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By J. H. Frye, J. W. Caum

ONE of the most important methods of increasing the hardness of metals is alloying. In spite of the widespread use of alloys, the fundamental mechanism of alloy hardening is little understood. This is true even of the simplest form of alloy, the primary substitutional solid solution in which solute atoms substitute for solvent atoms at random in the crystal lattice of the latter. A fundamental understanding of the mechanism of solid-solution hardening would be important, both because of the widespread use of alloys of this type and because of the light that might be thrown on the mechanism of hardening in more complicated alloys. The present investigation covers the hardness of primary substitutional solid solutions of zinc, gallium,, germanium; and arsenic in copper. All of these are B subgroup elements from the third period of the periodic table. Cu, Zn, Ga, Ge, and As are in groups I, II, III, IV, and V, respectively and lie just to the right of the transition elements. Because of their cost, it is unlikely that Ga-Cu and Ge-Cu solutions will ever be of commercial importance, but the intent of this study has been to discover some of the fundamentals of solid-solution hardening and it has been demonstrated that such a study is far more likely to be fruitful if alloys are made up on the basis of position of the constituent elements in the periodic table than if commercially important alloys are used. Many investigations have. been made of the hardness of substitutional solid solutions, but lack of attention to purity of the metals, infrequent grain-size control, and the use of varying testing techniques have virtually invalidated any comparisons. The purpose of most investigations has been to solve immediate problems and not to solve the primary problem: Why do solid solutions usually have a greater hardness than pure metals? PREVIOUS WORK Theories have been advanced to account for the hardness of solid solutions,, but relatively little experimental work has been done. Perhaps the first experimental work of merit was that of Norbury1 on copper alloys. He showed that for several alloys there was a correspondence between the hardness of one atomic per cent solutions and atomic volume of the solutions. More recently Brick, Martin, and Angier2 have investigated the effect of various solute elements on the hardness of copper. They concluded that the hardening effect of these solutes depended "primarily on the difference in atomic volume of solute and solvent or, relatedly, upon the parameter, change of the solvent or the extent of solid solubility." They also observed the effect of these elements on hardness and texture developed by rolling and by annealing of rolled material. Austin3 examined the hardness and response to heat-treatment of various iron solid solutions. Frye and Hume-Rothery4 measured the hardness of a number of silver solid solutions containing approximately

Jan 1, 1943

By V. G. Mooradian, John T. Norton

THE diffusion of metal atoms into the crystal lattice of another metal and the assumption of regular positions to form a homogeneous alloy are some of the most fundamental phenomena of structural. metallurgy. The mechanism of this process has been the subject of a great deal of study from many viewpoints, but the picture is still far from complete. It is generally believed that if one metal is to diffuse into another, the first must have some solubility in the second1. This means that the solvent must be able to accommodate the stranger atoms, either on points of its own lattice or in the interstices between, without losing its own crystallographic identity. It is also a general observation that cold-working is a distinct aid in the diffusion process, causing it to take place with greater rapidity at the same temperature or with the same speed at a lower temperature. There is considerable doubt, however, as to the real significance of the deformation in its effect on the diffusion mechanism. Several factors associated with the cold-working. may be responsible for the increased diffusion rate. The plastic deformation causes a distortion of the solvent lattice, which may be an aid in the assimulation of atoms of another kind. There are many references2 in the literature that suggest that some distortion or "loosening" of the lattice is necessary for atomic migration and that diffusion cannot take place in the undis-

Jan 1, 1935

By J. Moore Samuel

THE CHAIRMAN (WALTER DOUGLAS, NEW YORK, N. Y.).-Perhaps there is no problem that causes the modern metallurgist more worry than the question of unaccounted for loss. He has not the advantage of the metallurgist of the early days here, who could sleep peaceably with the settled conviction that there were certain copper mineral constituents of the ore which were volatile, and there was therefore nothing to worry about. The slag contents and volatilization accounted for the balance of the copper that went in the top of the furnace after the weighing of the bullion. There have been great strides in recent years toward reducing this loss. Perhaps the Anaconda company is the one we have to thank for the original pioneer work along the lines which we are all today following. We would be glad to hear from some gentlemen present with reference to their experience with this question of dust losses. E. P. MATHEWSON, Anaconda, Mont.-You mentioned the Anaconda company, Mr. Chairman. I would like to say something about what we have been doing there, and the troubles we have been having. We have a tremendous volume of .gas to handle. We adopted the system of large chambers, lessening the velocity of gases, and incidentally cooling the gases. Unfortunately in one sense and fortunately in another, we were compelled to increase the amount of gas handled in the flue system, and the results were then not so good. Still, we get a very good recovery. Our system of taking a sample is similar to the one described by the writer of the paper. We have tried all kinds of apparatus for getting a fair sample. We divided the area of the flue into imaginary squares, and have taken samples for a certain period of time from each square; and have used the asbestos bags. At present, there is a large unit of the Cottrell apparatus almost ready to connect up on the roaster flue to catch the dust from flotation concentrates. The worst things smelters have to handle at the present clay, they are coming in the Southwest as well as the Northwest, are of material much of which is as small as 500 mesh, and the ordinary methods of catching dust will not apply to flotation concentrates. The Cottrell process is going to be tried out at our plant for this material. We have devised special forms, with a view to preventing the formation of dust from this material, and we are pleased with the results so far obtained. There is another point in connection with this subject that I want to put before the members here, so they will be thinking about it. You know there has been a great deal of litigation between the farmers

