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By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data

By H. C. Boynton, Albert Sauveur

In the course of some experiments conducted in the Metallographical Laboratory of Harvard University, some interesting facts were brought to light which appear to be worth recording in advance of a more elaborate and exhaustive paper which the authors hope to present to the Institute in the near future. Fig. 1 shows, under a magnification of 100 diameters, the microstructure of the cross-section of a steel bar 1/2-inch square, containing 0.52 per cent. carbon, heated to 1100 degrees C. and cooled slowly with the furnace. Fig. 2 illustrates the structure of the same steel, heated to the same temperature but cooled more rapidly in the air. Both samples were cut from the same bar and heated side by side in the furnace. When a temperature of 1100 degrees C. had been reached, one sample was taken out of the furnace and allowed to cool in the air, while the other was cooled with the furnace. The only difference, therefore, in the treatment of both samples will be found in their respective rate of cooling. This variation in the rate of cooling resulted, as shown

Jan 1, 1904

By C. M. Fellman

AVAILABLE data for the first nine months of the Year indicate that accident occurrence in metal mining was well on its way to an all-time low for 1939. However, the relatively rapid pickup in mining production in the fall will be likely to boost both accident occurrence and also accident rates. Results of the National Safety Competition for 1938, the fourteenth of its kind conducted by the U. S. Bureau of Mines, were published in August, 1939. W. W. Adams, statistician of the bureau, states that "with 345 mines and quarries competing, more than in any previous year except 1931, the contest revealed low accident rates at many of the enrolled plants and, which is even more remarkable, it revealed 113 mines and quarries at which no lost- time accidents occurred during the con- test year." The National Safety Competition provides a means whereby mines and quarries may engage in active competition to stimulate their safety programs. Companies in the contest can compare their records with those of similar plants operating elsewhere and thereby determine to what extent their safety programs are successful. The Joseph A. Holmes Safety Association gave over 150 awards for safety performance in the mineral industries in 1939 and a remarkable phase of these awards was the considerable number given to individual miners who had worked fifty or more years without sustaining a lost-time accident.

Jan 1, 1940

SOUTHERN CALIFORNIA LOCAL SECTION Executive Committee THEODORE B. COMSTOCK, Chairman SEELEY W. MUDD, Vice-Chairman FREDERICK J. H. MERRILL, Secretary-Treasurer, 300 Germain Building, Los Angeles, Cal. C. COLCOCK JONES FRANK ROBBINS The February meeting of the Southern California Local Section-was held at the headquarters in the Chamber of Mines and Oil of. Los Angeles on Feb. 17, C. Colcock Jones presiding. Fourteen members were present. The subject announced was Ore Sampling. W. M. Watts opened the discussion by a general outline of the important points to be covered, in sampling a mine and the methods to be used in the various stages of the work. All the members present successively contributed details from their personal experience. The March meeting of the Section was held at its headquarters on Mar. 15. Twelve members were present, with Dr. Theodore B. Comstock in the Chair. The subject announced was Secondary Enrichment and all present took part in the discussion, Frank Robbins contributing a short paper on some observations in Central America. The next meeting will be held on Apr. 14, at which time the subject of Mine Accounting will be discussed. F. J., H. MERRILL, Secretary.

Jan 5, 1914

By R. H. Wightman, G. H. ADAM

In order to secure good results in the prevention of accidents, it is generally recognized that the desire for such accomplishment, as well as the aggressive and constructive action to achieve it, must emanate from the Top Management and permeate successively down through the "Chart of Authority" to the workmen. Several years ago, with the above as a basis and with full support of the Top Management, the Mining Department started a program of selling the foremen and bosses the idea that safety could be achieved and that it was desired and required. Using psychology, persistence and numerous other methods, the foremen and bosses were finally impressed with the idea that "It can be done" and "It will be done." With this in mind, new ideas were brought forth by the foremen and bosses regarding the caving operation and the specific jobs in the operation. These new ideas were taken up in round-table discussions and resulted in certain changes in the undercutting method and the actual drawing of the blocks. These changes resulted in increasing fragmentation of the blocks which prevented the usual hang-up areas in the blocks. With the rock smaller in size and within reasonable reach from the tapping drifts, accidents were prevented in the tapping section. At the same time, an enforced campaign of housekeeping throughout the mine was undertaken with very beneficial results. The foremen and bosses then, in turn, educated and trained the workers themselves to become safely conscious. In so doing, a constant re- minder was given on all jobs assigned that the job was to be done safely as well as efficiently. No man is assigned a job who is not qualified for the type of work required. Efficiency and safety go hand in hand.

