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By R. A. Bergman, C. J. B. Fincham

THERMODYNAMIC properties of many high-temperature systems containing sulfur, such as slags, metal sulfides, and solutions of sulfur in liquid metals, have been studied by means of equilibration with known gas mixtures.'" This method presupposes a complete and accurate knowledge of the thermodynamic data for all possible components of the gas phase at high temperatures. However, a survey of the data available up to 1952 on the thermodynamics of gaseous sulfur species and compounds, by Richardson and Jeffes,' showed that there was considerable uncertainty in the values of the free energies of formation of S, SO, HS, and CS. In many cases, this uncertainty made it impossible to decide whether or not these species would form a significant proportion of the sulfur present in the gas phase in any given system. After the review by Richardson and Jeffes had been published, St. Pierre and Chipman6 measured, by an indirect method, the free energy of formation of SO. This also enabled a clear choice to be made among the three possible spectroscopic values for the dissociation energy of S2 into atoms10 thereby determining the free energy of formation of S from S2, and fixing the free energy of formation of HS more accurately" The main purpose of the present investigation was to measure the free energy of formation of CS, which was still in considerable doubt. For example, at 1600°C, it could be estimated to be +6 +25 kcal per mole,* most of the uncertainty being in the * Based on the dissociation energles of CS6 and S2,5 the heat of sublimation of graphite, and, the assumption that the entropy of formation of CS is the same as that of CO. value of the dissociation energy." A secondary purpose of the investigation was to determine more accurately the equilibrium sulfur pressures over dilute solutions of sulfur in carbon-saturated liquid iron. General Method Dilute solutions of sulfur in liquid iron, saturated with carbon, were brought to equilibrium at 1600" and 1800°C, with known gas mixtures consisting, initially, of A and CS2. After equilibrium had been reached, the melts were quenched and analyzed for sulfur. In the high temperature region of the furnace, an equilibrium was set up between the various possible sulfur species and compounds in the gas phase; namely, CS2, CS, S2, and S. (It can be calculated that the amounts of S6 and S, are negligible at these temperatures:) Morris and Bueh17 and Kitchener, Bockris, and Libermana had previously studied the corresponding

Jan 1, 1958

By William F. Ward

One often reads of the rich placer gravels in many of the citnoe-trav-elqd rivers of South America. The apparent richness of these gold-bearing gravels impresses the traveler, and in fact he may see batea after batea showing enough colors to figure over a dollar per cubic yard. These workings are called "playas" from the Spanish word playa, meaning shore or beach. Many workings have been reported in tropical rivers, but to my knowledge no dredge has made a success in such deposits. Investigation generally shows that the area of richness is limited and especially that the depth of the rich concentration is hardly ever more than a few inches. The Cauca river in Colombia, South America, is noted for its many rich playas. This river rises near .Popayan in the southern part of Colombia, flows north through a narrow valley between parallel mountain ranges and empties into the Magdalena river near Maganque. , The airline distance between source and mouth of this river is only about 500 miles. The rainfall is large and the lower Cauca appears to be about the size of the Missouri river in the United States. From its mouth up to Valdivia, in the State of Antioqua, it is navigable. Above Valdivia is a narrow gorge, above which the river is again navigable for some distance. The part of the Cauca where the play a panning is most noticeable is from Valdivia down to where the Nechi river enters the Cauca, a distance along the river of about 100 miles. The current in this part is swift, so that the stern-wheel river steamers make the trip with some difficulty. In the course of my work in this section of Colombia I have had the opportunity to make a study of several of these play a workings and will give in detail the conditions observed. The Island"Playa" The richest of the island playas is about 40 miles below Valdivia and a little below the old town of Caceres. The shape of the river and the location of the deposit are shown in Fig. 1, which indicates the condition at low water. The river at this place is about 600 ft. wide and the island about 75 ft. wide by 300 ft. long. The island is made up of coarse pebbles, some of which are as big as a man's head. In times of high water this island is under several feet of water and in a swift current. When the river lowers the current is still fast enough to prevent sand or silt from covering the coarse pebbles.

