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By D. K. Deardorff, Earl T. Hayes

An improved technique is described for the accurate determination of melting points of metals in the temperature range 1500' to 2500°C. The improvements consist of gradient heating and refinements in cavity preparation to obtain true black-body conditions. The melting point of hafnium, as determined by this method, is set at 2222°±30°C. This is over 200°C higher than one of the values reported earlier. Discrepancies in the previously reported values for the melting point of hafnium are explained. The melting points of zirconium and titanium are found to be 1855O±15OC and 1668°±10°C, respectively. Reproducibility of results was ±3OC. PRIMARILY, this report is being made to correct a 1975o±25oC1 value for the melting point of hafnium, and to present an improved method for melting point determination. As a matter of interest, the technique was also applied to determining the melting point of zirconium and titanium. There is a wide difference in the melting point of hafnium as reported by competent investigators. DeBoer and Fast' reported a value of 2230°±500C, and later work of McPherson, as reported by Aden-stedt, placed the melting point at 1975o±25oC. Zwikker" calculated that the melting point was 2430°C. In resolving this discrepancy, improvements were made in the procedure for determining the melting points of refractory metals in the range 1500" to 2500°C. Special techniques are necessary to determine the melting point of these metals accurately. Since the metals oxidize in air above 900oC, the determinations must be carried out in an inert gas or vacuum. Also, every known refractory contaminates them to some extent. In addition, the attainment of true black-body conditions is always difficult. DeBoer and Fast actually determined the melting point of Hf-Zr as-deposited iodide process alloys and extrapolated to 100 pet Hf. McPherson employed a tungsten wire suspension similar to that described by Schramm, Gordon, and Kaufmann,1 and used hafnium metal produced by the iodide process. There was no apparent reason for the wide spread in melting points, since the quality of the metal was very good and the work was under the direction of highly competent investigators. Retracing some of this work revealed one understandable error in the case of hafnium, and led to development of an improved technique for determining melting points of reactive metals in the range 1500" to 2500°C. Material Crystal bar hafnium, zirconium, and titanium were used for this work, with analyses as shown in Table I. The hafnium was of the highest purity that has been prepared, though not as pure as the zirconium and titanium. At the instigation of the Pittsburgh Area Office of the AEC, a special lot of Hfo2 was purified, converted to the tetraflouride, and bomb-reduced with calcium, all at the Iowa State College Laboratories. This crude hafnium metal was then refined by the iodide process at the Foote Mineral Co. All specimens were cut with a Sic wheel, ground, pickled, and dried carefully before use. Procedure General Tungsten Suspension Method—In this method, a small specimen is suspended by a fine tungsten wire in a slender, induction-heated tungsten or tantalum cylinder, all under vacuum. The melting point is determined by heating the specimen slowly while observing it with an optical pyrometer focused upon a portion of the specimen that radiates as a black body. This means that there should be no reflected radiation, either from colder objects near the pyrometer or from hotter surfaces. The induction heater would be the only hotter object and, if it is slender enough, the specimen will attain the same temperature. Often a slender hole is drilled into the specimen as a source of black-body radiation. This was the general method used by McPherson in obtaining his value of 1975°C for the melting point of hafnium. In trying to repeat this work, it was found that the points of contact between the

Jan 1, 1957

By A. D. Hughes

A relatively small area in Malaya, about 200 miles long by 40 miles wide, is the most important source of tin in the world. Some tin is recovered in other parts of the peninsula. Of the tin mined, 98 pct is recovered from alluvial deposits. From 1935 to 1941 the average annual world production of tin was 190,000 tons. The average annual production from Malaya during the same period was 62,000 tons or about one third of the total. Other producing countries, in order of importance, were the Netherlands East Indies 34,000 tons, Bolivia 30,000, Belgian Congo, Nigeria, Siam, Burma, China, and a few others with smaller amounts. The serious shortage of tin during the war period was due to the fact that the Japanese were occupying Malaya, Netherlands East Indies, Siam, Burma, and China which, together, formerly were producing 65 pct of the world supply.

Jan 1, 1949

By R. M. Bird

FEW persons outside of the foundry trade have any conception of the great variety of sands now regularly specified and furnished, nor of the differences in foundry practice frequently resulting from apparently minor changes in sands. Conditions in each locality where the sands are mined and prepared necessitate special equipment designed to perform the work efficiently. The description that follows of the foundry sand producing operations is typical of the areas in New York and New Jersey, and particularly refers to the operations of the George F. Pettinos Co.

