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By G. B. Gould

EVERY mathematical statement of a measure of anything (as distin-guished from a count) is followed by a qualification always implied if not explicity stated--that the statement is only an estimate, which may vary from absolute accuracy within certain limits, according to the accu-racy of the measuring instrument. This basic fact, so obvious to engineers, is not so well understood by many that make use of laboratory coal tests. The tolerances that must be allowed in measurements of coal quality are very important in both their commercial and engineering applica-tions-and the significance of these tolerances depends upon the use made of the laboratory coal test. Only in recent years has there been any intensive study of this ques-tion of tolerances as applied to measurements of coal quality. There is very little in our published literature on the subject, and what has been published is not, readily comprehended by those who sell coal, or buy coal and use it, unless they happen to have made a study of the subject them-selves. There is great need for more widespread understanding of what has been discovered and how it applies to the use of laboratory coal tests. What follows is an attempt to condense into a few pages the results of the major investigations so far reported, and to explain their meaning in simple nontechnical language, with the addition of some recent illustrative experiments.

Jan 1, 1937

By Frederic Dewey

BONE-ASH cupels have been used from time immemorial to absorb litharge, and accompanying oxides; in assaying. Doubtless, also, from the earliest days cupels have been most unjustly blamed for much poor assaying. It has long been known that the precious metals go with the litharge into the cupel. This occasions a loss of precious metals and reduces the results of the assay. There have been many investigations of cupels and the most diverse views have been expressed, the extremes being the statements of Lodge 1 that every cupel has some effect upon the loss in assaying telluride ores and of the Campredons2 that coarse and fine and hard and soft cupels all give the same loss of silver when cupelling the same weights. The truth lies between these statements and much nearer the latter. In a vast majority of cases the influence of the cupel is not dominant and is outweighed by other conditions, particularly the temperature of the cupelling bead. At the Spokane meeting of the Institute I presented a paper on the Assay and Valuation of Gold Bullion,3 which recorded the results of many hundreds of assays made in the Mint service under everyday commercial conditions, which of necessity differ from scientific conditions. In following this matter up, for the purpose of increasing the accuracy of our commercial methods of bullion assays, the question of the absorption of gold by the cupel was found to be a most important one and was taken up for investigation. In a lesser degree, the silver absorption is important and interesting, but at present it appears to be far more complicated and, while many figures showing silver absorption may be found through this paper, much further investigation is required to put the subject upon a satisfactory basis.

Jan 11, 1917

By Dr. O’Neil Thomas J., Donald W. Gentry

"We should be concerned about the future be- cause we will have to spend the rest of our lives there. " -Charles Kettering INTRODUCTION Since the early 1970s, there has been no economic phenomenon that has been more widely discussed or experienced in the United States than inflation. Al- though its precise definition and measurement are elusive, inflation has had pro- found and extensive impacts on the manner in which nearly everyone lives. It is painfully obvious to consumers that inflation is characterized by a continuing up- ward spiral of prices. In a capital-intensive industry like mining, those increases can be positively breathtaking. An interesting example is shown in Table 1. Table I shows that on a unit basis, the equivalent 1980 capital cost of Cuajone was over six times the cost of the adjacent and quite similar Toquepala operation completed in 1959. Such sobering statistics weigh heavily on the minds of executives who are contemplating major investments in new mining facilities. In spite of its monumental presence, inflation has usually been either inadequately covered or totally ignored in textbooks on engineering economy. The reasons for this are not entirely clear, but a contributing factor is the inherent difficulty in accurately predicting inflation. However, under certain conditions, inflation may become the most important factor in a mining investment, and it can rarely be safely ignored in capital investment analyses. DEFINING AND MEASURING INFLATION Defining inflation and related terms is relatively easy. Its measurement, how- ever, is the source of almost endless debate in economic and political circles. How- ever, much of that debate is not relevant to the scope of this book, so that only those issues which impact directly on the capital investment decision are covered in this section. Inflation is the general decline in the value of money as measured by what it will buy. It is clear, then, that the rate of inflation varies with the particular currency under consideration as well as the type of goods and services being purchased. One would find, for example, that the general rate of inflation relative to German marks

