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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 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 Anderson, Burton E.

FOR several centuries diamond mining has been an adventurous, profitable and enticing industry in Brazil. Some of the world's most valuable diamonds have been found in this country. Two of the most famous stones are the "Estrella do Sul" (Southern Star), weighing 2541/ karats, and the "Branganca," weighing 1680 karats in the rough and 367 karats cut. For a great number of years the stones extracted and sold were mostly the white diamonds used for jewelry. Within the last thirty years black diamonds have been developed as an abrasive cutting material and in these black diamonds the State of Bahia, Brazil, has a monopoly of the world supply. Carbons, as they are commonly called, are being used for core-drilling, polishing, cutting, wire-drawing, and vari-ous other applications in which such a hard substance is required. Bernard Bandler & Sons, of New York City, have selected, graded and delivered these carbons to the United States markets.

Jan 1, 1932

By Joseph W. Leonard

The purpose of this paper is to review and discuss some of the less evident and sometimes neglected opportunities for progressive developments in coal research. While a great deal of both promotional and technical information flows from some areas of coal research, output deficiencies in other areas of activity have reached a magnitude where important developments have been, and will increasingly be, unfavorably affected. These areas mainly involve coal mining and preparation. Some recommendations for the intensification of effort in these areas follow: Coal Mining While a huge tonnage of in-the-ground coal is assured, the location and distribution of these tonnages are becoming less favorable. The easy-to-mine coal which is located in or near population centers has been, or is being, mined. The vigor with which the less accessible reserves are recovered by the mining industry depends largely on the condition of the coal market at the time of mining. Hence, during a buyer's market, the commercially oriented mining industry is compelled to mine the easier and less costly reserves. Conversely, during a seller's market, the need to rapidly expand production results in more difficult mining and higher cost coal as few obstacles are encountered in finding markets. Hence, a seller's market tends to enhance the recovery of reserves while a buyer's market does not. One reason for today's fuel supply problems is that the Nation has recently emerged from a long-term coal buyer's market which lasted from about 1950 to 1968. During that period, national policy caused severe production cutbacks which regretably drove the industry to mining only the more accessible and better quality reserves. Often in order to remain in business, many hundreds of millions of tons of more difficult to mine reserves were abandoned and lost behind caved areas. Many of these reserves are close to population areas and would not have been lost in a more stable economic climate. It is difficult to fully account for all the impacts that were caused by the great buyer's market of the 1950s and 1960s. Besides the obvious loss of reserves that were once considered national wealth, the mining of better reserves tended to produce a generation of technically optimistic mining people. Mining people frequently became accustomed to looking at nothing less than outstanding mining conditions as a result of the declining market. Many are now and have long since received a re-education in the other half of mining. Going from many years of mining accessible, select and easy-to-win reserves, to the crash-driving of development entries in reserves that were considered unworthy of mining during 50s and 60s, frequently results in a much higher rate of encounter with in-seam and out-of-seam rock as well as with coal-deficient areas or "washouts." Intensive entry driving activity and compulsory non-selective mining in sometimes lean reserves were brought on by the need to rapidly open up new supplies of coal. Working under these requirements presents a continuing reminder that much more needs to be known about the relatively esoteric art of planning the best direction for driving entries in order to insure that a more consistent and greater supply of coal is available during early mine development. All of the preceding discussion tends to point to a need for a better estimate of those reserves of coal that are likely to be mined in the future. Such estimates should not be limited to the compilation of the amount of coal in the ground; but, where possible, should also include information concerning the capability for producing this coal. After all, a coal seam of ample thickness may have a degree of thickness variability, undulation, bad roof or floor, so as to make what would otherwise appear to be an attractive mining condition untenable. Underlying the problem involving the feasibility of producing known reserves is the need to develop better methods for the characterization of coal seams and associated lithotypes, based on drill core data, once at area is selected for mining. Reserves and their characterization involve aspects of exploration technology that are frequently considered mature. The resulting technological deficiencies may be the main reason why coal exploration frequently does not end with core drilling of a property, as it should, but extends into the mining operation during the driving of development entries. When exploration is extended to the driving of development entries, the near absence of integrated decision-making theory involving mining, geology, mathematics, and economics becomes, once again, all too painfully apparent and frequently results in very costly rationalizations. Hence, by the formal initiation of a concentrated program to combine the cyclical effects of economics with geology and mining, more relevant estimates of reserve distribution, tonnages, and production capability should be forthcoming. Moreover, a similar formal effort is needed to develop a combination of the most advanced concepts of mathematics, geology, and mining to better "see" coal seams as a means to favorably implement many long-range decisions involving mine safety and productivity. Much more applied research needs to be done on coal mining systems for mining in thin seams and/or under bad roof. Current difficulties in both of these areas at recently opened coal mines should provide a sobering glimpse into the future. Full-scale applied research, sponsored by appropriate federal agencies, is urgently needed on a scheme involving a new combination of established mining and preparation elements. The scheme may include: (1) a continuous mining machine remotely operated by a miner stationed at some distance behind the machine using a cord attached control box; (2) hydraulic transport of coal through pipes from the mining machine to a coarse refuse removal grid, crusher, and then on to portable concentrating equipment; (3) the hydraulic transport of clean coal out of the mine in pipes to the surface for thermal dewatering, if neces-

