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By John Henry Harden

IN 1874, with Mr. H. Y. Attrill, of Baltimore, Md., I made an examination of some property at Goderich with reference to sinking for and mining salt. With this end in view we visited all the wells in the neighborhood, but the information sought being of so unreliable a character I advised the putting down of a borehole on the property. This has since been done, the result of which has lately been published by Dr. T. Sterry Hunt in the Toronto Globe. From this there appears to have been passed through six beds of salt of an aggregate thickness of 125 feet. Rock-salt was known to exist, for, by the boring of existing wells, small crystals had been brought to the surface in the dirt, but no attempt had before been made to obtain a reliable sample or to prove the number and thickness of the beds. The question now remaining for discussion is, shall the present method of obtaining the salt be continued, or shall the beds be won by a shaft in a regular mining fashion, by which means the salt may be gotten in a condition almost ready for the market? The present mode of obtaining salt is by boreholes from 6 inches to 8 inches in diameter drilled to the beds, into which is inserted a pump. The "feeders" of fresh water intersected in drilling the well are allowed to descend on the outside of the pump-tube to the salt beds and there become saturated, when, on use of the pump, brine is obtained for evaporation. In the beginning brine can only be had in limited quantity, but by the daily application of the pump, and the gradual solution of the salt, a larger surface becomes exposed to the action of the fresh water, and a continuons supply of brine is obtained. It will then be understood that the supply of brine is dependent upon the feeders of fresh water intersected in boring the well, which, we are told, have never shown any sign of diminution, and this is the water that must be encountered in sinking a shaft. There are ten wells in operation at Goderich, the most important one to the present project being known as the Hawley Well, located at an elevation a few feet above Lake Huron at the mouth of the river Maitland, at, a much lower level and nearer to the proposed shaft than any other well in the district. At this well the feeders

By A. B. Kinzel

SILICON, unfortunately, is not in the same category as some other metals with respect to the absolute value of the highest purity material prepared. Tucker, in England, and Becket, in this country have devel-oped procedures for the purification of silicon, and Becket's process has made industrially available silicon of a purity of 99.8 per cent or better. However, even the term "silicon metal" may be a paradox to some people, although not more so than the term "amorphous" as applied to silicon. These terms come from commerce, and "metal" is used to distinguish industrially high-purity silicon from ferrosilicon, silicon-aluminum, and other high-silicon alloys. Alloys of iron and silicon with 95 per cent Si or less are known as ferrosilicon, with a designation of silicon content where necessary, and the terns "silicon metal" is invariably applied to the grades containing 96 per cent Si and higher. The Becket method of purification was referred to in a monograph on the Alloys of Iron and Silicon, and the Tucker procedure was described in some detail in that publication.1 In order to get silicon of still higher purity, a sample, prepared by the Becket method, analyzing 99.84 per cent Si, 0.020 Fe, 0.016 Al, 0.005 Ca, 0.025 C, 0.033 per cent 02, 0.006 H2, 0.006 N2, and 0.001 per cent Mn, was crushed to pass a 100-mesh sieve said further purified by a modification of Tucker's procedure. This modification differs from Tucker's method in that after treatment the 100-mesh alloy was centrifuged to remove the last traces of acid. Our directly determined analysis of this purified sample shows: Si, 99.952 per cent; Fe, 0.009; Al, 0.012; Ca, 0.003; C, 0.006; or 99.982 per cent. Silicon by difference equals 99.97 per cent. The variation between silicon by difference and silicon as directly determined is important. Although Tucker mentions the amount of insoluble matter in commercial silicon both before and after his treat-ment, he does not mention the existence of carbon in the alloy; neverthe-less, lie reports silicon by difference. Any final figure as to purity obviously results from agreement between direct determination and

