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By Roscoe C. Clark

In a previous technical note' by Walter Rose, evidence is offered in support of the contention that "the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely." It is not the purpose of this note to present further discussion of this possibility but rather to point out that the argument presented there does not appear to be generally valid. In the cited note' reference is made to the experiments of Welge2 wherein it was shown that when water was displaced by oil from a core the pressure in the water phase was less than in the oil phase but that when this oil was then produced by water drive the pressure in the water phase was greater than in the oil phase. Rose has concluded from these observations that conditions of static equilibrium did not obtain since the fluid saturations were such that phase discontinuities seemed unlikely. The argument from which this conclusion was drawn is based on the contention that "the pressure is always greatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase." This premise appears to have been reached from a consideration of capillary phenomena in cylindrical tubes, although it may a1so hold for other types of pore geometry, hut as will be shown below it does not hold for all pore shapes and hence is not generally applicable. Since the pore structure of porous media such as reservoir rocks i- in general so complex as to defy exact description. it is undoubtedly of great value to establish a model in terms of pore shapes of known geometry, provided of course that the limitations of the model are recognized. That the limitations of the capillary. or cylindrical, tube model have not always been fully recognized will be evident from the following discussion of a pore of different shape hut one which may a. logically he considered a.; the capillary tube. The pore space to be considered is that shown in Fig. 1, which may be thought of as the "hole in a doughnut."* Consider the interface, A-B-A', between two immiscible fluids, P, and P2, which interface meets the solid alone a line, A-C.A'-C'. The interface A-B-A' is the surface of a spherical segmen† while the line of mutual contact be-

Jan 1, 1950

Edward Halse, Puerto Berrio, Colombia, So. Amer. (communication to the Secretary*): The Taviche mining-district is generally known as " Taviches," being named from the two villages called respectively San Pedro Taviche and San Jero-nimo Taviche. It is so called by Jose G. Aguilera, in his paper on the Geographical and Geological Distribution of the Mineral Deposits of Mexico;' and in published reports by the late N. W. Rudston Read ;2 and by Juan de Dios Villarello3 The region is a large one, measuring about 24 miles long and 7 miles wide. Dr. Chance, in his interesting paper, tells us very little about the nature of the ores, and, with regard to the geology of the district, contents himself with observing that " the country, as a rule, consists of eruptive rocks; and no evidences of sedimentary strata appear near the mines." The latter part of the above statement is hardly correct. The formation is mainly

Jan 1, 1906

By S. J. Prison, C. R. Smith

The effect of fluid injection to control water coning in oil and gas wells was investigated. Analytical and model techniques were employed. The factors investigated were the position and length of the completion interval, the point of fluid injection, the viscosity of the injected fluid and the relative thickness of the oil and water sections. The resulting influence of these factors on the net producing water-oil ratio was determined. Several important conclusions can be drawn from the study. In general, it was found that the net producing water-oil ratio can be reduced by fluid injection. The magnitude of this reduction depended on the factors listed above. An important practical consideration is that the injection fluid may be either oil or water. If the injected fluid is less dense than the connate water of the reservoir, the fluid will not be lost. This fact is reassuring when valuable oil is being injected. Efforts to suppress water production were more successful when the injection fluid was more viscous than the reservoir oil, or when a zone of reduced permeability existed in the vicinity of the point of fluid injection. Under test conditions, little benefit was derived through the use of impermeable barriers or cement "pancakes". INTRODUCTION The occurrence of water coning has been known for at least 60 years. In thin oil or gas pay sections, the presence of an oil-water or gas-water contact hinders production and often causes early abandonment of the afflicted well if a completion is even attempted. Even when relatively thick pay sections are found, the encroachment of water when a water drive is present will eventually pose serious water coning problems. This water is often corrosive, expensive to separate from the oil or gas and is costly to dispose of. The theory of water coning has been discussed by a number of authors. 1,2,3,4 Briefly, water coning to the producing interval in a well is due to pressure gradients resulting from the production of fluid from the reservoir. These pressure gradients will cause a water cone to rise toward the bottom of the producing interval if a water-oil or water-gas contact exists. The tendency of the water to cone is offset or partially offset by gravity forces since the water has a higher specific gravity than the oil. A balance then exists between two forces, gravitational forces arising from the difference in specific gravities of the oil and water, and the pressure gradients causing the flow of fluids to the wellbore. If the pressure gradient exceeds the gravitational force, water coning to the wellbore occurs and water production results. Through the years considerable thought has been given to the water coning problem. More than 50 U. S. Patents have been granted to inventors on the subject. A relatively complete literature review of the water coning problem has been made. 5 A number of these patents hold considerable promise for the solution or the partial solution of the water and/or the coning problem. Very little has been written describing field tests of techniques for the suppression of water coning. A notable exception is the paperby West. 6 He reports success in reducing gas coning by a combination of gravel packing and oil injection above the oil-producing interval. He also describes a comparable method to prevent water coning, but provides no field examples. This study experimentally and analytically verifies the benefits of oil injection as a means of partially or completely suppressing the water cone. While the gas coning problem was not treated, it is anticipated that results comparable to those obtained in water suppression could be obtained with reduced oil injection since the viscosity contrast between oil and gas exceeds that between oil and water. For the purpose of this study, the conventional potential flow theory was applied to the water-coning problem. The experimental verification centered on both a radial and a linear model. The model study permitted the investigation of complex flow configurations and the use of fluids of differing densities and viscosities. No analytic expressions are available to permit a solution of the problem as stated (see Fig. 1).

