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By Richard P. Rothwell

Fires in mines are so serious in their consequences and of such frequent occurrence, that their causes and the means of extinguishing them are certainly questions of the greatest interest to a large part of the engineering profession. We have already, in this country, many mines which have been burning for years, and though our hard anthracite is so difficult to ignite that for a quarter of a century after it was first discovered it mas not known how to burn it except with the aid of an artificial blast, yet most of the fires which have occurred underground have been in anthracite mines, and in the coal itself. The injury which these fires have caused to properties in various parts of the anthracite regions, and the cost of extinguishing them, would amount to many millions of dollars, and they have also occasioned the loss of many valuable lives. It is not surprising, therefore, that the subject has already attracted much attention, and the exercise of great ingenuity; and the present communication is made less with the expectation of announcing anything new, than with the object of putting upon record the present state of our knowledge on this subject, or, in other words, of indicating how defective are the present means of combating underground conflagrations. Causes of Mine Fires.—Even upon the surface, fire is a terrible foe to contend with, and there is probably no other which inspires such thorough and well-founded alarm. With what feelings, then, must we look upon this destructive element, when its field is in the narrow galleries of a mine, where the poisonous products of combustion, spreading in every direction, protect, in the most effectual manner, the fire itself from the attacks of extinguishers, while, if the face of attack be ventilated so as to enable then] to approach the seat of the fire, the air current simply increases the extent and violence of the conflagration. Fires underground originate in as various ways as those on the surface, and it is scarcely necessary to say that, except in the rare cases where they are the result of design, they are invariably classed as " accidents," and most generally as " unavoidable accidents." In reality, by an intelligent understanding of their causes and with due precautions, they can almost always be prevented. Ignorance and

By S. J. Rothman, A. L. Harkness, L. T. Lloyd

Self-diffusion in Y uranium has been measured using U235 as the tracer isotope. The diffusion coefficient fits an Arrhenius-type equation D = 2.33 x 10 -3 exp (- 28,5000/RT) cm2/sec The values of Do and Q are unusually low and are not consistent with the values expected from theories based on a simple vacancy mechanism of diffusion. CYLINDRICAL samples, 1 cm in diam and 1/2 to 1 cm long, were prepared from high-purity uranium containing 0.0343 pct u235, Table I. The samples were water quenched from 690°C (the a-ß transformation is at 668°C) to remove preferred orientation, and annealed at 450 "C to minimize residual stresses. One end of each cylinder was polished on a 1-µ diamond lap and electropolished in a phosphoric acid solution. After a final cleaning by cathodic sputtering, a 1- to 3-µ thick layer of the tracer isotope, uranium containing 93 pct u235, was sputtered onto the sample.' To prevent contamination during the diffusion anneal, the diffusion couples were placed in a tantalum cup and covered with another piece of uranium, and the whole assembly was sealed off in an evacuated quartz tube. Annealing temperatures were constant within +2.0°C. The samples were heated and cooled slowly between room temperature and the ß-? transformation (774°C) in order to minimize distortion of the sample surface that might arise from aniso-tropic thermal expansion and density changes during phase transformations. After machining off 1/16 in. from the radius to

Jan 1, 1961

By Everett D. Jackson

The largest deposits of chromite in the United States occur in tabular layers in the lower part of the Stillwater Complex, Montana. Nearly 900,000 long tons of chromite concentrates have been produced from mines and mills in this area, and reserves equivalent to more than 2,500,000 long tons of Cr2O3 remain in the ground. Layered concentrations of chromite (known as chromitite zones) occur only within olivine-rich layers of the Peridotite member of the Ultramafic zone of the Stillwater. As many as thirteen chromitite zones, lying conformably one above another, have been found, but only five of them are thick enough to be of any conceivable economic interest, and only two of them have been mined to date. Individual chromitite zones can be recognized by their distinctive internal character and by their stratigraphic position in the Peridotite member. The chemical composition of chromite varies consistently between and within the different chromitite zones. The zones range in thickness from about an inch to more than 12 feet, and the Cr2O3, content of their chromite ranges from 36.6 to 49.2 weight per cent. In any given area, the G chromitite zone is the thickest, but the chromite of the H chromitite zone has the highest grade. Laterally, the thickness of the chromitite zones is related to the thickness of the Peridotite member; in general all are thicker in the eastern part of the Stillwater than in the western part.

