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By O. R. Morris, G. L. Hawkes

A galvanic cell, using as electrolyte a fused salt solution of calcium carbide and as electrodes carbon and a Fe-C alloy of known composition, has been set up to study the thermodynamics of Fe-C alloys in the temperature rmzge 800" to 1000°C. Time independence and reproducibility of the cell electromotive force were taken as evidence of the reversible behavior of the cell. Carbon was believed to be present in the electrolyte as the so-called acetylide ion, C;-. The plots of the cell electromotive force us temperature for a specific alloy composition were straight lines within the limits of experimental error. The average Partial molar enthalpy of carbon in iron relative to pure carbon was found to be +10,610 i 93 cal per g-atom C. Thermodynamic analysis of the data has led to the following equation for the carbon activity, ac, based upon pure carbon as the standard state: In ac = In Zc + 10,560/RT + (10.02 + 77O/T)ZC - 2.350 where ZC is the lattice ratio [nC/(nF, - nc )] and T is the absolute temperature. This equalion gives carbon activity values generally slightly lower than those from gas equilibration studies reported in the literature. METAL LOGRAPHIC examination of a polished cross section of the steel anode used in the electrolysis studies of fused salt solutions of calcium carbide by Morris and Harry revealed extensive carburization of the steel by the electrodeposited carbon. This carburization was reflected in the variability, with time, of the applied potential to the electrolysis cell, necessary to maintain a constant current density at the electrodes. This observation suggested the setting up of a galvanic cell of the "alloy concentration" type to study the thermodynamics of some metal-carbon alloys. Cells of this general type have been widely used for the study of alloy systems.2 In view of the availability of published data in respect of the austenite phase of the Fe-C system, it was decided to carry out measurements upon these alloys before proceeding to studies of less well documented systems. The galvanic cell may be written: where [C] is carbon dissolved in iron. The electrolyte was a fused salt solution of calcium carbide, containing some 5 to 10 mol pct of carbide. The cell reaction is believed to be: C(s)-[CI [I1 Carbon forms an interstitial solid solution in iron, with the atoms located in the octahedral interstices. In the fcc crystal structure of austenite there is one octahedral interstice per iron atom. Thus, the lattice ratio, ZC, shown by Gurney3 to be the fundamental concentration parameter in the context of interstitial solutions, is given by: where nc and nFe are the number of carbon and iron atoms, respectively. chipman4 has recently shown empirically the advantages of using this concentration parameter instead of the more usual atom ratio or atom fraction. The cell electromotive force, E, assuming reversible behavior, is related to the carbon potential or the partial molar free energy of carbon in the solid solution relative to pure carbon at the same temperature and pressure, GP at the composition ZC, by the equation: where z is the carbide ion valency and F is the Faraday constant. An activity of carbon, ac, in the solution relative to the value of unity assigned to pure carbon, and an activity coefficient, qC , are defined such that: where R is the gas constant and T the absolute temperature. GF is further related to the relative partial molar enthalpy Hm, and the temperature coefficient of the cell electromotive force, (aE/aT)Zc, by the equations: Measurement of the cell electromotive force thus enables calculation of the relative partial molar thermodynamic properties of carbon in iron, if z is known. At E = 0, the solid solution is in equilibrium with pure carbon. More convenient for many purposes is the standard state based upon the infinitely dilute solution, Henry's law. The relationship between the activity coefficient of carbon based upon this standard state, and that based upon the pure carbon standard state, qC , may be obtained by considering the free energy of transfer of carbon from the latter standard state to the former. The relationship is: where +:H is the activity coefficient of carbon in the hypothetical standard state based on a reference of

Jan 1, 1969

By John Cogan

INTRODUCTION Lake tapping is a method of blasting an intake into a body of water from below the natural water surface without first lowering that surface or installing a protective cofferdam around the tap hole. Lake taps are done by first excavating a tunnel almost to the water/rock contact and then blasting out the final protective rock plug at one time to allow water to suddenly inflow into the tunnel from the lake. This procedure can be done "dry" or "wet." In the dry method the tunnel is empty of water before the final plug blast while in the wet method it is partially filled with water. This paper describes a wet method lake tap as performed at Alaska Power Authority's Tyee Lake Hydroeletric Project in southeast Alaska. The Tyee Lake project is located approximately 40 miles southeast of Wrangell, Alaska, in a glacially formed valley called the Bradfield Canal. The project consists of a powerhouse located at sea level on the canal, a system of tunnels and shafts connecting the powerhouse to Tyee Lake at elevation 373 m (1225 ft), and an 129 km (80-mile) electrical transmission line leading from the powerhouse to Wrangell and then Petersburg, Alaska. Tyee Lake itself is a natural lake gouged out of the rock by glacial ice during the last ice age. The objective of the project was to tap into the lake and use the water as a source for power production. The techniques used for lake taps have been developed in Norway where conditions are favorable for their use in hydroelectric proj¬ects. Over 100 have been performed. In the United States the Tyee