By M. A. Mahtab, T. M. Yegulalp

This paper presents the development and application of an approach for clustering fracture orientation data. Data are projected on the surface of the unit upper hemisphere and the clustering approach is applied in three steps: (1) randomness test and identification of dense clusters, (2) estimation of cluster statistics, using Bingham distribution, and (3) rejection of extremal data based on Chauvenet's criterion.

Jan 1, 1982

President MRS THORNS E LLOYD 14 Green Hill Road Morristown, N J First Vice-President MRS A B PARSONS 52 Edgewood Road Scarsdale, N Y Second Vice-President MRS H A PROSSER 1001 Park Avenue New York, N Y Third Vice-President MRS HARRY J WOLF 3 Glenwood Avenue Littleneck, N Y Fourth Vice-President MRS MARK LAWRENCE REQUA 140 North Plymouth Blvd Los Angeles, Calif Fifth Vice-President MRS NEWELL G ALFORD 314 South Homewood Avenue Pittsburgh, Pa

Jan 1, 1952

By Eugene A. Alexandrov

The Minister of Geology of the Soviet Union P.Ya. Antropov, recently visited China and claims that this country occupies one of the foremost places in the world in reserves of tin, tungsten, molybdenum, antimony, iron ore, coal, and phosphates. Occurrences of economic value of chromite, nickel, gold, beryllium, tantalum, niobium, rare earths, and asbestos have also been reported. MINERAL RESOURCES Coal: The inferred reserves of coal are estimated at at 1,500 billion tons. A considerable part of the coal reserves is represented by coking coal, 80% of which is bituminous. Thicknesses of coal seams range up to 150 ft in the principal deposits located in northern and northeastern China. The total output of coal in 1958, 270 million tons, was produced by an army of 20 million people mainly in small mines operated by the agricultural communes. Modern hydraulic mining is applied besides primitive, obsolete methods and equipment

Jan 3, 1960

E. G. SPILSBURY, New York, N. Y.-I would like to ask Mr. Wemple what is the total loss in redistillation; not merely the weight of the lead removed, but also the loss clue to rehandling of a large amount of blue powder, and that clue to the final remelting in the tank furnace? LELAND E. WEMPLE.-The loss of zinc by redistillation, on the first operation, is approximately 5 per cent. This loss does not cover the lead

Jan 4, 1918

E. H. Dix, JR., Chairman L. W. M. PEIRCE, Past-chairman R. F. MEHL, Vice-chairman ALBERT J. PHILLIPS, Vice-chairman E. M. WISE, Secretary International Nickel Co., Bayonne, N. J. W. M. CORSE, Treasurer LOUIS JORDAN, Executive Secretary 29 West 39th St., New York, N. Y. Executive Committee W. H. BASSETT, JR. R. H. LEACH' W. H. FINKELDEY W. E. REMMERS2 J. A. GANN H. J. ROAST G. O. HIERS C. S. SMITHS L ZICKRICK