Jan 1, 1915

By Simon D. Strauss

INTRODUCTION The changes in ownership, management, and operation of the non-fuel minerals industry since the Second World War have been dramatic. World-leading enterprises have lost their identity; host countries have taken over operations from multi-national firms; marketing practices have been drastically altered - and yet the world industry is supplying minerals on a scale far greater than had been anticipated in projections made at mid-century. The world's known mineral resources have been enormously expanded, despite the doom sayers who for decades have been predicting that depletion of non-renewable resources would impose limits to growth. PALEY REPORT One can set the stage by reviewing how the minerals outlook was regarded in a thoughtful and comprehensive analysis made in the years 1950 and 1951. During the War years, President Harry Truman of the United States had come to appreciate the decisive role played by minerals resources through his chairmanship as a U.S Senator of a committee that investigated the procurement and allocation of natural resources. In 1950, in the Cold War era that resulted in actual military conflict in Korea, he appointed a prestigious five-man commission to study the problems of Materials Policy over the following quarter century. Their findings, published in five impressive volumes in early 1952, became known as the Paley report. The text was prepared by expert scientists and economists who spent 18 months assembling statistics, making projections of future demand, and interviewing leaders in industry, academia, and government. [ ] The Commission had correctly foreseen that aluminum would replace copper as the largest volume non-ferrous metal, but it had fallen short of reality by a wide margin indeed for all three materials. Even though the Commission's expectations for growth proved to be extremely understated, it had concluded its report with grave foreboding about the effect of its estimates of demand in relation to supply, as follows: "Consumption of almost all materials is expanding at compound rates and is thus pressing harder and harder against resources which, whatever else they may be doing, are not similarly expanding. This materials problem is thus not the kind of 'shortage' problem, local and transient, which in the past has found its solution in price changes which have brought supply and demand back into balance. The terms of the materials problem we face today are larger and more pervasive." With respect to some minerals, the Paley Report expressed scepticism that, in fact, supplies would be forthcoming regardless of price. Because the Paley demand forecasts understated the actual growth in demand for virtually every mineral, one could logically have expected frequent and protracted shortages in the years since 1950.

Jan 1, 1985

By J. Moore Samuel

THE CHAIRMAN (WALTER DOUGLAS, NEW YORK, N. Y.).-Perhaps there is no problem that causes the modern metallurgist more worry than the question of unaccounted for loss. He has not the advantage of the metallurgist of the early days here, who could sleep peaceably with the settled conviction that there were certain copper mineral constituents of the ore which were volatile, and there was therefore nothing to worry about. The slag contents and volatilization accounted for the balance of the copper that went in the top of the furnace after the weighing of the bullion. There have been great strides in recent years toward reducing this loss. Perhaps the Anaconda company is the one we have to thank for the original pioneer work along the lines which we are all today following. We would be glad to hear from some gentlemen present with reference to their experience with this question of dust losses. E. P. MATHEWSON, Anaconda, Mont.-You mentioned the Anaconda company, Mr. Chairman. I would like to say something about what we have been doing there, and the troubles we have been having. We have a tremendous volume of .gas to handle. We adopted the system of large chambers, lessening the velocity of gases, and incidentally cooling the gases. Unfortunately in one sense and fortunately in another, we were compelled to increase the amount of gas handled in the flue system, and the results were then not so good. Still, we get a very good recovery. Our system of taking a sample is similar to the one described by the writer of the paper. We have tried all kinds of apparatus for getting a fair sample. We divided the area of the flue into imaginary squares, and have taken samples for a certain period of time from each square; and have used the asbestos bags. At present, there is a large unit of the Cottrell apparatus almost ready to connect up on the roaster flue to catch the dust from flotation concentrates. The worst things smelters have to handle at the present clay, they are coming in the Southwest as well as the Northwest, are of material much of which is as small as 500 mesh, and the ordinary methods of catching dust will not apply to flotation concentrates. The Cottrell process is going to be tried out at our plant for this material. We have devised special forms, with a view to preventing the formation of dust from this material, and we are pleased with the results so far obtained. There is another point in connection with this subject that I want to put before the members here, so they will be thinking about it. You know there has been a great deal of litigation between the farmers

