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By S. W. Churchill

A digital computer was used to obtain an exact numerical solution for the transient behavior of the insulation and earth adjacent to an isothermal, submerged flat surface for a single set of parametric values. Comparison of the computed results with analytical solutions for limiting conditions revealed that a complete and general solution for all parametric values could be constructed from these limiting solutions. Complete and general solutions for insulated spheres and cylinders can also be constructed from limiting solutions. The procedure is illustrated in part for an insulated spherical tank. The heat flow was found to fall rapidly to a pseudo-steady state; after some time, it then decreased slowly to zero for a flat plate and cylinder, and to a low steady-state rate for a sphere. The accumulative heat flow during the initial falling-rate period may be a significant fraction of the heat flow during the entire first year. INTRODUCTION Underground storage of liquefied natural gas and liquefied petroleum gas has received considerable recent attention. The rate of heat flow from the earth to the storage cavity and the resulting temperature field in the earth are important factors in the technical and economic evaluation of such storage facilities. The objective of this paper is to indicate how complete solutions can be developed for the transient flux and temperature field for various geometrical configurations. The representative properties and dimensions, and the resulting parameters utilized in the illustrative results, are indicated in Table 1. The results presented herein are for dry earth. The effect of the latent heat of solidification of water in the soiI will be described in a subsequent paper. The temperature field in the insulation and earth is determined by energy balances, boundary conditions and initial conditions. The physical problem can be described mathematically with virtually no idealizations insofar as physical properties are known. It appears possible to solve the equations by numerical integration on a high-speed digital computer for any geometrical configuration and conditions. For complex situations, however, the computations are expensive and the results are highly specific. Analytical solutions have been developed for a few simple but important geometrical configurations and conditions, including one-dimensional heat transfer from (or to) earth at an initially uniform temperature to (or from) flat plates, spheres and circular cylinders. The solution for an insulated flat plate has also been derived but is in the form of a slowly converging series involving taklated functions. It was planned to use a computing machine to evaluate this series for a number of representative conditions. However, upon examination of the results of preliminary computations it was discovered that a complete, general and accurate solution could be developed by interpolation between several much simpler solutions for limiting conditions. This technique then was used to develop a a complete solution for an insulated sphere. The equations presented herein are derived in Carslaw and Jaegerl and other books on applied mathematics, or they are simple extensions of these previous results. Hence, all derivations are omitted. Emphasis is instead placed on the results and their

[ ] ST. JOSEPH Lead Co., is entering the oil business. Andrew Fletcher, St. Joseph president, stated that plans call for a contract with the Continental Oil Co., to drill 11 exploratory wells. Six will be in Texas, one in southern Louisiana, one in northern Louisiana, and one each in California, Oklahoma, and Montana. St. Joseph is also negotiating a contract with the Zephyr Drilling Co., for wells in Wyoming and Colorado. St. Joseph is planning to drill another well on a 6000 acre plot in southern Illinois. Proxies issued before a special meeting of the board, said the new venture is not intended to change the general character of the company's business, or to involve a significant part of its resources. If gas, oil, or minerals are discovered in paying quantities, the company will develop and operate the deposits and dispose of the products for the joint account of Continental Oil and St. Joseph Lead. The mining company will contribute a proportionate share of the cost, but will have definite limitation of its obligation. The amendment to St. Joseph's certificate of corporation, passed by the board meeting, also extended the power of the company to include mining operations of all kinds.

