smasher plate which is driven by a solenoid into a stationary plate. The solenoid is activated by a drop passing through the photoelectric cell and is powered by discharging an adjustable 350-v capacitor bank with a 66-amp peak current into it. This power supply is designed so that the solenoid is powered for 2 m-sec after plate closure to minimize the rebound effect. There is an adjustable time-delay mechanism between the photoelectric cell and the solenoid. Both smasher plates have changeable inserts so that a variety of materials can be used to smash the molten drop. The shaft of the moving plate is guided in an adjustable housing which has ball-bearing walls. The cabinet shown to the left of the drop smasher in Fig. 1 contains the power supply and receiver for the photoelectric cell, the time delay mechanism, and the capacitor bank. The drop smasher can be placed inside a vacuum chamber, for use with radioactive materials, with the upper plate forming the lid, as shown in Fig. 2. On top of the vacuum lid is an induction coil, powered by an Ajax induction generator, which is used to melt drops from the end of the rod extending through the vacuum seal on top the quartz tube. OPERATION The drop smasher shown in Fig. 2 is operated in the following manner. The smasher plates are separated and the unit is lowered into the vacuum chamber using a pressurized cylinder. The induction coil, quartz tube, and lid with sliding vacuum seal are then assembled on top the vacuum chamber. A rod of the material for rapid quenching studies is connected to the rod extending through the sliding vacuum seal. The vacuum chamber is then evacuated and the desired atmosphere established. The photoelectric cell is turned on, and the capacitor bank is charged and armed. Power is supplied to the induction coil, and the rod of material for rapid quenching studies is lowered into the induction field. A molten drop forms on the end of the rod, drops off, falls through the light beam of the photoelectric cell, and is then caught between the smasher plates. .

Jan 1, 1970

By C. F. Allen, G. B. Walker

The sink-float methods designated by heavy-media separation processes were pioneered by C. Erb Weunsch for the treatment of base metal ores as an improvement over jigs. The work of Weunsch was further developed by Victor Rakowsky and The American Zinc, Lead and Smelting Co. Early in the development of the processes, the inherent unsuitability of galena as the solid constituent of the medium was recognized and ferrous media amenable to magnetic recovery and control were developed. The high efficiency and low cost of magnetic recovery and cleaning of ferrous media regardless of particle size, slime contamination, or surfacial oxidation had led to the adoption of ferrous media by all of the sink-float plants operating under the heavy-media separation processes patents controlled by American Zinc, Lead and Smelting Co. Approximately 2,000,000 tons of base metal and nonmetallic minerals are treated each month by these methods. Heavy-media separation processes are a modern practical and economical adaptation of the well-known laboratory procedure for separating a mixture of two solids by immersing the mixture in a liquid having a specific gravity intermediate the specific gravities of two solids. The lighter solid floats while the heavier sinks. This method of separation has been attempted on a commercial scale, but the high loss and high cost of the organic liquids halted the development of the process. Many attempts have been made to simulate a heavy liquid by using a suspension of a finely divided solid in water. If the solid phase of the suspension is ground fine enough, the suspension can be made stable or so slow settling that a substantially uniform specific gravity can be maintained from top to bottom of the bath. However, any material separated by such methods will inevitably be contaminated by some slime which will eventually accumulate in the bath and cause a viscous medium at the expense of separating efficiency. Therefore, it is necessary to provide means for continually cleaning a portion of the medium to eliminate slime at the same rate at which it is introduced to the medium. The problem of efficiently cleaning the medium limits the minimum grain size of the solid of the suspension in the case of the Chance sand process for cleaning coal, because de-cantation is the only cleaning method available. If the sand is too fine, it will be lost along with the slime. Therefore, coarse sand must be used, and to maintain a semblance of a uniform suspension, it is necessary to use strong rising water currents. The combination results in a separation based more on hindered settling classification than on sink-float principles. As previously mentioned, galena was used as the solid constituent of the medium during the early stages of the development work. The high specific gravity of galena made it suitable for the preparation of medium for high specific gravity separations. Galena can be cleaned by either decantation or by froth flotation. As with sand, de-cantation limits the minimum particle size of the media that can be cleaned without excessive loss. Froth flotation for cleaning galena medium has been used, but the problem of floating fine galena that has been exposed to extensive oxidation is well known to be a most difficult one. Last year the largest heavy-media plant m the world, and the second plant to be installed, converted from galena medium to ferrous medium despite the fact that the ore contains galena which can be used as medium. The change to ferrous medium has been beneficial in many ways. Today all the heavy-media plants have been converted from galena to ferrous media. Unquestionably, ferrous media have the widest application of any media developed, for the following reasons: 1. Ease of recovery and cleaning by magnetic means. Particle size or surface condition not a factor. 2. Low consumption per ton of ore treated. 3. Resistance to abrasion. 4. Widest range of media densities, including higher workable densities (1.25 to 3.4) than have been found possible with nonferrous media. 5. Space required for recovery and cleaning of ferrous media is considerably less than that for nonferrous media. 6. Ferrous media require lower capital investment and operating costs for media recovery and cleaning. Advantages of Heavy-media Separation Processes Heavy-media separation processes offer the following positive advantages, amply demonstrated on a wide variety