Jan 1, 1984

By WALTON H. HAMILTON

THE demand for "production control" has, like the poor, been with us always. With the development of the nation, the accumulation of business experience, and a maturing understanding of how our many and varied industries work, it is increasingly evident that an uncontrolled output is a source of great mischief and that order and performance demand a control of production. To see clearly the demand for "production control" we must look in detail at the ways in which industries operate. General pictures, grand aggregates, situations as "wholes," and smoothed curves are likely to be deceptive. An industry may seem to keep the even tenor of its ways, and yet the establishments which made it up may experience a great range of fortunes. A nice bundle of statistics may show in the aggregate a lovely regularity which is not shared by the firms which make up a trade. An industry may appear to be reasonably profitable, and yet the profits may be very unevenly distributed. The people in an industry, and dependent on it, are managers, laborers, stockholders, creatures of flesh and blood, such as you and I. General pictures and abstract statements must not blind us to what is happening to firms, corporations and individuals.

Jan 1, 1929

Jan 1, 1978

By Erwin S. Sperry

The presence of small amounts of tellurium in certain binds of copper, and its exceptionally deleterious* influence in producing red-shortness of this metal, led the author to conduct a few experiments on the influence of tellurium on the properties of brass. While these experiments were not intended to be exhaustive, they demonstrate that, as far as the rolling of brass is concerned, tellurium, unless it occurs in far greater amounts than exist in refined copper, cannot be called an injurious impurity. In comparatively large amounts it appears to impart cold-shortness to high-brass. Tellurium, the rare element that it is considered to be, has recently been extracted on a large scale from the slimes of an American electrolytic copper-works. They have, in attempts to discover some commercial use for it, sent it out promiscuously and gratuitously in quantities which would lead the young chemical student to fancy that a rare element exists only in name. Through the courtesy of Mr. R. L. Whitehead, of Baltimore, the author was able to obtain somewhat over 2 lbs.,? and use it in quantities which, at the market price, would be prohibitive. In order to add specific quantities of tellurium to brass, a rich alloy of copper and tellurium was previously made. The method was as follows, viz.: Nine and one-half lbs. of Lake copper were melted un-. der charcoal in a new plumbago crucible, and then pound of tellurium was added in small portions at a time. The mixture was stirred with a plumbago-stirrer and poured into

Jan 1, 1903

By CHARLES E. W.

I. LOCATION. THE Mojave mining district is situated in a group of small hills centering around Soledad peak, in the Mojave desert, Kern county, Cal. These hills are about 4.5 miles SSW. of Mojave, a railroad town at the junction of the Santa Fé and Southern Pacific railroads. The town of Mojave is about 50 miles north of Los Angeles, to which it is connected both by telegraph and by rail. The distance on the Southern Pacific railroad is 102 miles, covered in 3 hr. and 45 min. by express train. A sketch-map of this region is shown in Fig. 1. The Mojave district is relatively isolated. The only other mining towns in this section of California are Randsburg and Johannesburg, in a district (containing the well-known Yellow Aster mine) at the northern end of a low ridge of hills, which begins about 20 miles NE. of Mojave, runs nearly N. for 35 miles, and varies in width between 3 and 6 miles. As will be seen later, the origin and formation of these hills are not the same as those of Soledad peak. II. CLIMATE AND VEGETATION. The climate and vegetation of the Mojave district are typical of the arid regions of the southwestern United States. During the winter and spring there is some rainfall, and the tempera-ture is generally from 60° to 70° F. in the day-time. The rainfall in the spring is often very considerable for short spaces of time, and cloud-bursts are not infrequent. In summer there is continual sunshine, with temperatures, as a rule, exceeding 100° F. in the day-time, while 115° F. in the shade of a house is not at all unusual; but at night the temperature falls considerably. No rain falls during the summer. The vegetation

Jan 1, 1906

By John M. Kelly

This report covers the development, exploratory drilling, and production of oil and gas in New Mexico during 1945. The statistical information was gathered from state regulatory agencies and other sources believed to be reliable; it is presented here in combined form for general information only, and the author assumes no responsibility for its accuracy or completeness.

