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By J. J. Wilson

To explain in detail the manufacture of seamless pipe and tubes is something I venture to say that has never been done to a point entirely satisfactory. The manufacture of seamless tubes dates back to 1885, when Mannesmann Brothers invented the roll-piercing mill. Ten years later R. C. Stiefel invented the disc-piercer, which first came into general use in this country. At the present time the Mannesmann roll and the Stiefel disc-piercers are used, the Mannesmann rolls particularly for the larger size billets. Sizes produced at first were relatively small and the product was cold drawn to provide a smooth surface. The early uses of seamless material were chiefly for mechanical purposes, such as boiler tubes and bicycle tubing, and the latter for some years taking the heaviest tonnage. Improvements in the hot process were gradually made; the early Pilger type rolls were largely superseded by the two-high rolling mill for rolling out the tube after being pierced, the reeling machine for diagonal rolling, the sizing mill for giving exact outside diameter, and finally the sinking mill for reducing larger diameter tubes to smaller diameters.

Jan 1, 1932

The first mention of the occurrence of native copper near Lake Superior is found in a book by Lagarde, published in 1636. The letters of the Jesuit missionaries in the seventeenth century refer to the use of this copper by the Indians. Francesco Bressani, an Italian friar, says, in 1653: "There is a copper ore, which is very pure, and which has no need of passing through the fire; but it is in places far distant and hard to reach. We have seen it in the hands of the barbarians".* Father Jerome Lalemant, writing in 1659, says that the coast of Lake Superior is "enriched with copper of such excellence that pieces as large as one's fist are found, all refined.† These pieces of copper were hoarded by the Indians as mascots. The mention of the metal as having been already refined by nature recalls the fact that the old Greek historians spoke of gold-dust as being apuron, or not needing the fire. Father Claude Allouez,‡ writing in 1666, says: "One often finds at the bottom of the water [of Lake Superior] pieces of pure copper, of ten and twenty livres [pounds] weight. I have several times seen such pieces in the savages' hands; and since they are superstitious [as if the padres themselves were not!], they- keep them as so many divinities, or as presents which the gods dwelling beneath the water have given them, and on which their welfare is to depend. For this reason they preserve these pieces of copper, wrapped up, among their most precious possessions".

Jan 1, 1932

By H. P. Rue

The Bureau of Mines has recently collected two samples of crude oil from wells in the Greasewood Flat, area of northeastern Colorado. Sample 31310 was taken from the Continental Oi1 Co.'s well Briggs No. 1 which came in on September 27,7.931, with a maximum production of 940 barrels per day. Sample 31311 was taken from the Reiter-Foster Oil Co.'s well Ida Johnson No. 1 which came in on August 24, 1931 with a maximum production of approximately 1000 barrels per day. These two samples of crude oil are typical "intermediate base" crude oils according to the classification defined by Smith and Lane. The characteristics of these two samples, as shown by the Hempel analyses, indicate that they are almost identical. They have a very low sulphur content, and the residuum has a low carbon-residue content which would indicate that they are excellent crude oils for refining. Crude oils yielding a residuum which has a carbon-residue content of 4 per cent or less usually make good material for the manufacture of cylinder stocks. The pour points of the samples and the cloud test of the fractions obtained from the vacuum distillation indicate that the Greasewood Flat oil contains considerable wax. The high wax content would cause some difficulty in transmitting this oil through a pipe fine during extreme cold weather.

Jan 1, 1932

By Wilhelm Rohn

IN discussing the influence of a content of gases on metals and alloys we should probably first consider the physical and chemical conditions under which these gases may be present. By a chemical analysis, such as the total extraction of gases from the liquid metal by melting in a graphite crucible in vacuo, we find only the sum of gaseous chemical elements contained in the metal in any form and no reference is made to the special form under which they have been present previously. CONDITION OF GASES IN METALS In considering. gases in metals we may first turn our attention to gases simply dissolved. Because the solubility of almost, any gas decreases suddenly at the freezing point, most of them are released during solidification, developing rise of ingots and blowholes. If only a little gas is dissolved in the molten metal the size of such blowholes may be miscroscopical, or even submicroscopical, resulting in, a certain reduction of the notched-bar impact test values. Hydrogen is believed to become less soluble as the temperature is lowered and therefore increasing quantities of this gas may be evolved during cooling between the freezing point and room temperature, leading to unsoundness of the ingot at weak spots; i.e., at the grain boundaries. This gas at the grain boundaries probably is present at high pressure and therefore impairs the mechanical properties to a degree similar to that found in the hydrogen embrittlement of copper. Usually we may trace such gases by observing rising ingots, or at least by the formation of a characteristic pattern of small grooves upon etching. Another condition of gases present within metals is that of chemical compounds, the most common being oxides and mostly present as slag inclusions of various kinds. If such oxides are insoluble in the liquid metal and emulsify with it, we find microscopical or submicroscopical slag inclusions distributed homogeneously throughout the metal and spread through the whole mass of the crystals. This special form does little harm to the mechanical properties. Some oxides are somewhat soluble

