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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 JAMES GAYLE

(Presented at the Washington meeting, May 3, 1905, and simultaneously sent to the Iron and Steel Institute, for presentation at the meeting of that Society in London, May 11, 1905.) IT is to be regretted that the data respecting the use of dry-air blast, which was presented to the Iron and Steel Institute at its meeting in the United States, in October, 1904, should. have been restricted to the period from August 25th to September 9th inclusive, and from September 17th to 30th inclusive. In order to present the paper at all it was found necessary to limit the record of operations to the period above stated. In the discussion of the paper it would appear from the conclusions of some participating therein, that they have been placed at some disadvantage in considering the economies obtained through the use of dry-air blast, by reason of the data covering such a short period. It is the purpose of this communication to present in detail the record of operations of the Isabella Furnaces from November, 1904, to March, 1905, inclusive, as shown by the furnace-records. The month of October, 1904, is not included, as the furnace using dry-air blast was stopped several times for repairs, and while the record was a very good one considering these interruptions, yet it was not a continuous one. The record for Furnace No. 1 using dry-air blast, and the comparison with Furnace No. 3 using natural air for the month of November, 1904, is set forth in Table I. By a reference to my former paper it will be noted that the month of November is the beginning in this country of the winter period, when the atmosphere decreases rapidly in humidity. The month of October being the transition month in the autumn and April in the spring, and furnaces using natural air approach more closely, from November on, to the conditions obtained by the use of dry-air blast. The data given in

Jul 1, 1905

By C. P. Sandberg

INTRODUCTION. NOTWITHSTANDING the growing importance of this subject, no work specially devoted to it has hitherto been published. Having had to inspect during the last twenty years nearly a million tons of iron and steel rails for various countries, I have obtained experience of what rail manufacturers can practically execute, as well as of what railway engineers practically require. Bearing these two points in mind, I have from time to time published observations with a view to unite both interests, -that of the producer and that of the consumer,-and to reduce the specifications and the forms of sections to standards, or types, in order to facilitate the execution of the works and to improve the construction of permanent way. The Swedish government railways, as well as private companies owning railways in Sweden, Norway, and Denmark, have during the time above mentioned consulted with me and intrusted to me their rail inspection. I therefore owe to these countries much of the opportunity which I have enjoyed of gaining experience and position. Next to Sweden, America is the country which has most liberally favored me with its confidence in placing these matters in my hands. Through circumstances not under my control there has been little exportation to, and less work done by Europe for, America during the last six years ; but the recent revival of the rail trade has been the more gratifying to me, seeing that almost all the importers of American rails are still specifying for the Sandberg rail sections and inspection. It is therefore with .feelings of gratitude that I now beg to lay before the American Institute of Mining Engineers, and I hope, through that body, before the American railway world, the results of some experience which I have gained in the execution of work for their country, and which therefore belongs rightfully to

Jan 1, 1881

The industrial might of the Bowen Basin is primarily the result of Utah Development Co.'s work- which has opened up the Blackwater, Goonyella, Peak Downs, and Saraji mines; built the Hay Point port; and is now developing the Norwich Park mine.

