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This dictionary is published by the Bureau of Mines as a contribution to the mining and mineral literature in the belief that it will fill a recognized need. Several attempts have been made over the years to revise Albert Fay's Glossary of the Mining and Mineral Industry which first appeared in December of 1918. Frank L. Hess of the Bureau of Mines worked on a revision, but his untimely death prevented its completion. Subsequently, the writer was employed to compile and edit this dictionary in cooperation with the technical staff of the Bureau of Mines. Fay's glossary contained about 18,000 terms with 27,000 definitions; the present compilation contains about 55,000 terms with approximately 150,000 definitions. These terms are of both a technical and local nature, and they apply to metal mining, coal mining, quarrying, geology, metallurgy, ceramics and clays, glassmaking, minerals and mineralogy, and general terminology. Petroleum, natural gas, and legal mining terminology, unless of a general nature, has been excluded, as has been foreign terminology where there is an English equivalent. Several thousand Spanish-American mining terms that appeared in Fay's compilation have been removed to make way for the thousands of new English terms that have evolved over the years. Those Spanish-American and Mexican terms still used in the Southwestern United States have been retained.

Jan 1, 1968

By H. H. Bird

Kilembe is situated in the foothills of the Ruwenzori Mountains in Uganda. Precambrian stratiform copper de-posits are currently being mined at a rate of 90,000 tons per month. Complex ore structures and variable ground conditions have led to diverse mining methods in the past. New mining areas contain more shallow-dipping, highly contorted orebodies, in heavy ground. Cut-and-fill mining will be practised in the future. The geology, mining and milling are described.

Jan 1, 1968

By L. C. Graton

At the Tenth International Geological Congress, Mexico, 1906, Waldemar Lindgren presented "The Relation of Ore Deposition to Physical Conditions." Retrospect ranks it as the outstanding offering at that Session and as the most fundamental contribution up to that date on the philosophy of ore deposition. Elaborating thereon in his text-book "Mineral Deposits," Lindgren analyzed ore-forming processes under conditions prevailing from great depth up to surface; explained the nature of deposition in each environment; and developed a comprehensive genetic ore classification, which brought wide acceptance and enriching contributions by many. Since Lindgren's latest edition (1933), have come wealths of material relevant to ore genesis, particularly through amazing renaissance and proliferation throughout science. Current publication regarding ores now emanates largely from a generation caught in pressures of the breathless modern tempo, which tempts scant reflection upon earlier truths. Consequently, today's thrilling output contains not a few offerings that need challenge because supplanting interrelationship and system by what seems, collectively, an assemblage of strange, ad hoc and often self-contradictory concepts. From these latter some merit may eventuate but at the probable cost of present confusion and delayed progress. The following pages, naming numerous post-Lindgren advances, record the conviction, held by many, that Lindgren's philosophy, progressively improved, remains the soundest approach to understanding ore genesis.

Jan 1, 1968

By W. F. McDermott

The transportation of solids by pipeline is not new. In 1891 a United States patent broadly covering a method of pumping coal with water was granted to W. C. Andrews. His pilot plant was constructed on what is now the site of the New York Public Library in Manhattan. His process was applied to pumping coal mine waste back into the worked out portion of coal mines. On October 26, 1967, the world's first long distance iron ore slurry line was put into service by Savage River Mines. The commissioning of this 5.0 million dollar installation climaxed three years of development, testing, and construction and proved the Company's faith in pioneering this unique transportation method for iron ore. This paper will discuss some of the more pertinent items in connection with that three- year period. Also to be discussed will be the operation of this line during the past eleven months.

