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[NOTE.-The names of authors of papers are printed in small capitals, and the titles of papers, in italics. Casual notices, giving but little information, are indicated by bracketed page numbers. Large Roman numerals are volume numbers; small Roman numerals after volume numbers following titles indicate the page on which the presentation of the paper is mentioned; Arabic figures refer to the text of the printed papers.] A Use Classification of Coal, (ASHLEY) LXII [xiv]; LXIII, 782; Discussion: (HALL), 794; (ZERN) , 795; (ASHLEY), 795 Absorbent material, liquid-oxygen explosives, LXXI, 1251. Absorbents for liquid-oxygen explosives, LXIX, 292, 299. Absorption : cupellation : gold, special cupels, LIX, 194. primary and secondary, LIX, 213. ratio of silver to gold, LIX, 212. silver, specla1 cupels, LIX, 195. Absorption method, gasoline from natural gas, LIX, 584, 585. Absorptzon of Sulfur from Producer Gas zn Open-hearth Furnaces (NEAD), LXX, 176; Discussion: ( WATERHOUSE), 184 ; (REYNDERS) , 184; (KINNEY), 184 Accelerated wearing tests, bearing metals, LXIX, 973. Accident prevention, results, Utah, LXVIII, 360 Accident Prevention, 1919 (SINN), LXIII, [xiii] Accidents: causes in coal mines, LXXI, 1229. classification, Anaconda Copper Mining Co., LXVIII, 9. coal mining: comparison with metal mining, LXVIII, 360. pillar mining, LXVIII, 323. relation to method, LXVIII, 323 shafts, LXVIII, 207, 209 Utah, LXVIII, 363 - concentrating mills, Utah, LXVIII, 362 liquid-oxygen explosives, LXIX, 330, 339 losses through, LVIII, 65 metal mining, LXVIII, 361, 363. mine: causes, LIX, 652. curve of decrease, LIX, 655 days of greatest frequency, LIX, 657 human element as cause, LIX, 652, 653. intemperance as cause, LIX, 658 labor relation, LIX, 652 prevention, LIX, 653. record, New Jersey Zinc Co., Franklin mine, LIX, 655 time of greatest frequency, LIX, 657, 658 Utah, LXVIII, 360 prevention, LVIII, 65 report blanks, Anaconda Copper Mining Co, LXVIII, 13, 15. statistical base, Anaconda Copper Mining Co, LXVIII, 9 time lost, LVIII, 70 transportation, Clifton-Morenci district, LXX, 851.

Jan 1, 1926

TO WE BOARD OF DIRECTORS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-The following report covers briefly some of the more important activities of the Institute during the year 1923. In my report for the year 1922, I drew attention to the falling off in membership of the Institute due to the depressed condition of the mining industry in several lines and the inability of many of our members to find profitable employment in mining or its associated branches. A number who were unemployed during 1922 established connections during 1923, but a still greater number have been forced to resign or drop their membership during 1923. Fortunately, the number dropped is not so great as in the previous year. The Employment Service conducted by the four Founder Societies bears witness to the trend in business. For the young men just out of college, there are plenty of opportunities at small salaries, there are plenty of opportunities for them as laborers; but for the mature members, those of experience, there are few calls. During the last eighteen months, our Employment Service has been able to place only six of our members out of every hundred engineers for whom it has found work. Another loss which this Society has suffered, but which is not felt so keenly by our sister societies, is in its foreign members. The A. I. M. E. has always had a large foreign membership, but of recent years exchange has been so heavily against many European and South American countries that a large number of members residing abroad have been compelled to relinquish their membership. Almost invariably these members express keen regret because of the necessity that confronts them, and almost invariably the writers express hope that present conditions will not last long and that they will soon be able to ask for reinstatement. Having stated the darkest side of the picture first, it may now be drawn to your attention that in spite of these losses the number of persons applying for membership was decidedly encouraging. From the quality point of view, the membership has not gone backward. The Membership Committee has declined to recommend many

