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By Frances Hurd

WHEN 60:40 brass is heated to 825° C., given a drastic quench to obtain the beta solid solution, and reheated, various changes take place in the structure. Reheating at 200' C. causes a fine, granular, sorbitic structure to appear which has been considered alpha solid solution. These particles coalesce at higher temperatures of reheating, and at 470° C., the alpha forms twins. A further study of these transformations was considered worth investigating.

Jan 1, 1927

By H. G. Schneider

The Smackover oil and gas field lies in Ouachita and Union Counties, Ark., in the south-central part of the state, in T.15 and 16S., R.15, 16, and 17W. It is 10 miles north of El Dorado, the principal business and railroad center in the south-central part of the state, and extends from the town of Smackover in all directions. Productive territory having an aggregate area of nearly 55 sq. mi. has been developed. It extends 6 miles from north to south and 12 miles from east to west. The field may be divided into two parts: the east district, which includes the area east of the town of Smackover, and the west district, which includes the area west of the town of Smackover. In relation to the neighboring productive fields of Arkansas, the Smackover field is 9 miles north of the El Dorado oil and gas field, 8 miles slightly west of north of the East El Dorado oil and gas field, and 16 miles east of the Stephens oil field. Smackover was discovered in May, 1922, when the Oil Operators Tnist drilled well No. 1 on the J. T. Murphy farm, in the southeast quarter of sec. 8, T.16S., R.15W. This well is located almost on the top of the Norphlet dome and was drilled to the Nacatoch sand. It had an initial open flow volume of 30,000,000 cu. ft. of dry gas per day, and a rock pressure of 950 lb. per sq. in. In July, 1922, the V. K. F. Co. completed the first oil well in sec. 29, T.l5S., R.l5W., on the north side of the Norphlet dome, and 3 miles north of the first gas well. This well started the active development of the north and northwest sides of the dome.] The field was extended westwards, when oil was discovered in the Nacatoch sand, during October, 1922, in sec. 4, T.l6S., R.l6W., 51/2 miles west of the original gas well. This opened up the so-called "light oil district," which is located on a structural terrace, for which the name

Jan 1, 1924

By AIME AIME

SILVER reached a new high, with the ceiling the limit, at the annual Institute dinner at the Commodore on Washington's Birthday night. Carrying along as ballast other commodities, such as rolls, roses and ferns, souvenir boxes and table number placards, hundreds of silvery balloons, cut loose from their moorings at the tables, bounced idly against the plaster decorations high overhead. At the head table, Scott Turner, retiring President, pre- sided as toastmaster, with the new President, Frederick M. Becket, on his right, and the Chairman of the New York Section, Sydney H. Ball, on his left. Many other distinguished Institute members, medalists, and representatives of organizations and committees, ranged to the east and west. Each had the opportunity at least to rise and bow.

Jan 1, 1933

By Dunbar D. Scott

The development in the perfection of mine-surveying instruments has been by no means rapid, as it has depended somewhat on the details of construction borrowed from astronomical and geodetic theodolites, largely on the restrictions laid down by mining companies and the prejudices of mine managers themselves, but more than all on the methods used in conducting surveys and the importance attached thereto. Mine-surveying, in some form or other, has been practiced from the very earliest times; but it has never kept pace with the other branches of surveying, or even with the art of mining itself, and cannot be recognized as an exact science until shortly before the beginning of this century. The works of Hero of Alexandria, who lived in the second century B.C., are still extant, and contain descriptions of a rectangular sighting-instrument, which he invented and called a diopter. His improvement upon this simple construction, which possibly he devised for use in the Greek mines for rough leveling-purposes and for laying out any angle, must be considered, says Hübner," as the origin of the highly perfected theodolite of to-day. Whether this instrument came into general use during the first centuries of the Christian era, is not recorded; in fact, no writer undertakes to tell how mine-surveying was conducted until 1556, in which year Agricola expounds the principles of mining and metallurgy in his De Re Metallica, devoting the entire fifth chapter to the practice of mine-surveying (see Fig. 1). In mediæval times those who possessed any knowledge of engineering skill made strenuous effort to keep their art a secret, partly on account of the miners' proverbial conservatism and partly for their own personal aggrandizement, and were, in

