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By F. B. Plummer

PETROLEUM ENGINEERING deals with the production, transportation, and refining of crude oil. Refining is chiefly the work of the chemical engineer; production, that of the petroleum engineer. Production engineering only is discussed in this paper. Petroleum production engineering is closest related to and, in fact, is a branch of mining engineering. Formerly, many petroleum engineers were trained as mining engineers or mining geologists. The profession is related also to mechanical and civil engineering to about the same extent that mining engineering is. Petroleum production draws upon the mechanical branch for drilling and pumping machinery and upon civil engineering for the construction of transportation lines, water supplies, and water-disposal plants. Fundamentally, petroleum production engineering deals with the removal of the oil from the reservoir rocks, just as mining is concerned with the removal of ore. The process of oil production demands a specialized knowledge just as distinct from mechanical and civil engineering as mining is distinct from operating a Diesel engine. Even though the chief tools of the petroleum engineer are the drill and the pump, these may be of little avail, and certainly not efficient, if their selection and use is not based on a knowledge of the physical chemistry of oil, the geology of the formations, the structure of the oil sand, the hydrodynamics of the reservoir, and the interrelation of all these many factors.

Jan 1, 1936

By William H. Shockley

[SECRETARY'S ]NOTE.-The following notes, arranged and edited in this office, but not yet revised by the author, were placed at my disposal with much modest hesitation (due to their incomplete and fragmentary character), upon my earnest request, and my argument that such recent and trustworthy data concerning a new and important mining industry ought not to be withheld from our Transactions, simply because they are not sufficient to constitute a, complete academic treatise on the subject. This argument is recommended to the attention of many other members, who are waiting for the opportunity to contribute something "monumental" to our Transactions. In a number of instances, death has nulli¬fied this ambition, and the intended "monumental" contribution has turned out to be an obituary notice by the Secretary, instead of a valuable record of the professional experience thus hopelessly lost to the world.-R. W. R.] The official publications of the the Russian Government give fairly complete statistics of the dredges operated in the Empire; and in a recent English bluebook, Mr. Cook's report on Siberian Trade presents a brief account of dredging in Siberia. The data in Table I. (not given by Mr. Cook) have been taken from the Gold Mining Messenger (Russian) for July, 1905. These interesting statistics, though incomplete, show that the Yenisei dredges are working on poor ground and yield small returns. According to report, but few yield a profit exceeding 10 per cent. per annum on the capital invested. In the summers of 1904 and 1905, I traveled in the Urals as far north as lat. 61° N., long. 61° E., on the the Lozva river, a part of the vast system of the 01) river. This clear-water stream starts from the summits of the Urals at an altitude of 4,000 ft., and flows through a flat country, densely wooded with larch, spruce, pine, fir, birch and poplar. The river is full of fish, and is navigable for good-sized steamers as far as Ivdell. Winter lasts from early November to late April, the temperature rang¬ing from -60° F. to a summer maximum of 90° F. The rain¬fall is 20 in.. The climate is healthy, although mosquitoes,

Jul 1, 1906

By W. S. Tower

STEEL is the basic metal, the main metallic prop of the modern industrial world, a good gage for measuring the state of our complex economy. Any who had doubts on that score should have had them dispelled by the many evidences of public concern over the affairs of the steel industry in recent months. I do not need to relate the various criticisms of the industry, nor the questions about its policies and performance which have come in a rising flood, especially from unthinking and irresponsible sources. But judged from the standpoint of production, or from plans to improve and expand facilities, or from technical progress, the facts about the steel industry are proof of

Jan 1, 1948

By Allen Rogers

IT IS universal practice for corporations, at the end of the fiscal period, to call in a firm of chartered accountants to audit the books. The effect of this is to put an independent organization's seal of approval on the accounting of the business done by the management. Their report lets the stockholders know that the accounts rendered truly present the results of the year's business. This is as it should be; the average stockholder has no personal contact or even acquaintance with the managers of his enterprise and the approval of their stewardship by an indepen-dent agent is very desirable for maintaining confidence in their honesty and ability. But such an examination deals only with what may be called the arithmetic of the business; even the most elaborate audit, as the practice is at present, goes no further than to verify the items of the inventory. In other words, while checking up the entries showing the transaction's of the year and certifying to the correct-ness of the items of the balance sheet, such a report gives the stockholder no idea of the ability with which his affairs have been managed. If the profit and loss balance is satisfactory, as certified by the public accountants, he assumes that the management has been able; where it is not, he turns to the president's report and usually finds an explanation. Such an explanation never takes the form of admission of mis-takes in business judgment or of bad technical manage-ment. It could hardly be expected that it would. The stockholder is generally furnished, therefore, with a certificate of the honesty of his management, but never one of its ability. He does not worry about the latter as long as dividends come in; when they cease, his action generally finds expression in replacing the management. In other words, so long as profits are realized, he assumes the management to be good, even though its success is a matter beyond its control and better management would make larger profits. When there is no profit, the stockholders have no means of knowing whether it is due to conditions beyond the control of the management, as the annual report is sure to allege, or whether, by better management, profit is possible. Here is where the technical audit comes in.