Jan 1, 1932

By H. J. Struth

Economic law was accorded considerably more recognition by the oil industry last year than perhaps ever before. While proration was undoubtedly given added impetus in 1931, and the list of proponents of unit operation was noticeably lengthened, predominant evidence plainly shows that the functioning of economic laws dominated collective efforts to reduce the excessive above-ground supply of petroleum. Crude oil production was reduced more than 48,000,000 bbl. last year; imports from other parts of the world were substantially lower; stocks of crude were drawn upon to the extent of nearly 48,000,000 bbl.; domestic gasoline demand increased 2 per cent—and yet, prices of petroleum and its products were at the lowest levels in many years. To say that the ills of the oil industry during 1931 were due to the general depression that was felt in all other lines is tantamount to attaching an air of uncertainty to a group of commodities that have been proved to be an ever increasing necessity, even in times of depression. TO say that the potential productivity of proven oil-producing areas has been responsible for the unsatisfactory state of affairs last year, and now, is to admit failure to carry out the principles designed to control production in accordance with the limits prescribed by demand. In fact, there is no reason why a large proven potential supply of oil should not be considered a valuable asset to the industry; an assurance against future needs; a stabilizing influence in building up confidence in the ability of the industry to supply this and future generations with fuel and lubricant requirements at reasonable prices. At any rate, an assured future supply of oil should be interpreted to the public to mean that the oil industry is a legitimate, progressive industry, and not a group of prospectors madly searching for "liquid gold." There has been a great deal of romance connected with the history of the oil business—so much that the public has come to associate the word "oil" with untold riches. However, the financial statements of 1931 will furnish conclusive proof to the contrary. Too much oil, too many refineries, too many filling stations, too much capital invested; these and other "too muches" and "too manys" have perhaps been given more publicity than necessary. We seldom hear these

Jan 1, 1932

Jan 1, 1932

By C Gunther

Mining examinations are of several kinds and the scope of the investigation depends in each case upon the purpose for which the examination is made. A formal examination of a developed mine is an expensive undertaking; from one to several months are allowed for the work according to the size of the property; many samples are taken; investigation is made of the geological features, including, perhaps, a topographical and geological survey of the surface; the metallurgical treatment of the ore is studied; finally, a determination of costs is demanded. Formal examinations are made for prospective purchasers or as a basis for the consolidation of several properties, and occasionally, in the owner's behalf, to verify the work of resident engineers, or to determine the readiness of a mine for equipment and the kind and capacity of equipment it shall receive. A formal examination of a mine should not be undertaken until a preliminary examination has shown that it is justified. It is regrettable that some engineers are in the habit of prosecuting long and exhaustive examinations of properties whose lack of merit should be, and perhaps is, apparent from the start, or of continuing their investigation long after an unfavorable result is seen to be inevitable. This wasting of a client's money is a species of trickery difficult to prove, and therefore the more contemptible. Preliminary examinations are precisely what the term implies, and are undertaken to determine the advisability of making