Jan 1, 1925

By H. J. Rose

Sixty-five million net tons of coal were carbonized in the by-product and beehive coke ovens1 of the United States during 1924. This tonnage represented 13.4 per cent. of the bituminous coal which was mined in that year. Table 1 shows production and disposition.2 Table 1.—Production and Disposition of Ocen Coke in 1924 By-product Beehive Total Coal charged into ovens, tons................ 49,061,339 15,914,310 64,975,649 Coke produced (exclusive of screenings and breeze), tons............................. 33,983,568 10,286,037 44,269,605 Average yield of coke, per cent ............. 69.3 6.46 68.9 Disposition of coke, per cent.: Blast furnace.......................... . . 82.6 Foundry............................... . 13.3 6.6 Domestic.............................. . 1.4 6.7 Water gas manufacture and all other uses.. 4.6 . 4.1 Cokes having somewhat different combinations of chemical and physical properties are desired for the various uses listed above, and these properties depend primarily upon the types of coal used. American coals have a wide range of purity and coking quality, and the chief subject of this paper will be the selection of coals for the manufacture of blast furnace, foundry, domestic, and water-gas coke, in by-product coke ovens. It will obviously be necessary to include a discussion of those physical and chemical characteristics that are generally considered essential or desirable for each type of coke. Suitable Coals The examination and development of new sources of coking coal are important because of the irregular and limited distribution of high-grade

Jan 1, 1927

By A. C. Lane

Relations de la profondeur de plissement avec la gravita-tion et la hauteur des montagnes dans les Alpes. Par A. Heim (Zurich) 50me Anniversaire, Livre Jubilaire Soc. Geol. De Belgique, Rome, Fascicule 1, 17 to 28. Measurements show a negative anomaly, less densities of .the material below sea level. The author expresses it in terms of the thickness of rocks of an arbitrary density, 2.4, which might be considered wanting. The accordant heights of the summits, the depths of the folds, the deficiency in .gravity, and denudation he finds to be connected. The Alps float on the lightness of the folds of "sal" of weight 2.6 to 2.75 plunged into the heavier "Sima" according to a for-mula: P = h (2.7/2.8-2.7) where - P is the depth of fold-ing below sea level; 2.7 is the weight of the material accu-mulated in folding; 2.8 is the weight of the material dis-placed by it; and h is the mean height of the mountainous regions. For instance, between the valley of Saar and the Val de Bagne in Valais the depth of the folds according to Ar-gand's profiles is between 30 and 40 kilometers. The loss of gravity has been estimated in this region as 1450 X 2.4 = 3480 in units of weight. Obviously errors in the densities would profoundly affect the estimates of the thickness of folding, but his depths of folds are obtained from sections, and from them he works back to the densities. Of course other densities might be placed in the formula. Zur Dichte bestimmung von Tonen. By J. Koenigsberger, Berg u. Hüttenmannisches Jahrbuch, 75, I. Discusses Dr. B. Wilser's investigations as to the best way of obtaining the weight of rocks per unit volume. The use of mercury for rocks affected by water as there recom-mended may easily give too large volumes unless 1 to 3 atm. pressure is used. Thick machine oil is recommended for large lumps of clay.

Jan 4, 1928

By Basil B. Zavoico

PRODUCTION of crude it in the United States during 1939 totaled about 1.255,776,000 barrels, an average of 3,440,482 barrels per day, 3.41 per cent above the 1938 output of 1,214,355,000 barrels but 1.83 per cent below the record pro¬duction of 1,279,160,000 barrels, in 1937. However only the two-week shutdown of oil fields in the Southwestern States in August and September prevented the domestic crude production from establishing an all-time record in 1939. Demand for all petroleum products for the first ten months of 1939 showed an increase of 7.04 per cent over the similar period of 1938. Domestic demand for all petroleum products was particularly benefited by the increasing industrial activity, advancing 8.37 per cent above the like period of the preceding year equivalent to a volume increment of 256,810 barrels per day; with motor-fuel demand gaining 5.83 per cent and demand for all fuel oils gaining 12.15 per cent over the corresponding period of 1938. The export demand for the first ten months of 1939 was slightly below the export movements during the same period of 1938, declining 0.56 per cent. The European war was a major factor in 1939 for the petroleum industry in the United States, even if, at the end of the year, the war had not yet resulted in the expected large shipments to England and France.

