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By F. Keller, E. H. Dix

The use of magnesium as an alloying element in aluminum alloys has been limited, in general, to comparatively small quantities. In duralumin-type, strong aluminum alloys, magnesium is present to the extent of 35 to 3/4 per cent. and various grades of Magnalite and the "Y" alloy of the National Physical Laboratory of England contain up to 1 1/2 per cent. In this country small quantities of aluminum alloy sheet containing 4 per cent. magnesium are produced commercially. All commercial aluminum contains sufficient silicon to convert a portion of the magnesium added to the compound Mg2Si. It is well known that the solubility of both magnesium and magnesium-silicide decrease with decrease in temperature. It is, therefore, impossible to separate the age-hardening effect of the magnesium-silicide from that of magnesium, except by the use of aluminum of such high purity that the silicon content is negligible. The present paper is the fifth l, 2, 3, 4 of a series from the laboratories of the Aluminum Co. of America reporting the results of investigations of the equilibrium relations in aluminum-rich alloys made from the high-purity aluminum manufactured by this company. 5 Previous Investigations A number of investigations have been made of the constitution of the complete aluminum-magnesium system and several determinations made

Jan 1, 1929

By D. G. Russell

Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary eflects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estitnates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. On the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. INTRODUCTION The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottom-hole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + ?t)/ ?t (where At is shut-in time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "afterproduction" or "fill-up" portion of the pressure build-up. During the period that the well fill-up effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the afterproduction period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the afterproduction period is a paper by Gladfelter, Tracy and Wilsey.1 In the approach of these authors it is necessary to measure the rate of influx into the well during the afterproduction period. This is done through sonic measurements or through measurement of tubing-head and casing-head pressures simultaneously with

Jan 1, 1967

[Aase, Qlenn D., (Junior Member '40) Jr. Met.. American Smelt. & Refin. Co., Selby. Calif. Abadie, Henry G., (Junior Member '43) Petr. Engr.. Avenal, Calif. Abbott, Clarence E., (Member '04) Civil En=.. V.P.. Tennessee Coal. Iron & R.R. Co., 1542 Brown biarx Bldg.. Birminpham, Aln. Abbott. Fred E., Jr., (Member '44) Petr. Engr., C/O Arabian Anierican Oil Co.. A.P.O. 816. c/o Postmaster, New York, N. Y. Abel, Raymond L., (Member '28) Chem. Engr.. C. O., Pittsburgh Chem. Warfare Procurenlent Dist.. American Bank Bldg., Pittsburph. Pa. Abel, Walter D., (Member '32) Min. Engr.. Supvr. Engr.. RFC, Los Angeles, Calif.]

Jan 1, 1946

By Herluf P. Nielsen, Robert I. Jaffee

IN recent years much attention has been given to high-melting alloy systems, It has been of interest in this respect to investigate the alloys of platinum and tungsten, which were known from the literature to have very high melting points up to about 50 pct tungsten, but about which little had been published on the high-tungsten side of the system. Powder metallurgical methods were used throughout this investigation for the preparation of the alloys, utilizing electrical sintering techniques such as are used for tungsten and molybdenum. In the course of the work it was found desirable to determine fusion temperatures of the alloys, and it was possible from these and other data to draw a tentative constitutional diagram (solidus, mostly) applicable to the high-temperature part of the system. No attempt was made to determine solid solubility vs. temperature data, nor to investigate the lower temperature transformations in the solid state. Data on the microstructure, hardness, and a note on oxidation resistance of the sintered alloys were obtained. PAST WORK Müller1 determined liquidus temperatures of platinum-rich alloys to 50 pct tungsten, using a radiation method employing a photoelectric cell, and found that the melting points increased progressively from 1771°C for platinum to 2350°C for the 50 pct alloy. Microscopic evidence by Müller that complete solid solutions exist to 50 pct tungsten was not checked by Kremer2 who, according to Vines and Wise,3 found that "although the 8 pct tungsten alloy was a solid solution, the 26 pct tungsten alloy contained a eutectic or an intermediate phase." Hultgren and jaffee4 using X ray methods found continuous solid solutions to at least 33.6 pct tungsten (35 at. pct) after annealing in vacuum for 6 days at 1000°C. Vines and Wise3 report work communicated to them by E. C. Rhodes on wrought alloys to 7 pct tungsten, which showed that tungsten hardened platinum extremely rapidly, and was one of the most potent hardeners of the binary additions to platinum. Considerable quantities of 4 pct tungsten platinum wire have been produced for grids in radar tubes and for aircraft spark plugs. Some of the alloy for the latter application is made by sintering, the remainder by smelting and casting. MATERIALS The platinum powder used in this work was kindly supplied by the research and Development Laboratory of the Owens-Corning Fiberglas Corp., Newark, Ohio, It was prepared from scrap platinum. After dissolving in aqua regia and evaporating almost to dryness, the solution was worked up several times with concentrated HCI. the resultant platinic chloride was diluted considerably, and metallic zinc was added, which precipitated the platinum in a very finely divided form. After dissolving the