Jan 1, 1984

By Bernard York, John J. Reed

Mine opening stability was investigated by loading model openings to failure. Eight-inch plaster blocks were cast with small uniform section openings passing through the centers. After curing, the models were jacketed and loaded hydrostatically in a closed vessel. Opening size, shape, and orientation were varied to determine how these factors influence opening stability. THE investigation described in this paper is a continuation of a project begun in 1946 by Bernard York and W. E. Bush. .The experimental method used in the investigation involves the hydrostatic loading of a model mine opening to failure. Most investigators agree that this loading closely approaches actual conditions in very deep mines. The conditions are further idealized by using an essentially isotropic model material. The experiments consist of casting 8-in. plaster cubes, or 8-in. diam cylinders 8-in. long, having a relatively small uniform section hole passing through their centers. After thorough drying, the models are jacketed in a flexible plastic bag and loaded hydrostatically with water in a closed vessel. At about 300 to 500 lb per sq in. pressure the central opening fails. The fracture pattern resulting from opening failure is studied in a plane normal to the longitudinal axis of the opening. The model block is sawed through its center after loading to expose this plane and to eliminate the possibility of end effect. By changing

Jan 1, 1954

By Ralph E. Davis, Lyon F. Terry

The rapid expansion of the natural gas industry in this country during the past three or four years has necessitated the construction of a number of long and comparatively large diameter high-pressure pipe lines This period of expansion and construction is still at high tide, and the current year will doubtless surpass all prior years in mileage and capacity of gas line installation. The fundamental economics of the business of long-distsrier transportation of natural gas may be briefly and simply stated, although most careful consideration must be given the actual determination and integration of the several more important factors which determine the ultimate success or failure of such a project. Reduced to its simplest form, a sound natural gas transportation project requires: 1. A competent source of gas, where the combination of quantity of gas available, cost of production, and longevity meet the given requirements. 2. A market, reasonably certain to endure in the face of any probable competition, of satisfactory size and price, and having a sufficiently favorable load factor. 3. A cost of installation of pipe line systen and an operating cost such as will, with honest and reasonably efficient management, afford a net operating return sufficient to attract the necessary capital required. In a11 new projects of this kind it is necessary that thehe three cssentials to ultimate success be assured. Hence the necessity of competent surveys of gas supply, and of market, both industrial and domestic. The prudent engineer will allow for "factors of safety" in reaching his conclusions just as he would in the design of a bridge. This paper deals primarily with but one of the major considerations enumerated above, I. e, the economic design of the pipe line system. The "pipe line system" will be considered to include (1) the pipe Iine, and (2) a series of compressor plants along the pipe line for maintaining

Jan 1, 1929

Jan 1, 1940

By John E. Dorn, Oscar E. Harder

The phenomenon of diffusion, according to the most prevalent conceptions at the present time, undoubtedly played an important part in the formation and distribution of metals and minerals in the earth's crust. Apparently there is good evidence that in the geological rate of cooling diffusion caused numerous materials to separate into individual masses or into duplex structures. As is well known, the early steels were made by cementation; that is, by heating wrought ferrous metal in contact with carburizing materials so as to produce a relatively high carbon content on the surface. If the process was continued long enough, the carbon diffused throughout the piece. A more homogeneous product depended upon further heating and forging, so that the carbon diffused to a fairly uniform concentration throughout the metal. In the modern metallurgical industry, diffusion is the basis for many operations; for example, the production of hard surfaces on steels by carburizing, nitriding, cementing with chromium, silicon, boron and beryllium. Castings or ingots as they solidify do not have homogeneous structures, but these structures are made largely homogeneous by suitable process of heat-treating and the resulting diffusion. It is in modern physical metallurgy, however, that we become greatly concerned about the mechanism of the phenomenon of diffusion. The rates of diffusion, effect of temperature and time on diffusion, and the relation of diffusion to the many properties of the parent metal and the diffusing metal have become important; also, we are concerned with the diffusion of a single metal into a complex alloy. For example, what is the mechanism whereby carbon and nitrogen travel into steel? What is the effect of alloying elements in the ferrous material on the rates of diffusions? What is the effect of simultaneous diffusion of carbon and nitrogen? How does chromium, beryllium, boron, or the like, diffuse into the steel, and what are the effects of alloying elements in the steel previous to the cementation process? These inquiries are by no means limited