Jan 1, 1936

By J. F. Blandy

IN October last, I was call upon to examine a copper deposit in the South Mountain, near the Pennsylvania and Maryland boundary. The specimens shown me contained oxides and carbonates with native copper, and were similar to some that had been described to me some years ago as existing at the Luray Gap in Virginia. An examination of Rogers's Report on the Geology of Pennsylvania, led me to expect to see his so-called "Primal Formation," such as exists throughout the southeastern district of the State. I was therefore much surprised on arriving at the summit of the Western Maryland Railroad to find myself on familiar ground. Instead of the "Primal" as I had known it in Southeastern Pennsylvania, I soon decided that the rocks were identical with the "Lake Superior Copper Formation." My visit was unfortunately a short one, part of two days, and in that time I had to pass over a good many miles, but I saw sufficient to convince me that instead of the Lake Superior Copper Formation being a local geological feature, it would have to be considered as a widely extended series of rocks. I was unable to even approximately estimate the thickness either of the trap zone or other members, schists and slates, of the series. In an article on the Copper Range of Michigan, prepared by C. P. Williams and myself in 1862, and published, in vol. xxxiv of the American Journal of Arts and Sciences, we endeavored to divide that range into zones, according to the character of the traps. The limited nature of the explorations at that time made this work very imperfect. Subsequent explorations have confirmed my notes then

Jan 1, 1879

By J. F. Blandy

In October last, I was call upon to examine a copper deposit in the South Mountain, near the Pennsylvania and Maryland boundary. The specimens shown me contained oxides and carbonates with native copper, and were similar to some that had been described to me some years ago as existing at the Luray Gap in Virginia. An examination of Rogers's Report on the Geology of Pennsylvania, led me to expect to see his so-called "Primal Formation," such as exists throughout the southeastern district of the State. I was therefore much surprised on arriving at the summit of the Western Maryland Railroad to find myself on familiar ground. Instead of the "Primal" as I had known it in Southeastern Pennsylvania, I soon decided that the rocks were identical with the ('Lake Superior Copper Formation." My visit was unfortunately a short one, —part of two days, and in that time I had to pass over a good many miles,—but I saw sufficient to convince me that instead of the Lake Superior Copper Formation being a local geological feature, it would have to be considered as a widely extended series of rocks. I was unable to even approximately estimate the thickness either of the trap zone or other members, schists and slates, of the series. In an article on the Copper 'Range of Michigan, prepared by C. P. Williams and myself in 1862, and published. in vol. xxxiv of the American Journal of Arts and Sciences, we endeavored to divide that range into zones, according to the character of the traps. The limited nature of the explorations at that time made this work very imperfect. Subsequent explorations have confirmed my notes then

Jan 1, 1879

By THOMAS G. FEAR

THE COAL DIVISION started its share of the annual meeting Monday morning with a study of coal classi fication. A. C. Fieldner was in the chair. The report of the tellers of the ballot for division chairman, stating that Thomas G. Fear had been elected to that office, was read by M. D. Cooper. Mr. Fear acknowledged the honor in a few words. In reviewing the history of the Coal Classification Committee the chairman pointed out that this was its third symposium, the last previous one having been held at the 1930 Annual Meeting. Throughout its work the com¬mittee has had the active cooperation of the Canadian workers who are interested in the subject which should result in a uniform scheme of classification in Canada and the United States. F. E. Lathe, of the National Research Council, Ottawa, abstracted the first two papers of the session entitled "Determination of the Alkali-Soluble Ulmins in Coal," by Edgar Stansfield and K. C. Gilbart, and "Moisture Determination for Coal Classification," by the same authors. The third paper "Condition of Water in Coals of Various Ranks"' was presented by its author, A. W. Gauger. Written discussions of these papers were presented by H. C. Porter and Gilbert H. Cady. In the oral discussion which followed, W. T. Thom, Jr., brought out the advisability of considering age as a factor in classification. Mr. Fieldner favored retaining bed moisture as a partial classification basis, stating that a review of many coal analyses revealed a remarkable consistency in this item in samples from a given mine particularly where the moisture content was not high. Mr. Porter pointed out that the structure and porosity of coal often have much to do with its moisture content and that these vary in different parts of a seam, particularly in anthracite. Mr. Gauger expressed doubt as to whether the Stansfield method gives the true moisture content of coal, which is needed for classification purposes.

