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ON Oct. 5, 1926, the day before the general ses-sions of the fall meeting of the American Insti-tute of Mining and Metallurgical Engineers at Pittsburgh, a round table conference on the combus-tibility and testing of coke was held at the Bureau of Mines Experiment Station. There were about fifty present, with A. C. Fieldner, chief chemist of the Bureau of Mines, as chairman. The following organi-zations were represented: American Institute of Min-ing and Metallurgical Engineers, American Society for Testing Materials, American Gas Association, Eastern States Blast Furnace and Coke Oven Association, Gas and Fuel Division of, American Chemical Society, and Southern Ohio Pig Iron and Coke Association. In opening the proceedings, Mr. Fieldner explained that the meeting had been called at the suggestion of several members of the Institute and members of other organizations. The subject is of interest to the pro-ducer and the user of coke whether it be in a blast furnace, cupola furnace, house-heating furnace, open grate, gas producer, or in a water-gas generator. There has been much confusion on this subject largely because there is no common definition of combustibility. Does the blast-furnace superintendent, the coke-oven operator, and the fuel engineer have the same under-standing of the term "combustibility"? If a common understanding can be reached, many differences of opinion will disappear. COMBUSTIBILITY OF COKE R. H. Sweetser of Columbus, Ohio, disagreed with the statement of P. H. Royster, T. L. Joseph, and S. P. Kinney in Reports of Investigations, Serial No. 2524, of the Bureau of Mines, in which it was stated that the coke-oven op-erator cannot change coke combustibility by modifying oven practice. Mr. Sweetser held that the coke-oven man can change the combustibility of coke. Blast-furnace men know that coke that will burn easily with low pressure and will. come down in the regular way in the furnace can be pro-duced from a given mixture of coal. His idea of the combustibility of coke is the rate of flow through the com-bustion zone of the blast furnace. If the coke does not pass through in normal manner it is highly incombustible. H. J. Rose of the Koppers Co., Pittsburgh, objected to being pinned down so closely on this phase of the com-bustibility and incombustibility of coke. Coke-oven men are frequently obliged to change oven conditions to make a coke which gives blast-furnace men what they want. The size of the coke and the screening have an important bear-ing on combustibility, and there are many cases on record where by simply changing the different sizes of the coke, everything worked smoothly, and that is a much more combustible coke.

Jan 1, 1927

By Ross Blake

THE St. Joseph Lead Co. became interested in the Tri-State district in 1921 through acquisition of prospecting and development rights on approximately 20,000 acres of land extending northeastward from the Picher mining field, mostly in Kansas. Prospecting with churn drills was begun the same year and the first commercial ore body was found on the Jarrett tract at the then northern limit of the main Picher field. Operations at this mine began in 1923. Kansas Explorations, Inc., was organized in 1923 by the St. Joseph Lead Co. as a wholly-owned subsidiary to carry on its operations in the Tri-State District from an office at Joplin, Mo. As prospecting of the original acreage proved largely negative, attention was subsequently turned to other sections of the district. Numerous additional leases were acquired and prospected. The Company was successful in developing into operating properties the Jarrett, Isherwood, Robinson, Sullivan and Lotson tracts and, in more recent years, the Ritz, Snapp, Buckingham, Gibson and Jasper mines.

Jan 1, 1947

By J. R. Guard

Development of electrical power in coal mining has been an outstanding example of adaptbility. It has accommodated itself to new inventions, changing mining methods, increasing demands, increasing safety requirements and many other new conditions. With the appearance of the continuous miner in the mining machinery picture, those engineers interested in the application of electricity to mining have been thinking about what new comination of electrical apparatus will best suit this newcomer. It is the purpose of this paper to discuss the relative costs of supplying d-c versus a-c power to mining equipment with particular reference to continuous miner setups. Assume that a-c power will be delivered to the mine at some high voltage suitable for transmision to the various substation locations. Typical voltage for this purpose is 4000 volts. The problem then is to change the power to some kind of power suitable for driving the motors of mining equipment. For safety and other reasons the voltage to be delivered to the motor terminals must be under 600 volts.