Jan 12, 1916

Jan 1, 1918

[ ]

Jan 1, 1938

[EXECUTIVE COMMITTEE OF THE BOARD OF DIRECTORS LOUIS S. CATES, Chairman DONALD H. NCLAUGHLIN, Vice-Chairman JOHN L. CHRISTIE JOHN R. SUMAN CLYDE E. WEED]

Jan 1, 1946

Jan 1, 1949

By H. M. Zoerb

Based on the belief that operating details are a definite contributing factor to major economies, this paper traces the development of crushing cavity design in Symons cone crushers to attain maximum liner utilization. Wear rates are analyzed and compared in this presentation and drawings illustrate succeeding design changes.

Jan 6, 1953

By Ernest L. Bohnet

Jan 1, 1985

Jan 1, 1947

Jan 1, 1899

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore-guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. The following question has been suggested for discussion: "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein.† Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line? In some multivein districts the line for any given vein may be approximated by simple interpolation or extrapolation. Where this is possiblc the bottoms of the lowest ore shoots in the various veins are points on an imaginary, gently rolling surface. The trace of this surface upon the vein is our critical line for that vein. The imaginary surface rolls so gently that it may be projected from two or more known veins to an unexplored vein near by. Here is a criterion for the bottoming of ore that has nothing to do with changes in the appearance of the vein in question; it rests solely on the depth at which the ore bottomed in adjacent veins. The method is not applicable in districts only slightly explored in depth, nor where the lower limit of the ore-bearing horizons

Jan 1, 1941

By Raymond Mancha

A test of any fan requires the determination of such data as fan pressure, air volume handled by the fan, and power input to the fen shaft. When testing operating mine fans of the centrifugal type, test methods have been employed, for the sake of convenience, that permit great latitude in detail of procedure resulting in wide variance in results by different investigators. Some controversial aspects of field fan testing are the result of past failure to define clearly the various forms of fan pressure and to a lack of understanding of the accurate procedure for the measurement thereof. Also, the anemometer for air-volume measurement, although convenient, if carelessly used and maintained is subject to a wide error range with variation in method of application and in instrument accuracy. The appearance of the axial-flow type of mine fan offers the possibility of refinements in field testing that were impractical with the centrifugal fan. First of all, the fan inlet and outlet are more sharply defined, giving closer agreement as to just where the fan begins and ends; thus there is less disagreement as to the proper location for measurements of fan pressure. The area of passage into the inlet of an axial-flow mine fan usually constricts, causing high air velocities with accompanying steadiness of flow. Thus the fan inlet offers an ideal location for accurate air-volume measurements with the pitot tube, the proper use of which is well established by code. Thereby the controversial aspects of such measurements are eliminated. Use of the Pitot tube also facilitates a more accurate measure of fan pressure, since the individual pressures measured can be properly weighted, as will be explained later. Determination of power input to the axial-flow mine fan operating in the field is subject to the same inaccuracies as with the centrifugal fan if the axial-flow fan is also belt driven. However, because of the higher rates of rotation usual with axial-flow fans, direct-driven units are more numerous and it is unnecessary to assume a drive efficiency, thus eliminating one possible source of error. It is the purpose of this paper to define and explain the various types of pressure measurements involved in a field test of an axial-flow mine fan, and to further explain the proper use of the Pitot tube when measuring pressures and volumes. DefinitioN of Fan Pressures The two fan pressures most commonly discussed are fan total and fan static pressure, each of which has the same meaning regardless of whether the fan is blowing, exhausting, or blowing and exhausting, as in the case of a fan with ducts connected to both outlet and inlet. Fan total presscre is the amount by which the total pressure of the air delivered by the fan exceeds the total pressure of the air received by the fan. This pressure is a measure of the maximum amount of the work done on the air by the fan that is available for external use.

