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By Auguste J. Rossi

We cannot expect, within the limits of this paper, to treat this subject exhaustively, but will endeavor, in the following, to present it in as concise a manner as is consistent with a clear exposition of its importance. Ores of titanium, titaniferous iron-ores (that is, iron-ores containing a notable amount of titanic acid, TiO2,, say not less than 5 per cent., generally 10 to 20 per cent., and frequently more, up to 40 per cent. or thereabout), occur all over the world in immense quantity, " in mountain masses," constituting in some localities, as in Sweden, Norway, Canada, the Adirondacks (N. Y.), in North Carolina and other States of the Union, the geological formation itself, the igneous rocks having, in many places, been so permeated with the metallic oxides as to justify their being called iron-ores. As a rule they are Bessemer ores, quite free from phosphorus and sulphur, though not invariably so. When the percentage of titanic acid is very high, that of the iron is low, but the proportions do not necessarily vary in the same ratio; that is, a rich ore may contain more titanic acid than one lower in iron. The percentage of iron varies, being as low as 35 to 36 per cent. in real ilmenite. It is more generally not less than 50 to 55 per cent., reaching often an average of 58 to 60 per cent., and as high as 63 to 65 per cent. It is obvious that if these ores were to be considered in the same light as other iron-ores, equally rich in iron, they would form an excellent stock for blast-furnaces for years to come, as their supply might be called inexhaustible, and they could

Jan 1, 1903

By Sidney Wise

WHILE the installation of mine bulkheads to retain water under high pressure is y no means a rarity, the following points Which arose in the designing and placing of two of these bulkheads may be of interest: The Hibernia magnetite mine, located about 40 miles west of New York, in the State-of New Jersey, is partly filled with water. This mine is located on an ore lens, the outcrop of which is over a mile long. The ore has been mined from this lens from the surface to a depth of more than 1,500 ft. It was held desirable to- separate the old workings from the new, and to allow the former to fill to the 850-ft. level. Two weak places existed between the new and old workings below this level: namely, a temporary bulkhead on the 10th level and a rock bulkhead of indeterminate thickness on the 16th level. When the matter of allowing the old workings to fill was investigated, the fact was developed that if these old workings were filled, the bulkhead on the 10th level would be subjected to a water pressure of about 50 lb. per square inch, and that 200 lb. per square inch would act on the 16th-level bulkhead. As the above-mentioned barriers were not deemed of sufficient strength to permit of these pressures, it became necessary to design and install new bulkheads. Design As the 16th-level bulkhead was required to withstand a pressure of 200 lb. per square inch, it presented some difficulties. A careful consideration of the various types of mine dams now in use led to the adoption of a design of the form of a truncated wedge. In this, the pressure side of the dam is of greater area than the back, so that the resultant action is similar to driving the wedge. By cutting generous skewbacks in the walls, roof, and floor, this type in reality becomes an invisible arch. The wedge feature tends to compress the materials in the bulkhead, thereby adding to its imperviousness.

Jan 8, 1914

By T. A. Simpson

The search for ore continued at its relentless pace throughout 1967. Canada, South Africa and Australia plus a few scattered localities on the globe reported minerals finds of significant importance. Many of the reported finds were not high grade ore, but they nonetheless will assist in sup- plying a highly industrialized, mineral hungry world. No longer does inaccessibility and remoteness close an area to mineral exploration and development. The communication and transportation systems of today have closed the gap and, moreover, the demand for essential mineral commodities is causing price shifts which encourage exploitation of deposits heretofore considered uneconomical.

