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By S. H. Ash

More than 100 minerals are mined and processed in the U. S. Management and labor have negotiated wage-scale agreements that have balanced wages and affected cost of labor in such a manner that comparisons can be made of transportation costs. Transportation of materials underground has become of vital importance. This report describes underground haulage methods and equipment, presents cost analyses, and discusses future plans for underground transportation in metal mines. It does not cover hoisting in shafts or slopes by cage, skip, or cars. Advancements have been made by the metal mining industry in lowering transportation costs in several mines, making it possible to mine orebodies or portions of orebodies not considered economically recoverable a few years ago. Numerous reports have been written on transportation at metal mines; this report covers recent haulage at some representative mines throughout the U.S. The term metal mine is used to include all noncoal mines from which up-to-date information was obtainable.

Sep 1, 1956

By H. M. Rutherford

THE reflection method in seismic prospecting has aroused much interest in the past few years. The purpose of the present paper is .to present the method of reflections in the mapping of geologic structure and also to give some indication of its limitations. The reflection method is well adapted to the mapping of geologic structure in the Mid-Continent fields, and has been found most useful there. The refraction method is ideally suited to the finding of structures, such as domes, where the amount of relief is very large. This explains the brilliant success of the refraction method in the Gulf Coastal region of Texas and Louisiana. The additional fact that salt has a much higher velocity than the sur-rounding sediments made their discovery much easier. By the use of the reflection method, differences of relief of 25 to 50 ft. to the mile may be detected at a depth of 5000 ft., and the depth points accurately plotted on a map. This is hardly possible by the use of the refraction method. The reflection method has been in almost continuous use in the Mid-Continent area since 1926, but very little, if anything, has been published until recently(7) ? regarding either the method or the results. The dis-covery of several oil fields is now attributed to the use of the reflec-tion method. Reflection methods have been used by the Germans to find the thick-ness of the ice of several glaciers. (2,8) The depths there considered were of the order of only a few hundred feet. For the method to be of any practical value in this country, it must be able to work to depths of several thousand feet. As was indicated above, this is now possible, though there are many problems connected with the reflection method yet to be solved. The refraction method requires that the shooting be done over long ranges. It was necessary, for example, to take distances out to several miles in order to penetrate some five thousand feet. Naturally this uses a good deal of dynamite. In the reflection method the distances are much shorter and the amounts of dynamite are much smaller, within limits which will be noted below. The chief distinction between refrac-tion and reflection methods is to be found in the analysis of the seismo-gram. Refraction shooting makes use of only the first arrival of energy

Jan 1, 1932

By J. P. Witherow

MR. BIRKINBINE'S description of the bad working and sudden chilling of the Warwick Furnace last summer, seems to me quite phenomenal in blast-furnace practice. During my connection with the management of blast furnaces for many years, in the anthracite, coke, and raw-bituminous coal districts, such a case has never come under my notice. It seems to me that the scaffold in the zone of fusion could not have established itself (so that the whole power of the engines, with a blast pressure ranging from 12 to 18 pounds per square inch, could not penetrate), unless the furnace was previously badly scaffolded and bridged in some of its upper sections, from 15 to 30 feet above the hearth level, either in the zone of chemical action or the beginning of the zone of fusion. Such a "barrier to the upward gaseous currents would cause a suspension of combustion which may have superinducedd the scaffold that is assumed to have existed in the zone of fusion. It is Difficult to conceive' that an agglomerated mass almost across the section of the lower bosh should have formed all at once, if the furnace was free and porous for the reaction of the gaseous currents above. Therefore, I think, the Warwick furnace was by no means in as free, open, and fine internal condition at the time the trouble commenced as the description of its regular working would lead us to suppose. I do not question the accuracy of the statements relative to the output of iron, etc. I merely claim that the phenomena., as described, could not have been almost instantaneously developed, unless there had been an incipient seaffold and lodgment above the zone of fusion. I would state my hypothesis to be that the stock lodged or collected in some of its upper sections during the process of blowing-in, on which, as a basis, more or less accumulations may .have lodged, and thus, indirectly, caused the formation of the suc- * This paper was not presented to the Institute in its present form, but is based on remarks, in discussion, by the author on Mr. Birkinbine's paper on, a Short Blast at the Warwick Furnace, and Mr. Witherbee's paper on Two Scaffolds at the Cedar Point Furnace.