Jan 1, 1946

By AIME AIME

The Bulletin. As already announced in the January Bulletin, this publication will be issued during the coming year monthly instead of bi-monthly as heretofore. Among other reasons for this change, it is desired to effect thereby the earlier transmission to members of important papers, lists of candidates for membership, and other items of timely information. The New Haven Meeting. As already announced in special circular, the XCVIth meeting of the Institute for the reading and discussion of papers will be held at New Haven, Conn., beginning Feb. 23, 1909. The Secretary of the Local Committee is Prof. J. D. Irving, Box D, Yale Station, New Haven. The program embraces visits to many interesting works in New Haven, Ansonia, Bridgeport, etc. The leading topics for discussion at the sessions will be: The Conservation of Natural Resources; A Sea-Level Canal at Panama; and The Technical Education of Mining Engineers. But papers on other subjects also are announced. A supplementary session of this meeting will be held in New York City, at some time during March, 1909, as a joint session with other national engineering societies, for the further discussion of the subject of The Conservation of Natural Resources. A Pacific Coast Meeting. The XCVIIth meeting will be held on the Pacific Coast, including a visit to the Exposition at Seattle, and various other points en route going or coming, depending upon the route and program finally adopted. More definite information will be announced at the New Haven Meeting, or at the earliest possible date thereafter.

Feb 1, 1909

By J. G. LECKIE

During the first ten months of 1943 copper was produced at a higher rate than in 1947. However, on Oct. 24 one of the large mines was shut down due to a strike. As of Dec. 31 the strike was still in effect and had already resulted in a loss of production of 50,000 tons of copper. The demand for copper was considerably greater throughout the year than the supply. The price of electrolytic copper delivered at the Atlantic Seaboard refineries advanced from 21.20 to 23.20 cents per lb during the year. This sustained demand for copper, together with the increase in price, has had the natural effect of spurring interest in uncovering new deposits, and in re-examination of known low-grade deposits and old tailing clumps. This is in addition to the usual reevaluation activities which normally result from the constant improvements in efficiency of ore concentration.

Jan 1, 1949

Executive.. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS. ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANEWAY, Jr., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L, YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library. JAMES F. KEMP, Chairman. JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALES. C. HUMPHREYS 4 BRADLEY STOUGHTON.

Jan 7, 1913

By AIME AIME

THE 140th meeting of the Institute will be held in the Engineering societies Building, 'New York, Feb.: 16-19, and one of the most important features, one which cannot be reduced to text in the TRANSACTIONS, will be the opportunity to renew old friendships and make new friends, to talk things over -to orient one's self in these troublous .times. There will be daily get-together luncheons for all, luncheons and dinners for specialized groups, an informal dance, the annual reception and banquet, and a smoker. And such a smoker! It starts with dinner at .dinnertime, shows signs of cabaret, turns smoker, and then goes entertainment-all for the price of one. This year one can stay long after 11 o'clock-there will be time and opportunity to amble around and meet everyone present. The formal program is rapidly rounding into shape. The annual business meeting will -be held on Tuesday morning and the banquet will be at the Commodore. The four Divisions and the various, Technical Committees are arranging their sessions. and scheduling for these a long list of significant papers. A .feature of the meeting will be a number of round tables on timely subjects.