Jan 1, 1899

Charles H. Morgan, Worcester, Mass. (communication to the Secretary): In connection with Mr. Douglas's mention of the continuous charcoal kiln used at Kopparberg, some further data concerning this important invention may be of interest. Before giving these, however, I will say a word or two concerning other features of Swedish practice. In 1894 I spent two days at Soderfers with Mr. Tom Bergendal, the manager of the works, and was specially interested in the gas-producers and wood-drying kiln, illustrated in the paper contributed to our Transactions by Mr. Odelstjerna in that year.* The wood-drying kiln is, however, quite different in design and construction from Ljungberg's charcoal kiln. In the summer of 1894 it was discovered that by placing the gas-producer as close as possible to the open-hearth furnace, and working the producer hot, ordinary weather-dried wood, still containing a considerable percentage of moisture, could be used to advantage in the melting-furnace. Hence, the dryingkiln was needed for wet wood only. One of the iron-works of the Udeholm Go. was the first to adopt the Lundin saw-dust gas-producer and condenser, enabling them to make gas from saw-dust containing 45 per cent. of moisture, and convey the gas from the condenser through wooden pipes to the Siemens steel-melting furnace.† This sawdust gas gave very satisfactory results in iron-works; but the proprietors experienced much trouble by reason of the pollution of rivers by the tar-water from the condenser. On my visit, in 1894,I found that the Udeholm Co. had put in for their steel-melting furnaces the same wood-gas producers

Jan 1, 1899

By Zay Jeffries

Tungsten has the highest melting point of all the known metals, namely 3350 C.; it is one of the hardest of the metals; it has the highest equiaxing or recrystallization temperature after strain hardening, of any pure metal known. It is particularly distinguished because, when composed of small equiaxed grains, it is extremely brittle and fragile at room temperature, and when possessing a fibrous structure it may be ductile and pliable at room temperature. The common ductile metals act in exactly the opposite manner in this respect. The present paper will include a brief note regarding the manufacture of wrought and ductile tungsten. The metallography of wrought and ductile tungsten in the various stages of manufacture will be considered more or less in detail. The general relationships between the properties of tungsten and other metals will also be considered. A discussion will be given explaining why fibrous tungsten is ductile at room temperature, even though past experience with other metals would indicate that it should be brittle. Finally, a brief note regarding some new fundamental metallographic propositions relating to all metals will be given. Manufacture of Wrought and Ductile Tungsten Up to about 10 years ago, it had not been possible to work tungsten mechanically. About the year 1908, Dr. William D. Coolidge, of the General Electrie Go., produced ductile tungsten from what was then supposed to be an inherently brittle metal and which, in fact, was inherently brittle in its normal state, that is, when composed of equiaxed grains. Since that time many products, chief among which are the filaments for electric incandescent lamps, have been made from wrought and ductile tungsten. Tungsten is produced chiefly from the minerals wolframite and scheelite.1-8 The ores may be reduced in many ways. For example, the ore may be fused with alkali carbonates and the fusion dissolved in water; sodium tungstate is formed, which is soluble in water. This

Jan 1, 1919

The cables brought the news last spring that the Institute had lost by death one of its most distinguished foreign members, Hjalmar Sjogren of Stockholm. For thirty-one years, Professor Sjogren had been one of our number. He was elected in 1891, joining the Institute at the time he was in the United States, in attendance at the Fifth International Geological Congress, which was held in Washington in the late summer of that year. Professor Sjogren was once more in America in 1906 and again in 1913, and on both of those visits his friends in New York had the welcome opportunity of extending courtesies to him. He was thus well known to a wide circle in our membership. His keen interest in the geology of iron ores brought him in touch with the many Americans who have studied them and who have been active in the important productive districts which he visited. Our Transactions contain (Vol. XXXVIII) one very important paper of seventy pages on the Geological Relations of the Scandinavian Iron Ores, which he contributed. Sten Anders Hjalmar Sjogren, to give his full baptismal name, was born June 13, 1856, and was the son of Anton Sjogren, a mining engineer, at the time in charge of the iron mines at Persberg, in the east and west iron-ore belt of central Sweden, about 160 miles west from Stockholm. The Persberg orebodies yielded magnetite and specular hematite from schists, with which limestones. were interstratified as well as the peculiar Swedish rocks called "halleflinte." The mines were also well known to collectors and students of minerals. While Hjalmar Sjogren was yet a lad, his father was advanced to the superintendency of a number of famous mining localities in this same district of Wermland. Paisberg, famous for its native lead, was one; and two others, Langban and Nordmarken, were among the most prolific sources of interesting minerals in all Sweden. In several localities, the pre-Cambrian limestones had obviously experienced the recrystallizing influences of intrusive igneous rocks and had been charged with the so-called "contact" minerals, which have found their way to the museums of the world. Anton Sjogren, the father, was a keen mineralogist and Hjalmar, the son, grew up in a favorable environment for receiving training and enthusiasms of the same sort. One is not surprised, therefore, to find Hjalmar Sjogren, in the long run, turning to mineralogy and geology as his final career.

