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By K. D. Hester, A. C. Anderson

The Elliot Lake uranium deposits are contained in a pebble conglomerate which is similar throughout the basin. This paper compares the solid-liquid separation circuits of two nominal 3000 T/d acid leach uranium concentrates treating Elliot Lake ore. One concentrator employed rotary vacuum drum filtration for solids removal and washing, the .other used counter current decantation in torque arm thickeners. Capital and operating costs, operation and maintenance, and metallurgical performance of the two solution recovery methods are compared and contrasted. A recent development, removal of the sand fraction ahead of C.C.D. and separate sand washing in hydraulic cyclones, is also discussed.

Jan 1, 1973

By John Gill

THE purpose of this paper is to invite attention away from the obvious, direct monetary costs of oil-field overdevelopment (as dis-tinguished from "social costs") to a consideration of the role played by the exercise of freedom to create even allegedly excessive1 plant facilities in contributing to the maintenance of equilibrium in the whole economy and in promoting material progress. The obvious and most commonly discussed effect of overdevelop-ment of oil fields is illustrated by the allegation that already the excessive development of the East Texas field has cost upward of $162,000,000;2 in other words, the drilling of 12,500 wells more than the number esti-mated as the requirement for economical recovery of the reserve has unnecessarily raised the total cost of development that amount. Many other illustrations of so-called excessive development of oil pools could be presented. Some of them, like Cushing, Powell and Long Beach, might be drawn from the era antedating widespread discussion in the trade of such matters as optimum well spacing, reservoir energy, the conservation rate of depletion of reserves, etc. Numerous other cases can be found in the records of the current era, which began with the introduction of rationalized restriction of production. Besides East Texas, there may be mentioned Oklahoma City, Centralia and, more recently, the town-lot development of Bloomingdale, Michigan.

Jan 1, 1939

By John A. Church

EARLY in the month of August, 1877, a miner in Gold Hill, Nevada, made the unlucky remark that, according to his observation, that month was usually quite free from accidents in the mines. Never was presage wider from the truth. When the month closed twelve mishaps had occurred, killing six and wounding nine persons, and for the rest of that year the Comstock mining communities were kept in a ferment by the frequent occurrence of appalling disasters. There was a real tidal wave of calamity sweeping over the mines, which has not been repeated since, and according to common report was never known before on the Comstock. I was much interested in studying the character of these misfortunes, which also aroused concerted action on the part of the miners, and I have collected a list of the accidents which took place from July, 1877, to May, 1879. The number in this period of twenty-two months

Jan 1, 1880

By John A. Church

Early in the month of Angust, 1877, a miner in Gold Hill, Nevada, made the unlucky remark that, according to his observation, that month was usually quite free from accidents in the mines. Never was presage wider from the truth. When the month closed twelve mishaps had occurred, killing six and wounding nine persons, and for the rest of that year the Comstock mining communities were kept in a ferment by the frequent occurrence of appalling disasters. There was a real tidal wave of calamity sweeping over the mines, which has not been repeated since, and according to cornmoll report was never known before on the Comstock. I was much interested in studying the character of these misfortunes, which also aroused concerted action on the part of the miners, and I have collected a list of the accidents which took place from July, 1877, to May, 1879. The number in this period of twenty-two mouths