Jan 1, 1948

By John D. Morgan

Uncertain world conditions of the present time require that this country be prepared to meet: 1) all out nuclear war with attack on the U. S.; 2) limited wars; 3) political, economic, and/or pyschological warfare. Our present position as a major world power derives in large measure from our free institutions and great industrial productivity, and this productivity in turn depends on a continuing flow of raw materials-metals, minerals, fuels, and agricultural products. The U. S., with only about 6 pct of the world's population, uses from one to two thirds of the world's annual supplies of most metals and minerals. The U. S. strategic materials stockpiling program is designed to enhance our national security position: as stated in the preamble of the Stock Piling Act, to decrease and prevent wherever possible a dangerous and costly dependence upon foreign nations for supplies of strategic and critical materials in times of national emergency.

Jan 8, 1960

By S. A. Swensrud

REPORTS from smelters show that all were so occupied with the in- creased production called for during the first half of the year that little time was devoted to metallurgical developments. Improvements which have been made such as gas-firing and other alterations ill the reconstructed Hayden smelter, will require time for reporting. The labor situation at all plants held the most prominent place and put all other problems in the background. Coming events of considerable importance concerti the construction of two new smelters. The Chino unit of Nevada Consolidated which has long had its concentrate smelted at the El Paso plant of the American Smelting and Refining Co. is constructing its own smelter at the property in New Mexico. The newest Phelps Dodge development of the Clay ore body at Morenci, Ariz., will call for another new smelter.

Jan 1, 1938

By C. Scala, F. Bernstein

General expressions are derived relating the streaming potential to the electrochemical potential of a permeable junction separating two electrolytic solutions. By the methods of irreversible thermodynamics, these potentials are related to the flux of mobile species arising from differences in pressure and chemical composition. The flux is conveniently expressed as a transference number, the equivalents of a mobile species transferred through the junction per faraday of electricity. At constant pressure, the flux equation gives the electrochemical potential across the permeable junction. The streaming potential across the junction is obtained by imposing the condition of constant chemical composition. The familiar expression for the borehole SP is shown to be a particular solution of the general flux equation. The derived exprersions were verified in experiments with seven shale samples. Both the theory and experimental data provide additional proof of the presence and magniturle of the streaming potential in shales. INTRODUCTION In the interpretation of electric logs, there has been much concern over the correction to be made to the recorded SP for an electrokinetic or streaming potential originating from the difference in pressure between the mud column and the formation. It was long recognized by M. R. J. Wyllie that such an electrokinetic potential source mas in the mud cake opposite permeable sands.' More recently, M. Gondouin and C. Scala2 showed an additional but opposing electrokinetic source of potential to be in shale beds. Their work was supported by the very extensive and excellent work of Hill and Anderson.3 n the present contribution, the general relationships between the electrochemical potential and the corresponding streaming or electrokinetic potential are examined and clarified. A notable advance towards understanding the relation between the various sources of electrical potential in a borehole has been the application of the now common methods of irreversible thermodynamics to describe the passage of ions and water through charged electrolyte junctions such as in shales.' The advantages of these methods are twofold. Unlike classical thermodynamics, they can be applied to non-equilibrium sys- tems, i.e., systems in which flow takes place, provided the flow processes have reached a steady state. They also permit conventional thermodynamic properties to be related to the steady-state dynamic properties. These methods arc used here specifically to derive expressions relating the potential behavior of shales in terms of ion and water transport. Experimental verification of the expression for the shale streaming potential is given which in turn offers theoretical support to the existence of a streaming potential in shales.' Importantly, the relative contribution of transport parameters to the SP is clarified. The theoretical treatment is essentially that of Lori-mer, Boterenbrood and Hermans3 ut has been extended to derive the general expression for the SP.