Jan 1, 1968

By Louis W. Huber

The Liberty tunnels extend through a very steep hill in Pittsburgh (locally called Mount Washington) for a distance of slightly over a mile. The two tunnels parallel each other and are 59 ft. apart, center to center (Fig. 1) They are for vehicular traffic, and in each there is ample space for two lines of vehicles. Northbound traffic, toward downtown Pitts- burgh, is confined to the east tunnel and southbound traffic to the west tunnel. The South Hills residential district is separated from downtown Pittsburgh by Mount Washington, a steeply rising escarpment south of and adjacent to the Monongahela River. The Mount Washington district immediately south of the Monongahela River has been reached, for many

Jan 1, 1927

By David Russell, Courtland Lee

FOREWOHD-Americans have been able to create wealth from the nation's natural resources to an extent unprecedented in recorded history, thanks largely to the existence of a free market and of a rational body of laws. The General Mining Law of 1872, for instance, by establishing the rules of the game, was quite effective in channeling the ability of Americans to discover and develop mineral deposits. Another example was the Mineral Leasing Act of 1920 which made available the more easily discovered mineral deposits by spelling out the conditions and rules under which miners could obtain leases on federal lands.

Jan 5, 1977

By Donald H. McLaughlin

THE activity and enthusiasm of pioneers still prevail among workers in applied geophysics1.- Within the year, new devices have .been tried out, instruments and technique have been improved and the methods of application to commercial problems have been increased in many ingenious ways. There is still great need for more skillful interpretation of results in terms of geology, but oil the whole geophysical prospecting is making encouraging progress toward finding its proper place and function in engineering and geological practice. Spectacular successes continue to be reported, particularly .from the Gulf Coast, where the race for salt domes has not slackened, and encouraging results have been giined elsewhere in the mapping of structures in the search for oil. In the mining field, however, it can hardly be claimed that the same measure of success has been obtained, for brilliant efforts worthy of wide recognition have been overshadowed to some eatent by the unfortunate outcome of surveys undertaken unwisely without recognition of the limitations of the work. Consequently, hopes were aroused that could not be fulfilled, and it must be admitted in an impartial survey that there are a few regions, chiefly in the far north, where the standing of geophysical prospecting is somewhat doubtful and where the course of public opinion regarding it shows a certain similarity to the history of the market during the past few months. Reliable work, however, is steadily going 011 and it can confidently be expected that the methods will eventually be regarded in many regions as an essential part of the technique of securing geologic data needed for intelligent exploration.

Jan 1, 1930

By H. K. Najarian

AT Josephtown, Pa., on the south hank of the Ohio River about thirty miles northwest of Pittsburgh, is the Josephtown electrothermic zinc smelter, which operates as a custom smelter receiving both domestic and foreign concentrates. Constructed in 1930, the plant was designed to produce zinc oxide and to process 124 tons per day of zinc concentrate obtained mainly from the Company's New York State mines. Zinc condensing equipment was developed in conjunction with the St. Joe electrothermic. furnace and commercial production of zinc metal started in 1936. Expansion of the plant and equipment during 1939 and 1940 brought the processing. capacity to upwards of 300 tons of concentrate per day; and the plant operated at peak capacity during the war years, earning the Army-Navy "E" award and three subsequent stars. A postwar plant expansion is now under way, designed to increase the capacity to 500 tons per day of concentrate, with an estimated daily production of 160 tons of zinc metal of various grades, about 100 tons of zinc oxide, and 425 tons of sulphuric acid as major products.