Jan 12, 1916

By James T. Wood

Stratigraphy, structure and closure of the Paloma field are discussed, with some details regarding the present state of development. The Paloma anticline, a large dome modified by faults, is the largest single closed dome in the southern San Joaquin valley without surface outcrop or topographic expression. It owes its discovery to geophysics. Of nine wells drilled to the Stevens sand, seven are productive. The ultimate productive area may approximate 3000 acres when the limits of the field are determined. Introduction The Paloma field derives its name from the Paloma school, ½ mile north of what is now the center of the field. The field is 17 miles southwest of Bakers-field, in the south central part of the San Joaquin Valley (Fig. I). The present developed area and its expected extensions are in townships 31 and 32S., R.26E. It is the most southerly of several fields that produce from the Stevens sand zone. The first well to produce condensate was a joint test drilled by the Western Gulf Oil Co. and The Texas Co. near the center of sec. 3, T.32S., R.26E., well No. 54-3. This well was completed on Aug. 31, 1939, at a depth of 10,178 ft. The initial production was 2280 bbl. a day of condensate and 14,750,000 cu. ft. of gas (½-hr. gauge) through a ?-in. bean. Prior to the drilling of this well, the Ohio Oil Co. discovered and developed a small gas field, which embraces a part of three townships about their common corner but lies chiefly in secs. 31 and 32, T.31S., R.26E. The first well was completed on July I, 1934, at a plugged depth of 5239 ft. after having been drilled to 7957 ft, production was found in a 59-ft. zone IIO ft. below the Fourth Mya bed, within the Sari Joaquin clays. Until recently this field was known as the Buena Vista gas field. It is now carried by the Division of Oil and Gas as the Paloma gas field. Production within the Paloma gas field is derived from six wells, producing from several different zones in the interval from 4177 to 5548 feet. Geology Stratigraphy The sediments penetrated by wells in the Paloma held range in age from Recent to Upper Miocene. The entire section, which exceeds 10,000 ft. in thickness, conforms generally to the standard section of the south central San Joaquin Valley. The producing zone, sometimes called the Paloma sand, is the approximate equivalent of the Stevens sand zone of the Ten Section, Canal, Coles Levee and other fields. The stratigraphic section is shown in Table I. Paloma Producing Zone* (Stevens Sand Zone, Upper Miocene) .-The Paloma producing zone (Fig. 2), frequently referred to as the Paloma sand, is encountered at depths ranging from 9950 to 10,300 ft. In general, it is a massive, firm to hard, not too well sorted, fine to medium fine sand. It is interbedded with thin, hard, calcareous sand shells of similar texture and cherty

Jan 1, 1942

By Theron Wasson

The discovery of two new fields—the Reed City area of Osceola County and the Headquarters field, of Roscommon County —and the important development in Winterfield township, Clare County, again demonstrate the fact that it is the unknown and unexpected that enter very definitely into the oil-producing history of Michigan. This is particularly true in the area of thick glacial drift in the north central part of the state, where the new prolific fields have been discovered this year. This shifts the interest from the southwestern part of the lower peninsula, where a number of pools were rapidly developed during 1939 and 1940, back into the Central Basin area. As a result of strict proration in the new areas, the production for the state of Michigan for the year has not been as great as in 1940 or 1939. In 1941 the total production was 16,300,000 bbl., in 1940 it was 19,551,000 bbl., and in 1939, which was the peak year, it was 23,300,000 bbl. However, the discovery of the new fields this year nearly doubles the estimated reserves for Michigan reported at the end of 1940 In 1941 about 12,000,000 bbl. of oil was produced from the older fields, in which the individual well productions were so small that proration was not an important factor. The total production for the state from the discovery of oil in 1925 through 1941 now stands at 161,205,000 barrels. ActIVe Oil Fields Reed City Field.—In the Reed City field, Lincoln township, Osceola County, only small oil wells were completed during 1939 and 1940. The discovery of much larger production in wells drilled somewhat deeper, by The Pure Oil Co. and the Weber Oil Co., in the early part of 1941, led to the rapid development in this area. Some wells have had initial productions as high as 10,000 bbl. By the end of the year III producing wells were completed, with an average depth of 3600 ft., from the Detroit River formation of Devonian age. The entire development of the field to the end of 1941 was on 20-acre spacing. Headquarters Field.—The Headquarters field, which lies along the line between Clare and Roscommon Counties, was one of the most important discoveries of 1941 and will be the scene of vigorous development during 1942. Production so far has been from the Traverse lime at about 3400 it., and development has indicated that this is probably one of the most productive Traverse pools yet discovered. One well had been given a potential of 10,000 bbl. per day. Dry holes well located in relation to big producers indicate that it is a typical Traverse development. Winterfield Field.-This field, in Winter-field township, Clare County, was discovered late in 1940. By December 1941, 14 Dundee and 5 Traverse producers had been completed. The Dundee lime is found at a depth of 3750 it. and the Traverse lime at 3070 it. Producing conditions in the Dundee seem to be erratic because of varying porosity in the dolomit-ized limestone. Kawkawlin Field.—The Kawkawlin field, which was discovered by the Gulf Refining Co. in 1938, is in Monitor and Kawkawlin townships, Bay County. Small production