Jan 1, 1926

By Frederic Carter

THERE have been many attempts to prove that platinum was known to the ancients, but since no traces of the metal have been found in the relics of early times, it must be concluded that it had not been known to them. As far as records go, it was actually first discovered in the 16th century in a Spanish mine on the Pinto River in South America; from which source it received its name of Platina del Pinto (little silver from the Pinto). It was more or less of a rarity and was a subject of interest to a few chemists only, until the year 1822 when the metal was first discovered in Russia. In 1819 there had been noticed in the washings of the gold sands of the southern part of the Ural Mountains, grains of a heavy white substance, but it was not until three years later that this substance was found to contain platinum. While at first the amounts of platinum brought from the Urals had been meager, prospecting soon disclosed rich deposits extending over a considerable area, and nuggets from 10 to 20. lb. were by no means rare. This discovery assured to chemists an ample supply of platinum for their crucibles, etc. The ore is now found in various parts of the world but the richest deposits are still found in the Ural Mountains. The platinum of commerce is obtained entirely from alluvial deposits at depths varying from 6 to 40 ft. The sand and gravel of former river beds are subjected to a series of screenings and washings to effect the separation of the ore. Actually, probably all gold-bearing gravel beds of the world contain platinum, and it is more than likely that large quantities of platinum ore have been thrown away with the black sand washings from gold placer deposits. This is especially true of the alluvial deposits of the Pacific Coast in California and Oregon. Platinum ore is usually found in the form of rounded or, flattened grains of "sand," and occasionally in irregular lumps of the size of peas. Large nuggets are very rare. The ore has a metallic luster and is distinguished by its steel gray color, but shows light gray streak when rubbed on a hard white surface; it has a high specific gravity, 16 to 19; is infusible in the hottest blast furnaces, and insoluble in any single acid. Platinum ore is a complex body consisting of the metal in combination with varying proportions of the other members of the platinum group; iridium,

Jan 1, 1928

By Sidney H. Haughton

FOLLOWING the discovery of diamonds in 1870 and the Witwatersrand gold fields in 1886 South Africa changed from a predominantly pastoral country with a scattered white population into a land whose economy came rapidly to be based primarily on mining. The total value of the mineral output of the Union in 1944 was approximately $493,000,000, to which gold contributed 84 per cent. Gold furnished some 33 per cent of the Union Government's total revenue in that year, and approximately half the country's population obtained its livelihood directly or indirectly from the gold mining industry. In any review of the Union's mining activities and in any consideration of the country's future, gold mining must occupy a prominent place. It is generally conceded that the present structure is not properly balanced and that an economy based on a preponderance of a single nonpermanent factor possesses potentialities of serious instability.

Jan 1, 1946

By Peter N. Blakey, Thiann R. Yu, Douglas O. Tansey

A flexible, efficient, and relatively low-cost drilling and blasting operation has evolved at Texasgulf Canada, Ltd.'s Kidd Creek underground mine. Located 32 km (20 miles) north of historic Timmins, Ontario, the underground operation utilizes a sublevel open stoping method developed with large-diameter blastholes. Over the years, Kidd Creek engineers have experimented with various drill-and-blast techniques, leading to the present-day practice. Continuing work is being conducted to further mechanize the blasting operation.

Jan 6, 1976

By Gordon MacVean

THE adoption of rock dusting, as a safety measure, has made notable progress in the West Virginia coal mines since May, 1925. At that time there were but two mines in the State that were thoroughly rock dusted, mines No. 2 and No. 12 of the Boone County Coal Corp., at Sharpless. Since then it is probable that 75 per cent of the coal operators in the State have given consideration at one time or another to rock dusting. This growth of interest followed the meetings of the various mining institutes all over the country, during the summer of 1925, at which papers were presented, drawing the attention of the coal mining operators to the merits of this safety measure. Yet outside of the experience with rock dusting at the Old Ben Coal Corp., of Southern Illinois, and the Carbon Fuel Co., of Rains, Utah, there had been no actual occurrence in the coal mines of the United States, which could be taken as positive evidence of the efficacy of rock dusting in the prevention of the propagation of coal dust explosions. The U. S. Bureau of Mines, however, had run innumerable tests under conditions which closely approximated actual coal mining conditions and had clearly shown that rock dusting was effective.

