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By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x'1 x'2 x'3) system is x1 x2 x3 X'1 a11 al2 a13 x'2 a21 a22 a23 x'9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965

By J. L. Taylor, P. Duwez

The phase boundaries in the ternary system Ti-Cr-Al have been established at 1800° and 1400°F for alloys containing more than 60 pct Ti. The martensite transformation temperature has been measured for the titanium-rich alloys. THE studies of binary alloys of titanium with the transition elements which have been published so far1-0 ndicate clearly that the solubility of these elements is always much greater in the high temperature body-centered cubic form of titanium (ß phase) than in the low temperature hexagonal form. In this category of alloying elements are iron, nickel, chromium, manganese, vanadium, molybdenum, tungsten, columbium, and tantalum. Although studies of the nontransition elements have been rather limited, early work on titanium binary alloys'" has shown that most of them were not very soluble in the a form, with the exception of aluminum, for which the solubility in a is about 25 pct.13, 12 In addition to this large solubility in a, aluminum is also soluble in ß titanium to the extent of about 35 pct and the transformation temperature from ß to a is raised with aluminum content. This effect is also typical of aluminum, in contrast with that found for the transition elements which lower the ß to a transformation temperature. Therefore, it may be anticipated that tprnarv titanium alloys with aluminum and any one of the transition elements will constitute a class of ternary alloys having characteristic features absent in alloys involving two transition elements. Chromium was chosen as a typical transition element for the present study because ternary alloys of Ti-Al-Cr commercially produced have been found to possess very interesting physical properties (MST-3 pct A1-5 pct Cr of Mallory-Sharon).'" Binary Systems The binary systems Ti-A1 and Ti-Cr have been established recently by several investigators. The data used in this investigation were taken from the complete diagram of Bumps, Kessler, and Hansen." This diagram agrees quite well with earlier investigations." For the Ti-Cr system, the phase boundaries at 1800" and 1400°F were taken from refs. 6 and 7. The binary system Cr-A1 has been studied recently by Bradley." This system is rather complex and contains not less than seven intermediate phases. The present study was limited to the titanium corner of the ternary system (less than a total of 40 pct Cr plus Al) and none of the phases present in the Cr-A1 binary alloys were found in the ternary alloys investigated. Experimental Technique Microscopic observation and X-ray diffraction measurements were used to identify phases and de-

Jan 1, 1954

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting passed the following resolution: "The Board of Directors, having been appealed to by several Local Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of policy is formulated;

Jan 1, 1932

By David R. Maneval

At the turn of the century, 90% of the energy output in the United States was generated by coal, and Pennsylvania was the ranking producer of this fuel. With the huge resources of easily accessible coal found by its early settlers, the Commonwealth was the nation's chief powerhouse for nearly 100 years. In 1928 alone, Pennsylvania mined a billion dollars' worth of coal-or enough to fill a train reaching more than twice around the world at the State's latitude. Coal constituted nearly 67% of the freight of Pennsylvania and was responsible for the State's $4-billion iron and steel industry. Pennsylvania was slow to take up its position as the greatest coal-producing state in the union, but the knowledge of its coal assets was not slow in accumulating. In fact, long before the white man arrived, the Indians were aware that many of the hills were underlain by black stones that would burn. But awareness was not enough. The early Pennsylvania settlers confined themselves to the southeastern corner of the State and had little need or concern for resources further inland.

Jan 1, 1971

By J. L. Weeks

THERMAL conductivities of several samples of uranium and uranium alloys were determined using an apparatus previously described.' The value previously reported for uranium,' 0.035 cal per sec per cm per "C at 70°C, is in error due to the failure of a thermocouple during the determination on uranium. The defective thermocouple was detected after a reanalysis of the data obtained during the run and since has been replaced. Subsequently, runs on several samples of uranium show the thermal conductivity of uranium to be 0.069 cal per sec per cm per 'C at 70°C. The accuracy of the determinations was checked by measuring a sample of synthetic sapphire whose thermal conductivity was previously reported and found to be in agreement with other values."-" The values given in Table I are believed correct to % 3 pct or 0.003 cal per sec per cm per "C, whichever is larger. The samples were provided by J. H. Kittel of the Argonne National Laboratory, Metallurgy Div. References J. L. Weeks and R. L. Seifert: Apparatus for the Measurement of the Thermal Conductivity of Solids. Review of Scientific Instruments (1953) 24, pp. 1054-1057. J. L. Weeks and R. L. Seifert: Note Regarding the Thermal Conductivity of Synthetic Sapphire. Journal American Ceramic Society (1952) 35, p. 15. :' J. Francl and W. D. Kingery: Thermal Conductivity: IV, Apparatus for Determining Thermal Conductivity by a Comparative Method; Data for Pb, Al2O3, BeO, and MgO. Journal American Ceramic Society (1954) 37, No. 2, Part 11, pp. 80-84. (Part 11: special issue on thermal conductivity.) ' W. D. Kingery, J. Francl, R. L. Coble. and T. Vasilos: Thermal Conductivity: X, Data for Several Pure Oxide Materials Corrected to Zero Porosity. Journal American Ceramic Society (1954) 37, No. 2, Part II, pp. 107-110. (Part 11: special issue on thermal conductivity.) Edwin Ruh: New Jersey Ceramic Research Station, Rutgers University. Private communication.