Jan 1, 1939

By C. L. Berrien

Before the present company was formed, in 1916, each group of mines comprising the old organizations made its detailed daily and monthly mine cost records along the lines used before the consolidation; that is, there was no attempt made to standardize and compare the stope costs of all mines. The general cost sheets for all mines, however, were standardized, and cumulative labor cost sheets were compiled in the general superintendent's office. At most of the mines, a daily record or distribution sheet for each working place was kept, showing the number of men, hours of drilling, hours of timbering, hours of tramming, cars of ore, cars of waste, sticks of powder and feet of fuse. This information was kept by each shift boss and entered on the distribution sheet by him or, at some mines, by a tram boss. The superintendent solved his own problems under the direction of the general superintendent, but without coming in touch with other superintendents, either through records or general conferences. Probably 95 per cent. of the stopes were square-set worked by day's pay; there were some back-filling and shrinkage stopes. Many of the development places, such as shaft sinking, station cutting, drifting and raises had always been run by contract. These contracts were given, for no definite period, at so much per linear foot and were measured monthly, or when completed, the men being paid monthly. In some cases, fairness to the employee was not maintained. On the whole, there was no standardization. There were no stope contracts, because of the objections of the Western Federation of Miners to general contracting in the mines. Changes in Stoping Methods Early in 1916, W. B. Daly, then general superintendent, and the author, then assistant general superintendent, visited the Southwest mining districts with the object of finding some improved mining

Jan 1, 1923

By C. L. Berrien

Before the present company was formed, in 1916, each group of mines comprising the old organizations made its detailed daily and monthly mine cost records along the lines used before the consolidation; that is, there was no attempt made to standardize and compare the stope costs of all mines. The general cost sheets for all mines, however, were standardized, and cumulative labor cost sheets were compiled in the general superintendent's office. At most of the mines, a daily record or distribution sheet for each working place was kept, showing the number of men, hours of drilling, hours of timbering, hours of tramming, cars of ore, cars of waste, sticks of powder and feet of fuse. This information was kept by each shift boss and entered on the distribution sheet by him or, at some mines, by a tram boss. The superintendent solved his own problems under the direction of the general superintendent, but without coming in touch with other superintendents, either through records or general conferences. Probably 95 per cent. of the stopes were square-set worked by day's pay; there were some back-filling and shrinkage stopes. Many of the development places, such as shaft sinking, station cutting, drifting and raises had always been run by contract. These contracts were given, for no definite period, at so much per linear foot and were measured monthly, or when completed, the men being paid monthly. In some cases, fairness to the employee was not maintained. On the whole, there was no standardization. There were no stope contracts, because of the objections of the Western Federation of Miners to general contracting in the mines. Changes in Stoping Methods Early in 1916, W. B. Daly, then general superintendent, and the author, then assistant general superintendent, visited the Southwest mining districts with the object of finding some improved mining

Jan 1, 1923

By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By Samuel Lasky

WITH the movement of American capital into foreign investment, a new field of specialization for the American mining engineer is gradually opening a field hitherto entered almost wholly by chance and without full appreciation of its possibilities. Our age has been fitly called the "Age of Specialization." The special application of one's knowledge and ability to a definite and restricted branch of .his profession is purely a modern condition. Any profession, or branch of a profession or, industry, in which the problems may be segregated into definite types, calls for specializa-tion. Modern industry demands efficiency and that, reduction and ultimate annihilation of waste. Effort and time wasted by workers' on a problem with which they are not familiar is as flagrant a waste of money -the final standard-as any waste of materials. One of the subdivisions of mining engineering which is beginning to be recognized is of engineers who are clearly conversant with the particular and peculiar problems obtaining under foreign operating conditions. The need is as yet obscured, however, by the domestic prosperity of our American mining industry. The opportunity here lies more with the American engineer than with other nationals. The foreign en-gineer now in that service is not there through a realiza-tion of the special opportunities that exist, but through necessity, whereas, with the American engineer, more especially ,the recent graduate or those who will soon graduate, this is a new field to be entered wholly by choice. As a matter of fact, many engineering students will find it necessary to seek foreign service if they wish to remain in mining. Although the scope of the domes-tic industry is tremendous and there are many positions open to the junior engineer, there are not enough for the great number of graduates turned out yearly from our, mining schools. Educators tell us that less than 40 per cent. of the students in engineering schools gradu-ate; and of these but a minority continue in engineering. Even this minority is too great for our domestic. In-dustry, and although the young engineer realizes that condition after a few years he rarely seeks foreign work. A. perusal of the directory of the American Institute of Mining Engineers indicates that, but about one-half of one per cent of the Junior Associates are in positions outside of North America. Granting that most of them are still in school, the figure is surpris-ingly small.

