Search Documents

By G. Ferrara

The reserves of lead and zinc ores in the metalliferous district of Iglesias in south-western Sardinia are today estimated at about 30 million tons, grading from 4 to 10% Pb + Zn. Of these reserves, about 40% are in the mines owned by AMMI Sarda S.p.A. The working of these resources goes back to ancient times. Not infrequently, traces of old Roman workings and remains of ancient implements are come upon in the higher parts of some of the ore bodies. Exploitation of these mines on larger scale, however, dates from the middle of the 18th century. Initially, the more accessible zones of the ore bodies and the richer ores were worked - the galena and the rich oxidized ores (calamine* with 25-35% Zn), which were often found in large masses, the enormous empty cavities of which still remain. The poorer grade deposits have been gradually rendered workable by the development of technology - the perfecting of the

Jan 1, 1970

By Oscar E. Harder

THE TERM "physical metallurgy' is used in the title of this lecture in preference to "metallography ?because the former has a broader meaning with most audiences, some people thinking of the latter as being limited to work with the microscope. This distinction, how- ever, has not been held by the out- standing workers in the field of metallography, such as the late Professor Sauveur. In the broadest sense metallography is essentially the same as physical metallurgy. The American Society for Testing Materials has adopted-the following definition: "Metallography is that branch of science which relates to the constitution and structure, and their relation to the properties of metals and alloys." This definition might be improved by adding after "properties" -"and their industrial and scientific uses." Metallography has also been defined as the science of metals and alloys. Physical metallurgy is to be distinguished from process metallurgy in that the latter relates particularly to the production of metals from the ores.

Jan 1, 1940

By F. B. Foley

A description of tests made by a committee of the Division of Engineering of the National Research Council to determine whether velocity of impact affects the formation of Neumann bands. FOREWORD Not infrequently, in the case of the failure of a metal structure, such as a bridge, tank, airplane, gun carriage, etc., a doubt arises whether the failure was due, among other causes, to the effect of an overburden or of an explosive maliciously or accidentally exploded in contact with it. As few means of discriminating between the effects of these causes have been known and these means were of a rough qualitative character, it was surprising to find in the record of an inquiry into the failure of a structure, the statement that, by observations on the Neumann bands in the structure, it was possible to determine the speed of breakage in the metal and to distinguish between a fracture caused by an explosion and one caused by an ordinary mechanical strain. Such a criterion, if well proved, was of value to the explosives experts of the Bureau of Mines, the Ordnance Department of the United States Army and the Bureau of Ordnance of the United States Navy, but search showed no record of it in the literature nor did any of the metallurgists and metallographers consulted know of any data on which such a criterion could be based having been assembled and critically studied. However, it was universally held that there was promise in the idea and that there existed unique facilities at the Bureau of Mines Experiment Station at Pittsburgh for the preparation, under definitely known conditions, of material for study by metal-lographers, and that material of value might also be obtained from the proving grounds of the Army and Navy. Therefore, with the approval of the Director of the Bureau of Mines and the Chiefs of Ordnance of the War and Navy Departments, the Chairman of the Division of Engineering of the National Research Council, on April 12, 1919, appointed a Committee on the Investigation of Neumann Bands, which has since been engaged in this study and which, after some slight change in its personnel, consists now of the following: Dr. William Campbell, Advisory Metallurgist, Bureau of Ordnance, Navy Department. F. B. Foley, Metallurgist, Bureau of Mines. S P. Howell, Explosives Engineer, Bureau of Mines. Comdr. O. M. Hustvedt, U. S. N., Bureau of Ordnance, Navy Department. Dr. Charles E. Munroe, Chief Explosives Chemist, Bureau of Mines.

