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"Coulter's Rainbow and Crooked Falls are situated about five miles below the City of Great Falls. Coulter's, the first of the series in the course of the river, is unimportant and has been submerged by the Rainbow dam. Next below Coulter's is the Rainbow Falls, 47 feet in height. Following Rainbow Falls is the Crooked Falls, 21 feet in height. The power developed at this point is such that the one clam, power house and tail-race utilize the power from all three of the above falls.The development at Rainbow was started October, 1908, and completed July, 1910. It has a total capacity of 21,000 k-w. in generators, and 36,000 h-p. in waterwheels, and operates at 105 foot head. The general scheme of development is typical of what may be called standard practice in the west for plants of medium head, and consists of a low diverting clam, a double pipe line feeding into a balancing reservoir near the plant, and individual pen-stocks supplying the turbines from this reservoir.The dam is a rock-filled crib structure 1,146 feet long and 29 feet high, the up-stream side of which slopes at such an angle that the stability of the clam is assured even under the greatest floods, the weight of the water acting to hold it down, so that the higher the flood the greater the stability. The down-stream side is also sloping and tapers off into a long apron so designed as to take care of any overflow which may occur without shock or commotion. The clam is founded on solid rock throughout its entire length."

Jan 1, 1913

By G. A. Reinhardt

THE Youngstown Sheet & Tube Co. has produced a large tonnage of 0.35 to 0.45 carbon forging steel, the acceptance of which was based on the physical properties of test specimens obtained by forging the original 5 3/4 in. (14.5 cm.) square bloom to a ¾ in. (1.9 cm.) round. Annealed and tempered specimens were required. The test bars were annealed by heating from 900 ° to 950° C. and cooling slowly in mica. The test bars were tempered by heating to 825° to 875° C., quenching in water, and drawing to 515° to 535° C. Immediately after heat treatment, the test pieces were machined to a diameter of 0.534 in. (1.38 cm.) and tested. Very good physical properties were obtained and no difficulty was experienced in meeting the specifications called for. ULTIMATE STRENGTH, ELONGATION, LB. PER SQ. IN. PER CENT. IN 4 IN. NOT LESS THAN Annealed specimens 78,230 to 92,450 18 Tempered 120,000 to 149,350 9 After experience oil this material, production of slightly higher carbon forging steel was started. The method of testing this material required that test blooms be either normalized or annealed. The normalizing consisted in heating to 850° to 900° C. and cooling in still air; the annealing, in heating to 850° to 900° C. and cooling in the furnace or in mica. From the treated bloom, the test pieces were taken either by core drilling or by sawing from points midway between the edges and the intersection of the diagonals. The cores or blocks were turned to a standard 2-in. test piece with a diameter of 0.564 in. and tested without further treatment. The physical requirements of the test pieces were:

Jan 7, 1919

By AIME AIME

AN outstanding session of the Annual February Meeting was one held under the joint auspices of several groups on Tuesday afternoon, Feb. 22, as a symposium on the question of preserving peace in the postwar era through the control of the supply of sundry minerals vital to the Axis nations. D. H. McLaughlin and R. C. Allen were associate chairmen. And C.K. Leith led the discussion.

Jan 1, 1944

By W. E. STOKES

SOME extension of flying service to the mining industry occurred in 1938, particularly in Canada, where freighting activity radiated from Edmonton into the new northern mining districts. Again the airplane demonstrated its usefulness in getting new equipment rapidly into the field and in decreasing shutdown time while waiting for repairs. An 18-ton Caterpillar tractor with shovel attachment was disassembled, brought in by plane, and placed in operation at Berens River, Ont., within seven days after its de- livery at Winnipeg. At Central Patricia a mill breakdown required the replacement of a full mill head and trunnion with ball bearings, weighing 2700 lb. The Canadian Airways Junkers, termed the "flying boxcar," was called in from Yellowknife, 1300 mi. away, and the new installation was completed three days later.

