Search Documents

Discussion of the paper of ROSWELL H. JOHNSON, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 221 to 226. A. C. LANE, Tufts College, Mass.-About a year ago Mr. Washburne read a paper on the same characteristic oil-sand waters, discussing their chemical character, and the possibility of their chemical character being modified by adsorption in passing through the shale. We are used to consider circulation as being in one stratum, and I have often gone so far as to think that 2,000 or 3,000 ft. clown I could recognize the chemical character as in part connate to a given water. For instance, the St. Peter sandstone, far underneath oil sands, seems to retain' a relatively fresh and peculiar character. I am, therefore, tempted to ask the writer if in his experiments lie has made any test to see whether the chemical character of these waters is also changed, where there is any adsorption, so that the water passing through these fine-grained beds should leave behind its salt as well as its oil. In many cases salt-waters are associated with oil and-gas. A second question has occurred to me. In these days when we hear a good deal about oil flotation, may it not be well to repeat these experi-ments with pyritic concentrates, and see if they observe precisely the same with regard to the selective accumulation of oil and gas. ROSWELL H. JOHNSON.-I thank Profesor Lane for bringing this question forward. I recognize its importance, but. am not able to say I have any data upon that point. It is also very interesting in connection with Dr. Day's hypothesis of fractional filtration, and we may very easily get something happening to the water corresponding in some degree to what we get with oil. D. B. REGER, Morgantown, W. Va.-Mr. Johnson in his paper states his belief that the oil is formed originally from organic matter in the shale, and is forced out of the shale into the porous reservoir of the sand above the shale. He states further, that as you go deeper iii the measures where there is an increasing overburdens, the oil becomes less and the gas increases in large proportion, or lie says that the oil is forced back out of the sand by pressure, into the shale.

Jan 5, 1915

By E. G. Leonardon

THE first to appreciate and foresee the value of applying electrical measurements to structural studies was Prof. Conrad Schlumberger, Professor of Physics at the School of Mines in Paris. One of his earliest practical undertakings in this line was carried out, in the field, at Fierville-la-Campagne, Normandy, in 1912. His book, published in 1920,1 still stands as an authoritative, fundamental treatise on the use of the electric current in geological studies, in spite of the rapid evolution of geophysics during the last seven years. A remarkable feature of this book is that, even then, it stressed the role of electricity in structural investigations and made public the first successful results obtained therewith. Stratigraphic studies have been pursued continuously by Conrad Schlumberger and his associates since 1912, the only interruption being the World War. The results attained demonstrate the wide possibilities of electrical exploration in structural work. This field of activity is, at the least, as varied and valuable as the search for ore. It is curious that until very recently it has so slightly attracted the attention of geophysicists and geologists on this continent. The purpose of this paper is to present briefly some examples of the practical application of the potential methods to geological studies. These examples are chosen from a number of problems solved in the field by our firm, in the course of its consulting practice. Certain fundamental points are briefly stated before the field operations and interpretations are described.

Jan 1, 1928

By R. E. Boni, G. Derge

Application of surface tension measurements has been made to molten silicates in order to determine the effect of sulphur upon the surface tensions of synthetic blast furnace slags. In melts with the same molar ratios of AI2O3 + SiO2 to the basic oxides BaO, CaO, and MgO, the surface tensions increase in the order of oxides listed. Sulphur lowers the surface tensions of the basic BaO, basic CaO, acid BaO, acid CaO, and acid MgO slags in that order; and the concentration of excess sulphur at the slag surface increases in this same order of slags. The rate and amount of desulphurization of iron by these slags is favored by a low excess surface sulphur in the slag. IN a previous paper,1 the authors discussed the applications of surface tension measurements of molten silicates to problems of metallurgical interest. Of major importance is the aid that such studies lend to forming a working concept of slag structure. Since the ability of a slag to desulphurize metal depends strongly upon its composition,2"4 fundamental information about the structural differences between various slags which contain sulphur should aid the development of better desulphurizing media. For that reason, the present investigation concerns the effect of sulphur upon the surface tensions of synthetic blast furnace slags. Experimental Procedure , The maximum bubble-pressure method was used to measure the surface tensions of synthetic blast furnace slags in the temperature range 1300° to 1600°C. The method is based upon the equation which was developed by Schrödinger5 from a consideration of the forces of hydrostatic pressure and surface tension of a liquid which oppose bubble formation when a gas is forced through a tube immersed in the liquid. where y is the surface tension between argon and slag in dynes per centimeter; g is the gravitational constant, centimeters per second2; H is the manometer reading in centimeters; s2 is the density of manometer fluid in grams per cubic centimeter; S1 is the density of the medium in grams per cubic