Jan 2, 1968

By G. S. Rice

Some form of longwall mining is generally used in Continental Europe; also in Great Britain where the coal is weak and friable, or the coal bed provides material for pack walls and filling, or where the bottom is soft and squeezes up easily, or the roof is pliable, or the bed is thin and brushing provides building material, or the thick multiple seams are mined in layers, such as the 24-ft.seam at Weymss, Scotland, or the 10-yd. pitching bed near Coventry, England. Pillar methods have been retained in British fields where the coal beds are from 5 to 9 ft. (1.5 to 2.7 m.) thick, and free from thick partings or binders or without draw slate, which would provide waste rock for pack walls, or where the roof is hard and requires shooting to bring down, and also the bottom or floor is comparatively hard. The room-and-pillar system, by which probably 95 per cent. of the coal of the United States is produced, is now found in only a few mines in Wales, where it is known as the pillar and (single) stall method. The American room-and-pillar system is not equivalent to the bord-and-pillar or stoop-and-room system. The essential difference between the bord-and-pillar and the average American room-and-pillar system is probably due to natural conditions. The majority of the coal mines in the United States have a depth of less than 700 ft. (213 m.). The bulk of the coal mined in Europe comes from a depth of more than 1200 ft., while the deepest mines in Great Britain, Belgium, and France reach 3500 to 4000 ft. In deep workings wide spans are impracticable, even with the use of abundant timber; accordingly, as the mines in the United States become deeper the rooms will become narrower and the pillars thicker, and the bulk of the coal will be extracted on the retreat. It is generally conceded, without reference to the cost of production, that the larger the pillars left on the first mining, the more thoroughly can the coal be extracted. In Europe complete extraction is generally compelled either by the lessors or by the governments; whereas in this country it has been more largely a question of competitive cost of production, or the support of the surface in the flat farming districts of the

Jan 1, 1922

By Earl R. Parker, Ralph Hultgren

DURING the past year publications in physical metallurgy have not been abundant when compared with the output of prewar years. Nevertheless, some noteworthy contributions have been made to the literature. Because of the necessity for war production, much of the metallurgical effort has been directed towards the solution of problems of production processes. The limited amount of time devoted to other problems is reflected in the small number of papers devoted to nonapplied research, though a few excellent contributions have been made to the fundamentals as will become evident in the following pages. Results of many of the government-sponsored research investigations have been released to the public and are being published in the technical journals. Many more of these papers may be expected to appear in the 1946 publications.. Public distribution of information obtained in the course of these investigations should be of great value to American industries in the postwar era. Continued activity in research of all kinds is apparently assured because of intense

Jan 1, 1946

By L. H. Reiss, J. Groult, L. Montadert

Many fields, where the reservoir is composed of sandy layers, show great complexity because of the lack of continuity which results from a particular type of seditnentation. This complexity may be a factor of prime importance in studying reservoir drainage, especially in the displacement of oil by water or gas. This paper describes work done to study this heterogeneity and its influence in the exploitation of the fields of the lower Devonian sandy shale in the Fort Polignac Basin in Algeria. Two lines of research were followed. 1. On the border of the hasin, a detailed sedimentological study established rules for the distribution of the sandy zones, which furnished hypotheses necessary for devising a geologic model of the reservoir. A certain number of sandy zones were recognized and characterized by their sedimentation. 2. In the interior of the basin, production logs deterrnined the productivity profile. Study of these point data led to a description of the distribution of oil and gas phases in the reservoir so that the continuity of different zones between the wells could be deduced. These techniques were applied to the study of the lower Devonian sandy shale reservoir of Zarzaitine. The sedimentological study guiding the correlation work, with the aid of the conventional static data (logs and cores), led to the establishment of a useful geologic model of the reservoir. Production logs, thanks to the contribution of dynamic elements, permitted corrobora-tion of the model. In particular, the logs confirmed separation, as proposed by the sedimenfological study, of two comparable sandy groups by revealing the continuity of a thin impermeable layer, invisible on conventional logs. INTRODUCTION The heterogeneity of sandstone reservoirs considerably influences the distribution of fluids, as well as their displacement in the reservoir. Rational development of a field and maximum recovery of hydrocarbons are closely tied to an exact and precise knowledge of the intern architecture. We will try to show how it is possible I refine the knowledge of the reservoir by seeking qui different and varied sources of information. Productic geology, the group of techniques which leads to idei concerning reservoir architecture and its geometric descris tion, furnishes the framework of this undertaking. Of these techniques. those used so far are qui varied. Descriptive as well as quantitative, the technique partake as much of classical geology as of reservo science. They include (1) geologic studies of the enti basin, especially a stratigraphic and sedimentologic study of the reservoir member at its outcrop, detail1 observations of cores taken from wells and, finall oriented cores; (2) interpretation of geophysical dat (3) interpretation of electric logs, nuclear and sonic lo and dipmeters: (4) petrophysical study of the reserve on samples taken from wells; (5) reservoir dynamics (stu of the production history and, in particular, interpretati of production logs); and (6) analysis of the fluids a thermodynamic studies. This incomplete list could also include (1) study the migration of the fluids, (2) geochemistry (chemi characterization of the oils), (3) regional hydrodynamii and (4) injection and detection of tracers. If most of these techniques are classic, attention i nevertheless be called to applying two of the techniql in conjunction: the study of the reservoir member its outcrop and the study of dynamic distribution fluid phases in the reservoir through use of product logs, used in the study of the sandy shale reservoirs the lower Devonian of the Fort Polignac Basin, Alge in particular, their application to the study of the 2 zaitine field where they have led to a new and satisfact model of the reservoir will be described. THE ZARZAITlNE FIELD Situated in the interior of the Fort Polignac 8 about 150 kilometers (km) north of the lower Devol outcrop, the Zarzaitine Devonian oil field was discovc On Ian. 28, 19'' (Figs. 1 and l8). It is in the fern a monocline truncated by two perpendicular fault: great throw, with a downthrown section to the north\: Erosion at the top of the structure has caused one of it to disappear. It is a reservoir with a gas cap an m coefficient on the order of 1:5, open to the aql On the northeast, with the oil zone covering an Of 106 sq km and with initial oil reserves of 222 mi

