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By J. B. Fletcher

The Miami mine first started operations in 1910. For convenience, the history of the orebody can be divided into the following categories (Fig. 1): 1) 1910 to 1925: 24.4 million tons of high grade ore, mined by top slicing, sublevel caving, etc. 2) 1926 to 1954: 102 million tons of low grade ore, mined by block caving.

Jan 1, 1961

By J. L. LeBlanc, R. L. Lewis

This study presents an analysis of annular backpressure variations associated with controlled gas kicks and their pronounced effect on casing .strings and exposed under lying formations. A mathematical model describing the volumetric behavior of an extraneous gas as it is transported from reservoir to .surface conditions under changing temperatures and pressures has been programmed in a Kingston FORTRAN II language for digital computer analysis. The gases under investigation typify Gulf Coast reservoir gases within a 0.6 to 0.7 .specific gravity range. The program output has been substantiated by actual field cases. of gas kicks encountered in Gulf Coart we1l.s. The development of empirical equations for calculating suitable gamy deviation factors for unique temperatures and pressures was incorporated in the program to provide realistic solution.. An output listing of annular backpressures and corresponding equivalent fluid densities resulting at a predetermined critical depth (casing setting depth) and total depth for selected .stages of circulation is provided in a chronological .sequence. Additional information including reservoir pressure and temperature, kill rnrid density, produced gas or surface volume of the expanded gas intro vion, drill pipe and annular volumes can he obtained from the model. This paper illustrates that a precise knowledge of the volumetric behavior of extraneous gases in annular flow and its effect on equivalent fluid densities at a critical depth is significant and should receive .serious consideration in controlling threatened blowouts and in the design of drilling programs. Surface pressures in excess of formation limitations are a threat to zones of lost circula/ion and are potentially injurious to productive intervals. A knowledge of annular backpressure and equivalent fluid density profiles for probable gas kicks aids in a technological accomplishment of drilling programs and provides a .sale tolerance in the event a threatened blowout is encountered. Introduction Drilling operations are frequently interrupted when the drill bit penetrates permeable gas sands with reservoir CtfuJ manuscript was received in Society of Petroleum Engineers ofice Am. 1 1967. Revised manuscript received JuIy 7. 1968. Paper (SPE 1860) kae presented at SPE 42nd Annual Fall Meeting held in Houston. Tex., Oct 1-4, 1967. @ Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineem, Inc. pressures greater than that exerted by the drilling fluid. The differential pressures resulting permit an extraneous influx of gas into the wellbore. A suspension in drilling progress is necessary to restore fluid equilibrium throughout the system. Whether formation gas kicks originate unintentionally or by design, the prospect of a threatened or actual blowout exists and a method assuring a safe and effective well control procedure must be observed. A significant contribution to well control technology was advanced by Records et a1.l in 1962. Using the concept of transmitting a constant equivalent formation pressure at the point of intrusion, Records et al. introduced a calculation technique providing the annular backpressures encountered in a well control environment as a func tion of the volumetric behavior of a 0.6 specific gravity natural gas. In essence, the procedure outlined an annular backpressure schedule in terms of fluid volume circulated at different stages of a well control operation. A number of other publications2-' proposing various techniques for controlling gas intrusions in a wellbore achieve pressure control essentially through maintenance of a constant bottom-hole pressure by surface choke adjustments. The subsequent pressure effects induced in the annulus unfortunately receive little emphasis. Due to the tedious and repetitive nature of annular backpressure computations, a theoretical solution by digital computer is introduced for predicting annular backpressure and equivalent fluid density profiles associated with controlled gas kicks. We point out the effects of volumetric behavior of extraneous gases in annular flow and related field phenomena on equivalent fluid densities at a critical depth. The investigation indicated that equivalent fluid densities at a critical depth are of significance and should receive consideration in the control of threatened blowouts and in the design of drilling programs. Theoretical Considerations The mechanism of vertical gas flow through an annulus is governed by the PVT properties of the fluid, the pressure distribution within the system, the fluid flow rates and the geometry of flow. Due to the numerous variables involved in this type of problem, certain assumptions were imposed in deriving the mathematical model and in establishing the solutions. Two gases, characterized by specific gravities of 0.6 and 0.7, were selected to typify Gulf Coast reservoir fluids. The gas intrustion entered the wellbore as an immiscible 'References given at end of paper. JOURNAL OF PETROLEUM TECHNOLOGY

Jan 1, 1969

By Russell Gibson, F. S. Turneaure

The tin deposit of Monserrat, Bolivia, consists of one major vein 1600 m in length. The ore is unusual because of the notable quantity of teallite, even though cassiterite is the principal tin mineral. The deposit, formed at shallow depth under a wide range in temperature, may be classed as xenothermal. Polished sections reveal a complex history of replacement, with low-temperature minerals deposited before high-temperature minerals.