Jan 1, 1949

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By AIME AIME

MESSRS. BURT and Shockley and others have been for three years urging upon the Institute the matter of simplified spelling. The Institute endeavors to be progressive in the matter of spelling and. is in cooperation with the national body which has this in hand and which has its principal office in New York. Our spellings are changed as fast as-good usage will permit (so it seems to the Board of Directors) and the national body, which is the real representative of the simplified spelling interests, deems that the Institute is making real progress, although not quite as fast as extremists would wish. In January, 1919, Mr. Shockley sent out letter ballots which created a misconception in the minds of many members, who received the impression that the communications came from the Institute instead of from a small group of members. As a result of this propaganda 163 proposal-ballots were sent in to the Institute divided as follows: Yes ?114 No ?20 Negative letters ?9 Split ballots ?20 Total ?163 The total membership at this time was about 7200. The disgusted members would not vote.

Jan 1, 1920

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, also Assoc. Mem. Am. Soc. of C. E.; excellent technical education, and best of references covering 12 years in responsible charge of work; experienced in surveys, construction, prospecting, mine

Jan 12, 1917

By WILLIAM E. NEWNAM

THE molding and loading of pig lead has, in the past, been accomplished mainly by the strong arm method and, as the pigs are usually loaded directly into the cars, it has been a hot and laborious task. Of late years it has been difficult to obtain men willing to perform such labor and the need has been felt for loading and molding machinery which would eliminate all manual handling of the hot pigs and which would be sufficiently compact to permit of installation in existing plants with little or no

Jan 1, 1924

THE New York Petroleum Club has elected the following officers for the current year: Chairman, William B. Heroy; vice-chairmen, Edwin B. Hopkins, Warren. A. Sinsheimer; secretary, A. C. Hunter. This is the local section of the Petroleum Division. It holds monthly lunch-eons, usually in the rooms of the Railway Club.

Jan 3, 1927

For the year ending February, 1919 PRESIDENT SIDNEY J. JENNINGS, NEW YORK, N. Y. PAST PRESIDENTS L. D. RICKETTS, NEW. YORK, N. Y. PHILIP N. MOORE, ST. Louis, Mo. FIRST VICE-PRESIDENT C. W. GOODALE BUTTE, MONT. TREASURER GEORGE D. BARRON, NEW YORK, N. Y. SECRETARY BRADLEY STOUGHTON NEW YORK, N. Y.

Jan 2, 1919

By J. W. Downey, M. V. Nevitt

DURING the course of the present investigation of alloy phases involving transition metals, phases were found in the systems Os-Ta, Os-W, and Ir-Ta. The (Os, W) phase was also recently reported by Raub.1 Pertinent information is given in Table 1. The approximate composition range of sta- bility was determined metallographically on arc-melted buttons that were annealed 72 hr at 1200°C and water quenched. X-ray powder patterns were obtained with a 114.6 mm diam powder camera using filtered copper radiation. The composition for (Os, W) given by Raub (66 atomic pct W) is in agreement with the composition range reported here. However, the lattice constants reported by Raub are: a0= 9.913±0.007, c/a= 0.515. The reason for the discrepancy between the lattice constants reported by Raub and those given here is not known. Acknowledgments The authors wish to thank M. H. Mueller and H. W. Knott for assistance with the X-ray diffraction work, and R. A. Morris for the preparation of the alloys. This paper is based upon work performed at the Argonne National Laboratory under the auspices of the Atomic Energy Commission.

Jan 1, 1958

By J. J. Gilman

RECENT experiments have shown that the mar-tensite reaction in a standard tool steel is influenced by the history of the reacting austenite. The martensite reaction proceeds to a given extent at a higher temperature in austenite formed from an annealed spheroidal structure than it does in austenite formed from tempered martensite: that is to say, a prequench lowers the temperature range of the martensite reaction in this steel. Furthermore, a prequench alters the appearance of the martensite as compared to martensite formed from "virgin" austenite. The steel used for this work was a manganese nondeforming tool steel of the following composition: C, 0.85 pct; Mn, 1.43; Si, 0.23; Ni, 0.12; Cr, 0.59; and W, 0.59. A piece from a rolled bar was forged to Vz in. sq and annealed to a spheroidal structure. Disks 1/8 in. thick were used in the experiments. Several sets of the specimens were prepared and austenitized in lead at 1475°F. Three sets were held at 1475°F for 15 min, quenched in water, and immediately reheated to 1475°F. After this quench the three sets were held for 5 min, 30 min, and 3 hr, respectively, at 1475°F and then the individual specimens in each set were quenched in molten baths to 325", 300°, and 275ºF, respectively, and held for 15 sec. Immediately after the quenching treatments? the specimens were tempered at 600°F for 30 sec to darken the martensite and then were quenched in water. The holding times were short enough to avoid isothermal transformation. Three other sets of specimens were given the same final quenching treatments as the first three, but they were austenitized at 1475°F for 20 min, 35 min, and 3 hr and 15 min, respectively, without an intermediate water quench. The two individual specimens from each set were quenched together in order to eliminate quenching errors. Several experiments were run in this way but only the six sets referred to are described in detail because they all yielded essentially the same results. By means of the stated heat treatments the martensite reaction was investigated for: 1—austenite formed from an annealed structure, and 2— austenite formed from tempered martensite. The martensite reactions of the two types of austenite differed significantly. This is shown by Figs. 1 and 2. Comparison of the photographs on the left in Figs. 1 and 2 with those on the right shows that less martensite was formed by a quench to a given temperature from prequenched austenite than from austenite formed from an annealed structure, that is, the prequench suppressed the martensite reaction. The effect was observed for specimens austenitized 20 min, 35 min, and 3 hr and 15 min. A comparison of Figs. 1 and 2 shows that the martensite reactions in both sets of specimens occurred at lower temperatures with increased austenitization time. This was caused by the increased dissolution of residual carbides with time at 1475°F. However, the difference in amount of martensite formed in prequenched austenite as compared to virgin austenite was approximately the same for all three austenitization times. One further observation should be noted. The needles of the martensite formed from virgin austenite are somewhat longer on the average and show less of a tendency to cluster than those of martensite formed from prequenched austenite. This causes the martensite on the right in Figs. 1 and 2 to have a more acicular appearance than the martensite on the left. Since the sets of specimens used in this work were austenitized for identical total lengths of time and the effect of a prequench on the martensite reaction existed for specimens held at the austenitizing tem-