Jan 9, 1922

By W. C. MENDENHALL

THE problem of maintaining the mining industry is two-fold; finding new supplies in the face of increasing difficulties, and making such advances in the arts of extraction and preparation as to use supplies of lower grade. Progress in mining and reduction methods and in transportation makes ore today of that which was waste yesterday. These are the fields of the metallurgists and the transportation engineers. The geologists and mining engineers must work together on the problem of ore finding. As the old prospector fades from the scene, men with equal hardihood and patience and equal power to meet the physical obstacles which confront the seeker after ore, must take his place, armed with all that has been learned from human experience about the causes, the controlling conditions, the indications, and hiding places of the metals. Such a seeker is dealing with some of the most complex and obscure of natural phenomena. In nature's laboratory, tremendous forces are at work. Tempera-

Jan 1, 1926

By Graham Bright

T HE chairman of the Mines Committee of the A. 1: E. E. for 1920-21 has had the honor of being also the chairman of a similar committee, the Mine Equipment Committee, of the A. I. M. E. It has been the endeavor during the past year to have the two committees work together since the object of these committees is very much the same. A meeting of the committees was held in Chicago in November of 1920, at which time it was decided that one of the best ways to work together would be to foster joint meetings of the local sections of the A. I. E. E. and A. I. M. E. By these meetings, it was hoped that various engineers in the local sections interested in mining subjects could be brought together and not only become better acquainted but be greatly benefited by the interchange of ideas and by the discussion of papers presented on mining subjects.

Jan 1, 1921

By B. D. Thomas

When the origin and early plans, of Battelle Memorial Institute were described in this journal in October 1929 by R. W. Gillett the first director, the doors of the laboratory had just been opened and the hope of the founder that the institution serve the world by research for industry still existed only as an ideal in the minds of the thirty or so employees who then constituted the staff. Since that time the country has experienced troublous times. A devastating depression plunged the entire world into an unprecedented period of financial and industrial inactivity; and the slow recovery of the late thirties was soon to be overtaken and overwhelmed in the violence of war. Through this time of stress Battelle has continued to grow. The staff has increased to almost 600; buildings and equipment have been added, until now it stands in a place of pre-eminence in the metallurgical and engineering world.

Jan 1, 1944

By William B. Plank

NEVER before have so many men chosen the mineral technology field for their college training. In the college year 1936-'37, 7190 such students were enrolled in the 53 schools of the United States. My last study of the mineral technology schools of the United States and Canada was made for the year -1934-'35, and the current study, as the previous one was made for the A.I.M.E. under the auspices of the Division of Mineral Industry Education. Altogether, four studies of enrollment have been made. The first three were for successive college years beginning with 1932-'33. This present one covers a two-year period, for the purpose of these studies may he served satisfactorily if they are made biannually. The data on the schools were collected in the same way as for former studies, 'namely, by questionnaire, dated in this case Nov. 18, 1936. The figures reported are therefore comparable with those of former cars.

Jan 1, 1937

By AIME AIME

A CORPORATION would go into bankruptcy if its affairs were conducted as are those of the state of New York, according to the Committee on New York State Government Reorganization of the American Engineering Council of the Federated American Engineering Societies, in a report to the chairman, of the Joint Judiciary Committees of the Senate and Assembly. The report, just made public, was signed by the three members of the committee who were appointed by Herbert Hoover. They were H. de-B. Parsons, chair- man, Paul G. Brown and Lewis B. Stillwell. Although the American Engineering Council is a national organization, it decided to aid in governmental reorganization in New York State because of the magnitude of the task. The Council's committee in its report urged the passage of three state reorganization amendments for consolidation of departments, an executive budget system, and a four-year term for the higher state officials. In the words of the report :

Jan 1, 1921

By Edward H. Robie

HOW have recent events affected the general trend in world mineral production? What effect has the World War, with its resultant boom and depression, had on the long-term trend of output? Have all of the principal metals and fuels been similarly affected, or have some boomed or slumped much more than others? The trend of world production of coal, iron, the principal nonferrous metals, and petroleum is shown in the accompanying chart, covering the period from 1882 to 1931 inclusive-the last fifty years. The curves are plotted logarithmically to show the comparative trends. In the lower left-hand corner of the chart is a slope diagram to aid in visually evaluating. the average yearly rate of increase in production; from this one can easily see, for example, that the petroleum production curve indicates an average annual increase of around 8 per cent, and that up to the period of the World War the average annual increase in copper production was about 6 per cent.