Jan 1, 1880

By David White

IN these days, when detailed investigations of stratigraphy, structure, and sand conditions so frequently result in the discovery of new oil fields, and applause from oil companies and the public, geologists do well to walk humbly, and punctiliously to admit that the geologic principles controlling the distribution of oil and gas have as yet been discovered only in part, and that what remains yet to be learned is probably vastly more than what is already known. The few experiments already at-tempted have been fragmentary, and somewhat desultory, and however positive each of us may be with respect to certain theoretical conclusions, many of the fundamental questions as to the origin and mode of occurrence of petroleum are subject to radical disagreement. Of the chemical changes attending the generation of petroleum from organic matter, little is actually known. Most of the postulated formulas are liable to be misleading, through ignorance of essential factors. Open-mindedness is therefore a prime essential at the present stage of our science. Nevertheless, adopting the hypothesis that oil originates in some manner fundamentally connected with the organic theory, and in possible departure from such open-mindedness, the writer will pay no attention to the so-called inorganic theory, since every attempt to apply this theory to the study of old oil fields, or to the discovery of new ones, affords cumulative evidence of its inadequacy. In this paper, some of the factors affecting the occurrence of petroleum that the writer believes worthy of consideration by the prospector for oil in any new region will be discussed. Some of these, which are less generally understood, will be considered somewhat in detail. Other points, the significance of which cannot now be determined, require more field study, and for that reason are here brought to the attention of the field geologist. On the other hand, certain theoretical points which do not bear especially on the oil possibilities of a new region will be given little

Jan 2, 1920

By W. L. Phillips

Stress-strain data are reported for sodium chloride, lithium fluoride, and magnesium oxide tested in compression at diffevent strain rates in the telrlperature range from 70° to 873°K. Quantitative equations are given for the stvain-rate dependence of the critical resolved shear stress and the initial rate of work havdening. The properties so determined are compared with results previously reported for metals. ALTHOUGH the effects of strain rate and temperature on the stress-strain characteristics of metals have been extensively investigated1,2 these effects have not been studied in detail in ionic crystals. In the only previous investigations on the effect of strain rate on the deformation of ionic crystals. Gilman and gohnston3 and Hulse and pask4 have shown that the yield stress of lithium fluoride and magnesium oxide at room temperature is proportional to the ninth or tenth root of the strain rate. CRYSTAL PREPARATION Lithium fluoride, sodium chloride. and magnesium oxide single crystals were purchased from the Har-shaw Chemical Co. The compression fixture and sample preparation have been described in detail previously.5 The detectable impurities in MgO were eight parts in 105 of Fe and six parts in 105 of Si; in LiF, six parts in 105 of Mg; and in NaC1, two parts in 105 of Fe and four parts in 10&apos; of Mg. The cleaved samples measured - 0.1 in. by 0.1 in. by 0.3 in. Prior to testing all samples were annealed at -0.8 of their melting point and cooled to room tempera- ture at 50 C per hr.&apos; Samples were strained at rates (<) of 0.1, 0.01, 0.002, and 0.0002 in. per in. per min. EXPERIMENTAL RESULTS Fig. 1 is a plot of the critical resolved shear stress a,. (extrapolation of slope of easy glide region to zero strain) of sodium chloride, lithium fluoride, and magnesium oxide tested at different strain rates as a function of temperature. In all crystals at all strain rates a, decreases with increasing temperature according to an equation of the type397 where uo is a stress constant, K is a constant, and T is the absolute temperature. The points in Fig. 1 are the average of six tests. It is evident that there is a break in the log 0,- temperature plots at a characteristic temperature T,. The constant K of Eq. [I] is dependent on strain rate, Fig. 2. The relationship

Jan 1, 1962

By H. l. Burghoff

THE presence of tellurium in copper and, by inference, in copper alloys, has been considered seriously detrimental and has been avoided. In particular, very small amounts of tellurium have been found to produce red-shortness, although the effects on cold-working and ordinary physical and mechanical properties have not been known so definitely. References in the literature are few, but as long ago as 1881, Egleston1 reported that 0.083 per cent tellurium in fire-refined copper rendered the copper red-short and therefore worthless for hot-rolling. In hot-rolling copper cakes containing this amount of tellurium, he found that fine cracks appeared in the cakes on the first pass through the rolls, the cracks opening further in successive passes. When cold, the metal was said to be tough and malleable. A few years ago, during the course of an investigation in our laboratory on copper-base alloys, it was found that tellurium-bearing alloys could be machined much more freely than similar alloys not containing tellurium. The study was pursued further in this direction, and considerable data were obtained, which indicated that certain tellurium-bearing alloys might have properties of commercial interest. The work eventually led to patent protection,2 a wide range of tellurium-bearing copper-base alloys being covered. This article presents results obtained on the effect of tellurium on the. mechanical properties of three copper-base alloys: commercial bronze (90 Cu, 10 Zn), 1.5 per cent tin bronze (98.5 Cu, 1.5 Sn), and silicon bronze (96 Cu, 3Si, 1 Zn).