Jan 1, 1967

By J. Gurland

THE microstructure of sintered carbides consists of particles of metal carbides, such as WC and TiC, embedded in a metallic binder which is usually a cobalt—or nickel-rich solid solution. One of the important factors influencing the strength of the alloys is the degree of dispersion of the carbide particles in the binder matrix. While it is generally accepted

Jan 1, 1960

By C. H. Mathewson, P.W. Bakararian

The greatcr part of the literature on the plastic behavior of magnesium dates back to that active period of research in crystal mechanics immediately following the widespread preparation of isolated metallic crystals large enough for the application of conventional methods of mechanical testing. These investigations, performed on single crystals, revealed an analogy between zinc and magnesium with respect to their fundamental mode of deformation. in the operation of glide and twinning, respectively, on crystallographically similar planes. Mathewson and Phillips (1928)' by geometrical analysis identified the plane in magnesium as the twinning plane. Schiebold and Siebel (1931) confirmed this twinning planc, established the basal plane as the plane of slip, and a digonal axis I as the slip direction. They also rcported twin formation in a secondary role on the {IOI} plane. Schmid (1931)³ summarized and discussed the earlier evidence and presented the results of his own experiments on the effect of temperature and small amounts of soluble elements. From X-ray studies on extended wire single crystals, he concluded that slip along the basal plane in the direction of the digonal axis I closest to the stress direction was the sole slip system operating at atmospheric temperature. This conclusion was based on experiments with crystals of many different orientations relative to the stress axis. Special attention was directed to the basal plane and the digonal axis I, as the plane and direction of greatest atomic density. Determinations of resolved shear stress at the onset of plastic yielding-—i.e., the critical resolved shear stress—were also made; the average of these calculations showing 82.9 grams per sq. mm. This value varied only slightly up to 300°C. at which temperature it was found to decrease to 70.5 grams per sq. mm. The extension of his crystals at temperatures above 225°C. further disclosed the presence of new slip systems. After the origince specimens of circular section had been

Jan 1, 1943

By C. H. Mathewson, P. W. Bakararian

The greatcr part of the literature on the plastic behavior of magnesium dates back to that active period of research in crystal mechanics immediately following the widespread preparation of isolated metallic crystals large enough for the application of conventional methods of mechanical testing. These investigations, performed on single crystals, revealed an analogy between zinc and magnesium with respect to their fundamental mode of deformation. in the operation of glide and twinning, respectively, on crystallographically similar planes. Mathewson and Phillips (1928)' by geometrical analysis identified the plane in magnesium as the twinning plane. Schiebold and Siebel (1931) confirmed this twinning planc, established the basal plane as the plane of slip, and a digonal axis I as the slip direction. They also rcported twin formation in a secondary role on the {IOI} plane. Schmid (1931)³ summarized and discussed the earlier evidence and presented the results of his own experiments on the effect of temperature and small amounts of soluble elements. From X-ray studies on extended wire single crystals, he concluded that slip along the basal plane in the direction of the digonal axis I closest to the stress direction was the sole slip system operating at atmospheric temperature. This conclusion was based on experiments with crystals of many different orientations relative to the stress axis. Special attention was directed to the basal plane and the digonal axis I, as the plane and direction of greatest atomic density. Determinations of resolved shear stress at the onset of plastic yielding-—i.e., the critical resolved shear stress—were also made; the average of these calculations showing 82.9 grams per sq. mm. This value varied only slightly up to 300°C. at which temperature it was found to decrease to 70.5 grams per sq. mm. The extension of his crystals at temperatures above 225°C. further disclosed the presence of new slip systems. After the origince specimens of circular section had been

