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(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during January: A. Neustaedter, Jersey City, N. J. William Jones, Kent, England. A. J. Sweetser, Boston, Mass. Percy E. Barbour, Candor, N. C. Algernon Del Mar, Los Angeles, Cal. Herbert S. Kohlberg, El Paso, Texas. W. B. Cogswell, Syracuse, N. Y. I. N. Knapp, Ardmore, Pa. R. E. Chambers, New Glasgow, N. S.

Jan 2, 1914

By M. R. J. Wyllie

In a recent publication1 wetting phase relative permeability was exvressed as: and it was stated that a similar expression applied, mutatis mutandis, to non-wetting phase relative permeability; i.e., In Equations (1) and (2), Sw and S0 are respectively the wetting and non-wetting phase saturations as a fraction of the pore volume; PC is the capillary pressure; I; the wetting phase electrical resistivity index; IN, the analogous non-wetting

Jan 1, 1951

By M. R. J. Wyllie

In a recent publication1 wetting phase relative permeability was exvressed as: and it was stated that a similar expression applied, mutatis mutandis, to non-wetting phase relative permeability; i.e., In Equations (1) and (2), Sw and S0 are respectively the wetting and non-wetting phase saturations as a fraction of the pore volume; PC is the capillary pressure; I; the wetting phase electrical resistivity index; IN, the analogous non-wetting

Jan 1, 1951

By M. R. Pickus, C. H. Mathewson

THE study of the plastic deformation and recrystallization of metals has been the subject of many investigations. In regard to the simple deformational processes, such as tension and compression, the early knowledge gained from studies of polycrystalline material has been supplemented by many significant researches on the behavior of single crystals. Unfortunately, this has not been true for more complicated deformational processes. As far back as 1927, G. I. Taylor1 wrote: It is impossible in the present state of knowledge to do more than give a possible reason why (face-centcred cubic) crystals set themselves with a (110) direction in the plane of rolling, and at right angles to the direction of rolling. The explanation of why the orientation of the crystal axes round the transverse direction is what it is, must be left till the distortion of metals, and particularly single crystals of metals in the process of rolling, has been studied in greater detail. That this gap in the systematic study of deformation and recrystallization has not yet been filled was indicated by C. H. Samans,2 who wrote in 1934 that "only four investigations upon cold-rolled single crystals of any of the face-centered cubic metals have been reported in the literature." Of these four studies, only those of S. Tanaka3 and T. Sakao,4 both of whom worked with aluminum crystals, had quantitative significance. The other two, carried out by F. Wever5 and W. G. Burgers," were of a qualitative nature. It is our hope that the present investigation may contribute something to the knowledge necessary for a rationalization of the origin of rolling textures in terms of the known behavior of single crystals, and may add pertinent information concerning the recrystallization characteristics of deformed single crystals.

Jan 1, 1938

By M. R. Pickus

THE study of the plastic deformation and recrystallization of metals has been the subject of many investigations. In regard to the simple deformational processes, such as tension and compression, the early knowledge gained from studies of polycrystalline material has been supplemented by many significant researches on the behavior of single crystals. Unfortunately, this has not been true for more complicated deformational processes. As far back as 1927, G. I. Taylor1 wrote: It is impossible in the present state of knowledge to do more than give a possible reason why (face-centered cubic) crystals set themselves with a (110) direction in the plane of rolling, and at right angles to the direction of rolling. The explanation of why the orientation of the crystal axes round the transverse direction is what it is, must be left till the distortion of metals, and particularly single crystals of metals in the process of rolling, has been studied in greater detail. That this gap in the systematic study of deformation and recrystalliza-tion has not yet been filled was indicated by C. H. Samans,2 who wrote in 1934 that "only four investigations upon cold-rolled single crystals of any of the face-centered cubic metals have been reported in the literature." Of these four studies, only those of S. Tanaka3 and T. Sakao,4 both of whom worked with aluminum crystals, had quantitative significance. The other two, carried out by F. Wever5 and W. G. Burgers,6 were of a. qualitative nature. It is our hope that the present investigation may contribute some-thing to the knowledge necessary for a rationalization of the origin of rolling textures in terms of the known behavior of single crystals, and may add pertinent information concerning the recrystallization characteristics of deformed single crystals.