Jan 1, 1926

By OWEN H. PERRY

One of man's primary tools is the ordinary screen. Whether of mesh or punched plate, it is fundamental in principle, primitive in its origin, and common in its application through all the world; and yet the screen goes only a part of the way toward the completion of its job of separating materials according to size. It will give a practical and continuous separation according to "size," as generally understood (accurate according to the breadth), but the accurate and continuous separation as to thickness is not a practical function of the screen. Still, all through history, the thickness of particles of material must have been important to many people; therefore, one would expect that some standard method of sizing for thickness would long since have been evolved and that equipment applying that method would be readily available to any in¬dustry. This, however, seems not to be so.

Jan 1, 1949

By A. W. Hale

IN a work published in 1838, De Morgan, the author of the article on "Probabilities,' in the Encyclopedia Metropolitana, says " The method of least squares is not yet introduced into the affairs of common life,….that many things which are demonstrable only by the higher branches of mathematics are looked upon as useless." And he mentions an instance in which "a method was suggested for estimating the relative importance of boroughs, by considering their population and contributions to the revenue com-

Jan 1, 1881

By H. M. St. John

MAINTAINING a satisfactory structure in brass and bronze castings has always been a foundry problem of great practical importance. While metallurgists and scientific investigators have not entirely ignored this matter, it has received less of their attention than has been given to iron, steel and the wrought copper and aluminum alloys. Investigation in this field has probably been discouraged to some extent by the complicated nature of the alloys involved. Hundreds of alloys are in more or less common use, most of them containing copper, zinc, lead and tin in-widely varying proportions. They also contain appreciable percentages of iron and antimony as impurities, and often phosphorus, which has been added as a deoxidizer and fluidifier. Small amounts of sulfur are usually present. It is not uncommon to find nickel, sometimes in rather substantial quantities. Traces of other metals are frequently present. So complicated and variable a mixture obviously offers difficulties in. any investigation of the various factors that influence the structure and other properties of the casting.

Jan 1, 1930

By RALPH HAYES SWEETSER

IRON ore and bituminous coal are the two basic raw materials for the whole iron and steel industry. The ore furnishes the iron and is absolutely necessary-all iron and steel products come directly or in- directly from the iron ores. The bituminous coal furnishes the carbon needed for the smelting of the ores and for the fuel used in all the processes of iron and steel manufacture. The necessary carbon could be furnished in some other form besides bituminous coal. In fact, it is only since the Civil War that bituminous coal has been the chief source of the carbon for metallurgical fuel. For many years only charcoal made from the forests furnished the carbon for smelting iron ores. About 90 years ago, anthracite coal was first used as blast-furnace fuel and for many years continued to be the chief blast furnace and steel making source for carbon. Even in my own blast-furnace experience, I have used charcoal in Canada and anthracite in Pennsylvania for smelting ores in an iron blast furnace. Bituminous coal, now almost exclusively the source for the carbon used in smelting iron ores, also furnishes most of the heat used in the steel-making processes. It is seldom used in blast furnaces in its natural condition, hut is first coked in beehive, or in by-product coke ovens; such bituminous coal is called "coking coal." Bituminous coal that is suitable for making the producer gas used in the open-hearth steel process is called gas coal. Any bituminous coals suitable for making blast-furnace coke or foundry coke, or that can be satisfactorily used for making producer gas, are classed as metallurgical coals and as such are to be considered in my proposed plan for the evaluation of metallurgical coals. According to Bureau of Mines Bulletin No. 449 these coals comprised 22 per cent of the bituminous coals mined in this country in 1923.

Jan 1, 1926

By AIME AIME

THE first meeting" of the Iron and Steel Division was held Tuesday afternoon, Feb. 17, with nearly 100 men present and C. B. Murray as chairman. This was a round table discussion of iron ore beneficiation and of its relation to blast-furnace operations, and only one paper was presented, by Clyde E. Williams. Mr. Williams discussed the future of the Lake Superior district in its relation to the iron and steel industry. He stated that although estimates had shown that the total life of the present known iron ore reserves of the Lake Superior district was 20 to 30 years and that many believed that as a result of this depletion foreign ores would be brought to the Atlantic Seaboard, thus causing a displacement of the steel industry to the East, he believed that the Lake Superior district would continue to be the important producer of iron ore used in this country for decades beyond the predicted time before the exhaustion of the present known reserves. He described the three general types of ores that required concentration and pointed out the needs for research and the proper methods to be used in processes for the beneficiation of these low-grade materials. He discussed the effects of fine concentrates and the use of agglomerated ores in the blast furnace. This general summary led to interesting and valuable discussion on the various economic, ore-dressing, and blast-furnace problems in large-scale development of beneficiation. Perry Harrison described recent developments in sintering and the properties of iron ore sinter. T. B. Counselman and W. H. Coghill discussed the merits of classification of iron ore previous to tabling. Robert Faulkner and J. E. Little described the beneficiation plant of the Bethlehem Steel Corporation.