Jan 1, 1940

By R. S. Shoemaker, F. W. McQuiston

CARLIN GOLD MINING COMPANY 1974 Operating Data to October MINE LOCATION: 40 miles from Elko, Nevada ORE DESCRIPTION: Gold with minor amounts of mercury occurring in siltstone and carboniferous limey shales. TYPE OF MINE: Open pit ORE HAULAGE TO MILL: By trucks up to a distance of 12 mi1es MILLING CAPACITY: 2500 tons per day ORE GRADE: 0.20 oz per ton oxide ore 0.25 oz per ton carbon type ore PRODUCTS: Gold bullion 993 fineness, by product quicksilver RECOVERIES: Oxide ore 887'0 Carbon ore 83% POWER FOR GRINDING: 7 Kwh/T POWER, other than grinding: 14 Kwh/T WATER SUPPLY: Pumped from wells 2- 112 miles through 13,000 ft of 8" buried pipe 6 ft underground. Consumption 0.60 tons of new water per ton of mill feed. TAILINGS: By 10" woodstave pipe a distance of 2500 ft to mine waste filled dam. RUNNING TIME: 10 ft x 10 ft mill on oxide ore, 98% 7 ft x 8 ft mill on carbon ore, 937'0 Principal causes of lost time, power outages and problems of feeding gaseous chlorine to carbon ore agitators. LABOR, TONSIMAN SHIFT: See detailed data sheet ILL BUILDING DESCRIPTION: Framed structural steel with sandwich type walls of marine plywood, then packaged pre - fabricated insulation and outer sheeting of galvanized corrugated steel.

Jan 1, 1975

By David B. Reger

New discoveries of gas in the southern counties featured the petroleum industry in West Virginia during 194;. Drilling for oil increased slightly over 1944 and a small increase of initial production resulted. Out of 28 wildcats drilled, there were 16 gas discoveries and 12 dry holes. No commercial oil was found in the 28 wells.

Jan 1, 1946

By Paul M. Tyler

ROUGHLY one-half the value of mineral products at mines or quarries must be spent for wages. In view of the steady increase in hourly wages that continued for several decades prior to the onslaught of the recent depression, it is perhaps surprising to discover that labor's share of the gross proceeds of the mining and quarrying industries of the United States declined to 46.8 per cent in 1929, compared with 52.2 per cent in 1919 and 53.2 per cent in 1909. The actual percentages vary in different branches of the industry and in different localities but the downward trend is unmistakable. For the period 1909 to 1919 it was quite marked in every industry and from 1919 to 1929 it was apparent in all but six: namely, gold and silver lode mining, placer gold mining, crude gypsum production, marble quarrying, asbestos production, and fluorspar Tninino mining

Jan 1, 1933

By Arthur Bell

(San Francisco Meeting, September, 1915) . PRIOR to 1908 the oil production in the State of California, had been almost entirely a heavy fuel, oil, with a high flash point, hut changed within a-short period to a large percentage of refining oil with a low flash, by reason of the coming in of the Santa Maria field, the Midway field, and the increased production of the Fullerton field. This is clearly shown in the following tabulation of California's production: Year Barrels . Below -20° Be, Above 20° Be,, Per Cent_ Per Cent. 1905 48,307,000 90 10 1910 77,698,000 SO 20 1912 90,075,000 6o 31 1914 10:3,600,000 47 53 The bringing in of these high percentage's of light oil with their dangerous low flash and the increasing demand for the refined products necessitated the devising of some cheap and efficient means of quickly separating the lighter elements either in the field or at the main distributing points; also it became necessary to remove the excessive percentage of water which many of the light oils carried in emulsion.

Jan 9, 1915

By Thomas V. Falkie

Mining and exploration, in the year 1971, can be characterized as a year of politics and the beginning of an era of legislation. Certainly the activities of our state and federal lawmakers and international politicians over-shadowed technical developments, which are outlined in the following pages. The nationalization of the Chilean copper industry was the most far-reaching event of the year. Not only will it have an effect on international metal trade, but the nationalization will also affect the major mining companies in such a way as to cause strategic, managerial and technical adjustments in metal mining and exploration efforts in other parts of the world.