Jan 1, 1943

By N. A. Gokcen, J. Chipman

Aluminum and oxygen dissolved in liquid iron were brought into equilibrium with pure alumina crucibles and atmospheres of known H2O and H2 contents to study the reactions: 1—Al2O3(s) = 2 Al + 3 0; 2—Al2o3(s) + 3H2(g) = 2Al+ 3H2o(g); and 3—H2(9) +O = H2O(g). Aluminum strongly reduces the activity coefficient of oxygen and similarly oxygen reduces that of aluminum. Values of the product [% All" • [% O]3 are much smaller than those found in previous experimental studies and are of the order of magnitude of the calculated values. ALUMINUM is the strongest deoxidizer commonly A used in steelmaking, but the extent to which it removes dissolved oxygen has been debatable. The relationship between aluminum and oxygen has not been determined reliably not only on account of the usual experimental difficulties at high temperatures but also because of uncertainties in the analyses of very small concentrations of oxygen and aluminum. The earliest experimental attempt of Herty and coworkers' was followed by a more systematic study of Wentrup and Hieber.' These authors added aluminum to liquid iron of high oxygen content in an induction furnace and considered that 10 min was sufficient to remove the deoxidation products from the melt. Parts of the melts thus obtained were poured into a copper mold and analyzed for total aluminum and oxygen (soluble plus insoluble forms), assuming that the insoluble parts were in solution at the temperatures from which samples were taken. It is conceivable that the furnace atmosphere in their experiments, consisting of mainly air at 20 mm Hg pressure, was a serious source of continuous oxidation and therefore that their oxygen concentrations were correspondingly high. Scattering of their data was explained to be well within the maximum inaccuracy of 10°C in the temperature measurements and errors of ±0.002 pct each in the oxygen and total aluminum analyses. Maximum and minimum deoxidation values, i.e., values of the product [% All' . [% O] differed by factors of 10 to 15; mean values of 9x10-11 and 7.5x10-9 ere reported at 1600" and 1700°C, respectively. Hilty and Craftsv determined the solubility of oxygen in liquid iron containing aluminum, using a rotating induction furnace. Pure alumina crucibles used in their experiments contained the liquid iron which in turn acted as a container for slags of varying compositions consisting mainly of Al2O3, Fe2O3, and FeO. The furnace was continuously flushed with argon, and additions of aluminum and Fe2O3 were made in the course of each experimental heat. The inner surfaces of their alumina crucibles were covered with a substance other than pure Al2O3, containing both iron oxide and alumina. Although frequent slag additions can change the composition of slag in the liquid iron cup formed by rotation, the inner surface of the crucible must depend upon the transfer of oxygen or aluminum through the liquid iron for any adjustment in composition. It is not clear that their metal was in equilibrium with the crucible wall, but it is clear that it was not in equilibrium with Al2O3. Their deoxidation product, [% A].]" • [% O]3, varied by a factor of more than 50; the average values of 2.8x10- and 1.0x10-7 were selected for temperatures of 1600" and 1700°C, respectively. Aside from the experimental determinations, attempts have been made to calculate the deoxidation constant for aluminum indirectly from thermody-namic data. Schenck4 combined the thermodynamic data for Al2O3 and dissolved oxygen in liquid iron by assuming an ideal solution. His calculated values are 2.0x10-15 and 3.2x10-13 at 1600" and 1700°C, respectively. Later, Chipman5 attempted to correct for the deviation from ideality and derived an expression which led to deoxidation values of 2.0x10-14 and 1.1x10-12 at 1600" and 1700°C, respectively. The errors in these treatments originate mainly from inaccuracies of thermal data and uncertainties regarding the activity coefficients of dissolved oxygen and aluminum. The purpose of this investigation was to study the equilibria represented in the following reactions in the presence of pure alumina: Al2O3(s) = 2Al + 3O K = aAl2.ao3 [1] Al2O3(s) + 3H2(g) = 2Al + 3H2O(g) H2O K2 = aAl2(H2O/H2 ) [2] H2(g) +O = H2O(g) K3 = 1/ao (H2) [3] The experimental method consisted of melting pure electrolytic iron, usually with an initial charge of aluminum, in pure dense alumina crucibles under a controlled atmosphere of H,O and H2 and holding