Jan 1, 1977

By Peter K. Strangway

During 1973, a 20,000 net ton (18 100 metric ton) formcoke test was carried out at Inland's 26.5-foot (8.08-meter) hearth diameter on NO. 5 Blast Furnace. The formcoke briquettes were produced from Elko1 coal by FMC at their pilot plant in Kemmerer, Wyoming. The briquettes were shipped to Inland in open railroad cars and most of them were placed in an outside storage field until a sufficient amount was available for the actual blast furnace test. The test consisted of three phases: an initial four-week base period; the actual 33-day formcoke test period; and a final three-week post-test base period. During the formcoke test period, the regular coke skip loads were gradually replaced with skips of formcoke until, after a three-week period, the replacement ratio reached 80%. The furnace operated smoothly and quality hot metal was produced. The burden remained permeable and it was possible to maintain wind rates 9 of over 100,000 scfm (47 Nm3/s) without significant blast pressure increases. Dusting from the formcoke was not a problem either in the stockhouse or in the top gas. The formcoke briquettes maintained their original shape and density as they descended through the furnace. When the 80 percent replacement level had been reached, the inwall temperatures became higher than normal (about 2000 ºF (1090 ºC)) and followed an unusual steady pattern. In addition, the top gas temperature became higher than normal, and the hot metal analyses and temperatures began to fluctuate unacceptably. In general, it is felt that the high inwall temperatures were a result of channeling of the hot furnace gases along the stack walls. This channeling appears to have been promoted by a change in distribution of the burden in the top of the furnace which, undoubtedly, was caused by the increased increments of formcoke. Since it was felt to be unsafe to operate the furnace for an extended period of time with the inwall temperatures at the high level, a decision was made to remove the formcoke from the furnace. When this was done, the inwall temperatures returned to normal. Once the inwall temperatures had returned to normal, the remaining 3,800 net tons (3450 metric tons) of formcoke were used in the furnace at a nominal 40% replacement level for five continuous days. The furnace operated smoothly during this period, and the results were representative of satisfactory furnace operation with partial replacement of regular coke with formcoke. The test was successful in proving that formcoke can replace up to about 50% of the regular coke in a large furnace operating at high wind rates. However, additional work will be required to develop acceptable charging practices for using higher levels of formcoke replacement.

Jan 1, 1977

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 ALFRED KAUFFMAN

NO matter what position we hold, workman, foreman, superintendent, manager, president, or what not, let us fail to give or to make good products, then see how quickly we'll be called to account for- our work by the buying public. The waves of progress taught us that millions were wasted in unnecessary strikes-we also learned that many losses were due to neglect on the part of manufacturers to give the same consideration and attention to the human element of their factory as they gave to their machinery. The employees learned also that the employer was their agent who found purchasers for the product of their labor. So between the two we learned that many years of labor were needed in order for a worker to recover his wasted savings, or for the manu¬facturer to replenish his loss. Treat 'em rough, and tell 'em nothing, was not very far from the true relationship between management and employees in manufacturing plants in the early days. Today just exactly the opposite views are held by executives whose function is the handling of employees. Men today want to know what it is all about. They are intelligent enough to comprehend the facts, and to use them constructively, and it is good business to give them the information.

Jan 1, 1929

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By Thomas Read

IN speaking of immaterial problems of industry I am using the word immaterial in its original sense, not consisting of matter; not in its derived sense, unimportant. There is nothing of a paradox in saying that immaterial problems are the most important in human life, for His a matter of everyday observation that much of the news in the daily papers, and most of the world's best literature and drama, deal with human conduct that has for its motive forces that are but little concerned with material things. The engineer's preoccupation with physical forces, in extending his control over them, has not blinded him to the impor-tance of forces that, for want of a better word, I call immaterial; but he has considered that dealing with the one is his job and the other is not. All the evidence of the past decade indicates that the latter are so in-extricably interwoven with the former in modern in-dustrial life that the engineer will have to concern himself with them whether he wants to or not. Some of the most important of the problems arising from the action of these forces relate to the mental hygiene of the workers in industry. Mental hygiene in industry was concisely defined, in terms of the best present knowledge, by Dr. C. Macfie Campbell, speaking last April before the executive com-mittee of the Associated Industries of Massachusetts, and as his statement can scarcely be bettered, I quote it below: "The term mental hygiene is apt to appear vague. The actual stuff with which mental hygiene deals may be briefly reviewed.