Jan 1, 1950

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole'') and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-') is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-' using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- ' torr, Maiya and lakel measured y as 39 kcal mole-' using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-': there is evidence also for a low temperature value of about 20 kcal mole-'. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.'-'' Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A', C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2'3 M = mass of an evaporating molecule

Jan 1, 1970

By J. E. Warren

In their analysis of Eqs. 29 and 30, the authors correctly deduce the following behavior limits for the "differential capacitance model". 1. When the rate group a is sufficiently large, the model reduces to that implied by Eq. 1, i.e., the simple convection-diffusion model. 2. When the rate group a is sufficiently small, the model reduces to that implied by Eq. 1 with 1 replaced by 1, i.e., the simple convection-diffusion model with a total pore volume equal to that occupied by the mobile fluid in the original model. Unfortunately, the authors' solution, Eq. C-1, to the transformed versions of Eqs. 29 and 30 does not exhibit the same limiting behavior. For example, as a approaches zero, Eq. C-1 reduces to the solution to Eq. 1 or, equivalently, the solution to Eqs. 29 and 30 for sufficiently large values of a. Therefore, it can be concluded that Eq. C-1 is not a general solution to Eqs. 29 and 30; this conclusion can be easily verified by substitution. I suggest that the correct form of Eq. C-1 is the following: It is generally realized that accounting for dispersion effects is an extremely tricky business; therefore no one should criticize the pragmatic approach of Coats and Smith who proceeded by accessible theory, made use of some available phenomenology, and who then took the trouble to check the consequences, against their own carefully undertaken experimental results. Here I should like to defend three assertions: (1) Coats and Smith copy the error of previous authors in the formulation of the so-called simple diffusion model (which error is then retained in their differential capacitance model); (2) improving the fit between data and the predictions of an arbitrary model by increasing the number of parameters is a triviality unless the parameters are disposable by being independently determined; and (3) existing experimental procedures lack sufficient resolution to clarify some current theoretical uncertainties. Taking first the view that all theoretical approaches (whether constructed by statistical, finite difference, or continuum arguments) tend to reduce to the same model form as fixed by the number and nature of the disposable parameters, one notices that the "finite-stage" model of Deans1 is equivalent to the Coats and Smith so-called differential capacitance model for the pertinent case where a