Jan 1, 1952

By E. J. KENNEDY

THE 142D MEETING of the Institute is rapidly shaping up with splendid prospects of a strong technical program and the lighter side of this annual occasion amply provided for. The date is February 20 to 23. The technical sessions will be held in the Engineering Societies building; the smoker-dinner, the informal dance, and the annual reception and dinner, at the Commodore Hotel, Monday, Tuesday and Wednesday respectively. The news to date on the technical side is as follows: Mining Methods-Subsidence The Mining Methods Committee has prepared an interesting program which will be divided into two sessions to be held early in the week. At the first there will be papers on mining methods and development, including a description of the "Sinking and Equipment of No. 2 Shaft at Minas de Matahambre," by Dudley D. Homer and R. H. Cromwell. They describe in considerable detail the equipment used and the practice followed in sinking this important shaft, giving detailed costs and performance figures. Hoist¬ing ?arrangements and mining practice at the "Red Ore Mines of the Woodward Iron Co. at Bessemer, Ala.," are described by Tenny C. DeSollar, superintendent of mines, in a second paper. At this session of the Mining Methods Committee, H. M. Roche and R. E. Crockett, of the Committee on Eastern Magnetite Mining and Milling Methods, will present their paper, "Iron Ore Mining at the Scrub Oak Mine." This mine is in the highlands of New Jersey about 40 miles west of New York City. Prof. Robert K. Warner of Yale University will present a paper on "The Selection of a Mining System," which should have an interesting discussion. Pierre R. Hines, of Portland, Ore., will present, with stereopticon slides, his paper on "The Owyhee Tunnels, U. S. Reclamation Project, Owyhee, Oregon," describing one of the recent irrigation undertakings.

Jan 1, 1933

By J. L. Lytton, J. E. Dorn, L. A. Shepard

Single aluminum crystals were subjected to creep in simple shear on the (111) planes in the slip direction. The activation energies for creep were calculated from the effect of small abrupt changes in temperature on the creep rate just before and immediately following the temperature change. The results definitely establish the fact that creep of single aluminum crystals occurs by-three unique processes, characterized by thethree distinct and isolatable activation energies: The 35,-500-cal-per-mole activation energy obtained at the highest temperatures was ascribed to a dislocativationtion climb process; the 28,000-cal-per-mole activation-energy process, occurring over the intermediate-temperature range was attributed to a cross-slip mechanism; and it was suggested thot the 3400-cal-per-mole process observed below 400°K may be the Peierls energy. THE most pertinent question regarding the phenomenon of creep in crystalline materials is concerned with the identity of the crystallographic mechanisms of deformation that control the creep rate. For many years slight progress was made in uncovering the basic mechanisms for creep. Over the past 10 years, however, two parallel lines of investigations have contributed to a more definitive understanding of the processes involved in creep. The extensive development and maturing of dislocation theories for deformation of crystalline materials' proved to be of paramount importance for this progress. And second in importance was the replacement of the former prosaic methods of creep testing by new techniques'." which were especially

Jan 1, 1959

Jan 1, 1880

By E. S. Wheeler

The rapid increase in the use of monel metal and malleable nickel in the form of sheet, rod and tube has resulted in a similar increase in the demand for these metals in the form of castings. These castings range in size from small valves and pipe fittings weighing a few ounces to large centrifugal pumps, gate valves and marine propellers, some of the last weighing as much as 24,000 lb. A group of such castings is shown in Fig. 1. A large nickel agitator is shown in Fig. 2. Monel metal castings are widely used in accessories for steam power plants and in a variety of chemical plant equipment where the corrosion resistance, high strength and toughness characteristic of this metal render it particularly valuable. Nickel castings find extensive use in the construction of corrosion-resistant apparatus, and are often used in conjunction with wrought nickel sheet and tube in the fabrication of equipment for handling a variety of chemical and food products, particularly dairy products. In response to this demand for castings, numerous foundries have undertaken the production of castings of these metals and have met with varying degrees of success. The successful production of castings of monel metal and nickel requires careful attention to molding practice, proper melting equipment