Jan 9, 1927

By Ernest F. Burchard

PAGE. I. Introduction,........... 75 II. Outline of the Geology......... 76 1. Stratigraphy............ 76 A. Clinton Formation........ 77 2. Structure...........82 3. The Ore..........85 A. Character............ 85 B. Geographic Distribution....88 III. Local Descriptions........... 88 1. Birmingham District.......... 88 A. Topography and Its Relation to Industrial Development... 88 H. Distribution and Structure of Formations.... 89 C. Divisions of the Birmingham District. 95 Division A (Description of the Ore-Beds), . 95 Division B.........105 Division C.......... 106 Division D,..107 Division E,...........108 Division F........ 111 Division C.......... 112 D. Mining .Development.... 113 2. Northeast Alabama........114 IV. Possible Origin oF the Ore......... 119 V. Relation of Origin to Quality and Extent of Ore... 122 VI. Estimates of Ore-Reserves,......... 125 1. Method of Making Estimates......... 125 2. Data and Results....126 VII. Production and Consumption oF IRon-ORe,.... 132 I. Introduction. Brief and interrupted studies of the Alabama Clinton iron-ores have been made within the last four years by members of the IT. S. Geological Survey. Reports on the progress of this

Jan 1, 1910

By P. W. Bridgman

DURING the war, the Navy undertook the construction, under my direction, of an experimental gun embodying features designed to lessen the cost and time of production. These experiments were initiated after representations as to their, desirability had been offered by myself, by the Naval Consulting Board, and by the National Research Council. The first drawings were made in June, 1917, and the experiment was completed in November, 1918. For the sake of clearness it will pay to recapitulate briefly the fundamental idea of gun construction. It is well known that if a hollow cylinder is subjected to internal fluid pressure, the maximum stress occurs in the inside layers, the outer parts carrying much less than their due share of the stress. This inequality of stress is more pronounced the thicker the walls of the cylinder. If such a cylinder is pushed to the elastic limit, failure in elasticity will take place long before the outer layers have reached the limit of their capacity. Economical use of the material would demand, however, that all parts of the cylinder reach the limits of their capacity simultaneously. This may be brought about, at least in cylinders of not too great thickness, by producing in. the inner layers an initial compression, and in the outer layers an initial tension. The effect of internal pressure is at, first to relieve the compression of the inside layers, while increasing the tension of the outside layers. If the initial stresses are properly distributed, all parts of the cylinder will reach their elastic limits simultaneously, thus giving a cylinder of maximum strength for its weight. In gun construction as hitherto practiced, this initial distribution of stress is produced either by winding the inner tube with wire, a common English practice, or by shrinking hoops over the inner tube, which has been the standard American practice. Either process is long and expensive, particularly with the larger guns, 12- or 14-in., which require

Jan 2, 1920

By C. M. Weld

(Cleveland Meeting, October, 1912.) IN the course of my professional work in China during the fall of 1907, I had an opportunity to visit the iron-ore mines at Ta-yeh in Hu-pei province (long. 114° 50' E., lat. 30° 20' N.). It occurs to me that a rescript and discussion of my notes taken at that time should be of interest, particularly as supplementing the exceedingly interesting recent paper-of Thomas T: Read on The Mineral Production and Resources of China.1 Ta-yeh is situated near the right bank of the Yangtze river. The mines are at an average distance of about 16 miles from the river-port Shi-hui-yao, which in turn is some 70 miles S-E. of Hankow. The ores are shipped to the works of the Han-Yeh-P'ing Iron & Coal Co. at Hanyang, as also very largely to the Japanese government iron- and steel-works at Wakamatsu, Japan. Smaller quantities have been exported to the Pacific coast of the United States. These ore-deposits have been briefly noticed in a number of publications, but, so far as I know, Mr. Read's description, in his chapter on the iron-ores of the Chinese Empire,2 contains the first attempt to define their geological character. In his more recent paper Mr. Read follows very closely the text of his earlier description. To quote briefly from the recent paper, he says : " The iron-ores at Ta-yeh . . . . lie along the contact between a marble and an intrusive body of a dark-gray syenitic rock." He refers to a figure which exhibits in plan, but not in section, the relative positions of the syenite, ore-bodies, and limestone. The contact is seen to trend approximately E-W., with the syenite on the north and the limestone on the south. " The syenite lies to the north of the marble, and a few miles farther north the marble again' appears, iron-ore again being present along the contact." No litho- 1 Bulletin Bulletin No. 63, March, 1912, pp. 293 to 343. 2 The Iron Ore Resources of the World', vol. ii., p. 913 (Stockholm 1910).