Jan 1, 1942

By Gloyd M. Wilkes

The eastern section of the Park City district is drained to an elevation of 6300 ft, by means of the Ontario drain tunnel owned and maintained by Park Utah Consolidated Mines Co. This elevation represents a depth of 920 ft, in Park City Consolidated Mines Company's property. When development below the 900-ft. level was commenced, sinking was attempted through an incline winze in the fissure. The intensely fractured quartzite forming the walls of the vein could not be held after water was encountered, so it was decided that further sinking should be done in a vertical winze far enough in the foot-wall to be in the more solid quartzite outside the fractured zone containing the vein. Progress was good until a depth of 200 ft. below water table was reached, where the flow of water became serious. Sinking progressed 300 ft., to the 1200-ft. level, and there approximately 750 gal. of water per minute was being pumped. The last 20 ft. of sinking cost more than $200 per foot direct charges, whereas the over-all cost for the 300 ft. was $100 per foot. This high last cost was caused by excessive lost time in pumping. Crosscutting to the vein disclosed the fact that the 1050-ft. level had been developed only after drainage had been effected from the 1200-ft. level, but that the 1200-ft. level could not be opened because of the great amount of water encountered when the fractured zone was intersected. The ground in the fractured zone is so finely crushed that it precludes any possibility of economic support when it is wet. Furthermore, mining costs were found to be prohibitive after caving of vein walls had taken place as a result of an attempt to drive drifts before complete drainage had been effected. More than 3000 gal. per minute was pumped from the 1200-ft. level and the water table remained 75 ft. above this plane even after five crosscuts were driven to the fractured zone at 50-ft. intervals along the strike of the fissure from a footwall drainage drift. It was evident, therefore, that complete drainage must be effected before the fractured zone could be opened in any future development. After extensive investigations in this connection, a well-drilling campaign was decided upon to effect drainage of the fissure in advance of sinking and level development, so that all mining operations would be carried on in dry ground. Drilling Procedure A crosscut was driven through the hanging wall of the fissure on the 1050-ft. level, which was the deepest dry level at the time, to a predetermined location from which a vertical hole should reach the fractured zone at about 400 ft. below this level. A drill station was made and a raise was driven over the location for the hole, to act in lieu of a derrick or drill tower. This raise

Jan 1, 1943

By L. H. Levenson, Charles S. Barrett

Numerous determinations1-' of the texture of cold-rolled polycrystalline iron, steel, and ferritic alloys have been made with good agreement among the various observers as to the principal features of the texture common to all, but there has been no adequate explanation of the texture in terms of, the behavior of individual grains. This study presents an explanation of the texture based on the observed rotation of single crystals when deformed in a manner similar to a grain in the aggregate, a method we have found useful in leading to a better understanding of compression and tension textures;8,9,10 in particular, the aim has been to determine experimentally the end orientations of rolled single crystals of iron. These are discussed in connection with the point of view of Weverl and of Boas and Schmid2 that the rolling texture is a simple compression texture (compression normal to the rolling plane) superimposed on a simple tension texture (tension in the rolling direction), and the point of view of Kurdjumow and Sachs3 that three ideal end orientations exist. Experimental Method The single crystals used were in the form of disks cut from a stock of crystalst pre- pared in this laboratory by a strain-anneal method from mild steel decarburized and purified in hydrogen, the details of which have been described elsewhere.11 To ensure maximum elongation in the rolling direction and to simulate approximately the rolling of a grain in an aggregate, lateral flow was constrained by placing each crystal in a close-fitting hole in a plate of copper or iron of equal thickness and rolling the plate and crystal together. About one-third of the crystals were rolled in a "sandwich" pack by adding top and bottom cover plates. The two-high mill used had 8-in. diameter rolls and was operated at 15 r.p.m. The initial diameter of the crystals was between 1/4 and 1/2 in., while the starting thickness varied from 0.031 to 0.376 in. With a single exception, which was rolled 63 per cent, the crystals were rolled to a final reduction in thickness of 82 to 97 per cent in 20 to 40 passes, alternately changing the sense of the rolling direction. The initial orientations of the crystals were determined either by X-ray back reflection12 or by optical reflectionl3 from etch pits; the mean final orientations were determined by X-ray Laue photograms using molybdenum, silver, or tungsten radiations, by optical reflection, and in many cases by both methods. Results Twenty-six crystals were studied. It was found that there were three typical be-