Jan 1, 1932

By Sherwin F. Kelly, Bela Low, William B. Creagmile

Electrical methods and instruments for geophysical exploration have been almost exclusively applied, during these years of development of the art, by a few companies specializing in this field. The control of patents, the cost of the instruments and the general lack of published information on details of field procedure and office interpretation have given these owners a monopoly in carrying out electrical surveys. The development of the Megger Ground Tester1 seems likely to change this situation, and to enable mining engineers and geologists, without special training in geophysics, to carry out simple reconnaissance electrical surveys. Nevertheless, the need for such special training and experience in planning surveys and interpreting their results remains, and probably i always will remain, indispensable for a successful outcome. The unique thing about, the Megger Ground Tester, which gives rise to this hope for its general use, is its simplicity of operation. The four binding posts of the instrument are connected by insulated wires to four stakes driven into the ground at appropriate points. The crank of the Megger is then turned, and the resistance of the ground between the two inside stakes is read directly, in ohms, by the deflection of a pointer over a scale. The apparatus is shown in Fig. 1. Fundamentally, the principle of operation is that of determining the resistance of a four-terminal conductor, as applied by Frank Wenner to the measurement of earth resistivity. "A four-terminal conductor is a conductor provided with two terminals to which current leads may be connected and two terminals to which potential leads may be connected. The resistance of such a conductor is the difference in potential between the potential terminals divided by the current entering and leaving

Jan 1, 1932

By Ogden Malin

IN conducting the manufacture of extruded brass rods and brass forgings it has been noticed that there is considerable variation in the physical properties, particularly the machinability of different rods and forgings, even though the composition, working temperatures and method of manufacture remain the same. It is the purpose of this paper to attempt to establish the cause and extent of this variation, and also to determine whether variations in composition within certain defined limits influence hardness and machinability to any marked degree. The writer believes that this variation probably is due to the variation in grain size of the metal, therefore the microstructure of several compositions under various conditions of working were examined in an effort to establish this as a fact.

Jan 1, 1932

By William Fink

THE constitution of the aluminum-cobalt alloys has been the subject of relatively few investigations. Brunck1 analyzed the residue which remained after treating the 17 per cent cobalt alloy with dilute hydrochloric acid. The results of the analyses indicated the existence of a compound Co3Al13. Guillet2 published a liquidus for the aluminum-cobalt system which contained two maxima corresponding to CoAl6 and CoAl2 and two eutectic points at 30 and 74 per cent Co. The most extensive investigation of the system was carried out by Gwyer,3 whose results are summarized in Fig. 1. It will be noted that at the aluminum end there is a suppressed eutectic at 644° C. By extrapolation of the duration of the eutectic arrest to zero, the composition of the compound was placed at Co3Al13. Another thermal arrest was noted at 550° C., which Gwyer attributed to a peritectic reaction. The present investigation of the aluminum end of the aluminum-cobalt system is the eleventh of a series dealing with the constitution of aluminum; rich alloys prepared from electrolytically refined aluminum.4 Preparation of Alloys.-The alloys used in this work were all prepared from electrolytically refined aluminum, the analysis of which is shown in Table 1. In preparing some of the alloys, metallic cobalt (98 to 99 per cent) was used either directly or in the form of an intermediate alloy, the composition of which is given in Table 1. In order to obtain alloys of higher purity, cobalt was introduced into some of the alloys by means of chemically pure cobaltous chloride which was readily reduced by the aluminum. A small electric furnace with nickel-chromium heating elements was used in the preparation of the alloys.

Jan 1, 1932

By William L. Fink, H. R. Freche

The constitution of the aluminum-cobalt alloys has been the subject of relatively few investigations. Brunckl analyzed the residue which remained after treating the 17 per cent cobalt alloy with dilute hydrochloric acid. The results of the analyses indicated the existence of a compound Co3Al13. Guillet2 published a liquidus for the aluminum-cobalt system which contained two maxima corresponding to CoA16 and CoAl2 and two eutectic points at 30 and 74 per cent Co. The most extensive investigation of the system was carried out by Gwyer13 whose results are summarized in Fig. 1. It will be noted that at the aluminum end there is a suppressed eutectic at 644' C. By extrapolation of the duration of the eutectic arrest to zero, the composition of the compound was placed at Co3Al13. Another thermal arrest was noted at 550" C., which Gwyer attributed to a peritectic reaction. The present investigation of the aluminum end of the aluminum-cobalt system is the eleventh of a series dealing with the constitution of aluminum-rich alloys prepared from electrolytically refined a1uminum.l Preparation of Alloys.—The alloys used in this work were all prepared from electrolytically refined aluminum, the analysis of which is shown in Table 1. In preparing some of the alloys, metallic cobalt (98 to 99 per cent) was used either directly or in the form of an intermediate alloy, the composition of which is given in Table 1. In order to obtain alloys of higher purity, cobalt was introduced into some of the alloys by means of chemically pure cobaltous chloride which was readily reduced by the aluminum. A small electric furnace with nickel-chromium heating elements was used in the preparation of the alloys. Chemical Analysis.—An analysis sample from each melt was chill-cast in the form of a plate 3/16 in. thick. In all cases the casting temperature was well above the liquidus. Cobalt was determined electrolytically in all alloys containing more than 0.05 per cent cobalt and by the nitroso-