Jan 1, 1881

By M. G. Corson

INFORMATION regarding the use of manganese alloys has hitherto been incomplete and available only from widely scattered sources. This paper attempts a systematic description of properties and uses of alloys other than manganese bronze, manganin and duralumin, which are probably the only non-ferrous alloys associated with manganese in the minds of most metallurgists.1 PROPERTIES OF MANGANESE Manganese can react either acid or basic; it is hard to obtain in the pure state; it has two different crystalline lattice structures, both of the cubic system, one stable above 850° C. and the other below 650° C., both coexisting in the intermediate range. Although the commercial product is hard and brittle, the pure metal seems to be ductile. In fact Zhemchuzhny, in Russia, was able to obtain ductile manganese and draw it to fine wires by the simple expedient of adding about 3 per cent. copper to the alumino-thermic product. Copper most probably brings the silicides, aluminides, nitrides and carbides present in the commercial product into a much less harmful form of distribution. One industrial use that can be foreseen for wrought manganese articles is as anodes for electrolytic processes in sulfate and nitrate solutions, particularly with high voltages. A practically insoluble skin of manganese peroxide is likely to form in such cases and an insoluble and strong anode material will be available. MANGANESE AS A SCAVENGER Because of its activity manganese might become the most efficient scavenger and refiner of copper, were it not for the fact that 0.01 per cent.

Jan 1, 1928

By W. E. Ruder

IT has been pointed out by Stead 1 that grains of considerable coarseness may be developed in steels containing from 3 to 5 per cent. of silicon, and in a previous paper 2 the present author has shown that under the proper conditions of annealing single grains having an area of 50 sq. cm. may be obtained. It is the purpose of this paper to discuss in more detail the conditions, promoting the growth of these grains, in the hope that the experiments described may throw some additional light upon the general problem of grain growth in metals. These silicon steels lend themselves particularly well to such experiments because of the ease with which the change in structure may be followed and because of the fact that the effect of the carbon present is largely obliterated by the high percentage of silicon. This forms a solid solution with the iron, which acts very much like a pure metal. This alloy has been found to have but one critical point, viz., Are. This point, determined by Roberts-Austen for Hadfield's 4 per cent. Si alloy, was found to lie at 703° C. Vigouroux3, in working with pure Fe-Si alloys, finds this point to rise from 750° C. for 0.5 per cent. Si to 860° for 6 per cent alloy, with a flat region in the curve from 3 to 4 per cent. Si. No accurate determination of this point has been undertaken by the present author, but it has been roughly determined to lie between 730° and 750°.

Jan 12, 1913

By Parke A. Dickey

POTENTIAL differences between strata of shale and sandstone have been recognized for about 15 years, and they form the basis of the electrical logging of oil wells. Hitherto these potentials have been ascribed solely to electrochemical reactions caused by the disturbing effects of the water in the drill hole through which they are generally measured. Observations by the author in wells empty of water and in a mine shaft suggest that potential differences between sandstones and shales are natural and specific properties of the rocks, although they are modified to measurement by the disturbing effects of the water in the drill hole. The cause of these potentials probably is to be sought in the relative polar adsorptive capacities of quartz and clay particles.

