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By F. S. Crawford

IRON and copper are mined in the Lake Superior district. The iron mines of the district have the best safety record for that industry in the country as a whole, while the copper mines of the district rank second in two of the four years recorded (Table 1). In Utah copper comes mainly from open-pit mines, which enables that state to lead easily in safety. All of the Michigan production comes from deep underground workings. About 60 per cent of the iron miners in St. Louis County, Minnesota, are employed at open-pit mines; this favorably affects the combined open-pit and underground accident-frequency rate, as this county provides most of the Minnesota-mined iron ore. In Michigan, however, there are few open-pit mines, the bulk of the production coming from underground mines, while all of the Wisconsin production, just across the state line from Michigan, is from underground mines. In spite of the fact that fewer mines in Michigan use the safer open-pit method, the iron-mining industry of that state maintained a consistently low record from 1931 to 1934; however, it was many points behind its nearest competitor, Minnesota, with its much greater production from open-pit mines.

Jan 1, 1939

By K. S. Milliken

NORMAN W. Lord&apos; has shown that the resultant impurity distribution after n zone passes is given by in the ingot section OSa<N—n, where a is the displacement in zone lengths, N is the ingot length in zone lengths, C,, is the initial uniform impurity concentration, k is the segregation constant = Ceoll C,,,,,,,, at equilibrium, and The foregoing expression is formidable in respect to computational labor. However, the triple sum can be reduced as follows is better if computing for only a single value of n. For k<l, it can be shown that this last equation is equivalent to The infinite series is useful only when k is small enough to force rapid convergence. In such cases, the absence of subtraction from unity has the definite advantage of preserving accuracy. Acknowledgments It is a pleasure to acknowledge stimulating correspondence with Dr. Howard Reiss of Bell Telephone Laboratories Inc. This note is published by permis-sion of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By Robert F. Mehl

PROGRESS in the general field of nonferrous physical metallurgy during the past .year has been uneventful but healthy. A continued increase is apparent in the number of useful alloys and in the mechanical treatment and heat- treatment of finished metals and alloys nothing can hinder the multiplication of alloys or the diversification of their treatment as knowledge of the behavior of .alloys increases; as ternary and quaternary alloys are better understood, hundreds of new metal combinations with unusual properties may well be expected. Evidence of rapid progress is already at hand.

Jan 1, 1936

Jan 1, 1908

By R. G. Hudson, L. Yang

In electrochemical separation of metals, it is necessary to control the potential applied between the electrodes so that only the desired electrode reactions can occur. A knowledge of the minimum potential needed for a given electrode reaction to take place continuously is therefore pertinent to the success of the process. In molten chloride systems at high temperatures, activation polarization is believed to be small,1,2 so the minimum potential needed for the electrolytic decomposition of a molten metal chloride MC1n (n = valence of the metal ion) is therefore essentially the equilibrium electrode potential E of the metal-chlorine galvanic cell in the solution. If the decomposition products are pure M and chlorine at a pressure of p atm, E*Eo-rt/nf in [i] Since EO (the standard electrode potential of MCln) is a constant at a given temperature and R (the gas constant), and F (the Faraday&apos;s constant) are all constants, the variation of E with the electrolytic bath conditions is largely determined by the effect of the latter on the activity of the metal chloride amcln (standard state = pure MC1,). Measurement of E and study of how amCin varies with temperature and concentration, the nature of the solvent, and that of the coexisting solutes are therefore pertinent in the selection of optimum operating conditions for the electrochemical separation of metals. Because of its low melting point, high decomposition potentials of its components, and the low solubility of heavier metals in it, the LiC1-KC1 eutectic melt is a useful solvent and has been used in the electrodeposition of Mo,3Ce,4 and u5 metals. Senderoff and Brenner3 measured the potentials of Zn/Zn++, Fe/Fe++, Cu/Cu+, Mo/Mo+++, and Ag/Ag+ against an Ag/AgCl (pure) reference electrode at 600°C and a concentration of 4.1 mole pct of each chloride and came to the conclusion that complex ion formation occurred in some of the melts. Laitinen and LiUe gave an electromotive force series at 450°C for a number of {Metal/Metal ions (unit activity)) electrodes in LiC1-KC1 eutectic melt, the {pt/pt++ (unit activity)) electrode being chosen as the reference. Walker and Danly7 studied the ther-modynamic properties of NiC12 in LiC1-KC1 eutectic melt over a wide range of temperatures and concentrations by measuring the electrode potential between a nickel electrode and a chlorine electrode in the melt. Since potential measurements made by using the chlorine reference electrode are of more direct significance both in the study of electrochemical separation and in the evaluation of the thermodynamic properties of the melt, it is therefore decided to measure the electrode potentials of cells of the type {M/MCin (mole fraction = N) in LiC1-KC1 eutectic melt/Cl2 over a range of N values and temperature for a number of metal chlorides. The results should indicate the order by which the various metals plate out on the cathode and how this order is affected by temperature and the concentration of the metal chloride in the solu-