Jan 1, 1965

By G. H. F. Gardner

The velocity and attenuation of elastic waves in sandstones were measured as a function of both pressure and fluid saturation. A large change occurs in these quantities if water is added and the rock is not compressed, but the change is small if the rock is subjected to a large overburden pressure. Measurements were made by vibrating cylindrical samples in both the extensional and torsional modes at frequencies up to 30,000 cycles/sec. Formulas were derived which enable the attenuation of dilatational waves in dry rocks to be deduced from the data. Similar experimental methods were used to investigate the properties of unconsolidated sands. Velocities were found to vary with the 1/4 power of the overburden pressure and attenuations to decrease with the 1/6 power. The effects of grain size, amplitude and fluid saturation were studied. Formulas by which the effects produced by a jacket around the sample may be calculated were derived. The practical application of these results to formation valuation is discussed. INTRODUCTION The attenuation of elastic waves in the earth has been of interest to the seismologist and geophysicist for many years, but only recently to the petroleum engineer. Engineering interest has been brought about by the success of velocity logging devices, for it is possible by modification of these instruments to measure the attenuation of sound waves in addition to their velocity and, hence, deduce the mobility of formation fluids as well as the porosities of the rocks which contain them. The main problem is to decide whether field measurements can be made with sufficient accuracy to be of practical use. This problem can only be solved after we know the magnitude of the attenuations which are typical of the earth at various depths. The logarithmic decrement of a fluid-saturated rock is the sum of a "sloshing" decrement and a "jostling" decrement, the former caused by the mobility of the fluid contained within the rock and the latter by the granular framework of the rock. Sloshing decrements can be calculated' using Biot's theory, but the jostling losses are less well understood. The present paper reports an experimental investigation of jostling losses in consolidated and uncon- solidated sands, particularly with respect to the effect of overburden pressure and fluid saturation. Born' showed that the decrement of a sandstone may increase dramatically when only a few per cent by weight of distilled water is added, and that the additional loss is proportional to the frequency of vibration. His measurements were made with no compressive stress on the framework of the rock. M. Gondouin3 investigated similar phenomena for fluid-saturated plasters but also did not compress the samples. In the present paper it is shown that compression of the framework reduces this effect, so that at depth the jostling decrement of a sandstone may be expected to be almost independent of fluid saturation and frequency. Decrements for many sedimentary rocks have been given by Volarovich,4 but all for the state of zero overburden pressure. Anomalously low velocities have been logged in shallow unconsolidated gas sands. Results of the present investigation confirm that these velocities are not caused by correspondingly high attenuations, because the jostling decrement in a packing of sand grains is small and much less than in a consolidated sandstone at the same depth. Velocities in sands have been measured by Tsareva5 and by Hardin6 as a function of pressure, but the corresponding decrements do not appear to have been measured previously. The widely used "resonant bar method" of measuring velocities and decrements was employed. Comments on variations of this technique have recently been published by McSkimmin.7 The main novelty of the present technique was the application of pressure to the samples. It was found possible to do this by placing the apparatus inside a pressure vessel, provided the conditions leading to large additional losses were avoided. These conditions are discussed below. EXPERIMENTAL TECHNIQUE Cylindrical samples were caused to vibrate in both the extensional and torsional mode of vibration and the amplitude of vibration was measured as a function of frequency in the neighborhood of a resonant frequency. The resonant frequency, fr, is related to the corresponding elastic modulus by the formulas where E and N are Young's modulus and the modulus of rigidity, p is the density of the sample, and A the wavelength of the vibration.