Jan 1, 1927

By W. L. Saunders

It has been estimated that the value of the mineral products of the United States is about $2,000,000,000 a year; that about $25,000,000 is expended annually for explosives and that about double this sum is paid in wages where blasting is done. The value of the mineral products does not adequately express the importance of the industry involved in the excavation of rock and ore because of the enormous sums of money expended in tunnel driving, in quarries, and in open-cut excavation generally. We know that the Catskill Aqueduct in the neighborhood of New York, which is now nearing completion, has cost some $165,000,000 and that about one-third of this may be rated as rock excavation. These illustrations are given in order to call attention to the great importance of an industry the extension and development of which in our industrial life depend so much upon the economics of rock drilling. Reference has been made to the new Catskill Aqueduct. There are three aqueducts leading into New York, each built at periods separated by some 20 years of time. The first one, known as the Old Aqueduct, conveys the waters of the Croton river to New York City in a manner which reminds one of the old Roman aqueducts, the ruins of which are still in evidence. The engineers who laid out these old conduits sought to direct their lines around the hills and into the valleys, at all times avoiding the rock. When it was necessary to cross a river or a deep ravine, a bridge or causeway was constructed. High Bridge, over the Harlem river, is an arched masonry viaduct differing in no essential features from the aqueducts of the Romans. When the second Croton Aqueduct was built, about the year 1890, the art of drilling rock had been so far perfected, and the use of explosives, through the invention of dynamite, had become so general, that this waterway was planned and executed on straight lines, following rather than avoiding the rock. The second Croton Aqueduct is a tunnel through rock, about 32 miles in length; material gneiss, almost as hard as granite. Its construction was made practicable by sinking

Jan 1, 1914

By Thomas J. O’Neil

During the past five years, the mining industry has been subjected to new operating constraints that are unprecedented in number, scope, and urgency. The industry must operate in a safer, cleaner manner, yet produce more without large price increases. Compliance with any new sweeping legislation is always difficult-and particularly so in today's adverse economic climate, which is being aggravated by the steady stream of environmental control and tax-reform programs. In effect, while government is unwittingly but surely undercutting the country's productive capabilities, it blames industry for the resulting failure to meet consumer demand. Any such real or alleged failure then brings heightened bitterness from Congress. During the recent energy shortage, for instance, threats of nationalization were ventilated in public along with proposals to abolish the mineral depletion allowance.