Jan 1, 1941

By Lewis W. MacNaughton, F. L. Burchard

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Coolie, Foard, Hardeman, Knox, Montague, Wichita, and Wilbarger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. DevELopments during 1941 Nearly 1600 wells were drilled in the district during 1941 as compared with more than 1700 in 1940. However, the ratio of successful drilling operations was higher and some 1200 oil wells were completed. Production held about even with the previous year, as did the number of producing oil wells. Known oil reserves increased slightly throughout exploration, which generally was carried on at greater depths than in former years. The average depth of discovery wells was 300 ft. deeper than in 1940. Although discoveries were evenly divided numerically between horizons above the base of the Strawn series and those below the Strawn, the deeper horizons, including the Bend series of the Pennsylvanian, the Mississippian limestone, and the Simpson and Ellenburger of the Ordovician, furnished most of the increase in oil reserves. The largest single addition to the reserves was in the Ellenburger formation in the K.M.A. field. During the year 112 wells were completed in this horizon, bringing the total developed acreage to some 4600 acres. The Straan series in K.M.A. also received considerable development in 1941, with 114 completions. K.M.A. Pressure Maintenance Satisfactory progress was made by the K.M.A. Pressure Maintenance Association in 1941. At the end of the year, 99 wells were being used for input and total monthly volume of gas returned to the reservoir reached a high of 340,548 M cu. ft. in December from a low of 208,853 M cu. ft. in February. Total volume of gas returned during 1941 was 3,306,052 M cu. ft. To the end of the year, 150 cu. ft. of gas had been returned for every barrel of oil produced from the reservoir while the input ratio for December was 397 cu. ft. Per

Jan 1, 1942

By P. E. Fitzgerald, Dana G. Hefley

An apparatus has been developed which permits selective acidizing of producing formations and determination of the relative permeability of a formation by fluid injection. This apparatus, known as the "Electric Pilot," is an electrical fluid-interface locator, the electrical circuit of which is completed when the elec-tcodes in the well are in contact with a conductive fluid, but is not completed when immersed in a nonconductive fluid. Results are given for a number of typical acidizing applications in which the interface locator was used to control the acid. Description of the method used in making a permeability survey and the data obtained are also included. Introduction Early in the development of the acidizing industry it was recognized that one of the most important problems to be solved in the chemical treatment of any well was the determination of what part of the exposed section in the well should be treated and the selection of the technique that would insure treatment of the desired section. One of the first techniques adopted for assisting in proper placement of the acid, which is still widely used, is the method of confining the acid to the producing section by means of a column of oil, which is known as the Carr1 method of treatment, named for its inventor. In the Carr method it is not possible to selectively acidize a specific horizon in a multiple pay zone, so many improvements and modifications of the basic Carr technique were devised to accomplish this result. In order to overcome the possibility of the acid entering an undesirable section at the bottom of the well, organic gel plugs2 were introduced into the bottom of the well, which served to halt the entrance of the treating solution into these zones.3 These chemical gels later liquefied because of bacterial action and were removed from the well with the produced fluid. In fields where a gas cap existed, as in the Goldsmith field of Ector County, Texas) it was imperative that a treating technique be evolved that would confine the acid to the oil-producing zone below the gas cap. By so doing the oil-productive capacity of the wells could be improved without greatly increasing the gas production and this would lower the gas-oil ratio of the well. ~h, technique employed4 to achieve this effect utilized two pumps, one for pumping the chemicals down the tubing, the other to simultaneously force oil down the annular space to confine the acid to the oil pay, thus preventing the chemicals from entering the upper gas-bearing zones. Experience has indicated that gas wells and certain types of oil wells respond better to ''stage treating.'' This technique utilizes the introduction of a certain volume of acid and then allows the well to ''clean up99 before introduction of the next and usually successively larger stages. Where such methods are employed steps must be taken to keep a disproportionate share of the acid from entering the most permeable and previously treated Zones. A special tool

Jan 1, 1944

By J. H. Frye, J. W. Caum

One of the most important methods of increasing the hardness of metals is alloying. In spite of the widespread use of alloys, the fundamental mechanism of alloy hardening is little understood. This is true even of the simplest form of alloy, the primary substitutional solid solution in which solute atoms substitute for solvent atoms at random in the crystal lattice of the latter. A fundamental understanding of the mechanism of solid-solution hardening would be important, both because of the widespread use of alloys of this type and because of the light that might be thrown on the mechanism of hardening in more complicated alloys. The present investigation covers the hardness of primary substitutional solid solutions of zinc, gallium, germanium, and arsenic in copper. All of these are B subgroup elements from the third period of the periodic table. Cu, Zn, Ga, Ge, and As are in groups I, 11, 111, IV, and V, respectively, and lie just to the right of the transition elements. Because of their cost, it is unlikely that Ga-Cu and Ge-Cu solutions will ever be of commercial importance, but the intent of this study has been to discover some of the fundamentals of solid-sdstion hardening and it has been demonstrated that such a study is far more likely to be fruitful if alloys are made up on the basis of position of the constituent elements in the periodic table than if commercially important alloys are used. Many investigations have been made of the hardness of substitutional solid solutions, but lack of attention to purity of the metals, infrequent grain-size control, and the use of varying testing techniques have virtually invalidated any comparisons. The purpose of most investigations has been to solve immediate problems and not to solve the primary problem: Why do solid solutions usually have a greater hardness than pure metals? Previous Work Theories have been advanced to account for the hardness of solid solutions, but relatively little experimental work has been done. Perhaps the first experimental work of merit was that of Norbury1 on copper alloys. He showed that for several alloys there was a correspondence between the hardness of one atomic per cent solutions and atomic volume of the solutions. More recently Brick, Martin, and Anger2 have investigated the effect of various solute elements on the hardness of copper. They concluded that the hardening effect of these solutes depended "primarily on the difference in atomic volume of solute and solvent or, relatedly, upon the parameter change of the solvent or the extent of solid solubility." They also observed the effect of these elements on hardness and texture developed by rolling and by annealing of rolled material. Austin3 examined the hardness and response to heat-treatment of various iron solid solutions. Frye and Hume-Rothery4 measured the hardness of a number of silver solid solutions containing approximately 1 References are at the end of the paper.