By Kenneth L. Clifford, Thomas G. White

Many changes have occurred in lead-zinc milling in the U.S. since the 1970 Lead and Zinc Symposium. New mills have been built, novel flowsheets devised, and the use of process control techniques is increasing. The Missouri concentrators produced in 1976 more lead and zinc concentrate than those in any other state. The Tennessee mills produced nearly as much zinc concentrate in 1976 as Missouri and with some very highly developed flowsheets. Progress in the Western U.S. is centered around new operations in Colorado and Utah. New mills in New York and Missouri incorporate many of the newer control concepts. Most of the older concentrators have undergone flowsheet changes to accomodate different ore types or because of the availability of new and better equipment.

Jan 1, 1977

NEW MEMBERS The following list comprises the names of those persons who became members during the period Sept. 10, 1916, to Oct. 10, 1916. BLOOMFIELD, EDWIN CHARLES, Min. Engr., 1012 Standard Bank Bldg., Vancouver, B. C., Canada. BRINGS, HENRY, Min. and Met. Engr., Chief Engr., and Geol., Mollet-Mesrine, 1212 Mills Bldg., El Paso, Texas. CHASE, MARCH F., Vice-Pres., Commercial Acid Co., 1906 Boatmens Bank Bldg., St. Louis, Mo. CUMMINGS, ALVIN M., Asst. Mine Supt., Witherbee, Sherman & Co., Inc., Mineville, Essex Co., N. Y. DOUGLASS, GEORGE M., Genl. Safety Inspector, Amer. Smelt. & Ref. Co. 120 Broadway, New Fork, N. Y. EMRICH, CLARENCE T., Chief Chemist, Old Dominion Copper Min. & Smelt. Co., Box 1163, Globe, Ariz. GARDANIER, SUTTER ALBERT, Assayer, Mgr., Douglas Assay Co., Douglas, Cochise Co., Ariz.

Jan 10, 1916

By T. Koulomzine

The theory of the Askania mag-netometer, as well as a complete discussion of all factors influencing magnetometer readings, is very ably described by J. Wallace Joyce.1 We will assume that the reader is thoroughly familiar with this theory and we will use whenever possible the same notations for the physical values involved in the theory. On the other hand, we believe that the principal formulas of the magnetometer can be deduced much more easily by the use of differential calculus than by the methods employed by Joyce. Consequently, we are presenting herewith a resumé of the theory of the vertical magnetometer in order to determine the correct formula of the temperature coefficient which we propose to compensate. Short Theory of the Vertical Magnetometers We shall accept the following notations: m = total mass of the magnet system, in grams. g = acceleration of gravity, in dynes. a = projection on the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. h = projection on the perpendicular to the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. M = 2pL = M, magnetic moment of the magnet system. Z = vertical component of the earth's magnetic field. ? = deflection angle of the magnet system. = focal length of objective lens in the optical system S = scale reading. In a vertical magnetometer the axis of the magnet system is kept horizontal within 2". Therefore, referring to Fig 1, we see that the magnetic torque of the magnet system influenced by Z must be counterbalanced by the gravity torque. MZ cos ? = mga cos ? + mgh sin ? or dividing by cos ? MZ = mga + mgh tan ? If we now move to another magnetic station and the temperature conditions change, the values of all the variables will change also: M, a, and h under the influence of temperature. 2, both with time and space. ? and S, as a result of all the above changes. Taking increments in Eq 2 we obtain: (Mo + ?M)(Z + ?Z) = mgao + mg?a + mg(h + ?h) tan (? +??) but tan (? +??), because ? is small, can be replaced by tan ? + tan ??; in fact tan (?+ ??) = sin ?.cos ?? + cos ?.sin ??/ cos ?.cos ?? — sin ?sin ?? but sin ? sin ???0 tan (8 + ??) ? tan ? + tan ??. Fur-thermore, neglecting all terms of the equation containing two differentials becomes: or a differential and a tan ??, Eq 3