Jan 1, 1938

PERSONAL (Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Oct. 10 to Nov. 10, 1914: Jintaro Kojima, Ashio, Japan. E. R. Hinckley, Seoul, Korea. J. Homer Stover, Trenton, N. J. S. A. Taylor, Pittsburgh, Pa. Kirby Thomas, New York, N. Y. Lawrence Addicks, Douglas, Ariz. Keijiro Nishio, Tokyo, Japan. Noel Cunningham, Bethlehem, Pa. Alexander K. Hamilton, Chicago, Ill. E. C. Vigeon, London, England. Harold N. Lawrie, Portland, Ore. S. E. Fairchild, Jr., Philadelphia, Pa. C. Spence Thomas, Cardiff, Wales. W. C. Schmidt, Jr., New York, N. Y. Henry Tackmann, New York, N. Y. Kenneth C. Browne, New York, N. Y. Dr. David T. Day has resigned his position with the U. S. Geological Survey and opened an office at 1331 F Street, N. W., Washington, D. C., for practice as a consulting engineer.

Jan 12, 1914

[Admissions: Aurel E. Smith, Chairman Edmond F. Egan Lawrence S. Fennell John S. Fuller Howard J. Ritts, Jr. Gene E. Roark Kenneth W. Robbins Ben M. Gottlieb Advertising: Bernard F. Klein, Chairman Henry N. Lyle R. E. Howard H. M. Krause, Jr. Mrs. Evelyn R. Robertson]

Jan 1, 1961

By B. E. Eakin, A. L. Lee

Atmospheric pressure viscosity values For light hydrocarbons were calculated by a simple mixing rule based on the Sutherland constants for pure components. This method was further extended so that the atmospheric pressure viscosity of a mixture may be calculated based on the molecular weight information only. INTRODUCTION A proven method for estimating the gas-phase viscosity of a mixture is the one by Herning and zipperer.l This mixing rule has the following form: One method for calculating the pure component viscosity i is the Sutherland equation,2 which has the following form: The Sutherland constants B and S are determined from experimental data. A set of Sutherland constants for light hydrocarbons based on the data of several investigators3-5 is presented in Table 1. APPLICATION The Herning-Zipperer equation and the Sutherland equation were used to obtain an equation for calculating the gas-phase viscosity of light hydrocarbons. This equation has the form, Eq. 3 was used successfully in the study of methane-n-butane mixtures.6 Further analysis indicated that the Sutherland constants are a function of molecular weight.7 The gas-phase viscosity may be calculated based on molecular weight information only. The following equation was developed: The atmospheric pressure viscosity of ethane, propane, n-butaneand four methane-propane mixtures calculated on the basis of Eq. 6 are compared with the data of other investigators in Tables 2, 3, 4 and 5, respectively. A plot of atmospheric pressure viscosity vs molecular weight based on Eq. 6 is presented in Fig. 1.

Jan 1, 1965

By C. W. Merrill

Minerals research by the U.S. Bureau of Mines embraces the mining and metallurgical problems of some 80 metals and nonmetals excluding the mineral fuels. It requires the energies and talents of about 1400 persons, almost half of whom are professionally trained in the physical sciences or engineering. Of approximately $13 million appropriated to the Bureau for minerals programs in Fiscal Year 1962, 76% has been allotted to technologic research and 24% to resources examination and appraisal. In addition, almost $2 million will be made available to the Bureau for minerals research from other Government sources and from private organizations that wish to utilize Bureau experience and capabilities in cooperative studies.

Jan 11, 1961

By F. H. Deily, H. W. Lownie, E. A. Loria, L. W. Ledgerwood, M. W. 207-000-000-012 Mallett, J. E. Eckel

MANY investigations have been made of the residual gas content of iron and steel. Very few, if any, quantitative measurements have been made on the oxygen content of cupola-melted iron.' The fact that cast iron is a complex alloy rather than

Jan 1, 1957

By Claude H. P. Lupis, John F. Elliott

QUITE generally an increase in the temperature tends to bring a system closer to ideality. It is reasonable as a first approximation to consider that the excess free energy will vary linearly with the temperature, or: where t may be defined as the "characteristic temperature" of the solution, or the temperature at which the system would become ideal if the results at T were linearly extrapolated. It must be emphasized that consideration of this hypothetical property is an appeal to intuition rather than an established physical concept. The order of magnitude of 7 for dilute solutions will depend on the nature of the solvent; a value of 3000° + 1000°K may be suggested for ordinary metallic solutions. In terms of free energy, entropy, and enthalpy first-order interaction coefficients, differentiation of the above equations with respect to composition leads to The concept of t offers a simple and plausible interpretation of Chipman and corrigan's3 recent empirical correlation between and a for a number of groups of ternary systems 1-24. The authors found that in each group the ratio was approximately constant. The corresponding calculated from their data by Eq. [4] are listed in Table I. The expected order of magnitude is obtained for 7. As noted by Darken,4 if a regular solution is not assumed, thus if utj) # 0, Chipman and Crrigan's results imply that, as T is increased, ultimately changes in sign, Fig. 1. Clearly Eq. [4] is valid only in a limited range of temperatures since at the temperature 7 at which the system becomes ideal not only should become null but also and . Thus, both and are functions of