Jan 1, 1930

By C. O. Lee, Z. W. Bartlett, R. H. Feierabend

DESPITE the fact that American brimstone production has increased 2 ½ times since the prewar period 1935-1939, the demand for sulphur exceeds the supply. To alleviate this situation efforts are being made to increase the production of sulphur and bring the shortage to an end. The most important developments are being undertaken on the Gulf Coast. One new brimstone mine has been put into operation and three others are being developed. These projects are expected to account for a large part of the additional sulphur production now anticipated for the free world.1,2 Except for a small amount of byproduct sulphur from sour natural gas and refinery gases, American brimstone is produced by the same process devised by Frasch 60 years ago, consisting essentially of the injection of superheated water at about 325°F into sulphur-bearing formations through wells which are drilled from the surface by standard oilfield methods. Sulphur deposits vary in depth from a few hundred feet to 2500 ft from the surface; in a typical deposit the sulphur occurs as crystalline aggregates in porous limestone and gypsum in concentrations varying from 5 to 40 pct, the thickness of the formation ranging from a few feet to several hundred.3 The deposits are usually surrounded by formations impermeable to the flow of hot water, the top and sides being enclosed by impermeable sediments and the bottom by dense impermeable anhydrite. As the hot water leaves the well bore, it percolates through the formation and transmits its heat to the rock and sulphur. When the sulphur reaches 240°F it melts, separates from the rock, and flows through the hot channels downward to the bottom of the well. Here it is freed from incoming water and from formation water, which saturates the porous rock, by gravity separation, liquid sulphur being 1.8 times as heavy as water. It then is pumped to the surface in a relatively pure state, 99.5 pct or better. Chief contaminants are organic impurities, such as petroleum residues, which are soluble in sulphur and tend to discolor it.4 Sixteen deposits of commercial magnitude have been discovered in the Gulf Coast area. Five of these deposits have been depleted and abandoned with production totalling more than 26,886,000 tons. Eight properties are operating and have produced 65,875,000 tons to Jan. 1, 1952, for a total Frasch-type production of 92,761,000 tons. Three new deposits are under development. Aforementioned deposits are listed in Table I. Each of these deposits has been found in the caprock overlying shallow intrusive salt plugs or domes and buried in several hundred to as much as 2500 ft of sediments. All salt domes do not contain sulphur; only 16 sulphur deposits have been found in a total of 231 salt domes which are known to exist in the Gulf Coastal states of Texas, Louisiana, Mississippi, and Alabama. Ten of the salt domes lie in the Gulf of Mexico offshore from the Texas and Louisiana coasts. Additional offshore domes may be found, but their value as a sulphur potential is questionable owing to the great hazard and high cost that can be visualized at these exposed locations where depths of water reach 50 ft. Marsh operations of Freeport Sulphur Co. are in the southeast section of Louisiana. In general, the country is low, flat, relatively uninhabited marshland broken by many shallow lakes and bayous which extend for irregular distances inland. Geologically, the coastal area is of sedimentary origin, having been built up gradually under the sea by deposition of material carried down by large streams to their deltas. Offshore bars were formed enclosing

Jan 1, 1952

By Donald F. Saunders

Means and relative standard deviations were calculated for eU, eTh, K, and their ratios for aerial gamma-ray spectral data in 29 quadrangles at 1:250,000 scale. Known or suspected uraniferous provinces were characterized by: 1) Higher eU, eTh, and K means (due to generally higher radioelement concentrations); 2) Higher relative standard deviations for eU, eU/eTh, and eU/K (reflecting the presence of local uranium enrichments); and lower mean eU/eTh and eU/K values (showing uranium loss from "average" rocks to form local enrichments). "Uranium favorability indexes," i.e., combinations of the sensitive variables, show an excellent qualitative relationship to known occurences and geologic favorability. Results appear to confirm the existence of long-term crustal uranium provinces formed at the time of emplacement of the oldest known rocks.

Jan 1, 1980

By Samuel Wyer

1. THE following is an abridgment of a recent report made by the author, covering an investigation of (A) The necessary use of natural-gas compressors; (B) The effect of gas compressors on natural-gas field operating conditions in Ohio, with special reference to the working pressure relations of gas wells of one company discharging by natural rock pressure flow without compressors, and adjacent wells of other companies, discharging into intake lines to gas-compressing stations. Tests were made at 107 different places in the counties of Fairfield, Licking and Knox, Ohio, which required 7,000 miles of automobile driving, and consumed 6 months' time. 2. A proper conception of. the necessary use and effect of natural-gas compressors in natural-gas production necessitates a clear understanding of certain fundamental definitions and judicial doctrines, which are given herein. 3. Gas is a fluid composed of a large number of molecules which are vehicles of energy continually in motion, and having an inherent. tendency to get farther and farther apart. The range of motion of the molecules is limited only by the volume of the closed containing vessel in which they constantly move to and fro. The most distinguishing characteristic of gas is its universal property of completely filling an inclosed space.