Jan 1, 1923

The cables brought the news last spring that the Institute had lost by death one of its most distinguished foreign members, Hjalmar Sjogren of Stockholm. For thirty-one years, Professor Sjogren had been one of our number. He was elected in 1891, joining the Institute at the time he was in the United States, in attendance at the Fifth International Geological Congress, which was held in Washington in the late summer of that year. Professor Sjogren was once more in America in 1906 and again in 1913, and on both of those visits his friends in New York had the welcome opportunity of extending courtesies to him. He was thus well known to a wide circle in our membership. His keen interest in the geology of iron ores brought him in touch with the many Americans who have studied them and who have been active in the important productive districts which he visited. Our Transactions contain (Vol. XXXVIII) one very important paper of seventy pages on the Geological Relations of the Scandinavian Iron Ores, which he contributed. Sten Anders Hjalmar Sjogren, to give his full baptismal name, was born June 13, 1856, and was the son of Anton Sjogren, a mining engineer, at the time in charge of the iron mines at Persberg, in the east and west iron-ore belt of central Sweden, about 160 miles west from Stockholm. The Persberg orebodies yielded magnetite and specular hematite from schists, with which limestones. were interstratified as well as the peculiar Swedish rocks called "halleflinte." The mines were also well known to collectors and students of minerals. While Hjalmar Sjogren was yet a lad, his father was advanced to the superintendency of a number of famous mining localities in this same district of Wermland. Paisberg, famous for its native lead, was one; and two others, Langban and Nordmarken, were among the most prolific sources of interesting minerals in all Sweden. In several localities, the pre-Cambrian limestones had obviously experienced the recrystallizing influences of intrusive igneous rocks and had been charged with the so-called "contact" minerals, which have found their way to the museums of the world. Anton Sjogren, the father, was a keen mineralogist and Hjalmar, the son, grew up in a favorable environment for receiving training and enthusiasms of the same sort. One is not surprised, therefore, to find Hjalmar Sjogren, in the long run, turning to mineralogy and geology as his final career.

Jan 1, 1923

By Zay Jeffries

Each generation accepts the developments of the preceding generations without full appreciation of the difficulties that had to be overcome or of the effect of any given development on society. Today, the production of pig iron is the yardstick with which general industrial health and progress are measured. So natural and logical does this seem to us, that it is difficult to picture conditions prior to the fourteenth century when pig iron was unknown. Not only was pig iron unknown but iron or steel could not be melted and poured into castings; all iron and steel articles were forged from sponge iron. All castings, as well as many worked articles, were made of non-ferrous metals or alloys. In many parts of the world, over long periods of time, not only was the annual exchange value of non-ferrous metals greater than that of iron and steel, but their combined tonnage was greater. At present, the value of the pig iron produced in a year is of the same order of magnitude as that of all non-ferrous metals combined; the tonnage of pig iron is, however, about twenty times that of all non-ferrous metals combined. Owing to lack of records, we will probably never know the relative importance of the various metals at all periods in historic times. A certain conclusion is that the iron and steel industry, since the discovery of pig iron and the cheap methods of converting it into steel, has grown at a much more rapid rate than the non-ferrous metal industries. Notwithstanding their fundamental fitness for man's needs, iron and steel owe their importance in no small degree to the low cost of production. The low cost was a result of increased knowledge of the production appliances and of the metallurgical processes. This increased knowledge is the key to our modern industrial civilization. It will remain for future generations to determine whether there is now going on a gradual change toward greater importance of the non-ferrous metals, as compared to iron and steel. The world's pig iron production in 1920 was slightly more than twice what it was in 1890, whereas the non-ferrous metals production in 1920 was about two and one-half times that in 1890. Every non-ferrous metal industry has shown marked growth during the last thirty years. During this period, the production of cop-