Jan 1, 1931

By Davenport, Edmund S.

THE specific aim of this work has been to study certain forms of internal deterioration which occur in tungsten filaments when subjected to high temperatures under various conditions, and to determine the cause of such deterioration. This would naturally lead to a consideration of methods of control or means of prevention of the phenomena. The deterioration was first noticed as a peculiar condition in the grain boundaries of certain tungsten filaments which had been burned t for long periods in lamps. In these cases it was noted that the grain bound aries contained a number of minute black dots which were at first thought to be non-metallic inclusions. It was demonstrated later that these dots or pits, as they were designated, could be readily produced by burning filaments in an atmosphere of flowing hydrogen. This method was convenient and adequate for the purpose, and was adopted for most of the work discussed in this paper. The evidence accumulated to date indicates that these pits arc actually small voids between the grains. The purpose of this paper is to, present the information on this interesting subject gathered during a period of about 3 years. As applied to tungsten, the subject appears to be of considerable importance, experience having shown that this pitting is frequently associated with poor performance of filaments in lamps.

Jan 1, 1927

By Welton J. Crook

Unless present, in considerable praportion, metals of the precious-metal group—other than gold and silver—are not readily detected by the methods of fire assaying usually applied to ores and metallurgical products. Platinum, when present in small quantity, will ordinarily be reported as silver unless special methods of parting are used. Other elements occurring in the gold itself are all fluxed and slagged in the assay operation and if analyses are made on bullions the melting and slagging operations to which the bullion has been subjected may eliminate most of the associated elements. On the other hand, the analysis of precipitate from the cyanide treatment of gold ores may reveal the presence of many unexpected elements, such as tungsten and molybdenum. It is uncertain, however, whether many of the elements present in the precipitate are derived from the ore gangue or from the gold itself. No very general survey of the distribution of metallic elements in gold seems to have been made. Rose and Newman,l in connection with the composition of native gold, say in part as follows: Gold is occasionally found alloyed with copper and sometimes also with iron, bismuth, lead, mercury, tin, antimony, palladium or rhodium. Rhodium gold from Mexico was found to be of the specific gravity 15.5 to 16.8 and contained 34 to 43 per cent of rhodium. The native alloy of palladium, gold, and silver from Porpez contains 85.98 per cent of gold, 9.85 per cent palladium and 4.17 per cent silver. Mal-donitk, from Victoria, contains gold 64.5 per cent, bismuth 35.5 per cent (Louis). Dana2 says that native gold is usually alloyed with silver in varying amounts, and that sometimes it also contains traces of copper and iron. Rare varieties contain palladium, rhodium and bismuth. Other authors, for instance Zeigler3 and Clark,4 give similar information. Most references on the subject agree that ordinary native golds contain, in common, the elements silver, copper and iron. After completion of the work of which this paper is a record, the conclusion is reached that all ordinary native gold probably does contain these elements and, although in certain cases other elements may be found to be present, that it is difficult to

Jan 1, 1943

By Welton J. Crook

Unless present, in considerable praportion, metals of the precious-metal group—other than gold and silver—are not readily detected by the methods of fire assaying usually applied to ores and metallurgical products. Platinum, when present in small quantity, will ordinarily be reported as silver unless special methods of parting are used. Other elements occurring in the gold itself are all fluxed and slagged in the assay operation and if analyses are made on bullions the melting and slagging operations to which the bullion has been subjected may eliminate most of the associated elements. On the other hand, the analysis of precipitate from the cyanide treatment of gold ores may reveal the presence of many unexpected elements, such as tungsten and molybdenum. It is uncertain, however, whether many of the elements present in the precipitate are derived from the ore gangue or from the gold itself. No very general survey of the distribution of metallic elements in gold seems to have been made. Rose and Newman,l in connection with the composition of native gold, say in part as follows: Gold is occasionally found alloyed with copper and sometimes also with iron, bismuth, lead, mercury, tin, antimony, palladium or rhodium. Rhodium gold from Mexico was found to be of the specific gravity 15.5 to 16.8 and contained 34 to 43 per cent of rhodium. The native alloy of palladium, gold, and silver from Porpez contains 85.98 per cent of gold, 9.85 per cent palladium and 4.17 per cent silver. Mal-donitk, from Victoria, contains gold 64.5 per cent, bismuth 35.5 per cent (Louis). Dana2 says that native gold is usually alloyed with silver in varying amounts, and that sometimes it also contains traces of copper and iron. Rare varieties contain palladium, rhodium and bismuth. Other authors, for instance Zeigler3 and Clark,4 give similar information. Most references on the subject agree that ordinary native golds contain, in common, the elements silver, copper and iron. After completion of the work of which this paper is a record, the conclusion is reached that all ordinary native gold probably does contain these elements and, although in certain cases other elements may be found to be present, that it is difficult to