Jan 2, 1916

By R. T. Hukki

This paper presents a preliminary analysis of the fundamental relationship between the net energy used and the respective product size throughout the entire range of sizes covered by crushing and grinding, and an attempt to find a sensible correlation between the existing theories. Walker, Lewis, McAdams, and Gilliland' have given the following differential equation of a general form for comminution: dE = -C§ [1] where E is the net energy required per unit weight in a certain process of comminution; x is the factor indicating the fineness of the product; n is the exponent indicating the order of the process, and C is a constant related with the material, units chosen, etc. H exponent n in the above equation is replaced by numerical figures 2, 1, and 1 1/2, the integrated form of the general equation leads to the well known fundamental theories represented by the law of von Rittinger,' law of Kick, and the third theory of comminution by Bond, respectively. The total net energies (E) from infinite feed size to a product of size x are as follows: The net energy required in a certain process of comminution is proportional to the new surface developed according to the law of von Rittinger, to the weight or size of the bodies treated according to the law of Kick, and to the length of the new cracks formed which initiate breakage according to the theory and explanation by Bond. On a logarithmic paper, where particle size is presented on the abscissa and energy consumption on the ordinate (see Fig. 21, all three relationships are represented by straight lines. The slope m of the line according to the law of von Rittinger is equal to -1.0; of Kick, 0; and of Bond, -0.5. Experimental evidence in favor of the law of Rittinger has been presented, e.g., by Gross and zimmerley5 on quartz crushed in a drop weight crusher and evaluated for surface by the method of dissolution, by Dean on magnetite crushed by a similar method and evaluated for surface by the determination of coersive force, by piret7 and co-workers on a group of minerals crushed again by a similar method as well as by compression and evaluated for surface by permeability and gas adsorption methods, and by schellinger8 on a group of minerals ground in a calorimetric ball mill and evaluated for surface by gas adsorption. Experimental evidence in favor of the law of Kick seems to be scant in the field of comminution. On the other hand, in the field of mechanical engineering Kick's law seems to be of fundamental nature in processes such as cutting, pressing, shaping, and rolling of metallic substances. Experimental evidence in favor of the third theory has been provided by Bond." To a large extent, data are based on the vast amount of grindability tests performed in the laboratories of Allis-Chalmers Manufacturing Co. In addition to the devoted proponents of one or the other of the basic theories listed above, certain investigators have indicated that one of the theories might be applied for a certain range of sizes, while another theory might be used for other sizes. In a discussion of a paper by Bond," Dobie" presented a statement at the International Mineral Dressing Congress in London (1952) indicating that 1) for large particles, the law of Kick was approximately correct; 2) for finer particles, von Rittinger's suggestion was nearer to the truth; and 3) Bond's new

Jan 1, 1961

By T. B. Counselman

Continuous countercurrent decantation calculations have always been a headache to the cyanide man (and the chemical engineer) because of the simultaneous equations involved. These are tedious to solve, and there is considerable opportunity for mathematical error. This paper presents a shortcut method for making these calculations, which has been in successful use for twenty years by the author, and which is particularly valuable in selecting the best of several possible flowsheets, or evaluating the effect of various assumptions.

Jan 2, 1950

By Ralph Arnold

SOUTH of Havana, there is a geanticline that extends from Madruga to Bejucal. The older formations outcrop in the. east and gradually go under until in the Bejucal region the entire geological column lies below the surface, with the Nazareno formation at the top. The well we are now drilling is located at the deepest part of the section. I think there is a good chance to obtain oil, for the conditions are like those in the Santa Maria field in California. In both places asphalt occurs in the upper shales in the form of dikes that break through the older formations. The drilling in the Santa Maria field was brought about by the evidence offered by the asphalt deposit, which overlaid the oilfields. Detailed geologic work in both fields discloses pretty well defined domes with minor faults. Between Madruga and Bejucal, the San Francisco formation has come, to the surface in a dome and still farther east there are other domes near the base of the formation in which the Madruga chalk is the surface rock. The Bejucal dome was selected for drilling because, it gave the greatest evidence of petroleum in the form of asphalt and because it offered three chances of striking oil in the three possible oil horizons below the top of the Nazareno formation. The hole is now 2600 ft. deep and has shown considerable gas and some oil. The lowest gas sand will probably yield from 2,000,000 to 3,000,000 cu. ft. per day. Very heavy mud has been used in drilling this hole and this has held back gas and oil indications.