Jan 1, 1965

By Michael A. Toole, O&apos

INTRODUCTION The tremendous capital investment required to produce a low grade ore deposit demands a reliable answer to the question: "How much does it cost to drill a well to produce the uranium that geologists have indicated is there in the ground?" However, you will find the answers given will be many and varied, depending on whether they come from the operating company, the drilling contractor, a geologist, a reservoir engineer, purchasing agent, or whoever. Each generally considers only a limited area of the total operation. The operating company usually depends upon the drilling contractors, service companies, and consultants to supply expertise. Because it is often difficult to see the "whole picture" or even to agree upon what the "whole picture" is, planning a well program and its costs is often done piecemeal. Frequently, costs "saved" in one area of the program are needlessly spent in another, because the effect of one area upon the other was overlooked. Since the drilling fluid is such an influential part of the drilling program, it should be given utmost consideration when planning the overall program. As W. D. Lacabanne wrote in 1954: "The drilling fluid system is understandably called the heart of the rotary oil drilling rig. Any other type of rotary rig.... should benefit by the incorporation of mud fluids in the drilling scheme." And G. R. Gray mentions that "The driller recognizes the drilling fluid as one of the useful tools available to solve drilling problems." However, in minerals drilling, only in recent years has the drilling fluid been considered as more than a tool to get through special problem areas. Although there are many similarities between drilling for oil and gas and drilling for minerals, the differences in the drilling equipment used justifies designing specific fluids for the minerals drilling industry. NL Baroid/NL Industries, Inc. has been a leader in introducing such fluids and in providing technical know-how to the minerals drilling industry. The purpose of this paper is: (1) to discuss the selection of drilling fluids to meet specific drilling conditions during both exploration and production and (2) to show the interrelationship among factors present in the exploration and production phases that influence total well costs. DRILLING FLUIDS FOR DRILLING PROBLEMS The drilling fluid is a tool that can be used to improve drilling performance by improving hole cutting, cleaning, stability, and formation productivity. Properly formulated and maintained drilling fluids enable the drilling operation to be carried out with increased efficiency and lower total (overall) costs. However, it should be noted that not all drilling problems can be solved by even the most carefully prepared and maintained drilling fluids. Of the many possible drilling problems encountered in a well before reaching target depth, this paper will discuss only those most likely to be present in the shallow [61 to 610 m (200 to 2000 ft)] drilling operations in South Texas. LOST CIRCULATION Loss of circulation is the most common problem encountered in drilling. Because the losses occur under varied conditions, it is often difficult to determine the exact causes. "Lost circulation" or "lost returns" means the partial or complete loss of drilling fluid to voids in the formation. "Loss of water" while drilling with water may take place into any permeable section and should be distinguished from "water loss" or filtration of fluid through the filter cake of mud solids laid down on a permeable formation. "Loss of water" can frequently be stopped by the addition of colloidal sized clay particles such as high yield bentonites, whereas "water loss" may be controlled with organic polymers. Subsurface conditions that lead to loss of circulation can be classified as: (1) natural fractures, (2) induced fractures, (3) unconsolidated or highly permeable formations (loose gravel), and (4) cavernous formations (crevices and channels). Loss of circulation may occur whenever the borehole pressure exceeds the formation pressure. The greater the differential pressure, the more likely it is that circulation may be lost. To stop loss of whole mud, voids must be bridged so that a filter cake can be laid down on the permeable section. The plugging material must be of the proper size and shape to offer greater resistance to the fluid flow around it than the flow up the annulus. A plugging composition that satisfies these requirements may not be able to be handled by the small rig pump available.

Jan 1, 1979

By R. E. Boehler, N. C. Ludwig

At Buffington Station, Gary, Ind., Universal Atlas Cement operates fourteen 8 x 101/2 x 155-ft cement kilns in mill 6 and two 11 x 360-ft kilns in the Harbor plant. The No. 11 and 12 kilns in mill 6 are equipped with Manitowac recuperator sections. This report describes studies in measuring exterior shell temperatures on several of these kilns and the development of a traveling radiation pyrometer with certain novel features. Preliminary Work: At first various temperature-sensing devices were placed on the steel shell: 1) crayons with calibrated melting points, 2) colored paints with temperature-calibrated pigments, 3) aluminum paints with temperature-calibrated binders, and 4) metal-stem dial thermometers. The colored paints and aluminum paints failed to indicate the temperatures correctly. The crayons and thermometers did indicate fairly correct temperatures, but it proved impossible to apply enough of these on the shell to detect all the potential areas where hot spots might develop. Furthermore, considerable labor was required to apply these sensors and read the temperatures. Consequently no further work was done with these devices. Formation of Hot Spots: In the burning or clinker-ing zone of a cement kiln, the thickness of the protective coating and thickness of the brick govern the amount of heat transmitted to the steel kiln shell. Usually the protective coating consists of 4 to 8 in. of fused cement clinker. The formation of a hot spot is usually caused by loss of coating? that is, localized areas of the coating become thin or fall away from the refractory. This is generally caused by excessive temperature in the burning zone over a fairly long period of time. It may also be caused by a sudden thermal change in the burning zone. Variations in raw feed composition and in feed rate require changes in the fuel and air rates, and when these are not appropriately altered, conditions may develop in the kiln that will result in loss of coating. Luminescence on the kiln shell indicates that a hot spot has developed to a point that usually alters the refractory's thermal conductivity properties. When this thermal weakness zone occurs in the burning zone of the kiln, constant vigilance is required to protect it by maintaining proper coating. Even so, it has been the writers' experience that within a period of several days to about four weeks the hot spot usually recurs with greater severity. This necessitates shutting down the kiln and re-bricking the affected area. One of the prerequisites of a good burnerman is the ability to maintain a protective coating despite the many variables in operation. When he knows that it is getting thin or that an area has dropped off, he reduces the firing rate and kiln speed and brings feed into the affected area in an effort to rebuild the coating. But when powdered fuel is burned, the atmosphere of the kiln may prevent the burnerman's observing the condition of the coating closely at all times without taking off the fire. It is not considered good practice to do this frequently, as it imposes a thermal shock on the coating and upsets operation of the kiln. To help the burnerman scan the shell of the kiln along the burning zone, therefore, a radiation pyrometer, connected to a potentiometric recorder, was mounted on a slowly moving steel cable. The theory of operation, construction details, and adaptability of the radiation pyrometer are included in an excellent monograph' and also in a textbook.' Shell temperatures of the Atlas Cement kilns were measured with a Brown Instruments Div. low intermediate range Radiamatic unit, of range 200" to 1200°F, and a circular chart Electronik potentio-metric recorder, of range 500" to 1000°F. In Bulletin 59095M the supplier publishes standard calibration data (millivolts vs degrees Fahrenheit) for this radiation pyrometer, These data, however, apply only to flat surfaces having emissivities of unity. Calibration of Radiation Pyrometer for Use on Curved Surfaces: When applied to surface temperature measurements, the radiation pyrometer reading depends on the nature of the surface, the material of which it is composed, and also to some extent on the temperature of the surroundings. Although the present radiation pyrometer is designed to give a calibrated response under ideal (black body) conditions when used commercially, it must be calibrated empirically. The calibration procedure, given below, follows that described by Dike (Ref. 1, pp. 38-39). Calibration tests on plane and curved surfaces showed that the response of the radiation pyrometer was very