Jan 10, 1950

By R. F. Mehl, C. S. Barrett, A. H. Geisler

THE studies of the mechanism of precipitation and of the resulting property changes in aluminum-silver alloys1-3 have presented some new concepts of the aging reaction-concepts that may be fundamental in establishing a complete quantitative theory of age-hardening. With both aluminum-copper and aluminum-silver alloys, thin platelike aggregates form parallel to the Widmanstätten planes of precipitation.1,4 These platelets grow in lateral dimensions and in thickness with aging time until they are thick enough to produce an X-ray diffraction line pattern. Their structure is that of a transition lattice which is coherent with the matrix, since the atomic spacings in the matrix and the precipitate are the same on each side of their common interface.2,4 The equilibrium precipitate forms later from and at the expense of the transition lattice. Since age-hardening occurs during the formation and growth of the transition lattice, the major contributor to the hardening no doubt is the stress condition in the matrix resulting from the matrix holding the precipitate in the coherent condition. The development of these stresses also appears to be responsible for an increase in the electrical resistance superimposed on the normal decrease resulting from a change in the concentration of the matrix during aging.3 The two consecutive reactions constituting the aging process are accompanied by characteristic microstructural alterations. The initial precipitation process results in the formation of a Widmanstätten figure, while the later transformation of the transition lattice to the equilibrium lattice is accompanied by a coalescence, in the case of aluminum-copper alloys,5 and by the appearance of light areas at the grain boundaries with aluminum-silver alloys showing a structural rearrangement of matrix and precipitate.3 This latter reaction is similar microscopically to the so-called "discontinuous precipitation." Possibly discontinuous precipitation is a process that often if not always follows true precipitation of a coherent lattice and during which the transformation of the coherent transition lattice to the equilibrium lattice takes place accompanied by matrix recrystallization.3 EXPERIMENTAL PROCEDURE The alloys were made using 99.97 per cent Al or distilled magnesium, with

Jan 1, 1943

By O. T. Marzke, Robert F. Mehl

A study of the structures arising from the decomposition of the ß solid solutions in the Cu-Zn and the Cu-A1 systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution— the Widmanstätten structure—-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the ? phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series—that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-—which at present seems the only a1ternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the ß and in the precipit'at.ion of the y phase from the y in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point, of view.

Jan 1, 1931

By Richard E. Chism

I have thought it well to lay before the Institute some account of the Vallecillo Mines, now, I believe, the only paying ones in American hands in northeastern Mexico, including the States of Nuevo Leon, Coahuila and Tamaulipas. The authentic history of these mines dates from their ownership by an American Company in the year 1851, when they were bought by the Vallecillo Silver Mining Company of New York. They had been worked before by the Spaniards, but had been abandoned for many years, on account of the heavy expense of drainage and the constant incursions of the Indians. The company commenced work with several well-known New York capitalists among its stockholders, and had a large fund of both money and enthusiasm. The first point of attack was at a shaft on a mine known as the Jesus Maria, which had the most favorable traditions. Extensive buildings were put up, and two sets of pumps were successively tried. After the second pump, with a steam-cylinder 5 feet in diameter and 10 feet stroke and a plunger 20 inches in diameter, had failed to do more than hold the water, with infinite labor, at the 250 feet level, and after a thorough exploitation of the whole mine above that level had failed to yield more than some $30,000 worth of ore, it was resolved to abandon the effort. Operations were accordingly transferred to the old Dolores shaft, at a point about 21/2 miles to the

Jan 1, 1885

Jan 1, 1941

By Emil Schroedter

The death, on May 6,1908, of Dr. Hermarnn Wedding, Privy Mining Councilor of the Kingdom of Prussia, and Professor of the Metallurgy of Iron and Steel at the Royal Mining Academy of Berlin, was a loss keenly felt by the whole metallurgical world. Not alone in his native land, but also in foreign countries, did he enjoy an esteem of which the title of honorary membership in the American Institute of Mining Engineers, the United States Association of Charcoal Iron-Workers, and the (British) Iron and Steel Institute bears eloquent testimony.