Jan 1, 1932

By H. M. Howe

THIS paper presents an experimental verification of some of the predictions made by one of us' concerning 'the influence of certain conditions of casting upon the size and position of the pipe', and the position of the segregate, in steel ingots. The predictions which we have been able to verify are the following A. That the pipe is shortened and the segregate raised 1. By slow casting; 2. By casting with the large end up instead of down; 3. By retarding the cooling of the top, e.g., by means of a sinking-head. B. That the pipe is shortened by slow cooling. C. That the pipe and segregate lie in the last freezing-part. Our procedure was to cast ingots of wax (commercially pure stearic acid) containing a little bright green copper oleate (usually 1.5 per cent.) under varying conditions; to saw each ingot open along a longitudinal plane passing through its axis ; and to examine the longitudinal section thus laid bare. In order to make the segregate or enriched part more distinct in color from the impoverished part, a very little red cerasine was added. An experiment which will be described later showed that the cerasine itself does not segregate markedly, if at all. Hence we may assume that the strong contrasts between the green and red shown in so many of our ingots are due, not to segregation of cerasine, but to that of the green oleate, in the wax which in itself is uniformly reddened with cerasine.

Jul 1, 1907

By Brandon H. Grove

The Zistersdorf field, near Vienna, continues to be Austria's only producing area. During the year the field was slightly extended by Rohol Gewinnungs A.G. in its Rag 2, which in April came in for an initial 120 tons daily through an 8-mm. (0.315-in.) bean, from the twelfth Sarmat sand at 1447 m. (4747 ft.). The amount of fluid produced by this well has remained essentially constant, but after the first several months water appeared and increased to some 50 per cent of the total. TWO subsequent extension wells, Rag 3 and Rag 5, northeast and west of Rag 2, found only water-bearing sands, and drilled through the main fault and into the Flysch at 1683 and 1401 m. (5522 and 4596 ft.), respectively. At the close of the year preparations were under way to deviate both wells away from the fault to test still deeper sands. Within the previously proven area of the field Erdolproduction's Gosting VII came in flowing a maximum of 440 tons daily, the highest individual production yet recorded. This company's Gosting VIII also yielded an initial production of 20 tons daily, and its Gosting XI, drilling

Jan 1, 1938

[ZAY JEFFRRIES, Vice-chairman PAUL D, MERICA, Chairman W, M, CORSE, Secretary Executive Committee J. It, FREEMAN, JR., Local Section S. SKOWRONSKI, Papers Committee R. S, ARCHER, Non-ferrous Data Sheets H, C, JENNISON, Membership Committee E, C, BAIN, Journal Committee L, W. SPRING Local Section Committee J. R, FREEMAN, JR,, Chairman R. J, ANDERSON, Cincinnati R. L. DOWDELL, Minneapolis R. S. WILLIAMS, Boston G, H, CLAMER, Philadelphia W. A. SCHEUCH, Chicago R, F, WOOD, New York]

Jan 1, 1928

By George Burgess

THE Pyrometer Committee was. formed Sept. 20, 1918, at the suggestion of Dr. H. M. Howe, Chairman of the Engineering Division of the Research Council, for the purpose of developing a pyrometric method suitable for open-hearth steel practice so that the effects of temperature in the various stages of the processes of steel making might be correlated quantitatively with the other factors influencing the production of sound .steel. As finally constituted the Committee consists of Dr. George K. Burgess, Chief Division of Metallurgy, Bureau of Standards, Chairman. Dr. Paul D. Foote, Chief of Pyrometry Section, Bureau of Standards, Secretary. Dr. H. M. Howe, Chairman Engineering Division, National Research Council, ex officio. Prof. G. H. Clevenger, Chairman Metallurgical Section, National Research Council, ex officio. Mr. F. E. Bash, Leeds & Northrup Co., Philadelphia, Pa. Mr. R. P. Brown, The Brown Instrument Co., Philadelphia, Pa. Prof. G. H. Brown, Rutgers College, New Brunswick, N. J. Mr. R. C. Drinker, metallurgical engineer, Boston, Mass., Dr. W. E. Forsythe, Nela Research Laboratory, Cleveland, Ohio. Mr. J. T. Hall, Taylor-Wharton Iron & Steel Co., High Bridge, N. J. Mr. J. S. McDowell, Harbison-Walker Refractories Co., Pittsburgh, Pa. Mr. Malcolm McNaughton, Joseph Dixon Crucible Co., Jersey City, N. J. Mr. A.' H. Miller, Midvale Steel Co., Philadelphia, Pa. Mr. F. E. Walduck (since deceased), The Norton Co., Worcester, Mass.