Jan 1, 1938

By Oswald J. Heinrich

During the last twenty years much has been done to investigate and define the Mesozoic formatibn of the United States along the Atlantic States, as well as in' the Territories. The investigations of Professors Hitchcock, Emmons, Hayden, H. D. Rogers, and those now in progress in connection with the geologicd surveys of Penn-

Jan 1, 1879

By T. A. Wright

The sampling of waste materials containing copper, lead and tin has taken on a new significance within recent years, and is of increasing importance, on account of the entry of some of the copper refineries into this field and the tendency towards consolidations among the smelters. In the past, such material was sold on the basis either of a rough or grat) sample or of casual inspection of the lot. The two principal sources of this waste are the processes of fabrication and the scrapping of automobile, electrical, plumbing, railroad and other equipment. In both cases rnuch material can bc sorted, salvaged and sold by classification and grade to be melted "as is" or with the addition of new or virgin metal. The increasing care in classifying exercised in the large manufacturing plants tends to incrcase the proportion of this usable scrap; on the contrary, the increasing use of more complex and special non-ferrous alloys tends to makc sorting and grading more difficnlt in turnings, borings, clippings, etc., and conseqllcntly is making sampling of more moment. In tin, lead, alumiinum, and zinc furnace by-products such as ashes, drosses, skimmings, etc., the trade practice of evaluation has not varied much. For instance, tin drosscs, battery lcad, and aluminunl skimmings are ordinarily sold on what is called "metallic button" or "metallic recovery" or "metallic yield." Coppcr and Icad wastcl, howcvcr, is being sold more and more on actual copper and lead contents bascd on sarrlple and chemical analysts. This paper will be dcvotctl chiefly to the sampling of niaterials suitablc only for refining and recovery of one or more of the metals present. The methods described are often bascd on thc fact that but one, metal, such as copper, is to be paid for. The loss of volatile constituents in melting does not appreciably affect thc final copper result, as the "after-melting" assay can be readily calculated to the "bcfore-nltltingl' basis, but if smelter efficiency continues to increase, so that in tiltie zinc, for instance, may be rccovrred on a paying basis, thc method of sampling dirty brass, for example, will have to bc changed also. As a matter of fact, we may cxpect that improved refining proresses will make possible the partial reeovrry of lcad and tin which are now lost

By Oscar E. Harder, John E. Dorn

The phenomenon of diffusion, according to the most prevalent conceptions at the present time, undoubtedly played an important part in the formation and distribution of metals and minerals in the earth's crust. Apparently there is good evidence that in the geological rate of cooling diffusion caused numerous materials to separate into individual masses or into duplex structures. As is well known, the early steels were made by cementation; that is, by heating wrought ferrous metal in contact with carburizing materials so as to produce a relatively high carbon content on the surface. If the process was continued long enough, the carbon diffused throughout the piece. A more homogeneous product depended upon further heating and forging, so that the carbon diffused to a fairly uniform concentration throughout the metal. In the modern metallurgical industry, diffusion is the basis for many operations; for example, the production of hard surfaces on steels by carburizing, nitriding, cementing with chromium, silicon, boron and beryllium. Castings or ingots as they solidify do not have homogeneous structures, but these structures are made largely homogeneous by suitable process of heat-treating and the resulting diffusion. It is in modern physical metallurgy, however, that we become greatly concerned about the mechanism of the phenomenon of diffusion. The rates of diffusion, effect of temperature and time on diffusion, and the relation of diffusion to the many properties of the parent metal and the diffusing metal have become important; also, we are concerned with the diffusion of a single metal into a complex alloy. For example, what is the mechanism whereby carbon and nitrogen travel into steel? What is the effect of alloying elements in the ferrous material on the rates of diffusions? What is the effect of simultaneous diffusion of carbon and nitrogen? How does chromium, beryllium, boron, or the like, diffuse into the steel, and what are the effects of alloying elements in the steel previous to the cementation process? These inquiries are by no means limited