Jan 6, 1950

By James W. Malcomson

The Tigre Mining Co. of Mexico, owned by the Lucky Tiger Combination Gold Mining Co. of Kansas City, decided early in 1910 to enlarge its mill, which consisted of a concentrator milling 3,000 tons of ore per month. The enlarged plant was designed to crush and concentrate 6,000 of ore and to cyanide 7,500 tons per month. The extra tonnage cyanided was to be obtained from tailings which were stored below the old mill. Power was supplied to the old mill from four boilers; a 150-h-p. Corliss engine and two Weber 60-h-p. gas-engines using producer-gas made from charcoal. The total horse-power required, including 60 h-p. used for machine-drills in the mine, was approximately 275. Cord-wood cost $4.32 per cord, 8 by 4 by 3 ft., and charcoal $15 per ton. The fuel supply in the surrounding country was approaching exhaustion; more than 150 mules and 50 men were engaged in cutting and transporting this fuel, and the unsettled political conditions in Sonora were such that it would be practically impossible to keep an organization of this kind together. The price of fuel was steadily rising and at times it became almost impossible to get sufficient fuel to operate. It was estimated that the enlarged plant, together with the mine, would require 750 h-p., as follows: Horse-Power. Old mill, which was left unchanged,..............180 New concentrator,.......................90 Cyanide-plant,........................380 Mine and other requirements,................. 100 Total,........•..................750 In a study of the best manner to obtain power the following alternative propositions were considered:

Jan 1, 1914

By P. T. Gallagher, W. A. Oates, J. A. Lambert

FAIRLY extensive equilibrium data exists for carbon dissolved in r iron.1-8 However the temperature coefficients of the carbon activity, ac , are insufficierltly preciseto reveal whether the heat of solution of carbon, ?HC , varies with composition. It is doubtful

Jan 1, 1970

By R. S. Burns, J. G. Erskine

The performance of the nine 5.5 m diameter x 6.4 m mills (18 x 21 ft) initially installed at Bougainville Copper Ltd. did not meet the laboratory and pilot plant derived design expectations as measured by Bond Work Index. During the post-commissioning period, inefficient grinding of coarse material resulted in a build-up of large circulating loads and led to reduced throughputs because of pump and cyclone overloading. Installation of larger pumps and cyclones and development of an improved circuit control philosophy alleviated materials handling problems and permitted higher tonnages to be attained. Since 1977, plant throughput has been increased by installation of three additional mills. These are 0.9 m (2.9 ft) longer than the other nine and have a higher capacity. Developments in classification and mill speed-up, together with a finer ball mill feed size and substantial improvements to mill availability (99% in 1982) have further increased plant capacity. There is a continuing emphasis on improving grinding circuit efficiency in terms of throughput/grind. Current development work includes trials of graded ball charges, different liner profiles, and assessment of scalping/regrind proposals.

Jan 1, 1985

By Cyril Wells, Robert F. Mehl

The two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these data are needed chiefly in order to treat data on carburization, on rate of formation of pearlite, and on rate of austenit-izing in a quantitative way.1'2'9'10 In the present investigation rates of diffusion of nickel in ?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of im- purities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel in y-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200ºC., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. Method and Materials Method.—Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

The two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these data are needed chiefly in order to treat data on carburization, on rate of formation of pearlite, and on rate of austenit-izing in a quantitative way.1'2'9'10 In the present investigation rates of diffusion of nickel in ?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of im- purities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel in y-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200ºC., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. Method and Materials Method.—Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

THE two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these [] data are needed chiefly in order to treat data on carburization, on the rate of formation of pearlite, and on the rate of austenizing in a quantitative way. 1,2,9,10 In the present investigation rates of diffusion of nickel in -?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of impurities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel [ ] in -?-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200T., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. METHOD AND MATERIALS Method.-Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By Thomas V. Falkie, Robert Stefanko

Recently The Wall Street Journal featured a series of articles titled "The Dirty Work-Brutal, Mindless Labor Remains a Daily Reality for Millions in The US.-Mining Coal, Shoveling Slag, Gutting Hogs Pays Bills But Can Drain Spirit, Hope." The article was devoted to describing how tough and dangerous is mining (and some other jobs) and how rough life is for miners and their families. Similarly during the past few years some psychiatrists and sociologists have devoted increased attention to the attitudes and life styles of miners. Unfortunately most of their approaches have been neither scientific nor objective, and very little good clinical research has been done on the subject.