Jan 1, 1967

By R. G. Stickney

INTRODUCTION The Basalt Waste Isolation Project, conducted by Rockwell Hanford Operations under contract to the U.S. Department of Energy, is assessing the feasibility of the disposal of commercial radioactive spent fuel/high-level waste in deep geologic formations in basalts beneath and within the Hanford Site in southeastern Washington State. The Basalt Waste Isolation Project mission is to identify and characterize a potential geologic repository site in basalt and to develop associated facilities and technology required for the potential permanent isolation of radioactive wastes in basalt formations. In support of the Basalt Waste Isolation Project, a laboratory testing program was conducted to evaluate the performance of the Council for Scientific and Industrial Research's "Doorstopper" biaxial strain cell. To support site characterization studies and the design of repository openings, in situ stress measurements will be conducted within the reference repository horizon (~970 m). The Doorstopper is one of the instruments being considered for use in these measurements. It was selected because it requires only a small volume of work to achieve stress relief, which is important in a closely jointed basalt. Also, test durations are short, permitting a large number of measurements to be made within a given time to increase confidence in the results. Within the reference repository horizon, temperatures are expected in the range of 40º to 60°C with a humidity of up to 100%. For this testing program, test conditions were selected to closely resemble those expected within the repository horizon. The Doorstopper test, mainly developed by Leeman (1964), is a strain rosette relief method of measuring rock stress in situ. The Doorstopper consists of a four element, 45º strain gage rosette

Jan 1, 1984

By John C. Branner

Stratigraphic Position of the Deposits.—During the progress of the geological survey of Arkansas, in the northern part of that State, it was found that the interval between recognizable Lower Silurian rocks below and recognizable Lower Carboniferous rocks above contains no representatives, or but poor representatives, of the whole Upper Silurian and Devonian series. In some places one passes in the space of a foot from Lower Silurian rocks to the Lower Carboniferous—the Boone chert of the Arkansas survey, or the " Burlington " beds; at other places this interval is 3 or 4 feet thick, but it is generally concealed by the ready decay of the black shale—the Eureka shale—which fills it, so that for a long time it was passed over undetected. It was only after considerable work in the region lying north of the Boston mountains, and by the valuable palzeontologic work of Dr. Henry S. Williams, of Yale University, who kindly accompanied me on a trip through this part of the State, that the importance of this interval came to be recognized, and the thin beds occupying it to be critically studied. It then appeared that this interval was occupied, for the most part, either by a greenish or black shale or by a sandstone; and eventually the sandstone was found to have a maximum thickness of 40 feet on South Sylamore creek in 15 N. 11 W., Section 21. It was, therefore, called Sylamore sandstone. The shale of this interval is generally from 3 to 10 feet thick; it is a constant feature of the geology through Carroll county, and is well exposed in the streets and cuts in and about Eureka Springe, and was for this reason named the Eureka shale. Its maximum thickness is 50 feet in the northwestern part of Benton county. The relations to each other of the Sylamore sandstone and the Eureka shale I have never determined satisfactorily; for

Jan 1, 1897

By W. E. Crawford

The Fresnillo Company's mill at Fresnillo, State of Zacatecas, Mexico, treats oxide ores from the Fresnillo mine, dump ores and underground ores from the Plateros district, company leases and custom ores from the Zacatecas district, custom ores from other districts and tailings from old dumps at Fresnillo. The normal capacity of the mill is approximately 2600 dry short tons per 24 hours (a ton of 2000 lb.). The final product of the mill is a precipitate containing gold and silver, which is smelted and shipped as doré bullion to the refinery of the Compania Minera de Penoles, S.A., at Monterrey, State of Nuevo Leon, Mexico. The geology of the district was described in 1923, by T. C. Baker,' from whose paper the following data have been taken: The mineralization of the district was effected in the Tertiary period, following the intrusions and preceding the appearance of the flows. The area within which productive veins have been found is 1 mile long by 1/2 mile wide. The important units of each of the four general fracture systems meet in the central portion of Proano hill, which is an outcrop of graywacke, and where the rock was also intensely fractured by subsidiary movements, resulting in a shattered zone 1200 ft. long by 400 ft. wide. The mineralization was more intense in the immediate vicinity of the principal channels through which the solutions rose. The valuable metals are silver and gold, the ratio by weight of the former to the latter being 1000 to 1.5. Argentite is the predominant silver mineral, and is associated with pyrite and manganese mineral. The sulfides are primary throughout. A slight secondary action is represented by small quantities of native silver and silver halides, principally cerargyrite, which are found in the upper part of the mine. Oxidation has penetrated with great thoroughness to the lowest horizon so far exposed, this being 420 ft. below the present ground-water level. The shattered mass within the central portion of the hill and near the surface was sufficiently mineralized to produce a large stockwork