Jan 1, 1938

By George H. Eldridge

The existence of phosphate of lime within the State of Florida has been known for over a decade; but until the spring of 1887, the extent and value of its deposit.;, possibly with one exception, were unsuspected. In that year Col. T. S. Moorehead, induced by a statement made by Mr. J. F. Le Baron, examined the gravels of the Peace river, recognized the importance of the deposits, acquired such tracts as were regarded as desirable, and established the pebble-phosphate industry, making his first shipment in May, 1888, to the Scott Manufacturing Company, of Atlanta, Ga. The establishment of the pebble-phosphate industry upon Peace river was followed, a year later, by the discovery in Marion county of an entirely different class of phosphate, now commonly known as hard-rock phosphate. This discovery was made early in June, 1889, by Mr. Albertus Voght, in a well which he was sinking upon his place near the site of the present town of Donnellon, about 20 miles southwest of Ocala. To it, more than to any other cause, is due the rapid and remarkable development of the present great industry of the State. It was, however, Mr. John F. Dunn, of Ocala, who turned to advantage the accidental discovery of Mr. Voght. After acquiring a knowledge as to the chemical composition and value of the material, Mr. Dunn and hid associates purchased several thousand acres of land and organized the Dunnellon Phosphate Company for active operations. From Dunnellon as a center, prospecting rapidly extended in all directions, until at the present day important mines have been opened over a well-defined tract more than 200 miles long and about 6 miles wide. This tract lies par-

Jan 1, 1893

This paper "On Coal" was published in three issues of The Western Gleaner in 1814. Name of author is not given. This magazine was started by Cramer, Spear & Eichbaum, in Pittsburgh, Pa., in December 1813, and ran for about two years. Copies are very rare, and this one is made from an original in the Darlington Library, University of Pittsburgh. This is almost certainly the first general article on coal published west of the Allegheny Mountains, and one of the earliest in this country. ON COAL Its Natural History-Mining of Coal-Phenomena occasioned by Fire-damp-Method of Coking-Distillation of Tar from Pit-coal-Gas-light-Coal, a Manure I. NATURAL HISTORY OF COAL There are few productions of nature which present to the philosopher a wider field of investigation than pit-coal. A substance highly inflammable is found in the deep recesses of the earth, sometimes loaded with numerous superincumbent strata of hard rock, and extending frequently along with these strata through a vast expanse of territory. Though metals may be said to be inflammable substances, as they combine more or less rapidly with oxygen when placed under particular circumstances, yet the character of rapid combustion with disengagement of light and heat, seems to belong. principally to such substances as are derived either from the animal or vegetable kingdom. That this is probably the case with regard to coal we are further induced to believe, by the remarkable circumstance, that the chemical analysis of this natural production yields especially, though in various proportions, those materials which constitute essentially the vegetable. And if any thing was wanting to confirm, us in that opinion we might trace in a number of fossile substances the gradual transition of the vegetable into the state of mineral coal. This fact is so intimately connected with the natural history of coal, that we cannot think it superfluous to give it some farther development. Among the great number of principles which the chemist is capable of tracing in the vegetable kingdom, the presence of extract, resin and fibre seem to form the characteristical marks of plants.-If vegetable matter be boiled in water, and the water, after having been strained and filtered, be exposed for some time to the open air, a flocculent precipitate takes `place from every part of the liquor; which soon subsides to the bottom of the vessel containing it. This is the extract; altered, indeed, by exposure, and now no longer soluble in water, a change which is supposed to depend on the absorption of oxygen; and if, by any means the proportion of oxygen be increased, the extract gradually becomes of a darker color, blackens, and approaches to the state of charred wood.

