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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

W. L. SaundeRs, New York City (communication to the Secretary*):—Notwithstanding the sweeping statements made by Mr. Clarke in this paper, the friends of compressed air are not dismayed. There is no war between electricity and compressed air. Each one has its field of usefulness, and in that field each is supreme. In spite of commercial interests, in spite of prejudices and the enthusiasm of the inventor, the thing that is best will survive and flourish. At least ten years ago, our engineering papers contained large advertisements and pages of reading-matter about the application of electricity to mines, recording the introduction of numerous rock-drilling plants, and claiming that the problem had been solved, greatly to the advantage of the miner and with promise of large profits to the manufacturers of electrical apparatus. Edison and Thomson labored to apply electricity to mines, and each believed that the probabilities of success were great. This was the period of the solelloid rock-drill, which mas admirably suited, theoretically, to the percussive principle and in the development of which hundreds of thousands of dollars have been spent without satisfactory result. I have searched in vain for a standard mining equipment where electric rock-drills are in constant, commercial operation. During a recent trip made from New York to California, I visited most of the important mines of the West and failed to discover a single electric equipment, so far as this class of mining-work is concerned. If any one will inform me where there exists today an electric-drilling equipment in constant service in mines in the United States, I shall be glad to receive the information. Mr. Clarke has been for some years an active and intelligent writer on the subject of electricity for mining. Whenever his

Jan 1, 1904

By S. H. Chauvenet

Jan 1, 1882

By BARONJUPTNER VON JONSTORFF, Andrew A. Blair, GUNNAR DILLNER

IT is a well-known fact that the results of different analysts, when operating on the same identical sample of steel or iron, are far from concordant, and it not infrequently happens that great annoyance and trouble in the commercial community are occasioned by these discrepancies. Attempts have been made at various times to investigate the causes of such differences and to obtain more reliable methods of analysis. The most important of these was made by the British Association in 1889: The following gentlemen, with Sir W. Roberts-Austen as Chairman, and Professor T. Turner as Secretary, were constituted as a committee to investigate the question, viz.: Sir F. A. Abel, Mr. Edward Riley, Mr. G. J. Snelus, Mr. John Spiller, Professor J. W. Langley, and Professor Tilden. Average .samples of steel were prepared in America under the superintendence of Professor J. W. Langley. The steels, in the form of turnings, were divided and distributed to sub-committees in Great Britain, America, France, Germany, and Sweden. In Sweden Professor Åkerman acted as Secretary to the Swedish committee. The Government Department of Tests was appointed in Germany; Mr. Ferd. Gautier in France; the British Association Committee in England; Messrs. William