Jan 1, 1943

By James Pollock

The possibility of colloidal deposition of cinnabar has been neglected. In opalite deposits cinnabar exists in particles within or near the colloidal size range. Colloidal processes have been admitted to be operative in hot springs and low-temperature deposits similar to most cinnabar deposits. Mercuric sulphide sols are stable to elevated temperature and pressure, and in nature probably are chiefly affected by the electrolytes in solution, dilution of colloid, and presence of protective colloids as silica. The stability of mercuric sulphide sols to electrolyte is measured, and shown to be greatly increased by dilution and by the protective action of silica. Mercuric sulphide sols follow the Schulze-Hardy valency rule, therefore the precipitating power of complex mixtures of electrolytes can be computed roughly. The stability of mercuric sulphide sols is shown to be greater than the equivalent precipitating power of the electrolytes in a hot spring depositing mercuric sulphide. It is concluded that finely divided or earthy types of cinnabar are colloidally deposited. Possibility of Collodial Deposition While colloidal solution has been suggested as a means of transport for a number of minerals, such as the sulphides of antimony, arsenic, and iron, it has been neglected in connection with mercury. This is surprising because there exists positive evidence that cinnabar is present in certain deposits in particles of colloidal or near colloidal size. Colloidal transport could result from either the rapid dilution or neutralization of alkaline sulphide solution bearing mercury coming in contact with deep ground waters, or from colloidal solution near the original source and subsequent flow to the point of deposition unchanged. That the dilution of a mercuric alkaline sulphide solution will precipitate mercury sulphide in colloidal form has been demonstrated a number of times and is easily confirmed. The dilution hydrolyzes the alkaline sulphide Na2S to the corresponding hydroxide and hydrosulphide NaOH and NaHS, and the diminution of the concentration of alkaline sulphide reduces the solubility. It is not the contention of this writer that colloidal deposition is the mode of transport of mercuric sulphide in all mercury deposits, but that the stability of a mercuric sulphide sol, as demonstrated below, in waters that are similar to those that have deposited mercuric sulphide necessitates consideration of this possibility in many deposits, especially those of the hot-spring and so-called opalite type. Evidence of Colloidal Deposition Ross1 has shown that most deposits of quicksilver are formed at low temperatures and pressures, and probably by solutions that have relatively simple chemical compositions. In most cases the solutions are probably similar to those observed in hot springs, and in two instances—at Steamboat Springs, Nevada, and Sulphur Bank, California—hot springs have been reported by Becker as actually depositing cinnabar.2 Opalite deposits were believed by early investigators to be surface phenomena

Jan 1, 1949

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By James T. Wood

Stratigraphy, structure and closure of the Paloma field are discussed, with some details regarding the present state of development. The Paloma anticline, a large dome modified by faults, is the largest single closed dome in the southern San Joaquin valley without surface outcrop or topographic expression. It owes its discovery to geophysics. Of nine wells drilled to the Stevens sand, seven are productive. The ultimate productive area may approximate 3000 acres when the limits of the field are determined. Introduction The Paloma field derives its name from the Paloma school, ½ mile north of what is now the center of the field. The field is 17 miles southwest of Bakers-field, in the south central part of the San Joaquin Valley (Fig. I). The present developed area and its expected extensions are in townships 31 and 32S., R.26E. It is the most southerly of several fields that produce from the Stevens sand zone. The first well to produce condensate was a joint test drilled by the Western Gulf Oil Co. and The Texas Co. near the center of sec. 3, T.32S., R.26E., well No. 54-3. This well was completed on Aug. 31, 1939, at a depth of 10,178 ft. The initial production was 2280 bbl. a day of condensate and 14,750,000 cu. ft. of gas (½-hr. gauge) through a ?-in. bean. Prior to the drilling of this well, the Ohio Oil Co. discovered and developed a small gas field, which embraces a part of three townships about their common corner but lies chiefly in secs. 31 and 32, T.31S., R.26E. The first well was completed on July I, 1934, at a plugged depth of 5239 ft. after having been drilled to 7957 ft, production was found in a 59-ft. zone IIO ft. below the Fourth Mya bed, within the Sari Joaquin clays. Until recently this field was known as the Buena Vista gas field. It is now carried by the Division of Oil and Gas as the Paloma gas field. Production within the Paloma gas field is derived from six wells, producing from several different zones in the interval from 4177 to 5548 feet. Geology Stratigraphy The sediments penetrated by wells in the Paloma held range in age from Recent to Upper Miocene. The entire section, which exceeds 10,000 ft. in thickness, conforms generally to the standard section of the south central San Joaquin Valley. The producing zone, sometimes called the Paloma sand, is the approximate equivalent of the Stevens sand zone of the Ten Section, Canal, Coles Levee and other fields. The stratigraphic section is shown in Table I. Paloma Producing Zone* (Stevens Sand Zone, Upper Miocene) .-The Paloma producing zone (Fig. 2), frequently referred to as the Paloma sand, is encountered at depths ranging from 9950 to 10,300 ft. In general, it is a massive, firm to hard, not too well sorted, fine to medium fine sand. It is interbedded with thin, hard, calcareous sand shells of similar texture and cherty