Jan 1, 1968

By Wilbur H. Smith

Geologic mapping techniques at the Bingham Mine have evolved as rapidly expanding applications of geological data have caused new methods to be utilized. The most significant changes in method have been in the preparation of the base map and in computer application of collected data. Formerly maps were prepared by surveying with transit or plane table. Currently a photogrammetric map, on the scale of 1-inch equals 200-feet, is prepared semi-annually and continuously updated to keep pace with the removal of more than 350,000 tons of material daily. Larger scale bases for specific problems, such as areas having unstable slopes, are prepared by use of aerial and terrestial photography and photo mosaics. Note sheets designed for computer application enable fast processing of the data. Application of geology at the Bingham Mine has been increasing rapidly in recent years. The effect of structure, rock type, and alteration on slope stability, the relationship of sulfide mineral distribution to concentrating results, the effect of rock and mineral types on waste dump leaching, and requirements of a reliable internal source of silica flux for smelting are a few of the problems which require the collection and application of geologic data.

Jan 1, 1968

Helium has probably aroused more varied scientific curiosity than any other single element. Discovered by spectroscopic examination of the sun during an eclipse in 1868, helium is now known to exist not only in the sun and other stars but on earth occluded in minerals, accumulated with natural gases in pockets in the earth's crust, and in the atmosphere surrounding the earth. Astronomers study its presence in the various stars of the universe for clues to their origin and history. Geochemists and geologists study its occurrences in rocks, minerals, and meteorites to determine the age of the earth and the manner of its formation. Pathologists study its effect on living tissues in search for the ideal combination with oxygen for artificial breathing mixtures in medicine, diving operations, and space vehicles. Chemists study its physical properties and use it to trace the sequence of events in reactions in which it does not participate. Geneticists and bacteriologists use it for special studies. Physicists study its behavior when liquefied and the behavior of materials cooled to nearly absolute zero by its use. Nuclear physicists learn more about the universe through study of the nuclear reactions that produce it. Through study of helium and greater knowledge of its origin and properties, science continues to unlock some of nature's more closely guarded secrets. Unknown on earth before 1895, and not discovered as a minor constituent of natural gas until 1905, helium with its simple atomic structure--a nucleus with two electrons orbiting in a closed shell--is a unique element. It is next to the lightest gas, only hydrogen is lighter. It occupies position number 2 in the Periodic Table of the Elements and heads the list of so-called "rare" or ?noble? gases. Most of the naturally occurring helium has an atomic mass of 4.003874 (oxygen = 16). A trace (1.7 x 10-5 mol percent) is the light isotope helium-3 whose atomic mass is 3.0169800 Unstable isotopes of mass numbers 5 and 6 have been authenticated. Isotopes of mass numbers 7 and 8 have been reported, but their existence is less well established. All the heavier isotopes are radioactive and are the product of nuclear reactions.

Jan 1, 1968

By Charles L. Elliot

Data on worldwide geophysical activity in application to mining exploration programs is collected annually as part of a continuing service to the mining and petroleum industries. The data for mining geophysical activity in 1966 has been made available to SME by the Society of Exploration Geophysicists. This data is based on 288 voluntary responses for a return of 59% to 487 questionnaires that were circulated among worldwide mining companies, universities, and government institutions that conduct or utilize mining geophysical surveys or carry out allied research efforts. This data is herein published in condensed form with the permission of the SEG.

Jan 11, 1967

For handling rough rock, the shovel-train system is unexcelled. The ideal application is a physically large, but not excessively deep, open-pit mine from which the coarsely blasted ore and waste must be transported distances in excess of three miles. If, in addition, a high production rate is to be maintained, railroad haulage will probably afford a lower cost per ton transportation than will any other haulage method. Relatively gentle grades must be employed- usually 3% for uphill hauls and 4% for downhill hauls. The greater the differences in elevation the greater are the railroad track grade space requirements. By way of illustration, a 3% ramp out of a pit only 300 ft deep must be almost two miles long. Mainline track locations should be selected carefully so that the frequency of movements during the life of the mining operation is minimized. This applies both to ore and to waste haulageways. Such moves are not only expensive but difficult to execute without adversely affecting production rates. The large mine affords greater opportunities for judicious location of semi-permanent trackage.