Jan 3, 1925

By Guilliaem Aertsen

The derivation of the word tire (or tyre, as it is spelled in England) is obscure. Some dictionaries suggest that it is the aphetic form for "attire, covering," so called as being the outside covering or band of a wheel; also as a corruption of "tier," the band which holds, or "ties," the rest of the wheel together. One dictionary states: "The supposed derivation of the word is that bands were first used on wheels in the City of Tyre, Syria." In the infancy of railroads, the tracks consisted of flat bars of iron, spiked or bolted to the upper surfaces of longitudinal timbers, which, in turn, rested upon masonry foundations. Stone blocks installed for this purpose on the old Germantown & Norristown Railroad, now the Chestnut Hill branch of the Philadelphia & Reading Railway, were to be seen for many years on the right-of-way, north of what is now Wayne Junction, Philadelphia, Pa. The "cornerstone" of the Baltimore & Ohio Railroad was laid Apr. 4, 1828, and the fist locomotive in America was built by Peter Cooper at the St. Clair Works, Baltimore, Md., in 1829 "to demonstrate its adaptability to a curved road." It is believed that the first successful locomotive was built in Philadelphia by Tyler & Baldwin in 1832 for the Germantown & Norristown Railroad. Rufus Tyler and Matthias Baldwin were brothers-in-law; the latter's name will be identified with American locomotives until locomotives are forgotten. The wheels on these first locomotives, designed to run on this primitive rail, mere shod with plain iron bands, bent and welded. The flanges consisted of separate iron bands, bent sidewise,welded, and bolted to the sides of the wooden fellies, or rims. Before many years had elapsed the tires were fabricated of iron bands, rolled in one piece with the flange projection on the side. The tire for each wheel was bent and welded and subsequently attached to the wheel center by shrinkage, bolts, rivets and various mechanical devices. Germany is generally given the credit for first making such tires of

Jan 1, 1917

By R. E. Hummel, J. W. Koger

IT is generally accepted that the martensitic start temperature (Ms) can be determined by resistivity measurements and is that temperature where the resistivity vs temperature curve on cooling first deviates from a straight line.1-4 Both Titchener and ever' and pops5 have used resistivity measurements to follow the martensitic transformation in b1 Cu-Zn and ternary Cu-Zn-based b-phase alloys, respectively. Actually because of the nature of their measurements the temperature of minimum resistivity (M) was used by these authors to determine "Ms" . Also, due to experimental difficulties in detecting M, with resistivity measurements, Pops and Massalski 8 determined M, by optical microscopy. The present communication is concerned with high-precision, low-temperature resistivity measurements which reveal a definite M, temperature which differs from the temperature of minimum resistivity (M). It is also shown that M is merely the result of the geometry of the percent-transformation curve and the temperature coefficient of resistivity of the alloy. In other words, it will be demonstrated that M has no apparent significance (except that it denotes a temperature at which some percent of martensite can be detected in a given alloy). Alloy specimens were made by melting 99.999 pct Cu and 99.9999 pct Zn in sealed and evacuated quartz tubes and homogenizing them at 601PC for 300 hr. After the alloy was cold-rolled into foils suitable for resistivity measurements, it was quenched in ice water from 871PC. The chemical analysis showed a zinc content of 38.8 wt pct. The cooling rate during the martensite transformation was 1°C per min and was controlled with a thermistor. Electrical resistivity measurements were made using a K-3 type potentiometer; the reproducibility of the resistivity values was better than 0.03 pct. Temperatures were measured with a thermocouple to an accuracy of better than 0.2° C. Fig. 1 shows the resistivity vs temperature curves of the martensitic transformation in B1 Cu-Zn for both cooling and heating. The starting point of the martensitic transformation (M,) was taken as that