Jan 9, 1919

By B. Fitch

This paper deals with the behavior of sedimenting suspensions. More particularly, it treats, in as organized a manner as possible, the body of knowledge, theoretical or empirical, by which one predicts the behavior of miscellaneous swarms of particles in suspension. Such knowledge is necessary for precise and economical design of equipment. While the behavior of a single spherical particle settling through an infinite sea of quiescent fluid is well understood, practical sedimentation processes are almost always concerned with particles of assorted sizes, densities, and shapes, in such concentration that there is profound particle interaction. Such swarms of particles are observed to settle in any of four markedly different manners. Which one they follow is governed by particle interaction. It is determined largely by the dilution of the suspension, and the relative tendency of the particles to cohere. TYPES OF SEDIMENTATION The relationship between the different modes of sedimentation is shown paragenetically in Fig. 1. The left side of the diagram represents particles having little tendency to cohere; the right side represents particles for which interparticle cohesion is large compared to the settling force. The vertical axis represents dilution. As seen in the diagram, sedimentation is divided into three broad fields or regimes. At high dilutions there exists a regime here named 'clarification.' Particles in clarification may settle either individually, or by collecting into separated floccules. Thus there are two different possible modes of settling in the clarification regime. It is characteristic c~f this regime that there will be no clear line of demarcation between settling suspension and a supernatant. Faster particles settle out ahead of slower ones. In batch tests there develops a gradation of both particle sizes and pulp density due to progressive depletion of the largest particles from any given pulp level.

Jan 1, 1962

The following is an incomplete list of members and guests who called at Institute headquarters during the period June 10, 1919, to July 10, 1919. Anvil A. Anderson, Rapid City, S. D. Roy N. McBride, U. S. Army. R. Hay Anderson, Mexico City, Mex. R. S. McIntyre, Berkeley, Calif. W. A. Barnes, San Francisco, Calif. H. R. Maier, Brooklyn, N. Y. Bennett R. Bates, Denver, Colo. Wm. D. Mainwaring, Philadelphia, Pa. Harlan H. Bradt, Duluth, Minn. Wm. E. Milligan, Chrome, N. J. H. Brings, San Francisco, Calif. Willard S. Morse, Tacoma, Wash. Robert S. Burg, Ocean Park, Calif. Arthur Notman, Bisbee, Ariz. D. W. Butner, Congo Belge, Africa. P. Nugue, Chalon Sr. Saone, France. George A. Camphuis, El Paso, Tex. George A. Packard, Boston, Mass. Fred Canan, Denver, Colo. C. L. Petzel, New York City. Walter H. Coleman, Prescott, Ariz. V. Porreaud, Paris, France. Fred Crabtree, Pittsburgh, Pa. Fred S. Porter, Seattle, Wash. Ross E. Douglas, Rancagua, Chile. R. W. Prouty, Morenci, Ariz. F. A. Downes, Golden, Colo. Charles E. Prior, Brooklyn, N. Y. W. G. Eberhardt, Tucson, Ariz. Louis Ravicz, Minneapolis, Minn. Charles H. Fulton, Cleveland, Ohio. Wm. Reed, El Oro, Mexico. Wm. R. Grunow, New York City. E. J. Ristedt, Globe, Ariz. Orr R. Hamilton, Lansing, Mich. A. M. Rodgers, Middletown, N. Y. T. N. Havlin, St. Louis, Mo. J. C. Scoles, Salt Lake City, Utah. G. M. Henderson, Weston, Mass. C. E. Siebenthal, Washington, D. C.