Jan 1, 1961

By C. N. Garman

Homestake-New Mexico Partners operate a 750-tpd carbonate leach uranium concentrate mill near Grants, N.M. The highly mineralized water available as process water leaves much to be desired. The 628 ppm as CaCO 3 makes the use of raw water very troublesome in pipes and on filter cloths. However, the residual sodium carbonate in the final filter cake going to tails makes an ideal softening agent. To take advantage of this fact, all makeup water used in the mill is first used as tailing slurry dilution water and comes to the mill from the tailings pond. The 5-acre tailings pond serves as a thickener and 100 to 150 gpm of nearly clear solution is decanted to a pump to be returned to the mill. Since this tailings water has small quantities of uranium in the solution an ion exchange scavenger unit was installed to remove as much uranium as possible. The ion exchange raffinate is then used as final filter wash ahead of the tailings slurrying step. In spite of the large settling area this return water is not clean enough for ion exchange feed. The solids present are very fine and composed of approximately 15 pct (by weight) burnable carbonaceous material common to the sandstone uranium ores in the area, 40 pct SiOz plus 45 pct CaC03. Laboratory work showed that this material responds very well to flotation. Before deciding to use flotation, various clarifying systems such as pressure leaf filters, sand filters, and continuous vacuum pre-coat filters, were considered. Each of these could have solved the problem but with much more operating labor, more reagents and greater installation costs than the flotation step. About 100 to 150 gpm of fouled water is fed to two 66-in. Fagergren cells, in series. Reagents used at the beginning were Arquad 2HT75 and Arquad C50, at the rate of about 1% lb per 8-hr shift, or about 0.0053 lb each per ton of ore. This did not completely remove the solids but does an acceptable job. Approximately 75 pct of the slimes are a size that can be caught on a 41-Whatman Paper are removed. Removal of these slimes also allows much better settling of the coarse nonfloatable material. Advantage is also taken of this fact in a small settling tank ahead of precipitation. Removal of this amount of the slimes makes the ion t:xchange feasible. PREGNANT SOLUTION CIRCUIT The carbonate? leach-caustic precipitation method of uranium concertration does not provide for any process purification step ahead of precipitation. Therefore, any fine solids getting into the pregnant solution through the filter cloth show up in the final concentrate. This, of course, lowers the grade, and, at times, the slimy nature of these very fine solids rendered final filtration of the concentrate difficult if not impossible At Homestake-New Mexico Partners a 75-ft thickener was available for gravity clarification of 100 to 120 gpm of this pregnant solution. However this did not sufficiently remove the slimes. Laboratory investigation of the whole range of flocculants that were suggested by literature, salesmen, and friends failed to turn up anything of consequence. A continuous vacuum pre-coat filter would do the job and was investigated. The capital cost and the operating labor and materials made this a last chance choice. Following work done in the metallurgical laboratory on the tailings return water, it was found that some changes in the reagent strengths and combinations made a very definite decrease in the solids in the pregnant solution. Concentrate grade improved about 5 pct anti the final product after drying had an appreciably greater bulk density. Compared to a cost of about 2.2e per ton for pre-coat filter opelation for cleaning just one circuit, flotation costs less than 1.0 per ton of ore for cleaning two circuits. While a pre-coat filter would do a more thorough job, the flotation does all that is required for either circuit. Gravity causes the froth produced to run back into the leach circuit. This does not appear to result in a build-up of objectionable slime. No extra manpower is required; the operators in the separate areas can observe the operation of the cells and mix the small quantities of reagents as needed. Normally the 66-in. Fagergren cell requires 15 hp per cell, but this very dilute slurry needs only 10 hp for both cells. Originally, a combination of the two Arquads mentioned previously served as frothers and promoters. As further testing