Jan 1, 1939

By Alvinus Brown Wood

THE ancient copper-mines of Lake Superior, having been destroyed or covered by-modern mining-dumps, are not accessible to the present inhabitants of that region, and, since no more are likely to be found, some account of those already discovered, from one who has seen them, may be acceptable to the Institute. Early in May, 1855, 1 took a party of men to open an ancient pit on the Quincy mine-location. Mr. C. C. Douglas was the Agent.," as mine-managers were then called on Lake Superior. The Quincy Co. had previously done work on a fissure-vein, several hundred feet west of the Amygdaloid lode (afterwards called the Pewabic lode), on which was the ancient pit herein described. It was at this pit that the Quincy' main shaft was subsequently stink. The ancient pit showed an apparent depth of about 4 ft., but when cleaned out it was shown to be 14 ft. deep, having been filled up by the sliding-in of material composed largely of broken rock, taken out in sinking the ancient shaft, and left near its mouth. Midway of the shaft, and below water-level, was found a scaffolding, of white-birch poles,- which had been used as a landing, to assist in removing the excavated rock. The shaft was 7 ft. in diameter. The excavation had been done by first building fires in order to disintegrate the rock, as was proved by the abundance of charcoal found; then breaking the softened rock with hammers of diorite, such as is found in the greenstone range on Keweenaw point. These hammers had about. the size of large paving-stones. Only broken ones were found, the whole ones having been doubtless carried away for other work, such as could be traced on the lode for a hundred feet or more to the south. At the place where this shaft was stink, barrel-copper (i.e.,

Mar 1, 1906

By Victor Lenher

The interest shown recently in selenium and tellurium has brought many requests for an assembling of the analytical chemistry of these two elements. The intention of this paper is to discuss all of the chemical principles utilized in the detection and quantitative determination of these elements, as well as to describe the works methods actually followed by producers of tellurium and selenium in the United States. These methods have been furnished by S. Skowronski of the Raritan Copper Works, H. D. Greenwood of the United States Metals Refining Co., F. F. Colcord of the U. S. S. Lead Refinery, and E. W. Rouse and A. E. Hall of the American Smelting and Refining Company. Occurrence Selenium is found associated with sulfur, to which in many respects it is quite similar. Occasionally deposits of native sulfur, notably those in the Lipari Islands, Kilauea, and Japan, show a red-brown coloration, I which is readily distinguished from that of other sulfur; this red-brown * sulfur contains a small amount of selenium. Not infrequently, the , sulfides of the heavy metals are accompanied by selenium and tellurium, • presumably as selenides and tellurides. The Scandinavian pyrite, which is one of the large sources of European sulfuric acid, when roasted has fur- - nished a large part of the selenium that has come to the United States; it I was in flue dust from the roasting of Scandinavian pyrites that the element was discovered by Berzelius in 1817. Greek and Spanish pyrites also

Jan 1, 1923

By Victor Lenher

The interest shown recently in selenium and tellurium has brought many requests for an assembling of the analytical chemistry of these two elements. The intention of this paper is to discuss all of the chemical principles utilized in the detection and quantitative determination of these elements, as well as to describe the works methods actually followed by producers of tellurium and selenium in the United States. These methods have been furnished by S. Skowronski of the Raritan Copper Works, H. D. Greenwood of the United States Metals Refining Co., F. F. Colcord of the U. S. S. Lead Refinery, and E. W. Rouse and A. E. Hall of the American Smelting and Refining Company. Occurrence Selenium is found associated with sulfur, to which in many respects it is quite similar. Occasionally deposits of native sulfur, notably those in the Lipari Islands, Kilauea, and Japan, show a red-brown coloration, I which is readily distinguished from that of other sulfur; this red-brown * sulfur contains a small amount of selenium. Not infrequently, the , sulfides of the heavy metals are accompanied by selenium and tellurium, • presumably as selenides and tellurides. The Scandinavian pyrite, which is one of the large sources of European sulfuric acid, when roasted has fur- - nished a large part of the selenium that has come to the United States; it I was in flue dust from the roasting of Scandinavian pyrites that the element was discovered by Berzelius in 1817. Greek and Spanish pyrites also