Jan 2, 1972

By N. E. Maccallum

(Cleveland Meeting, October, 1912.) ALMOST half a century has passed since the Siemens brothers, after tedious and costly experiments, finally began the manufacture of open-hearth steel. The furnace of that time was very small, having a hearth-capacity of from 3 to 4 tons, and we can appreciate the wonderful development that has taken place in those 50 years by the knowledge that to-day furnaces of 50 times the original capacity are in operation. As the new steel process assumed importance, and furnaces began to grow in number and in size, a question arose, to which no satisfactory answer has ever been given, and that was: ?What is the safe and economical limit of the open-hearth furnace?" Various stopping-places have been suggested, and 20, 30, 40, and 50 tons have each been advocated, but all such arbitrary restrictions have been passed, and 60 tons would probably represent the average furnace, although in a few instances from 70 to 80 tons are regularly tapped into one ladle. The furnaces which are the subject of the present paper have gone far beyond even these limits, and since, in my opinion, they mark another step in the progress of open-hearth steel, they will be considered fairly and frankly, in order that those to whom the matter may be of interest may be able to judge and form their own Conclusions. Short accounts of the work of these furnaces have appeared from time to time in various technical journals, of which the following is a brief résumé. These furnaces are the property of the Phoenix Iron Co., of Phoenixville, Pa., and their distinctive and important feature is, that they charge to twice the capacity of one ladle, and tap simultaneously into two ladles, with a device for controlling the flow into either. In this way the capacity of the furnace is not limited, as formerly, but heats of any size within the capacity of two ladles may be charged.

Oct 1, 1912

By AIME AIME

MODERN metallurgy is an art and a science. The art is process metallurgy-extracting metals from their ores, refining them, and alloying them with one another and with certain nonmetals to produce thereby a variety of metallic materials which, owing to a wide range of useful properties, are for many purposes more valuable to man than the individual metals themselves; process metallurgy also includes shaping or otherwise treating metals and alloys to form objects useful to a complex industrial world. The science is physical metallurgy-organized knowledge of the constitution and internal structure of metals and alloys, of the relation of their composition and structure to properties, and of the laws, theories, and hypotheses that purport to explain this relation.

Jan 1, 1942

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of April, 1913: BARNES, BLAKESLEE, Min. Engr Burrwood, La. BOYLSTON, HERBERT M., Cons. Met. Engr 26 Abbot Bldg., Cambridge, Mass. BUEHLER, HENRY A., State Geol Rolla, Mo. CASTO, WILLIAM H., JR., Mining Bonanza, Idaho. COHEN, MAXWELL B., Mill Operator Miami, Ariz. EVANS, MILTON R., Shop Draftsman 92 Division St., Kingston, Pa. HARPER, WALTER S., Asst. Treas 42 Broadway, New York, N. Y. JAMES. JAMES S.. Min. Engr Telluride. Colo.

Jan 5, 1913

* Kennecott Copper Corp. gets Charles R. Cox as president on Jan. 1. Mr. Cox is resigning his position as president of Carnegie-Illinois to take the new post with Kennecott, left vacant by the death of Mr. Stannard in September. •The ECA signed a contract in December to advance X3,600,000 to Newmont Mining Corp. to aid development of lead and zinc mines in French Morocco. The funds are to be repaid in lead and zinc for the United States' stockpile over a period of seven years. The mines are owned by the Societe des Mines de Zellidja, with which organization Newmont is associated. • Under the direction of John M. Brooks, Jr., general manager, the Matahambra mine in Cuba, will probably produce sufficient tonnage to make 4 million lb of copper per month during 1950. The grade is presently running between 7 and 10 pet. •S. H. Ash reports that the fatality rate per million-man-hr for the anthracite industry for 1949, through November, is 0.78. This is 15 pct better than that achieved during 1948, which was the lowest fatal injury rate in coal mining history. The first full year on record without a major disaster was recorded in 1949 (p. 34). •The Atomic Energy Commission has authorized the production of 200 lb of uranium metal for use under AEC license in non-Commission research projects. •A national survey of projected 1950 purchases of new machine tools, machine tool accessories, materials handling equipment, etc., just completed by the American Society of Tool Engineers reveals that, of the companies reporting, 80 pct state that they plan to buy either more equipment or the same amount as in 1948. • Armour Research Foundation is conducting investigations for the use of clay and shale deposits to make lightweight aggregates. The material is heated until it expands and forms material suitable for mixing with cement which it is hoped will be lighter, stronger, have better insulating qualities and will lower the cost of concrete. •In the first six months of 1949 the bituminous coal miners' average hourly earnings were $1.94 -as compared with X1.392_ national average for all manufacturing. Average annual earnings of full-time employees in the bituminous coal mines in 1948 were $3387 as compared with $2809 for all industry. •LaSalle Business Bulletin reports: "year ends on a rising trend in industry and trade ... nearly record-breaking demand from almost all sources keeps business high... most indicators but little below postwar peak... forces keeping activity high arestill powerful--changes in general business conditions likely to be slow and moderate." •Office of Internal Trade of the Commerce Department requests that technical data significant to the national security which is to be sent outside of the United States be submitted to it for an official opinion on the desirability of transmitting such information. This voluntary compliance program is part of our national security control. • Blast furnace slag reduced to 12 to 16 mesh is being used for sanding track at the Mont Coal mines of Armco. The slag replaces silica sand which caused silicosis. It has proved so effective and cheap that tests are being made to use the slag for rock dusting.