Jan 1, 1910

Buffalo Society of Natural Sciences, Buffalo Museum of Science, Humboldt Park, Buffalo, N Y. Of the many scientific bulletins issued by the Society only one of those now available is of particular interest in this directory. Vol 7 (1901), Bulletin 1, Guide to the geology and paleontology of Niagara Falls and vicinity, by A. W. Grabau, $1 unbound or $2 bound. The bulletins are distributed through the Research Librarian at the above address

Jan 1, 1933

By Francis B. Foley

THE casting of steel in large molds brings into play all of the undesirable effects that result inevitably from slow cooling. The origin of the molten metal, whether basic or acid open hearth or electric furnace, has little if anything to do with the phenomena involved. If the quantity of molten metal to be cast in a single mold is large enough, there is very little one can do about it-the metal will cool so slowly that 'nothing one can do, other than to provide as good feeding as practicable from an adequate reservoir of metal in the sink head, will be of any avail. Recently we have had occasion to cast a 108-in. octagon ingot weighing 545,700 lb, necessitating the combining of metal from three 100-ton open-hearth heats. This is one of the largest ingots ever made. The body of the ingot weighed 448,800 lb, which includes a bottom pool of about 7500 lb of metal, and the sink-head weight was 96,900 lb, or about 18 pct of the total weight.

Jan 1, 1947

By C. C. McDermond, Others, B. N. Zavoico

Production of crude oil in Venezuela for the year 1937 was 186,653,-916 bbl., as compared with 155,228,982 bbl. produced in 1936, an increase of almost 31,500,000 bbl. The oil-field strike, which started on Dec. 14, 1936, lasted until Jan. 25, 1937, when a total of 10,000,000 bbl. of production was estimated to have been lost (5,750,000 bbl. in 1936 and the remainder in 1937). Of the total of 186,653,916 bbl. produced in 1937, the Lagunillas field contributed 45.6 per cent, a drop of approximately 10 per cent under 1936 figures; Tia Juana, 14.3 per cent; Quiriquire field, 14.0 per cent; La Rosa area, 13.3 per cent and the Mene Grande field, 7.6 per cent, these being the five leading contributors of the year's production. Detailed production figures by fields and by companies are shown on Table 1. Of the total production of Venezuela the following four major companies accounted for the greater proportion: Standard of Venezuela and Lago Petroleum Corporation together, 48.3 per cent; Shell, 37.4 per cent and Venezuela Gulf, 14.0 per cent. At the end of the year, 2491 wells were producing, of which number 1291 wells were pumpers, or about 52 per cent. Production The accompanying statistics of production record of Venezuela oil fields from its inception to Dec. 31, 1937, shown on Table 2, indicates that the cumulative production reached 1,503,283,228 bbl. In order of importance, Lagunillas leads all the fields, having accounted for about 50 per cent of Venezuelan production, followed by La Rosa area, which produced about 21 per cent; Mene Grande, which produced about 13 per cent, and Quiriquire, which produced 6.5 per cent. Table 3 shows the age of each field. Mene Grande is the oldest, having produced for 24 years; Tarra is next, 21 1/2 years old, and El Mene third, 171/2 years. The gravity of the crude from the various fields, also shown on Table 3, remained unchanged, the only addition being the new Tia Juana field, which averages 15.6' A.P.I. Table 4 shows the method of production by fields as of Jan. 1, 1938; at the end of the year 2491 wells were producing, compared with 2005 wells producing at the beginning of 1937, or an increase of 486 wells. The completions for the year reached 512. Of the 2491 wells producing crude oil, 1291 wells, or approximately 52 per cent, were pumping, 925 (approximately 37 per cent) were flowing naturally and 275 (11 per cent) were on