Jan 1, 1968

By R. R. Webster, H. T. Clark

The side-blown converter has been investigated as a possible commercial process for the production of low nitrogen steel. During this work, two converters of 3-ton and 22-ton capacity were operated on a pilot plant basis for a total of 214 heats. The steel made in these converters was low in nitrogen and possessed good cold working properties. Some problems of converter operation remain to be solved. IN plants operating with a high iron capacity, sev-eral different refining methods are used in the conversion of the molten pig iron to steel. These include various ore practices in stationary and tilting open-hearths, the duplex process employing the Bessemer converter and open-hearth, and the Bessemer process. At J&L, a considerable part of the iron produced is handled by the Bessemer process, either alone or in conjunction with duplexing, and therefore an appreciable portion of the steelmaking research effort has centered about the method. This paper covers research work on the development of the side-blow converter for the commercial production of low nitrogen ingots and includes descriptions of the operation of a 3-ton and a 22-ton experimental converter at the Aliquippa Works. The refining of iron to produce steel requires the removal of a large portion of the carbon and silicon and the control of manganese, phosphorus and sulphur which are present in the iron in varying amounts. The first large-scale means of refining iron was the acid Bessemer process which was brought into use almost 100 yr ago. This method, using compressed air as the refining medium, accomplishes substantially complete removal of carbon, manganese and silicon. Phosphorus and sulphur are not affected but, by choice of an iron composition sufficiently low in these elements, a commercial product can be produced. Since the process will handle large tonnages rapidly, operates without external fuel and with a minimum of additional equipment, it quickly became the major tool in the early expansion of the steel industry. Later, the basic open-hearth process, by affording control of phosphorus and sulphur and by consuming the large quantities of steel scrap that were becoming available, forced the acid Bessemer process into a secondary position in the industry. During the past two decades the demand for steel to be used in cold forming and drawing operations has gradually increased. Bessemer steel, because of its work hardening and aging characteristics, is not as suitable for these applications as basic open-hearth steel, consequently the decline of the process was accelerated. More recently, because of changing economic conditions, this long range trend appears to have been arrested or perhaps reversed. Ingot production data for recent years furnishes only an incomplete picture of the importance of the converter in the American steel industry; open-hearth furnaces utilize large tonnages of blown metal for which no published statistics are available. Metallurgical Aspects The fundamental difference between Bessemer and open-hearth steels apparently lies not in the method of manufacture but, rather, in the differences in chemical composition of the two steels. It is further believed that the principal features distinguishing Bessemer from open-hearth steel are the higher nitrogen and phosphorus contents of the former. Evidence supporting this position is supplied by tests on laboratory induction furnace heats that were made to contain varying amounts of phosphorus and nitrogen but were otherwise similar to normal low carbon silicon-killed steels. Fig. 1, 2 and 3, summarizing the test results, are taken from G. H. Enzian's paper titled, "Some Effects of Phosphorus and Nitrogen on the Properties of Low Carbon Steels."' Fig. l indicates that phosphorus has a marked effect on the cold work embrittlement of steel as shown by the work brittleness test of Graham and Work.' In the low nitrogen steels, which as a group have the better cold working properties, the effect of phosphorus variations is the more pronounced.

Jan 1, 1951

By J. I. Budnick, W. B. Ittner III, D. P. Seraphim

A reliable technique has been developed for producing single crystals of tantalum in the form of small diameter wires. By suitably heat treating these and polycrystal samples, first in an oxygen atmosphere and finally in vacuum, it has been found possible to reduce residual resistivities to 10-3 microhm-cm. The purity of these samples is thus comparable to the purities obtained in zone-refined silver, copper, and aluminum. THE growth and purification of pure single crystals of the transition metals is, in general, difficult. The high melting and annealing temperatures of these metals make it necessary to employ rather special techniques in any crystallization process. In addition, the transition metals show a great affinity for and are easily contaminated by nitrogen, oxygen, and carbon. Recently, however. a number of investigators have been successful in growing,