Mar 1, 1905

By N. S. Wagner, R. S. Mason

The production of lightweight aggregates in Oregon is a new industry, and, like all new enterprises, it is suffering from growing pains characterized by numerous, small operations some of which flourish for a short time and then cease altogether. Norinally all industrial mineral products are produced in a highly competitive atmosphere. At the present time this condition does not exist to a very marked degree in the state because as yet producers have not saturated the constantly expanding market. This paper has been prepared with the intention of outlining very briefly the current status of the various products now heing used as lightweight aggregates in Oregon. The present piche will surely change, perhaps quite radically within even a short space of time. Lightweight Aggregates Used in the Northwest PUMICE Interest in Oregon pumice is not new. Deposits are abundant. Successful development, however, dates only from 1946. During 1948 a total of nine operations was engaged in full or part-time production of aggregate. The postwar building boom and increased public consciousness regarding the value of insulation are the immediate reasons behind the current development. Just how firmly this production of pumice aggregate may be established is something which cannot be foretold at the present time. Much will depend upon how successfully the pumice aggregate construction already installed stands the test of time. Some fine pumice aggregate products have been made and it seems probable that because of its unique properties a certain demand for pumice aggregate will continue in the future. Fire-proof, rodent-proof, decay-resistant properties supplement the lightness in weight and insulation properties of pumice aggregate products in rendering them particularly ideal for many types of construction. In addition there has been fabrication in the form of reinforced fence posts, street markers, and similar products of a specialized-product nature and these are not to be overlooked in terms of future production. Also pertinent to how soundlj pumice aggregate production is established will be possible future competition with other lightweight aggregates. However, this situation will be governed largely by competitive costs of production and marketing. For its present use, which is almost exclusively limited to the manufacturing of building blocks, the market for Oregon pumice aggregate has been extended from the mining area around Rend and Chemult to points as far distant as San Francisco and Seattle. Naturally enough the bulk of the production goes to the Portland and eastern Oregon consumers. Shipments are made by both rail and truck. Early in 1947 the State Department of Geology and Mineral Industries made a canvass of all pumice producers in the state. The production for 1956 amounted to 26,614 cu yd and was valued at $13,649 at the plants. The United States Bureau of Mines estimates the production for 1947 as 33,240 short tons valued at $111,380. This is roughly 65,000 cu yd. No data are available for the 1948 production but it is understood to exceed that for 1947. The Oregon pumice occurrences originated largely from the eruption of Mount Mazama, the name of the formerly active volcano and the location of Crater Lake. Other lesser volcanoes throughout the area contributed to the present occurrences, however, and it has been estimated by Moore' that the pumice deposits cover an area of some 3500 square miles. This area lies east of Crater Lake between Bend and Klamath Falls and embraces the southern portion of Deschutes County, the northern part of Klamath County, and the northwest corner of Lake County. Thickness of the pumice ranges from thin skims to local thicknesses of as much as 30 to 40 ft. Fragment size also varies greatly. Any attempt to describe the situation by giving screen analyses would be confusing because of the wide variations to be found in all area of this size. The picture can best be summed up by stating that places showing great variations in fragment size can be found if a search for extremes is made. For mining purposes in connection with aggregate production, it call be stated that miles and miles of pumice exist in which the fragrnent sizes range from an inch or so downward. The usual color of the pumice is a light gray to off-white. A typical pumice analysis shows a silica content of about 69 pct, alumina 15 pct, and sodium oxide about 5 pct. Potash, lime, and water are the next three most abundant constituents, running just a little over 2 pct each. Iron oxides are fairly constant at 2.75 pct. Titanium, manganese, magnesium, and phosphorus occur in amounts of less than 1 pct. All of the foregoing substances are combined as a glass exhibiting cellular structure. The weight of crushed but otherwise pit-run (undried) pumice runs around 1100 Ib per cu yd according to figures furnished by various producers. The minimum and maximum weights per cubic yard reported are 1050 and 1400 lb, respectively. The 1400 lb per cu yd pumice contrasts with the pumice from most of the other

Jan 1, 1950

By O. J. Hollister

Jan 1, 1888

By Charles Will Wright

Brief descriptions of the occurrence of the various deposits of strategic minerals then known in South America are published in "The Mineral Deposits of South America," by B. L. Miller and J. T. Singewald, 1919; in "Ores and Industry in South America," by H. F. Bain and T. T. Read, 1934; and in many publications on the individual countries. To give a gen.era1 idea of the situation today and possibilities for future output of strategic minerals in several of the countries, the following notes are offered. All tonnages are in metric units.

