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By Bruce W. Gonser, A. U. Seybolt

A few copper-zinc-hasp alloys mppt die-casting requirements reasonably well, although improvements are desired. Aluminum bronzes, high-tin bronzes and some copper-nickel-zinc alloys can be die-cast, according to Herb,' but seldom are because of such factors as higher melting ranges and greater cost than certain of the brasses. Fox2 has summarized the copper-base die-casting alloys that were in commercial use in 1937 and has given the effects of different alloying constituents. Table 1 gives some of the properties of these alloys as reported by Fox. a Properties reported by Fox.2 b Trade name of Brastil, Doehler Die Casting Co., similar to Webert Alloy,34 American Brass Co., and Tombasil Alloy,5 Ajax Metal Co. e Trade name Tinicosil, Titan Metal Manufacturing Co. Melting point (liquidus) of the yellow brass is given by Herb1 as 1650" F., of the high-silicon Brastil (with 4.5 to 5 per cent Si) as 1600" F., and of the nickel silver as 1675" F. d Criterion not stated.

Jan 1, 1940

By A. U. Seybolt, Bruce W. Gonser

A few copper-zinc-hasp alloys mppt die-casting requirements reasonably well, although improvements are desired. Aluminum bronzes, high-tin bronzes and some copper-nickel-zinc alloys can be die-cast, according to Herb,' but seldom are because of such factors as higher melting ranges and greater cost than certain of the brasses. Fox2 has summarized the copper-base die-casting alloys that were in commercial use in 1937 and has given the effects of different alloying constituents. Table 1 gives some of the properties of these alloys as reported by Fox. a Properties reported by Fox.2 b Trade name of Brastil, Doehler Die Casting Co., similar to Webert Alloy,34 American Brass Co., and Tombasil Alloy,5 Ajax Metal Co. e Trade name Tinicosil, Titan Metal Manufacturing Co. Melting point (liquidus) of the yellow brass is given by Herb1 as 1650" F., of the high-silicon Brastil (with 4.5 to 5 per cent Si) as 1600" F., and of the nickel silver as 1675" F. d Criterion not stated.

Jan 1, 1940

By William E. Ford, Edward Salisbury Dana

The important BARITE GROUP is the only one among the anhydrous sulphates and chromates. Mascagnite. Ammonium sulphate, (NH4)2S0,. Orthorhomhic. Usrially in crusts and stalactitic forms. p = 1.523. Occurs about volcanoes, as at Etna, Vesuvlus, etc. Taylorite. 5K2SOa.(N&)ySOd. 111 small compact lumps or concretions. From the guano of the Chincha Islands. Thenardite. Anhydrous sodium sulphate, Na2S04. In orthorhombic crystals, pyrarnidal, short prismatic or tabnhr; also as twins (Fig. 384, p. 160). White, to brpwnish. 0 tically +. p = 1.477. Soluble in water. Often observed in connection with salt lates, as on the shores of Lake Balkhash, Central Asia; similarly elsewhere; also in South America in Tarapaca, Chilc. In the United States, forms extensive deposits on the Rio Verde, Aria. In Cal., at Borax Lake, San Bernardino Co. Aphthitaiite. Arranite. Glmerite. (Ii,Na)&O1. Rhombohedral; also massive, in crusts. Color white. From Vesuvius, upon lava; at DouglashaU near Weateregeln, Ger- many, in hloditc; Stassfurt, Germany; Rocalmuto, Sicily.

Jan 1, 1922

By S. Mellgren, W. Opie

AN equilibrium state of importance in the process of electrolytically depositing titanium from fused chloride electrolytes is that which exists between titanium metal, titanium dichloride, and titanium trichloride. This can be expressed by the reaction titanium concentration of the solution, temperature, and the proportion of strontium chloride and sodium chloride in the solution. Procedure The general procedure used consisted of the following steps: 1) Development of an analytical method for determining Ti+2 and total titanium. 2) Preparation of batches of fused salt solutions containing various amounts of total titanium, Ti+2 and Ti+3 3) Blending of the prepared batches and excess titanium metal in Vycor tubes and allowing the solutions to come to equilibrium. By blending, solutions with different total titanium content could be prepared and equilibrium could be approached from the high Ti+2 and low Ti+2 sides. 4) Studying the effect of titanium concentration, temperature, and the mole ratio of the solvent chlorides, SrC1, and NaC1, upon the equilibrium.