Jan 1, 1942

By T. Egleston

THE ores of mercury of North California are composed of metallic mercury and cinnabar. They are found in serpentine, and are very often associated with chalcedony, in masses more or less irregular, often concentrated enough, however, to furnish ores yielding from three to ten per cent., and sometimes richer. This deposit makes its appearance in Vallejo where it has been worked. North of here the mines are more developed. Most of the quicksilver mines, how¬ever, are situated in Sonoma and Napa Counties. On its outcrop the serpentine rocks have become decomposed, and have often been washed away to a considerable depth, so that in many cases in their neighborhood, what is apparently nothing but ordinary dirt, will frequently contain from two to three per cent. of metallic mercury, with but a trace of cinnabar, in which case, as at the Sonoma mine, it is made up into adobes and distilled. Such material does not require to be mixed with dirt to be made into adobes. Very often, also, the outcrop of the rock, where it is not decomposed, is filled with metallic mercury, so that by striking a pick into it, as at the Rattle-snake mine, a pound or more of mercury at a time will sometimes spurt out. Such rock as this is found in several localities in every stage of impregnation, and usually makes very rich ore. There is generally, however, very little of it, and it is found only in the first workings ; the ore in depth is always cinnabar. At the Rattlesnake mine near Pine Flat, where large quantities of metallic mercury are found, the rock contains so much petroleum that it has been necessary to make special arrangements to burn the carbides of hydrogen, since the distillation of the petroleum causes an extra quantity of poor soot to be formed in the condensation-chambers. At the Geysers the ore is associated with large quantities of sulphur and gypsum, so that in a hand specimen there is often more sulphur than cinnabar, which is a serious impediment to working, especially for the modern style of furnace with iron condensers, and causes so much soot to be formed that it has been known to penetrate as far as the blower, and to so completely clog it as to prevent its revolution. The ore coming from the mine is more or less hand-picked. In one or two cases attempts have been made to treat the poorest, and especially the very fine ores, mechanically as at the California works.

Jan 1, 1875

By J. M. W. Mackenzie

A microelectrophoresis technique has been used to measure the zeta potential of quartz over a range of pH and ferric iron concentration. The results have been discussed in terms of the adsorption of ferric cations and ferric hydroxide to the quartz surface. Possible relationships between the experimental results and the flotation of quartz have been examined. The adsorption of multivalent cations at the surface of quartz has been studied by many investigators who have used a variety of experimental techniques ranging from streaming potential 1 to radiometric2 measurements. Two possible mechanisms of cation activation of quartz have emerged from the results of these investigations viz: the adsorption of the cation to the negatively charged quartz surface, followed by adsorption of the collector anion to the adsorbed cation site, or: formation of a cation-collector complex which is then adsorbed to the quartz surface. In many natural and industrial systems one of the most prevalent activating species for quartz is ferric iron, this is especially so in the acid-circuit, anionic flotation of iron ore. The adsorption of ferric iron to the quartz surface is complicated by the ability of ferric iron to form complexes with anions, a phenomena which is of minor importance in one of the most widely studied quartz activation processes, ca ++ activation.* *The pK value for [ca(oH)+]/ [ca2+] [oh-] is 1.46 indicating that the influence of Ca (OH)+ ions will be minor in all but strongly alkaline solutions. In order to obtain a better understanding of quartz activation by ferric iron the zeta potential of quartz in the presence of ferric iron has been measured over a range of pH and ferric iron concentration. EXPERIMENTAL METHODS Materials: Selected samples of "rock clystal" quartz from New England, N.S.W., were ground in a pebble mill, washed for three hours in boiling concentrated hydrochloric acid, washed in hot chromic acid and then washed repeatedly with distilled water until the washing water gave no trace of chloride ion.