Jan 1, 1954

By M. Mathieu

The Rove tunnel is the means by which the canal from Marseilles to the Rhone Riverl penetrates the hills of Nerthe, lying between Mar- seilles harbor and Lake Berre, Fig. 1. The canal will communicate at sea level with both terminals. The original project planned a lock near the village of Marignane; but observations, pursued for more than three years, showed that the water surface gradient would average only 0.015

Jan 1, 1923

By M. Mathieu

The Rove tunnel is the means by which the canal from Marseilles to the Rhone Riverl penetrates the hills of Nerthe, lying between Mar- seilles harbor and Lake Berre, Fig. 1. The canal will communicate at sea level with both terminals. The original project planned a lock near the village of Marignane; but observations, pursued for more than three years, showed that the water surface gradient would average only 0.015

Jan 1, 1923

ON FEBRUARY 13, 1953 the Miami Copper Company signed a contract with the United States Government, through the Defense Materials Procurement Agency, whereby it under- took, with a base price of 27.359 per lb (subject to escalation based on wage scales and wholesale-price indices), to exploit a new ore body in its mine in Gila County, Arizona. Recoverable ore was estimated at 23,000,000 tons, averaging about 0.677 per cent copper. Moreover, the proportion of oxidized copper, difficult to recover by flotation concentrating, was so high that an average net recovery of only ten pounds per ton (0.5 per cent) was expected. The company proposed to mine the ore by the underground method known as undercut block-caving. Unfortunately the ore body, as has been true of all Miami's ore bodies, lay so deeply buried that no possibility existed of adopting opencut mining as has been done in recent years at Miami's neighbors, Ray and Inspiration. Probably the most distinctive characteristic of Miami's operations has been the extent to which it has developed and improved methods and equipment for underground mining. True, necessity was a potent stimulant, because its available ores since 1926 have been exceptionally low-grade; so, if the enterprise were to survive, it was necessary to keep costs at the minimum. This fact does not detract, however, in any way from the remarkable achievements of Miami engineers in conducting efficient and low-cost underground mining.

Jan 1, 1957

By R. Steven Maxwell, Ulrich Petersen

Most minerals have experienced a slow hut perceptible decline in their annual primary production growth over the past hundred years. This decline is due to a combination of factors: (1) increased recycling; (2) exhaustion of the more accessible or higher grade ores; (3) partial substitution; (4) the more efficient use of materials; (5) progressive saturation of markets as living standards rise. Therefore, future demand for new mineral resources will probably be lower than anticipated. As the world population stabilizes, this slowdown in production growth will become even more pronounced.

Jan 1, 1979

By Edward Keller

(Canal Zone Meeting, November, 1910.) UNDER the title, Labor-Saving Appliances in the Works-Laboratory, I published a paper1 in which was described how multi-manipulations, in a works-laboratory, and in the furnace-room of an assay-laboratory, can be condensed into single manipulations by applying the proper mechanical devices. For example, I now deposit in, or withdraw from, a muffle a set of 48 cupels as one unit. The front row. (8) of these. are blanks or heaters; the other 40, when they have attained the proper temperature in the muffle, are charged simultaneously with the 40 lead-buttons. Three manipulations here accomplish an operation which by the generally customary method requires 136, and this number is only limited by the size of muffle and cupels. This operation is an enlargement of what I have already described in my former paper, and Fig. I shows the improved implements. In the paper referred to I described a gold-silver bead parting-bath, which is the last of the devices used in regular sequence in practice. This bath was designated as being convenient, but was not a labor-saver properly. Fig. 2 of the present paper shows a new device. Instead of the original tray, there are now sectional holders for the test-tubes, each having a wooden handle on either end, so that the holders may be removed from the boiling bath, and the acid or water poured off from each set of tubes (in this case, 7) without waiting to cool. The tubes, held in place by clutches, as shown in Fig. 3, rest in holes in the base-strip, having a smaller diameter than the tubes. Each holder is stamped at either end with a number, so that the bath becomes further useful by permitting several men to use it at the same time without interference. Apart from the handles, the holders are made of sheet-copper. ' Trans., xxxvi., 3 to 18 (1906).