Jan 1, 1962

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940

By K. E. Nelson

The effect of thorium and zinc variations on the strength and 100-hr creep characteristics of Mg-Th-Zn-Zr alloys was investigated. Optimum resistance to creep at 650° and 700°F are attainable within a certain range of thorium and zinc contents. This range does not conform to that which develops maximum tensile properties. RAPID advances have been made during the last few years in the development of magnesium alloys for elevated temperature applications demanding high resistance to creep. The beneficial effect of rare-earth metals on the creep resistance of magnesium alloys has been emphasized by a number of publications1-13 and such alloys are now in commercial production. The use of thorium as an alloying ingredient in magnesium was mentioned by McDonald and also in two Alien Property Custodian patent applications.10,17 The initial observation of Sauerwald that thorium contributes still higher creep resistance to magnesium than is attainable with rare-earth metals has recently been substantiated.&apos;" " In fact, it has been demonstrated that the useful temperature range of magnesium alloys is appreciably extended by the use of thorium. In all cases, it was observed that zirconium must be included in the alloys in order to render them fine grained and more readily castable. Several recent publications:2-27 indicate that a still further improvement in creep resistance and a further extension of the useful temperature range can be realized by the addition of zinc to alloys. The primary purpose of this paper is to present the results of a comprehensive study of the effect of zinc on the strength and creep characteristics of Mg-Th-Zr alloys. Compositions covering the range of thorium content from M to 6 pct and zinc content from 0 to 5 pct have been investigated. The creep characteristics at 650" and 700°F reported in this paper are based on results of tests of 100-hr duration. It is appreciated that creep tests of 100-hr duration might not yield adequate data for design purposes for parts with much longer expected life. However, for the purposes of the present discussion, it is felt that the combination of stresses and temperatures used in the 100-hr creep tests have yielded a clear representation of the compositional variation of creep resistance at the temperatures investigated. Creep tests of 1000-hr duration are now in progress on a few of the most promising alloys. Preparation and Testing of Alloys The alloys studied in this intensive investigation were prepared in 25 lb capacity mild steel crucibles. The thorium, zinc, and zirconium were alloyed and poured as described in earlier publications The thorium was introduced into the melt in the form of a Mg-Th hardener," the zinc added in the metallic form, and the zirconium alloyed in the form of the commercial hardener containing magnesium and 30 to 50 pct Zr.10, 26 Fluxing practices for melting and refining were the same as for magnesium-rare-earth metal-zirconium alloys. The melts were sampled for analytical determinations and poured into separately cast 1/2 in. diameter standard tensile bars. The test bars were given a precipitation treatment of 16 hr at 600°F in laboratory furnaces. It has been shown by other tests that a high temperature solution treatment followed by an aging treatment is unnecessary for the development of optimum properties in Mg-Th-Zn-Zr alloys. The selection of 600°F as the aging temperature was based on an attempt to achieve metallurgical stability without coalescence of the undissolved phases and the attendant loss in strength. The thorium, zinc, and zirconium contents of each melt were determined chemically. The zirconium contents are reported in two parts, "soluble" and "insoluble," referring, respectively, to the portions present in the alloy which are soluble and insoluble in dilute HCl acid. Distinction is being made between these two components of the zirconium content in the alloys because it has been found that only that portion of the zirconium content which is soluble in dilute inorganic acids affects the structure and properties of the alloys. The usual impurities consisting of copper, iron, manganese, and nickel were determined spectroscopically. The analysis for each melt is listed in Table I. A description of the methods of tension and creep testing has been detailed in earlier papers. The tests were performed with the cast skin re-