Jan 1, 1967

By John W. Cahn

The spinodal has long been regarded as a limit beyond which a homogeneous phase could no longer be metastable. But only recently has it become apparent that a phase beyond the spinodal would decompose by simple diffusional clustering mechanism quite different from the nucleation and growth mechanisms encountered for metastable phases. The theory of spinodal decomposition, which is based on the diffusion equation modified by thermodynamic requirements , is phenomenological, and each parameter can be measured by independent thermodynamic or diffusion experiments. The details of the theory have been carefully verified in a number of simple systems. It appears that the spinodal mechanism is commonly encountered in clustering reactions in solids and glasses. HISTORICAL INTRODUCTION The understanding of the earliest stages of precipitation in alloys has been the subject of three prior Institute of Metals Lectures. In 1932 Paul ~erica' reviewed the puzzling evidence that hardening of duralumin is completed before precipitation of CuAlz takes place and suggested that hardening occurs when the copper atoms "assemble in random groups on lattice positions of the duralumin, not of the CuAlz lattice". He called these random groups knots. This modification of his dispersion hardening theory seemed to fit all the facts, but Merica worried that the required diffusion "is just the reverse of what we deem normal; although quite spontaneous, it proceeds uphill, if you please". The reality of Merica's knots was quickly confirmed by Guinier's' and preston's3 X-ray work and these knots are today known as G.P. zones in their honor. Theoretical justification for uphill diffusion was also quickly provided by Becker and Dehlinger~ who noted that the diffusion coefficient could be negative in certain regions of phase diagrams. The boundaries of such regions could be described by a 90-year-old thermodynamic concept first described by ~ibbs' in 1877 as a limit of metastability for fluid phases, which by 1890 had received the name spinodal (see Appendix A). Spinodal in fluids is as old as nucleation theory. Both appear for the first time in the same paper by Gibbs who called the spinodal the limit of metastability. For the first 50 years, nucleation theory was forgotten and the spinodal was extensively treated in every good thermodynamics textbook.81Q The idea was simple and logical and it was accepted as part of a rigorous thermodynamic development of metastable phases, and for a while it was extensively investigated theoretically.

Jan 1, 1969

By J. R. Thoenen

THE consensus of opinion in the published literature on. Grecian magnesite is that it has been formed by alteration of the serpentine, which in turn was itself a product, of metamorphism from the original olivine intrusion. The general opinion seems to be that the magnesite was formed by descending waters heavily charged with CO2. Inasmuch as this opinion is held by engineers far better qualified than I to speak authoritatively on this subject, I hesitate to dispute that theory. However, certain occurrences coming under my observation do not, to me at least, seem to-entirely substantiate this theory. LOCATION Most of the Grecian magnesite comes from the Island of Euboea, although more recently some deposits have been opened on the mainland near the City of Saloniki, which prior to the war was Turkish. The island, comprising a state or province in the Greek political structure, is roughly 110 miles long and varies from 10 to 30 miles in width. It lies off the east coast of the Greek peninsula in the AEgean Sea with its long axis extending in a northwest-southeast direction. It is separated from the mainland by a long narrow arm of the sea known as the Atalanti Canal. Chalkis (Halkis), the capital on the west coast of the island, is the northern terminus of a branch of the state-owned railway and is connected with the mainland by a single-span, movable, highway bridge, roughly 150 ft. long.