Jan 1, 1942

By Ronald W. Klusman, Erik B. Nelson

The Front Range portion of the Colorado Mineral Belt is an extensive area of mineralization with mining activity dating from 1859 with the discovery of large gold deposits. After an initial boom period and gradual diminishing production, present activity is restricted to molybdenum in Clear Creek County, uranium in Jefferson County, and several small operations extracting gold and silver in Clear Creek and Gilpin Counties. Gold and silver have dominated the production in the Front Range, though the complex mineralization created milling and smelting problems and it is postulated that considerable amounts of precious metals remain in the mine dumps. This area is plagued by a severe mine drainage problem, with Clear Creek most impacted by many draining mines and tailings in the basin. Boyles et al. Moran and Wentz, Wentz, Wildeman et al., have examined various aspects of the impact of mine drain¬age in the Clear Creek basin. The primary objective of this study was to collect data on the tailings, drainages, and leaching experiments in order to make preliminary suggestions for reducing the impact while recovering metal values to offset treatment costs. A variety of leaching experiments were performed on tailings from the Nevada Gulch area in the Central City mining district. Leachings were performed in vertical tubes indoors and wooden boxes exposed to the outside environment. In the leaching experiments, the leaching solution, grain size, and residence times were varied, while forced aeration was used in some experiments. Bacterial nutrient 9K° and mine drainage were used in some of the experiments. A total of 14 additional tailings samples were analyzed for base and precious metals. The composition of the mine drainage and tailings used in the leaching experiments, as well as data on the additional samples are shown in [Table 1]. Leachate samples were taken periodically for analysis until compositions leveled off. Results and Discussion Leaching with distilled water was used as a control and best illustrates the basic behavior of the leaching process for zinc in a vertical tube [(Fig. 1)]. More acidic leachings increased concentrations of metals as did smaller grain sizes, though the time required increased significantly. Mine drainage with its high concentration of dissolved iron sometimes decreased the heavy-metal concentration in the leachate due to oxidation of Fe 2 and precipitation of Fe(OH)9 which absorbs some of the dissolved heavy metals. In the larger scale experiment carried out in the simulated leaching pad, substantial concentrations of metals were attained in the final leachate after one month. In this experiment the leachate was not recycled, but allowed to saturate the tailings continually with evaporation loss made up by additions of Quartz Hill drainage and nutrient 9K. The concentration of the metals in the leachate and the increase over the input solution are given in [Table 2]. Heap leaching of low-grade copper and uranium ores is successfully carried out in many districts, enhanced by the metabolism of autotrophic bacteria of the Thiobacillus-Ferrobacillus group. These ubiquitous organisms enhance metal leaching, and general aspects of heap leaching are discussed by Malouf, Trudinger, Pings, and Duncan et al. Conclusions and Recommendations Returning to the primary objective, how to reduce the mine drainage impact and recover metal values, we need to consider how the data may suggest avenues toward this objective. Boyles, et al., considered various