Jan 1, 1971

By Frederick H. McDowell

Notwithstanding the rapidly increasing use of copper, due to the extension of its applications within the last few years, the fact of its continued steady decline in price stands prominently forward. Nor have we far to look for the cause. The opening up of the vast copper-deposits of our Western States and territories is the metallurgical event of the last five years. We must not forget, in looking at the new field, the changed conditions under which the metallurgist must work, as compared with the previous history of copper-smelting. Until quite recently, the copper-plants of the country were few in number; and the concentration of industry implied in this circumstance, allowed many practices which must be considered as inapplicable to the conditions offered at the many mines which have of late become such important factors in our copper-production. Thus the old style of smelting the ore for matte in brick furnaces, involving great expense and time in their construction, while deservedly losing repute even in its old strongholds, in comparison with water-jacketed smelters, is still in some cases adhered to. But to put up such furnaces at Western mines would be out of the question. The large and continual need of brick for relining and repairs acts as an effectual bar, when such furnaces come into competition with the light, portable, and easily managed water-jacketed smelters of improved types. It is owing to the present unusual activity, manifested in the opening up of new copper-properties and the erection of plants for working them, that any improvement in furnace-construction is of especial interest and importance. The method in which processes are copied without variation in the rapid growth of metallurgical interests, has already been strikingly exemplified in the history of

Jan 1, 1885

By R. B. Russell

The expansion coefficients of hexagonal (a) zirconium have been calculated from the lattice expansionparameters of both coefficientsofhexagonallow and high hafnium alloys in the range 0° to 600°C. It is found parametersofboththat the coefficients are straight-line functions of the temperature and that the effect of hafnium is to depress the mean coefficients by about 1 pct at room thattemperature and 9 pct at 600°C. The cubic (ß) form was stabilized so that its coefficient could be determined from 400' to 900°C. COEFFICIENTS of thermal expansion for hexagonal-close-packed (a) zirconium were determined up to 600°C (1112°F), without any interference from the effects of preferred orientation, by measurement of the lattice parameters obtained from a symmetrical back-reflection focusing X-ray camera. This paper combines the results for a 1.2 atomic pct hafnium alloy from an earlier report' with those for hafnium-free zirconium. The problem confronting the investigator is essentially that of getting sharp, high-angle diffraction lines which represent the material at a known constanl. temperature and chemical composition. In order to do this, it was necessary to use the proper X-ray emission wave length (Co K was chosen) and to have a fine-grained metal whose atomic spacings would be free from effects of cold work (the specimen was annealed) and to prevent a changing composition owing to gas absorption during the heating of the metal to temperature (the sample was heated in a vacuum). A summary of the effect of temperature on properties is listed in Table I which gives data for ordinary zirconium, as well as new values for the low hafnium metal. The coefficients of the linear thermal expansion that have been reported are given in Table 11. The discrepancies shown may be explained perhaps by the effect of preferred orientation, and McGeary and Lustman2 have done this successfully for sheet metal. The differences in texture cannot explain all the differences in expansion coefficient shown in Table II. liesults by the author agree most closely with those of Kroll.3 Chemical analysis of the high hafnium metal pre- viously reported1 showed that it was 98.22 atomic pct (97.40 wt pct) pure. The low hafnium metal was dehydrogenated Westinghouse crystal bar, designated SMZ-137A. Its analysis was as given in Table 111 (chemical analyses 5377, 5431, and 5432).

Jan 1, 1955

By C. R. King

Most of the acid volcanic glasses such as obsidian, perlite, pitchstone, pumice, and pumicite (volcanic ash) are susceptible to some expansion if suddenly subjected to a suitably high temperature in a properly designed furnace, and subsequently suddenly cooled. Expansion results from the action of chemically combined or dissolved water expanding as a vapor within the softened heated rock particles. This expansion forms countless minute bubbles within the pasty mass of the natural glass particles. If the particles are cooled before these bubbles can escape, the resulting products are cellular, more or less spherulitized glass froths or hollow glass spheres of many types. Chemically, they are essentially aluminum silicates containing about 70 to 75 pct silica, 10 to 16 pct alumina, and 2 to 7 pct sodium plus potassium oxides. They are relatively resistant to attack by acids or alkalies, are resistant to heat up to over 1000°F, and are completely inert to insect or fungus attack.