Jan 6, 1922

By Max Roesler

W. L. CUMINGS,* Bethlehem, Pa. (communication to the Secretary+). -In this discussion of Mr. Roesler's paper, I shall follow Kemp in using the term "granite" to refer to the acid rock called syenite by Kimball. Diorite, as I understand it, is the dark basic rock invariably closely associated with the orebodies. The types of rock of intermediate composition, mainly intrusives, are not under discussion. It is difficult for me to conceive that this granite is the ore-bearing agent, for the following reasons: 1. No isolated orebodies in the granite are known. It would seem that if this rock is the mineralizer, some small bodies, or at least patches and small masses of ore so situated would exist. 2. In 1909 the writer conducted explorations on the Pequena and Grande claims about 1 mile north of West Mine No. 5. This work was done after a very careful magnetic survey had shown a large and uniform area of attraction. As exploration progressed, it became evident that in this case the magnetic attraction was due to disseminated magnetite. Much ore of 40 per cent. Fe was found, but very little commercial ore was shown up. This ore was entirely in the diorite and no granite outcrops are near. The occurrence could easily have been described as "ore formation but very little ore." I cannot conceive how a remote granite intrusion could impregnate a diorite mountain with 40 per cent. of Fe, and prefer to believe that this 40 per cent. of iron was in its real home, rather than in a sort of dioritic "boarding house" after having been evicted by granitic parents. 3. The Ocaña mine, which has produced nearly 500,000 tons, shows no evidence that the granite is the mineralizer. This is admitted by Mr. Roesler on p. 1827. 4. I believe it will not be disputed that all the iron-ore deposits extending along the south coast for 60 or 70 miles are of a similar origin. Evidence available at other points might properly be referred to in discussing the article under review. At the La Plata mines, about 60 miles west of Santiago, the writer has also made explorations. No granite is in evidence. At one point in the bed of a creek is a small body of magnetite about 10 ft. long, entirely surrounded by a hard fresh diorite. To me

Jan 3, 1917

By Robert Bedford

THE objects of this paper are: 1. To give cost data on drilling obtained at the North Star mine in California; 2. To describe the methods of testing drills employed there, giving the results of shop tests, and the correlated data obtained underground; 3. To demonstrate that these tests form a satisfactory basis upon which to judge rock drills. The rock at this mine is either close-grained diabase in the upper levels, or tough grano-diorite in the lower levels. The vein, which has an average dip of 23°, consists of about 5 ft. of "formation" lying between walls of unaltered country rock. Of the 5 ft., solid quartz and stringers make up 18 in. of pay ore. The formation, which consists of but slightly altered country rock, is almost as hard as the unaltered walls. From 4 to 42 ft. is sent to the mill. One-third of the holes are drilled in the quartz; two-thirds in the formation. The holes are about 42 ft. deep and break on the average of 1.15 tons per hole. The average number of holes per stope drill shift is at present 5.65. The number of drill shifts throughout the mine in 1913, was 18,679, and the cost of labor for drilling, power, supplies, upkeep of machines and air lines, tool sharpening, and distribution, amounted to 33 per cent. of total mining expense. To do this work there are in commission 43 No. 12A, three No. 17V and eight No. 16V Waugh stopers, three Jackhamers, two Waugh pluggers, and 17 No. 8 ,and two No. 7 water Leyners. For the past three years a record has been kept of the repairs on each machine and number of shifts operated by it. The figures given in Tables I and II for the cost of repairs per drill shift have been taken from this record. The underground air pressure is about 90 lb. The air consumption per drill shift was measured by, aerometers. The leakage of pipe lines between compressor and meter is not included. From the number of pieces of steel sharpened for each type of drill during the year the average used per drill shift has been ascertained. For other supplies the figures given represent a year's average.