Jan 1, 1940

By G. M. Crosby

Seven mines with important production records in the Coeur d'Alene lie adjacent to the Gem stocks —the Frisco (Gem), Hercules, Interstate, Rex (Sixteen to One), Success (Granite), Sunset, and Tamarack. Old records are incomplete, but available data given in Table I show these mines have produced 10.550,721 tons of ore containing more than 50 million oz of silver, more than 1.5 billion lb of lead, and about 1 billion lb of zinc (approximately 1.25 million tons of lead and zinc combined). Average ore grade is 4.8 oz of silver per ton, 7.2 pct Pb, and 4.6 pct Zn. This impressive production represents about 12 pct of the District's yield. At present metal prices, with modern beneficiation, the gross value would be more than $400 million. THE GEM STOCKS The Gem stocks, considered to be outliers of the Idaho batholith of Late Cretaceous age, are located in the northern half of the Mullan quadrangle, and extend from the town of Gem, Idaho, along a strike of N30°E for a distance of approximately five miles. They occur as two major masses of monzonitic rocks commonly referred to as the North stock, which covers an area of 1.1 sq miles, and the South stock, which covers 2.6 sq miles. The areal pattern is roughly club-shaped, the North stock representing the handle and the South stock the head of the club. Two and a half miles west and five miles northeast are two groups of smaller stocks, isolated from the main masses but of the same general rock type. This discussion is limited for the most part to the North and South stocks. At the north end, where the intrusion is about 3200 ft wide, the walls are about parallel and dip very steeply west. At the south end, where the mass is about 7000 ft wide at surface, the walls dip away from each other at moderately steep angles. An aeromagnetic survey' detects and outlines with surprising accuracy the two main stocks. as illustrated on the magnetic contour map (Fig. 2). Of particular interest is the location and shape of the magnetic anomaly representing the South stock. The anomaly is centered over the south end of the outcrop, and a westerly extension joins it with a smaller anomaly over the Dago Peak stocks. The latter anomaly, likewise, is located over the south end of the isolated stocks. This pattern suggests the intrusion has greater extent at depth to the south and west. Though correlation between the Dago Peak stocks and the larger masses is suggested, the controversial aspects of the Dobson Pass fault, which separates the two areas, casts doubt on a correlation. Topographically the monzonite stocks are ignored by the drainage pattern indicating these rocks, and the invaded rocks of the Lower Belt Series react similarly to erosion. The drainage patterns of Nine Mile and Canyon creeks cut indiscriminately across the monzonite-Belt contact, resulting in both valleys and ridges in the southern end of the intrusion. Nine Mile Creek traverses diagonally the entire five-mile length of the stocks. The monzonite rocks of the intrusion are referred to locally as granite, but granite is rare and the rocks comprise a wide variety of types. Their characteristics, described in detail by F. L. Ransome and F. C. Calkins,' are summarized by P. J. Shenon.' The principal rock type is coarse-grained, light gray, porphoritic monzonite containing black crystals of hornblende. Pyroxene, epidote, and titanite

Jan 1, 1960

By R. Gilman Brown

INTRODUCTION. MINES are interesting by reason of what they have done for man, or of what has been done for them by nature. Not all are interesting on both scores. Many profitable mines are commonplace to the geologist; and many presenting unique geological conditions have been sad failures commercially. The Standard group at Bodie has produced in 25 years, $14,500,000, paying $5,000,000 in dividends.' On the other hand, this output has been mined (almost wholly above the 1,000-ft. level) from a system of more than 100 veins, ranging in thickness-from 0.5 in. of "specimen rock" to 30 ft. of clay and quartz; distributed through a zone about 2,000" ft. in width, and representing from three to five distinct periods of formation. This group, therefore, by reason of its industrial record as well as its geological features, may fairly be regarded as doubly interesting. The Bodie district occupies an island of recent (Tertiary) hornblende-andesite, surrounded by a complex of igneous rocks and breccias. It lies at the summit of the eastern foot-hills of the Sierra Nevada mountains, and within the Great Basin, a few miles from its western edge, marked here by Mono lake on the line of the Great Fault. The average elevation of the outcroppings of the veins may be taken at about 5,700 ft. The andesite projects from south to north in a great tongue, 12,000 ft. long and 5,000 ft. wide, reaching an extreme height at the northern end of perhaps 1,000 ft. above the adjoining small canyons. These separate it from the main mass of the foot-hill