Jan 1, 1931

By John Chipman, Carl F. Floe

A year ago the authors published a paper on the solubility of sulphur dioxide in molten copper.l The data in that paper agreed closely with that obtained by previous investigators, which, however, did not agree with the theoretical predictions for solubility of triatomic gases of this type. It has generally been assumed that the reaction of solution is: 6Cu(l) + SO2(g) = Cu2S (in Cu) + 2 Cu2O (in Cu) [I] _ (CU2S)(CU2O)2 K = (Cu)6(Pso2) [2] Neglecting the slight change in copper concentration and considering that the concentrations of sulphur and oxygen are both proportional to the volume of gas absorbed, it follows that this volume should be proportional to the cube root of the pressure. It was found that a plot of the volume absorbed versus the cube root of the pressure gave a straight line, but that this line did not pass through the origin. Calculations of the equilibrium constant for the reaction showed that it was fairly constant for pressures above 100 mm. but that actually it approached zero at lower pressures. The conclusion was made therefore that the solubility as determined could not be expressed by Eq. I or by any other simple equation, particularly at low pressures. Other investigators have concluded that the solubility of sulphur dioxide in copper as well as in several copper alloys is more nearly proportional to the square root of the pressure.* Such a conclusion, however, does not satisfactorily account for the results, even when rather complicated mechanisms for the solution are assumed. The highly improbable speculations of Lepp2 and of Schneider and Esch3 based upon hypothetical dissociation pressures of Cu2O and CU2S dissolved in copper illustrate the type of reasoning that has been used to account for the discrepancy. In the discussion of the previous paper, the authors pointed out that the discrepancy might possibly be due to impurities in the copper, although the purest form available was used. Further consideration of the problem suggested that the impurities likely to have the greatest effect on the solubility of so2 in copper were oxygen, sulphur and carbon. Accordingly, further experiments have been made to show the effects of these elements. Experimental Methods The apparatus used for measuring solubility was essentially the same as that shown in the previous paper. However, since it was desired to make measurements at low pressures, a McLeod gauge was added and 6-mm. glass tubing was substituted for the capillary. This increased the "hot volume" considerably but was necessary in order to obtain good vacuums in a reasonable length of time. A mercury diffusion pump was also installed.

Jan 1, 1942

By Carl F. Floe, John Chipman

A year ago the authors published a paper on the solubility of sulphur dioxide in molten copper.l The data in that paper agreed closely with that obtained by previous investigators, which, however, did not agree with the theoretical predictions for solubility of triatomic gases of this type. It has generally been assumed that the reaction of solution is: 6Cu(l) + SO2(g) = Cu2S (in Cu) + 2 Cu2O (in Cu) [I] _ (CU2S)(CU2O)2 K = (Cu)6(Pso2) [2] Neglecting the slight change in copper concentration and considering that the concentrations of sulphur and oxygen are both proportional to the volume of gas absorbed, it follows that this volume should be proportional to the cube root of the pressure. It was found that a plot of the volume absorbed versus the cube root of the pressure gave a straight line, but that this line did not pass through the origin. Calculations of the equilibrium constant for the reaction showed that it was fairly constant for pressures above 100 mm. but that actually it approached zero at lower pressures. The conclusion was made therefore that the solubility as determined could not be expressed by Eq. I or by any other simple equation, particularly at low pressures. Other investigators have concluded that the solubility of sulphur dioxide in copper as well as in several copper alloys is more nearly proportional to the square root of the pressure.* Such a conclusion, however, does not satisfactorily account for the results, even when rather complicated mechanisms for the solution are assumed. The highly improbable speculations of Lepp2 and of Schneider and Esch3 based upon hypothetical dissociation pressures of Cu2O and CU2S dissolved in copper illustrate the type of reasoning that has been used to account for the discrepancy. In the discussion of the previous paper, the authors pointed out that the discrepancy might possibly be due to impurities in the copper, although the purest form available was used. Further consideration of the problem suggested that the impurities likely to have the greatest effect on the solubility of so2 in copper were oxygen, sulphur and carbon. Accordingly, further experiments have been made to show the effects of these elements. Experimental Methods The apparatus used for measuring solubility was essentially the same as that shown in the previous paper. However, since it was desired to make measurements at low pressures, a McLeod gauge was added and 6-mm. glass tubing was substituted for the capillary. This increased the "hot volume" considerably but was necessary in order to obtain good vacuums in a reasonable length of time. A mercury diffusion pump was also installed.