Jan 1, 1953

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

By Walter J. Johnson

The coals in northern Wyoming and Montana are free-burning and non-caking and range from lignite to bituminous C in rank. Strip and underground mining are employed to supply railroad, utility, industrial, and domestic fuel. The market area includes Iowa, Nebraska, Minnesota, North and South Dakotas, Wyoming, Montana, the Pacific Northwest, and western Canada.

Jan 12, 1953

REPORT OF PRESIDENT C. F. RAND FOR THE YEAR 1917 The noteworthy occurrences during 1917 were the creation of Engineering Council; the completion of the addition to the Engineering Societies Building. and the occupation by the American Society of Civil engineers of the space thus provided for it; the addition of 67,000 vol-

Jan 3, 1918

By O. M. Schaus

REDUCED activity of mining, because of the business recession, had the effect of lowering working time, hence of reducing exposure to accidents, so it is probable that 1938 will be found to have had a lesser number (both fatal and nonfatal) though the accident rate may remain about the same as in 1936 and 1937. During periods of re-employment, such as occurred during 1936, 1937, and 1938, the new men entering the industry are less experienced and not as well trained in accident prevention as are the older, more experienced men and are frequently subject to more accidents. This situation should tend to correct itself as the new employees be- come better trained.

Jan 1, 1939

By M. King Hubbert

In 1856 Henry Darcy described in an appendix to his book, Les Fontaines Publiques de la Ville de Dijon, a series of experiments on the downward flow of water through filter sands, whereby it was established that the rate of flow is given by the equation: q= - K(h2- h2)/I1 in which q is the volume of water crossing unit area in unit time, I is the thickness of the sand, h1 and h2 the heights above a reference level of the water in manometers terminated above and below the sand, respectively, and K a factor of proportionality. This relationship, appropriately, soon became known as Darcy's law. Subsequently many separate attempts have been made to give Darcy's empirical expression a more general physical fornzulation, with the result that .so many mutually inconsistent expressions of what is purported to he Darcy's law have appeared in published literature that sight has often been lost of Darcy's own work and of its significance. In the present paper, therefore, it shall be our purpose to reinform ourselves upon what Darcy himself did, and then to determine the meaning of his results when expressed explicitly in terms of the pertinent physical variables involved. This will be done first by the empirical method used by Darcy himself, and then by direct derivation from the Navier-Stokes equation of motion of viscous fluids. We find in this manner that: q = (N4(p/p)[g - (l/p) gradPI = WE, is a physical expression for Darcy's law, which is valid for liquids generally, and for gases at pressures higher than about 20 atmospheres. Here N is a shape factor and d a characteristic length of the pore structure of the solid, p and IL are the density and viscosity of the fluid, a = (Nd2)(pip) is the volume conductivity of the system, and E = [g - (l/p) grad p] is the impelling force per unit mass acting upon the fluid. It is found also that Darcy's law is valid only for flow velocities such that the inertial forces are negligible as compared with those arising from viscosity. In general, three-dimensional space there exist two superposed physical fields: a field of force of charucteristic vector E, and a field of flow of vector q. The force field is more general than the flow field since it has values in all space capable of being occupied by the fluid. So long as the fluid density is constant or is a function of the pressure only, curl E = 0, E = - grad F where F = gz + dp/p The field of flow, independently of the force field, must satisfy the conservation of mom, leading to the equation of continuity div pq = — f ap/at , where f is the porosity, und t is the time. For steady rnotion ap/at = 0. and div pq = 0 .

Jan 1, 1957

We are glad to print the following letter from Herbert C. Hoover, who has recently been appointed Food Administrator, by President Wilson. Mr. Hoover has a tremendous task before him, and we are sure that mining engineers will give him their hearty support by responding to his appeal to stop the waste of food.

Jan 7, 1917