Jul 1, 1907

By S. H. Chauvenet

HARRISBURG is situated on the Pennsylvania Railroad, one hundred and five miles from Philadelphia, two hundred and forty-eight miles from Pittsburgh, and ninety miles from Baltimore, and has running through it the Pennsylvania, Northern Central, Philadelphia and Reading, and Cumberland Valley Railroads, and the Pennsylvania Canal. Surrounded by a thickly settled farming country, from which to draw native labor, within easy distance of anthracite and bituminous coal, with ores and limestone near at hand, and with the Susquehanna River as a never-failing water supply, Harrisburg has advantages for manufacturing which warrant the investment of the capital that has already been made, and has a future as a manufacturing city second only to Pittsburgh and Philadelphia. THE PENNSYLVANIA STEEL COMPANY, L. S. BENT, SUPERINTENDENT. The works of this company, the largest in Harrisburg, lie between the Pennsylvania and the Philadelphia and Reading Railroads, on. the Pennsylvania Canal, and are essentially devoted to the manufacture of Bessemer steel rails. Capital stock, $2,000,000; invested in business, $5,000,000; wages per month, $80,000; employs 2000 men; capacity, 100,000 tons of rails per year, which is being increased to 130,000 tons. The plant, as it now stands, comprises five Bessemer converters, two 7-ton and three 8-ton converters, two 15-ton open-hearth furnaces in operation, and two 30-ton open-hearth furnaces in course of construction, one blooming mill, one rail mill, seven steam hammers, two blast furnaces in operation, two blast furnaces in course of construction, foundry, pattern $hop, machine shop, blacksmith shop, and frog shop, and merchant mill in course of construction. Bessemer No. 1 was built in 1865, with two 7-ton converters, 2 spiegel cupolas, 3 feet diameter, and 3 iron cupolas 6' 6" diameter,

Jan 1, 1882

By Tracy C. Jarrett

In making gold alloys possessing certain physical properties, such i~nportant factors as corrosion resistance, color, hardness and melting points must be considered. All of these requirements depend directly upon the composition. It is possible to obtain the same colored gold alloy by using different compositions, but in doing so one may bring in some undesirable property. Other investigations have been carried on in this field by F. E. Carter,' E. M. Wise12 and L. Sterner-Rainer2 To make a complete study of the effect of composition upon these properties, a systematic investigation was carried on involving a range of copper content from 85 to 65 per cent. Elements such as zinc, silver and nickel were used to replace in part the copper content. The gold content in all the alloys remained constant. Only 10-karat gold alloys of those containing 41.6 per cent gold will be considered. All of the alloys were made in an induction furnace. Each alloy was cast in a 3 by 1/4 by 3/4-in. ingot. The method of obtaining the melting points and making color determinations was described in a previots paper.4 The Rockwell B scale with the 1/16-in. ball and 100-kg. weight was used for all hardness determinations. The submersion of test pieces in concentrated nitric acid is one of the standard corrosion tests used in the optical trade. A test piece in the 50 per cent cold-worked condition, % by 2 by 0.045 in., is blanked from a skip using a die, and the weight loss per square inch of surface is taken as a means of comparison. The time for this test is 2 1/2 hr. of actual submersion of the test picce in the acid. This standard test was applied to all of the 10-karat gold alloys discussed in this paper. The tensile tests were made upon strips of the dimensions shown in Fig. 1. The test pieces after blanking were annealed at 1300" F. for 20 min. and cooled in air. Thc "drop of the beam" method was used in determining the yield point, as there was a very marked "drop" when the yield point was reached.

Jan 1, 1940

By Tracy C. Jarrett

In making gold alloys possessing certain physical properties, such i~nportant factors as corrosion resistance, color, hardness and melting points must be considered. All of these requirements depend directly upon the composition. It is possible to obtain the same colored gold alloy by using different compositions, but in doing so one may bring in some undesirable property. Other investigations have been carried on in this field by F. E. Carter,' E. M. Wise12 and L. Sterner-Rainer2 To make a complete study of the effect of composition upon these properties, a systematic investigation was carried on involving a range of copper content from 85 to 65 per cent. Elements such as zinc, silver and nickel were used to replace in part the copper content. The gold content in all the alloys remained constant. Only 10-karat gold alloys of those containing 41.6 per cent gold will be considered. All of the alloys were made in an induction furnace. Each alloy was cast in a 3 by 1/4 by 3/4-in. ingot. The method of obtaining the melting points and making color determinations was described in a previots paper.4 The Rockwell B scale with the 1/16-in. ball and 100-kg. weight was used for all hardness determinations. The submersion of test pieces in concentrated nitric acid is one of the standard corrosion tests used in the optical trade. A test piece in the 50 per cent cold-worked condition, % by 2 by 0.045 in., is blanked from a skip using a die, and the weight loss per square inch of surface is taken as a means of comparison. The time for this test is 2 1/2 hr. of actual submersion of the test picce in the acid. This standard test was applied to all of the 10-karat gold alloys discussed in this paper. The tensile tests were made upon strips of the dimensions shown in Fig. 1. The test pieces after blanking were annealed at 1300" F. for 20 min. and cooled in air. Thc "drop of the beam" method was used in determining the yield point, as there was a very marked "drop" when the yield point was reached.