Jan 8, 1914

By William Hague, Robert H. Bedford

The objects of this paper are: 1. To give cost data on drilling obtained at the North Star mine in California; 2. To describe the methods of testing drills employed there, giving the results of shop tests, and the correlated data obtained underground; 3. To demonstrate that these tests form a satisfactory basis upon which to judge rock drills. The rock at this mine is either close-grained diabase in the upper levels, or tough grano-diorite in the lower levels. The vein, which has an average dip of 23", consists of about 5 ft. of " formation" lying between walls of unaltered country rock. Of the 5 ft., solid quartz and stringers make up 18 in. of pay ore. The formation, which consists of but slightly altered country rock, is almost as hard as the unaltered walls. From 4 to 44 ft. is sent to the mill. One-third of the holes are drilled in the quartz; two-thirds in the formation. The holes are about 4 1/2 ft. deep and break on the average of 1.15 tons per hole. The average number of holes per stope drill shift is at present 5.65. The number of drill shifts throughout the mine in 1913 was 18,679, and the cost of labor for drilling, power, supplies, upkeep of machines and air lines, tool sharpening, and distribution, amounted to 33 per cent. of total mining expense. To do this work there are in commission 43 No. 12A, three No. 17V and eight No. 16V Waugh stopers, three Jackhamers, two Waugh pluggers, and 17 No. 8 and two NO. 7 water Leyners. For the past three years a record has been kept of the repairs on each machine and number of shifts operated by it. The figures given in Tables I and II for the cost of repairs per drill shift have been taken from this record. The underground air pressure is about 90 lb. The air consumption per drill shift was measured by aerometers. The leakage of pipe lines between compressor and meter is not included. From the number of pieces of steel sharpened for each type of drill during the year the average used per drill shift has been ascertained. For other supplies the figures given represent a year's average.

Jan 1, 1915

William B. Phillips, Birmingham, Ala.: The analysis of Pratt coal made by myself, and given by Mr. Ormsbee in his paper (p. 113), is likely to mislead the reader as to the real nature of this coal. It represents the very purest coal that I have been able to get, and does not represent the average composition of the lump-coal as prepared for market. I wish it were true that the coal had no more than 2.50 ash and 0.83 sulphur. The analysis of McCalley is nearer the real figures than any of the others. There is no use in giving an

Jan 1, 1896

By Gilman C. Ritter

Moisture sampling of uranium ore should coincide as nearly as possible with weighing of the lot represented by the sample. This requires care by the sampler since the sample must usually be taken as a grab from each truckload as dumped. Correct proportions of coarse and fine material are necessary. A sample of at least 10 lb should be collected, placed in an air tight container, and promptly taken to the moisture determination room. Further, the sample should be dried for a minimum of 24 hr or until there is no further apparent loss of weight at a temperature no greater than 110°C.

Jan 10, 1958

ENGINEERS AVAILABLE (Under this Beading will lie published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member,, technical graduate, aged 38, 14 years' experience in engineering, exploration, and management of copper, pyrite, and large iron mines, safety work, professor of mining in large university. Married. Open for position after June 10. No. 205. Member, graduate engineer, aged 44, with over 20 years' experience in connection with large coal and coke operations in different parts of the country, desires position as general superintendent of large coal company, or will take an interest with the management in a smaller company. No. 206.

Jan 5, 1915

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members. ) Member, age 33, single, desires position as null superintendent or charge of mine and mill. Twelve years' milling, cyaniding and flotation in the southwest and Mexico. Will go anywhere. No. 458. Member, mining engineer and geologist, graduated, from- mining college, age 27, single, exempt, with practice in metal mining, surveying of any kind, field geology and ore testing, desires to .engage as geologist or mining engineer with a reputable concern in the west or east of. U. S. Hard worker and reliable. No: 459.

Jan 6, 1918

By Robert Lewis

Some recent experiments in the use of compressed air for rock drills at higher than usual pressures, up to 150 lb. per sq. in., emphasize the importance of maintaining the compressed-air system in the best condition if the greatest possible over-all efficiency is to be secured. No claim of high over-all efficiency can be made for the compressed-air system of braking that is used on railroad trains, yet the air brake works effectively. Compressed air is not used efficiently in the rock drill, but no other type of machine drilling is yet a serious competitor of the air-driven rock drill.