Jan 1, 1944

By C. H. Green

. RECENTLY two papers on the structure of eutectics were read before the British Institute of Metals, one by F. L. Brady1 and the other by A. Portevin.2 In the preparation of photomicrographs of laboratory specimens as illustrations for student work, and in connection with various researches; the writer has been working along the same line for some, time and, therefore, was much interested in the results given, especially those of Portevin. He has correlated the information on the subject and has outlined a broad scientific basis for future work along this line. It is largely with the idea-of adding something by way of illustration to the work already done that this paper is written. The eutectic is generally understood to mean the alloy having the lowest melting point of any alloy of the system, and in which the melt becomes supersaturated with reference to the two or more phases which, separate out simultaneously (or alternately). From the surface pattern, the eutectic means; a structure with no primary crystals. It is not always easy to get the exact eutectic composition in making any alloy; in fact, a slight range in composition may be expected and some of the coarser particles may be richer in either of the composing metals. Even when chemical analysis shows the right composition, differences in density of the pure metals may cause segregation, or. supercooling resulting from different crystallizing properties may give a surface pattern the appearance of being on one side of the eutectic point. However, the alloys on either side of the eutectic composition, showing primary crystals of one of the phases and the effect of the pro-eutectic form on the surface pattern of the eutectic make a very interesting study, which is slightly touched upon in this paper. The phases, or microconstituents, of a eutectic may be pure metals (Pb-Sb, Tl-Au), solid solutions (Cd-Zn), a pure metal and a solid solution; (Ag-Sn), or a pure metal or solid solution with an intermetallic compound (Sb-Mg, Sb-Cu, As-Cu, Bi-Te, etc.).

Jan 2, 1925

By Jesse Betterton

IN the Parkes process of lead refining, after desilverization has been completed by means of zinc additions, there will remain in the lead from 0.5 to 0.6 per cent zinc. At this stage in the refining practically all impurities are reduced to refined lead specifications except zinc and antimony. All excess of copper and nearly all the arsenic goes out with the silver. Silver remaining should not exceed 0.1 oz. per ton. It thus remains only to remove zinc and antimony to produce refined lead. The older practice was to complete refining by means of oxidation processes in reverberatory furnaces. Essentially this consisted of heating the lead to 1200° to 1300° F. and allowing it to come in contact with a considerable excess of air passing through the furnace, or accom-plish the same result by blowing the lead with steam by means of pipes introduced for that purpose, at the same time allowing air to enter the furnace. Usually some procedure involving alternate oxidation and reduction with fine coal or coke was employed in order to reduce the weight of dross or skim finally removed from the furnace. This practice had many elements of weakness in that the main flow of lead, after the preceding expensive operations had been performed, and the whole refining process nearly completed, was subjected to an operation at a comparatively high temperature, which involved much lead loss if the furnaces were not on bags, and the production of 3 to 5 per cent of the weight of the lead as dross or skim, which had to be resmelted and the lead either refined or produced as antimonial lead. In addition, the operating expense of the process was a considerable item. The, process of dezincing with chlorine was developed as a substitute for the foregoing described oxidation process, and finally resulted in such advantages as nearly equal operating costs, a practical elimination of the lead loss, and the direct production of a very valuable byproduct, zinc chloride, that may be sold as such or retreated for its zinc and chlorine contents, both of which can be reused in the refining processes.

Jan 1, 1933

By James Howard

ON Aug. 25, 1911, a rail failed on the Lehigh Valley Railroad, causing a disastrous wreck. The surface of the fracture was in a plane at right angles to the length of the rail. There was a dark-colored, oval spot on this surface, located on the gage side of the head, representing the part of the rail which was the first to fracture. The nucleus of this spot showed that the fracture had an interior origin. Other fractures of this kind, the peripheries of which had not reached the surface of-the rail, presented surfaces having a silvery luster. The darkened surface of the present fracture was caused, doubtless, by the air having had access to it. This fracture was recognized as a fatigue fracture, of a modified type, its interior origin having been due to a component in the rail which is not usually present in cases of fatigue fractures. The metal next the running surface of the head of the rail was in a state of internal compression, this being the component not commonly met with in other cases, and which caused the fracture to have its interior origin. For the purpose of giving this modified type of fatigue fracture a specific name, for identification, the term "transverse fissure" was applied. No mystery was thought to attach to its formation, or to its development. The explanation of its occurrence was obvious in the light of common knowledge upon the behavior of steel under repeated alternate stresses. By reason of the state of internal compression at the running surface, the maximum tensile stresses in the head, under bending loads, were along an interior element. Here the tensile strains were higher than in the fibers more remote from .the neutral axis. Under such conditions the fracture of the rail would be expected to have an' interior origin. A discussion of the subject of transverse fissures essentially becomes a discussion of fatigue fractures, since they are identical. The descriptive term employed, merely for the identification of this type of fatigue fracture, had the appearance of creating alarm. Apprehensions arose that a new phenomenon in the physical properties of steel had presented itself, the explanation of which was sought in every