Jan 1, 1954

By John Griffen

THEORY HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as fo1lows:l Nomenclature r represents, in a particle of irregular shape, the round-hole screen through which the particle would pass, or some other linear dimension of the particle equivalent to d, the diameter of a sphere. s, the specific gravity of the particle. 1, the specific gravity of the water used as a medium. K, a constant. W, the velocity of the water. In an Upward Current of water 1. A particle will move upward if [V > K dr(s - 1)] and, by suit- ably regulating the speed of the water current, the larger and heavier particles may be made to fall downward against the current, leaving the smaller, lighter particles in suspension in the current. 2. Particles such that [- = -] cannot be separated in an upward- current classifier with any one velocity of current. Coal particles having a specific gravity of 1.35 cannot be separated from refuse particles of [2.5 - 1 2.5 sp. gr.] unless the ratio of diameters is less than [ 4.3 to 1, 1.35 – 1] and the raw coal must be screened to size limits within this ratio if they are to be separated. Cone-shaped vessels or vessels of other shapes that allow the use of different velocities of current at different points in the flow are used to modify this limitation.

Jan 1, 1943

BARBOUR, PERCY E., Deputy Supt., (Captain), New York State Troopers; Captain, 22nd Regiment, N. Y. N. G. BARLING, 1i. B., 1st Lieutenant, Engineer Officers&apos; Reserve Corps. CHAPMAN, R. H., Major, Engineer Officers&apos; Reserve Corps. DUNN, THEODORE S., 1st Lieutenant, Engineer Officers&apos; Reserve Corps. DWIGHT; ARTHUR S., Major, Engineer Officers&apos; Reserve Corps. FORBES, CARROLL R., Captain, Engineer Officers&apos; Reserve Corps. GOODSPEED,. G. E., JR., 1st Lieutenant, Engineer Officers&apos; Reserve Corps.

Jan 7, 1917

By Walter S. Weeks

THE process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case 1 If compressed air is allowed to expand to the atmospheric pressure through an orifice in an sir line that is supplied by a running compressor, no cooling results except the negligible one due to the Joule-Thompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. Cv Specific heat of air at constant volume, B.t.u. per lb. per deg. F. Cp Specific heat at constant pressure, B.t.u. per lb. per deg. F. T1 Absolute temperature of air in pipe, deg. F. T3 Absolute temperature of air outside after expansion and mixing and coming to rest. J Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