Jan 1, 1958

1. Healthy and active Local Section organizations are vital factors in promoting the vigor and growth of the Institute. 2. Activity on the part of Local Sections should be recognized and stim¬ulated by appropriation of funds from the Institute's treasury; and these appropriations should be as large as is consistent with the relative needs for other activities. 3. As between different Sections, the amount of such appropriations should be based primarily on the extent of activities as reflected in the number and character of meetings .held and the attendance of the members at such meetings. 4. In making a request for funds for any year, the officers of a Local. Section should submit: (a) a report showing in reasonable detail its income, and expenditures for the preceding calendar year; (b) a statement of the number of. members to whom announcements of each meeting had .been mailed; (c) a record of meetings held, the character of the program, and _ attendance of members at each; and (d) any further facts having a bear¬ing on its financial requirements for the coming year.

Jan 1, 1937

By R. Maddin, R. Pond

THERE have been many recent studies of nonequi-librium alloy structures using specimens which have been formed by rapid solidification.' The general methods for achieving nonequilibrium structure utilize high velocity impingement of a liquid metallic droplet(s) and one or more substrates of relatively high heat conductivity. Specimens formed by current popular techniques are small and have various forms of irregular geometry which severely limit their use for many measurements of physical or mechanical properties. As a result of geometric limitations most research has been restricted to X-ray diffraction, electron microscopy, and to a small degree, electrical resistivity. Recently several attempts in mechanical property evaluation have been reported.2,3 A technique for casting large quantities of regular, rectilinear, continuous metallic fibers has existed for a number of years.4 We have utilized this technique with some slight modifications to produce nonequi- librium alloy structures. The apparatus is composed of a small open tube furnace, a pneumatic cage which raises and lowers a graphite ejection mold, and a

Jan 1, 1970

The thirty-ninth meeting of the Boston Section was held at the Engi- neers? Club on Monday evening, Dec. 4, 1916. Thirty-three members and guests sat down to dinner; There were present as section guests; Dr. L. D. Ricketts, and Prof. Bradley Stoughton, President and Secretary of the parent society, and each was called upon to speak. Mr. Stoughton spoke of the growth of the Institute during the past year and described the very numerous and important activities, of which the junction of the American Society of Civil Engineers with the other three societies is perhaps the most important. Dr. Ricketts, the advertised speaker of the evening, spoke on Recent Progress in Mining and Metallurgy of Copper Ores. In discussing the improvements in mining, he traced the mining methods from square- set mining to the modified Ohio System now so successfully used at Inspiration: In metallurgy, he described the growth of reverberatory-smelting ant1 allied problems such as the utilization of the waste heat for generating steam. He laid stress on the importance of sampling and bedding of

Jan 6, 1917

By J. M. Lohr

A COMMERCIAL development requiring a suitable alloy or alloys for sealing into various grades of glass made it desirable to have a more exact knowledge of the expansion characteristics of the nickel-iron alloys than appeared in the published literature. The expansion of the more common. FIG. I.-EXPANSION CURVES OF SEVERAL FIG. 2.-EXPANSION CURVES OF TWO TYPES OF GLASS. (Courtesy of R. C. A.) TYPES OF GLASS. (Courtesy of R. C. A.) types of glass under consideration varies from 2.7 to 10.4 X 10-6 per degree Centigrade, over the range 20° to 400° C. For reference, the thermal expansion curves f several types of glass used for sealing by the lamp and tube industries are given (Figs. 1 and 2). This paper covers a detailed investigation of the thermal expansion of a series of nickel-iron alloys in which the nickel content varies from 30 to 70 per cent. Particular stress is laid on the alloys that contain between 40 and 55 per cent Ni.