Jan 1, 1932

By William M. Barret

In order properly to evaluate the data related to geomagnetic surveys, it is highly desirable to have all the available information concerning the magnetic properties of the involved media. This is true of surface as well as subsurface formations and becomes of increasing importance as advancement in instrumental and interpretative technique permits the analysis of relatively slight magnetic reflections of buried masses. Since the magnitude and areal distribution of the usually complex resultant magnetic field at the surface of the earth is a function of the susceptibility1 of the involved matter, it necessarily follows that susceptibility determinations will afford valuable data for geophysical correlation. The present method was developed to meet the need for routine analysis of specimens in the geomagnetic laboratory where it was felt that general utility, ruggedness, ease of manipulation and reproducibility of results were of greater importance than extreme sensitivity. Electric Circuits The electric circuits are illustrated diagrammatically in Fig. 1. Current from the battery, B, passes through the variable resistance R1, reversing switch S1, double-break key K1 to switches S2 and S3. From S2 it flows through variable resistance R2, ammeter A2, to the primary coils of the fixed mutual inductance Mf and variable mutual inductance M,. . From S3 it passes through variable resistance R3, ammeter As, to the primary winding of the fixed mutual inductance MI, which is designed to receive the test sample. The ballistic galvanometer2 or fluxmeter3 G is connected in the circuit containing the double-break key

Jan 1, 1932

Upper Peninsula W. O. HOTCHKISS, Chairman C. H. BAXTER, Secretary-Treasurer, Michigan College of Mining and Technology, Houghton, Mich. S. R. ELLIOTT RUDOLPH ERICSON W. H. SCHACHT Utah Meets second Thursday of each month, October to May, inclusive B. L. SACKETT, Chairman C. T. VAN WINKLE, Vice-chairman G. L. OLDRIGHT, Secretary-Treasurer, U. S. Bureau of Mines, Salt Lake City, Utah A. E. RING L. A. WALKER

Jan 1, 1932

By George M. Fowler, Joseph P. Lyden

PaGE Scope of this Report.................................................... 206 Production of Tri-State District.......................................... 207 Historical Sketch....................................................... 207 Location and Topography............................................... 211 Geology............................................................... 212 The Tri-State District.............................................. 214 Stratigraphy........................................................... 217 General Geological Section in Tri-State Region....................... 217 Stratigraphic Section of Mineralized part of Boone Formation........... 218 Stratigraphic Section Bird Dog Well.................................. 219 Metamorphism........................................................ 220 Structure............................................................. 225 Regional.......................................................... 225 Due to Metamorphism.............................................. 229 Ore Deposits.......................................................... 231 Types............................................................ 232 Hard-ground Deposits.......................................... 232 Brecciated................................................. 232 Stratified............................................ 232 Sheet Ground............................................. 232 In Dolomite............................................... 233 In Shale.................................................. 233 Soft-ground Deposits.......................................... 233 In the District as a Whole....................................... 233 Ore Minerah and Analysis......................................... 233 Paragenesis....................................................... 234 Conclusions........................................................... 236 Structure.......................................................... 236 Genesis of the Ore.................................................. 237 Future of the District............................................... 239 Acknowledgments..................................................... 239 Discussion............................................................ 239 Scope of This Report The Tri-State district. as outlined in this paper. refers to the entire mineralized area in sout'hwestern Missouri. southeastern Kansas and