Jan 1, 1924

By H. C. Gatos, Ahmed Azzam

A UTORADIOGRAPHY would appear to be sim-A pler and less time-consuming for diffusion studies than any of the radioactive tracer techniques commonly employed, namely, the sectioning, surface increase, and surface decrease techniques.' Accord- ingly, it was felt worthwhile to investigate the applicability of autoradiography to self-diffusion measurements, and gold was chosen for this purpose. The radioactive isotope Au'!'' was used, as obtained from the Brookhaven National Laboratory. Its radiation consists of p (0.97 mev) and y (0.41 mev) rays, and it has a half-life of 2.69 days. No-Screen X-ray film was found suitable for these experiments: the film has the desired high speed for recording P rays and yet is practically insensitive to y rays. On the other hand, due to the high atomic weight of gold, this metal is a strong absorber for p rays. The

Jan 1, 1953

By AIME AIME

THE paper by C. H., Lieb on the "Economics of Oil-Producing Practice" (June issue, M. & M.) contains much food for thought. The engineers should be gratified that an executive with Mr. Lieb's. responsibility should recognize their standing in the industry. Yet after giving them that recognition, he proceeds to spur them on to greater accomplishments by pointing out that their job is only partly done and in some instances poorly done. The operating policies in this paper when applied to new pools with flowing wells are sound. Neither do I take exception to their application to pumping wells. But I do wish to comment on what lie says about price when applied to the many more wells that are approaching abandonment that is, the small producing wells. Mr. Lieb states in effect that higher prices would be detrimental from the long range viewpoint. I doubt that the present prices of crude will provide an ample return from the hundreds of thousands of small wells that have possibilities of substantial recovery by means of water-flooding, repressuring with gas, and air drive. Probably expenditure for experimental work can he justified, but at this time it must usually be considered as experimental. Recently I visited a property where it was estimated that $250,000 would be spent on a 160-acre tract for flooding purposes. The rate of r e t n r n and amount of profit at today's prices are uncertain. It can be argued that if this type of recovery is not economic with crude at $1 then it can he delayed as it is now possible to secure economically an ample supply of crude from our flush fields. But these old fields still retain large quantities of crude in a dormant state, and should not he abandoned per-

Jan 1, 1936

By E. Horton Jones

CONTENTS I Page Introduction ....:......................... 3 Chapter I. Unit Costs. . ...................... 4 Chapter II. Comparative Costs ..................... 20 Chapter III. Composite Costs..................... 32 Chapter IV. Wage Scale....................... 36 Chapter V. Raw Material Prices................. 37 Chapter VI. Description oF Costs ................... 64 Introduction We have endeavored in the following "sheets" to give the unit construction costs derived from 'the building of the Arizona Copper Co.'s new smelter, Clifton, Ariz., starting in February, 1912, and completing February, 1914.l In Chapter I—Unit Costs—are to be found the most elementary total unit costs which the accounts provide for. They are usable in the Clifton district. Here too are found the percentages to be added to an estimate for Engineering and General Expense. In Chapter II—Comparative Costs—these elementary costs have been classified, averaged and reported as labor and material unit costs. In such form the labor unit costs, when properly applied to similar conditions as these under which they were derived, are usable anywhere. The material unit costs are better disregarded for more accurate estimates and replaced by a newly priced bill of material. In Chapter III Composite Costs are given. They are unit costs built up from several elementary units, and likewise units of larger dimensions and simpler application, valuable for

Jan 1, 1915

By HORACE H. EJIRICH

(New York Meeting, February, 1912.) PREFATORY NOTE.-The first part of this paper was sent to me by Mr. Emrich nearly nine months ago ; and. I held it, waiting for the second part, which he had promised to forward soon, so that I might submit the whole to some of his former professional associates, and advise him of their criticisms and suggestions before offering his work to the Institute. But, five days before the second part reached me, I received by telegraph the news of Mr. Emrich's sudden death. The paper has therefore not had the benefit of such a revision by the author as might have made it in some respects clearer and more complete. Nevertheless, I believe that experts in the branch of metallurgy with which it deals will find it both original and suggestive.-A. EILERS. I. PARTIAL REFINING IN THE ANODE-FURNACE. During my connection with one of the large New Jersey copper-refineries, and probably before that period, from 15 to 20 per cent. of the copper-bullion received was the very foul, leady blister-copper produced from lead blast-furnace matte. It had been customary to mix a small part of this blister with each charge of purer pig-copper, in the effort to dilute it as much as possible before casting into anodes; but tank-house conditions were such that I was led to try making entire furnace-charges of this blister, and refining it as much as possible in the furnace-afterwards casting to anodes and refining electrolytically, in tanks and solution separate from the main bulk of the purer copper. In making this experiment, notes were made, for several furnace-charges, of everything thought to have a bearing on the question, and some interesting facts were brought out, both in the furnace-working and afterwards in the tanks.