Jan 1, 1930

OUR 78th Annual Meeting was, technically and attendance-wise, one of the greatest to date. No one who came to New York's Hotel Statler had time to hear all 266 papers, or to attend all 70 sessions and 27 committee meetings, or to shake the hands of the more than 3000 engineers, educators, students and executives who attended-but no one was lost in the crowd. For crowds always dwindle down to groups of two and three and four, and those are the little sessions which make our meetings well worth attending. Herewith four pages of photographic highlights and sidelights on the February gathering.

Jan 3, 1950

By Roger L. Brockenbrough

Steels available for mine-shaft applications are discussed, and the use of steel linings for round and rectangular shafts is reviewed. For rectangular shafts, frameworks constructed of square or rectangular steel tubes offer advantages. Also, corrugated steel sheeting provides a suitable alternative to timber lagging for spanning between the main shaft supports. For round shafts, self-supporting cylindrical steel liners, with circumferential stiffeners to prevent collapse, have been used to depths up to 6000 ft. Several large-diameter round shafts have been constructed with a concrete lining and an internal framework: of high-strength low-alloy steel tubes. It is concluded that in any new shaft construction steel designs should be investigated as economical alternatives to designs using other materials.

Jan 1, 1976

Discussion of the paper of GEORGE K. BURGESS and SIR ROBERT A. HADFIELD, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 455 to 468. ALBERT SAUVEUR, Cambridge, Mass.-There is a definiteness and finality in the investigations that have been conducted by the Bureau of Standards and in the method of presenting the results that is most satisfactory and refreshing.. A year ago Dr. Burgess and his co-workers investigated the question of critical points in carbonless iron, and they settled the question once for all. No one can now claim that the thermal point A2 in carbonless iron does not exist. At the past meeting of this Institute in Pittsburgh, Dr. Burgess showed the worthlessness of the shrinkage clause. To my mind after his demonstration no one can again claim that the shrinkage clause renders any service. He also showed us that it was a practicable proposition to use pyrometers in steel work in order to ascertain the finishing temperatures of rails. No one can again come before this body and make the claim that it is not a practical proposition. And now Dr. Burgess shows us that steel ingots can be made in a commercial way, practically free from pipe, from segregation, aid from blow holes. It places again before us in a very clear manner the question of piped ingots and of segregation, a question which has been debated for 20 years or more. I know very well the attitude of the standpatters in the matter. They claim that most of the pipe is removed in the discard, and that if a little is left it is so thoroughly welded that it does no harm. I for one am not convinced of the soundness of the argument. I do not believe there is any one present who would claim that, given an ingot free from pipe, free from segregation, and free from blow holes, better rails will not be made out of that ingot than out of the ordinary piped or segregated metal which is used by almost all of our steel mills. In my opinion, if we give our sanction to the casting of steel in the shape of piped or segregated steel ingots, we are guilty. If we give our sanction to the rolling of rails from such metal, we are guilty. It is our duty as experts, as steel makers, and as steel consumers to make and to use the best steel obtainable on a commercial basis, for the manufacture of rails. Now, we have been shown that sound ingots can be produced from which superior rails can be made. If we do not insist upon these sound ingots, then we fail in our duty. I think that the art of casting steel ingots has advanced to such a point that the casting of steel ingots piped and segregated ought no longer to be tolerated.

Jan 5, 1915

By E. Sengier

At the Director's dinner of the A.I.M.E. on. April 22, Mr. Sengier of the Union Minière du Haut Katanga was a guest. Though a member of the Institute for sev-eral years this was the first occasion on which he had had opportunity to meet with it, and in response to an invitation from President DeGolyer, after expressing his pleasure at being present, he told informally of the present development of the Congo with which he has been so closely related. From his remarks the follow-ing has been prepared.-EDITOR. AS you know, the Belgian Congo, a fairly large colony compared with the territory of Belgium, is in the center of Africa. Natural waterways, railroads now built and new railroads under construc-tion, give increasing means of transportation and are helping toward development. The mining industry is by far the most important part of our colonial activity. Considering that we are all engineers, I will confine my figures to mining enterprise. First I will show you the relative importance of the mining industry com-pared with the total exports of the Belgian Congo. During 1925 there was exported 100,000 tons of cop-per, valued at about $25,000,000; 900,000 carats of diamonds, 8000 lb. of gold, 1700 tons of cassiterite, 300 .tons of cobalt, and 20 grams of radium, of a total value of about $35,000,000. Other products to a value of about $12,000,000 and consisting mainly of palm nuts, palm oil, cotton, ivory, copal, rubber, were also exported. From this you will see that mineral products account for about 72 per cent of the total exported value. Copper alone amounts to 52 per cent of the total and 72 per cent of the mineral exports. All minerals, with the exception of gold, which is mined by the government, belong practically toy two mining companies in which American and British capi-tal is interested with Belgian. These two companies (one called Forminière, interested in the diamond busi-ness, and the other called the Union Minière, interested in copper, cobalt, tin and radium) were formed twenty-five years ago. They started producing in 1911, but the war prevented normal operations, and active de-velopment could only be carried on after the Armistice.

