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By J. C. Detweiler

THE Jacksonville plant of Humphreys Gold Corp., operating under leases from National Lead Co. and Rutile Mining Co. of Florida, recovers rutile, ilmenite, zircon, and monazite from an ancient beach deposit containing about 2.5 pct of these minerals in combination. The location of the plant is unique, being situated about ten miles from the center of Jacksonville, Fla., surrounded by a thriving suburb. Two four-lane highways pass within 1 ½ miles of the plant. An expressway now under construction will pass over the tailing pile, within 500 ft of the mine office. The elevation at the plant site is approximately 50 ft above sea level. This is one of two mines producing titanium minerals and zircon in Florida. Another mine is also operated by Humphreys at Starke, about 50 miles southeast of Jacksonville. The Jacksonville deposit extends about six miles in a north-south direction, averaging approximately one half mile wide and twenty ft thick. Values begin at the surface over most of its length and ter-

Jan 1, 1952

By Douglas D. Donald

The New Jersey Zinc Co. successfully holed through a 2 1/2-mile haulage tunnel connecting its new Ivanhoe shaft with the Van Mater Shaft at Austinville, Va. This 8x 10-ft cross-section tunnel was driven from both ends and met at a point approximately a mile from one shaft and a mile and a half from the other. In order to make certain that the faces met accurately on line and grade it was necessary to refine conventional mine surveying practices. The mines that are serviced by these shafts are located in the southwestern part of Virginia approximately midway between Roanoke and Bristol at the west foot of the Blue Ridge. While the presence of lead-zinc sulfide ores has been known in this area for more than 200 years, it was in 1902 that New Jersey Zinc Co. acquired the Austinville property, which has been in constant operation since that time. About ten years ago the company undertook an extensive diamond drilling program at Ivanhoe several miles to the southwest. This program was successful in locating sufficient ore to justify the purchase of a number of the properties in this area and plans were made to develop the new orebodies. The discovery of this ore as well as substantial addi- tional reserves at Austinville resulted in a decision by the company to increase its daily milling capacity to 3000 tons, of which about 1000 tons would be supplied from the Ivanhoe mine. After careful consideration of all possible methods of transporting this volume of ore from Ivanhoe to the mill, it became evident that diesel locomotive haulage through a 2½-mile tunnel between the two mines would best suit prevailing conditions. Since the lowest operating level, known as the 1100 level, of each mine would be at approximately the same elevation, it was obvious that such a tunnel should be driven on this level. Not only would this tunnel facilitate feeding Ivanhoe ore into the underground crusher and skip loading installation at Austinville, but it would also open up a known orebody 5000 ft southwest of the Van Mater shaft. In addition it would provide a valuable diamond drilling base from which a large and a potentially favorable but untested block of ground might be explored. In order to hasten the completion of the tunnel, it was felt that it should be driven from both ends. ENGINEERING CONTROL PROCEDURES It was vital that the tunnel junction be made accurately on line and grade; thus it was felt that engineering control of an unusually high degree of reliability was required to prevent an accumulation

Jan 1, 1959

By H. E. Wheeler

The work described was carried out during 1917 and 1918 at the testing laboratory of Watertown Arsenal at the instigation of the Nitrate Division and later with the concurrence of the Cannon Section of the Ordnance Department, U. 8. A. The experiments follow three principal lines of work: First, the effect of nitrogen under pressure on steel containers of various compositions at a red heat; second, the effect of decomposing ammonia on various alloy steels, iron, and non-ferrous alloys; third, a new theory of the erosion of guns in respect to the effect of nitrogen in steel. Part I In the Haber process for the manufacture of ammonia from its elcnlents, it is necessary to have nitrogen and hydrogen of 1500 lb. per sq. in. (105.5 kg. per sq. cm.) at a temperature of 500 to 600' C. The steel containers for these gases gave trouble by failing without apparent cause. When the General Chemical Co. began to develop its method for the production of ammonia, it experienced the same difficulty and, knowing that the Haber process had solved the difficulty by the use of alloy steels, it made several small steel bottles of different compositions and kept them filled with these gases at this pressure and temperature until they failed. The time of service varied from a few days, for the plain steel casting, to two years for a chrome-vanadium forging. Four of these steel bottles were sent to this laboratory for investigation; they were a plain carbon-steel forging, a nickel-stee1 forging, a chrome-vanadium steel forging, and a chrome-steel forging. The time of service was as follows: plain carbon steel, 4 mo.; nickel steel, 6 mo.; chrome-vanadium steel, over 2 yr.; chrome steel, 4 mo. When these containers were cut open and the cross-section surface polished, they showed an inside zone with a different luster from the rest of the metal. Upon etching, this zone was almost unaffected while the rest of the steel etched normally.