Jun 1, 1912

By H. DeWitt Smith, W. H. Sirdevan

The mine operated by the United Verde Copper Co. is situated near Jerome, Ariz., on the eastern flank of the Black Hills, at an elevation of approximately 5500 ft. (1676 m.) above sea level. The mine and the town of Jerome are located on a steep hillside, which slopes rapidly to the valley of the Verde River. The smelter town of Clarkdale is situated in the Verde valley 4.1 mi. (6.5 km.) distant in an air line from Jerome, and at an elevation of 3560 ft. The two towns are connected by the standard-gage railroad of the Verde Tunnel & Smelter R. R., a subsidiary of the United Verde Copper Co. This road is 11 mi. long and has a compensated 4 per cent. grade. At Clarkdale, it connects with the Verde Valley branch of the Santa Fe R. R. The narrow-gage (36-in.) line of the United Verde & Pacific Ry. was, until 1919, Jerome's only rail connection with a main trunk line. This road connects with a branch line of the Santa Fe system at Jerome Junction, after traversing 26 mi. of mountainous country. From the time of its location, in 1876, until its purchase by Senator W. A. Clark, of Montana, in 1889, the United Verde mine was worked on a small scale and shipments of high-grade gold-silver ore were made from the surface workings. Until 1894, when the narrow-gage railroad to Jerome Junction was completed, all supplies for the mine and smelter

Jan 1, 1922

By Michael S. Koleda

Less than two years ago, the, Congress, with broad bipartisan support, passed the Energy Security Act of 1980. A decade marked by ten- fold increases in world oil prices and two major interruptions in oil flows from the Middle East had ended. An all-out national commitment to transform America's vast tar sands, oil shale and coal resources into conventional fuels had begun. The national synfuels effort was to be public-private cooperation at a scale unmatched in peace time. Private industry would own and operate the synthetic fuels facilities. Government would reduce market uncertainties to acceptable levels. The potential government commitment was substantial. Up to $88 billion would be available through the Synthetic Fuels Corporation, principally in the form of contingent financing. Billions more would be spent through Department of Energy programs. Additional incentives for alternate energy development were contained in the Energy Tax Act of 1978. The Energy Security Act clearly specified national synthetic fuels production objectives: 500,000 barrels per day by 1987 -- 2 million barrels per day by 1992. Finally, said Congress, Uncle Sam was going to do something about rapidly rising oil prices, uncertainties of energy supply, and the resulting disruption to the U. S. economy. Simply put, the purpose of the Energy Security Act of 1980 was to provide government guarantees sufficient to get synthetic fuels projects off the private sector drawing boards and into commercial production. Because of their huge cost, technological uncertainty, and lengthy pay-out period, these projects were always second place to projects of smaller size, known technology and more rapid pay-out. The Energy Security Act was the legal expression of public policy to bring the free-market synfuels timetable into line with the faster paced political timetable in the interest of national energy security.

Jan 1, 1982

By R. E. Allen

THERE was once a time when a practical oil man would appraise or buy a producing property on the basis of from $200 to $500 per barrel of average daily settled production. Curtailment-has, for the present at least, caused a virtual abandonment of the "barrel -of settled production" as a yardstick of, oil property value and in its place has come the "barrel of allowable production," which, although an artificial thing, is nevertheless now the principal factor governing the rate of ?pay out? or investment return. The potential production of a well, settled or otherwise, is of less importance in determining the present worth of a well than is the rate at which it may be produced. Speaking only of true potential for the moment, it is obvious that of two similar wells having the same potential, the one having the highest rate of allowable production would be worth proportionately more than the one of lesser allowable. The discount factor for deferred return and risk can easily vary the present values of the two wells by as much as 20 per cent when allowable rates are not greatly different.

Jan 1, 1934

Sailing westward from the Society Islands in the fall of 1774, England's noted explorer Captain James Cook discovered New Caledonia-that long, linear island that has played such an important and varied role in the history of nickel. Upon his return to England the following year, Cook's announcement of this uncharted island generated governmental interest, but its distance from the Island Empire, the troubles in the colonies, and the difficulties with France combined to keep English interest indirect and in the background of the then-current events.