Jan 1, 1938

By John K. Hammes, Stanley D. Michaelson

Generally, the mining costs reported for the large open-pit operations in the United States and South America lie within the range of $0.20 to $0.30 per ton of material moved. (These operations have strip- ping ratios ranging from 1.5 to 4.0.) Productivities for the larger North American properties are in excess of 200 tons of material per man shift, while those for the South American operations are less than 200 tons per man shift. The most significant variations in cost are in the categories of haulage and general mine cost. Haulage costs vary, as expected, according to the mine elevation, pit profile, crusher location, and accessibility of a dump area, and general cost variations depend largely on the overhead cost items included in this category. Drilling and Blasting Practice The majority of open-pit copper mine production drilling is performed by rotary drills. Hole diameter varies from 6 in. to 12 in., with 9-in. holes being most common, and penetration rates vary from 35 ft to 60 ft per hour.

Jan 1, 1968

Minnesota School of Mines Experiment Station, University of Minnesota, Minneapolis, Minn For copies of Bulletins or a list of publications, address The Director Bulletins available are Bulletin 1, Iron mining in Minnesota, by C. E Van Barneveld (1912), $1, 2, Concentration tests on Mesabi ores, by W R Appleby and E Newton (1913), 3, Preliminary concentration tests on Cuyuna ores, by W. R Appleby and E Newton (1915), 4, Bibliography of Minnesota mining and geology, by W. Gregory (1915); 5, Manganiferous iron ores of the Cuyuna district, by E Newton (1918), 7, The future of the Lake Superior district as iron-ore producer, by E W. Davis (1920), 9, Magnetic concentra¬tion of iron ore, by E. W Davis (1921); 10, Ball mill crushing iii closed circuit with screens, by E W Davis (1925); 12, Minnesota manganiferous iron ore in relation to the iron and steel industry, by T L Joseph and S P Kinney (1927). A mining directory of Minnesota, by J J Craig, is published annually.

Jan 1, 1933

Geological Survey of Alabama, University, Ala. A complete list of publications will be sent upon request Requests for publications should be addressed to Walter B. Jones, State Geologist, University, Alabama Publications of the Survey, of most interest to the general public, comprise (1) Special Reports, (2) Monographs, (3) Bulletins, (4) Circulars, (5) Maps The Special Reports mostly deal with a special coal field, mountain, valley, or series of formations, while the Monographs treat of some industry, resource, or group of organisms throughout the state or as far as it extends The Bulletins deal with a variety of subjects, but are usually smaller and less technical than the Monographs and Special Reports Maps now available comprise a map of the Cahaba coal field, one of the Coosa coal field and a small geological map of the state, in addition to a large geological map, 28 by 42 inches, 8 miles to the inch (1926) (also bound with Special Report 14) Price of the large geological map of Alabama, folded in manila envelope, is $1.03 postpaid

Jan 1, 1933

By Francis A Thomson

Montana Bureau of Mines and Geology, Montana School of Mines, Butte, Mont Francis A Thomson, President. The Bureau of Mines and Geology was formerly known as the Bureau of Mines and Metallurgy. A list of publications will be sent upon request¬ A series of six Bulletins and five Memoirs liave been issued by tlie Bureau, as well as several miscellaneous contributions Where the price is not indicated in tlie following selected list of those publications which are now available, the publications are presumably distributed gratis: Bulletin 3, Mechanical ore sampling in Montana, by H B Pulsifer (1920); 6, Geology and ore deposits of Bannack and Argenta, Montana, by P. J Slienon, 50 cents, Memoir 1, The Kevin-Sunburst and otlier oil and gas fields of the Sweetgrass Arcli, by E S Perry (1929), 2, Natural gas in Montana, by E S Perry (in preparation), 4, Tlie geologic structures of western Montana, by C H Clapp and others (in preparation), 5, Placer mining possibilities in Montana, by O A Dingman (1932).