Jan 1, 1932

By Gilbert P. Moore

Petroleum operations in Bolivia are still limited to those of the subsidiaries of the Standard Oil Co. of New Jersey. Development work is being carried on at Sanandita and at Bermejo and testing operations in the north. Five wells have been completed at Sanandita. Wells 1 and 2 are producers, 3 and 5, which are north of 1 and 2, are poor wells, and well 4, to the south, was dry. In the Bermejo field, well 5 has just been completed. No information as to the production is obtainable. In the north one string was operated at each of the following locations: Machareti, Camatindi and Camiri. The well completed at Machareti during the year was a failure. The result of the others is not known. It is reported on good authority that a pipe line will be completed in 1931 to connect the Sanandita field with the Lomitas field in the Argentine. This will place Bolivia among the ranks of the producing countries of South America for the first time. This development indicates that some arrangement has been arrived at with the Argentine Government for the importation of Bolivian oil. During 1930 the Bolivian Government declared in effect the new Petroleum Law which had been expected for such a long time. One of the first acts of the military junta, which rose to power through a coup d'état, was to cancel this law, so that Bolivian oil operations are still under the old law of 1921. One new local company was formed to exploit 1,500,000 hectares near the town of Cochabamba. The Bolivia Concessions, Ltd., which had a concession permitting the selection of 17,000,000 acres in eastern Bolivia, is reported to have failed in 1930 and is now being liquidated. Chile During 1930 the Chilean Government entered into a contract with an individual to explore in five distinct zones of the Republic. According to the contract, geologists must be at work there by May 1 of this year and a well must be started by the end of 1931. If the operations are

Jan 1, 1931

The pattern of the coal industry west of the Mississippi River, so far as its history is concerned, is entirely different from that to the east of the "Father of Waters." When the Louisiana Purchase was consummated, one of Jefferson's first thoughts was to ascertain what sort of a country had been purchased, and to that end he sent Lewis and Clark to ascend the Missouri River and to reach the Pacific Ocean if possible, but above all to bring back a report showing the character of the country, its mineral and other resources, inhabitants, etc. This first expedition was supplemented by others to various parts of the vast domain for the same purpose; years later, when transportation routes were necessary to hold and develop the western country, a number of expeditions were sent to explore possible routes for railroads. The records of nearly all of these explorers, as will be shown later, contain references to coal in many localities, the possible value of which was realized but its potential value remained dormant for many years until increasing population and methods of transport made markets available. Missouri was the first state west of the Mississippi in which coal was produced and the names of a number of places show that the French were familiar with the coal deposits there. Lewis and Clark, soon after they left St. Louis, passed "a remarkable Coal Hill on the Larboard Side, called by the French Carbonere, this hill appeares to Contain great quantity of Coal."1 This hill was about seven miles below St. Charles. No other outcrops were seen by them until they had passed the present limits of the state. The Louisiana Gazette of April 9, 1805 contained an article on "The Missouri," author not stated, which said, "the short stay we have generally made among the savage nations has prevented us from making those researches, which would have supplied us with a more extensive information respecting the various mines found on the borders of the Missouri; we know with certainty only those of iron, lead and coal." In 1806 Pike passed through Missouri on his tour to Mexico. On August 17th, along the Osage River he remarked, "here the river-bank is

Jan 1, 1942

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

By V. H. Gottschalk, R. S. Dean

In the theoretical study of metallurgical reactions, it is necessary to make certain assumptions concerning the nature of metal-gas systems. The assumption usually made is that the reaction in such systems takes place predominantly with gas that is in "solution" and that the amount of solution follows the rules which have been developed for aqueous solutions; namely, Henry's law. The purpose of this paper is to inquire whether these assumptions are the best ones that present knowledge of gas-metal systems permits us to make. In the first part the extent to which a gas will dissolve in a metal and still follow Henry's law is considered. The conclusion is believed justified that the number of molecules of gas that can dissolve in a metal and have the system follow Henry's law must be small indeed. It is therefore improbable that the first assumption concerning the predominance of these dissolved molecules in reaction is correct. It is suggested that some improvement in the correlation of the probabilities with the assumptions made in the mass law equations would be made by the use of the dp law of Sieverts in place of Henry's law. However, the amount of gas that may be held in a metal so that it follows either Henry's or Sieverts' law is considerably outweighed in most metallurgical reactions by that held in gas-metal systems of entirely different structures and concerning which little experimental evidence is available. Some speculation concerning the nature of these is offered. The conclusion is that attention should be given to the determining of the nature of gas-metal systems and that the really fruitful application of the mass law and its connected calculations will have to await a more complete knowledge of these systems than we now possess. DISCUSSION (Paul D. Merica presiding) P. D. Merica, New York, N. Y. (written discussion).—The solubility relations of gases in metals, in so far as they are known from the pioneer work of Sieverts and others, have from the first presented certain challenging peculiarities. The authors have emphasized the significance of these characteristics and suggest that they point