Jan 1, 1940

Organization Place Date 1919 National Drainage Congress St. Louis, Mo. Nov. 11-13 American Mining Congress St. Louis, Mo. Nov. 1.7-21 Canadian Mining Institute Vancouver, B. C. Nov.. 26-28 American Society of Mechanical Engineers:.... New York, N. Y. Dec. 2-5 American Institute of Chemical Engineers Savannah, Ga. Dec. 3-6 Geological Society of America...; Boston, Mass. Dec. 29-31. American Society of Heating and Ventilating 1920 Engineers New York, N. Y. Jan. Mining and Metallurgical Society of America ... New York, N. Y. Jan. 13. American Institute of Min. and Met. Engineers... New York, N. Y. Feb. 16-19 American Ceramic Society Philadelphia, Pa. Feb. 23-26

Jan 11, 1919

Executive-A. R. Ledoux, chairman. Membership-J. V. W. REYNDERS, chairman. Finance-J. V. N. Dorr, chairman. Library-E. GYBBON SPILSBURY, chairman. Papers and Publications--BRADLEY STOUGHTON, chairman. Nominations-Pope YEATMAN, chairman.

Jan 11, 1919

Executive-A. R. LEDOUX, chairman. Membership-J. V. W. REYNDERS, chairman. Finance-J. V. N. Dorr, chairman. Library-E. GYBBON SPILSBURY, chairman. Papers and Publications-BRADLEY STOUGHTON, chairman. Nominations-POPE YEATMAN, chairman.

Jan 12, 1919

COUNCIL OF EDUCATION OF AIME (Formerly Mineral Industry Education Division) Established as a Division January 15, 1932 Established as a Council February 26, 1957 John C Calhoun, Jr, Chairman 0 Cutler Shepard, Vice-Chairman Thomas A Read, Secretary-Treasurer Dept of Mining & Metallurgical Engrg University of Illinois Urbana, Illinois COUNCIL OF ECONOMICS OF AIME (Formerly Mineral Economics Division) Established as a Division December 15, 1948 Established as a Council February 26, 1957 Louis C Raymond, Chairman Lorin A Cranson, Vice-Chairman Henry T Mudd, Vice-Chairman Adam K Stricker, Jr, Vice-Chairman Paul F Yopes, Secretary-Treasurer U S Bureau of Mines Albany, Oregon

Jan 1, 1957

Organization Place Date 1917 American Electro-Chemical Society Detroit; Mich. May 2-5 American Waterworks Association Richmond, Va. May 7-11 American Institute of Electrical Engineers New York City May 18 America' Society of, Mechanical Engineers Cincinnati, Ohio May 22-25 American Iron and Steel Institute New York City May 25-26 ' Interstate Oil Mill Superintendents Association. Augusta, Ga. May (last wk.) Electric Power Club Hot Springs, Va. June 11-14 Society for the Promotion of Engineering Education .... Evansville, Ind. June 19-22. American Institute of Electrical Engineers Hot Springs, Va. June 25 American Society for Testing Materials Atlantic City, N. J. June 26-30