Jan 1, 1932

By W. E. Rice

The ceramic industry has to do with forming or molding articles of clay, and imparting to them their characteristic properties of permanence, strength and color by subjecting them to heat treatment in kilns. This heat treatment is commonly known as "firing" or "burning." The art of firing clay ware antedates the industrial use of coal; hence wood was the fuel first used, and the earliest kilns were built to burn wood. The majority of the clay ware produced today is fired in periodic kilns that are essentially enlarged structures similar to the earliest enclosed kilns; a kiln consists of a large chamber 16 to 32 ft. dia. (or rectangular) in which the ware is charged and fired either in direct contact with flame or hot gases from the fuel, or in saggers which shield the ware from direct contact with the gases. The fuel is burned in a number of small furnaces built in the thick wall that encloses the chamber; these furnaces are from 16 to 36 in. wide and from 3 to 5 ft. long; some of them have horizontal or sloping grates, but many have no grates; the last are called "dead-bottom" furnaces. The temperature necessary to mature the charge in the kiln varies for different clays; for some it is as low as 1800°, and for others as high as 2700" F. Wood was an ideal fuel for the low temperatures that were used in early kilns; it burns freely and produces a long, clean flame, which promotes uniform distribution of the heat in the kiln; it does not coke and so restrict the passage of air through the fuel bed; the ash does not melt in the fuel bed to form clinker; and the ash that is carried into the chamber and deposited on the charge does not contain iron and sulfur to discolor the clay. The extent of the ceramic industry now precludes the general use of wood in kilns, so that today this industry is one of the large users of bituminous coal, burning more than eight million tons annually in kilns. Manufacturing plants usually are at or near the source of clay, with deposits of coal suitable for kilns occurring near the clay. The cost of coal is the largest single item of expense in the manufacture of clay ware, and, because all coals are not equally suitable for the process, the careful selection of coal is important. In this selection the desidera-

Jan 1, 1932

By J. B. Umpleby

The function of gas in the development and production of oil has far-reaching consequences that should be emphasized. The technical aspects of the subject have recently had a great deal of attention but less thought has been given to fundamental concepts underlying oil and gas law and the many customs and practices that have grown up in the industry. I shall review briefly the advance in knowledge of the subject and attempt to relate these concepts to legislative, judicial and operating problems. Early writers on oil and gas in Pennsylvania noted their close association in oil pools and their contemporaneous decline in output; also, that as gas pressure decreases so does production, that new offset wells reduce the output of existing wells, and even that tubing a well lengthens its flowing life. Expanding gas was deduced as the principal expulsive force. These fundamental observations had been made at least as early as 1880.1 They were treated, however, as academic considerations and did not greatly influence law or practice for many years except to instill into all operators an urgent desire to hasten offset drilling in order to obtain as much of the flush as possible. The most noteworthy later advance in knowledge came in 1926 when Beecher and Parkhurst published their paper on Effects of Dissolved Gas upon the Viscosity and Surface Tension of OiL.² This paper added to the old idea of an expelling force the concept of a modifying agent that actually changes the physical characteristics of the oil and facilitates its movement through the pore spaces of the reservoir rock. Largely since the publication of this paper, intensive study and concerted effort have been given to means of using to a maximum, in producing oil, these combined properties of gas. This is shown clearly by the number of papers dealing with the subject, and the new and revived terms now widely used to express thought, such as the expressions gas energy, reservoir pressure, reservoir energy, gas-oil ratio, bottom-hole pressure, beaning, tapered tubing and back-pressure. These terms, some of which are

Jan 1, 1932

By Karl Sundberg

ELECTRICAL investigations carried out in regions containing sedimen-tary rocks showed that sediments generally are good electrical conductors, a fact which at the present time is used for structural investigations by electrical methods. It is of fundamental importance, not only for these investigations but also for electrical prospecting in general, to know the electrical properties of various soils and rocks. It will be useful, there-fore, to discuss this question with the hope that the general points of view discussed in this paper will perhaps be, completed by further observations and determinations of material from various localities. This paper is based principally on the study of literature, and the purpose is primarily a discussion of the main factors that determine the electrical conductivity of soils and rocks. It will follow, however, that the factors discussed here also frequently decide how far a certain orebody can be regarded as a good electrical conductor compared with the sur-rounding rocks. All-rocks are more or less porous; and the pores are filled with liquids and gases. Their electrical conductivity, therefore, depends on the following factors: 1. The electrical conductivity of minerals composing the rock. 2. Electrical conductivity of the liquid filling the pores. 3. Proportion of the volume of liquid filling pores of the rocks to the solid rock material. 4. Shape of the pores. 5. Arrangement of the particles of gas and liquids. 6. Temperature. Dry minerals, with the exception of certain ore minerals, are complete nonconductors from the point of view of applied geophysics; in the present investigation we deal with rocks which have no conducting minerals, and factor 1, therefore, is not important. The same is true of soils. The liquids contained in soils and rocks in most cases are waters, some-times oil. As oil is a nonconductor of electricity, the impregnating waters will determine the electrical conductivity of soils and rocks.