Jan 1, 1960

By Richard P. E. Hermsdorf

IN the nonferrous sessions this year, magnesium wiggled its way into a dace of prominence such as it has never before enjoyed. This was evidenced not only by the number of papers presented on that metal but by the attendance at the meetings. The atmosphere permeating these magnesium meetings was similar to that which exists in a family with a new baby. Everybody crowded around to see what it looked like and then wondered whether it would be a success and credit to the family. Well. magnesium appeared to be a vigorous youngster, full of life, and raring to go. A close relative of maenesium named " aluminum, although much more grown up, also attracted much attention. From the activity and spirit in these sessions

Jan 1, 1944

By C. R. Van Hise

PART I.-GENERAL PRINCIPLES. [ ]

Jan 1, 1902

By Michael S. Koleda

Less than two years ago, the, Congress, with broad bipartisan support, passed the Energy Security Act of 1980. A decade marked by ten- fold increases in world oil prices and two major interruptions in oil flows from the Middle East had ended. An all-out national commitment to transform America&apos;s vast tar sands, oil shale and coal resources into conventional fuels had begun. The national synfuels effort was to be public-private cooperation at a scale unmatched in peace time. Private industry would own and operate the synthetic fuels facilities. Government would reduce market uncertainties to acceptable levels. The potential government commitment was substantial. Up to $88 billion would be available through the Synthetic Fuels Corporation, principally in the form of contingent financing. Billions more would be spent through Department of Energy programs. Additional incentives for alternate energy development were contained in the Energy Tax Act of 1978. The Energy Security Act clearly specified national synthetic fuels production objectives: 500,000 barrels per day by 1987 -- 2 million barrels per day by 1992. Finally, said Congress, Uncle Sam was going to do something about rapidly rising oil prices, uncertainties of energy supply, and the resulting disruption to the U. S. economy. Simply put, the purpose of the Energy Security Act of 1980 was to provide government guarantees sufficient to get synthetic fuels projects off the private sector drawing boards and into commercial production. Because of their huge cost, technological uncertainty, and lengthy pay-out period, these projects were always second place to projects of smaller size, known technology and more rapid pay-out. The Energy Security Act was the legal expression of public policy to bring the free-market synfuels timetable into line with the faster paced political timetable in the interest of national energy security.

Jan 1, 1982

By JAMES QATLEY

THE atmosphere, which plays such an important part in the manufacture of iron and steel, is the most variable element involved in its several processes; and particularly is this true of the blast-furnace process, which consumes air in large quantities. At no time since the blast-furnace became an important and widely used apparatus-even when it was operated in the most crude manner-have the variations in composition of the raw materials used been as frequent and as great as the variations in humility of the atmosphere. Important, improvements have been made in the blast furnace and its accessories, such as the hot-blast stoves, the increase in size and change in the shape of the furnace, more efficient blowing engines, the increased protection given to the bosh walls, and the careful preparation of&apos; the raw material, all of which have exerted a pronounced influence on the furnace-operations from a metallurgical standpoint. But during the past eight years little advance has been made in this direction; the fuel-consumption has not diminished, nor has there been any material increase in production. Within that period, however, there has been witnessed the greatest development in appliances for the economical handling of material. So complete has been the work in this direction, that, except in isolated cases, in this country at least., a further extension does not hold out much promise of a satisfactory return on the investment required. It seemed that, with the exception of the gas-engine, we had about reached the limit, for like a strong wall, the atmosphere, with its humility as variable to-clay as when first blown into a primitive blast-furnace, appeared to stand as a Barrier to