Jan 1, 1957

By Oliver Bowles

DISCUSSIONS of trade and commerce are generally more comprehensive today than in the past; the problems are approached with a vision unrestricted by national boundaries, and broad enough to comprise the entire world. The extent to which the limited viewpoint that has characterized past ages is yielding to an economy of world-wide scope is exemplified by the Atlantic Charter which blazes a trail in the direction of trade principles that aim to preserve the interest of each individual country in the commonwealth of nations. Its fourth article promulgated the principle that all nations should have access on equal terms to the trade and to the raw materials of the world which may be needed for their economic prosperity. Future developments in reciprocal international trade may have some effect upon the flow of nonmetallic minerals but such effects are not likely to be great because tariffs and trade policies have not affected that flow profoundly in the past. Nevertheless conditions may change and new problems may arise demanding important decisions. Sudden changes are not to be expected, but rather an orderly evolution in which national interests will merit due consideration in establishing broader policies.

Jan 1, 1945

By Joseph B. Umpleby

PROGRESS in the petroleum industry in 1929 has been characterized by outstanding accomplishments in the fields of new discovery of supply, economic control of production, increased efficiency and reduced costs of recovery, and lowered costs and greater flexibility in manufacture. Resources have been developed in an outstanding degree in the Kettleman Hills. California, the Oklahoma City field (which adds a large potential area in central Oklahoma), the discovery of Woodbine sand production in East Texas, and the discovery of Wilcox sand production in west-central Kansas. Engineering technique has progressed both along the lines of development and production, with a net result that costs have been reduced and extraction increased in notable degree, although it is impossible to give a close measure of either. In the field of re- fining crude oils variations to the end of promoting reduced cost and greater flexibility has been more important than genera! acceptance of innovations in practice.

Jan 1, 1930

By R. S. Newlin

IN reality, the Butte district is the birthplace of the Anaconda Copper Mining Co., for it was here that strength was gathered and means provided for later expansions of the Company. The Butte district was organized at a miners' meeting on Aug. 20, 1866, primarily for gold placer-mining operations. Substantial amounts of placer gold were recovered from gulch gravels during the period 1862 to 1868. The earliest lode claim locations in the district were recorded in July and August 1864. Copper ore was first shipped, to Swansea, Wales, in 1866. In November 1866, according to the Montana Post, construction of a smelter was started to treat the silver

Jan 1, 1948

By ELIHU THOMSON

IN 1877, Professor Thomson delivered at the Franklin Institute, [Philadelphia, five lectures on electricity. The object of the lectures and the demonstrations, which were numerous and many of them original even to the employment of special apparatus constructed by the lecturer, was to show clearly that electricity, of whatever name, was the same., differing only in tension (as it was termed) and in the current flowing, or quantity (the old term), in steadiness or in wave-like character. In those days, the textbooks divided the subject into statical and dynamic electricity, with sub-divisions such as frictional electricity, voltaic electricity, magneto electricity, electromagnetism, thermo electricity, and animal electricity. The well-known Ruhmkorff coil,' or spark coil as it is now called (as when used for the ignition of automobiles), was employed to step, up a battery current to a high-tension discharge which would charge condensers, such as Leyden jars.