Jan 1, 1977

By H. V. Winchell

It seems to me that uniformity of mining law in North America must of necessity start with uniformity in each country. I understand that the Provinces of Canada have the right to make their own individual laws and conditions, to prescribe the terms under which the prospector or the applicant for mineral titles may secure the same. That is not true of the states in the United States. In this country, the Federal Mining Law was made applicable to the public domain, which, at the time of the adoption of this Act in 1872, was chiefly west of the Missouri River; it is impossible to locate a mining claim in most of our eastern states. It is true, however, that there are certain holdover rights, mostly obsolete, arising from the fact that at the time of the formation of the Confederation of States, the land that belonged to each state became the property of the Federal Government. I am not quite correc-t in that, it was sometime after the adoption of our Constitution, I think it was 1778, but those rights were largely, by agreement, surrendered to the Federal Government; but it is a fact that the great acquisitions of territory in the West, with the single exception of Texas, were of domain that came into the possession of the Federal Government and our Federal Mining Law applies to that territory. No state has the right to (by legislative enactment) enlarge upon the rights given by the Federal Mining Law, governing the acquisition of mining claims in its territory, within its boundaries. Each state, however, may, and some of them do, limit somewhat the rights given to the prospector. For instance, the Federal Mining Law provides that a claim may be taken, staked upon the public domain, of 600 ft. in width and 1500 ft. in length. Some of the states, like South Dakota and Colorado, have at times said "that is an excessive amount of land for a single mining claim; we will therefore limit it to 300 ft. or 200 ft. in width." There is, therefore, not any direct and immediate need for uniformity of mining laws in the United States, such as there might possibly be if it were considered at all desirable upon the whole in Canada. The initiation of mining rights under the Federal Mining Act is the act of discovery of valuable mineral in place, referring now to the lode mining claims, but the same is true of the placer claim. It is true that the emphasis has never been laid upon the word valuable and that

Jan 1, 1920

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore-guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. The following question has been suggested for discussion: "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein.† Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line? In some multivein districts the line for any given vein may be approximated by simple interpolation or extrapolation. Where this is possiblc the bottoms of the lowest ore shoots in the various veins are points on an imaginary, gently rolling surface. The trace of this surface upon the vein is our critical line for that vein. The imaginary surface rolls so gently that it may be projected from two or more known veins to an unexplored vein near by. Here is a criterion for the bottoming of ore that has nothing to do with changes in the appearance of the vein in question; it rests solely on the depth at which the ore bottomed in adjacent veins. The method is not applicable in districts only slightly explored in depth, nor where the lower limit of the ore-bearing horizons

Jan 1, 1941

By H. G. Dwyer

CONSIDERATION for future expansion influenced the design of the new smelter at Chuquicamata. The section of the smelter now going into operation, while large, represents only little more than half of the ultimate plant. Equipment for the direct smelting of raw concentrates has been arranged in the conventional manner although needless details have been eliminated wherever possible while mechanical and electrical features not usually found in copper smelters have been incorporated. Access is afforded to all equipment but platforms and walkways have been held to a minimum. The poling and other platforms in the converter aisle, normally subjected to battering by ladles and other heavy equipment in transit, are of concrete construction with steel grid armor embedded in the exposed surfaces. Noticeably absent are the many platforms formerly required for the handling of converter flux since this material is charged to the converters through the side walls of the converter uptake hoods. Clear space with ample headroom is provided under each converter and converter puncher's platform to permit clean-up by small bulldozers. Remote controls have been introduced at many points. Electrical control rooms and control centers have been conveniently located. An electrical tunnel with cross tunnels and escapeways is situated under the entire length of the converter aisle for power feed lines. Skull breaking facilities are in a separate building near the smelter. A silica-slurry building with brick storage area is adjacent to the smelter building so that elevator service is available to both buildings. A smelter office, a change house and lunchroom are provided in convenient locations. Units of the smelter as presently constructed are shown in the plan and table on page 1194. The ultimate smelter will house 7 reverberatory furnaces, 14 waste-heat boilers, 9 Peirce Smith converters, 4 casting furnaces serving 2 casting wheels, and one holding furnace serving a straightline casting machine. Additional crane requirements in the converter aisle will necessitate the installation of special hoisting equipment in space already provided in a raised section of the roof over the casting end of the aisle. Thus a complete crane may be lifted high enough above the crane rails to permit the passing of another crane underneath thereby giving all cranes full use of repair facilities already installed. For the collection of gases, 2 dust chambers, each with separate stacks, will collect converter gases and 2 balloon flues with separate stacks will collect reverberatory furnace gases. Extensions necessary to complete the ultimate plant will be possible with little interruption to normal operations since the future converters and reverberatory furnaces will be added at the east end while additional casting facilities will be added at the west end of the present plant. The future units may be added singly or all at one time depending on requirements.