Jan 1, 1943

By J. A. Burkhardt

Field measurements and theoretical studies have been made of pressure surges—momentary variations in fluid pressure—produced by movement of pipe in mud-filled boreholes. Pressure measurements were recorded by five pressure gauges located at various positions in the borehole. An important positive pressure peak was found to occur as the casing moved with maximum velocity. Important negative peaks were found as the casing was lifted from the slips and as brakes were applied to stop pipe movement. A rigorously formulated theory has successfully predicted the sequence and magnitudes of these positive and negative surges and has established a basis for understanding how they occur. Both the measurements and theory indicate that the most important pressure surge is usually due to viscous drag of the flowing mud. The theory of viscous-drag pressure surges has been approximated by simplified graphs and calculation procedures to facilitate ready use in field operations. Comparison of measured results with those predicted by the simplified theory shows that the magnitude of this surge can be predicted accurately. INTRODUCTION It is widely recognized that raising or lowering pipe in a fluid-filled borehole produces momentary variations in fluid pressure, commonly called pressure surges. Both negative (or "swabbing") surges and positive (or "fracturing") surges may occur. In 1934, Cannon1 measured the negative surges and showed that they could be large enough to cause flow of formation fluids into the well-bore and, in extreme cases, lead to blowout conditions. Later, Coins2 measured the positive surges associated with lowering pipe. His results and subsequent field operations strikingly demonstrated that pressure surges could be an important factor in some cases of lost returns. In addition, although the evidence is less clear than in the case of blowouts and lost returns, other investigators 3, 4 feel that pressure surges probably play a part in many instances of minor gas cutting, salt-water flow and other hole trouble. The importance of pressure surges in drilling operations led naturally to attempts to explain the physical causes, nature and magnitude of the surges. Cardwell5 was the first to publish a theory which allowed the quantitative prediction of momentary pressure variations. He assumed that the drilling fluid was a 300-cp Newtonian fluid in turbulent flow. Most field muds have a considerably lower viscosity and are generally believed to be Bingham plastic in nature.6 However, card-well's results were useful because they were presented in a form convenient for field use and, in some cases, gave a reasonably accurate predicted value for the maximum pressure surge. Subsequently, Ormsby7 published a more comprehensive theory of pressure surges. He discussed both laminar and turbulent flow and considered the theory of mud-bypass devices for reducing pressure surges. As a consequence of his more rigorous approach, his results were more accurate but more complex and difficult to use. Further, both Ormsby and Cardwell considered only the pressure surge arising from viscous drag of the moving mud. Clark later published idealized graphs of surges and presented equations for predicting their magnitudes. In addition to pressure variations arising from viscous drag, he considered those caused by inertial effects. His theory was in this respect more complete than those of Cardwell and Ormsby, although he did not discuss pressures due to breaking of the gel. Furthermore, his equations, while not exceptionally complicated, were too complex for ready use at a drilling location. One difficulty common to all three theories is that none was tested rigorously by direct comparison with measured pressure surges. Their accuracy, therefore, could, not be demonstrated. Further, the two theories based on most realistic assumptions (Ormsby and Clark) required the solution of one or more rather complex algebraic equations. The research described in this paper was undertaken to supplement that described and to overcome some of the difficulties noted. It seemed obvious that a fully satisfactory study of pressure surges should encompass three main phases. 1. A valid theory useful in all field situations must be developed. This theory must be based upon realistic assumptions, must be formulated rigorously and should lead to clear concepts whereby the nature of pressure surges can be easily understood. 2. The theory, however complex and involved, ultimately must be presented in simplified form for convenient field use. This may involve extensive machine computations and the use of figures and empirical equations. 3. The accuracy of the simplified equations must be established by comparing measured pressure surges with those predicted by the theory. These must agree both in their characteristic nature and in magnitude. 'This means that careful measurements of surges occurring in actual field operations must be made.