Jan 1, 1950

By AIME AIME

MONDAY, Feb. 21, evokes memories of the Silver Corridor at the Waldorf to be recalled and reflected upon for time to come when thoughts drift to the Annual Meeting of 1944. Crowded though it was, on occasion there lurked in the mind's eye a vision of what might have been had the 2886 persons who put in an appearance at one time or another milled around in the lobby of 29 West 39th Street. Some confusion resulted from difficulty in locating meeting rooms, but for the most part everyone found what he wanted. The usual bulletin board of members registered was missing this year and rumor has it that tile Waldorf didn't approve. Registration broke all previous records with many a busy engineer realizing that the program had something to offer that would be of use in his particular job. It might be noted here that "Arpad" co-operated nicely, previewing spring days on Monday, Wednesday, and Thursday; Tuesday was a bit damp.

Jan 1, 1944

By Walter S. Weeks

In this paper the effect of natural ventilation pressures is considered a part of the mine resistance and it is shown that their effect on the mine resistance is not the same as the total natural ventilation pressure of the shafts if the mine has several levels. It is shown that increasing the fan pressure causes the division of the air to approach the condition that would obtain if there were no natural ventilation pressure present. It is shown that if an appreciable difference in pressure is maintained between the beginning and end of a group of splits, the value of the integrated effect of the natural ventilation pressures on the individual splits does not change substantially with moderate changes of this pressure. A method is outlined for determining the resistance factor of the mine and the value of the effect of natural ventilation with the fan operating; also a method for determining this factor when circulation is caused by natural ventilation alone. Natural Ventilation Pressure Natural ventilation pressure (N.V.P.) is caused by the difference in weight of the air in two similar columns between two horizontal planes, and the difference in weight is caused principally by the difference in temperature of the two columns. The fan pressure causes some variation in density, but, since it is usually small and affects both columns, its effect is relatively unimportant. It has been suggested that "N.V.P." be called "stack effect"; but, since the term N.V.P. was used in a previous Institute paper,' applied in exactly the same manner, the term will be used. Frictional Resistance The frictional resistance to flow in a mine without natural ventilation may be expressed as RQ2 where R is a constant for a given air density and Q is the rate of flow. This frictional resistance plus the effect of velocity changes will be called the F pressure (F.P.) and a curve of F.P. against Q, the F characteristic of the mine. If a pressure is applied to a mine by a fan, the air flow so adjusts itself that the drop in pressure through any path from entrance to exit of mine, due to frictional resistances and velocity changes, is the same as that in any other path. The mine resistance varies as the square of the quantity. The air distribution without N.V.P. will be called "normal." Natural Ventilation Present When N.V.P. is irregularly distributed in a mine, it is more convenient in analysis to consider the N.V.P. as a part of the duct resistance. If it is so considered the resistance no longer varies as the square of the quantity, and if N.V.P. exists between levels the distribution of the air is no longer normal. The total N.V.P. of the mine is the pressure caused by the full length of the shafts. If a mine has several levels, N.V.P. exists