By M. Cohen, P. E. Beaubien, D. Caplan

Addition of 1 pct Mn to Fe-26 CY ca/(ses a12 increase in scaling rate at 870° and 1090°C. Whereas only the rhombohedral oxide, formrs on tire manganese-free alloy, with manganese present major amounts of the spinel .Mn0 . Pro-duced through which diffusion is more rapid. At 1090°C the scale formed OH Mn is highly, irregular due to blistering and sintering, This is a second cause of faster oxidation Since much of the blistered oxide does not participate as part of the protective layer. The oxide phases that form at different times depend on the degree to which the surface metal has become depleted, in manganese by preferential oxidation. PREVIOUS work has demonstrated that the oxide scales formed on chromium steels at high temperature consist of both spinel and rhombohedra1 phases and may contain considerably more manganese, especially in the spinel phase, than is present initially in the alloy.&apos; It has further been observed that a binary Fe-26 Cr alloy scaled less rapidly than an equivalent commercial steel and formed no spinel.&apos; However, it is not established if manganese in chromium alloys actually promotes formation of spinel nor if it affects oxidation resistance. It seemed expedient to try to evaluate the specific effect of manganese by oxidizing an Fe-26 Cr alloy containing a small manganese addition under the same experimental conditions as used for the manganese-free alloy.&apos; EXPERIMENTAL Table I shows the composition in weight percent of the Fe-26 Cr-1 Mn alloy and of the Fe-26 Cr alloy used as reference. The alloy with manganese was prepared from the vacuum-melted Fe-26 Cr alloy by remelting in vacuum with the proper manganese addition. The ingot was rolled to strip and specimens 1.1 by 0.035 by 5 cm and 1.1 by 0.5 by 4 cm cut out or machined. As previously described2 the specimens were smoothed by abrading through 600-grit Sic paper, electropolished in acetic-perchloric acid (20 to 1) to remove 10 p of metal, annealed at 1100°C in 20 torr of purified argon, and electropolished to remove a further 10 p of metal. They were then either rinsed in water and methanol and blotted dry or immediately etched for 45 sec in deoxy-genated 4 N HC1 under cathodic polarization at 10 pa per sq cm. Oxidation runs were carried out in a vertical tube furnace in a flow of purified oxygen at 1 atm while the weight increase was recorded continuously on a* automatic balance.3 Alter 98 hr at 870.C or 20 hr at 1090"C the specimens were removed to flowing argon and observed microscopically for evidence of spalling as they cooled. Subsequently they were examined by X-ray diffraction, the oxides analyzed chemically, and metallographic cross settions prepared. RESULTS Figs. 1 and 2 show the oxidation curves of Fe-26 Cr-1 Mn at 870&apos; and 1090C. The Fe-26 Cr reference runs are shown as dashed curves. Experimental details of the six runs are included in Table 11. The first 20 hr of run 1 is repeated in Fig. 2 to show the effect of temperature. At 8&apos;70°C the weight gain for Fe-Cr-Mn is about twice that of Fe-Cr (curve 1 vs curve 2, Fig. 1). Both alloys show regular oxidation curves. On parabolic coordinates (right-hand scale of Fig. 1) the

Jan 1, 1965

By J. S. Hromatko, L. J. Gurevich

In the course of the examination, at the BureLu of Standards, of fusible tin boiler plugs for the Steamboat Inspection Service, it became evident that an investigation should be undcrtaken to determine the precautions necessary in the manufacture of acceptable plugs. The results of the tests of these plugs show that their manufacture has improved, though at present not all of the plugs tested are, satisfactory. Table 1 gives the result of tests of some 1500 plugs from about 100 makers. Records of the tests show that several of the makers were able to produce satisfactory plugs with every pouring. The Steamboat Inspection Service has the following specifications for fusible plugs: "Fusible plugs for use in boilers of steam vessels under the jurisdiction of the Steamboat Inspection Service shall be made of bronze casing with the bore tapering continuously and openly from end to end, and filled from end to end with tin not less than 99.7 per cent. pure and to contain not more than 0.1 per cent. of lead and not more than 0.1 per cent. of zinc. The small end of the bore may be countersunk not more than 1/32 in. in depth and width, but no recess, thread, or cavity other than this countersink shall be allowed." Table 1.—Thirty-"five-mdh Testing Record of Fusible Plugs Causes of Rejection Inspection Period June-November, 1916.................. 311 32.8 47.2 3.8 11.5 15. 1 10.9 1 1.9 4.5 December, 1916-May, 1917............. 318 71.4 28.6 2.2 4.4 12.8 5.9 i ... 2.8 June-November, 1917.................. 228 73.0 27.01 ... 9.6, 5.2 9.6&apos; ... 0.8 December, 1917-May. 1918............. 214 72.028.0 0.9 0.4 11.6 7.0 ... 7.9 June-November, 1918...............250 70.7 29.3 ... 2.0 20.0 5.2 ....2.8 December, 1918-April. 1919............ 23378.121.9 7.2 1.2 1 4.7 3.0 ... 6.0 Total 35 months....................1544.69.7 30.3 2.3 4.8 11 0 6.9 0.3 4.1

Jan 1, 1921

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade&apos; in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965