Jan 1, 1922

By H. E. Wheeler

The work described was carried out during 1917 and 1918 at the testing laboratory of Watertown Arsenal at the instigation of the Nitrate Division and later with the concurrence of the Cannon Section of the Ordnance Department, U. 8. A. The experiments follow three principal lines of work: First, the effect of nitrogen under pressure on steel containers of various compositions at a red heat; second, the effect of decomposing ammonia on various alloy steels, iron, and non-ferrous alloys; third, a new theory of the erosion of guns in respect to the effect of nitrogen in steel. Part I In the Haber process for the manufacture of ammonia from its elcnlents, it is necessary to have nitrogen and hydrogen of 1500 lb. per sq. in. (105.5 kg. per sq. cm.) at a temperature of 500 to 600' C. The steel containers for these gases gave trouble by failing without apparent cause. When the General Chemical Co. began to develop its method for the production of ammonia, it experienced the same difficulty and, knowing that the Haber process had solved the difficulty by the use of alloy steels, it made several small steel bottles of different compositions and kept them filled with these gases at this pressure and temperature until they failed. The time of service varied from a few days, for the plain steel casting, to two years for a chrome-vanadium forging. Four of these steel bottles were sent to this laboratory for investigation; they were a plain carbon-steel forging, a nickel-stee1 forging, a chrome-vanadium steel forging, and a chrome-steel forging. The time of service was as follows: plain carbon steel, 4 mo.; nickel steel, 6 mo.; chrome-vanadium steel, over 2 yr.; chrome steel, 4 mo. When these containers were cut open and the cross-section surface polished, they showed an inside zone with a different luster from the rest of the metal. Upon etching, this zone was almost unaffected while the rest of the steel etched normally.

Jan 1, 1922

[Chairman ZAY JEFFRIES, Vice-chairman S. SKOWRONSKI, Chairman WILLIAM M, CORSE, Secretary Executive Committee J. R. FREEMAN, JR., Local Section G. E. JOHNSON R. S. ARCHER, Non-ferrous Data Sheets P. D. MERICA EDGAR C. BAIN, Journal Committee L. W. SPRING SAM TOUR, Papers Committee F. L. WOLF H. C. JENNISON, Membership Committee 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, Woon, New York Papers Committee S. SKOWRONSKI, Chairman F. H. DIx, JR.-Aluminum E. R. DARBY-Bronze C. S. WITH ERELL-Copper H. A. BEDWORTH-Brass W. K. FRANK-BRONZE F. W. HARRIS-Copper R. L. SUHL-Nickel H. M. ST. JOHN--Foundry Metallurgy R. S. DEAN-Theoretical Metallurgy]

Jan 1, 1928

By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7' ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01' calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i'rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.' Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water

By C. E. Gerity

Near Bunker, Mo., in the New Lead Belt, Ozark Lead Co. operates a 6000 tpd lead-zinc mine. Mined ore is transported to the surface in three mechanized and automated steps. The mine is developed by a rectangular-shaped sublevel haulage drift 15 ft high by 28 ft wide, driven on strike below the ore zones. Ore transfer raises were driven from the sublevel at locations near the shaft, 1500 ft distant, and on subsequent 1000 ft centers. These 6 x 5-ft raises are slashed to obtain maximum storage below dump points. These dump points are located on each mining level and are of steel and concrete construction. Spiral 12 X 24-ft inclines driven from the sub-level provide access to these levels for equipment and mine utilities.

Jan 11, 1972

By Hugh S. Spence

IN MAY, 1930, G. LaBine and E. C. St. Paul, prospect¬ing round the southeastern shore of Great Bear Lake, in the North West Territories of Canada, discovered pitchblende at what is now LaBine Point. At the same time, they also found native silver in a small sheared break on an island lying off the point. Late in 1930, samples of the pitchblende were sent to the Mines Branch, at Ottawa. The material consisted of several fair-sized slabs of botryoidal pitchblende banded with a brownish quartz. A small amount of chalcopyrite was visible as small particles and fine veinlets, and the pieces were rather heavily stained a yellowish-green by secondary copper-uranium salts. Analyses were run in the Mines Branch Ore Dressing Laboratories on two samples, and small-scale concentration tests were made on one of them. The results of this work were published in a Memorandum Series report (No. 48) of the Mines Branch, in March, 1931.