Jan 1, 1942

CARL A. WENDELL, New York, N. Y. (written discussion*) .-I have never seen in print anything that even remotely has approached this article in clearness and important conclusions in conjunction with work done on the sink-and-float test. I have had many hundreds of these tests made and on different specific gravity solutions and the resultant product analyzed, but I have never grasped nor been able to show what this article sets forth. This article brings out one factor very clearly to my mind; what is to take the place of the solutions of different specific gravities used to obtain the laboratory results, when it comes to washing on a large scale, since water has one constant weight only? The answer is, sizing of coal. And as we know the importance of size versus specific gravity of the material to be washed, perhaps defined (practical) lines can ultimately be gotten up so that the sizing, if any, may be determined at the same time as the laboratory work on the coal is being done. G. R. DELAMATER, ? Steelton, Pa. (written discussion?).-The authors' deductions are well founded and although they disclaim any wide experience in commercial coal washing, practically all of the data presented are applicable to coals of all parts of this country. The paper clearly sets forth the great necessity of careful preliminary investiga-tion of each contemplated washery undertaking and contains the follow-ing very true statements. "It is not safe to assume that any coal which can he successfully washed on coarse coal jigs can be cleaned more com-pletely by washing at a finer size on tables," and "The effect of finer crushing upon the completeness with which impurities may be separated from coal depends upon two opposing tendencies. First, that the more finely a raw coal is crushed, the more completely will the particles of impurities be detached from the particles of clean coal. Second, the finer a coal is crushed the more difficult it becomes to separate the pieces of clean refuse from the pieces of clean coal."

Jan 12, 1919

By A. B., Sabin

THERE are many who know The Lucky Tiger and will remember the 35-mile road from Esqueda, a station on The Nacozari Railroad in northern Sonora, Mexico. They will remember the box canyons of the Agua Caliente Mountains which are scarcely wide enough for two cars to pass; the Bavispe River which one hour may be a lazy trickle and the next a sweeping torrent, and the tortuous road up Tigre and Espuela canyons, now following the wash, now hugging some gigantic red cliff. It is still the same. From camp the view of the distant blue-gray mountains is the same. But one thing a visitor of a former day might miss: The hundreds of pack mules and burros, loaded with concentrates from the mill, which used to take most of the road and show up at the most inopportune places, have almost disappeared, replaced of course by the auto truck.

Jan 1, 1929

Jan 1, 1880

?ADAIR, ARTHUR C., Corp 4th Co., 1st. Training Bat., 154th Depot Brigade. ADAMS, HENRY, Major: Chemical Warfare Service. ARLUCK, A. A Headquarters, 1st Corps of Artillery. ASKIN, THOMAS B. H Ensign. BANKS, H. R., 2d Lieut Canadian Engineers. BAYLESS, G. E. S Supply Dept. U. S. Submarine Base. BELL, L. R Co. C, 302d Engineers. BELLIS, ARTHUR E., Capt Ordnance Reserve Corps. I BIRRETT, HOWARD, Lieut., Aviation Section, U. S. Signal Corps, Ellington Field. BOISE, PAUL T 2d Regiment, 24th Squadron. ?BRADLEY, CLARENCE I Convois Automobile Section 585. BROWN, GEORGE M Co. G lot Engineer Replacement Regiment. BUCKINGHAM, ALBERT U. S. S. " Coronet," S. P. 194, Section Base No. 7. BURNS J. J Co. 1-B, E. R. O. T. C. BURT, Co. B, let Engineers Replacement Regiment. ||BYERS, WHEATON B., 2d Lieut Ordnance Dept. CANTON, WILLIAM R., Sgt Headquarters Co., 80th F. A. CARSON, JOSEPH A., Capt A.S. S. R. C.' CHAPMAN, LEWIS C. Corp 29th engineers. CHETNEY, P. C., 2d Lieut 15th Bat. Headquarters Co. CHEVRILLON Louis French Red Cross. CHIDESTER, W. B., 1st Lieut 24th Machine Gun Bat. CHURCH, JOHN L., Capt 308th Engineers. CLAGHORN, D. MONTGOMERY, 1st Lieut 45th Engineers. CLAQHORN, JAMES L., Lieut Aviation Section, Signal Corps. CLARKE, ALEXANDER F U. S. Naval Aviation Service. COMINS, WALDO H. Ca t 41st Co., 164th Depot Brigade. COOK, FREDERICK A., Capt., Engineer Reserve Corps, Asst. to Div. Engr. 79th Division. COOPER, CLAUDE H. Capt C. A. R. C., 50th Artillery. COPELAND, N. R., Lieut. ||CORBY H.. G., 1st Lieut Co. D, 109th Supply Train. CORSA, BEAN, Capt Co. D, 612th Engineers. CORTESE, EMILIO Italian Army. COULDREY PAUL S., Corp British Expeditionary Forces. || CRAGIN, RODNEY S Co. E, 115th Engineers. CURRIE, JOHN M., Ca t Royal Engineers. || CUTTING, G. W., 2d Lieut U. S. Reserves, Field Artillery. V DARRINGTON, PAUL N., 1st Lieut U. S. Infantry. DAVIS, ANGUS W., Lieut-Col British Expeditionary Forces. || DAVIS, THORNTON, 1st Lieut 13th Field Artillery. ELAND, FREDERICK A., Major Engineer Reserve Corps. DOUGLAS, JAMES $ American Red Cross. DOVE, D. R., Candidate 21st Training Battery, F. A. C. O. T. C. Dover JAMES J 6th Co. C. B. DOWS, DAVID,Capt Coast Artillery, Officers Reserve Corps. || DRAKE, M. 6., 2d Lieut Headquarters Co., 325th Infantry. I || EMMERSON, E. Roy British Navy. EVERIT, RICHARD STURTEVANT Heavy Artillery Officers' Training Camp.