Jan 1, 1947

By Robert Mehl

THE purpose of this investigation was to prepare high-purity iron-carbon alloys, to determine as precisely as possible the A3(GOS), the Acm(SE), and the A1(PSK) transformation temperatures in the meta-stable iron-iron carbide system (up to 1.4 per cent C), and to study the influence of carefully controlled and constant rates of heating and cooling (1/8 to 2° C. per minute) upon the transformation temperature and upon the resulting microstructure. Apart from the general metallurgical importance attending the completion of such a task, it will be noted that highly precise transformation temperatures are of interest and importance in the thermodynamic study of this system1. Several determinations of the iron-iron carbide diagram have been made. These suffer generally from the low purity of the alloys used, and from the application of methods of investigation of low sensitivity. Attempts to compare and weight the many data available in an effort to construct as accurate a diagram as possible have, in the main, been unsuccessful. In general, the wide differences in the results of different workers, the lack of complete analytical data, the omission of important details relating to the heat-treatment of the alloys, and the meager description of the methods of investigation applied, render such a process of averaging nearly meaningless. It may be seen from the summaries by Epstein2 and Körber and Oelsen1 that variations as great as 30° C. exist in the reported data on the A3 temperatures in iron-carbon alloys. For-tunately, the A3 temperature in pure iron is now known to be 910° C. ± 1° C.3 The best recent work on iron-carbon alloys is that of Esser4 on hypoeutectoid steels and that of Sato' on both hypoeutectoid and hyper-eutectoid steels.

Jan 1, 1937

By Theron Wasson

Michigan's production of 17,301,000 bbl. in 1945, which is in line with previous years, has been maintained by extensions to old fields like Deep River, Adams, Fork, and others. There were a number of new discoveries but, as in the past, these are not given very much importance because enough drilling has not been done to develop their potentialities; however, judging by the past, some of them will develop enough production so that 1946 -will probably be in line with other years. Activities in Michigan were confined to the Basin area of the lower Peninsula, which has been under development since 1925.

Jan 1, 1946

By L. Graydon Carpenter, Donald E. Garrett

Probably the largest single tungsten deposit in the U. S. is one that has yet to produce any tungsten; it is not even listed in tables showing U. S. reserves. This deposit is at Searles Lake, Calif., where the brine contains about 70 ppm WO3. Small though the concentration is, the amount of brine in the lake is so great that it is estimated at 170 million lb of WO3 (8.5 million units), equaling the total of all other known reserves in the U. S. This dry lake is located in the basin formed by the Argus and Slate ranges in the northeastern corner of the Mojave Desert (Fig. 1). It consists of a massive salt body some 35 sq miles in extent, varying in thickness from 0 to 120 ft and containing more than 3 billion tons of salt. A central section of about L. G. CARPENTER and D. E. GARRETT are with the Research Dept., American Potash & Chemical Corp., Trona, Calif. TP 47881. Manuscript, Nov. 4, 1958. AlME Trans., Vol. 214, 1959. 8 sq miles is exposed salt; the remaining area is overlain by mud. Except for the exposed sodium chloride (10 to 15 ft thick) the body consists of a very complex and heterogenous mixture of soluble crystals, containing at least eight major phases. It is only about 53 pct solid, the voids being occupied by a dense brine which is the raw material for two chemical companies operating in the valley.

Jan 3, 1959

THOSE NOT MARKED ARE MEMBERS; MARKED THUS t ARE ASSOCIATES. HEAVY-FACED TYPE SIGNIFIES HONORARY MEMBERSHIP. JUNIOR MEMBERS ARE MARKED II. THE FIGURES AT THE END OF THE ADDRESS INDICATE THE YEAR OF ELECTION. AARONS, J. BOYD, Genl. Mgr., Chaffers G. M. Co., Boulder City, West. Australia. '05 ABADIE, EMILE R., Min. Engr Box 291, Porterville, Tulare Co., Cal. '76 ABBOTT, CLARENCE E., Genl. Supt., Iron Mines Div., 1405 Minnesota Ave., Bessemer, Ala. '04 ABBOTT, J. W., Min. Engr., "St. Omer," 123 N. Grand Ave., Los Angeles, Cal. '94 ABBOTT, Louis BENJAMIN, Chief Engr., Consolidation Coal Co., Elkhorn Div., Jenkins, Ky. '15 ABBOTT, ROBERT R., Met. Engr., Peerless Motor Car Co., Cleveland, Ohio. '12 ABE, ASAKA Yamagano G. M., Satsuma-Gori, Satsuma, Japan. '14 || ABRAHAMS, A. I., Student 1391 Madison Ave., New York, N. Y. '14 tACKER, E. O'C., Met Bethlehem Steel Co., Bethlehem, Pa. '86 ACKER, Louis K., JR., Min. Engr 565 Highland Place, Bellevue, Pa. '08