Jan 1, 1905

NEW MEMBERS The following list comprises the names of those persons who became members during the period Oct. 10 to Nov. 10, 1914: Members ADDAMS, CHARLES EDWARD, Asst. Supt.. . Ray Consolidated Copper Co., Ray, Ariz. ALEXANDER, HARRY H., Asst. Mgr. and Mgr., American Smelting & Refining Co., Maurer, N. J. ALLING, MARK,N., Min Engr Downieville, Sierra Co., Cal. ANDERSON, LESLIE DOUGLASS, Supt U. S. Smelting Co., Midvale, Utah. ATKINS, WILLIAM, JR., Sec&apos;y Kingwood Coal Co., Howesville, W. Va. BLAKE, TRUE WALTER, Min. Engr Rombauer Coal Co., Novinger, Mo. BRACKETT, GEORGE SYLVESTER, Supt... Pittsvein Coal Co., Flemington, W. Va. BRAINERD, HOWARD STANFORD, Met Ingersoll-Rand Co., Phillipsburg, N. J. BROWN, THOMAS J., Genl. Supt., Nova Scotia Steel & Coal Co., Sydney Mines, N. S., Canada.

Jan 12, 1914

By AIME AIME

EVEN the weather man joined in a friendly conspiracy to make the fall meeting of the Industrial Minerals Division at Rolla, Mo., Oct. 23-25. the splendid surges that it was. Following weeks of rain, the foliage of the Ozarks was still green, merely enlivened here and there by splashes of autumn coloring. In contrast to the tranquil beauty of the School of Mines campus under smiling Indian summer skies, the pace of the meeting was lively. Registration was larger than at any previous meeting and included an unusual number of prominent names and delegates from all over the country. From 125 to 150 were present throughout the three technical sessions, at the Thursday evening smoker, and also at the banquet on Friday; when students trooped in to the technical sessions the audience was augmented occasionally to over 200.

Jan 1, 1941

1944 WALTER HULL ALDRIDGE New York, N Y 1946 PETER M ANDERSON Johannesburg, South Africa 1946 CHARLES CAMSELL Ottawa, Ont, Canada 1946 CHARLES AUGUSTUS CARLOW Fife, Scotland 1946 CECIL H DESCH London, England 1946 WILLIAM FRASER London, England 1917 HERBERT HOOVER New York, N Y 1941 DANIEL COWAN JACKLING San Francisco, Calif 1939 HENRY KRUMB New York, N Y 1942 ESSINGTON LEWIS - Melbourne, Vic , Australia 1921 C MCDERMID London, England 1944 WALTER C MENDENHALL Washington, D C 1942 PAUL DYER MERICA New York, N Y 1913 EZEQUIEL ORDONEZ Mexico City, Mexico 1938 A M PORTEVIN Paris, France 1937 GEORGE S RICE Washington, D C 1934 T A RICKARD Victoria, B C, Canada 1946 JOHN R SUMAN Houston, Texas 1946 WONG WEN-HAO Chungking, China

Jan 1, 1952

By James P. Savely, Victor L. Kastner

Inspiration Consolidated Copper Company is currently mining in four pit areas; Live Oak, Red Hill, Thornton and Joe Bush Extension, near Globe, Arizona. Small satellite orebodies lying outside the main pits have been mined out in a series of small open pits. Major slope instability has affected production in every pit. Some consequences of the instability have been; (1) Serious interruption of mining plans, which resulted in deferred ore production, lost ore, reduced mining rates and increased stripping requirements. (2) Forced replacement of crushing facilities. (3) Serious effects on other production facilities. The introduction of a slope stability monitoring and control function as an integral part of mine planning has been successful in reducing the impact of these failures and will eventually result in economic pit design based on probabilistic slope analysis. This case history presents a brief review of the problems associated with slope instability at Inspiration&apos;s mines followed by a more detailed report on one specific failure area in the Thornton pit where the use of horizontal drain holes for slope stabilization appears to be successful. Relationships between slope movement rate, rainfall, and mining activity are shown.