Jan 1, 1923

By H. G. Schneider

The Smackover oil and gas field lies in Ouachita and Union Counties, Ark., in the south-central part of the state, in T.15 and 16S., R.15, 16, and 17W. It is 10 miles north of El Dorado, the principal business and railroad center in the south-central part of the state, and extends from the town of Smackover in all directions. Productive territory having an aggregate area of nearly 55 sq. mi. has been developed. It extends 6 miles from north to south and 12 miles from east to west. The field may be divided into two parts: the east district, which includes the area east of the town of Smackover, and the west district, which includes the area west of the town of Smackover. In relation to the neighboring productive fields of Arkansas, the Smackover field is 9 miles north of the El Dorado oil and gas field, 8 miles slightly west of north of the East El Dorado oil and gas field, and 16 miles east of the Stephens oil field. Smackover was discovered in May, 1922, when the Oil Operators Tnist drilled well No. 1 on the J. T. Murphy farm, in the southeast quarter of sec. 8, T.16S., R.15W. This well is located almost on the top of the Norphlet dome and was drilled to the Nacatoch sand. It had an initial open flow volume of 30,000,000 cu. ft. of dry gas per day, and a rock pressure of 950 lb. per sq. in. In July, 1922, the V. K. F. Co. completed the first oil well in sec. 29, T.l5S., R.l5W., on the north side of the Norphlet dome, and 3 miles north of the first gas well. This well started the active development of the north and northwest sides of the dome.] The field was extended westwards, when oil was discovered in the Nacatoch sand, during October, 1922, in sec. 4, T.l6S., R.l6W., 51/2 miles west of the original gas well. This opened up the so-called "light oil district," which is located on a structural terrace, for which the name

Jan 1, 1924

By J. B. Austin

Jan 1, 1945

By W. C. Bleimeister

The rock salt deposits of the U. S. occur in five major basins: 1) the Eastern Basin (which includes parts of Michigan, Ohio, Pennsylvania, New York, West Virginia, and Ontario) ; 2) the Gulf Coast Basin (the northern rim of which includes parts of Alabama, Mississippi, Louisiana, Arkansas, and Texas, while its southern rim includes parts of the Isthmus of Tehuampetic and the Yucatan Peninsula of Mexico), 3) the Southwestern Salt Basin (which includes parts of Kansas, Colorado, Oklahoma, Texas, and New Mexico), 4) the Williston Basin (which under- lies parts of North Dakota, South Dakota, Montana, and Saskatchewan), and 5) the Green River Basin (whose periphery underlies parts of Wyoming, Utah, and Colorado). The greatest salt production in the U. S. is obtained from the Eastern Basin,-particularly from the areas of Michigan, Ohio, and Ontario. In 1958 the salt production from these areas amounted to 8.7 million tons or 35.3 pct of the combined total produced in the U. S. and Canada. Of the 24,286,000 tons produced by Canada and the United States, 6,443,000 tons were in the form of rock salt from dry mining, while 17,843,000 tons were produced from wells in the form of artificial brine, the result of dissolving the rock salt formation by fresh water. Three important factors lie behind the location and development of this salt mining area:

Jan 5, 1961

By N. A. Ziegler

THE chief difficulty in determining oxygen in steels is its tendency to form a variety of compounds. Almost every element, found as an ingredient in steels, maybe expected to be present as an oxide. Some of these oxides have widely differing properties, and consequently behave differently when attempts are made to reduce them by the vacuum fusion method. As I pointed out in a paper published in the Transactions of the A.S.S.T., Vol. 20, No. 1, many experimenters are spending considerable time and effort in attempting to deter¬mine the degree of completeness of the above reactions, and hold different opinions on the matter. In studying this subject the following table, taken from Hodgman and Lange's "Handbook of Chemistry and Physics" may be used as a guide.