Jan 8, 1919

By Wallace Ralston

The East Texas area includes the northeast 38 counties of the state of Texas. It covers all, and extends beyond, the borders of what is commonly described as the East Texas Basin. It is one of the most important oil and gas-producing areas of the Mid-Continent Province. It includes four important oil fields—Van, East Texas, Cayuga and Long Lake— and the recent extension of Rodessa field into Cass County, Texas, may prove to be of major size. Four commercial gas fields are in this area— Bethany, Waskom, Cayuga and Long Lake. Up to January, 1936, all of the oil has been produced from the Upper Cretaceous formations, and most of that from the basal member, the Woodbine sand. Gas is produced from both the Upper and Lower Cretaceous formations. Development in Fields East Texas Field.—This field continued to dominate the drilling and production situation throughout the United States. There were 4036 wells completed in this field during 1935; that is, 365 more wells than were completed during 1934. Drilling activity was due to close spacing of wells and the addition of 10,000 acres to the field. The field is now drilled to a density of one well to 6½ acres, which is certainly more wells than necessary for economic production of the field. The close spacing of wells is due mostly to the type of proration, which is per well allowable based on a potential test, and does not take acreage into consideration, and also to the numerous small acreage tracts such as town lots and excess strips. The field now has 19,519 producing wells. The allowable production for the field during 1935 was 161,118,659 bbl.; estimated production, including illegal or "hot oil," was 174,200,150. The illegal production of oil gradually decreased throughout the year, until an estimated low was reached of 20,500 bbl. daily during the months of November and December. The price of oil remained at $1.00 per barrel throughout the year. As stated, about 10,000 acres were added to the field during the year, making a total of 128,000 productive acres. There is a possibility that

Jan 1, 1936

By F. O. Willhofft

The symposium on mine safety held in connection with the annual meeting of the Institute three years ago, it. was pointed out that "at present no convenient, reliable, accurate means for determining the gas content of mine air is available, for use by the ordinary mine man." In a letter addressed to Coal Age and published on Feb. 25, 1925, Thomas T. Read, then Director of the Safety Service of the Bureau of Mines, stated: "It is to be hoped that sometime in the near future some-one will invent a reliable methane indicator that is con-venient to, use and will permit the keeping of all flames of every character out of bituminous mines, through doing away with the safety lamp." The Martienssen methane detector, which has re-cently received the official approval of the Bureau of Mines, is intended to. meet the demand for such an in-strument as expressed at that meeting and on many other occasions. The characteristics which qualify it for the task are the following: (1) simplicity; (2) small bulk and light weight; (3) ruggedness; (4) accuracy sufficient for the requirements; (5) safety; and (6) dependability. The principle on which the working of the instrument is based may best be explained by giving a brief out-line of the various stages of development through which the inventor, Professor Martienssen of the University of Kiel, Germany, advanced to the final solution of the problem which he had undertaken to solve.

Jan 2, 1928

By Henry Schaefer

Solution by electric analogy of performance problems of reservoirs containing oil and gas has heretofore depended upon a process of successive approximations based on material-balance calculations, because of variation in fluid compressibility. By the addition or subtraction of electric condenser capacity, the analogy network can be adjusted automatically for changing compressibility due to evolution of gas in the reservoir. The addition of a condenser is accomplished by an electronic circuit, which is described; subtracting a condenser is done by merely opening the electrical circuit by means of a relay. Introduction V. Paschkis and H. D. Baker1 first developed in this country a method of applying the analogy of flow of electric current in noninductive circuits to solution of heat-flow problems and suggested its application for certain other problems, such as flow of fluids or mass transfer and chemical diffusion. Necessary details for applying the analogy to flow of fluids in porous media were developed by IV. A. Bruce;= he classified3 the types of analysis and predictions that can be made by the analogy in class I, when the reservoir contains oil but no gas for the period under consideration; in Class 2, when both oil and gas exist in the free state in the reservoir sometime during the period under consideration. Duplication of bottom-hole pressure history and predictions for class I reservoirs can be obtained directly by electric analogy. Until now, the solution of problems pertaining to reservoirs in class 2 was obtained by successive approximations along with material-balance calculations. The object of this paper is to present a method for simplifying the application of electric analogy to class 2 reservoirs, resulting in a solution of these problems as direct as is possible for class I reservoirs. This is accomplished by an electronic control circuit, which adjusts the analogy network for changing compressibilities of fluids contained in the reservoirs. Analogy Network In electrical phenomena the analogy to two-dimensional fluid flow in a porous media is that of current flow through an ideal conducting sheet. This sheet, perfectly insulated on both sides, has resistance and capacitance uniformly distributed throughout its area but is of negligible inductance. The need for having the surface boundaries perfectly insulated is that good correspondence may be had with a permeable fluid-conducting stratum bounded above and below by impermeable media. 111 actual application the ideal conducting sheet, which has distributed parameters, is replaced by a network having lumped values of resistance and capacitance—the resistances are series elements and the capacitances are shunt elements. The larger the number of lumped

Jan 1, 1947