Jan 1, 1942

By W. D. Lowry

As most of the industrial activity of Oregon is centered in the Portland area, the foundries there consume the bulk of the foundry sand produced in Oregon. Although a number of the larger towns scattered throughout the state have gray-iron foundries, the sand used by most of them is of local origin. The yearly consumption of foundry sand of all types for the past few war years in Oregon is estimated to have been approximately 40,000 tons valued at about $285,000, of which an estimated 18,000 tons was shipped in from the Ottawa, Ill., district for use largely by the steel foundries. Until 1945 much of the silica sand consumed by the steel foundries in the Pacific Northwest, approximately 50,000 tons in 1944, came from Ottawa, Ill. and surrounding regions. Although some silica sand was shipped in from Belgium in the past, none is known to have been imported in recent years. Early in 1945, a very promising high-grade silica sand being produced near Eugene, Oregon, was introduced, and all but two of the Portland steel foundries are using this new sand. Until a few years ago, the search for good local (Oregon) foundry sands was carried on largely by the foundry supply houses. Recently the Oregon Department of Geology and Mineral Industries has investigated a number of deposits and has carried on and fostered research on the most bromising deposit near Eugene, about 120 miles south of Portland. High-grade silica foundry sand from this deposit is now being marketed in Oregon, Washington, and British Columbia. The Eugene sand is one of the very few outstanding western steel-foundry sands. Field investigations by the Oregon Department show that there are relatively few deposits of sand in Oregon suitable for foundry use. A knowledge of the geology of the state makes this readily understandable. The only major primary sources of the quartz present in sandstones in Oregon are the intrusive masses of granite, granodiorite, and quartz diorite of late Jurassic or early Cretaceous age found in the Siskiyou Mountains of southwestern Oregon, a part of the old Klamath Mountain highland, and in the Blue Mountains of northeastern Oregon. Transportation militates against the development of any possible deposits of foundry sand found east of the Cascade Mountains in central and eastern Oregon because few railroads traverse that area. East of the Cascades, which separate western from eastern Oregon, many of the older sediments of Paleozoic and Mesozoic age have either been metamorphosed or contain much volcanic eruptive material, and even if some of the Mesozoic sediments are highly quartzose in places, they are in relatively inaccessible areas. All the Tertiary sediments there are of continental origin and contain much ash and other volcanic debris, for there was great volcanic activity during much of that period. In western Oregon much the same is true of the Paleozoic and Mesozoic rocks

Jan 1, 1948

By E. H. Rose

The present symposium on flotation machines provides a unique opportunity for group reappraisal of standard or habitual viewpoints. A symposium is by definition a trading post- for observations that might prove complementary when put together, thus leading to useful thoughts that might not have been evident from the original observations individually. The present paper, pertaining to power consumption in flotation, is deliberately an experiment of that kind. Data were solicited from the operating superintendents of several of the major flotation plants on this continent. The information received, covering a total of 14 separate operations in seven plants, has been collated in terms of power intensity; that is, the total power input per cubic foot of cell volume. This departs somewhat from the conventional expression of power per ton of ore treated, though the latter figure is also given for the plants concerned. Because of wartime restrictions, particularly in Canada, identifying names of plants and machines are withheld. Not as a firm conclusion, but as a tender for symposium discussion, the following points are made: 1. That flotation is a power operation in much the same sense as ball milling. 2. That contact time is the complement of power intensity and may be decreased as the latter is increased. 3. That a decrease in flotation power per ton of ore can result from an increase in power intensity. Analogy with Grinding In grinding, it has become axiomatic that the more the power put into a given operation, the greater the work performance. The analogous view is now proposed that the effectiveness of any flotation operation will be related to the mechanical energy usefully applied to that operation. Under this view, each increment of properly directed input energy should give either an increase in unit tonnage or an improvement in the metallurgical separation (concentrate grade or tailing grade), until either the theoretical limit imposed by mineral constitution or surface condition is reached, or until further increments of power become uneconomic under the law of diminishing returns. Thus, as in grinding, there are two forms of output that greater power input or improved utilization of power can produce. As for the law of diminishing returns, lower unit cost of power through improved generating efficiency in the past decade has pushed the limit back. Over and above this, however, there is strong indication in the operationg data herein presented that higher power intensity results in an actual economy of over-all power consumption. Like crushing and grinding, flotation accomplishes a rupture of the forces of molecular attraction, by taking particles from the common environment and placing them in the two separate environments of