Jan 1, 1917

By K. J. McGrew, J. W. Murphy

Introduction Maximization of profit consistent with environmental protection is the principal goal of new applications development for any conventional or in situ mining technique. Efficient evaluation of all the parameters that contribute to mining costs and production hinges on proper design and evaluation of testing programs and data. The program discussed uses several field and laboratory procedures to estimate ore deposit characteristics and optimize lixiviant compositions. Ore characteristics and lixiviant compositions are then used in a long path leaching test (stream tube test). Stream tube test data are analyzed by mathematical models with computer assistance to predict such wellfield rate parameters as target metal production, lixiviant consumption, and restoration. When these predicted rates are combined with market values for target metals, capital expenditures, prices of lixiviant chemicals, and other economic variables (labor costs, power rates, and licensing fees), an assessment of the relative feasibility of various proposed mining plans is possible. The flowsheet in Fig. 1 illustrates this process. [ ] Field and Laboratory Procedures In general terms, the procedures followed in the evaluation of an in situ leaching application aim at accomplishing: •rapid leaching and maximum recovery of the target metal in a marketable form, •low consumption of lixiviant chemicals, •unquestionably satisfactory restoration of the mined aquifer, and •minimization of capital and operating costs for the above through development of an optimum mine plan. Keeping these goals in mind, the following minimum test program is generally recommended. Geology •Estimate of ore reserves and their variability. •Average disequilibrium value for uranium deposits. •Ore thickness, depth to ore, water level, degree of confinement, and consolidation. •Characterization of quality and quantity of other ore deposit constituents (e.g. sulfide minerals, ion exchange parameters). Hydrology •Single well pump and injectivity test. •Downhole vertical permeability test to compare flow rates of barren and mineralized formations. •Groundwater quality as it may affect licensing, hydro metallurgy, and restoration. Hydrometallurgy • Flask or autoclave tests for optimization of lixiviant parameters and determination of specific reaction rate constants. • Flask or autoclave tests for assessing amenability of lixiviant solutions with ore, consumption of lixiviant, stability of metal in solution contacting ore, and environmentally important species mobilized. • A long-path leach test for modeling the behavior of the lixiviant solution flowing through a long mineralized streamline (stream tube testing). •Metal recovery tests from lixiviant solutions (ion exchange, electrowinning, etc.). •Lixiviant regeneration tests. •Environmental restoration tests.

Jan 1, 1985

The Library of the above-named Societies is open from 9 A.M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The tine spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 10, 1917