Jan 10, 1967

By H. R. Spedden

As part of its broad program of educational assistance-including grants, fellowships, and scholarships -Kennecott Copper Corp. offers summer employment opportunities for college students at each of its operations. Originally, summer job programs were intended primarily to help students defray their educational expenses. But as the nation's economy expanded with increased production and a growing demand for well-trained engineers, summer employment became an important means to help qualify future professionals and fill industry's need for them. Both the employer and the student thus derive benefits from such training.

Jan 6, 1967

By Wayne E. Tuomi

The mining industry is faced with a pressing problem; that is, to develop more efficient methods of extraction, handling and upgrading-techniques that will do the job faster and better than ever before. New techniques require new machines, or applications of new and improved materials that can be used to modify and improve existing machine and equipment designs. The traditional approach has been to increase productivity by increasing equipment size. Prognostication indicates that the trend toward larger equipment sizes and capacities will continue as one answer to the challenge imposed by future increases in mineral demands. But what is the limit on the continued growth of equipment size? Until about 1930, there was a very definite limit-a limit imposed by the strength of the steels and the power plants then available. The equipment engineer had come to an impasse: even though it was easily possible, for instance, to triple the size of a bucket, it had become impractical to correspondingly enlarge the boom, the counterweight, and the power plant.

Jan 3, 1967

By Gill Montgomery

At this moment in the history of the world, the all- pervading and universally most important fact is that the world population is beginning to outgrow its food supply, and the United States has suddenly lost its ability to give away huge food surplus to any nation in the world with a food shortage problem. This, of course, means that, all of a sudden, our government must completely reverse its former bureaucratic stance regarding crop controls and agricultural price supports, to out-right incentives to increase farm production and bring more idle land into food-growing use.

Jan 2, 1967

By J. M. Singer

This study was undertaken to obtain some fundamental information about hazardous mixtures of coal dust and methane (firedamp) likely to occur in mines. Fuel concentration limits for ignition of mixtures of coal dust, methane, and air have been determined by a hot-gas ignition method. The limiting concentration of each of the two fuels was usually less than that corresponding to its lean flammability limit in air. The lean limits of flammability of coal dust vary with the type and size of the dust; in this study coal dust concentrations were less than 80 mg/liter. Ignition jets were turbulent pulses (emerging from a channel of 0.5 cm diam) resulting from explosions of stoichiometric mixtures of methane, oxygen, and nitrogen, Temperatures of the ignition jets were varied by changing the oxygen index (OI) = O2/(02 + Nj2) of the primary methane-oxygen-nitrogen mixture (adiabatic flame temperatures from 2,000° to 3,000° K). The objectives of the study were to establish quantitative relations between concentrations of each fuel at ignition limits of hybrid mixtures and to study the mechanism of ignition of these hybrid mixtures by hot turbulent gases, Empirical equations were fitted to concentrations for four coals, namely) Pittsburgh Seam (sizes A, B, and C), Sewell No.2 Seam, pocahontas No.3 Seam, and anthracite. Equivalences of coal dust to methane were computed from these equations; equivalence being defined as -Ac/Am, where c is the coal dust concentration and m is the methane concentration, each in milligrams per liter of air. It was found that the equivalence increases as the temperature of the hot-gas jet decreases. In general, the equivalence is also an inverse function of volatile content of the coal and a direct function of the particle size, However, volatile con-tent in itself is not a sufficient correlating variable, nor is the specific surface area of the coal dust.