Jan 5, 1927

By George W. Sears

In preparing this symposium, our ambition was to elicit authoritative expression of opinion concerning important selected phases of the industry from men active in it. Responses to requests for contributions were gratifying, especially so in view of the short time available. The generous and cooperative spirit of the industry as a whole is amply evident. Responses were received from the following, who are therefore the true authors of the paper: W. G. Adamson, General Manager of the pershin; Quicksilver Co., Lovelock, Nev.; Dudley Baird, Vice President, Pacific Foundry Co., San Francisco; Walter W. Bradley, State Mineralogist of California; W. D. Burcham, General Manager of the Brewster Quicksilver Consolidated, Terlingua, Tex.; William Forstner, San Francisco; H. W. Gould, of H. W. Gould & Co., San Francisco; Marcus Hulings, General Manager of the Chisos Mining Co., Terlingua, Tex.; Frank J. Katz, Chief Engineer, Division Mineral Statistics, United States Bureau of Mines, Washington, D. C.; Lloyd J. Lathrap, Superintendent, Nevada Quicksilver Mines, Inc., Lovelock, Nev.; W. R. Moorehead, General Manager, New Idria Quicksilver Mings, Inc., Idria, Calif.; F. W. Oakes, Jr., Terlingua, Tex.; C. N. Schuette, San Francisco. Brief Economic History of Quicksilver in the United States Quicksilver ore was first discovered in the United States at what was later the New Almaden mine in California, in the year 1824. Production also began here, but not until 1850, when it was stimulated by the active demand caused by gold-mining operations. Prospecting for quicksilver was active, high-grade ores were found and ample production lowered the price from $100 per flask in 1850 to about half that figure for the greater part of the next 10 years. During the succeeding decade, many new quicksilver mines were found; production increased at a time when the local demand diminished, so that most of the product was exported. The third decade of quicksilver mining in the United States witnessed the development of the pan amalgamation process, particularly in Com-stock silver-mining operations. A suddenly increased demand sent prices soaring, the all-time peak of quicksilver production followed, and the highest price was soon replaced by the lowest one on record. Huge quantities of quicksilver were exported between 1870 and 1880 and exports continued in decreasing measure for three decades to 1910. In

Jan 1, 1930

By Robert F. Brindisi

There are approximately thirty to forty operating mills in the United States which are currently producing uranium yellow cake. This figure includes a significant number of in situ and by-product operations however the conventional acid leach flowsheet depicted in Figure 1 is the most common process used by domes- tic yellow cake producers. Ground ore is leached with sulphuric acid and the solids are separated from the pregnant liquor and washed in a series of counter- current decantation thickeners. After clarification of the pregnant liquor, uranium is recovered from the solvent extraction/stripping circuit by the addition of ammonia with precipitation of ammonium diuranate, or simply yellow cake. The yellow cake precipitate is then thickened in a conventional thickener before re- porting to the dewatering/washing unit operation. De- watered solids subsequently report to thermal drying, and clarified liquor from the dewatering/washing step is recycled to the yellow cake thickener. The yellow cake dewatering/washing unit operation is generally accomplished using either a solid bowl centrifuge or a rotary vacuum drum filter. In most cases the underflow from the yellow cake thickener is pumped to the dewatering/washing unit operation at approximately fifteen to twenty percent solids. For the purpose of this discussion ammonium diuranate, the product of ammonia precipitation from a conventional acid-leach uranium mill flow sheet, as discussed earlier, will be considered. With only slight adjustment this discussion will be equally applicable to sodium diuranate or uranium perioxide precipitates and to either in situ or by-product operations where such precipitates are generated. Some of the domestic uranium mills which have selected solid bowl centrifuges instead of vacuum drum filters for the dewatering/washing unit operations are listed in Figure 2. Why have these uranium mills, as well as others not listed, chosen to use the solid bowl centrifuge for this particular application? It is simply a matter of performance, reliability and economics. In the remainder of this paper the performance, initial cost, installation cost, maintenance and power consumption of both the solid bowl centrifuge and the rotary vacuum drum filter will be com- pared. In order to provide a consistent basis for comparison the appropriate sized (centrifuge or filter) unit for the dewatering/washing of 400 to 500 pounds per hour of yellow cake solids will be considered. Such a flow will usually be generated by a typical 3,000 ton per day (acid-leach) uranium mill.