By J. P. Doan, G. Ansel

The important literature concerning zirconium in magnesium-base alloys is predominantly contained in patent references. Sauerwald, Eisenreich, and Holubl-4 discovered the profound grain-refining influence of small amounts of zirconium on cast magnesium and the attendant increases in strength and ductility. They extended their work to reveal that limited amounts of certain other elements, including zinc, could be added for further improvement in strength and hardness. British Patent 5111375 relates to the parent discoveries of Sauerwald, Eisenreich, and Holub. All of these references deal primarily with casting characteristics and properties in the cast state. Minor mention is made of desirable tensile strength, ductility, and toughness of wrought Mg-Zr alloys* modified by one or more additional elements. No extensive reference in the literature5. has been found to the particular characteristics of wrought blg-Zn-Zr alloys, with which the present paper is concerned. The work to be discussed represents essentially an extrusion study of the blg-Zn-Zr alloys and indicates that this system is highly interesting in the wrought state both academically and commercially. Accordingly, an important aim of this paper is to describe the hot-workability, tension and compression properties, metallography, and toughness of these alloys. Compositional variations are limited to the ranges 0 to 7 per cent Zn and 0 to I per cent Zr. Experimental Procedure Alloying and Casting Alloying ingredients were cell magnesium, commercial zinc (intermediate grade), and a chloride salt containing approximately 50 per cent ZrCl² and 50 per cent alkali chlorides. This salt is produced by Titanium Alloy Manufacturing Company. Melting, alloying, and pouring procedure essentially followed the crucible process as described by Nelson.6 The magnesium was melted using Dow No. 310 flux, and the temperature raised to 1350° to 1400°F for the alloying operations. After alloying of the zinc, the zirconium containing salt was added in small portions with vigorous stirring. This is an adaptation of the method described in British Patent 533264.7 The alloying efficiency of zirconium was approximately 30 per cent. During the alloying of zirconium, fluorspar was added in amount required as a flux-inspissating agent. Next the melt was refined with Dow No. 310 flux and held quietly for 15 min. Finally billets were cast in a book-type permanent mold

Jan 1, 1947

By G. Ansel, J. P. Doan

The important literature concerning zirconium in magnesium-base alloys is predominantly contained in patent references. Sauerwald, Eisenreich, and Holubl-4 discovered the profound grain-refining influence of small amounts of zirconium on cast magnesium and the attendant increases in strength and ductility. They extended their work to reveal that limited amounts of certain other elements, including zinc, could be added for further improvement in strength and hardness. British Patent 5111375 relates to the parent discoveries of Sauerwald, Eisenreich, and Holub. All of these references deal primarily with casting characteristics and properties in the cast state. Minor mention is made of desirable tensile strength, ductility, and toughness of wrought Mg-Zr alloys* modified by one or more additional elements. No extensive reference in the literature5. has been found to the particular characteristics of wrought blg-Zn-Zr alloys, with which the present paper is concerned. The work to be discussed represents essentially an extrusion study of the blg-Zn-Zr alloys and indicates that this system is highly interesting in the wrought state both academically and commercially. Accordingly, an important aim of this paper is to describe the hot-workability, tension and compression properties, metallography, and toughness of these alloys. Compositional variations are limited to the ranges 0 to 7 per cent Zn and 0 to I per cent Zr. Experimental Procedure Alloying and Casting Alloying ingredients were cell magnesium, commercial zinc (intermediate grade), and a chloride salt containing approximately 50 per cent ZrCl² and 50 per cent alkali chlorides. This salt is produced by Titanium Alloy Manufacturing Company. Melting, alloying, and pouring procedure essentially followed the crucible process as described by Nelson.6 The magnesium was melted using Dow No. 310 flux, and the temperature raised to 1350° to 1400°F for the alloying operations. After alloying of the zinc, the zirconium containing salt was added in small portions with vigorous stirring. This is an adaptation of the method described in British Patent 533264.7 The alloying efficiency of zirconium was approximately 30 per cent. During the alloying of zirconium, fluorspar was added in amount required as a flux-inspissating agent. Next the melt was refined with Dow No. 310 flux and held quietly for 15 min. Finally billets were cast in a book-type permanent mold

Jan 1, 1947

By AIME AIME

A PAPER recently presented before the Anthracite Section of the A. I. M. E. by S. J. Phil- lips, Mine Inspector, Fifth Anthracite District, Department of Mines of Pennsylvania, covering the water hazards in the anthracite coal mines of the Lackawanna River Valley, was especially timely because the conditions there are duplicated to a large extent in the Wyoming Valley, which is traversed by the Susquehanna River with its many large tributary streams. Also, in the southern anthracite field, where there are a number of large creeks, similar pumping problems and mine water hazards will in time be presented if mining is continued to its conclusion.