Jan 1, 1967

By P. Datta, L. L. Handy

For a wetting phase displacing a nonwetting phase from a porous medium the distribution of the residual fluid may depend on displacement conditions. Although this subject has been debated in the literature, only a few experiments have been cited to support the various conclusions. Experimental results presented in this paper show that fluid distributions are dependent on imbibition pmcedures. Results agree qualitatively with predictions from the pore doublet model. If the rate of water imbibition is restricted, the nonwetting phase is trapped preferentially in .the larger pores as expected. But if the rate of water imbibition is unrestricted, trapping occurs somewhat more in the smaller pores. These conclusions were deduced primarily from relative permeability measurements. INTRODUCTION Relative permeabilities are known to depend on the saturation history of the porous medium. For either continuously increasing or continuously decreasing wetting phase saturations, however, they have normally been assumed to be single-valued functions of saturation. Severat investigators have compared relative permeabilities measured by different methods and have reported acceptable agreement.1-5 Studies of simple models of the displacement process suggest that the distribution of residual fluids can be influenced by the displacement method. If this is so, relative permeabilities also should depend on the method of displacement. These predictions have not been supported by experimental data. The object of this paper is to investigate experimentally some of the predictions of these model studies. The particular question of importance is whether steady-state and unsteady-state methods should be expected to give the same values of relative permeability. Much of the reported data showing agreement between steady-state and unsteady-state methods have been obtained on un consolidated sand. Johnson, Bossler and Naumann, however, compared steady-state and unsteady-state results for Weiler sandstone and found no significant differences.5 Levine made a detailed study of pressure and saturation distributions for a laboratory waterflood in a consolidated system but made no attempt to calculate performance from steady-state relative permeability data Bail and Marsden in a somewhat similar set of experiments did attempt a comparison of observations with predictions but the results were inconclusive.7 Excluding gravity, two forces affect the distribution of wetting and nonwetting phases during an unsteady-state, immiscible displacement: viscous and capillary forces. If relative permeabilities are indeed the same when measured by steady- or unsteady-state methods, the fluid distributions at the same fluid saturations must be similar for both methods. Furthermore, the implication is that the relation between capillary and viscous forces is the same for both methods insofar as the effect on microscopic fluid distributions is concerned. Unsteady-state displacements are normally run at high rates to maximize the ratio of the viscous to capillary forces. The objective is to reduce the effect of capillary forces on macroscopic fluid distributions. For floods in which the phase which wets the porous medium displaces the nonwetting phase, capillary forces compete with viscous forces in determining fluid distributions.8 The residual nonwetting phase is discontinuous. Competitive aspects of viscous and capillary forces and the resulting effect on water-oil distribution in porous media have been illustrated in an elementary way using a pore doublet model. This model and predictions from it have been discussed at considerable length by Rose and Witherspoon, Rose and Cleary and by Moore and Slobod.9-13 Rose and Witherspoon show that so long as water invades the model at a rate equal to or greater than the free imbibition rate, the water will move through the larger capillary of a doublet first and trap oil in the smaller capillary. On the other hand, if a negative pressure is applied to the water

Jan 1, 1967

By F. X. Tartaron

Behavior of hard-burned quicklime was compared with that of soft-burned quicklime in an oxygen converter utilizing oxygen blowing in a rotating cylindrical vessel, set at a 30° to 60° angle to the horizontal and operated at a predetermined speed of rotation. Four pairs of tests were made) each comparing hard lime with soft lime. Three of the pairs differed from one another in the quantity of lime employed) and the fourth differed in blowing time, All four pairs showed an increase in yield when soft lime was used. Three of the pairs revealed that the ratio of the oxygen consumed with soft lime to the oxygen consumed with hard lime was the same as the ratio of metal yield with soft lime to the metal yield with hard lime. The fourth pair contained an error and could not be included. Finally, a close inverse relation was found between the combined iron in the slag and the combined lime in the slag, which can be expressed by the equation pct Fe = 52.67 -0,906 (pct CaO).