Jan 1, 1974

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 Hans Lundberq

WHEN geophysical methods were first employed in the search for ore deposits and oil accumulations, it was hoped that they would provide a direct means of locating such concentrations. Magnetized needles were used long ago in prospecting for magnetic iron ore, and soon after the discovery of galvanism in about 1790 attempts were made to find concentrations of valuable minerals electrically. Evidence indicating that the early geophyeical instruments were regarded merely as improved divining or dowsing rods is to be seen in the names "mineral finders," "ore finders," etc., that were applied to them. Today, appellations of this kind raise serious doubts in informed minds as to the intelligence and integrity of individuals advocating the use of such euphemistically named methods or instruments, for experience and research have shown that, geophysical, it is never a question of directly locating a given mineral but merely of delimiting its possible occurrence.

Jan 1, 1939

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 Frank Gilbreth

THE problem, of the crippled soldier in industry is not a problem of war work only; it is a problem of industrial development. As individuals, each one of you is seeking to provide our maimed heroes with such teaching as will render them, in the shortest possible amount of time, productive and satisfied members of the community. As individuals you are interested in the organizations that are preparing to receive these men, to train them and to place them at that work for which they are best fitted. As an organization, it is now your duty to take up the industrial end of the problem, to investigate existing conditions in the industries, to discover where the opportunities for employment lie, and so readjust industrial practice that the cripples may be utilized to their own and the community's good with the least shock to themselves or to the industries, and with the greatest amount of permanent benefit to all concerned. We have divided industrial opportunities suitable for cripples roughly, into three classes. First, such as already exist in the industries, which can be set aside for cripples only, present occupants being transferred to other work for which they can be fitted but which is not suitable for cripple work; second, opportunities in the industrial world that, through changes in the working equipment or tools, or through appliances attached to the cripple himself, can make the cripple a competitor of the sound worker; third, opportunities not existing at present in the industries, but which could be introduced for the good of the community, without placing the cripples into competition with any existing class of workers.

Jan 4, 1918

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 J. B. Mudd

Introduction It is difficult to think of any activity on which mankind has been more dependent than mining, and certainly there is much evidence in almost every part of the world of old workings that clearly demonstrate that man from earliest times has dug and toiled to take from the earth precious stones, metals and materials that from time to time have been essential or of value to him. In step with social development and industrial and technological advances the tempo of mining activity, regulated only by the laws of supply and demand, has quickened and in this century has accelerated rapidly in keeping with its dramatic development. Indeed, the rate of change of events has been such that if it were to continue to accelerate as fast as it has over the past decade there is reason to wonder how the insatiable demands for metals and minerals are to be met in the years that lie ahead. Shallow mines containing high-grade ore deposits either have been or are being rapidly mined out and their place can only be taken in general by ore lying at greater depth, or by ore of low grade, situated for the most part in remote and in underdeveloped areas. The cost of exploration and development is rising at an alarming rate, with the result that the expenditure now required to bring a mine to production far exceeds anything previously contemplated. It is estimated that the total capital required to maintain existing operations and develop new ones during the next 5 years will be of the order of $50,000 million and of this, new capital to bring new mines to production will be of the order of $3,000 million. Today no single mining finance company can, from its own resources, find all the money for a major mining development, and as a consequence there has been a strong trend toward joint ventures and to the formation of multinational consortiums. International lending institutions already play an important part in financing many new mining projects and their participation provides the financial umbrella under which other lenders can invest with greater security. There is little doubt that to finance the costly ventures in the future, governments and international lending agencies, banks and finance

Jan 1, 1971

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 FORTUNATO PEREIRA

(San Francisco Meeting, October, 1911.) I. GENERAL DESCRIPTION. The Department of Narino (formerly included in the Department of Cauca) is a narrow band about 170 km. (100 miles) wide in the southern part of the Republic of Colombia, FIG. 1.-SKETCH-MAP OF THE SOUTHWESTERN PART OF COLOMBIA. near the boundary of Ecuador, as shown in the sketch-map, Fig. 1. Its capital is Pasto, a small city of 25,000 inhabitants; the principal towns are Túquerres, Cumbal, Ypiales, Barbacoas, and Tumaco. The port on the Pacific ocean is Tumaco, and traffic in the interior is carried partly on the Patia river (steam navigation to the fluvial port of Barbacoas), and afterwards overland over poor roads by human bearers or on mule-back.

Aug 1, 1912

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 AIME AIME

A STUDY of subsidence and ground movement in the copper and iron mines of the upper peninsula of Michigan has been made by W. R. Crane of the United States Bureau of Mines and published as Bulletin 295 of 66 pages and 49 illustrations. As a result of subsidence, the country adjacent to the mines and over- lying the mine workings in this district is often broken to such an extent as to affect its value; mine shafts and development openings are occasionally so damaged as to be rendered useless, and water can enter the workings through fractures and cave-ins. The problem is more serious in the iron-mining districts, where villages and towns not owned by the operating companies have grown up around mining operations.

Jan 1, 1929

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