Jan 11, 1917

By B. F. Tillson

HAVING been asked to talk about recent devel-opments in mining equipment, I chose the sub-ject of small units of storage-battery locomo-tives which recently have been developed with the idea of motorizing transportation in the mines as far as possible, replacing the manual labor of hand-tramming. Metal mines are probably less advanced in this field than coal mines, where transportation of large ton-nages on any one level is quite common. Of course, metal mines, where large tonnages are handled on any one level, are as advanced as coal mines, and storage-battery locomotives for main haulages are used quite commonly in such metal mines, but the mines having levels at many intervals in the depth of the orebody, or a number of intermediate levels in which a consider-able amount of hand-tramming has to be done, and small metal mines in which the size of the orebody does not seem to warrant the initial capital expenditure for the driving of main haulage levels and installation of rock and ore chutes and raises for the delivery of the broken ore and rock to the cars have been at consider-able disadvantage in replacing manual labor by some mechanical means of transportation. Several years ago the field was canvassed among the manufacturers of electric-locomotive equipment and the conclusion was reached that the art had not been devel-oped to the advantage of metal miners who desire to replace small units of labor by locomotive equipment. The need for such small locomotives is all the more em-phasized by the development in the past few years of mechanical mucking-machines (loading equipment for filling the cars from muck piles on the level). Any me-chanical loader is a liability instead of an asset unless means are also provided for keeping the material away from the loading-machines. Therefore the transporta-tion system must be equal to the capacity of a loading-machine, otherwise the latter is idle such a large per-centage of its time as to prove an unprofitable invest-ment. So there is a need for portable, small haulage units to handle small mine cars in many metal mines, and, naturally, units are desired which can be so readily shifted from level to level as to facilitate their free use. Of course, in mines in which each level comes to the shaft it is not such a difficult problem, but many mines have a great many intermediate levels which must be approached through raises, timber slides or other small openings required to transfer ore and to get timber and other supplies to those levels.

Jan 5, 1927

By Earle J. Klohn

Mining operations have been carried out in British Columbia since the time of the first settlers in the area. The early developments were mainly small volume, high-grade operations, producing small quantities of tailings wastes. In these early days the nearest stream was a logical first choice for tailings disposal. Where streams suitable for accepting the tailings were not available or where streams crossing the International Border could not be used for this purpose, the nearest convenient land site was selected for storing the tailings. Old tailings waste piles exist at many locations in the Province and are readily evident, for example, in the Princeton and Hedley areas. Figs. 1 and 2 are photographs showing the present condition of two of these old tailings dams. [ ]

Jan 1, 1972

By C. W. Washburne

Professor Lane makes an interesting contribution to the study of cholride waters, in saying that calcium chloride waters occur not only in the greenstones of Lake Superior copper mines, but also in the interbedded felsitic conglomerated and…

Jan 1, 1915

The United States Geological Survey recently published Bulletin 690, which contains those papers dealing with zinc and copper. ores at Ophir, Utah; gravel deposits in Arkansas, with special' reference to their possible utilization as a source of hard pebbles for grinding mills; phosphate deposits in the Uinta Mountains, Utah; quicksilver deposits in the Phoenix Mountains, Ariz.; and manganese deposits near Butte and in Madison County, Mont. This bulletin is completely descriptive and contains important illustrations and maps.