Jan 1, 1947

By J. C. Williams

The operations described in this paper are those of the flotation plant of the Valley Forge Cement Co. at Conshohocken, Pa., and concern the use of a particular cationic reagent—namely, DP-243. The role of this reagent in this plant may be better understood by first considering the purpose of beneficiating cement rock in general and the specific problems at the Valley Forge plant. The ultimate purpose of beneficiating cement rock is to obtain a kiln feed of the desired chemical composition in a form suitable for the most efficient kiln operation. The chemical composition is governed by the type of cement to be made. Before government restrictions (the purpose of which is to simplify operations during wartime) limited the types of portland cement a manufacturer is permitted to produce, five principal types of cement were generally recognized by the industry. They are based upon chemical and physical specifications proposed by the American Society for Testing Materials, federal and other governmental agencies, state highway departments, water boards and other users of large quantities of cement. The physical as well as chemical specifications for any particular type of cement necessitate proper proportioning of the major components—that is, the silica, alumina, iron and lime—and it is necessary to establish and maintain definite limits for each in the raw mix. The manufacturer must then prepare a kiln feed of a composition that will yield a final product that will fulfill the desired specification. This step is further complicated for kilns using coal as fuel, by the amount and analysis of the ash introduced. The amount and nature of the dust lost during burning will also affect the composition of the kiln feed. The problem of preparing a kiln feed of the desired chemical composition is not a simple one, and it is the final product that governs the methods used to obtain such a feed. For example, in starting with a material deficient in lime for the mix sought, it may not be sufficient to raise it to the required lime content. The other constituents must also be present in the proper proportions. In some cases, it may be necessary to raise the lime content to a point greatly exceeding that of the final mix, then, by addition of one or more other materials lower in lime, obtain the mix. The rock used at the Valley Forge plant is a metamorphosed argillaceous limestone of the Jacksonburg formation, the same formation as that of the Lehigh Valley cement rock (which occurs approximately 50 miles north), and its oxide composition is similar to that of the latter. The only practical differences between the two are that, as a result of metamorphosis, crystallization of the Valley Forge rock is considerably coarser and it contains less carbon than the Lehigh Valley rock as well as slightly more magnesia in the form of magnesian mica. The calcium carbonate content of the various strata in the Valley Forge quarry ranges from about 65 per cent to over 85 per cent, the average for the entire quarry being somewhat under the requirement for manufacture of cement, which usually is from 75 to 76 per

Jan 1, 1947

By D. P. Morton

SINCE 1023, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (I) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.&apos; This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as loo, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods. Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. 2 (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should he the same. It is neces-

Jan 1, 1941

By K. H. Coats

In tnany oil and gas fields, significant investments are required in piping networks for collection, injection and disposal of various fluids. This paper treats the problem of optimally locating the trunkline(s) for a given systet to nlinimize both the total length of piping connecting the individual wells or lease batteries to the trunkline and the length of the latter. Single and multiple trunklines, varying line sizes, and grouping of wells are considered. Some attention is paid to the case of a curved trunkline. A field case is treated and conclusions are that the problem of locating a single trunkline is relatively straightforward while the location of multiple trunklines requires further research. INTRODUCTION la many oil and gas fields, significant investments are required in piping networks for collection, injection and disposal of various fluids. A single field may concurrently require piping systems for gathering of oil, gathering of gas, injection of water or gas and disposal of salt water. Two problems arise in the consideration of any one of these networks. The first involves the sizing of the various segments of the network to minimize piping and compression costs. The second problem, treated herein, is that of optimally locating the trunkline(s) for a given piping system to minimize the total length of pipe connecting the individual wells or lease batteries to the trunkline. This minimization problem may arise in field automation if it involves replacement of individual lease batteries by a central field battery which will require trunklines and connecting pipelines to individual wells. The problem also arises in connecting a gas pipeline through a subsidiary trunkline to wells in a gas storage field. The first analysis given below treats the case of a single trunkline and of separate connecting lines for all field units.* The analysis is then extended to consider multiple trunklines and common connecting lines for groups of field units. Varying sizes, and therefore costs, of the connecting lines are taken into account. A simplified development is given to illustrate the manner in which line sizing calculations may be integrated with the line placement problem. This study is primarily directed toward the placement of straight trunklines, although for certain field shapes or well distributions curved trunk-lines might be preferable. Some mathematical consideration is therefore given to the placement of a curved trunk-line in a field. The determination of optimal locations for two or more trunklines involves some difficulties which are discussed below. The need for further research in this area is emphasized. The problem of a single trunkline is solved in relation to an actual oil field. The problem of optimally locating two trunklines in the same field is also treated and the results are compared to the single-trunkline case. All calculations reported were performed on an IBM 7072 digital compker. The importance of right-of-way, roads and terrain in locating trunklines and connecting lines is realized. The present analysis is advanced on the premise that in planning piping networks one should start with the optimal conditions whenever possible and proceed therefrom.