Jan 1, 1980

By Donald Barton

THIS paper outlines a time-saving graphical method of calculation for application to the interpretation of observations with the Eötvös torsion balance. Preliminary to the treatment of this short cut method which has been found practicable, the principal formu-las by which the student of interpretation can calculate the gradient and differential curvature produced by different types of bodies in different types of situa-tions are presented and discussed. It is necessary to split most geologic bodies into a series of simpler ones for which not too complicated formulas are avail-able. The gradient and differential curvature effects are calculated for each of the simple bodies and then summed to the total effect for the whole body. The calculations are considerable in number and, though more tedious than difficult, should be' entrusted to an experienced calculator. Considerable facility in qualitative interpretation can be acquired by the geophysicist from experience and from a thorough study of the types of gradient and differential curvature anomalies produced by the dif-ferent types of possible structural situations. How-ever, semi-quantitative calculations' of the probable structure bring out many relations that are not evident in a simple inspection of torsion balance results ; it throws out as impossible or improbable certain of the alternative structural possibilities that may seem equally probable under simple inspection of the results; it will determine more accurately the position of the crest of the structure; and reduce considerably the un-certainty in the interpretation and it is necessary to intelligent interpretations. The calculation of such cross-sections consists of a trial-and-error calculation of a body that will give gradient and differential curvature effects as closely as possible the same as those observed. From his knowledge of the gradient and differential curvature produced by different types of bodies, the geophysicist sketches a tentative cross-section of the structure as indicated-to him-by the observed results of the torsion balance survey, and the calculator then splits the struc-ture into blocks, and calculates the gradient and differ-ential curvature block by block. If, as rather usual, the calculated .gradient and differential curvature pro-files diverge considerably from, the respective observed ones, it is necessary to add and subtract blocks from the cross-section until a close agreement is obtained .between the calculated and observed profiles. The com-plete calculations have to be gone through for each block that is added or subtracted.

Jan 9, 1928

By William J. Gillich, Gerald L. Moss

PREVIOUS studies of the shock loading of randomly oriented polycrystalline aggregates have firmly established that, after rather short load duration, hydrostatic compression closely approximates the shocked state.' However, McQueen deduced from pressure measurements with good time resolution that, during shock loading, metals begin to undergo a stress relaxation at the yield stress. He suggested that the relaxation is due to plastic deformation accompanying the change from a one-dimensional compression to a three-dimensional, hydrostatic, compression.' Stress relaxation may occur faster as stress is increased above the yield stress, but the existence of unidirectionally compressed states for finite times suggests that the concept of a unidirectionally distorted lattice should furnish considerable insight into the mechanical behavior of materials subjected to shock loading. Here, a crystallographic analysis is presented for the hypothetical situation where atom motion may be considered as unidirectional which, as indicated above, is a useful extension of the macroscopic concept of shock loading to the microscopic domain. Only motion caused by the com-pressive forces is treated; i.e., lattice vibrations upon which this motion is superimposed, as discussed by Fitzgerald, are ignored.3 The purpose of the analysis to be presented is to develop a description for single crystals of the lattice rotations that occur for idealized uniaxial strain deformation. The usefulness of such an analysis in realistic deformation is to give a method of specification of those properties of an initially distorted lattice which would affect the subsequent deformation. Non-axial complications that arise experimentally, such as off-axis rarefaction waves, must be treated in proper context. Consider the material element shown in Fig. 1 and let the compression be uniform at all regions of the element. Then, any interior point of the element is displaced in proportion to its distance from the base of the element. Accordingly, if the top of a unit element is displaced by an amount, (-K), with respect to the base, a point P(X, Y) will be displaced by (-KY). Crystal planes are, therefore, rotated by the compression. Analysis of this rotation may be accomplished from the geometry shown in Fig. 1 where the line OP is the edge of the plane {hkl} and N is its normal. The orientation of the crystal plane with respect to the shock direction is specified by the angle, before deformation. After deformation the edge of plane {hkl}

Jan 1, 1969