Jan 1, 1933

Reports on process control computer projects at the Kamioka Plant are summarized from the Japanese technical literature (see references). Fluidized Bed Roaster and Sulfuric Acid plant1 A small process control computer (Yokogawa CCS-200 with an OKITAC 5090P 8K central processor) was installed in the Kamioka smelter in the summer of 1964. A year-and-one-half installation project followed, which successfully brought the roaster and acid converters under computer control. The process plant consisted of two 130 RPD fluosolids roasters and two Monsan to acid units. The roasters are charged with lead-zinc concentrates with SO2 from the roaster processed to sulfuric acid. The computer system provides the following functions: 1) log data from the plant--the input is taken from 50 analog signals, 130 high-low digital alarm points, and 50 analog high- low alarm points; 2) set-point control on 18 control loops; 3) direct digital control (DDC) on eight control loops for which conventional controllers were difficult to adapt due to abnormal loop characteristics or delay times; 4) execution of a safe shut-down procedure

Jan 1, 1969

Dr. Rossiter W. Raymond, Past President, Honorary Member, and Secretary Emeritus, died suddenly of heart failure at his home, 123 Henry St., Brooklyn, N. Y., on the evening of Tuesday, Dec. 31, 1918. -He is survived by his' wife and daughter. He was one of the founders of the Institute and its second President, his genius was the Institute's guiding spirit for 47 years. Dr. Raymond was one of the most versatile men of the day; an able mining engineer; brilliant professional writer; an editor of the first rank and an acknowledged authority on matters of literary style; a creator in the fields of fiction, children's stories, poetry and music; for more than 50 years the superintendent of Plymouth Church Sunday School. He will be revered by thousands as a loyal friend, generous giver, and admired colleague. His passing marks an epoch in mining and metallurgical literature. A memorial service will he held in the Auditorium of the-Institute Headquarters on Monday, Feb. 17, 1919, at 4.30 P.M.

Jan 2, 1919

By W. J. Millard

Owing to a moratorium in the drilling of crown-land leases in Trinidad during the year of 1931, only 40 wells were spudded in during the first eight months as compared with 110 during the same period in 1930. Nevertheless the production will show an increase of about 400,000 bbl. over that of 1930. An estimate is given in Table 1. Since the oil produced in 1930 was 9,418,907 bbl. and that in 1931 probably will be 9,853,976 bbl., the year 1931 probably will see an increase of about 4.6 per cent. The gross production of crude oil in the colony has increased steadily year by year, with the exception of 1919, when there was a slight decline. A tabulated statement was given last year.' The Petroleum Times of March 21, 1931 (p. 413) gives the total production of 1930 as 9,418,000 bbl. and the average monthly production as 784,833 bbl. The same two items for 1931 are estimated at 9,853,976 and 821,165 bbl., respectively.

Jan 1, 1932

By M. L. Fuller

THE fundamental mechanism of the deformation of zinc has been thoroughly described by several prominent investigators, particularly Mark, Polanyi, and Schmid,1 Mathewson and Phillips,2 and Schmid and Wasserman.3 The deformation of zinc occurs primarily through slip along basal planes {00. 1 }, and secondarily through twinning on pyramidal planes of the form { 10.2). In addition to these basic studies on single crystals, there have been a number of determinations4,5 of preferred orientations developed in rolled, polycrystalline zinc. In no case, to our knowledge, has there been described the development of oriented struc-tures in zinc as a result of a, systematic series of rolling treatments. The work included in the present paper shows the changes in orientation produced in a zinc alloy by successively increasing degrees of cold-rolling reduction. This alloy has the same crystal form, hexagonal close-packed, as zinc, but its susceptibility to hardening for a given degree of working is much greater because of its higher recrystal-lization temperature.