Aug 1, 1910

By Ronald D. Irving

The object of the present paper is to give an outline account of the mineral resources of the State of Wisconsin, so far as they are now known, including both metallic ores and non-metallic useful mineral substances. Tl~e only previous publication making ally attempt at such an account is one of a popular nature, prepared by the writer for Snyder and Van Vechten7s Historicccl Atlas of Wisconsin, which was published at Milwaukee in 1878. The data upon which the statements of the following pages are based are chiefly from the

Jan 1, 1880

By Carl H. Schmuck

The terms "cable bolting," "extended ground support," and "grouted cable" are synonymous, and they have been popping up with much more regularity in the mining engineer s vocabulary. In simplest terms, lengths of u itensioned cable up to 18.3 m (60 ft) are grouted in drill holes prior to mining. This permits radical departures from mining practices that rely on conventional rock reinforcement. For example, by placing a pattern of cable bolts in the back of an open stope, ore can be mined in successive slices. After each slice is taken the protruding cable; are simply cut off and mining proceeds. When about 4.6 m (15 ft) of reinforced back remains, a crew places a new par tern of cable bolts in the ore.

Jan 12, 1979

By D. W. Philips

THE problem of strata control has of necessity been prominent in mining, and accounts of individual experience and research abound in the literature of most mining countries. Organized research began in Britain by the formation of a committee, upon the recommendation of the Safety in Mines Research Board in 1923, to investigate methods of reducing accidents from falls of roof in coal mines. This committee examined current practice in supporting underground workings in the principal coal fields, and its findings have been published in the Board's publications. Toward the end of these investigations it was suggested by the Chief Inspector of Mines that committees of the several mining institutes be formed to examine the problem in their respective districts. The formation of these committees marked a new phase in research on strata control. The work, though being done in the separate coal fields, followed a scheme outlined by the Chief Mining Engineer of the Research Board, and was coordi¬nated by his office. FACTORS INVOLVED The subject is being considered in Britain from two aspects: I. To provide, by supports, means to prevent falls of fractured ground. 2. To develop methods whereby the strata can be maintained in the least broken condition and thus make falls less likely. The first aspect is the one that will most likely lead to immediate results from the accident standpoint. It depends largely upon the assimilation of already acquired knowledge regarding the proper¬ties of supports and their correct applica¬tion. The second aspect is perhaps more fundamental, and involves also the proper¬ties of the strata and their behavior under the influence of the forces induced by mining. The problem involves many natural factors that cannot be controlled, such as depth, inclination and thickness of seam and nature of the rocks. Other factors, which may be considered to a certain extent controllable, cannot be varied readily and with sufficient fre¬quency to facilitate easy investigation; some of these are: rate of advance of the working face, length of face, direction of the face with regard to cleat and inclination, system and arrangements of rock packing behind longwall faces. In any given case the very many factors present have a mutual influence upon the effects produced in the mine. For example, a study of the effects of rate of advance cannot be done without considering the effects of other factors such as nature of strata, direction of face and quality and arrangement of supports. Conversely, the length and direction of a working face

Jan 1, 1946

By Ralph H. Sweetser

IN the recent world-wide deflation of commodity prices the coal industry, including both anthracite and bituminous coal, had reached a level where the actual delivered market prices received by the operators were usually less than the cost of production. Many steel companies and public utilities, operating their own "captive" mines, could have bought coal during the past three years for less money than the true cost of coal produced at their own properties. Competition within the coal industry itself was cruel to the point of profitless operation, and the competition of other forms of fuel was bearing heavily on the coal producers. They were thus forced into methods of production and utilization that they had hitherto ignored; there had been almost complete absence of any appreciation (by the bituminous operators especially) of the necessity of real research work in finding better methods of preparing coal for specific uses, and in finding new and profitable uses for different kinds and grades of coal.

Jan 1, 1933

By J. T. Richards

ELASTIC constants, including E-modulus, G-modulus, Poisson's ratio, and compressibility, are affected by temperature, but not necessarily to the same degree nor in the same direction. Theoretical expressions relating the temperature coefficients for the various elastic constants have been introduced by Gruneisen. In considering the thermoelastic characteristics

Jan 1, 1955