Jan 1, 1983

By Charles H. Behre

KEYNOTE of the mining geology sessions was the preparation for an extensive war with all that this implies as to the need for strategic minerals, both metallic and nonmetallic. Nevertheless the sessions also included many papers of less urgent, more theoretical interest. The stress of wartime production had the effect of giving an unusually full and rich program, the longest in recent years, with sessions continuing virtually throughout the meeting. Some papers dealt with geophysical prospecting as applied to mining geology; others were concerned with the grand strategy of mineral reserves and thus involved the industrial minerals; such "borderline" subjects were presented before sessions held jointly with the Geophysics Committee or the Industrial Minerals Division.

Jan 1, 1942

By J. G. EVANS

It is with a certain amount of trepidation that a man considers gathering his family of six, traveling across a continent, two oceans and a sea, and going to live in a foreign land. But "pioneering" is still possible, and a nation is "foreign" only until one has lived in it. We&apos;ve had eight years of pleasant experiences in South Africa on which to base that contention. It was in January 1938 that my brother first extolled the virtues of South Africa to us, and just three months and a thousand small problems later my wife, two daughters, three sons and I were boarding a ship in New York, bound for Cape- town. We arrived in May, and within a week had found a furnished home with beautiful lawns, tennis, court, a garden, and everything needed for family comfort. The children were soon located in school, and I settled down to the task of entering the importing business, as had been my original intention. The importing business started out slowly but was coming along nicely when on Sept. 3, 1939 the war started in Europe and a declaration of war by the Union of South Africa was made on the following day. With the declaration came import and export controls. In fact we were controlled completely out of business in one stroke. Liquidating the business, I went to Johannesburg intending to find work in one of the mines. Government health and safety regulations require that all underground mine employees have a red ticket from the Miners Phthisis Bureau certifying that they are not susceptible to silicosis, the scourge of the Witwatersrand gold mining industry. I made application to the Bureau, completed a form covering my whole past life, and was given a complete physical examination. The following day I was startled to find that I had not only been refused a red ticket but had been classified with a green ticket which for- ever bars one from working underground in any scheduled mine in the country, and all this in spite

Jan 1, 1949

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)&apos; where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)&apos;. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen&apos; extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen&apos; demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken&apos;s paper, are for the two terminal regions of binary systems. at infinite dilution and a&apos;s are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult&apos;s and Henry&apos;s laws as limiting cases. As pointed out previously,&apos; the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969

By Narendrakumar A. Chevli

Exploratory work was conducted in the fabrication of integrated circuitry, specifically linear amplifier circuits, by three general methods: 1) monolithic diffused silicon; 2) a combination of metal thin-film and monolithic diffused silicon; and 3) a hybrid of metal films and diffused silicon on an alunina substrate. In these linear amplifier integrated circuits the followzng conditions were desired: very high-frequency response, high voltage gain, and good thermal tracking stability of electrical characteristics. The resulting circuit designs imposed problems of isolation between elements, layout and smallness of size of active elements, and close tolerances on electrzcal characteristics of the passive elements. Interconnection problems for specific designs resulted from the small dimensions involved and the topography of the hybrid fabrication techniques. The desired integrated-circuit characteristics were achieved with the technologies of categories 2 and 3 above. Solutions to the problems imposed by these characteristics lay in the ability to isolate czrcuit elements of small size while providing a layout designed to minimize element-to-element variations. Sufficient freedom in the formation of passive elements was achieved by uniting the metal film and the monolithic silicon technologies. The most satisfactory designs were based on the beam-lead interconnection and isolation technique. SINCE the advent of integrated circuits, major emphasis has been on fabricating digital integrated circuits. Linear circuits require high performance, high voltage, and tighter tolerance components which are not always compatible with the capability of process technology available for fabrication of these circuits into integrated form. Fortunately the growth of newer and improved processes and materials for fabricating integrated circuits has been an accelerated one. This has now made possible the translation of stringent performance requirements of the linear circuits into microminiature integrated circuits of the same performance. In the exploratory work of fabricating high-performance Linear Integrated Circuits—LIC, the following objectives were formulated: i) fabrication of high-frequency transistors such as the type 2N918 isolated on a single silicon substrate; ii) fabrication of medium-frequency transistors having a very high gain at low collector currents such as the types 2N930/2N2484 isolated on a single substrate ; iii) fabrication of tight-tolerance, high-valued resistors having low temperature coefficients of resistance and stable thermal tracking characteristics, these resistors to be fabricated on an active or passive substrate; iv) simultaneous fabrication of complementary transistors—pn and pnp-on the same silicon substrate; v) fabrication of newer active elements such as MOS, FET transistors along with the conventional active and passive elements on the same silicon substrate. State-of-the-art assessment f all the available processes, materials, and technology to meet above objectives indicated that economic fabrication of LIC cannot be achieved by a single technology for all types of linear circuits. Where design and performance of a given linear circuit can be modified and tolerated to the extent of a particular technology, then alone is it possible to fabricate a LIC using a single process technology such as all diffused, planar technology. In order to evaluate this economic breakpoint with design and performance compromise in fabricating LIC, it is essential that a thorough understanding be obtained of techniques, potentials, and limitations of all the various process technology and materials