Oct 1, 1912

By Lawrence Wright

ON the steep slopes of the Kootenays, 15 to 20 miles south of Nelson, B. C., are a number of ore occurrences (Fig. 1). One that has many features of mining and geological interest is the Ymir Yankee Girl Gold Mines Limited. Discovery of this property was made in 1899 at an outcrop on the hillside, some 2500 ft. above the village of Ymir. This proved to be a branch vein 20 ft. long leading to two main veins, the Yankee Girl and the Spur (Fig. 5). The ore pattern as now delimited shows a remarkable increase in ore area with depth below the outcrop. This recent development is of interest particularly in view of the fact that the property was nearly con-demned, professionally. Another interesting feature, which has a bearing upon its history, is the persistent excess of tonnage produced from period to period over visible reserves. This is not ascribed to lagging mine development, but to detailed vein characteristics, which we will endeavor to make clear by giving a description of the veins and their surroundings.

Jan 1, 1938

Jan 1, 1926

RESOLUTION ADOPTED BY THE BOARD OF DIRECTORS AT ITS MEETING ON APRIL 17, 1936 Recognizing the fact that the problems of the committee named by the Board to prepare the " official ticket" for officers and Directors of the Institute are various and difficult; and desiring to assist this committee by setting forth some of the principles that should guide the committee and some of the qualifications that should be required of candidates, the following instructions are formulated and the Secretary is directed to publish them in MINING AND METALLURGY concurrently with the publication of the names of each newly appointed Nominating Committee and to send a copy to each member of the Committee. NOMINATIONS TO BE MADE Each year the Nominating Committee is to select "official" candidates for eight places, as follows: (1) President and Director (2) Vice-President and Director (3) Vice-President and Director (4) Director (5) Director (6) Director (7) Director (8) Director GEOGRAPHICAL DISTRIBUTION The Bylaws provide that "the Nominating Committee shall, so far as practicable, distribute representation on the Board geographically." Pursuant to this provision, the United States, Canada and Mexico have been divided into fifteen districts, as shown on the official map.* Districts 1, 5, 6, 10, 11, 12,13,14, and 15 are assigned one Directorship each; District 2, three Directorships; District 3, eight Directorships; District 4, two Directorships; and Districts 7, 8, and 9, two Directorships between them. It will be the duty of the Nominating Committee to make selections that will give effect to this allocation of Directorships. There is nothing to prevent a Director being named to succeed himself. Attention is called to the: fact that many Institute members now resident in New York formerly lived in the West, South, or North and still have intimate business connections that compel them to visit various parts of the country periodically. Such men are particularly valuable as Directors and their nomination and election tends to minimize the objection that a large number of Directors reside in New York.

Jan 1, 1940

By Ernst F. Eurich

(Cleveland Meeting, October, 1912.) ALEXANDER PARKES patented in England in 1851-52-53 a process for desilvering lead by means of zinc, making use of the greater affinity of silver for zinc than for lead, discovered by Karsten in 1842. The efforts in England to develop it commercially were not particularly successful, nor was the attempted introduction into the United States. This last was not surprising, as it was about the beginning of our Civil War, and at that period there was very little lead-bullion produced in the united States and there was no field for the process here. There was at that time on Staten Island an establishment that pattisonized lead, probably from Rossie, N. Y., and Chester, Pa., and possibly some Spanish lead, but the production of lead-bullion in the Far West had not yet begun. In 1864, Edward Balbach, of Newark, N. J., patented in this country a process for desilvering lead by means of zinc, and in 1867 Edward Balbach, Jr., patented a " movable black-lead retort with a neck, placed in a furnace," for the purpose of distilling the alloy of zinc, lead, and the precious metals. A brief comparison of the Parkes and the Balbach processes is interesting. The Parkes process as practiced in England consisted in stirring into silver-bearing lead, melted in a kettle, from 1 to 2 per cent. of zinc, cooling, skimming the alloy of lead, zinc, and silver that rose to the surface, liquating it in an iron retort, distilling the residual rich alloy in fire-clay retorts, thus regaining the zinc, and refining the desilvered lead at a low heat in a shallow cast-iron pan that formed the hearth of a reverberatory furnace. If the lead was too impure, it was first softened * Presented also at the Joint Meeting of the Institute and Section IIIa, Metal¬lurgy and Mining, of the Eighth International Congress of Applied Chemistry, New York, September, 1919, and here published by mutual agreement.