Jan 1, 1923

By R. Schuhmann, O. W. Moles

at temperatures of 1150°, 1250°, and 1350°C for liquid copper sulphides ranging in composition from saturation with Cu to about 21.5 pct S. From the experimental data, activities of Cu, S, and Cu2S in the melts were calculated. Also, the results furnish a new determination of the location of the curve showing the compositions of Cu-saturoted sulphide melts in the CU-S constitution diagram. THE "white metal" made as an intermediate L product in converting copper matte to blister copper is a matte approximating Cu2S in composition. It has long been known that liquid Cu-S mattes can exist at a given temperature over an appreciable composition range, with S:Cu ratios ranging up from a lower limit corresponding to equilibrium of the matte with a liquid Cu phase. The Cu-saturated matte has somewhat less S than Cu2S, although previous measurements of the compositions of Cu-saturated mattes are not in good agreement.'" As the S:Cu ratio approaches and slightly exceeds that for Cu2S, the partial pressure of sulphur gas over the liquid matte rapidly approaches atmospheric pressure,5 so that Cu-S melts with much more S than Cu2S can be made and handled only in pressure apparatus. Accordingly, the liquid copper sulphides of interest in copper smelting and readily studied experimentally fall in a relatively narrow composi- tion range about Cu2S. The freezing points of Cu-S mattes show a maximum of 1129°C near the composition Cu, dropping to 1105oC for Cu-saturated mattes having less S and dropping under 1100°C for higher S mattes.' Estimates of the sulphur pressure and other thermodynamic properties of liquid Cu,S were made by Kelley; based on extrapolations from equilibrium measurements on solid Cu,S. More recently, Cox and coworkers' studied equilibria in the reaction: Cu,S + H, e 2Cu + H,S over the temperature range 700" to 1250°C. They measured equilibrium H2S:H2 ratios presumably with both the sulphide and the metal phase present, so that their data above the melting point of Cu,S should measure the S pressure of Cu-saturated sulphide melts. The sulphur pressures of liquid copper sulphides of several S:Cu ratios at their freezing points can be estimated from data given by Posnjak, Allen, and Merwin." However, beyond these few data, no systematic study seems to have been made of the relations of sulphur pressure and other chemical properties of liquid copper sulphides to composition and temperature. The measurements of the sulphur pressures of liquid copper sulphides reported in this paper represent a first step in the quantitative study of the chemistry of mattes. Similar work is planned on

Jan 1, 1952

By A. S. Adams

A GLANCE at the list of papers1 that have been published since 1920 on the general subject of flotation suggests the variety of ideas that exist regarding the underlying cause of the phenomenon. Among these ideas, we find several coherent theories, but none that adequately and completely explain the phenomenon. Ralston2 and Bains3 suggested an electrical theory which has to do with the attachment of mineral particles to a bubble by the attraction of unlike electrical charges. This theory has its root in the fact that a bubble of air in pure water is electrified in such a way that the surface is negatively charged while the body of the water is positively charged. This result, which was first discussed by Helmholtz, also obtains when the water contains anything except a high concentration of hydrogen ions, or ions which are trivalent or tetravalent. The theory also holds that the mineral particles have positive charges on their surfaces, and so there is attachment between bubble surface and mineral particles by the old law of electrostatics, which states that unlike charges attract.

Jan 1, 1928

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