Jan 1, 1936

By Richard Hamburger

The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new & do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951

By William B. Phillips

The possible sources of potash salts in the United States have been considered from many points of view during the last several years, but it is only within the last two or three months that the situation has become acute. We import from Germany, the only sourcc of large supply, more than $10,000,000 worth of potash salts annually, and this business has been badly crippled by the European war. If there was ever a time in our industrial existence when the necessity of providing for our own needs was more acute than it is now, we are not aware of it. One has only to study the price lists of chemicals sent out by the large supply houses to see the change wrought within a very short time. Whether or not these prices are to maintain for a considerable time, no one can say; but it appears to be probable that we shall not see prices materially lower for a period of uncomfortable length, to say the least. It is not my purpose at this time to discuss the various sources of supply of potash salts that have been suggested or recommended. Some of them might afford a pleasing relief but all of them combined would not affect the situation seriously. If we are to have our own sources of potash salts, they will have to compare, in some efficient manner, with the sources upon which we have drawn during the last 20 or 30 years; i.e., they must exist in minable quantities. It seems to me to be quite idle to speculate upon our domestic sources of potash if those sources are not of a character similar to those upon which we have so long depended. A few thousand or, perhaps, a few hundred thousand dollars' worth of chemically derived potash may be produced under the stress of present conditions, but when we consider that each year demands more than $10,000,000 worth, we must look to underground sources; we must look to mines similar to the famous Stassfurt and Halle deposits. If we cannot mine potash salts, we shall have to do without them for a while.

Jan 1, 1915

By R. B. Gavert, David J. Mack

ROOM- and elevated-temperature compression tests were made on the binary 3/2 electron compounds AuZn, CuAu, AgZn, AgMg, AuCd, and NiA1. These compounds possess either the B2 CsC1-type ordered structure or the A2 bee disordered structure represented commonly as ß and ß on equilibrium phase diagrams. In testing at room temperature, cylindrical specimens 0.508 cm by 0.330 cm diam were seated directly on an instron compression load cell (CF 0 to 10,000 lb). At elevated temperatures, testing included a special apparatus with a furnace heat source and a protective atmosphere.' The specimens were strained at a rate of 1 pet per min. The compounds were prepared from 99.99 pet or better high-purity elements. Vacuum and/or argon cover gas was used throughout the mixing, melting, and specimen drawing processes. The generally equi-axed specimen grains varied in size from 0.5 to 1.5 mm for the five different compounds. The stress-strain curves in compression showed

Jan 1, 1968

By Richard Hamburger

(1) Introduction: The purpose of this paper is to call attention to certain methods which will shorten and simplify the calculation of plane tri-angulation. These methods, though not new,',2 do not appear to have been properly publicized in the United States. The cotangent (or tangent) solution of a triangle permits calculation of coordinates in a smooth series of operations of the calculating machine with a minimum of notation. The semigraphical solution permits the simultaneous solution of a number of intersections, at one station, without the added burden of solving additional triangles. This in turn encourages more numerous field checks and more complete office computation than would normally be undertaken. RICHARD HAMBURGER, Junior Member AIME, is Junior Engineer, Inspiration Consolidated Copper Co., Inspiration, Arizona. TP 2798 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Tables I and I1 show the distinct advantage which the combined use of the cotangent and the semi-graphical solutions hold over, what might well be called, the standard solution. It will be shown that the positions for the entire net in fig. 1 may be calculated without computing any distances, thus saving much computation. (2) Comparison of Cotangent and Standard Solutions: To compare the cotangent method with the standard method, the notation involved in the solution of triangle 1-X-4, fig. 1, by both methods is shown. Fig. 2 shows the given information, that is, the coordinates and azimuths of Stations 1 and 4, and angles of the triangle or the azimuths from Stations 1 and 4 to Station X. (Azimuths are used here because the author feels that they are easier to handle, but bearings may be used by those who prefer them). It will be seen from the above comparison that the advantages of the cotangent solution of a triangle are: (a) rapidity, (b) full use of the calculating machine, (c) the small number of

Jan 1, 1951