By AIME

THE wind howls almost incessantly over the mining engineers working in the near desert that is the Division of Namaqualand, the upper Atlantic coastal corner of South Africa's Cape of Good Hope Province. But when these men at the U. S.-owned mines called Nababeep South and East O'okiep (pronounced Oh-keep) tell you about their achievements, they can be heard above the wind. For their O'okiep Copper Co. Ltd. now produces over half the Union of South Africa's annual output of 30,000 tons of copper metal. Moreover, it is a very decent sample of U. S. geotechnical imagination. financial daring, and managerial skill, all operating successfully in a

Jan 1, 1947

By H. O. Hoffman, C. D. Demond

There are two methods of determining the fusibility or refractoriness of fire-clays, the theoretical and the experimental. In the former, conclusions are drawn from the chemical composition; in the latter, from the changes which the clay undergoes when subjeoted to intense heat. It is well to use both methods, beginning with the actual heat-test and explaining the results obtained from this by the help of the chemical analysis. In discussing the subject, however, it is better to reverse this order. I. The Theoretical Method.* Leaving out the hygroscopic and combined waters and any organic matter, as not directly affecting the fire-resisting property, the refractory constituents of fire-clay are alumina and silica, and the fluxing constituents magnesia, lime, soda, potash and ferric oxide. According to Bischof,† alumina is the least fusible component, and silica follows close upon it. If, however, a mixture of the two be heated, it will be found that its melting-point is much lower than that of alumina, as a silicate will then have been formed. The way in which silica affects the refractoriness of alumina has been strikingly presented by Seger 1 in a diagram reproduced in Fig. 1. The abscissæ represent the melting-points of Seger cones Nos. 26 to 36 (see p. 55); the ordinates, the relative amounts of alumina and

Jan 1, 1895

By J. S., Douglas

IN 1880, the late James Douglas, LL.D., was superintendent of the Chemical Copper Co., operating the Hunt & Douglas process for the treatment of the siliceous copper ores of the Jones mine at Phoenixville, Pa. In conjunction with this a refining furnace was operated. After correspondence with Ben Williams, of Bisbee Ariz., who was commencing the mining and smelting of the Copper Queen ore. Dr. Douglas decided-to make his first journey to Arizona. While making plans for the trip lie visited a friend in Philadelphia, a .Mr. Logan, a prominent lawyer. He, through Professor Treadwell, brother of the discoverer of the great Treadwell gold mine of Douglas Island, Alaska, had an option with his min¬ing partner, Mr. Lenig, on the Eureka and Wade Hampton claims near the headwaters of the Verde River in Yavapai County, Arizona. These two claims, later the source of practically all of the wealth of the Jerome district, were then owned by C. P. Head and Co. Prescott merchants. Hugo Richards, banker, and formerly sutler at Camp Apache; Rod and John McKinnon prospectors and Nova Scotians; and perhaps one or two 'other owners of minor interests. Mr. Logan, hearing of Dr. Douglas intended trip to Bisbee, asked him to go first to see the two mining prospects, and this, Douglas, in need of the $500 fee, agreed to do as the time on the option on the claims was running short.

Jan 1, 1935

By R. K. Govila, E. H. Parkison

THE interplanar angles for hcp metals vary with c/a ratio, and therefore must be computed separately for each particular metal or alloy. Manual computation of these angles is laborious and time consuming, and for this reason computer programs have been developed to accomplish this task.1"3 However, these programs have certain disadvantages. For example, they require prior knowledge and understanding of ALGOL or FORTRAN languages. Further, they will not print out specific angles but instead give all angles between given limits—thus program2 prints out a total of 26,649 angles between planes with indices and in the range from (4 4 4) to (4 4 4) for any given c/a ratio. The purpose of this note is to present a simple and inexpensive computer program for accomplishing this task. This program is written in BASIC language4 which does not require any prior knowledge of computer programming, and is ideally suited for nonprofessional programmers. It also provides flexibility for the user by allowing him to select any indices for as many or few planes as desired for any given c/a ratio. The computer program proposed below is based on the relationship in which + is the angle between any two planes and . TO illustrate use of the program, consider the problem of calculating the interplanar an-

Jan 1, 1970