Jan 1, 1932

Secretary's Note.—M. Beutter's introductory remarks, being simply a resume of Prof. Hone's paper, with a disclaimer of the intention to criticise it, have been omitted, and the remainder of this contribution lias been somewhat condensed, without omitting any essential statements. M. Beutter, St. Etienne, France* (communication to the Secretary†):—Professor Home observes in $ 47 of his paper that the fluid-compression of steel diminishes piping by forcing the liquid and viscous metal, while the pipe is forming, or after it has formed, into the space so produced, and proceeds to study the different systems of compression, alluding to the four principal ones: Whitworth, Illingmorth, Williams, and Harmet. Having now for many years had in use the last-named process, that of M. Henri Harmet, I shall attempt to explain the difference between it and the three other processes named. The Harmet process does not diminish or close the pipe after it has formed, but prevents it from forming; and I may add that it is the only one of the four which produces this result. It is true that the Whitworth process diminishes the interior hollow by localizing it around the central axis of the ingot, which is afterwards removed by trepanning the hollow forg-ings for which this process has been, I believe, always exclusively used. The Illingworth and Williams processes, which, in my opinion, are applicable only to small ingots, of necessity allow the pipe to form, or (to use the expression of Professor Howe) they allow the surface of the lake of liquid steel to sink into the interior of the ingot, since they involve waiting a certain time before compression, so that (in the case of the Williams process) the ingot-mold can be opened without danger, or (in the case of the Illingworth process) so as to avoid the risk that the steel may enter the grooves produced by the removal of the distance-bars. During the time required for

Jan 1, 1908

By E. F. Adkins, R. W. Douglas

The variation of the spectral emissivity of osmium and ruthenium with temperature can be expressed by the following relations: DURING a study of the sintering characteristics of osmium and ruthenium, discrepancies in the previously accepted melting points of the metals were noted. The melting temperatures had not been measured at the time of the work, but were estimated in the literature as 2700°C for osmium and 2450°C for ruthenium.' A recent investigation by Baird2 has shown the melting temperatures of osmium and ruthenium are 3000" and 2250° C, respectively. In the present work, osmium bars sintered at temperatures as high as 2900° C showed no evidence of melting, whereas ruthenium showed definite evidence of melting at temperatures as low as 2250°C. In view of the apparent discrepancies, the melting temperatures of both metals were determined. The spectral emissivities of both metals were determined as an aid to studies of the sintering characteristics of these metals. MATERIALS AND PROCEDURES The materials used in these studies were metal powders supplied by Englehard Industries, Inc., through the courtesy of The International Nickel Co. Analytical data from three laboratories, although not in complete agreement as to the purity of the material or the major impurity elements, indicated that the maximum impurity levels were 0.5 and 1.0 wt pct in osmium and ruthenium, respectively. The metal powders were pressed to 1/4 by 1/4 by 6-in. bars at 20Tsi using carbon tetrachloride as a lubricant. The pressed bars were presintered 1 hr at 1200°C after heating 1 hr at 400°C. The presintered densities of the several bars of the metals ranged from 65 to 80 pct of ideal density. Specimens were self-resistance heated in a vacuum sintering bell. Temperatures were measured with an L&N, disappearing filament optical pyrometer. True temperatures were read at the base of an 0.30-in.-diam, 0.150-in. deep hole drilled into the center of a presintered bar. Apparent temperatures were read from the surface of the bar adjacent to the hole. MELTING POINT DETERMINATION The melting temperature of the metals was determined as the temperature at which a slight additional increase in current through the specimen resulted in a reduced temperature at the base of the hole. The apparent reduction in temperature is a result of the liquid metal filling the hole, thus altering the black-body conditions. The melting points of osmium and ruthenium, based on three deter-

Jan 1, 1962

By D. E. Stephenson. Discussion by R. G. K. Morrison, L. Obert

R. G. K. Morrison (Chairman, Dept. of Mining Engineering and Applied Geophysics, McGill University, Montreal, Que., Canada) - The discing of drill core has been a recognized pressure phenomenon for many years but only recently has an interest been taken in the mechanism involved. The work of Jaeger and Cook is referred to in the text. The authors have now advanced the study to establish, within certain loading limitations, a direct relationship between axial and radial stress at failure. This is an important contribution. In mines generally, where pressure conditions result in the spalling of openings, the faces of drifts and crosscuts, on scaling, usually show a concavity with respect to the opening very similar to the face of the drill hole after the separation of the stub. The same holds for shaft sinks. This suggests a similarity between the mechanism of the discing of core and that of the spalling of an opening, under pressure, to develop a more stable outline. The latter, commonly regarded as shear, is the most conspicuous type of failure observed in