Jan 1, 1932

By George M. Fowler

THE Tri-State district, as outlined in this paper, refers to the entire mineralized area in southwestern Missouri, southeastern Kansas and northeastern Oklahoma (Fig. 1). The part of the district in Missouri and near Galena, Kans., is still sometimes referred to as the Joplin district (Fig. 2). The Picher-Miami area is that part of the Tri-State district located contiguously in Kansas and Oklahoma in the vicinity of Baxter Springs, Picher and Miami. This paper is confined almost wholly to the ore deposits of the Tri-State district and particularly to the Picher-Miami area. Our study of the ore deposits of this district dates from late in 1925 (by Fowler) and early in 1927 (by Lyden) to the present. Our work has been confined almost entirely to the search for ore for numerous companies and individuals. It was not possible for us to undertake numerous highly interesting investigations which presented themselves but which would not immediately help in finding ore. We particularly refer to the general structural geology of the Ozark uplift, the genesis of the ore, and other problems of a similar nature. The local and general structural problems of the district are being solved gradually as the work progresses. The factors that control the loci of the several orebodies are evident. This paper is based almost exclusively upon our own observations. Most of the important mines in the Picher-Miami area were studied in detail. A map (Fig. 5) is included which shows this area and the properties we have examined to date. When it was convenient we visited, studied and compared structural relations in numerous mines in states outside the district. Some of these observations are noted in this paper.

Jan 1, 1932

By G. F. Tagg

EARTH-REISTIVITY measurements are often of service in obtaining information regarding geological formations, particularly when applied to structural problems. In such problems the masses of the various bodies are large, and have a corresponding effect on the average resistivity of the soil. Much work has been done using such measurements, but in general the method of interpretation employed is empirical. Since certain simple cases can be investigated mathematically, it appears to be quite sound to endeavor to apply the mathematical solutions to the practical results, in order to deduce from the latter such unknown quantities as depth. This paper deals with such a method of interpretation for the simple case of a single horizontal stratum. SURFACE Of EARTH In the method described by FIG. 1.-WENNER'S METHOD OT MEASURING Wenner1 for measuring earth resis- EARTH RESISTIVITY. tivity, four stake electrodes are driven into the earth in a straight line as shown in Fig. 1. A current I amperes is passed between the two outer stakes and the potential difference . V volts between the two inner stakes is measured. Then if a is the electrode separation, the specific resistance of the soil, which is assumed to be homogeneous, is given by the formula

Jan 1, 1932

By Richard S. McCaffery

A Research on iron blast-furnace slags has been in progress since 1922 in the metallurgical department of the University of Wisconsin, supplemented by observations, tests and critical examination of operating records at 10 furnaces. From the data thus collected information has been put into forms suitable for use by furnace operators and is given in this report and the three accompanying papers.' In the viscosity results reported, it is estimated that temperatures were measured within 5" C. and that the viscosity determination of the particular slag investigated is accurate within ± 4 per cent. In the viscosity diagrams in the various papers, the equal viscosity lines were drawn in such a manner that in all cases they are located correctly with respect to the actual experimental results, but when determining a viscosity for a particular composition from the diagrams, the viscosity may. be slightly less accurate than the experimentally determined viscosity for the same slag, for the reason that the iso-vis lines interpolated between the experimental results may be shifted slightly without violation of the experimental data. The viscosity diagrams represent our judgment of their position under the above conditions, and we believe the relative accuracy of viscosity data taken from the diagrams is more than sufficient for any use to which the data may be put. Hundreds of samples of slags synthetically produced in the laboratory and of actual furnace slags have been studied in various ways. The ranges of compositions of slags used for viscosity measurements are: silica 25 to 55 per cent.; alumina 0 to 35 per cent.; lime 25 to 55 per cent.; magnesia 0 to 20 per cent. These measurements were made at temperatures of 1250°, 1300°, 1350°, 1400°, 1450°, 1500°, 1550°, 1600" and 1650" Centigrade. Descriptions of apparatus, methods used and statements of the problems investigated have been published in the papers listed in the bibliography beginning on page 120.

Jan 1, 1932