Jan 1, 1946

By Walter S. Weeks

IN this paper the effect of natural ventilation pressures is considered a part of the mine resistance and it is shown that their effect on the mine resistance is not the same as the total natural ventilation pressure of the shafts if the mine has several levels. It is shown that increasing the fan pressure causes the division of the air to approach the condition that would obtain if there were no natural ventilation pressure present. It is shown that if an appreciable difference in pressure is maintained between the beginning and end of a group of splits, the value of the integrated effect of the natural ventilation pressures on the individual splits does not change substantially with moderate changes of this pressure. A method is outlined for determining the resistance factor of the mine and the value of the effect of natural ventilation with the fan operating; also a method for determining this factor when circulation is caused by natural ventilation alone. NATURAL VENTILATION PRESSURE Natural ventilation pressure (N.V.P.) is caused by the difference in weight of the air in two similar columns between two horizontal planes, and the difference in weight is caused principally by the difference in temperature of the two columns. The fan pressure causes some variation in density, but, since it is usually small and affects both columns, its effect is relatively unimportant. It has been suggested that "N.V.P." be called "stack effect"; but, since the term N.V.P. was used in a previous Institute paper,' applied in exactly the same manner, the term will be used. FRICTIONAL RESISTANCE The frictional resistance to flow in a mine without natural ventilation may be expressed as RQ2 where R is a constant for a given air density and Q is the rate of flow. This frictional resistance plus the effect of velocity changes will be called the F pressure (F.P.) and a curve of F.P. against Q, the F characteristic of the mine. If a pressure is applied to a mine by a fan, the air flow so adjusts itself that the drop in pressure through any path from entrance to exit of mine, due to frictional resistances and velocity changes, is the same as that in any other path. The mine resistance varies as the square of the quantity. The air distribution without N.V.P. will be called "normal." NATURAL VENTILATION PRESENT When N.V.P. is irregularly distributed in a mine, it is more convenient in analysis to consider the N.V.P. as a part of the duct resistance. If it is so considered the resistance no longer varies as the square of the quantity, and if N.V.P. exists between levels the distribution of the air is no longer normal. The total N.V.P. of the mine is the pressure caused by the full length of the shafts. If a mine has several levels, N.V.P. exists

Jan 1, 1944

By RUSSELL C. FLEMING

THE important advances that have been made of recent years in mining and milling methods and in mechanical equipment at mines need no re- telling, but there has been a remarkable growth in one type of equipment which has gone nearly unnoticed. That is the increasing use of storage-battery locomotives underground. Since the war the number of these locomotives and their field of use have increased tremendously; their growing acceptance represents an al- most complete reversal of opinion from an earlier period when they were generally looked upon as in- adequate for the strain of mine service. At the time when storage-battery powered units were first making their bid for recognition, the use of power in haulage had already passed through several phases; hand tramming, rope haulage, compressed air locomotives, even gasoline locomotives, had all been used, ending finally in the general adoption of the electric trolley locomotive for practically all power-haulage requirements. It was, and is, conceded that the trolley loco- motive met more adequately the varied and severe conditions of mine service than any previous type of haul- age unit. Subsequent developments have had to endure comparison and surpass in performance that type of haulage before changes would be considered.