Jan 1, 1933

By William H. Radford

Having worked some rather lorn--grade gravel during the past season at a small profit, I give the actual figures, in the hope that other mining engineers interested in this line of work may be thereby induced to do the same, in order that we may all get more data on this little-ventilated subject. The property here referred to is situated in one of the northern counties of California, where hydraulic mining is still permitted by the courts. The water-right belonging to the mine is a good one, furnishing water during about nine months, whenever there is an average rain-fall, and a fair proportion of the precipitation is in the form of snow. The ditch, about 11 miles in length, is cared for during the rainy months by two men, and during the rest of the year by one; and the water cost last season, delivered at the mine, 0.69 cent per miners' inch. The season commenced in November, 1899, and ended the last of July, 1900. During this time, 655,657 miners' inches (an inch equals 1728 cu. ft. in 24 hours) of water were used for piping, and for sweeping the bed-rock at the end of the season. From actual surveys, this amount of water washed down 1,251,399 cu. yds. of material, consisting of pay-gravel lying on the bed-rock, and varying in thickness from a few inches to 8 ft., and practically barren top-material, consisting of mountain slide, carrying considerable broken rock, clay, and soil. The banks varied in height from 50 to 130 ft., the average height being 63 ft. The grade of the sluices was 7 in. to 12 ft., the boxes being paved with block-riffles 12 in. deep. Long bed-rock cuts extended from the heads of the sluices to within a few feet of the banks, and were kept practically to grade as the work advanced. At first, electric drills were used on this work; hut as it was found that heavy blasting shattered the rock too much, and caused slips, these drills were

Jan 1, 1902

Book Review MANAGEMENT AND MEN. By Meyer Bloomfield, Boston. The Century Co., New York, 1919, pp. 584, H.X. 5 1/2. $3.50. This hook is an exposition of English efforts to solve the problem of labor unrest in England. The first six chapters are reprinted from articles published in the Satur-day Evening Post, for whom the author went to England to study the problem at first hand. These articles deal with housing, increased production, eliminating the internal friction in the industrial machine and a chapter each devoted to the view-point of employer and employee. These chapters are written in the easily readable magazine style and give a complete general survey of the particular solution being tried. Perhaps their greatest., certainly not their least, worth lies in the fact that they form a vehicle for unusually voluminous appendices containing in full the famous Whitley Reports which are the basis of the new movement, together with various reports, which, except for this publication, would be largely inaccessible to those inter-ested in this country. The Whitley scheme considers each industry a unit and proposes to establish therein a Joint Standing Industrial Council composed of representatives of employers and employees to consider appropriate matters affecting the industry at large. There is to be a District Council for each industry which will, as its name implies, deal with the clatters pertaining to that interest in. the particular district. The third and last body in this scheme of Industrial Parliament is the Works Committee, which is com-posed of representatives of the management and of the workers employed in particu-lar plants or mines to act in close cooperation With the district quid national machinery. The Whitley or similar schemes have been tried in many communities in England and the book contains interesting comments on the result obtained, it being notable that most of the objections conic from plants which have not tried the scheme. Meyer Bloomfield, the author; is the specialist in industrial personnel problems who organized the industrial service activities of the United States Shipping Board, Emergency Fleet Corporation. P. E. B.