Jan 1, 1921

By S. A. Falconer

One of the outstanding achievements in connection with this country's war efforts has been the ability of our mining industry to supply from domestic sources many of the minerals of strategic importance that formerly were obtained principally from abroad. In order to meet the war-born demands for these scarce minerals, it has frequently been necessary to develop special methods for treating ores and waste products hitherto considered too lowgrade to be workable; and to improve the efficiency of older beneficiation processes. Important in this respect have been the recent technological advances in the field of froth flotation of nonsulphide minerals. Because of the refractory nature of many of these domestic ores, and, in many cases, the limited available technical data regarding their treatment, much research work has been necessary. The following examples describe the procedures and reagents used, and the results obtained, in certain laboratory flotation investigations conducted by American Cyanamid Company's engineers at the Cyanamid Ore Dressing Laboratory on ores containing such minerals as scheelite, manganese oxides and carbonate, ilmen-ite, brookite, kyanite, garnet, spodumene, mica, feldspar, celestite, fluorite, chromite, corundum, and cassiterite. In presenting these data, we wish to point out that many of the minerals listed have previously been tested, and their amenability to flotation reported, by other investigators—notably those of the United States Bureau of Mines. In some instances the procedures and reagents used in the treatment of some of the following described ores follow rather well-established lines, and with one or two exceptions, the reagents used were well known. However, many of the ores tested did not respond well to simple conventional procedures and it was necessary to adopt special methods of conditioning and desliming, reversal of the usual order of floatability of some of the minerals, multiple cleaning, etc., in order to secure separations. Except where otherwise noted, all numbered and trade-marked reagents mentioned in this paper are marketed by the American Cyanamid Co. or the American Cyanamid and Chemical Corporation. Tungsten ORes Tungsten minerals, vitally important in the war industries of the United States, rank high in the list of those we formerly had to import in order to supply our needs. Most of our domestic ores of tungsten contain scheelite as the valuable mineral. Today there are in the neighborhood of twelve tungsten operations in this country where flotation is used as the main or accessory form of benefication. It has, of Course, been known for some time that scheelite and other tungsten minerals respond to treatment by flotation.

Jan 1, 1947

By S. A. Falconer

One of the outstanding achievements in connection with this country's war efforts has been the ability of our mining industry to supply from domestic sources many of the minerals of strategic importance that formerly were obtained principally from abroad. In order to meet the war-born demands for these scarce minerals, it has frequently been necessary to develop special methods for treating ores and waste products hitherto considered too lowgrade to be workable; and to improve the efficiency of older beneficiation processes. Important in this respect have been the recent technological advances in the field of froth flotation of nonsulphide minerals. Because of the refractory nature of many of these domestic ores, and, in many cases, the limited available technical data regarding their treatment, much research work has been necessary. The following examples describe the procedures and reagents used, and the results obtained, in certain laboratory flotation investigations conducted by American Cyanamid Company's engineers at the Cyanamid Ore Dressing Laboratory on ores containing such minerals as scheelite, manganese oxides and carbonate, ilmen-ite, brookite, kyanite, garnet, spodumene, mica, feldspar, celestite, fluorite, chromite, corundum, and cassiterite. In presenting these data, we wish to point out that many of the minerals listed have previously been tested, and their amenability to flotation reported, by other investigators—notably those of the United States Bureau of Mines. In some instances the procedures and reagents used in the treatment of some of the following described ores follow rather well-established lines, and with one or two exceptions, the reagents used were well known. However, many of the ores tested did not respond well to simple conventional procedures and it was necessary to adopt special methods of conditioning and desliming, reversal of the usual order of floatability of some of the minerals, multiple cleaning, etc., in order to secure separations. Except where otherwise noted, all numbered and trade-marked reagents mentioned in this paper are marketed by the American Cyanamid Co. or the American Cyanamid and Chemical Corporation. Tungsten ORes Tungsten minerals, vitally important in the war industries of the United States, rank high in the list of those we formerly had to import in order to supply our needs. Most of our domestic ores of tungsten contain scheelite as the valuable mineral. Today there are in the neighborhood of twelve tungsten operations in this country where flotation is used as the main or accessory form of benefication. It has, of Course, been known for some time that scheelite and other tungsten minerals respond to treatment by flotation.

Jan 1, 1947

By Stuart Croasdale

Not long ago I was called upon to conduct some experiments on the treatment of ores from the New Cornelia copper mine, Ajo mountains, Arizona, for the Calumet & Arizona Copper Co. The problem was a very interesting one and contained some unusual features. Incidental with this problem was the utilization of a large amount of low-grade pyrite in the Bisbee mines of the company, provided this could be accomplished by any feasible method. The New Cornelia mine is situated 45 miles south of Gila Bend, the nearest railroad point, on the Southern Pacific Railroad. It is about 160 miles, almost due west, from Tucson. This section is one of the most arid in the United States. The normal annual precipitation, as given by the United States Weather Bureau covering a period from 1870 to 1901, is 3 to 5 in. During June and July, 1913, the records kept by the company gave the following results. These are all I have available, but they show the enormous evaporation that can be expected, which may be a factor in leaching operations on a large scale. Temperature, Degrees F. High Low Average June...................... 112 62 84.0 ' July...................... 115 71 87.8 Evaporation June July Concrete tank, inches............ 11.7 10.72 Iron tank, inches.............. 14.8 13.07 Rainfall, inches................ None 0.77 Cloudy days................... None 10.00 Aside from several springs about 10 miles from the property, the nearest known water in quantity at the time these experiments were made was the Gila river at Gila Bend, 45 miles distant. Part of the developinent of the property of course included drilling for water in the valley, which was in progress at the conclusion of my experiments. The ore deposit itself is unusual. It consists of of intrusive plug of monzonite or granite porphyry. Chalcopyrite, bornite, and magnetite are finely disseminated throughout the magma in sufficient quantities to make the greater part of the mass commercial ore to a certain depth.