Jan 1, 1933

By F. W. Gordon

Since the waste gases of the blast-furnace came to be generally utilized in heating the blast and raising steam, the gradual improvement in the economy of fuel, mainly through the nse of higher temperature in the blast, has impoverished the gases. The increased output per unit of measurement of the furnace, and the increased height of the furnace, have markedly increased the resistance to the blast, thus enormously increasing the duty required from the gases. In other words, a gas reduced in heating power by a further dilution of CO, is required to raise the temperature of the blast to 1800' Fahr., where formerly 600' was a good temperature, and at the same time to raise steam enough to drive the air into the furnace at a pressure of from four to eight pounds in coke practice, and from eight to twelve pounds in anthracite practice, and also pump at least double the water formerly used at furnaces. Hence the necessity for the employment of the best scheme for thoroughly consuming these gases with the least dilution of air, and the use of the best device for absorbing the heat prodnced for the purposes above mentioned. In a former paper before this Society the writer called attention to such improvements as had been made by his firm, by which it was claimed 1400' Fahr. could be maintained in the blast by a less consumption of gas than was required to maintain 900' when using pipe-ovens; and it would not be too much to say that 1600' Fahr. might now be written in place of the 1-400. The object of this paper is to give the practice of our firm in the

Jan 1, 1884

By H. H. Reamer, B. H. Sage

Attempts have been made to predict the volumetric and phase behavior of naturally occurring hydrocarbon mix-turesl-6 but these methods have not been extended to the higher pressures and tem-peratures that are currently encountered in some producing formations. Furthermore, the methods of prediction at present avail-able have not been tested in a sufficient number of cases to ensure their applica-bility to all naturally occurring hydrocar-bon mixtures, even at the lower pressures and temperatures. For these reasons the behavior of a number of hydrocarbon mix-tures from a field in which the subsurface pressures are above 4500 lb. per sq. in.t and the temperatures are in the neighbor-hood of 250°F. was investigated. Method The objective of this program was to determine the volumetric behavior of ma-terial as it existed in the reservoir as a function of pressure, temperature and com-position. Strictly speaking, this cannot be accomplished in any simple fashion. How- ever, the variations in composition that are encountered within a producing reservoir may be approximated roughly by means of mixtures made up of two arbitrarily chosen constituents. Experience indicates that the liquid and gas phases from a high-pressure gas trap afford a simple source of material for this purpose. Throughout this discus-sion the samples of the gas phase and liquid phase from the production trap will be called the "trap-gas sample" and the "trap-liquid sample," respectively. The volumetric behavior of both of the trap samples was determined throughout the temperature interval between 100" and 250°F. at pressures up to 5000 lb. per sq. in. In addition, the behavior of eight different mixtures containing varying proportions of the two trap samples was studied throughout the same temperature and pressure intervals. The experimental results yielded information concerning the specific volume of the material as a function of pressure, temperature and the relative quantity of the trap samples. The relative amount of each of the paraffin hydrocarbons of lower molecular weight than n-hexane was determined for each of the trap samples. In addition, the specific weight, viscosity and average molecular weight of the hexanes-and-heavier fraction of the trap-liquid sample were determined as well as similar information for each of five fractions separated from this material by distillation. From these data the weight fractions of each of the components from methane through pentane were determined for the trap samples and eight systematically chosen mixtures. Materials The gas and liquid samples were obtained from the production trap of a well in the Rio Bravo field in California during the fall of 1939. Information concerning the condi- 70