Jan 1, 1935

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By M. L. Fuller

During the last several years many papers have appeared dealing with the structure of highly polished metal surfaces. The awakening of interest in this subject is due to the applicability of the electron diffraction technique to the study of surfaces. The original theory of Beilbyl considered the surface of polished metals as of the nature of a supercooled liquid or a vitreous, amorphous solid. The electron diffraction effects from polished metals have been interpreted by rnany to be a direct experimental proof of the correctness of the Beilby theory. This interpretation has been strongly opposed by others, so that at the present time the subject is in an uncertain and controversial state. In the present paper new, and hitherto unpublished, electron diffraction effects from polished zinc are desrribed. These observations indicate that the polished surface of zinc is crystalline. Published Work Many papers2""10 have interpreted the electron diffraction evidence as proof of the Beilby amorphous theory. All investigators agree that highly polished metals give rise to two diffuse diffraction haloes, similar to those obtained by the diffraction of X-rays in liquids and vitreous solids. It is this similarity that leads to the amorphous-layer interpretation of polished metals. Strangely, the interatomic distances calculated from these haloes are very similar for the various metals investigated, in spite of a rather wide range of such distances in the crystalline and liquid states. The calculated atomic sizes are, furthermore, smaller than are experienced in the normal states of the metals. In spite of these anomalies, the amorphous-layer interpretation has been adhered to by many. One investigator, S. Dobinski," differs from the others in his experimental results. By polishing under benzene in order to avoid the possibility of oxidation, Dobinski obtains diffuse haloes of radii different from those previously obtained. He thus obtains a more rational quantitative correlation of the diffuse haloes with the amorphous-layer theory.

Jan 1, 1939

By M. L. Fuller

During the last several years many papers have appeared dealing with the structure of highly polished metal surfaces. The awakening of interest in this subject is due to the applicability of the electron diffraction technique to the study of surfaces. The original theory of Beilbyl considered the surface of polished metals as of the nature of a supercooled liquid or a vitreous, amorphous solid. The electron diffraction effects from polished metals have been interpreted by rnany to be a direct experimental proof of the correctness of the Beilby theory. This interpretation has been strongly opposed by others, so that at the present time the subject is in an uncertain and controversial state. In the present paper new, and hitherto unpublished, electron diffraction effects from polished zinc are desrribed. These observations indicate that the polished surface of zinc is crystalline. Published Work Many papers2""10 have interpreted the electron diffraction evidence as proof of the Beilby amorphous theory. All investigators agree that highly polished metals give rise to two diffuse diffraction haloes, similar to those obtained by the diffraction of X-rays in liquids and vitreous solids. It is this similarity that leads to the amorphous-layer interpretation of polished metals. Strangely, the interatomic distances calculated from these haloes are very similar for the various metals investigated, in spite of a rather wide range of such distances in the crystalline and liquid states. The calculated atomic sizes are, furthermore, smaller than are experienced in the normal states of the metals. In spite of these anomalies, the amorphous-layer interpretation has been adhered to by many. One investigator, S. Dobinski," differs from the others in his experimental results. By polishing under benzene in order to avoid the possibility of oxidation, Dobinski obtains diffuse haloes of radii different from those previously obtained. He thus obtains a more rational quantitative correlation of the diffuse haloes with the amorphous-layer theory.