Jan 1, 1930

By R. G. Charles, E. A. Gulbransen, S. Barnartt

KINETICS of the reaction of zirconium with pure oxygen at elevated temperatures have been studied by several workers for periods of time up to 6 hr.1-1 In two cases,3-4 . the experimental values of oxygen uptake, w, as a function of time, t, were best fitted to the parabolic rate law w2 = kPt + constant. In others,3,4 the cubic rate law w3 = kot + constant, showed better agreement. The most recent data of Gulbransen and Andrew4 indicate that the choice between the parabolic and cubic laws for empirical representation of the data will often be arbitrary. This is particularly true if the first few minutes of the reaction with a clean zirconium surface is attributed to a different oxidation mechanism, for deviations from either rate law were found primarily during the initial period. Thus, the kinetics of this reaction have been too uncertain to permit safe extrapolation to oxidation periods of practical interest (many hundreds of hours). The data to be described are of interest, for they indicate that the cubic rate law applies over long oxidation times. The reaction of zirconium with oxygen at 1 atm pressure was followed at 350" and 450°C for 500 and 200 hr, respectively. Abraded test specimens of pure zirconium sheet' 3.0 X 2.0 X 0.012 cm in size were oxidized by the procedure previously described,3 which included periodic cooling to room temperature for weighing. The surfaces were polished to a 4/0 finish using polishing paper wet with kerosene, then wiped with petroleum ether and washed in redistilled acetone. Fig. 1 shows plots of log ? vs log t. Each curve represents the average of duplicate measurements, and deviations from the average were generally less than 3 pet. The cubic rate law (slope = 1/3) is closely followed. The rate constants, 5.2, x 10 -6 and 2.4, X 10- (mg cm-2)3 per hr at 350" and 450 oC, respectively, are plotted as log k, vs 1/T in Fig. 2, together with cubic constants calculated from the data of Gulbransen and Andrew4 for abraded specimens from the same lot of zirconium. Their data refer to runs of 6-hr duration at a pressure of 0.1 atm 0 and under conditions of uninterrupted heating. In spite of these differences, the latter data yield a straight line which appears to apply equally well to the new extended time data. The energy of activation for the oxidation process, calculated from the slope of this line, i.s 38 keal per mole. This may be compared with the value of 47 keal per mole found by Belle and Mallett3 at higher temperatures. It may be concluded tentatively that extrapolation of short-term oxidation data for zirconium to obtain the long-term behavior is best done through the cubic equation ?3 = kpt + constant. References ' E. A. Gulbransen and K. F. Andrew: AIME Trans., 1949, vol. 185, p. A.515; JouRNal OF Metals, August 1949. 'D.p. Cubicciotti Journal Amer Chemical August1949.Soc., 1950, Vol. 72, P. 3 V. Belle and M. W. Mallett: Joulnal Electro chemical Soc., 1954, ' E. A. Gulbransen 339.and K. F. Andrew: Oxidation of Zirconium Between 400" Gulbransenand 800'C.and AIME Trarzs.. 1957, vol. 209, p. 394; JOUR-Nal of Metals, April 1957. IS Barnartt, B G. Charles, and E. A. Gulbransen: Oxidation of 50 weight pet uranium-zirconium alloy, Journul Electrochemical SOC., 1957, vol. 104, p. 218.

Jan 1, 1959

By N. Cabrera

IN a recent paper Kuczynski' studied the rate at which the crack between a metallic plane and a spherical particle of the same material is filled up gradually when heated at temperatures near the melting point. If x is the radius of contact between plane and sphere (fig. I), Kuczynski shows experimentally that x5 = At [1] where t is the time. Assuming that the mechanism of transport of matter is the volume diffusion of vacant lattice sites, he is also able to prove Eq 1 theoretically. The constant A contains as a factor the self-diffusion coefficient of the metal and he shows that the values for this coefficient deduced from his experiments yield the same activation energy as that calculated by other methods, which is a confirmation of this point of view. Kuczynski has also considered theoretically the law of growth of x which would be expected if surface diffusion were the important mechanism. He suggests that x should then obey a law of the form x7 = At, and claims to be able to decide the mechanism involved from the observed law of growth., The purpose of this note is to prove this incorrect. On the contrary, when the mechanism is surface diffusion Eq 1 is also obeyed, but with a different constant A. Following Kuczynski, we suppose the bottom of the crack (surface A A) to have an average radius of curvature p. As a result of this curvature the concentration of adsorbed atoms in this surface, n(p) per cm2, will be smaller, and the concentration of vacant lattice sites in the neighborhood, N(p) per cm3, will be larger than the corresponding concentrations, n(w) and N(w), for a flat surface. For all practical cases we can write Thomson's formula in the form n(co)— n(P) N(P)—N(cc) _ 2a-a" n(oo) JV(co) kTp [2] where u is the surface energy of the metal and a the interatomic distance. 1. Let us now consider the mechanism of surface diffusion. We suppose the concentration of ad-

Jan 1, 1951