By John J. McCabe

INTRODUCTION Over the years, Congress has written into the Internal Revenue Code various provisions aimed at lessening at least one financial burden faced by taxpayers in the mining industry - the federal income tax burden. These provisions include the election to deduct exploration expenses, the election to defer deduction of development expenses, and the percentage depletion deduction. Careful tax planning from the very beginning of a mining venture is essential in taking maximum advantage of these tax benefits. A major decision to be made is the choice of organizational structure. (For a more detailed discussion of this subject, see McCabe, John J., "Developing Structures for Investments in Mineral Property," New York University Institute on Federal Taxation, 42 NYU 24, 1984). One such structure is the use of multiple corporations, with mining activities conducted by one corporation and nonmining activities, such as manufacturing, financing and administration, conducted by the other corporation. This technique, which will be discussed in detail below, can be particularly advantageous in delaying recapture of previously deducted exploration expenses and in maximizing depletion deductions. TAX BENEFITS IN MINING Exploration Subject to certain restrictions discussed below, exploration expenditures (i.e., expenditures paid or incurred during the taxable year for the purpose of ascertaining the existence, location, extent, or quality of any deposit of ore or other mineral, and paid or incurred before the beginning of the development state of the mine are deductible at the election of the taxpayer (Section 617(a)).* Were it not for this option, exploration expenditures would be required to be capitalized and recovered through depletion, after production begins. Exploration of a mineral deposit can be very costly and may not result in commercial production for some time. If the taxpayer has income to he offset by the deductions, a mining venture can usually be structured in such a way as to allow the offset of mining losses against the other income. With today&apos;s high interest rates, this election can be quite valuable in present value terms. Corporate and noncorporate taxpayers are subject to different restrictions on this tax benefit. Corporations may elect to deduct only 85 percent of eligible exploration expenditures (Section 291(b)). (The Tax Reform Act of 1984 reduced this to 80 percent effective for expenditures after December 31, 1984, in taxable years ending after such date). The remaining 15 percent (20 percent after December 31, 1984) is capitalized and recovered at the same rate as five-year ACRS property (Section 291(b)). Individual taxpayers are not subject to this 85 percent rule; however, any amount deducted in excess of ten-year straightline amortization is a tax preference item for individuals (Section 57(a)(5)). Individuals may avoid the tax preference by electing to capitalize exploration expenditures and amortize them over ten years (Section 58(i)). In order to prevent the taxpayer from, in effect, converting ordinary income into capital gain by selling property that has given rise to exploration expense deductions, the Code requires recapture of such deductions upon the occurrence of certain events (Section 617): 1. Upon disposition of the property, adjusted exploration expenditures are recaptured to the extent of gain realized on the disposition (Section 617(d)). 2. If the property is leased, the lessor is disallowed any depletion deduction until his adjusted exploration expenditures have been recaptured in the form of foregone depletion deductions (Section 617(c)).

Jan 1, 1985

By W. D. Lowry

As most of the industrial activity of Oregon is centered in the Portland area, the foundries there consume the bulk of the foundry sand produced in Oregon. Although a number of the larger towns scattered throughout the state have gray-iron foundries, the sand used by most of them is of local origin. The yearly consumption of foundry sand of all types for the past few war years in Oregon is estimated to have been approximately 40,000 tons valued at about $285,000, of which an estimated 18,000 tons was shipped in from the Ottawa, Ill., district for use largely by the steel foundries. Until 1945 much of the silica sand consumed by the steel foundries in the Pacific Northwest, approximately 50,000 tons in 1944, came from Ottawa, Ill. and surrounding regions. Although some silica sand was shipped in from Belgium in the past, none is known to have been imported in recent years. Early in 1945, a very promising high-grade silica sand being produced near Eugene, Oregon, was introduced, and all but two of the Portland steel foundries are using this new sand. Until a few years ago, the search for good local (Oregon) foundry sands was carried on largely by the foundry supply houses. Recently the Oregon Department of Geology and Mineral Industries has investigated a number of deposits and has carried on and fostered research on the most bromising deposit near Eugene, about 120 miles south of Portland. High-grade silica foundry sand from this deposit is now being marketed in Oregon, Washington, and British Columbia. The Eugene sand is one of the very few outstanding western steel-foundry sands. Field investigations by the Oregon Department show that there are relatively few deposits of sand in Oregon suitable for foundry use. A knowledge of the geology of the state makes this readily understandable. The only major primary sources of the quartz present in sandstones in Oregon are the intrusive masses of granite, granodiorite, and quartz diorite of late Jurassic or early Cretaceous age found in the Siskiyou Mountains of southwestern Oregon, a part of the old Klamath Mountain highland, and in the Blue Mountains of northeastern Oregon. Transportation militates against the development of any possible deposits of foundry sand found east of the Cascade Mountains in central and eastern Oregon because few railroads traverse that area. East of the Cascades, which separate western from eastern Oregon, many of the older sediments of Paleozoic and Mesozoic age have either been metamorphosed or contain much volcanic eruptive material, and even if some of the Mesozoic sediments are highly quartzose in places, they are in relatively inaccessible areas. All the Tertiary sediments there are of continental origin and contain much ash and other volcanic debris, for there was great volcanic activity during much of that period. In western Oregon much the same is true of the Paleozoic and Mesozoic rocks

Jan 1, 1948