Jan 1, 1939

By M. L. Fuller

DURING the last several years many papers have appeared dealing with the structure of highly polished metal surfaces The awakening of interest in this subject is due to the applicability of the electron diffraction technique to the study of surfaces The original theory of Beilby1 considered the surface of polished metals as of the nature of a super-cooled liquid or a vitreous, amorphous solid The electron diffraction effects from polished metals have been interpreted by many to be a direct experimental proof of the correctness of the Beilby theory This interpretation has been strongly opposed by others, so that at the present time the subject is in an uncertain and controversial state In the present paper new, and hitherto unpublished, electron diffraction effects from polished zinc are described These observations indicate that the polished surface of zinc is crystalline PUBLISHED WORK Many papers2-10 have interpreted the electron diffraction evidence as proof of the Beilby amorphous theory All investigators agree that highly polished metals give rise to two diffuse diffraction haloes, similar to those obtained by the diffraction of X-rays in liquids and vitreous solids It is this similarity that leads to the amorphous-layer interpretation of polished metals Strangely, the interatomic distances calculated from these haloes are very similar for the various metals investigated, in spite of a rather wide range of such distances in the crystalline and liquid states The calculated atomic sizes are, furthermore, smaller than are experienced in the normal states of the metals In spite of these anomalies, the amorphous-layer interpretation has been adhered to by many One investigator, S Dobmski,11 differs from the others in his experimental results By polishing under benzene in order to avoid the possibility of oxidation, Dobinski obtains diffuse haloes of [radire] different from those previously obtained He thus obtains a more rational quantitative correlation of-the diffuse haloes with the amorphous-layer theory

Jan 1, 1938

H. McD. Lorain says in regard to his son, Captain S. H. Lorain; "It might be of interest to you to know that, although but 23 years of age, my son is captain of Co. C 107th U. S. Engineers, Thirty-second Division. He landed in France about the middle of February, 1918, and was commissioned a captain on Sept. 5, 1918. He started for the front the latter part of June and was there continuously until the armi-stice was signed, on Nov. 11, being on the front lines in the Argonne at that time. He is, at present, in Coblenz, Germany, with the Army of Occupation. Although much of his work was clone under artillery and machine-blur fire, as well as airplane bombs and fire, he escaped without a scratch. Once, he was the only one of a group who escaped without a scratch from an exploding shell." Lieut. Bernard H. Lasky, on a post card received a short time ago, gave the following brief record of his military career. "I have been serving with the 316th Engineers in France and in Flanders and had the satisfaction of being in the last big drive in Belgium which sent the enemy beyond Avaenarde and did much to increase their gait on their way to Brussels. On Oct. 1, I received a commission as second lieutenant and was assigned to Co. C of the 316th Engineers."

Jan 3, 1919

By D. P. Harris

The construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area is postulated. The questions (1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and (2) can this geology be related mathematically to mineral wealth and probability are answered in a case study of 97,000 square miles in Arizona and New Mexico. Measurements on mineral wealth and geologic variables of 243 cells were made. The geologic variables, valued in counts, percentages and lengths, quantified the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. The cells of explored area must be allotted the value class indicated by their cumulative production and estimate reserves (given well-defined geological relationships in a mineral wealth area), and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. This determines whether high value cells can be distinguished from low value cells by their geology as well as indicating those cells misclassified by the model into a higher value group than warranted by their known mineral wealth. The second use of the model is for extrapolation. It is demonstrated how geologic information on an explored area can be utilized in guiding exploration in an unexplored area. Exploration decisions can be predicted on explicitly determined measures of uncertainty (the probabilities). SUMMARY This study postulates the construction of a model to associate probability of occurrence of some measure of mineral wealth with the geology for each subdivision (cell) of the area. Such a model will distinguish those cells deserving further exploration on the basis of their geology: The basic postulates of this study are as follows: v = Q(R,S,F,A) P(V) = G(R,S,F,A,V), where V = a measure of mineral wealth P(V) = the probability of occurrence of V R = age and type of rock F = rock fracturing A =age of igneous activity and contact relationships. There are really two questions to be answered: 1) are the observations made in reconnaissance geology sufficiently related to mineral wealth to distinguish the cells of high value from those of low value, and 2) can this geology be related mathematically to mineral wealth and probability? In order to answer these questions, an area of about 97,000 square miles situated chiefly in Arizona and New Mexico was selected as a case study. This case study area was divided into 243 cells, each 20 miles square, and measurements were made on mineral wealth and geologic variables. Crude geologic variables valued in counts, percentages and lengths are constructed to reflect the above postulated variables. These measurement variables thus provide quantified values defining the theoretical concepts of the model. It was found that multiple discriminant analysis and classification analysis by Bayesian statistics and the multivariate normal probability function constitute a two-phase probability model that associates probabilities with geologic information and mineral wealth. Given the availability of an area that is well explored and upon which the relationships of mineral wealth to geology can be adequately defined, there are two ways in which the analysis outlined in this paper can prove beneficial. First, the cells of the explored area must be allotted the value class indicated by their cumulative production and estimated reserves, and a discriminant and classification analysis must be performed in which probabilities of the cell belonging to each of the value groups are generated as a function of the geologic variables. Such an analysis determines whether cells of high

Jan 1, 1967