Jan 11, 1974

By J. M. Locke

BRÜCKNER's revolving cylinders for roasting ores, etc., are now used at a number of the mills in Colorado and New Mexico, for the purpose of roasting and chloridizing silver ores, with highly satisfactory results, even from those cylinders of small size, erected before the many improvements of recent date. As examples of the larger improved cylinders, reference can be made to those erected at the Tennessee Reduction Works, Silver City, Grant County, New Mexico, and those which were built, in 1871, at the celebrated Caribou Silver Mill and Mines, Colorado, a mining enterprise which has proved so satisfactory as to have been lately sold to a Holland company for an enormous amount. These cylinders, as now constructed by Messrs. Lane & Bodley, of Cincinnati,, Ohio, are shown in Plate III, in which Fig. 1 is an elevation in perspective, Fig. 2 a longitudinal, and Fig. 3 a trans¬verse section. Fig. 4 is a sketch of a mill, with Brückner's cylinder. The exterior of the cylinder is a shell of boiler iron, 12 feet long by 5 feet 6 inches in diameter. The ends are partially closed with similar material, leaving in the centre a circular opening about 2 feet in diameter, bounded by a flange projecting several inches.. Upon one side is placed an opening closed by a hinged door. Upon the outside of the cylinder are bolted three bands, as shown in Fig. 1, in which the section of the first is square, and that of the third semi¬circular; the second, or middle band, is a strong spur gear. Passing through the cylinder are six pipes parallel to one another, in a plane at an angle of 15° to the axis of the cylinder; these pipes also lie in this plane at an angle of from 30° to 35° to the longitudinal, axis of the plane, as shown in Fig. 2, where the internal arrangement of the cylinder is seen, a perforated diaphragm being formed through part of the cylinder by means of perforated plates placed between

Jan 1, 1874

By Dae S. Young

A new probabilistic approach is introduced for slope stability analysis including adverse impact of blasting vibrations. The material strength within a slope area is randomized in this bi-variate joint probability analysis. To be a completely general engineering method, the new probabilistic approach employs the random variable transformation technique: the Hermite model of the Gaussian transformation function, which transforms the experimental histogram of strength values to the standard Gaussian variables. Because bi- normal joint probability is analyzed on the true probability region projected on the Gaussian transformed variable plane, it is an exact solution of slope stability based on the available sample data. Details of the probabilistic approach are given through a case study on an iron ore mine. The case study demonstrated that the probabilistic approach is effective and simple enough to be a routine engineering practice for slope analysis.

Jan 1, 1984

By L. C. Kern

This paper presents information on the use of a new propping agent (malleable aluminum particles) which has been used successfully for producing high-conductivity fractures. The conductivity of a packed fracture depends on the width of the fracture as well as the permeability of the propping material. It is significant that the flow capacity of a propped crack is often increased many fold by propping the crack with a sparse distribution of particles. However, the flow capacity of a sparsely propped crack can be limited by two phenomena: (I) crushing of the propping particles, and (2) embedment of the propping particles in the formation walls. Malleable aluminum particles exhibit interesting properties which tend to overcome these limitations. As high loads are applied to the particles they will deform slightly, rather than shattering. The deformation results in a greater bearing area against the formation wall. This reduces the stress on the particle and reduces particle penetration into the formation. The behavior of aluminum particles under load and the bearing capacities of serveral formation rocks have been measured in the laboratory. By properly using these data, as explained in this paper, the flow capacities of aluminum-propped cracks can be calculated for a variety of conditions. Aluminum particles have been used successfully in the field to prop fractures. Where high-conductivity fractures were needed, the aluminum-propped fractures have given greater well stimulation than could have been expected for conventional fracturing processes. INTRODUCTION The purpose of a hydraulic fracture treatment is to create a conductive channel from the wellbore out into the oil or gas formation. The word conductive is emphasized because we believe that the fracture conductivity (flow capacity) is one of the most important factors influencing fracturing results. Previous papers have pointed out the additional well stimulation that can sometimes be achieved by increasing fracture conductivity. Several years ago, we investigated in some detail the effect of fracture conductivity on productivity increases to be expeced from vertical fractures. Both electrical analog and theoretical studies of unsteady-state flow behavior were made. A discussion of the electrical analog equipment and some of the results of the study were given in a previous paper' by Dyes, Kemp and Caudle. Further details were given recently by McGuire and Sikora.5 Fig. 1 shows the remarkable influence of relative fracture flow capacity and length on well stimulation. Briefly, the study indicates the following. 1. High-permeability formations require high-conductivity cracks for best results. 2. The longer the crack, the higher the fracture conductivity required for best results. 3. If the conductivity of the crack is very large compared to the formation (i.e., flow is not being limited by crack conductivity), then the longer the fracture, the better will be the results. Judging from recently published articles,1,314 there is current interest in methods for obtaining high fracture conductivities. Hence, we would like to present in this paper a discussion of a new fracture propping process (use of aluminum particle) which we have used successfully to obtain highly conductive fractures. There are several factors which influence the conductivity of a propped crack. Conventional fracturing techniques frequently result in a crack completely packed with fracturing sand. For such conditions, the crack conductivity is the product of the width of the packed fracture and the permeability of the propping material. It is significant that a large increase in conductivity sometimes can be obtained by propping with particles which are distributed sparsely (less than a