Jan 1, 1915

By Charles E. Parsons

One of the greatest factors in our industrial development is cheap and convenient power. Long-distance electrical transmission has now reached such a stage that it is feasible, and practicable, to utilize the water-power of the country which was heretofore too remote for consideration. In all of the changes of energy from its various sources to its electrical applications, water-power stands pre-eminent in point of economy. Power-users the world over have endeavored to utilize this force in preference to any other, and until long-distance transmission was found practicable it seemed that every available water-power in this section of the country was doing its full share for the benefit of mankind. The success of each great industrial development has been clue in a greater part to some one man one who is just a step in advance of the rest in his particular field; one who is able to grasp a situation and foresee possibilities; and, above all, one who has that indomitable pluck and perseverance which sees in each obstacle one more step toward success. Such a mail is Eugene L. Ashley, for it was through his efforts that the development of the greatest power on the Hudson river was made possible. For several years prior to 1897 the various properties along the river between Glens Falls and Palmer Falls were in the hands of speculators. These men knew the value of waterrights, but they had not the ability to assemble the properties and finance such an undertaking. In 1897 Mr. Ashley began buying these water-rights, and, after two years of litigation, title mas secured to all of the properties along each side of the river, and the Hudson River Water-Power Company was organized to construct a dam and transmit power to the surrounding cities and villages. A contract was let for a dam

Jan 1, 1904

THE purpose of this chapter is to present a general outline of the basic open-hearth process for the benefit of students, practicing open-hearth operators, and metallurgists who wish to review the subject. The discussion is limited to a description of the sequence and purpose of the operations, illustrated by data and examples. Subsequent chapters deal with more detailed and fundamental studies of the subject. The function of the basic open-hearth furnace is to convert various types of ferrous material into finished steel of given composition and quality. In comparison with other steel-making methods, the basic open-hearth process is one of the most versatile, both from the stand- point of the raw materials that can be used and the types of steel that can be produced. The process can be considered as a sequence involving melting, refining, and deoxidation. In the case of some types of liquid-metal charges the melting stage is not present, but refining and deoxidation in varying degrees are fundamental features of the process. GENERAL DISCUSSION OF THE BASIC OPEN-HEARTH PROCESS The first consideration in open-hearth practice is the type of charge on which the operation is based. This consists of three components-fluxing, oxidizing, and metallic materials. Fluxes. In the basic process the fluxing material is primarily lime, added in the form of either limestone (CaC03) or burnt lime (CaO). This is supplemented by magnesia (MgO) and lime from the furnace bottom and banks. The function of these fluxes is to form a slag with the silica (SO2), manganese oxide (MnO), iron oxides (FeO and Fe203), and phosphorus oxide (P205) that are produced by the oxidation of varying amounts of the silicon, manganese, iron, and phosphorus in the charge during melting and refining. The slag, composed of the basic fluxes and the neutral and acid oxides, floats on top of the steel bath when the charge is melted. The composition of this slag depends on the amount of each slag-forming element present in the charge and on the extent of oxidation of these elements during the course of the

Jan 1, 1944

By L. O. Howard

THERE are three active mines in the Chewelah-Colville district, the United Silver Copper near Chewelah, and the Old Dominion and the Chloride Queen near Colville. The Admiral near Valley is also doing development work. The Chewelah district is in the south central part of Stevens County in the Colville Valley. Chewelah, a thriving town of 1600 people, and the scene of operations of the Northwest Magnesite Co., is about the center of the district. It is situated in a farming community on the Spokane-Nelson branch of the Great Northern railway, about 65 miles north of Spokane. Only two or three of the mines in the district have been extensively developed, although many have been prospected. The general elevation of the valley, is about 1600 or 1700 ft., that of the mountain ranges on each side about 3000 to 4000 ft., with gentle slopes and rounded glaciated tops. Prospecting is often difficult because of much glacial debris.