Jan 1, 1967

By Jack L. Henry

The monocarbide region of the ternary system U-C-O has been investigated at 1,700° C as the first phase of a more extensive study of a portion of the four-component system U-C-O-N. An area bounded by the following compositional limits in atomic percent was studied: U, 44 to 55; C, 30 to 60; 0, 0.2 to 20. Compacts composed of mixtures of uranium, graphite, and uranium dioxide powders were sintered at 1,700° C under an equilibrium pressure of carbon monoxide to produce uranium oxycarbide specimens having a variety of compositions. Sintered specimens were evaluated by X-ray, chemical analysis, and ceramographic techniques. Solid-solution boundaries and phase relations have been established, and the effects of composition on the lattice parameter as well as the decomposition pressure have been investigated. Oxygen can be substituted for carbon in stoichiometric uranium monocarbide to the extent of about 17 atomic percent at 1,700° C. The composition range of the oxycarbide solid solution extends from about 48 to 51 atomic percent uranium in the low oxygen region. Above 10 atomic percent oxygen the composition range narrows to less than 1 atomic percent uranium. Carbon monoxide exists as a gaseous phase in equilibrium with all compositions which contain oxygen. Five separate phase fields were found bounding the solid-solution area. Other phases within this portion of the system include uranium, uranium dioxide, uranium dicarbide, and uranium sesquicarbide. Decomposition pressures of oxycarbide compositions at 1,700° C have been found to vary from a few microns for stoichiometric and uranium-rich compositions to 35 torr for carbon-oxygen-rich specimens. Lattice parameters were found to depend upon the U to C + 0 ratio as well upon the extent of substitution of oxygen into the stoichiometric monocarbide lattice.

Jan 1, 1967

By R. B. Gordon, D. A. Koss

Ultrasonic-atlenuation changes due to the formation of free dislocations have been observed during tensile tests of magnesium and LiF single crystals and samples of polycrystalline Results on the LiF and samples are similar: A preyield attenzration increase is observed which, however, be-corlzes smaller as the magnitude of the drop in load al yielding increases. This indicates that the yield point observed in these materials is due to dislovation rather than dislocation unpinning and that the initial density ' free dislocations must be low if the yield point is to be sharp,. Tests on the magnesium ere conducted at both 27" and 200C. Magnesium has the unusual property that the yield drop is larger at the higher test temperature and is accomplished by a decrease in attenuation. The latter is due principally to the temprovary pinning of detained dislocations by highly solute atoms. After strain aging., a stress as low as 0.3 bur suffices to unpin dislocations; microstrain measuements of sufficient sensitivity should. reveal plastic flow at stress levels this low IN another paper,' we describe the technique of simultaneously observing ultrasonic-attenuation changes and plastic microstrain during deformation of spher-oidized carbon steels. Changes of ultrasonic attenuation indicate damping effects caused by the oscillation of long, freely moving dislocation segments. Simultaneous microstrain measurements are used to indicate total dislocation motion. The dislocation-damping observations are most useful in the study of the early stages of deformation where the dislocation density is low and the plastic strain is small and relatively difficult to measure. Particularly interesting results are found in materials which display sharp yield points. Observations of these phenomena are reported here for three materials: single-crystal LiF and magnesium, and poly crystalline molybdenum. EXPERIMENTS Dislocation-damping effects were observed by measuring changes in acoustic attenuation with the ultrasonic-pulse method. The end faces of each of the specimens were ground flat and parallel and a quartz 10 Mc per sec, x-cut transducer was attached to one face. The bonding agents used were: a) "Nonaq" stopcock grease with magnesium, b) beeswax with LiF, and c) salol with molybdenum. With the LiF, the best acoustic signals were obtained at 45 and 50 Mc per sec; all other measurements reported are at 10 MC per sec. The Sperry Ultrasonic Attenuation Comparator2 was used to measure attenuation changes. In the