Jan 1, 1949

By R. W. Gurry

When a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, yet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. Experimental Procedure Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;' it suffices to state here that the carburization lasted about I40 hr. at 760°C. (1760°F.) and 44 hr. at iiio°C. (2030°F.), these periods being long enough-—on the basis of the calculations presented later—to ensure that the specimen was about 99.9 per cent saturated at each temperature. The specimen was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully carburized specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

By R. W. Gurry

When a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, yet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. Experimental Procedure Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;' it suffices to state here that the carburization lasted about I40 hr. at 760°C. (1760°F.) and 44 hr. at iiio°C. (2030°F.), these periods being long enough-—on the basis of the calculations presented later—to ensure that the specimen was about 99.9 per cent saturated at each temperature. The specimen was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully carburized specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

By K. O. Stamm, B. A. Rogers

Because it is the basis of the economically important operation of hardening steel by quenching, the A3 transformation in iron has been the subject of numerous investigations. Although the contributions to this subject are interesting, no general review will be given here. Readers who care to follow the matter further are referred to the comprehensive summary by Cleaves and Thompson,l which covers the literature to about 1935. Their references to 53 papers on the subject suggest that further investigation is hardly justifiable. However, considerable interest has devel oped recently concerning the reversibility of the transformation. From thermo-dynamic considerations, the transition ought to occur at the same point on heating or cooling, if the change of temperature is sufficiently slow. Yet all of the earlier investigators found a difference of several degrees. Burgess and Crowe,2 who used thermal methods, obtained average temperatures of 912" for Ac3 and 900°C. for Ar3 on electrolytic iron. Their data indicate a considerable range of temperature over which the change occurs, both on heating and on cooling. Terry3 measured the susceptibility in the critical range and estimated from the steepest parts of his curves that Ac3 came at 9I8° and Ar3 at 903°C. Ishiwara4 was one of the first investigators to report a shorter interval between the temperature of the change in the two directions. He measured the change of susceptibility of kaolin-coated samples of steel, in a hydrogen atmosphere, at rater of heating and cooling so low that about 3 or 4 hr. were required for the transformation to complete itself. His results show some variability between samples, but indicate that the difference between Ac3 and Ar3 is in the vicinity of 6°C. Roberts and Davey5 measured the space lattice in pure iron in the vicinity of 900°C. and concluded that a change occurs reversibly between 907' 3" and 910" 3°C., probably between 907" and 910°C. Wells, Ackley, and Meh16 made dilatometric determinations of the Ac3 and Ar3 points in samples of hydrogen-treated carbonyl iron maintained under a vacuum. They used three rates of heating and cooling: 2°, ½°, and .?°C. per min. and found the spread between the two points decreased with low rates. At the slowest rate, the Ac3 transition occurred at 909° to 909. 5°C. and the Ar3 change at 907°C. in three of the samples believed to contain the lowest percentages of alien elements. They concluded that if the rate of temperature change and the content of alien eiements were low enough, the A3 transformation would be completely reversible at 909.50 + 1°C. The question of reversibility is an interesting one and when some iron with especially small percentages of alien elements became available the opportunity to conduct an investigation was welcomed. This iron was prepared by the Division of