Jan 10, 1919

The oil production in Bahrein for the year 1937 was 7,762,264 bbl., a monthly average of 646,855 barrels. Sufficient potential production had been developed in the Second Pay (Main Pay) at Bahrein by the end of 1936 to supply the anticipated crude demand, and the drilling program was changed from straight development to partial exploration during 1937. Two nonproductive wells were drilled to test the Third Pay at a depth of about 2900 ft., or some 900 ft. below the top of Second Pay. As a result of this exploratory work, the normal drilling program was slowed down and only eight new wells were completed in the Second Pay during 1937, making a total of 45 producers from the Second Pay. The deep test was drilling at 5081 ft. at the end of the year. A 550-ft. section (termed Fourth Pay) of porous limestone interbedded with anhydrite was topped at about 4150 ft. Numerous drill-stem tests indicated that the limestone was very permeable and that it carried large volumes of natural gas under high pressure together with a small amount of high-gravity oil or condensate. Drill-stem tests also indicated that the bottom 50 ft. of the 550-ft. section carried an encouraging amount of heavier oil, gravity about 37" A.P.I., with characteristics similar to the oil produced from the Second Pay. A well was started somewhat down-structure from the deep test to better determine the oil-producing possibilities of the Fourth Pay. Some refinements in drilling technique were adopted during the year. All wells started to the Second Pay were drilled with rotary from the surface. The top 1500 ft. of porous limestone section, formerly drilled with cable tools, is now drilled with rotary without circulation, using water to wash the cuttings into cavities. The shale section from this point to the top of the oil horizons is drilled with natural mud circulation. The productive horizons are drilled with oil circulation under pressure control. A second satisfactory method of completing wells was developed when the two Third Pay test wells were plugged back and gun-perforated through cemented casing opposite the Second Pay, with good results.

Jan 1, 1938

CHARLES F. WILLIS,* Bisbee, Ariz.-(written discussion?).-The consensus of the discussion of the paper of Dr. Lanza indicates that the physical examination, while it is probably a good thing, is fought by the workingman, and that, because of this fact, it has been proved unsuccessful. The physical examination standing alone is worth but little, and could easily be made a subject both of ridicule and dissension unless the company having such examination shows its own good faith in promoting a thoroughly better health program. It is easily seen why a workman would resent his employer expecting him to be physically fit, if at the same time the employer provides un-healthful, unsanitary, working conditions, or if the town in which the employees are expected to live is dirty and unkempt. One mocks the other. The employer cannot say, "You must remain healthy so that I can get by with unhealthy conditions." But if working- conditions are as good as can be obtained to keep men well, the employer can ask his men to be in a healthy condition. A State examination and standard would have many difficulties, owing to the fact that a man would pass or would not pass the standard set, thus eliminating the discretion on the part of the employer in placing men whose physical condition might well permit working in one place and not another. Any physical examination that is run for the purpose of eliminating the physically unfit is unjust, both to the worker and to the nation as a whole; a State examination would make a distinct dividing line, whereas examination by the employer is conducted with a vision of the positions available. The workman's opposition to the physical examination comes from the fact that he has been taught to believe that it is an interference in his personal affairs, that he can be clean or dirty as he chooses, that he can he healthy or unhealthy, and that it is nobody's business but his own. The war has taught us, however, that the individual is no longer the unit and that all such propositions must be based on the greatest good for the greatest number.

Jan 6, 1919

By J. T. Duce

There were no important changes in the producing situation in Colombia in 1930, because the emergency bill passed by the Colombian Congress in 1927 is still in effect, and therefore no change has taken place in the law governing petroleum. At the close of 1930 the Colombian Congress began to consider a new petroleum bill. This measure is an improvement on the preceding bills which had been the subject of so much debate in the Congress. However, it cannot by any means be regarded as perfect, and a number of criticisms may be justly leveled at it. The most substantial one probably is that the royalties on public lands, and the taxes on private lands, while apparently low, are deliverable at seaboard, or payable based on seaboard price at the option of the government. If the government exercises its option to take the oil at the mouth of the well, the cost of the transportation figured back into oil is also deliverable to the government. This phase of the law has the effect of making seemingly low royalties a burden on the operator. The fact that taxes on private properties are deliverable in kind is also an unusual provision for which there is no good precedent. The pipe line provisions are also noteworthy, and the government has authority to fix rates and also to deny permits to construct pipe lines for reasons affecting national economy. There are also clauses enforcing unit operation on both public and private lands, and collecting a tax of 1 c. per 1000 ft. of gas wasted. It remains to be seen whether this bill will be enacted, or whether it will be substantially modified. This much may be said, however, that unless it is modified, it will defeat its own purpose; i. e., promotion of petroleum development in Colombia. Company Activities The South American Gulf Oil Co. shut down its operations during the year, and now employs only watchmen at its camps, Las Monas and El Tigre. The Standard Oil Co. of California continued operations on the Coast at Repelon and Gualapa. At the close of the year Repelon