Jan 1, 1938

By C. H. Li, S. H. Bendel, J. A. Sartell

Small additions of Mg to a 62 Cu-38 Ni alloy reduce the oxidation yates drastically between 500° and 850°C. Metallographic examination of the oxide scale disclosed a continuous network, identified by X-ray diffraction as (Ni, Mg)O solid solutions, located along the former alloy grain boundaries. This network acts as a barrier to diffusion. It is thought to result from the segregation of mg to the alloy grain boundaries. Oxidation occurs preferentially in these regions because of the presence of this more active element. To substantiate these ideas, homogenized alloys ulere oxidized. No oxide network was produced and oxidation rates were the same as for the parent 62 Cu-38 Ni alloy. An interesting aspect of the oxidation of the 62 Cu-38 Ni alloy previously described by the present authors, is the relationship between oxidation kinetics and changes in the microstructure of the oxide.' The oxide scale on these alloys consists of two layers: a thin layer of CuO outside a much thicker layer of Cu20 in which particles of NiO are dispersed. In addition, immediately beneath the oxide-metal interface there is an internally oxidized zone in which NiO particles are dispersed in a copper-rich alloy matrix. Experimental observations on the growth of the individual layers under isothermal conditions have led to the conclusion that the rate-determining step in the oxidation of this alloy is the diffusion of anions through the Cu20 layer. It has been found that this diffusion rate is increased by the recrystallization of the outer CuO layer. Willardson and Gorton have reported that the addition of magnesium to the 62 Cu-38 Ni alloy causes a decrease in the oxidation rate.2 The present investigation was undertaken in order to determine the mechanism by which magnesium additions improve the oxidation resistance of the 62 Cu-38 Ni alloy. EXPERIMENTAL PROCEDURE Fifty-gram ingots of Cu-Ni alloys were prepared by vacuum melting materials of 99.999+ pct purity. These ingots were then remelted in a He atmos- phere and magnesium added in the form of a previously prepared and analyzed Cu-Mg master alloy. This procedure was necessitated by the high reactivity of pure magnesium at high temperatures. The proportion of the alloying elements was adjusted so as to obtain alloys with the desired magnesium content while maintaining a Cu-Ni ratio of 62 :38 by weight. (All alloy compositions will be given in weight percent.) Since it was considered desirable to study the oxidation of only single-phase, solid-solution alloys, it was necessary first to determine the approximate limit of solid solubility of magnesium in the 62 Cu-38 Ni alloy. A series of melts with various magnesium contents was made, homogenized by annealing for 48 hr at 975OC, then cooled in the furnace. Metallographic samples were prepared, etched in a potassium dichromate solution and examined at XI500 for the presence of a second phase. The alloys were then chemically analyzed and it was found that the approximate limit of solid solubility of magnesium in the 62 Cu-38 Ni alloy was 1 pct Mg. The ingots containing less than 1 pct Mg (0.19, 0.29, 0.58, and 0.87 pct Mg) were cold-rolled down to thicknesses suitable for oxidation experiments and specimens for gravimetric studies were cut to dimensions of 3.0 by 1.5 by 0.05 cm, specimens for inert marker studies, 0.6 by 0.6 by 0.17 cm. These were heat-treated in a protective atmosphere at a temperature (975" C) well above the oxidation temperatures and furnace-cooled to insure structural stability of the alloy during oxidation. Immediately prior to oxidation, the specimens were chemically cleaned by immersion for 1 min in a solution of 2 parts nitric acid, 1 part acetic

Jan 1, 1961

By H. H. Hausner, S. Storchheim, J. L. Zambrow

The solid state bonding of aluminum to nickel was studied as a function of temperature, pressure, and time at pressure. The initial results indicated that as the reaction conditions were varied, marked changes in tensile strength occurred. Plots of the log penetration coefficient vs the reciprocal of absolute temperature for various isobars were straight lines displaced from each other. THE techniques of bonding different metals to A each other include brazing, welding, welding by application of a molten phase, and solid state welding without any molten phase present. This last technique, the pressing of metals either at room temperature or at some temperature below the melting point of the metals to be joined, seems to offer interesting possibilities for bonding purposes. However, this technique has not been completely investigated, and very little is known about the diffusion phenomena which occur during solid state welding. Some previous work on the effect of pressure on diffusion1 was inconclusive. This paper is concerned with an investigation regarding the effect that the processing variables, such as pressure, temperature, and time at pressure, have in solid state bonding. The tests were made with aluminum and nickel and special emphasis was given to the strength of the bond between these two metals and to the intermetallic penetration rate during the bonding process. It seems that the effect of pressure on the intermetallic penetration is of particular importance for practical purposes and this effect was therefore studied in detail. Procedure Apparatus: The means of solid state bonding used for this study was that of the hot-pressing technique. This method requires the equipment pictured in Fig. 1 and involved the following procedure. The two metals to be bonded were placed in an aquadag lubricated 18-4-1 tool steel die, 16 in. high by 1.440 in. ID, between punches of 1.366 in. diameter made of the same material. A thermocouple