Jan 1, 1967

Organization Place Date 1919 American Chemical Society :.... Philadelphia, Pa. Sept. 2-6 National Assn. of Stationary Engineers Huntington, W. Va. Sept. 8 American Peat Society Minneapolis, Minn. Sept. 22-24 American Iron, Steel Electrical Engineers St. Louis, Mo. Sept. 22-26 American Institute of Min. and Met. Engineers. Chicago, Ill. Sept. 22-27 American Steel Treaters' Society, First Annual Convention Chicago, Ill. Sept. 22-27 National Exposition of Chemical Industries.... Chicago, Ill. Sept. 22-27 National Safety Council Cleveland, 0. Sept. 29-Oct. 2

Jan 7, 1919

Organization Place Date 1919 American Chemical Society Philadelphia, Pa. Sept. 2-6 National Assn. of Stationary Engineers Huntington, W. Va. Sept. 8 American Peat Society Minneapolis, Minn. Sept. 22-24 American Iron, Steel Electrical Engineers St. Louis, Mo. Sept. 22-26 American Institute of Min. and Met. Engineers. Chicago, Ill. Sept. 22-27 American Steel Treaters' Society, First Annual Convention Chicago Ill. Sept. 22-27 National Exposition of Chemical Industries.... Chicago, Ill. Sept. 22-27 National Safety Council Cleveland, O. Sept. 29-Oct. 2

Jan 8, 1919

By J. Spotts McDowell

Ackowledgments........................... 5 Introduction............................. 5 The Silica Minerals. Stability Relations......................... 6 Optical Properties........................ 9 Density.............................. 10 Melting Points....;..................... 10 Thermal Expansion..................,..... 10 Solubilities............................ 12 Identification of Cristobalite and Tridymite.............. 12. The Silica Refractories. Raw Materia1........................... 13 American Deposits....................... 13 Properties Determining Usability................ 15 Expansion on Heating..................... 16 Texture........................... 17 Silica Brick............................ 17 Manufacture........................... 18 Properties of Silica Brick .................... 19 Analysis ......................... 19 Density......................... 19 Porosity......................... 20 Strength....................... 21 Melting Point....................... 22 Specific Heat....................... 22 Thermal Conductivity................... 23 Expansion........................ 24 Effect of Rapid Temperature Change.........:... 26 Constitution......................... 26

Jan 1, 1918

By T. E. Schwarz

The Red Mountain district, in Ouray County, Colorado, has been already referred to in the Transactions of the Institute, and notably in papers by Mr. T. B. Comstock, on " The Geology and VeinStructure of Southwestern Colorado" (Trans., xv., 218), and on " Hot-Spring Formations in Red Mountain District, Colorado—A Reply to the Criticisms of Mr. Emmons" (Trans., xvii., 261), and in the paper of Mr. S. F. Emmons, on " Structural Relations of Ore-Deposits" (Tram., xvi., 804). The district has attracted much attention from those interested in geology, because it seems to present a variety of ore-deposits rarely, if ever, met with elsewhere, and one which cannot be described by such well-understood terms as fissure-veins, bedded-deposits, or contact-formation. It will be the scope of this paper to note briefly, from the writer's experience in developing the Yankee Girl, Guston and other Red Mountain properties,—first, observed facts as to the ore occurrence and formation, and second, certain unsolved geological questions. The Red Mountain district proper occupies the headwaters of Red creek, from Iron ton to the Divide, a distance of 5 miles. Its leading properties occur on the west slope of Red Mountain. The mode

Jan 1, 1890

By H. B. Charmbury, D. R. Mitchell

Everyone in the coal industry from top management to the preparation engineer is vitally interterested in recovering as much salable coal as possible from the run-of-mine product. Coal losses from a preparation plant occur in the solid refuse material being discharged from the plant and in the bleed-off slurry from the water circuit. The refuse is generally hauled from the plant in solid form by trucks, conveyors, or aerial trams to the refuse or culm banks or it may be crushed and transported by hydraulic methods to refuse ponds or dams. The loss of coal in refuse material and the extent of this problem has been covered in another paper. The loss of salable coal in the plant bleed-off slurry is one of the water circuit problems in coal preparation plants. Slurries originate at various places in the processing circuits and are usually disposed of by transportation to waste ponds known as slurry ponds. Even though the combustible material discharged as slurry and refuse from the plant is labeled a loss, the loss must only be considered temporary. There is a tendency at the present time to examine refuse and slurry losses and to reprocess these materials to recover valuable coal.