Jan 1, 1950

Jan 1, 1927

FOLLOWING- the major explosion disaster in the Orient No. 2 mine of the Chicago, Wilmington and Franklin Coal Co., West Frankfort, Ill., on December 21, 1951, resulting in the death of 119 miners, an investigation was made by the U. S. Bureau of Mines under the direction of J. J. Forbes, Bureau director. The subsequent report concluded that the disaster. was caused by the emergence of a-large body of explosive gas from an abandoned area and simultaneous short circuiting of the ventilating current; the gas was ignited by an electric arc from nonpermissible electrical equipment and the flame was propagated throughout a large part of the affected area by coal dust and possibly by gas from other worked-out and abandoned areas. An immediate repercussion of the disaster was the opening of hearings by the. Senate Labor and Public Welfare Subcommittee on the Neely Mine Inspection Bill (S. 1310, introduced April 11, 1951) which would give federal coal-mine inspectors power to enforce safety recommendations by ordering the withdrawal of all employees where conditions constitute an imminent danger to their safety. Two days of testimony, January 24 and 25, disclosed that coal operators were not in agreement on the bill, although John L. Lewis, speaking for the UMWA, and J. J. Forbes, for the Bureau of Mines, were advocates.

Jan 1, 1952

By E. G. De Coriolis

THE development of huge production facilities and of new or improved processes for manufacturing magnesium from its raw sources has been an outstanding achievement of this war. Furthermore, at least one new method has reached a stage of pilot production that offers promise. Its potentialities seem to indicate that a reduction in cost and simplification or elimination of problems incident to the use of at least one of the present processes are quite within the realm of possibility. Although magnesium of very high purity (99.9 per cent and higher) is obtained, and the rate of recovery reasonable (60 to 70 per cent), the ferrosilicon reduction process is open to a serious objection, which at the time its use was proposed was thought to be sufficient to raise some doubts as to its success, at least on a high production basis. The temperature range at which the reaction is carried out-namely, 2100° to 2150°F.-is very close to the failure temperature of the material of which the retort is made. It is so close that for a time it was assumed it might make commercial use of the process an impossibility. However, at the time under discussion, the demand for magnesium was so great that it was felt by those who had to go ahead and produce this essential metal that the emergency warranted their taking a chance on this process. Subsequent developments have fully justified the soundness of their decision. Fortunately for the war effort, when the plants were put into operation it was discovered that although the retorts did collapse in rather short periods of time, as predicted, they could be blown back into operable shape by application of high-pressure air. This practical method of operation so relieved the situation that the problem disappeared. Nevertheless, if the process had not been successful, or the production of magnesium by the electrolytic process had not been able to keep pace with demands, our war program would have been seriously impaired. "FIRELESS COOKER" PROCESS For this reason a program was set up and assigned for the development of a new method that had been suggested to the War Production Board in 1941. It is believed justifiable in terming the method "new" for several reasons: (1) while utilizing the same (ferrosilicon) process as the Pidgeon, hence involving similar reactions, the type of retort or furnace is essentially different, (2) the method of operation, reaction temperatures, etc., differ materially, and, most important of all, (3) the problems to be overcome in making the process successful were not and could not have been anticipated by anything previously known about the Pidgeon process. As will be shown later, the briquetting process, the condenser, the furnace lining