Jan 1, 1967

By R. F. Mehl, J. T. Ransom

For many years the Metals Research Laboratory of Carnegie Institute of Technology has been concerned with the statistical nature of the engineering properties of steel from an experimental viewpoint, particularly those properties representing ductility.&apos; In the past three years new work has been directed toward evaluating the statistical nature of the endurance properties. It has been shown that both the fracture curve and the endurance limit in fatigue are markedly statistical in nature. The S-N curve (and the endurance limit) of ferrous materials is often determined with specimens which number as few as ten. The common procedure is to test the first specimen at a stress well above the expected endurance hmit. Each succeeding specimen is then tested at a progressively lower stress, until, after five or six tests, a specimen runs ten million or so cycles without failing. Two or three more specimens are then used to find the highest stress at which failure will not occur; the limiting stress determined in this way is called the endurance limit. It has now been found, however, that the variability in the fracture curve and in the endurance limit in heat-treated alloy forging steels is so great that S-N curves must be drawn on the basis of distribution curves which can be appraised only by statistical methods. Two methods have been adopted in this study: (1) straightforward statistical studies of cycles to fracture of a number of specimens at each of a series of stress levels, and (2) a new abbreviated statistical method, known as "staircase testing."2 The latter corisists in testing a series of specimens, one by one, with the test stress for any given specimen automatically

Jan 1, 1950

By C. Q. Payne

(New York Meeting, February, 1912.) THE art of crushing ores and other materials by means of rolls is a comparatively recent one. While the first record of rolls using iron crushing-surfaces dates back to the year 1806, when they were employed in Cornwall, their principal development has taken place during the last 30 years. To Stephen R. Krom belongs the credit of the pioneer in introducing the belted high-speed roll, which has had its origin and a marked development in this country. His notable contribution to the art was in the use of a single bed-plate or frame supporting the roll-shafts, and to which levers holding the movable roll-bearings were pivoted. He also made use of steel tension-rods to support the crushing-strains, and of hammered-steel tires for the crushing-surfaces. These changes brought the design of crushing-rolls to a high level. Following closely thereon, about 1885, W. R. Eckart conceived the idea of the swivel or ball-and-socket support for the roll-shaft bearings. This is an excellent mechanical conception, especially for bearings held against a spring pressure, and while it may not be necessary for all types of rolls, yet it has been quite generally adopted by other roll-designers, and illustrates the refinement which roll-construction has now reached. Other engineers, as for example, Argall, Vezin, Roger, and Sturtevant, to mention only a few among many, have also given the closest attention to the various details of rolls, such as the frame, springs, bearings, and shafts, and have developed many novel and original designs. It has remained, however, for the boldness and originality of Mr. Edison to extend the field of crushing-rolls in two new directions, and to cause them to exercise new functions. In developing crushing-machinery for his Portland cement works, Mr. Edison constructed ? giant " rolls, having a diameter of 6 ft. and a length of. face of 7 ft.

Jun 1, 1912

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," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used&apos; 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&apos;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.&apos; However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,&apos; has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] 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&apos;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 unsym-metric 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 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: fP = -1/2-vE/m [2] Here fp 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 = nvm/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 (Poisson7 1831) P = /4 D2-pL-g-h + D.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 angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953