Jan 1, 1961

By J. F. Smith

ELASTIC constants of yttrium and eleven of the rare earth elements have been measured. This has been accomplished by measuring the propagation velocities of ultrasonic pulses. The velocity measurements were made by noting the elapsed time between an applied pulse and the appearance of successive echoes. The pulse-echo technique has become relatively common, and the basis of the measurement is outlined in several standard tests, e.g., Heuter and Bolt.1 Two important assumptions are made when using this method for the determination of elastic moduli. First, the pulse is assumed to propagate as a plane wave. To justify this assumption, the cross section of the test specimen should be large compared to the wave length of the transmitted pulse. For these measurements on the rare earth elements the minimum cross section wave length ratio was about 20. A second assumption which must be made when using polycrystalline specimens is that the grains are sufficiently numerous and randomly oriented so that the specimen may be approximated as elasti-cally isotopic. The grain size in the as-cast specimens which were used is believed to be sufficiently fine for this approximation, and the degree of preferred orientation is believed to be small. Supporting this viewpoint is the fact that elasticity measurements by the pulse-echo technique on as-cast specimens of other metals give results which are in satisfactory agreement with values obtained by other techniques. Hence, it is believed that the measured elasticity values for the rare earth elements are not apt to be seriously in error due to the assumption of elastic isotopy. The apparatus used in this determination was a modified Sperry Reflectoscope with a precisely calibrated time base circuit. Piezoelectric transducers were used both to generate the pulse and to detect the echoes. X-cut quartz crystals were used for the longitudinal modes, and Y-cut quartz crystals were used for the shear modes. Frequencies of 2.25 and 5 megacycles per sec were employed. Most of the specimens were 2.5 to 5.0 cm in length. Results Table I is a tabulation of the measured propagation velocities of longitudinal waves and of shear waves, together with densities obtained by Sped- ding, Daane, and Herrmann2 from lattice parameter measurements. The shear modulus, Poisson's ratio, and Young's modulus were calculated from the data in Table I through use of the following relationships: µ = pv32 [1] s=2-(vb/vs)2/2[1-(vb/vs)2] [2] and Y= 2µ(l+s) [3] where s is the shear modulus, Y is the Young's modulus, s is Poisson's ratio, p is the density, V0 is the longitudinal wave velocity, and v, is the shear wave velocity. The calculated quantities are shown in Table 11. Compressibility values can be computed from the relationship and the computed values may be compared with measured values obtained by Bridgman.8 Table III lists the data for such a comparison. The agreement is satisfactory, being particularly good for neodymi- um and gadolinium, poor for samarium, and intermediate for the other elements. Some variation is expected since Bridgman's measurements are isothermal, whereas the present measurements are adiabatic. In addition there may be some effect due to small variations in purity. Though most of the rare earth metals measured by Bridgman and all of the metals used in the present measurements were prepared at this laboratory, minor purity variations might exist since the samples came from different lots. Also, any imperfections such as dislocations, vacancies, voids, grain boundaries, microcracks, etc., should contribute to the volume change of a com-

Jan 1, 1958

By A. M. Gaudin, J. G. Morrow

FLOTATION requires the existence of a definite contact angle. This contact angle, the surface tension of the solution, and adsorption at the solid- fluid interface are quantitatively related. Adsorption of dodecylammonium acetate on hematite was measured for a wide range of concentrations of reagent in solution. Similar measurements for quartz have already been made.1 Contact angle measurements were then made on polished surfaces of hematite and of quartz immersed in aqueous dodecylammonium acetate solutions, and a functional relationship was sought between adsorption density at the mineral-solution interface and the contact angle. Finally, the surface tension of the aqueous amine acetate solutions was measured. These data were combined to give an evaluation of the work of adhesion for the three-phase system.