Jan 1, 1925

By C. P. Proctor, J. B. Morrow

With numerous plans under consideration for coal classification, and with the advent of the Bituminous Coal Code, the intelligent sampling of coal has become increasingly important. To us it is rather significant that there have been very few fundamental studies of coal sampling in American technical literature since those of E. G. Bailey, which appeared in the Journal of Industrial and Engineering Chemistry in March, 1909. He covered the subject up to that time so thoroughly and in such an excellent manner that perhaps many other later students have felt that they could add very little to his findings. The recent studies of the British Engineering Standards Association have indicated the possibility of a somewhat different interpretation of Bailey's results, permitting the taking of smaller samples, and perhaps it will now be helpful to reopen this question. C. W. H. Holmes, in an informative series of articles on coal sampling recently published in Colliery Engineering, makes two rather interesting statements, as follows: It is scarcely surprising to find a lack of interest and knowledge regarding the sampling of coal not only in the mining industry itself but also among consumers of industrial fuel: at its best coal sampling is a dirty business, regarded as a nuisance and an expense by the commercial man, and usually as a nuisance and nothing else by the chemist. The writer can conceive only two classes of people who have never experienced any difficulty in obtaining representative samples of coal from wagons; those who have never tried to, and those who have never had the necessity or desire to check the accuracy of their work. The primary purpose of this paper is to present some tabulated data of the more significant results of a sampling investigation undertaken during the last four years to obtain certain fundamental data on the variables connected with coal sampling and to point out that often assumptions have been made that are not in accordance with the facts. One of the standard sampling methods states:

Jan 1, 1936

By C. P. Proctor, J. B. Morrow

With numerous plans under consideration for coal classification, and with the advent of the Bituminous Coal Code, the intelligent sampling of coal has become increasingly important. To us it is rather significant that there have been very few fundamental studies of coal sampling in American technical literature since those of E. G. Bailey, which appeared in the Journal of Industrial and Engineering Chemistry in March, 1909. He covered the subject up to that time so thoroughly and in such an excellent manner that perhaps many other later students have felt that they could add very little to his findings. The recent studies of the British Engineering Standards Association have indicated the possibility of a somewhat different interpretation of Bailey's results, permitting the taking of smaller samples, and perhaps it will now be helpful to reopen this question. C. W. H. Holmes, in an informative series of articles on coal sampling recently published in Colliery Engineering, makes two rather interesting statements, as follows: It is scarcely surprising to find a lack of interest and knowledge regarding the sampling of coal not only in the mining industry itself but also among consumers of industrial fuel: at its best coal sampling is a dirty business, regarded as a nuisance and an expense by the commercial man, and usually as a nuisance and nothing else by the chemist. The writer can conceive only two classes of people who have never experienced any difficulty in obtaining representative samples of coal from wagons; those who have never tried to, and those who have never had the necessity or desire to check the accuracy of their work. The primary purpose of this paper is to present some tabulated data of the more significant results of a sampling investigation undertaken during the last four years to obtain certain fundamental data on the variables connected with coal sampling and to point out that often assumptions have been made that are not in accordance with the facts. One of the standard sampling methods states:

Jan 1, 1936

By R. B. Yerxa, C. F. Green, H. O. Hofman

MASSACHUSETTS INSTITUTE OF TECHNOLOGY, In refining copper, the metal is melted down in a reverbera tory furnace in a more or less oxidizing atmosphere and then further subjected to an oxidizing smelting in order to eliminate the common impurities, most of which have a stronger affinity for oxygen than has copper. In these operations some of the copper is oxidized to cuprous oxide and dissolved by the metal bath. When the quantity of dissolved cuprous oxide has reached about 6 per cent, the metal is said to have been brought to " set-copper." A button-sample will show a depressed surface and, when broken, a single bubble at the apex of the depression; the fracture will be brick-red and dull. It is essential to carry the oxidation to this point in order to know that the impurities have been oxidized as far as it is possible under the given working-conditions. Nearly all the cuprous oxide of the set-copper is now reduced to the metallic state by poling, when "tough-pitch" copper will be obtained. A button-sample will show a flat surface. Upon breaking, it will be found that the former bubble has disappeared and that the fracture has become rose-colored and shows a silky luster. The quantity of cuprous oxide allowed to remain in the copper will vary with the impurities still present in the metal and with the degree of pitch that it is desired to reach. It is essential for the general physical and the mechanical properties of the resulting copper that such impurities as arsenic, antimony, bismuth, lead shall be present in the oxidized state, as they are