Jan 1, 1952

By Raymond Mancha

A test of any fan requires the determination of such data as fan pressure, air volume handled by the fan, and power input to the fen shaft. When testing operating mine fans of the centrifugal type, test methods have been employed, for the sake of convenience, that permit great latitude in detail of procedure resulting in wide variance in results by different investigators. Some controversial aspects of field fan testing are the result of past failure to define clearly the various forms of fan pressure and to a lack of understanding of the accurate procedure for the measurement thereof. Also, the anemometer for air-volume measurement, although convenient, if carelessly used and maintained is subject to a wide error range with variation in method of application and in instrument accuracy. The appearance of the axial-flow type of mine fan offers the possibility of refinements in field testing that were impractical with the centrifugal fan. First of all, the fan inlet and outlet are more sharply defined, giving closer agreement as to just where the fan begins and ends; thus there is less disagreement as to the proper location for measurements of fan pressure. The area of passage into the inlet of an axial-flow mine fan usually constricts, causing high air velocities with accompanying steadiness of flow. Thus the fan inlet offers an ideal location for accurate air-volume measurements with the pitot tube, the proper use of which is well established by code. Thereby the controversial aspects of such measurements are eliminated. Use of the Pitot tube also facilitates a more accurate measure of fan pressure, since the individual pressures measured can be properly weighted, as will be explained later. Determination of power input to the axial-flow mine fan operating in the field is subject to the same inaccuracies as with the centrifugal fan if the axial-flow fan is also belt driven. However, because of the higher rates of rotation usual with axial-flow fans, direct-driven units are more numerous and it is unnecessary to assume a drive efficiency, thus eliminating one possible source of error. It is the purpose of this paper to define and explain the various types of pressure measurements involved in a field test of an axial-flow mine fan, and to further explain the proper use of the Pitot tube when measuring pressures and volumes. DefinitioN of Fan Pressures The two fan pressures most commonly discussed are fan total and fan static pressure, each of which has the same meaning regardless of whether the fan is blowing, exhausting, or blowing and exhausting, as in the case of a fan with ducts connected to both outlet and inlet. Fan total presscre is the amount by which the total pressure of the air delivered by the fan exceeds the total pressure of the air received by the fan. This pressure is a measure of the maximum amount of the work done on the air by the fan that is available for external use.

Jan 1, 1942

By T. T. Read

A short time ago, one of the large steel companies courteously furnished the author with detailed records of the operations of a considerable number of iron blast furnaces over a period of two months. These will be made the basis of a subsequent study, but in beginning this study one of the first points requiring consideration was the probable error of the records, for what otherwise might be regarded as significant differences of performance under different conditions were perhaps really due to errors of observation, or failure to observe and record variations. If it is assumed, in blast-furnace records and calculations, that known quantities or factors are constant, .when as a matter of fact they are variable, the effects of these variations may erroneously be ascribed to some other cause. This is quite clearly expressed in the following quotation from E. Buckingham:l Theory always operates on an ideally simplified picture of reality because real phenomena are unmanageably complicated. The results obtained are not exactly true for any real phenomenon, though they may be for an ideal one; and the approxi-mation with which a theoretical equation, however obtained, represents the actual facts, always depends on the approximation in essentials between the ideal picture and its real prototype. The purpose of dimensional reasoning is to find out how some quantity which is involved in the phenomenon under consideration is related to certain others; or to find the relation connecting two or more quantities which vary, or may vary, simultaneously during the course of the phenomenon. Since we know that we must have a complete equation to start with, we begin by thinking the matter over, to see whether the quantities we have in mind are the only ones involved. Usually it is evident that they are not; so we next make a list of all the quantities we can think of which might under any circumstances be important. Upon considering this list, which is often a long one, it is usually evident that under the actual circumstances a number of these quantities may safely be ignored; so we cross them off the list and thus pass from our most general conception of the phenomenon to an ideal simpler one, in which these quantities are not involved at all.

Jan 1, 1926