Jan 1, 1956

By P. C. Badgley

The purpose of this paper is to demonstrate the usefulness of systematic analyses of weakness patterns. The term weakness here includes structural features such as fractures, foliation planes, lineaments and bedding. Many of these features are mapped by geologists in the field, but analysis of the field date is frequently overlooked. Examples are presented to show the value of such studies in petroleum and mineral exploration, in dam site selection, and in regional tectonic interpretations. Numerous theories have been presented to account for the mechanics and time of origin of fracturing. This is an extensive subject and cannot be reviewed in detail here. The reader may wish to refer to other papers.*"5 It is sufficient to say that most fracture patterns can be related to one or more of the following force mechanisms: compression, tension, torsion and fatigue (inheritance by upward propagation of pre-existing fractures). Fractures generally occur in sets in a district. The angular relationships and other characteristics of the individual sets frequently help in determining the force mechanism and movement history of the deformation. From a geometric point of view fractures are commonly referred to as longitudinal, cross, or diagonal (shear), depending upon their orientation relative to other major structural features such as anticlinal axes and so forth. These terms will be used from time to time and are illustrated schematically in Fig. 1. FIELD PROCEDURE AND TREATMENT OF DATA In fracture studies it is very important to collect adequate field data. Fig. 2 illustrates a notebook sheet for recording significant field observations in sedimentary rocks. Slight adaptations have to be made for igneous and metamorphic terrains. Fracture density and persistence are very important factors in petroleum exploration for fractured reservoirs and mineral exploration. The density for each joint set is recorded in terms of number of joints per linear yard. The total number of joints at any one

Jan 1, 1962

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By Alfred H. Bell, Paul F. Simpson

The year 1929 was one of continued activity in the petroleum industry of Indiana and Illinois but the new production obtained has not been sufficient to offset the decline in the production of the old wells. (Table 1). Drilling costs have not changed materially during the year and the prices of crude oil have increased slightly so that the prospects for further testing are good. The total number of completions in Illinois in 1929 (Table 2) was greater than for any year since 1917. More than half of these were in the Dupo field, St. Clair County, and the development of this field was largely responsible for the increased ratio of producers to dry holes in the state as a whole. In the southeastern Illinois field which has produced about 97 per cent. of the state's petroleum the number of completions was greater than in 1928 and the percentage of producers was a little higher. Although a number of scattered wildcat tests were drilled most of them were not located on favorable structure and the only noteworthy discovery was that of a shale-gas horizon at shallow depth in Morgan County in western Illinois where gas has been produced for a number of years from sandstone and limestone. In Indiana the number of completions (Table 2) was only slightly less than in 1928. Most of the new wells were drilled in the southwestern part of the state, which now produces more than 90 per cent. of Indiana's petroleum.

Jan 1, 1930

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting passed the following resolution : "The Board of Directors, having been appealed to by several Local Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of policy is formulated;

Jan 1, 1934

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting. passed the following resolution: "The Board of Directors, having been appealed to by several Local . Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of policy is formulated:

Jan 1, 1937

By Irwin Roman

The literature of geophysics as applied to the discovery of mineral deposits has been very extensive during the past few years,' but there seem to be few references to the use of the method of least squares for obtaining better interpretations of the observed data.2 There seems to be a general reluctance among geologists and engineers to acquire the technique of least squares, in spite of the fact that a thorough knowledge of the theory is not necessary for the use of the method.