By H. M. Howe

It has seemed to the writer that one important, and indeed sufficient reason, for our slow progress in learning the relation between the chemical composition and the physical properties of cast-iron, has been that the problem has not been attacked properly. It would be well to select the most probable working hypothesis which we can find, and proceed to test that hypothesis by comparison with observed facts, and by making new observations specially designed for such a test. Our first step, then, is to select the most probable working hypothesis ; and to attempt this selection, to state the hypothesis and its immediate corollaries, and to take some first steps toward testing it, is the object of the present paper. Its chief purpose is to bring the hypothesis to the attention of those who are more familiar with the evidence than the writer can pretend to be, and in a better position both to present new evidence and to discuss it. The hypothesis here selected is, that composition governs properties in the case of cast-iron, in the same general way and for the same reasons as in the case of steel, mutatis mutandis. This hypothesis, which of course makes no claim to originality, certainly seems reasonable and probable; its exposition and discussion are made easy by our existing knowledge of the constitution of normal or " carbon " steel; it therefore seems worthy of consideration.

Jan 1, 1902

James Douglas will long be remembered as a distinguished mining engineer and metallurgist, as a scientist with broad vision, as an executive whose understanding of practical problems coupled with his knowledge of men and affairs enabled him to weld together great mining interests and to their service build railroads and bring power. More, he will be recalled as a philosopher and a writer of charm, a historian of no mean order, and one whose catholic tastes and enthusiasms led him into the fields of education, medicine and theology. His aim was to possess that which he considered made life worth while—friends and effectiveness in whatever task he undertook. In this aim he was successful to a degree exceeded by few, as thousands of his friends and associates could and can testify. Dr. Douglas was born on November 4,1837, at Quebec, Canada. His father, James Douglas, Sr., was a prominent physician and the leading surgeon of Canada. He also established the first retreat for the insane in the Dominion, the Quebec Lunatic Asylum, to which he devoted his services for years; The son followed in the footsteps of his father and studied medicine, not only in Canada but also in Scotland and in Germany. He entered the University of Edinburgh in 1855 but after two years at that institution returned to Canada and was graduated from Queens university at Kingston, Ontario, .with the degree of Bachelor of Arts. Later he went to Lava1 University, Quebec, and subsequently became professor of chemistry at Morrin College, Quebec. After he was graduated—at the time he considered his formal education completed—he traveled with his father in Europe and in the Orient; visiting Egypt, being especially interested in that country, several times. They gathered together an important archaeological collection which later was donated by them to the Metropolitan Museum of Art in the city of New York. James Douglas was also greatly interested in photography, a hobby in which he made use of his chemical knowledge. The writer can remember distinctly the descriptions he gave more than forty years ago in Arizona of the difficulties he encountered with the old wet photographic plates, especially while traveling in Egypt, when he prepared and used his own chemicals. In his humorous manner he told how he once discovered, in the nick of time, the nurse preparing to give the baby in the party a rub-down, using for that purpose the white, limpid