Jan 1, 1967

By Thomas C. Wilder

The concentration and activity of oxygen in liquid copper has been measured by the reversible galvanic cell: at 1100°and 1200°C for the concentration range of oxygen of 3 to 5600 ppm Measurements for approximately thirly alloys at each temperature indicate that the activity of oxygen roughly follows Henry's law, the activity coefficients of oxygen being 0.12 and 0.205 at 1100° and 1200°C, respectively. These results compare javorably with the results of seven other electrochemical and gaseous equilibrium studies on this system, the free energy of the solution reaction 1/2 O2 = O (7 at. pct in Cu, liq) being -18.10 * 0.30 kcal per gfw at 1200°C. Estimates of the standard molar free energy of formation of CupO(S) are also made. Praclicul consideration of this cell as an oxygen sensor for liquid metals is discussed briefly. SOLID mixed-oxide electrolytes which have a defect structure in the anion sublattice have recently become a very popular means by which the chemical potential of oxygen is measured at high temperatures. Since the pioneering work of Kiukkola and Wagner1 such electrolytes have been used in numerous cell studies for determining the thermodynamic properties of metallic oxides and oxy compounds, the partial pressure of oxygen in vacuum systems and other atmospheres, and the properties of oxygen dissolved in metals and alloys. The use of a solid electrolyte in a cell for a fast reliable method of oxygen determination in liquid metals would be a very important tool to the process metallurgist. In copper, for example, the oxygen content of the molten metal in the cathode furnace is a prime factor in determining the "set" or solidification profile of cast wire bars. In this investigation the activity of oxygen in liquid copper was measured by an electrochemical cell employing the electrolyte ZrO2 + 7 1/2 wt pct CaO. The cell used at 1100° and 1200°C was

Jan 1, 1967

By Leroy Dockter

The grinding characteristics of lignite in a ball mill were investigated. The variables studied were initial lignite moisture content, degree of in-the-mill drying, and lignite source. The mill tested was a pilot-p1ant-size conical ball mill which had a maximum output of from 80 to 180 lb/hr pulverized product depending on the lignite and test conditions. The capacity of the test mill ranged from 82 to 103 lb/hr depending upon mine source, in pulverization of as-mined lignite with minimum drying, The capabilities of the ball mill could not be correlated to Hardgrove index of the individual lignites or other observed physical properties. Predrying lignite from its 35 to 40 percent raw moisture content to about 10 percent moisture before grinding improved the mill capacity 87 percent, compared to an increase in capacity of 74 percent with in-the-mi11 drying to the same product moisture.

Jan 1, 1967

By Elton L. Litchfield

The Bureau of Mines determined minimum energies for direct initiation of expanding gaseous detonation waves in acetylene-oxygen mixtures. Composition limit ranges for the initiation of detonation with fixed energies have been compared to data in the literature. Assuming that the stored electrical energy is completely converted to thermal energy, the agreement between the energy of primary explosive initiators and the energy of electrical discharge initiators was good. Minimum energies for initiation of detonation in the most sensitive composition (40 percent C20 plus 60 percent 0 2) were: 0.64 joule at an initial pressure of 1/4 atmosphere, 5.0X10-2 joule at 1/2 atmos¬phere, and 3.7X10-3 joule at I atmosphere. Fuel concentrations in mixtures initiated to detonation by 4.9X102 joules ranged from 10 to 65 percent C2H2 at 1/4 atmosphere, 10 to 67 percent C2H2 at 1/2 atmosphere, and 9 to 68 percent C2H2 at 1 atmosphere.

Jan 1, 1967

By W. B. Hickman, J. J. Pickell, B. F. Swanson

Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquiri interfacial tcnsion and liquid-solid wetting conditions. The cnpillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent sur/acc conditions. Invcstigntiot2s indicate that residual non-wetting-phase saturations /ollozuir,g the imbibition process (i.e.,wetting phase displacing nor2-wctting phase) are dependent upon both pore structure and initial non-raetting phase saturation and suggest that residual fluid is distributed as Discontinuous ,globules, one to a few pore sizes in dimension, thrnugh the entire range 01 pore sizes originally occupied. It clppears that air-mercury capillary pressure dala adequntely rellect the distribution of fluiris in a water-oil system when strong wetting condition preliczil. An oil-air counter-current imbibition technique has also been found to provide a rapid rneans of obtaining residual-initial saturation data. In a majority of cnses, rcsidual saturations detf-rniinecl from the oil-air or air-mercury process reasonably approximate residual oil saturation following water drive of a strongly water-wet medium. INTRODUCTION A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measureqents of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in tile distribution of fluids and that viscous forces in the range normallv of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures.found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are decribed. Although air-nercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, hentane, octane or toluene is the wetting phase. INTERFACIAL TENSION AND CAPILLARY PRESSURE Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighbouring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions ml A 2 and are numerically equal.

Jan 1, 1967