Jan 1, 1928

amounted to about 2000 metric tons. The total output is increasing from year to year. Marine salt is now produced in Haiti in quantity sufficient to supply nearly all the requirements of this Republic, so production tax is now collected. Central America Guatemala-The major production of salt in Guatemala is solar salt derived from sea water, but the Indian population prefers salt derived by boiling coastal marine earth. Salt is taxed by the Government. The industry has been beset by controversies in recent years, especially following the revolution of October 1944. The Government issued a decree in August 1940 designed to control production and price of salt. The creation of a salt consortium was provided for and marketing was to be governed by production quotas. It is understood that the Government pool was later dissolved and the industry is now under older laws whereby production and sales have no limits. South America Panama-Output of salt in Panama in a very recent year was 11,000 net tons of solar-evaporated sea salt. A Government bank is in charge of output and distribution of the product. Colombia-Rock-salt deposits are known in five places-Zipaquira, Nemocon, and Sesquile, in the Department of Cundinamarca, the Cumural y Upin near Restrepo, and San Miguel y Barital, near Medina in Meta Intendency. The latter deposit never has been worked on account of its inaccessibility. Saline springs are worked in four locations. The largest producer among marine salinas is Manare but it is now planned to make Bahia Honda the largest. Some evaporated salt is made in vacuum pans. The deposits at Zipaquira, Nemocon, and Sesquile are believed to occur in the domal type of deposit. All the salt resources are under Government control. Venezuela-The salt industry in Venezuela is under Government control and is taxed. Taxes in recent years, however, have been reduced for salt used in curing hides and salting meats, fish and fish products. Production has approximated 25,000 metric tons yearly but may now be considerably above that figure. The basin on the peninsula of Araya, State of Sucre, which at present is the only important source of salt, could produce at least 175,000 metric tons if more ground were provided-a larger supply than the entire country could consume. This unique landlocked basin of nearly 1000 acres lies 12 ft below sea level. Ecuador-Salt is a Government monopoly in Ecuador and is produced chiefly by solar evaporation close to the shore. The main producing center is on the Santa Elena peninsula, which supplies about 90 pct of the salt. Small fields are at Punta Arenas, Payana, and Chara-

Jan 1, 1949

By Thomas Egleston

The ores of mercury of North California are composed of metallic mercury and cinnabar. They are found in serpentine, and are very often associated with chalcedony, in masses more or less irregular, often concentrated enough, however, to furnish ores yielding from three to ten per cent., and sometimes richer. This deposit makes its appearance in Vallejo where it has been worked. North of here the mines are more developed. Most of the quicksilver mines, however, are situated in Sonoma and Napa Counties. On its outcrop the serpentine rocks have become decomposed, and have often been washed away to a considerable depth, so that in many cases in their neighborhood, what is apparently nothing but ordinary dirt, will frequently contain from two to three per cent. of metallic mercury, with but a trace of cinnabar, in which case, as at the Sonoma mine, it is made up into adobes and distilled. Such material does not require to be mixed with dirt to be made into adobes. Very often, also, the outcrop of the rock, where it is not decomposed, is filled with metallic mercury, so that by striking a pick into it, as at the Rattlesnake mine, a pound or more of mercury at a time will sometimes spurt out. Such rock as this is found in several localities in every stage of impregnation, and usually makes very rich ore. There is generally, however, very little of it, and it is found only in the first workings; the ore in depth is always cinnabar. At the Rattlesnake mine near Pine Flat, where large quantities of metallic mercury are found, the rock contains so much petroleum that it has been necessary to make special arrangements to burn the carbides of hydrogen, since the distillation of the petroleum causes an extra quantity of poor soot to be formed in the condensation-chambers. At the Geysers the ore is associated with large quantities of sulphur and gypsum, so that in a hand specimen there is often more sulphur than cinnabar, which is a serious impediment to working, especially for the modern style of furnace with iron condensers, and causes so much soot to be formed that it has been known to penetrate as far as the blower, and to so completely clog it as to prevent its revolution. The ore coming from the mine is more or less hand-picked. In one or two cases attempts have been made to treat the poorest, and especially the very fine ores, mechanically as at the California works.