Jan 1, 1904

By Paul M. Tyler

THE farmer pays the phosphate miner! Phosphorus is used in fireworks; goes to battle in military smoke screens, incendiary shells, and tracer bullets; and, in vermin destroying pastes, does its part in the war against insects. A lemon phosphate can be had for a nickel at most soda fountains, and tens of thousands of tons of phosphate rock are mined annually for use in the food industries, chiefly for making monocaleium phosphate baking powder. Sodium phosphate cleaning, washing, and scouring compounds consume substantial quantities: the iron and steel industries buy a few thousand tons yearly to make ferrophosphorus and to balance foundry-iron furnace charges; and even nonferrous metallurgists use a little for phosphor bronze and other alloys. Phosphoric acid, its salts, and diverse other derivatives of this versatile element have countless applications, and industrial outlets are increasing rapidly, especially in the United States. Nevertheless, in this country nearly 90 per cent and in the whole world fully 95 per cent of the phosphate rock consumed is absorbed ultimately in agriculture.

Jan 1, 1938

By John Griffen

THEORY HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as follows: 1 Nomenclature r represents, in a particle of irregular shape, the round-hole screen through which the particle would pass, or some other linear dimen¬sion of the particle equivalent to d, the diameter of a sphere. s, the specific gravity of the particle. 1, the specific gravity of the water used as a medium. K, a constant. W, the velocity of the water. In an Upward Current of Water 1. A particle will move upward if [W > KVr(s-1)] and, by suitably regulating the speed of the water current, the larger and heavier particles may be made to fall downward against the current, leaving the smaller, lighter particles in suspension in the current. 2. Particles such that [T1= s2-1] cannot be separated in an upward-current classifier with any one velocity of current. Coal particles having a specific gravity of 1.35 cannot be separated from refuse particles of 2.5 sp. gr. Unless 2.5-1 the ratio of diameters is less than [1.35-1 or 4.3 to 1,] and the raw coal must be screened to size limits within this ratio if they are to be separated. Cone¬-shaped vessels or vessels of other shapes that allow the use of&apos; different velocities of current at different points in the flow are used to modify this limitation. 3. During the initial stages of motion, coal particles ascend more rapidly than refuse particles of the same size. 4. A particle will ultimately fall if [W < KVr(s-1).] If particles of

Jan 1, 1950

By A. F. Crowley, D. W. G. White

AS part of a continuing program of liquid metals research, the densities of liquid lead, tin, zinc, cadmium, and indium have been measured by a pycnometric method. The pycnometers are made of high-density graphite to the design illustrated in Fig. l(a). In pursuing this research program, emphasis has been placed on detailed experimental care. As a result, claims are made for densities accurate to within ± 0.05 pct over temperature ranges varying from about 100° to 200°C above the melting point. A paper reporting the densities of tin, lead, and Pn-Sn alloys has recently been published,&apos; while papers dealing with

Jan 1, 1969

By Ernest A. Hersam

The advantages of the tri-axial diagram in representing the composition of slags and silicates are well appreciated by many metallurgists. Prof. H. M. Howe* has pointed out the application of a fourth variable, in connection with the diagram, and has called attention to the usefulness of the general systern of tri-axial representation. In the discussion of Prof. Howe&apos;s paper, Mr. Firmstone† indicated how certain distances could be measured directly by projection. Prof. R. H. Thurston,‡ as early as 1877, had made use of a typtic model and of triangular diagrams, with contour-lines, rekrresenting varying physical properties corresponding to varying chemical composition. Still earlier, Prof. J. Willard Gibbs§ had used the diagram in similar work; and other scientists were thought by him to have preceded him in its use. During the period of nearly a quarter-century, following these early publications, there has been an ever-increasing use of graphic methods in numerous branches of scientific work, stimulated, in part, by the possibility of representation by three co-ordinates upon plane-surfaces. Yet the number of possible co-ordinates for graphic representation has always been, and always must be, insufficient to express many facts which are shown mathematically; while, without graphic representation, the involved nature of mathematical expression often fails to facilitate and promote research. The coming into use, therefore, of the fourth co-ordinate, permitting representation by four variables, marks but the beginning of some lines of research which could not well advance without this aid.

Jan 1, 1902