Jan 1, 1942

By B. A. Rogers, K. O. Stamm

Because it is the basis of the economically important operation of hardening steel by quenching, the A3 transformation in iron has been the subject of numerous investigations. Although the contributions to this subject are interesting, no general review will be given here. Readers who care to follow the matter further are referred to the comprehensive summary by Cleaves and Thompson,l which covers the literature to about 1935. Their references to 53 papers on the subject suggest that further investigation is hardly justifiable. However, considerable interest has devel oped recently concerning the reversibility of the transformation. From thermo-dynamic considerations, the transition ought to occur at the same point on heating or cooling, if the change of temperature is sufficiently slow. Yet all of the earlier investigators found a difference of several degrees. Burgess and Crowe,2 who used thermal methods, obtained average temperatures of 912" for Ac3 and 900°C. for Ar3 on electrolytic iron. Their data indicate a considerable range of temperature over which the change occurs, both on heating and on cooling. Terry3 measured the susceptibility in the critical range and estimated from the steepest parts of his curves that Ac3 came at 9I8° and Ar3 at 903°C. Ishiwara4 was one of the first investigators to report a shorter interval between the temperature of the change in the two directions. He measured the change of susceptibility of kaolin-coated samples of steel, in a hydrogen atmosphere, at rater of heating and cooling so low that about 3 or 4 hr. were required for the transformation to complete itself. His results show some variability between samples, but indicate that the difference between Ac3 and Ar3 is in the vicinity of 6°C. Roberts and Davey5 measured the space lattice in pure iron in the vicinity of 900°C. and concluded that a change occurs reversibly between 907' 3" and 910" 3°C., probably between 907" and 910°C. Wells, Ackley, and Meh16 made dilatometric determinations of the Ac3 and Ar3 points in samples of hydrogen-treated carbonyl iron maintained under a vacuum. They used three rates of heating and cooling: 2°, ½°, and .?°C. per min. and found the spread between the two points decreased with low rates. At the slowest rate, the Ac3 transition occurred at 909° to 909. 5°C. and the Ar3 change at 907°C. in three of the samples believed to contain the lowest percentages of alien elements. They concluded that if the rate of temperature change and the content of alien eiements were low enough, the A3 transformation would be completely reversible at 909.50 + 1°C. The question of reversibility is an interesting one and when some iron with especially small percentages of alien elements became available the opportunity to conduct an investigation was welcomed. This iron was prepared by the Division of

Jan 1, 1942

By R. W. Gurry

WHEN a steel in the austenitic state, with all its carbon in solution, is maintained, at constant temperature, in contact with a gas that removes the carbon from the surface, yet without otherwise altering the composition of the steel, the change in weight of the specimen, after any period of exposure, is a direct measure of the amount of carbon it has then lost. The purpose of the present paper is to show how, by application of established mathematical reasoning based on the fundamental diffusion law and on certain postulates, this loss of weight yields a complete picture of the distribution of carbon throughout a specimen of regular shape after any period of exposure, with all the accuracy required in any practical occurrence of decarburization. Precisely the same is true for the gain in weight during the reverse process of carburization, or for the gradual gain or loss of any element, so long as the steel comprises only a single phase at temperature, provided always that the experimental conditions conform to the postulates. The change in carbon content from surface to center of the specimen is always continuous, when everything is in solution, even though under the microscope the decarburized zone (or carburized rim) may appear to be sharply defined. The experimental procedure is described and some typical results are presented, which are then interpreted by application of the diffusion law. EXPERIMENTAL PROCEDURE Initially an endeavor was made to follow the gain of weight during the process of carburization in a hydrogen-toluene atmosphere, but it was soon found that the specimen became coated with graphite, which could not be removed without some loss of metal; therefore it was decided to continue carburization until the steel was saturated throughout, to remove all graphite from the surface of the specimen, and then to follow the loss of weight during decarburization in a moist hydrogen atmosphere at the same temperature as that used for carburizing. The carburizing procedure has been described in an earlier paper;1 it suffices to state here that the carburization lasted about 140 hr. at 760°C. (1760°F.) and 44 hr. at 1110°C. (2030°F.), these periods being long enough-on the basis of the calculations presented later-to ensure that the specimen was about 99.9 per cent saturated at each temperature. The specimen was a cylinder about 3.8 cm. long and 0.475 cm. in diameter; the materials were carbonyl iron, a commercial low-metalloid iron, and a steel with 3.6 per cent nickel and the usual proportion of other elements. The fully carburized specimen, after cooling at the top of the furnace tube, was placed in a lathe and sandpapered to remove all graphite; then the diameter was measured with a micrometer caliper, and the initial weighing (corresponding to complete saturation) was made. By means of a

Jan 1, 1942

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' 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.' 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: 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'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

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' 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.' 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: 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'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