Jan 1, 1934

By J. B. Dilworth

Outcrops of coal have been discovered in many localities in the Philippine archipelago, and practically all of the larger islands contain deposits of this mineral. Very little prospecting has been done to determine the value of the various cod-bearing areas, but so far as known, the largest and most promising fields are found: (1) in northern Cebu; (2) in the small island of Batan, a part of the province of Albay in southeastern Luzon; (3) in the somewhat larger island of Polillo, off the east coast of Luzon, and (4) in southern Mindoro, near the small coast town of Bulalacao. Northern Panny, south-central Cebu, and various localities in southern Luzon, Masbate, Negros, and Mindanao also afford evidences of the existence of coal-beds, the extent and value of which have not yet been proved. The general position of these islands and districts is shown on the map of a portion of the Philippine Islands, Fig. 1. Some of these coal-fields have been known for many years (coal was discovered in Cebu in 1827 and in Batan in 1842),'

Jan 1, 1909

By E. T. Turkdogan, J. H. Swisher

The solubility of oxygen in zone-refined iron was determined in the temperature range.from 881" to 1350°C. The solubility in a iron at 881°C ms found to be about 2 to 3 ppm; in y iron, the solubility was found to increase from about 2 to 3 ppm at 950°C to about 25 ppm at 1350°C. The permeability of oxygen in an iron -0.1 pct Al alloy was determined in the y iron range, using an internal oxidation technique. By combining the permeability and solubility data, the diffzisivity of oxygen in y and a iron was calculated. The oxygen diffusivity in solid iron may be s~immarized as follows: 8820 For 6 iron and IN a recent paper, Hepworth, Smith, and Turkdogan1 reported on the solubility, permeability, and diffusivity of oxygen in 6 iron, together with permeability data for oxygen in a iron. In the present investigation, similar measurements were made in the ? phase region. In addition, a solubility measurement was performed in the a phase region to permit calculation of the diffusivity of oxygen in a, iron. References to early work on this subject are given in the previous publication.' EXPERIMENTAL Solubility Measurements. The oxygen solubility was determined by equilibrating cylindrical samples 0.3 in. diam by 14 in. long of zone-refined iron in water vapor-hydrogen gas mixtures. The zone-refined iron was prepared by B. F. Oliver of this laboratory, using an apparatus and technique described elsewhere.2'3 Six zone-melting passes were used to achieve a total impurity level of about 30 ppm. Of this 30 ppm, the combined nickel and cobalt content was about 20 ppm, oxygen was 4 ppm, and all oxidizable impurities less than 1 pprn each. A vertical resistance furnace wound with molybdenum wire was used for the experiments. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. In the gas train, flow rates of hydrogen and argon were measured with capillary flow meters, and the resulting mixtures were passed through a column containing 90 pct oxalic acid dihydrate and 10 pct anhydrous oxalic acid to obtain predetermined ratios of H2O to H2. The vapor pressure of H2O above this mixture as a function of temperature is well-known.4 The exit gas was ana- lyzed periodically for H2O, and good agreement (+3 pct) with the calculated composition was obtained. The zone-refined iron specimens were held in the furnace for a sufficient length of time for equilibration, e.g., 18 hr at 1350°C and 1 week at 881°C, then quenched in a brine solution. After removing the surface oxide from the samples by machining, duplicate analyses were obtained by a combined vacuum fusion-infrared method; oxygen analysis was reproducible within 2 ppm. Permeability Measurements. The permeability of oxygen in alloys containing about 0.1 pct A1 was determined by internal oxidation and measurement of the subscale thickness as a function of time. The experimental alloys were prepared by adding aluminum to electrolytic iron (grade 104A plastiron) that had previously been vacuum-carbon deoxidized. The resulting ingots contained about 20 ppm O, 100 pprn C, 40 pprn Si, 50 ppm Mo, 20 ppm P, 20 ppm S, and 20 pprn Zr as the principal impurities. After hot rolling the ingots to 1-in.-thick slabs, specimens were machined from the stock in the form of rectangular plates, 4 by 5 by 2 in. The general procedure for the permeability experiments was the same as those for the solubility measurements. The specimens were cooled in a reducing atmosphere rather than quenched, however, in order to maintain a clean surface for measurement of the sub-scale thickness. This measurement was made on a polished cross section of each specimen, using a microscope with a micrometer stage. The inclusions formed at the lowest temperature 1033°C were too small to be seen with an optical microscope. An electron micrograph showing the size and shape of individual particles is shown in Fig. 1. The dark band in the picture is a boundary between two subgrains. The subscale thickness in these samples was measured with an optical microscope after heavily etching in 2 pct nital, which gave contrast between the subscale and the unoxidized zone.