Jan 1, 1955

By Y. L. Yao

It is suggested that the binary alloy systems of transition metals may be classified into groups according to "excess energy"E. For systems with positive ?E, the Laves phase, the TiNi3-, the TiCu3- and the Cudu-type rich in the smaller atom and the TizNi-type rich in the larger atom may exist. For systems with negative ?E and composed of two components of different crystal structures, the X, the Cr3O and the phase may exist on the side of the phase digrattz rich in the component with the higher "solubility factor" value am! the Cudu-type and the disordered hcp phase on the other side; if the crystal structure of two components is the same, the Cudu-type may exist on both sides. For systems with weakly positive ?E and cotnposed of different crystal structures, the u phase and the MgCd3-type may replace the Laves phase and the other types; the X, the Cr3O and the a phase may also exist. Finally, the equirnolar compounds of the CuAu- and the CsC1-type may exist irrespective of the sign of ?E. THERE are many factors which play a major role in the formation of binary intermediate phases in alloys, such as the crystal structure, the electronic structure, the atomic size and the electrochemical factor. To find the simultaneous effects of all these factors on the formation of intermediate phases of every metal would be a difficult task, especially because only a small fraction of experimental facts necessary for the complete formulation is known at present. Thus the past surveys of intermediate phases have been usually confined to few metals, several types of intermediate phases and some but not all controlling factors. In a previous paper1 the idea of "solubility factor" of metals was introduced. Although the suggested values are tentative and empirical, the formation of a continuous series of solid solutions in metals could be correlated with the interplay among the atomic size factor, the solubility factor and the crystal structure factor. The purpose of this paper is to demonstrate qualitatively the interplay of these factors in the formation of binary intermediate phases among transition metals. FACTORS CONSIDERED The Crystal Structure Factor. With rare earths excluded, the transition metals are classified into three common crystal structures listed in Table I. There is arbitrariness in the present classification of several allotropic elements. However, out of seventy-odd continuous solid solutions formed among transition metals, only six of them, namely, those

Jan 1, 1962

By David W. Pasho

The success of a collector vehicle, designed to recover manganese nodules under the conditions which exist in deep ocean mine sites will in part be determined by the effectiveness of pick-up and running gear mechanisms. For the purpose of qualitative comparison, some specific aspects of seafloor interactions with various concepts are reviewed utilizing existing data on seafloor characteristics and running gear/tool interaction with soils.

Jan 1, 1976

By George E. Roberts

The maintenance of the common gold standard is the most important cooperative undertaking in the world. The war broke up this relationship and brought about a state of great disorder in the currencies and exchanges. After the war the countries all began to grope their way back to the gold standard as the best means of establishing trade and financial relations with each other. With this movement began a general decline in commodity prices. The question has been raised whether the world's return to the gold standard was not forcing prices back to the prewar level. Also, the question is raised whether the world has not outgrown the supply of gold as the basis of credit. Because Europe readjusted its monetary units to conform to the higher level of prices there is no pressure on prices on this account. Furthermore, a large amount of gold formerly in hand-to-hand circulation passed out of circulation and has been added to the central bank reserves. The gold reserves of 36 countries increased approximately 100 per cent from the outbreak of the war to June 30,1930. The increase is much larger than the average increase of prices in any of the important countries, at any time since 192.5. As gold in the central banks of issue is far more effective for all business purposes than gold in circulation, the gold scarcity argument has little basis as applied to this time. The abnormal distribution due to the war was to the disadvantage of business everywhere. Credit was scarcer and dearer in some countries. The inflation in this country might have been greater had the production of gold been greater. The argument supporting the theory of a scarcity of gold assumes as fundamental that general price changes must be accounted for by changes in the price equation on the side of money. This is disproved in every period of business depression. A downward price movement is characteristic of every period of business recession. Important discoveries of gold must be made even to maintain present gold production, in the face of which the world's business is bound to continue increasing. It cannot be doubted that some way will be found

Jan 1, 1931

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

Jan 1, 1949

By A. Long, A. Silverman, J. L. Kulp

Garth Crosby has written an excellent geologic description of the deposits surrounding the Gem stocks in the Coeur d'Alene district. The ore deposits in the area of the Gem stocks may hold the key to the age and mineralization history of the entire Coeur d'Alene district. A recent isotopic study of the Coeur d'Alene district in this laboratory illustrates that a classical geologic interpretation of these deposits, with its implications for the whole district, may lead to erroneous conclusions. For this reason it seems pertinent to submit a summary of these results and an interpretation of the mineralizing history of the Coeur d'Alene districts.

Jan 5, 1960

LIMA (PERU) Established May, 1952 (Official year begins in June) Luncheon meetings third Wednesday monthly Ernesto A Baertl, Chairman Arthur C Hall, Chairman-elect Raymond R Beard, 1st Vice-Chairman Edgardo Portaro, 2nd Vice-Chairman Walter E King, Secretary-Treasurer Av Santa Cruz 331 San Isidro, Lima, Peru Alberto E Brazzini, Asst Treasurer Daniel M Rodriguez, Asst Secretary Robert P Koenig, '56, Section Delegate Arthur C Hall, Alternate Section Delegate

Jan 1, 1955