By C. C. Harris

The characteristics of some common size distribution equations are critically discussed. A generalized form of several well-known size distribution equations is obtained from a differential equation describing statistical distributions. The equation contains three parameters and can describe the major features of size distributions in the fine and the coarse size regions. A graphical method for its implementation is provided. The application of this and other equations to sets of data are compared both for the quality of fit and from a comminution kinetics viewpoint. If a narrow size range of a brittle material is broken sufficiently to obliterate the feed sizes, but not so severely that excessive secondary breakage occurs, a plot of cumulative fraction by weight undersize (Y) vs. sieve size (X) on a log log grid (sometimes called the Gates-Gaudin-Schuhmann plot)1-3 gives a straight line of slope ~ 1 over much of its range. On closer inspection, deviations in the extreme coarse range covering perhaps 10 to 30% of the total sample may be apparent (frequently, a change in slope from ~ 1 to a value different from unity) together with over-all slight irregular departures from a smooth line. One model of breakage postulates that the same fracture pattern persists throughout all size ranges.4 The fracture pattern is characterized by the slope of the line on a log log grid. Accordingly, a distribution of sizes broken in the manner specified earlier is expected to produce a size distribution having the same slope as that of a broken narrow size range. Additionally, the slight irregularities mentioned above should even out in the summation process, giving a smooth straight line of slope ~1 on a log log plot. This idealized state of affairs does not, however, describe the distribution of a multi-event process such as that for a tumbling mill product. On the average, these curves (plotted again log log) tend to have a slope in the fine region different from and usually less than unity,5 while the coarse size region curves with increasing slope for cases of mild reduction, and with decreasing slope when moderate or severe size reduction has occurred. In addition, there are usually slight irregular deviations from a smooth curve. Most curves display two distinct regions — fine and coarse — and a few curves show one or more intermediate regions. Feed size studies6,7 show an effect which theory is required to explain. For the same material, mill loading and other operating conditions, and the same time of grinding, plotting the dimensionless ratios Y vs. X/(feed size) does not reduce the size distribution data to the same curve. Y vs. X does not correlate the coarse region, but it can provide a crude correlation of the fine region which improves as size diminishes and as grinding time increases. The size distribution in the coarse region is somewhat more dependent on the feed size than is the distribution in the fine region wherein the degree of dependence diminishes as time proceeds; the distribution of sizes in the fine region are determined largely by the nature of the material and the comminution conditions. A comprehensive model of comminution must recognize that several different patterns or modes of breakage can occur in a mill; 5,8,9 that there can be some selection in that some size ranges are broken more than others; and that, while some particles may be the product of a single fracture event, or may even remain unbroken, others result from multiple rebreak-age. Thus, breakage in a tumbling mill is more complex than the Schuhmann4 model admits in that several different types of comminution micro-events* occur rather than just one type, and these events, though different in size scale, are of the same overall pattern as that which is visualized by the model. The concept of an average comminution micro-event has, therefore, a mathematical rather than a physical connotation, at least for tumbling milling. Equations with which to describe particle size distributions have been sought for over half a century.10-13 No equation presently in general use was first derived from an analysis of the statistical mechanics of breakage; whatever theoretical basis the existing

Jan 1, 1969

EXECUTIVE COMMITTEES OF LOCAL SECTIONS Arizona E. P. MATHEWSON, Chairman W. V. DECAMP, First Vice-chairman F. W. MACLENNAN, Second Vice-chairman E. D. GARDNER, Secretary-Treasurer, U. S. Bureau Of Mines, Tucson, Ariz. MICHAEL CURLEY J. P. HODGSON HENRY F.1 ASTER CLYDE E. WEED Boston Meets first Monday each winter month GEORGE A. PACKARD, Chairman FRANKLIN B. RICHARDS, Vice-chairman F. LEROY FOSTER, Secretary-Treasurer Rooms 8-219 Mass. Inst. of Tech., Cambridge, Mass. G. W. METCALFE D. H. MCLAUGHLIN

Jan 1, 1932