Jan 1, 1960

By Stephen Birch

THE Chitina mining district of Alaska is located at the headwaters of the Chitina and Copper Rivers. At present, the only producing min-ing properties are the mines of the Kennecott Copper Corpn. and the Mother Lode Coalition Co., which are situated 196 miles from Cordova the port of entry. The first claims, later acquired by the Kennecott Mines Co. and afterwards transferred to the Kennecott Copper Corpn., were discovered in 1900. The Copper River & Northwestern Ry., which connects the mines with tide water at Cordova, was completed in the spring of 1911. Contemporary with the construction of the railroad, aerial tram equipment was brought to the mines by pack train and a tramway, 3 miles, long, connecting Bonanza mine with the proposed railroad terminal, was finished, enabling shipments of high-grade ore to be made immediately on the completion of the railroad. A mill to treat the lower grade ore was begun the same year. The Kennecott company's holdings consist of 111 mineral claims. The Mother Lode Coalition Mines Co., which is controlled by the Kennecott Copper Corpn., owns 73 claims adjoining the Kennecott holdings. All data on operations and geology refer equally well to the Mother Lode property.

Jan 1, 1924

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

Industrial minerals enjoyed a fairly successful year in 1978, despite the sluggish economy, inflation, and environmental restrictions. A glance at US Bureau of Mines statistics shows that, in general, production of industrial minerals increased from + 1% (salt) to as much as 26% (sulfur, other than Frasch or recovered). A few industrial minerals showed a decline; fluorspar production, for example, registered a 23% decrease in 1978 from 1977 due to the closing of three domestic mines. Bromine, natural sodium sulfate, Frasch sulfur, and vermiculite also had production decreases of 2-6% in 1978.

Jan 5, 1979

By J. H. Swisher

An experimental study has been made of the possible mechanisms for foam stability in the system CaO-SiO2-Cr2O3, where Cr2O3is the foaming agent. The degree of lowering of surface tension by Cr2O3 was determined at 1600 "C for high -silica melts. Measurements were also made of foam stability under standardized conditions. The results of the two sets of measurements then were correlated by applying the Gibbs and Marangoni theories of film elasticity. It was demonstrated that the Marangoni elasticity effect is probably the largest single contributor to foam stability, although the high uiscosity of' silicate melts makes some contribution in controlling the rate of drainage of liquid from bubble lamellae. ThE tendency of metallurgical slags to foam has frequently been observed during steel-refining operations. In the open-hearth furnace,this tendency is considered undesirable because it slows down the rate of heat transfer from the burners to the molten-metal bath. On the other hand, it is sometimes desirable to have a "foamy" slag in the basic oxygen converter.' A more effective blanket over the steel bath is made by a "foamy" slag, and loss in yield of metal due to splashing is minimized. In addition, a flush slag can be removed more easily in this condition. Since slag-foaming problems in the field have been attacked largely on an empirical basis, it appeared desirable to obtain a better basic understanding of the mechanism of foam stability. The experimental work was directed almost entirely toward the behavior of Cr2O3 as the foaming agent in CaO-SiO,-Cr2O3 melts. In the first stage of the investigation, the degree of lowering of surface tension by Cr2O3 was determined at 1600°C. The second stage consisted of measuring foam stabilities under standardized conditions. The two sets of experimental results then were correlated by applying various theories of foam stability. For convenience in interpreting the surface-tension and foam-stability results reported here, a portion of the CaO-SiO2-Cr2O3 phase diagram2 is reproduced in Fig. 1. EXPERIMENTAL 1) Surface-Tension Measurements. Very little information is available in the literature on the lowering of surface tension of slags by foaming agents. Kozakevitch 3 mentioned that the addition of 1.5 pct Cr2O3 lowered the surface tension of FeO slightly. In another system, some data on the lowering of surface tension of foaming slags by P2O5 were reported by Cooper and Kitchener.4 The technique used for the surface-tension measurements was the maximum bubble-pressure method,' using a single tube immersed to various depths in the melt. This method has been used extensively in high-temperature systems, such as in liquid metals, slags, and glasses.6,7 It has the advantage that the contact angle between the liquid and the tube material need not be known. The equation used for calculating surface-tension values from maximum bubble-pressure measurements is the Schroedinger equatioq5 which can be written as follows:

Jan 1, 1964