Jan 1, 1941

By H. H. Reamer, B. H. Sage

Attempts have been made to predict the volumetric and phase behavior of naturally occurring hydrocarbon mix-turesl-6 but these methods have not been extended to the higher pressures and tem-peratures that are currently encountered in some producing formations. Furthermore, the methods of prediction at present avail-able have not been tested in a sufficient number of cases to ensure their applica-bility to all naturally occurring hydrocar-bon mixtures, even at the lower pressures and temperatures. For these reasons the behavior of a number of hydrocarbon mix-tures from a field in which the subsurface pressures are above 4500 lb. per sq. in.t and the temperatures are in the neighbor-hood of 250°F. was investigated. Method The objective of this program was to determine the volumetric behavior of ma-terial as it existed in the reservoir as a function of pressure, temperature and com-position. Strictly speaking, this cannot be accomplished in any simple fashion. How- ever, the variations in composition that are encountered within a producing reservoir may be approximated roughly by means of mixtures made up of two arbitrarily chosen constituents. Experience indicates that the liquid and gas phases from a high-pressure gas trap afford a simple source of material for this purpose. Throughout this discus-sion the samples of the gas phase and liquid phase from the production trap will be called the "trap-gas sample" and the "trap-liquid sample," respectively. The volumetric behavior of both of the trap samples was determined throughout the temperature interval between 100" and 250°F. at pressures up to 5000 lb. per sq. in. In addition, the behavior of eight different mixtures containing varying proportions of the two trap samples was studied throughout the same temperature and pressure intervals. The experimental results yielded information concerning the specific volume of the material as a function of pressure, temperature and the relative quantity of the trap samples. The relative amount of each of the paraffin hydrocarbons of lower molecular weight than n-hexane was determined for each of the trap samples. In addition, the specific weight, viscosity and average molecular weight of the hexanes-and-heavier fraction of the trap-liquid sample were determined as well as similar information for each of five fractions separated from this material by distillation. From these data the weight fractions of each of the components from methane through pentane were determined for the trap samples and eight systematically chosen mixtures. Materials The gas and liquid samples were obtained from the production trap of a well in the Rio Bravo field in California during the fall of 1939. Information concerning the condi- 70

Jan 1, 1941

By E. W. Filer, R. P. Smith, L. S. Darken

The solubility of nitrogen gas in purified iron and low alloy steels is determined for the y region (930° to 1350°C). The diffusivtiy of nitrogen is estimated from the rate of approach to equilibrium. The investigation of aluminum-killed steels, held in nitrogen, discloses precipitation of aluminum nitride, the solubility of which is determined. ALTHOUGH several investigations of the solu-bility of nitrogen gas in y iron have been reported, all have made use of the method adopted by Sieverts in his classic work, whereby the solubility is determined by the pressure or volume change of the gas. The agreement between different investigators* is rather poor, particularly as compared to the self-consistency of results of several individual investigators. The present report represents a portion of our investigation of the equilibrium of nitrogen and nitrogenous atmospheres with iron and steels. The method adopted in this temperature region (910" to 1400°C) consists of holding the specimen in gaseous nitrogen, quenching (or cooling), and determining the nitrogen content by direct analysis (solution in acid followed by distillation and titra-tion of the ammonia).** Up to 1050°C a 20 in. vertical wire-wound (Kan-thal) furnace was used; this was wound in three sections so that by proper adjustment of relative currents, and use of a modulator1 and a commercial controller (using a chromel-alumel control couple), a zone almost 6 in. long could be maintained uniform within a few tenths of a degree. Since the temperature coefficient of the nitrogen solubility is low, the full precision was not utilized and a variation of l° to 2" was tolerated; a variation of a similar amount also occurred occasionally between the beginning and end of the experiment. At higher temperature a vertically mounted, tubular Globar furnace and control unit was used; the zone of uniformity (l° to 2"C) was here limited to about 2 in.; fluctuations with time were comparable to those in the wire-wound furnace. Reported temperatures were measured by use of a platinum-platinum-rhodium thermocouple, which was frequently com- pared with a similar standard couple which was calibrated at the gold and palladium points and also compared with one certified by the Bureau of Standards; error from this source is believed to be less than 1 "C. Nitrogen gas from a commercial cylinder was mixed with slightly over 1 pct H by use of a gas mixer described previously.' This mixture was passed over hot copper and through ascarite and phosphorus pentoxide to remove oxygen and water vapor. The purified gas contained 1.05 pct H. This procedure was adopted to prevent the formation on the specimens of oxide film, which is well known to be nearly impervious to nitrogen; its success was attested by