Jan 10, 1968

By Donald A. Dahlstrom

In 1961 it became increasingly more evident that significant technological changes must be made in minerals beneficiation. The status quo in technology in today's competitive markets will not be tolerated. Higher productivity, greater recoveries and newer and better products must be sought and incorporated with lower operating costs. In other words, "when you build a new mill, don't build an old mill." Recommended reading for proof of the vital necessity of new methods and techniques is in the September 1961 issue of MINING ENGINEERING. The article by one of MBD's cherished and true veterans, E. H. Rose, is entitled "Iron Ore: The BIG Picture". Because of new beneficiation methods for iron ores, nearly 47 million tons of plus 60% iron concentrates will be produced and another 40.1 million tons of capacity will be under construction or committed. Thus in a relatively short period, 87 million tons of this high-grade iron concentrate with record low silica will be available. As Mr. Rose also points out, "in gross tons, without allowance for better grade, this is the equivalent of almost exactly two-thirds of all iron ore used for all purposes in the U.S. and Canada in the peak years of 1953 or 1957." Needless to say, improved mineral beneficiation methods have had far more reaching effects than just the production of higher grade iron concentrate.

Jan 2, 1962

Thomas Haight Leggett, London, Eng. (communication to the Secretary): Mr. Hammond has given us a concise yet complete description of the Witwatersrand gold-fields, and the character of the operations which have resulted in their remarkable development.

Jan 1, 1902

By J. R. Morison, M. P. O’Brein, J. W. Johnson, S. A. Schaaf

The force exerted by unbroken surface waves on a cylindrical object, such as a pile, which extends from the bottom upward above the wave crest, is made up of two components, namely: 1. A drag force proportional to the square of the velocity which may be represented by a drag coefficient having substantially the same value as for steady flow, and 2. A virtual mass force proportional to the horizontal component of the accelerative force exerted on the mass of water displaced by the pile. These relationships follow directly from wave theory and have been confirmed by measurements in the Fluid Mechanics Laboratory of the University of California, Berkeley. The maximum force exerted by breakers or incipient breakers is impulsive in nature, reaching a value much greater than that produced by unbroken waves but enduring for only a short time interval. This impulsive force represents the ultimate development of the accelerative force and is produced by the steep wave front and large horizontal acceleration at the front of a breaker. This impulsive force greatly exceed. the drag force computed from the particle velocities of the breaker. The reader is cautioned that these preliminary results are applicable only to single piles without bracing and are likely to be modified somewhat where multiple piles are driven, one within the influence of the other or where multiple piles are connected by submerged bracing. This paper is essentially a preliminary report submitted at this time because of the current importance of wave forces in the design of offshore structures. An extended series of additional experiments is planned for the near future. Theoretical Relationships For the sake of simplicity of treatment, the theory will be developed from the equations for waves of small amplitude. The horizontal displacement of a water particle is described by the equation 2p cosh — (d + z) H L 2pt X =----------------------sin ----- . , (1) 2 2pD T sinh------ L The horizontal component of the orbital velocity is obtained by differentiation with respect to time as 2p cosh — (d + z) pH L 2pt u = ------------------- cos— .... (2) sinh- L The acceleration of the water particles at any position is obtained by again differentiating with respect to time as 2p cosh — (d + z) 9 u -2vH L 2pt -----=----------------------------sin ----- . . (3) 3 t T2 2pd T sinh------ L where H = wave height — ft L = wave length — ft d = still water depth — ft z = depth below the still water measured negatively downward — ft. T = wave period — sec t = time — sec The force exerted on a differential section, dz, in length is pD2 s u pD 1 dF= [CM (p/4) st + Cn/2 u2] dz • • (4) where D = pile diameter — ft p = water mass density — slugs/ft3 C, = coefficient of mass C,, = coefficient of drag Substituting for a s u/s t arid u2 from Eqs. (3) and (2), the force per unit length at any position z is dF p2 pD H2 &apos; / = — [- fM sin ? ± fD cos2 ? ] . . . (5) dz 2T2 fM D fD 2pt Cm = pA/H:CD = A2;? = T [+ cos2 ? for 0 < ? < p/2 cosh— (d+z) 3p L — < o < 2p Sin L -cos2 ? for p/2 <? <3p/2 The sin 9 term (inertia) i- negative for 0 < 0 < p and positive for p < ? < 2p. Values of A and A&apos; appear in Fig. 1

Jan 1, 1950