Jan 1, 1968

By M. E. Wadswort, A. S. Peck

Infrared data disclose that phenacite reacts with oleic acid to form a chemisorbed oleate monolayer on the mineral surface. The absorption band characteristic of the antisymmetrical C = 0 oleate structure appears at a spectral wavelength of 1623 cm-'. Chemisorption also results in the displacement of OH- and silicate from the mineral surface. Infrared absorbance at 1623 cm-1 is correlated with float-ability at different pH for -60-mesh phenacite particles. Phenacite, Be2SiO4, is an ore mineral often associated with quartz, microcline, and chrysoberyl in pegmatites and mica schist. Experimental phenacite beneficiating processes have been confined principally to the flotation of low grade ores occur-ing in several mountain ranges of Utah and Nevada. The U.S. Bureau of Mines ' has recently reported on the separation of phenacite from ore deposits of Mount Wheeler, Nev. Infrared techniques were previously applied by the authors to characterize the role of sodium oleate and oleic acid in the flotation of several non-sulfide minerals.23 A parallel study was projected to the flotation of the orthosilicate mineral phenacite with oleic acid. Infrared spectra provided a 'molecular fingerprint' of the mineral surface and permitted identification of the reaction mechanisms. Infrared data were complemented with flotation and chemical tests. EXPERIMENTAL PROCEDURES The experimental procedures used in this investigation, for which data are presented in graphical or spectral form, are described in chronological test order. Phenacite crystals from Mt. Antero, Colo., were obtained from Ward's Co., Monterey, Calif. The crystals were fragmented in a porcelain mortar to -60 mesh and then pretreated with 0.5 molar HC1 for 15 min to remove iron. Then, the mineral particles were washed free of acid with distilled water and dried. Part of the dried material was ground to a fine powder with a Fisher Grinder using an agate mortar and pestle. Next, the powder was placed in a graduated cylinder and mixed with 500 ml of distilled water. The mineral in suspension was decanted from the settled fraction after 5 min, and the colloidal suspension was used for adsorption tests in which a high specific mineral surface area was required for adsorption and infrared analysis. Conditioning was performed in 50 ml glass centrifuge tubes for both infrared and flotation test determinations. Twenty ml of colloidal suspension was used for the infrared adsorption tests. One and a half g of deslimed -60-mesh HCl pretreated phenacite was added to 20 ml of distilled water for flotation conditioning tests. Six mg of oleic acid was used for each infrared adsorption test, and 0.2 mg of oleic acid was used for the flotation conditioning tests. HCl and NaOH were used for pH modification. The pulps were stirred at a speed of about 1500 rpm for 3 min. Then, the solids were separated out and either dried at 50°C or immediately transferred to a float cell. The pH of the residual liquid was determined with a Beckman Zeromatic pH meter. The flotation procedure is described as follows: 1) A 325-1111 glass micro-float cell was filled with distilled water. 2) Conditioned mineral was placed in the cell and the pulp was aerated through the glass fritted bottom at 7 psi pressure. 3) Floated mineral was skimmed from the cell with a glass slide until flotation ceased. (The end point was reached in all tests in less than 2 min.) 4) The flotation products were dried, weighed, and the recovery was calculated. Samples for infrared analysis were made into mulls using either oleic acid or series 13-21 Halocarbon oil obtained from Halocarbon Products Corp., Hacken-sack, N.J. The mulls were placed between two sodium chloride windows. A characteristic phenacite infrared band at 1868 cm-' was used as an internal standard for quantitative determinations in which absorbance at this position was quantified by the baseline-tangent method4 and related to absorbance at 1623 cm-'. The ratio obtained by dividing absorbance at 1623 cm-' by absorbance at 1868 cm-' was defined as an absorbance quotient for use in graphical presentation.

Jan 1, 1968

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