Jan 12, 1954

By F. D. Hoyt, H. L. Hartman

The development of new processes and methods by The Pennsylvania State University to improve slate quarrying technology has centered in recent years on cutting and sawing stone in the quarry to eliminate a second cutting process in the mill. Two machines exhibit promise for this work: 1) a circular saw mounting diamonds or hard inserts to produce smaller sizes of stone and 2) a chain saw with insert cutting teeth to produce stone in the larger dimensions. Prototype machines have been constructed and tested in several Pennsylvania slate quarries, and one commercial installation has been operated for several months with a circular diamond saw. Other kinds of dimension stones may be cut by these saws. Research at Penn State has begun to study the fundamental cutting action of rotary tools or saws in slate and other dimension stones. A laboratory drill press is being instrumented to permit thrust-torque-rotational speed us penetration rate studies of single tooth cutting surfaces on stone. Machinability studies of slate conducted with tungsten-carbide inserts have been performed. The dimension stone industry generally accepts the rather basic premise that the larger the block removed from the quarry, the more practical and economical the operation. Thus, the concept of cutting to size any dimension stone while it remains in place in the parent bed would receive little consideration from the majority of members of the industry. However, the slate industry, which is usually considered a separate member of the dimension stone family, is pioneering in the development of an in-place sawing method. Before any final decision can be reached concerning a proposed new system, it is essential to take a long, hard look at the present method of operation in order to determine if the new system is indeed an improvement or even desirable. In the following section is a brief description of present quarry practice in the slate quarries of eastern Pennsylvania. PRESENT METHOD OF QUARRYING SLATE In the numerous slate quarries of Lehigh and Northampton Counties of Pennsylvania, the grain and cleavage of the slate are most often at right angles to each other; if a third surface is broken at right angles to these two natural planes of weakness, blocks of more or less rectangular shape can be separated.' In conventional quarrying a large calyx core drill prepares holes of 36-in. diam in which wire-saw standards are positioned. By wire sawing between strategically located core-drill holes, large sinks or benches of virgin slate are opened up. The sides freed by wire sawing will vary from quarry to quarry but generally are rectangular in shape with dimensions averaging 20 ft in length and about 15 ft in depth. Some quarries are fortunate in having a joint or natural parting to work to, which of course diminishes the amount of core drilling and wire sawing required. Once the various benches have been developed either through wire sawing alone or through a combination of wire sawing and natural jointing planes, the block removal proceeds in the following manner. A plug hole is drilled in the block with a compressed-air hammer and a feathering chisel is inserted in the hole to cause a fracture of the rock either with or against the grain as indicated by the positioning of the so-called feathers. This operation is referred to as sculping. After a block has been freed with and against the grain by means of wedging from the cross fracture with long bars or levers, the block is further freed along the cleavage plane by shimming it up with small wooden pieces in an operation known as styling. A large steel loading chain is wrapped around a block thus freed and the chain is attached to the wheel of an overhead cable. The block is then hoisted vertically to the cableway and moved along this cableway laterally to the lip or edge of the quarry. From here it is unloaded onto a rail car or truck for transportation to the processing mill. Except for occasional blasting to free stubborn blocks,

Jan 1, 1961

By Plato Malozemoff, A. M. Gaudin

IN modern practice the major portion of an ore is reduced to flotation size by fine grinding. As the result of grinding fine enough to liberate most of the minerals, a substantial portion (generally 5 to 15 per cent) of the ore is inadvertently reduced to a size much finer than that necessary for liberation. This portion of most flotation pulps is very refractory to recovery by flotation. A reduction of one-quarter or more in recovery in this range of extremely fine particles can be observed. The loss in metals caused by overgrinding is appreciable. That this loss is characteristic of very fine particles has been suspected for some time;(l)† however, it was definitely quantified only recently.(2) Definite reduction in float-ability with reduction in particle size beyond a critical size of maximum floatability can be accepted now as an established fact. Formulating the Hypothesis In looking for the cause of the ill behavior of the finest particles it may be well to consider the essential differences between fine and coarse particles. A difference that immediately comes to mind is their intrinsic difference in size and consequently in relative extent of surface. If one agrees that attachment of mineral particles to bubbles must follow direct encounter of particles with bubbles one is forced to conclude(3) that the probability of encounter between a mineral particle and a bubble varies directly as the size of the particle, provided the particle is small compared to the bubble. In other words, the finer the particle the poorer its chance of being recovered in a given time of flotation. There is an effect, implicit in this theory, which should overcome the effect of excessive fineness of the particles; namely, flocculation of the particles. The floccules can be conceived as being simply larger particles and therefore capable of becoming attached to bubbles. And, indeed, in all the cases in which a sulfide mineral of near-colloidal size was successfully floated the mineral (but not necessarily the gangue) was flocculated. Moreover, it was shown experimentally(4) that galena previously flocculated by inorganic flocculators and then added to gangue

Jan 1, 1935