Jan 1, 1952

Executive Committee, Board of Directors Howard C Pyle, Chairman, J L Gillson, Vice¬Chairman, A W Thornton, Elmer A Jones, Augustus B Kinzel Finance Committee, Board of Directors J S Vanick, Chairman, John P Hammond, J W Woomer Investments Gail F Moulton, '60, Chairman, Andrew Fletcher, '62, John M Lovejoy, '61, C R Dodson, ex off as AIME Treasurer, J S Vanick, ex off as Chairman of Finance Committee Endowment Andrew Fletcher, Chairman, N G Alford, W J Coulter, Harold Decker, J V N Dorr, R B Gilmore, J B Haffner, Kenneth Hill, 0 H Johnson, J D MacKenzie, D H McLaughlin, J R McMillan, W S Morris, L F Reinartz, H DeWitt Smith, Wilfred Sykes, J R Suman, C E Weed Honorary Memberships C E Reistle, Jr, '60, Chairman, Grover J Holt, '61, Augustus B Kmzel, '62, (ex off as Past Presidents of AIME) M L Haider, '60, D H McLaughlin, '61, John M Lovejoy, '62, L F Reinartz, '63, Howard C Pyle, ex off as President of AIME

Jan 1, 1959

By B. Wilshire, W. J. Evans

W. J. Evans and 8. Wilshire SEVERAL recent investigations1-6 have shown that the strain, c, during transient and steady-state creep is well-represented by the expression: € = e0 + et(l - e-mt) + Esl [l] where Eo is the instantaneous strain on loading, ET the total transient strain, C, the steady creep rate! and m a constant relating to the rate of exhaustion of transient creep. However, it has been noted6 that deviations from this equation occur over the first 10 to 15 pct of the transient stage, when the creep rate, (. decreases more rapidly than is predicted by this equation. This rapid decrease has been attributed to a large change in work-hardening coefficient. It 1s widely accepted that steady-state creep results from a balance between the rate of strain hardcning h and the rate of recovery r (=-s(st) as: dE/dt = Es = r/h [2] Comparison of values obtained for h at the end of the initial extension and during steady creep suggests that h increases several fold during the transient stage. which has the effect of reducing the creep rate proportionally.7 To examine the dependence, on r and h, of the deformation behavior during transient and steady-state creep. a series of constant-stress creep tests was carried out at 413°C at 6000 psi using 70-30 a brass. Prelinlinary investigation showed that. with this material. the transient stage constituted a significant portion of the total creep life (-0.4tf. where tf is the time to fracture). The alloy. obtained from Metals Research Limited. was made from high-purity copper, 99.999 pct. and zinc. 99.99 pct. Heat treatment at 675°C for 4 1/2 gave a uniform grain size of 5 mm-1. Details of specimen preparation and creep testing procedures have been given previously.6 Values of h (?s/?E) were determined by measuring the instantaneous strain. ?E. which occurred on increasing the stress during creep by a small amount. ?s. Similarly. v (= -?s/ ?t) was derived from the incubation period. At, after a small decrease in stress.' Several values of v and h were obtained throughout duplicate creep tests. using different stress increments in the range 300 to 800 psi. The accuracy with which Eq. [I] represents the present creep curves was established by determining the best value of the constants Es, Et, m , and 6, using a digital computer program based essentially on the graphical solution for this equation devised by Conway and Mullikan.9 About 40 strain/time readings were taken during transient and steady-state creep. Over most of the creep curve, the average difference between the measured reading and the calculated strain at the appropriate time was less than 0.0001. However.