Dec 1, 1912

By E. S. Machlin

The possibility that formation of voids under creep-rupture conditions may take place by the condensation of vacancies has been investigated theoretically. It has been concluded that nucleation of voids under creep-rupture conditions by vacancy condensation is highly improbable. However, growth of pre-existant voids by vacancy condensation is probable. A number of predictions made in this theory have been verified by the data. It has been predicted and checked that the product of rupture life and steady-state creep rate for preannealed metals and single phase alloys is an approximately invariant quantity, independent of stress, temperature, and atomic number for a given type structure. The direction of the effect of cold work on this product has been predicted and found in agreement with experiment. A number of experiments to evaluate the vacancy condensation mechanism further are described. SEVERAL papers have appeared recently which speculate on the origin of voids formed at grain boundaries under stress.' ' The object of this paper is to examine quantitatively the proposition that the voids produced in a creep test are a result of vacancy condensation. A result of this paper is a theory of creep-rupture. Void Nucleation Application of standard nucleation theory" to the problem of void nucleation leads to the following conclusions: 1—Homogeneous nucleation of voids requires a supersaturation ratio (concentration of vacancies in supersaturated to that in saturated solution) of 400 for a reasonable surface energy of 1000 erg per cm-and 1.4 for the improbably low surface energy of 10 erg per cm. 2—Heterogeneous nucleation of voids at plane interfaces between two phases requires a supersaturation ratio of 2.5 for a typical contact angle of 145 3-—Void nucleation about a solid particle may be accomplished at a supersaturation ratio of 1.17 for a typical value of work of adhesion? of 60 erg per The work of adhesion is the surface work 10 replace two solid-vauor surfaces by a solid-solid interface. enr ' between an oxide and a metal in the presence of a surface active element such as sulphur. Estimates of the supersaturation ratio at which voids are produced in diffusion experiments yield a maximum of 1.01. Inasmuch as the foregoing mechanisms of void nucleation probably will not operate at this level—too low a surface energy is required—the investigatol. is led to the conclusion that voids must already exist. That is, nucleation of voids probably does not occur. Rather, existing submicroscopic voids grow out to visible size. Already existing voids might be produced during solidification or working. Supercritical sized parlicles which contain cracks may act as heterogeneous void nuclei. Gas pockets may act as void nuclei. Experiments are desired to determine the nature of the heterogeneous void nuclei which grow out to voids in both diffusion and creep experiments. Void Growth Void growth might occur in at least two possible ways, depending upon whether the already existing void nuclei are at grain boundaries or within the grains. In the case of a spherical void far from a crystal boundary, vacancies are generated during creep as a consequence of the migration of suitable dislocation jogs' and are also annihilated at sinks. Under these conditions, a steady-state concentration of vacancies is built up in the crystal, defined by the condition that for any differential volume the rate of generation of vacancies in that volume equals the rate of annihilation of those vacancies." This equality would lead to the development of a gradient of vacancy concentration radially outward from the void surface up to a radius where the vacancy lifetime becomes equal for all directions of vacancy migration. The distance over which this vacancy concentration gradient extends equals about 2vD,T* where D, is the vacancy diffusivity and T:' the vacancy lifetime in a crystal outside the gradient in a zone of constant vacancy concentration. The vacancies generated in the region over which the gradient exists will annihilate more often at the void than elsewhere. Approximately a little over one-half the vacancies generated in the gradient zone will annihilate at the void. Hence, the growth rate of the void is given by on where R is the radius of void in centimeters, is the atomic volume, and R is the rate of generation of vacancies, number per centimeter" per second. R D and T* may be estimated in terms of other physical parameters." In particular, R = n.j e/b [3] where n is the average number of vacancy produc-

Jan 1, 1957