Jan 1, 1932

By Irwin Roman

THE literature of geophysics as applied to the discovery of mineral deposits has been very extensive during the past few years,1 but there seem to be few references to the use of the method of least squares for obtaining better interpretations of the observed data .2 There seems to be a general reluctance among geologists and engineers to acquire the technique of least squares, in spite of the fact that a thorough knowledge of the theory is not necessary for the use of the method.

Jan 1, 1932

Man is born on Mother Earth without knowledge or skills. Soon he finds physical needs for food, clothing, shelter, exercise, and relaxation. His personal needs are self-expression, new experiences, and amusements, while his social needs have been classified as work, status, security, friendship, companionship, and love. He finds himself infinitesimal in comparison to the whole. Often- times when he feels smug, he is actually riding for a fall. And nothing is much worse than frustrated man. The postwar world does not provide the Utopia of peace and prosperity of which man had dreamed. In fact, it seems that the sacrifices and waste of that great struggle are being lost in the morass of stupidity, selfishness, and cupidity which unfortunately are still the most conspicuous traits of the human race. Perhaps it is too soon to expect the blessiilgs which are supposed to appear in a peaceful world, and man's thought is clouded with a pessimism engendered by the conflict itself, in which all activities tend to enhance his pessimistic nature. Must man submit that it is a law of nature for nations to go to war? The war has demonstrated that when faced with a common danger, peoples differing in antecedents, language, forms of government, and resources can unite for a time, pool their skills and abilities, and emerge victorious from a contest unparalleled in magnitude, ruthlessness, carnage, waste, and cost. This has been accomplished by great individual and national sacrifices, the

Jan 1, 1950

Long pipelines handling suspended solids find wide use throughout the mining industry. In phosphate, iron ore, and clay mining; in hydraulic stripping of overburden; in tailing disposal; and in transferring concentrates between plants pipeline transport may prove cheapest material handling method. One drawback is necessity for providing attendance at booster stations, both for control and for protection of pumping equipment from sudden surges and failures. Thiele Kaolin Co. in Georgia has come up with an installation where instrumentation does this job automatically, efficiently, and economically.

Jun 1, 1955

By John M. Pitt

A rapid in situ stress measurement technique was developed for exposed underground surfaces. The method applies radial stress in small diameter (38mm) boreholes, initiating fracture propagation which is monitored by measuring ultrasonic pulse velocity. Theoretical relations for stress concentrations near boreholes provide independent expressions for unknown principal field stresses at incipient fracture; fracture orientation defines principal stress orientation. Accuracy and precision were evaluated using blocks of brittle material subjected to known stresses. Results were comparable to those obtained by other in situ stress measurement techniques.

Jan 1, 1984

M. A. SCHEIL (presented in written form).-Messrs. Franks, Binder and Brown are to be congratulated for the splendid paper that they have presented. We have not made stress-corrosion tests with the cantilever type of specimen which they describe, but it is well known that a uniform stress across a certain portion of the gage length can be obtained with such a specimen. This type of specimen would appear quite expensive to make. The writer was interested in the authors' remarks concerning the erratic results obtained from specimens with cold sheared edges. It might be of general interest to record here some results we obtained with annealed sheet N4 in. thick of type 304 stainless steel. After specimen No. 4 had been exposed 65 days without any signs of cracking we applied a strain gage and measured the stress as 25,810 psi. This value is considerably higher than we find for some of the type 347 stainless alloys and suggests that 18-8 might have a different threshold value for stress-corrosion cracking than 18-8 columbium. The test data in Table I show that strain caused by cold work or polishing has a pronounced effect in lowering the time for failure. In my paper I showed values of 8 hr. and 17 hr. to stress crack cold-rolled type 301 stainless steel stressed beyond the yield point. This steel contained 8.31