Jan 1, 1945

By H. C. Howarth

THIS paper gives observations on ground movement and subsidence resulting from pillar drawing in the Lick Run section of Montour No. 10 mine of the Pittsburgh Coal Co. adjacent to solid coal owned by the U. S. Bureau of Mines at its Experimental mine in Snowden Township, Allegheny County, Pennsylvania. The investigation was planned by George S. Rice, chief mining engineer of the Bureau, who arranged the necessary cooperation with Dr. L. E. Young, vice president of the Pittsburgh Coal Co. Engineers of that company placed permanent monuments on the surface to establish the boundaries of the coal owned by the Bureau and to furnish fixed points to which all levels were referred. Engineers of the Experimental mine staff then covered the ground under observation with a checkerwork of monuments made of oak pegs set into the ground at 50-ft. intervals in two directions at right angles to each other. The level of these pegs was determined first from Dec. 16 to 30, 1929; again from May 25 to June 5, 1930, and finally from July 7 to 15, 1931. Observations were then discontinued because work had been stopped temporarily in this part on Montour 10 mine.

Jan 1, 1933

By T. B. Counselman

AFTER several years study, the Universal Atlas Cement Co. decided to rebuild its plant at Leeds, Alabama. The entire old plant, which was to operate during the new construction, was then to be scrapped with the exception of two kilns. The quarry was to be mechanized, new and larger kilns installed, with the most modern type of equipment all through the plant. Raw grinding operations at all of the Universal Atlas plants were dry. However, the dust hazard of this operation and the growing emphasis on occupational diseases made wet grinding attractive. Coal at Leeds is cheap, so that a slightly higher coal practice was unimportant. Power was cheap, so that waste-heat boilers were not desirable. Since new kilns were to be installed, these could be made long enough to make filters unnecessary. Wet raw grinding could be either the old practice of open-circuit compartment mills or closed-circuit grinding in accordance with metal-lurgical practice. The latter saved power and steel wear and saved initial investment. This had been demonstrated in cement plants. Also, the elimination of tramp oversize was a most important advantage. Ease of chemical control was another factor. Blending in the thickener, with elimination of slurry mixers had been found practicable. Therefore, if wet raw grinding were used at all, the advantages were clearly in favor of closed-circuit grinding. Detailed layouts of the most modern possible closed-circuit dry-grinding plant and of a closed-circuit wet-grinding plant were prepared, and careful estimates were made of initial invest-ment and operating costs. Full consideration of all the factors involved resulted in a decision to install wet closed-circuit grinding.

Jan 1, 1939

By Alvin Kaufman

At the turn of the century the U.S. had a gross ALVIN KAUFMAN Mineral Economist U.S. Bureau of Mines area slightly in excess of three million square miles, a population of 76 million, a gross national product of $37 billion (constant 1929 dollars) and a mineral production valued at $2 billion (1929 dollars). Some 60 years later its area had increased by 600 thousand square miles, population had risen 140%, gross national product was seven times greater and mineral production had grown to a value five times that of 1900. Of perhaps greater significance, however, were the changes wrought by technology. It was during this period that the "American Way of Life" was revolutionized by the introduction of the airplane and the automobile; man also took his first probing steps in the utilization of nuclear energy and pre- pared to unlock the secrets of space. It was during these six decades, also, that he learned to create additional new materials, some of which were from old sources such as plastics from petroleum and coal. These new materials have created competition and attendant problems for the traditional materials such as iron, copper, lead and zinc. Additional problems undoubtedly will be created by technologic advances in the future.