Jan 5, 1917

By Christopher Haycocks, Lawrence P. Johnson, George M. Neall, James M. Townsend

No method of roof control yet devised has proven to be universally acceptable for the wide range of strata conditions experienced in U. S. coal mines. However, a relatively new innovation, the roof truss, has proven itself capable of preventing roof failures which both conventional and resin bolting could not. Presently, the economics of roof trusses are not favorable when compared to bolting due primarily to drilling and installation procedures, but this is expected to change with improved truss and equipment designs. To realize the full potential of this new method of roof control, design criteria are needed which can optimize the effect of the truss for varying strata conditions. A review of the literature reveals that some work has been conducted on the roof truss. Cambrell and Haynes1 (1970) showed that the roof truss is superior to angled roofbolts installed through a header. Sheorey, Verma, and Singh2 (1973) used statics to prove that the optimum angle of inclination should be greater than 45°. However, to date, no systematic attempt has been made to establish design criteria. In this paper, the problem was approached in three ways. First, model studies were performed to determine general trends of truss support as a function of a number of variables. This provided a better understanding of the support mechanism involved. Secondly, beam theory was employed to calculate the actual support capacity of a truss, realizing the many simplifications, assumptions, and shortcomings of this approach to such a complicated problem. Last, field testing will be utilized to test the hypotheses previously developed and provide hard data to further synthesize roof truss design criteria. Field testing has recently commenced and should be complete before mid 1977.

Jan 1, 1979

SECTION I PAGE PAGE President's Western Trip v Presentation of the' John Fritz Hoover Makes Plea to. Stop Food Medal to Henry M. Howe.... xv Waste v International Mining Convention. xxxv. American Committee of Engineers Personal xl in London vii Employment xlii Proceedings, Meeting of Board of Local Section News xliii Directors : vii Forthcoming Meetings of Societies xlvii St. Louis Meeting V... Library xlviii The Woman's Auxiliary. xi Membership liv Members of the Institute in Mili- Biographical Notice of H. T. Chen. lxxiv tary Service xiv Institute Committees lxxv Officers and Directors lxxxii

Jan 7, 1917

By W. I. Duvall

A brief review of the resonant frequency and ultrasonic pulse methods for obtaining elastic constants of rock samples shows that the equations for an iso-tropic elastic solid commonly used to calculate Young's modulus, modulus of rigidity and Poisson's ratio can result in appreciable error if the rock is even slightly anisotropic. Consideration of the equations that relate bar velocities and free medium velocities to elastic constants for orthotropic, transversely isotropic and isotropic solids shows that a combination of the two methods can be used to determine average elastic constants for a single sample of rock. The determination of elastic constants in different directions requires a large number of tests on oriented samples. The use of both the resonant frequency and ultrasonic pulse methods is recommended so that the determination of both Young's modulus and modulus of rigidity is independent of the determination of Poisson's ratio. The dynamic elastic constants of rock can be determined in the laboratory from measurements on small samples which may be in the form of right circular cylinders (diamond drill core). Either the resonant frequency6 or ultrasonic pulse method1 can be used to determine the longitudinal and shear velocities in the same specimen. The resonant frequency method provides a measure of the longitudinal bar velocity, V,, and the torsional bar velocity Vt; whereas the ultrasonic pulse method provides a measure of the free medium longitudinal velocity, Vp, and the free medium shear velocity, V, . The elastic constants (Young's modulus E, modulus of rigidity G, and Poisson's ratio v) are calculated from the density of the specimen, p, and one of the pairs of velocities by means of equations from isotropic elastic theory. For the resonant frequency method the equations are: It should be noted that Eq. 5 is derived from Eq. 4 and 6 and the relation between the elastic constants for an isotropic solid as given by the first part of Eq. 3. The in situ determination of dynamic elastic constants is accomplished by generating a complex seismic pulse in the rock and measuring the arrival times for the longitudinal and shear phases of the pulse at two distant points.5 From these travel times and the distance of the travel path both Vp and Vs are determined. The density of the rock is determined from samples in the laboratory, and Eq. 4 to 6 are used to calculate the elastic constants. These three methods involve the assumption of isotropy and perfect elasticity, and require the use of the relation v = (E/2G) - 1, which holds only if the elastic constants are the same in at least two directions. The calculation of v by means of Eq. 3 introduces considerable error, as a 1% error in V, and V, results in a 20% error in v. If frequencies for samples with a length-to-diameter ratio greater than four and a length greater than 8 in. are measured carefully, the experimental error can be kept to 1%. However, it is not unreasonable to expect that the variation in Vb and Vt with direction may exceed 1%. Thus, for even a small percentage of anisotropy the use of Eq. 3 can result in considerable error in v. The calculation of v by Eq. 5 also involves some uncertainty as a 1% error in Vs and Vp can result in a 6% error in v. By means of the pulse method both

Jan 1, 1965