Jan 9, 1919

By George Anagnostache

AMONG the petroleum-producing countries of the world, Roumania occupies the fifth place; in Europe, it occupies second place, coming after Russia. The extraction and the use of petroleum in Roumania, may be trace( as far back as 1856, but the production on an industrial scale started in 1896, when the "Steaua Romana," was formed. From that time until the beginning of the war, the petroleum industry had a rapid growth the number of the producing companies increased to 37, and production FIG. 1.-ROUMANIAN OIL AND GAS FIELDS. increased from 81,571 tons, in 1896, to 1,898,545 tons, in 1912, when the greatest production was reached. In 1916, when the Germans invaded Roumania, the oilfields, at the order of the Allies and under British supervision, were destroyed, to pre vent their exploitation by the Central Powers; the wells were blown in the refineries and the storage tanks burnt, and pipelines put out of order This voluntary destruction, which weakened the resistance of the Central Powers, set back the petroleum industry at least one decade. Reconstruction after the war was slow, because of bad transportation conditions the scarcity of drilling and refining material, the insufficiency of. electric power, and the continuous depreciation of the Roumanian money, which made difficult the buying of the necessary materials for reconstruction.

Jan 3, 1925

By Edwin Hopkins

The year of 1924, in Venezuela, has been one of especial interest. The figures for production marketed are not so impressive, but to the well-informed followers of the development, the ease with which this production has been obtained and with which it apparently can be increased at will merits most careful consideration. For several years, the oil world, especially in the financial centers, has been closely following the slow unfolding. of the' Venezuelan developments, which has been, and still is, one of the great pioneering achievements in the history of oil exploitation. Venezuela, from the first days of its recognition by geologists and financiers as a great future source of oil, has been a field for the enterprising vision of the larger capital groups. The laws of the country have been drafted with almost an inspired foresightedness that has favored the exploitation of the resources along constructive lines, which' has eliminated the irrational promotion schemes that accompany many of the oil developments in the United States. Developments have been exclusively in the hands of strong financial groups, who have followed a conservative policy with respect to the dissemination of detailed information concerning the geological findings and detailed production data. Within the last year, however, the rapid expansion of the production phase of the developments has been on such an important scale and has involved such a large and rapidly increasing personnel, that further restraint with respect to information of a general informative' nature can serve no useful purpose. Certainly, from the volume of references to Venezuelan oil affairs, which are now of almost weekly occurrence in the oil trade journals, the public must appreciate the fact that in Venezuela, and in the Maracaibo district in particular, a new oil region of the first magnitude is about to emerge from comparative obscurity and occupy a commanding position on the stage of world oil affairs.

Jan 3, 1925

By H. S. George

A method of illumination that enhances the value of microscopic study of opaque materials, as in metallography. By simulating natural lighting, structures. That possess relief are given a natural appearance. An example is included of the revelation of a hitherto invisible microconstituent. Erroneous interpretation is avoided. For example, etching figures in ferrite, heretofore considered to be pits, are revealed as pyramids, standing in bas-relief. Suggestions on technique are given, for, while the method is obvious, practice and attention to detail are requisite. ON one occasion when it seemed desirable to reveal under the microscope not only the metallic structure of an alloy, but certain small non-metallic inclusions, that are ordinarily obliterated by etching, it was discovered that, by partly eclipsing the illuminating pencil of light rays, the residual light was thrown on the object from one side and the structure was brought out in relief. At the same time, the non-metallic inclusions were retained in clear view. In this first demonstration of lighting obliquely through the objective a card was thrust part way into the light beam between the arc iris, and the light filter; the shadow of the card on the filter served to locate its position. Next several stiff-paper disks of various diameters were mounted on flexible wires some plasticine on the other end of the wires made it easy to adjust and maintain a disk at any desired position in the light beam. To facilitate manipulation, an assortment of disks, was mounted on a wheel, as shown in Fig. 1. The purpose of partly eclipsing the light beam was discussed in an earlier paper.1 There it was pointed out that the usual methods of illuminating opaque objects for microscopic examination lend an, un-natural appearance to, the view, while the new method, which has been termed conical illumination, revels the true relationship of constituents by simulating natural lighting.