Jan 1, 1969

By Howard L. Hartman

The past 15 years have seen rapid advances in the metallurgy of materials for drill machinery and bits, but rock drilling itself continues to be largely an art. Jet piercing, roller bit rotary drilling, and rotary percussion are all promising new techniques, but the percussion rock drill, still used for 90 pct of the blastholes in U. S. hard-rock mining, has under- gone no major modification since pneumatic machines were first used successfully in the 1860's. This singular lack of progress stems directly from ignorance of the nature of impact failure of rock and the fundamentals of rock penetration in general. For nearly three-quarters of a century, mining engineers did not know what went on at the bottom of a drillhole.

Jan 1, 1959

By G. T. Jackson

PROPERTY AND LOCATION THE Alaska Gastineau Mining Co.'s mine is located at Perseverance, about 4 mi. east of Juneau, Alaska. Its property consists of a group of claims, the lode system traversing these claims for a distance of 11,000 ft. (3352 in.). It is shown in Fig. 1. FIG. 1.-ALASKA GASTINEAU MINING CO.'S PROPERTY NEAR JUNEAU. The ore deposits occur in what is known as the Juneau gold belt. This gold belt can be traced for about 50 mi. northwest of Juneau and 40 mi. southeast. It consists of a single band, several hundred feet wide, in which stringers and veins of quartz, carrying gold, occur in a slate formation near its contact with some altered volcanic rock known as greenstone.

Jan 9, 1919

By Robert E. Green, T. Hinton

The velocities of the three possible modes of elastic-wave Propagation have been calculated for single-crystal aluminum at 1-deg intervals throughout the standard steveographic triangle. The results are presented as isospeed contours. The deviations between the direction of maximum energy propagation and specirzen axes are presented as arrows drawn within the standard triangle. The orientation factors associated with dislocation nzotion on the primary slip system only and also on all twelve slip systenzs have been calculated for all three elastic waves. The orientation factors associated with a longitudinal standing--7aue resonant specivnen hazle also been calculated. The relevance of these results to ultrasonic attenuation measurements is discussed. DUE to the widespread use of ultrasonics in the investigation of the properties of solids a number of authors15 have discussed in detail the theory of elastic-wave propagation in solids. In this paper the modes of wave propagation are evaluated according to the procedure suggested by reeen' for the case of single-crystal aluminum at 1-deg intervals throughout the standard stereographic triangle. The wave speeds are presented in the form of contour diagrams within the standard triangle. The deviations between the direction of maximum energy propagation and the normals to the wave fronts are presented as arrows drawn within the standard triangle. The orientation-de pendent factors (orientation factors) associated with dislocation damping as derived in the preceding paper6 have been calculated for the case of aluminum at 1-deg intervals throughout the standard triangle. The orientation factors for dislocation motion on the primary slip system only and on all twelve slip systems are presented in the form of contour diagrams, for both the traveling- and the standing-wave conditions. The relevance of these results to ultrasonic attenuation measurements is discussed. ELASTIC-WAVE PROPAGATION Three waves can be propagated in a linear elastic homogeneous anisotropic medium. The velocity of propagation v of each of these waves in a medium of density p can be obtained from the determination of the eigenvalues and eigenvectors of the matrix equa- The A's are a series of moduli which are functions of the elastic constants cij and the direction cosines 1, m, and n of the specimen axis. In the case of cubic single crystals where there are only three nonzero elastic constants cll, c12, and C, the A's are, The solution of Eq. [I] will give the wave speeds (eigenvalues) and the direction cosines a, 0, and y of the particle displacements (eigenvectors). To obtain the direction of maximum energy flux requires the calculation of the energy-flux vector ET with com- w is the angular frequency, A, the amplitude, and v the velocity of the wave. The direction cosines a, b, and c of the energy flux vector are then given by

Jan 1, 1967