Jan 2, 1963

Jan 7, 1976

By H. Landsberg

MANY of the sedimentary rocks contain small amounts of radioactive constituents. These vary in quantity in different layers. Some recent deposits show rather high activity as; for example, the deep sea oozes and some lake deposits.1,2. Measurements made in boreholes have also shown considerable changes in activity from horizon to horizon. The first to publish data on this fact was Ambronn,3 and recently Russian geophysicists have shown remarkable variations of activity from one layer to the next in various wells. Spak4 felt even that he was able to line up horizons from data measured in two neighboring wells. ? The measuring of radioactive radiation is fairly difficult. Large errors are possible by the circulation of gaseous emanations in the well and porous strata. It is, therefore, never certain whether the activity of the layer where the instrumental device or collector is located will be measured, or that of some adjacent layer, For this reason it seemed to be advantageous to take samples of rocks into the laboratory and test them therefor their contents of radioactive material, Such a method has been followed in the past to distinguish radioactive ore from other rocks. Radioactivity of rocks, especially of the igneous type, was also deter-mined in the laboratory by numerous authors for absolute age investi-gations.6 Corresponding data from studies of sedimentary formations are scarce. Specimens taken from a core of the Bradford oil sandstone were tested by Landsberg and Ingham,7 with the results illustrated in Fig. 1, which shows that within relatively small vertical distances the differences of relative activity were considerable. If one assumes that the distribution of radioactive material is fairly uniform throughout a layer, measurements of radioactive radiation in various horizons would offer additional information for stratigraphic

Jan 1, 1939

By Walter H. Bucher

THIS symposium is designed to lay the basis for a general discussion of the place of geophysics in the training of geologists. As there is danger that in the ensuing debate individual interests may be given emphasis out of proportion to their place, we shall do well to view the whole field of geological inquiry in order to see the problem in true perspective. THE NATURE OF GEOLOGICAL INQUIRY "Basic" and "Complex" Sciences It is convenient to divide all science into two major divisions, the basic and the complex sciences. The basic sciences separate out from reality such entities as "substances" and "movements," describe their behavior in terms of arbitrary units of measurement and derive from them by progressive abstractions concepts and patterns of behavior that exist between them, so-called general "laws" and "properties" of nature. The complex sciences, on the other hand, deal, with little or no abstraction, with those objects of reality that are accessible to man in the atmosphere, the hydrosphere, the lithosphere and the biosphere.† Their work comprises two types of inquiry. One is concerned with abstractions to the extent of dealing with types rather than individuals-that is, with such things as plants, animals, protoplasm; clouds, streams, glaciers; volcanoes and mountain ranges. It comprises the search for general properties and patterns of behavior or "laws" that characterize the objects and their reactions to each other. These properties and laws apply always, everywhere. They are independent of the stream of time. We may call the results of this sort of inquiry timeless knowledge. The other type of inquiry is concerned with the objects themselves-that is, with this animal and that plant; this river system and that mountain chain; this glacier and that valley. Like all concrete objects in nature, they are subject to change with the passage of time, especially when it is measured in years, centuries, eons. The characteristics by which we recognize them -indeed, their very existence are dependent on their position at this point in the stream of time. This we may call time-bound knowledge. The so-called descriptive sciences are all bound to the past of which the objects of their study are the product and through which alone their present properties can be understood. They are historical sciences. This obvious fact is easily overlooked, which leads to serious misunderstanding, as we shall see later. Dynamic Geology With this broad picture in mind, let us now examine the nature of geological inquiry, defining, for the purposes of this discussion, geology as the science of rocks. Air is not a rock; water is. Meteorology and climatology are, correspondingly, gen-

Jan 1, 1941

By Frank Firmstone

Discussion of the paper of John B. Dilworth, presented at the Pittsburg meeting, March, 1910, and printed in Bulletin No. 35, November, 1909, pp. 1041 to 1043. FRANK FIRMSTONE, Easton, Pa. (communication to the Secretary*) :-Mr. Dilworth's formulas and tables are of course correct, and the extinction will occur as calculated, provided the money periodically set aside for sinking-fund be really invested. and the interest compounded as assumed in the calculation. Actually, in almost all cases, such funds are used "in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must be made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varying and continually increasing one until the date of extinction. On many accounts it seems more natural and convenient to make the extinction by a fixed periodical charge under the legal rule for partial payments, namely, that each payment should apply first to the interest due at the date of payment;: and any remainder, after this is satisfied, be deducted from the principal before the interest for the next period is calculated. The formula below is convenient for such calculations S, Principal to be extinguished. Q, Periodical payment or charge for sinking-fund. B, Balance unpaid at date of nth payment, but before that payment is made. r, Rate of interest per period per cent. n, Number of payments or periods. Then, B=S(1+r)n-Q(1+ r)n-(1+r) Received July 27, 1910.

Apr 1, 1911