Jan 3, 1924

By S. W. Parr

FROM a study of sulfur with reference to its specific combination in coal, published as University of Illinois Bulletin No. 111, 1919, it is now possible to determine the various forms of this constituent with a good degree of accuracy. This fact suggests two questions: (1) Are the same analytic methods applicable to coke? (2) Is there any correlation between the forms of sulfur as it occurs in coal and the residual sulfur found in the finished coke? The answer to the second question might be helpful in answering a still further question as to what chemical route the sulfur travels during the carbonization process. While the special studies along these several lines are by no means complete, a few preliminary statements are herewith presented. They may, at least, prove suggestive of further possibilities from a continuation of research along these lines. There is no reason, chemically, why the analytic methods devised for coal should not apply to coke and a fair amount of experience in connection with such use affords confirmation of this statement. The procedure in the case of coal may be briefly outlined as follows; Combinations of sulfur as sulfate, or sulfides other than FeS2, are readily dissolved without disturbing either the pyrite sulfur or the sulfur that is in organic combination by means of dilute hydrochloric, acid-1 part of concentrated HC1 to 10 parts of water or approximately 3 per cent. acid. Digestion at 60° C. for 24 hr. insures the complete removal of the sulfur thus combined. In freshly mined coal the amount of such sulfur is very small; weathering processes, however, may very materially increase the amount of sulfate present.

Jan 9, 1919

By William P. Blake

The occurrence of the manganiferous variety of wolframite at a new locality in Arizona was announced in the month of May last." It occurs in the granite hills of the Dragoon mountains, in Cochise county, about 6 miles north of Dragoon Summit station, on the Southern Pacific Railway of Arizona. It is found in veins of white quartz, traversing a coarsely crystalline granitic gneiss, and, so far as yet determined, is without association with other metallic minerals in the same veins, except small quantities of scheelite. It is a very pure form of the mineral, and contains but little iron, the base being manganese oxide. The color is brownish-red; it is nearly the same as the color of the mineral originally described by E. Riotte from Mammoth District, Nevada.† Thin films or plates on the broad cleavage-surfaces, and thin cleavage-flakes, seen by transmitted light, are ruby-red, or rather more like the color of red zinc oxide or the mineral known as clintonite. By long-continued weathering the surface becomes less deeply colored, and assumes a bronze-like luster, like the dull oxidized surface of

Jan 1, 1899

By C. V. Millikan

TEMPERATURE measurement in wells is an old practice and geothermal gradients have been of interest to geologists for many years.1,2 Their application to the operation of oil wells is a more recent practice. It has long been recognized that temperature anomalies occur in drilling and producing wells but thermometers that could obtain a satisfactory record of the anomalies were not available.3 The normal geothermal gradient is con-sidered as being about one degree Fahren-heit for each 60 ft. of depth.4 This "nor-mal" gradient varies in different areas, but whatever it may be in an area there is little variation from the surface to as deep as the drill penetrates. The normal gradient is appreciably changed by gas expanding from the reservoir into the borehole or by the movement of fluid through a borehole while drilling, producing, or circulating. It is the resulting anomalies and abnormal gradients from which conditions in wells can be interpreted. Some of the applications of such interpretations are locating the position of oil or gas sands, permeable strata in a reservoir zone, gas-oil contact, source of water, casing leaks, and the top of cement behind casing.

Jan 1, 1940

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally.' Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan,3 show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision; using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by, the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.5 However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: [3fB = 9.20•'./V•Vn- (n-1) • (n+2) /8[1]] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts' as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of, a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsymmetric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat I than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system, of one degree of freedom can be applied: [1E/m[2] fP = 27] Here f, is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: [t~ = 2/f = 7r\/m/E[3]] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson' 1831) [aP = 4 D2.pL•g•h +7rD•y sin a[4]] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, pL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of-the liquid in cm, y the surface tension in dynes per cm and a the supporting angle' or the one required to insure equilibrium, a being smaller than the contact angle ?. Although demonstrated by Poisson, it has not

Jan 1, 1952