Jan 1, 1934

By Edward H. Robie

NEVER before have the annual company reports in the mineral industry field exhibited the typo-graphical art so abundantly as does the current crop. Time was when most company reports made a drab appearance and dry reading, mostly confined to financial data and text that gave little information to the public or technical men. Now, the dollar statistics assume less importance. Considerable information is given on what is going on at the company's plants, new equipment being installed, new methods, properties under development, ore reserves and grades, and similar information of interest to professional men working in the field. We have one suggestion for further improvement: The names of the officers and directors of the company are always given, but only a few companies give the names of the principal operating officials. We think, in the case of a mine for example, that the name of the general manager, his assistant, the mine and mill superintendents, and any other top operating officials who have been largely responsible for the success of operations, are worthy of mention. The reports are now widely read and this recognition is due them. Conspicuous among the annual reports that we happen to have seen, in point of typographical attractiveness, are that of the Texas Co., celebrating its fiftieth anniversary with a gold-plated cover and gold printing inside; and that of Noranda Mines Ltd., with a red and black cover that would attract attention anywhere. Comment on economics, taxes, and labor give an excellent picture of what our industry is facing. Consider the following, from the report of the Union Oil Co. of California:

Jan 1, 1952

By S. F. Emmons

[The following notes of observations made during a visit of a few days in the month of October, 1886, which was cut short by a sudden summons East, are offered, in spite of their incomplete and tentative character, in the hope that they may aid the members of the Institute, in their coming visit to this region, to a clearer understanding of the general geological conditions under which the ore-bodies occur.] The Butte mining region lies in a sort of a depression in the mountains which is drained by Silver Bow creek and its various tributaries. On the east it is bounded by high north and south ridges of granite, and on the west by lower ridges, also running north and south, which, as far as examined, were found to consist of rhyolite. High mountains also inclose the depression on the north and south, but at a greater distance than the more immediate bounding ridges on the east and west, the distance between which is hardly more than six miles.

Jan 1, 1888

By Richard Rothwell

At the last meeting of the Institute, Mr. Per Larsson read a very interesting paper on the Chapin mine of Michigan, in which he described the systems of mining that had, at different times, been tried in that great ore-body, and especially the system now in use, which consists in working the ore out from the bottom upward in lifts. Shortly after that paper was written, but before it had been published, or that I had had an opportunity of reading it, I bad the pleasure of visiting the mine. At that time I was making a profes sional examination of a nnmber of the mines on theGogebic Range, and others in the Menominee region, Michigan and Wisconsin, and had occasion then, as during several previous visits, to study closely the methods and cost of mining in these districts. As the outcome of these investigations, it appeared evident to me that the system of working on the chamber-and-pillar plan, which up to that time had been the only method of underground work adopted in the Gogebic

Jan 1, 1888

By Augustus Locke

Jan 1, 1923

By Augustus Locke

Jan 1, 1923

By Wilhelm Borchers

In all special branches of the chemical and metallurgical industries, in which large electric furnaces became necessary for carrying out new processes or for the improvement of old ones, the development of the electric furnaces took place on much the same lines. The endeavors to make a success of a new idea brought forth many ingenious designs, which, however, almost without exception, furnished the proof that the safest and shortest way to practical success is the utmost simplicity of construction of the necessary apparatus. Our knowledge of the qualities of materials for building electric furnaces and of the constituents of the furnace-charges, especially their electric conductivity and their chemical affinity towards one another at high temperatures, is still far from being complete, and from this fact we must conclude that the smaller the number of elements in the construction of a furnace, the fewer the number of unreliable factors both in the construction and in the operation of the electric furnace. This conclusion deserves special attention when an electric furnace for making steel has to be chosen from the constantly-growing number of inventions, inasmuch as the chief constituent of steel, the element iron, is a substance which in its liquid phase has so great an affinity for those elemen'ts which are to be removed from the charge, that it is very difficult to comply with the following conditions: 1, to heat the refining-slag to the highest point of its chemical activity ; 2, to prevent the iron from entering the slag, or, where this cannot be done, to make it enter so that it finally appears in the end-product

Jan 1, 1911

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,' based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry' has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962