Jan 1, 1931

By O. Hall

DIAMOND drilling has become a very important factor in mining. It is the most satisfactory method of obtaining proof of the existence of an orebody and of determining the character and extent of the body, in measures where a core can be made. Large investments are based on the information obtained. The method of development, the mine and reduction plants, and subsidiary essentials as railways are often built without other information. The Mond Nickel Co. has drilled about 50,000 ft. (15,240 m.) per yr. for several years and has given considerable study to the question of improving the methods and of overcoming the limitations of this means of securing information. One of the main limitations of the diamond drill has been its inability to drill a straight hole. To depths of 1000 ft. (304 in.) the deflection is often not large but all holes tend to curve and take somewhat erratic courses. A hole running at a small angle to a fissure plane tends to run, along the fissure. If the hole is at a large angle, the tendency is to penetrate the fissure plane at right angles. The face of the bit having one side in solid formation beyond the fissure, the other in the selvage of the fissure tends to turn, the rods curving to the extent of their clearance in the hole. Usually rock measures have somewhat regular fissuring or strata and holes take somewhat similar courses, usually at right angles to the fissuring or strata. Excessive pressure or short or worn core barrels increase curvature. Slow speeds, correct feeds, sharp hits, and core barrels the full size of the hit, tend to decrease curvature but do not prevent it Curvature once started increases rapidly. The disappointments from crooked holes have been numerous. Discoveries have later been found to be on the properties of others. One Canadian company had a hole, supposedly discovering ore 300 ft. (91 m.) from old workings, unexpectedly turn in 8 ft. (2.4 m.) of wooden core from a timber in the old workings.

Jan 9, 1919

By H. A. McKinstry, F. F. Lange

A vector analysis of orientating single crystals using the Laue back-reflection X-ray technique is given. Briefly, the analysis involves using a few data taken from a Laue photography and defining the crystal co- ordinate axes in a reference coordinate system. After a few matrix multiplications, the proper goniometer angles can then be determined to orient the crystal coincident with the reference frame. This analysis is easily programed for a digital computer to provide a fast, precise, and efficient method of orienting many crystals which are identical. The general procedure is as follows. The crystal is mounted on a goniometer. Laue photographs are taken until an array of diffraction spots is observed that includes a Laue spot that represents a rotational axis of symmetry. The rotation angles of goniometer are recorded. These angles are defined as positive for a counterclockwise rotation. When the axis of symmetry is located on the Laue photograph, the crystal coordinate axes can be defined in the reference coordinate system* as follows. Two Laue spots are chosen, one of which corresponds to the rotational axis of symmetry and the other to a set of planes whose zone axis is a known crystallographic direction and normal to the rotation axis of symmetry. The Laue spots are used to determine these two crystal directions in the reference coordinate frame. This is done by placing the Laue photograph on a sheet of polar coordinate graph paper and determining the polar coordinates (r, o) of these two diffraction spots in the reference coordinate frame. Their third coordinate is the distance between the crystal and the film (-D). The coordinates Xni of the two crystal directions Nn, (n = 1, 2) in the reference frame are then calculated by the following equations: Xn1 = -D X2n = Ancos on X3n = A, sin on where -tan- 1 rn/D An =Dtan(tan-1rp/D/2) By taking the proper cross products of these two directions (normalized to unit vectors), the crystal coordinate axes 3 (i = 1, 2, 3) can be determined in the reference frame. This is illustrated in Fig. 1. The next step is to determine the relation between

Jan 1, 1969