Jan 1, 1945

By E. W. Gieseke

Coal preparation men today are confronted with problems brought about by changing feed characteristics. The size consist of the coal going to preparation plants has been getting finer and finer. In order to handle these sizes economically, operators are turning to Notation. American Cyanamid Co., in an effort to enable coal flotation plants to produce efficiently at maximum quality and capacity, wnducted experiments which demonstrated that synthetic flocculants are useful for increasing the capacity of coal and refuse filters and for clarifying coal and refuse slurries, and a wetting agent is beneficial in reducing the moisture content of filter cake. Coal preparation men are today confronted with problems brought about by the changing coal markets, changing feed characteristics, and ever increasing labor and supply costs. Small mines are finding it difficult to exist, and the larger mines are rapidly converting to fully mechanized and automated operation to survive. The size consist of the coal going to preparation plants has been getting finer and finer, and the problems facing the preparation plant personnel are growing larger and larger. Facilities can be provided to handle this plant feed in new plants, but the problems are generally not so simple in existing plants where equipment must often be used to perform tasks far beyond its rated capacity. In addition, various state conservation departments, water commission boards, and other Federal and state agencies are endeavoring to eliminate stream pollution. These problems, and many more not mentioned, have been forced on the preparation engineer for reasons of economy and the public interest. In the matter of stream pollution, a determined effort is being made by the coal industry to cooperate with the Federal, state, and local agencies. Economists predict it will be necessary to produce 600 million to 700 million tons of coal by 1970. Bear in mind that the greater proportion of this increased tonnage will have to be processed in existing plants, and you get an idea as to the problems facing the preparation engineer. Methods presently in use for preparing fine coal do an acceptable job down to 48 to 100 mesh. A very large percentage of the - 48 or -100 mesh fraction of the tonnage of coal produced now is being sent to settling ponds or sold at a low figure for reason of quality. This has caused operators to turn to flotation. Building settling ponds and impounding fines is a costly and, at times, impossible method of handling these sizes. Recently a number of flotation plants have been installed to beneficiate material finer than 48 mesh, and these plants have demonstrated that flotation can be successful and increase the plant realization. Coal is a low cost commodity and processes for its beneficiation must be low in cost. Flotation is such a process. It is easily adapted to handling fine coal, requires very little supervision when properly installed, and is economical to operate. Flotation separates coal from refuse and fine clay. For reagents, several combinations are used. Some

Jan 1, 1962

By Nelson Severinghaus

FOLLOWING the end of hostilities of World War II, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, one near Camak, one near Lithonia and one at Stockbridge. All have had excess fines or screenings in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed stone is generally sold with a relatively narrow margin of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. BY-PRODUCTS OF GRANITE DIMENSION STONE It sometimes becomes difficult to differentiate between main product and by-product. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I). They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1947

By W. B. Plank

THE figures on enrollment in the engineering schools of the United States and Canada indicate that the total number of students in these schools for the current year, 1949-50, is about 10% less than it was a year ago. This year, 226 - 533 undergraduates and graduate students are studying engineering in the United States and Canada as compared with. 249,913 students last year. These figures are taken from advance data in the Journal of Engineering Education for February 1950.

Jan 1, 1950

By C. S. Barrett, P. Coheur

AXnealing twins are common in the microstructure of copper that has been rolled and recrystallized. In such samples it follows that a twin relationship should exist between components of the re-crystallization texture,' and several examples of this have been reported. For example, twin relationships have been found in recrystallized electrolytic copper sheet, as indicated in Fig. I, from a paper by Coheur and Lejeune.2 In this pole figure the cube texture (100) [001] is indicated by the hollow squares in the lower half of the figure (the pole figure for 200 reflections) and in the upper, (III), part of the figure. The texture contains, in addition to this orientation, the first-order twins of it, shown in the figure by the filled triangles. This orientation relation has been suggested by others also, under certain annealing conditions,3'4 although pole figures have not been published to confirm it. Some orientations in recrystallized sheets are identical with their twins, because of the symmetry elements of the texture— this is true, for example, with the (113) [ZII] texture so commonly reported for brass—hence it appears impossible in such samples to decide whether the twin relationships result from twinning or merely from the symmetry of the deformation process. The present investigation of a commercial copper strip seems to yield an example in which annealing twins account unambiguously for the principal orientations present. It proves to be a case, also, for which the recrystallization texture cannot be viewed as derived from the deformation texture by a first or second-order twinning mechanism. Materials and Methods The samples investigated were of secondary copper (melted in belgium) to which 0.19 per cent iron had been added to raise the recrystallization temperature. How much the orientation characteristics of this metal can be ascribed to the iron content and how much to other impurities or to melting and pouring practice have not been investigated.* The rolling was done in one direction only, on a mill with rolls of about 20-cm diameter. A strip I. cm wide was reduced from 5 mm thickness to 0.05 mm by several cold passes at commercial speeds. The samples cut from this 99 per cent reduced strip were X-rayed throughout their entire thickness. A pole figure made soon after rolling and annealing was identical, within experimental error, with one that was made when a two-year interval occurred between rolling and annealing. X-ray patterns were made on a camera2 that traversed

Jan 1, 1947