Jan 1, 1937

By Walter S. Weeks

The process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. Case I If compressed air is allowed to expand to the atmospheric pressure through an orifice in an air line that is supplied by a running compressor, no cooling results except the negligible one due to the JouleThompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected. Symbols P1 Absolute pressure in pipe line, lb. per sq. ft. P3 Atmospheric pressure, lb. per sq. ft. V1 Volume occupied by 1 lb. air in pipe. V3 Volume occupied by 1 lb. air at P3. C, Specific heat of air at constant volume, B.t.u. per lb. per deg. F. C, Specific heat at constant pressure, B.t.u. per lb, per deg. F. T1 Absolute temperature of air in pipe, deg. F. T8 Absolute temperature of air outside after expansion and mixing and coming to rest. j Mechanical equivalent of heat (778 ft. lb.) R Gas constant for air, ft-lb. per deg. F. = 53.3. Formulas Consider 1 lb. of air moving out of a pipe. The air behind it does work on it to the extent of P1V1 ft-lb. This work is really done by the thrust of the piston of the compressor and does not come from any energy that exists in the air in the pipe. The pound of air contains

Jan 1, 1937

By G. Kimmel, A. Bar-Or

The rate of nucleation and the rates of both lateral and longitudinal growth of martensite plates (needles) in b—a transformation were determined as a function of temperature, in various U-Cr alloys. The activation energies for nucleation and both modes of growth were calculated from the experimental results. The identical values for lateral and longitudinal growth clearly indicate that both are controlled by the WHITE,&apos; Mott and Hines and Holdeen3 showed that characteristic martensite plates (needles) appear in U-Cr alloys during the transformation 8 —0 in the lower temperature range (up to -300°C). Holden pointed out that the rate of growth of the individual martensite plates under isothermal conditions is same mechanism. Lomer&apos;s suggestion that single-atom movement over subatomic distances controls the specially slow growth of martensite receives further support from the present kinetic study, which shows that the growth rate can be described quantitatively by known formulas for the growth rate in processes involving single-atom movement. very slow, and suggested that this is due to the slowness of the relief of the stresses engendered during the growth of the individual plates. lomer4 attributed the slow growth to the complexity of the atomic adjustment at the growing interface b/(u. In the present work the rates of nucleation and growth of martensite plates in U-Cr alloys were studied by direct observation, in order to elucidate the mechanism which controls their characteristic slow growth.

Jan 1, 1968

By A. C. Fieldner

A FORMER paper1 described in detail various methods of calculating coal analyses to obtain the composition and calorific value of the pure coal substance-that is, of the coal free from its mineral matter. The paper included a table showing calorific values of pure coal, as calculated from float-and-sink portions, by means of the Parr formula for "unit coal" and by the customary moisture-free and ash-free formula. A modification of the Parr formula was proposed, based on the assumption that one-half the sulfur present in coal occurs as pyritic sulfur and one-half as organic sulfur. In the published discussion of the paper Cady gave a table of results on a large number of Illinois coals as obtained by the Parr formula and the proposed modification thereof. The results obtained by Cady indicate that the Parr formula applies better to Illinois coals than does the modified formula proposed by Fieldner and Selvig. The present paper gives results obtained by applying the modified Parr formula to the analyses of the float-and-sink portions of the coals shown in the former paper, and results obtained by applying the Parr formula, the modified Parr formula, and the simple moisture-free and ash-free formula to various coals of the United States ranging in sulfur content from less than 1 per cent to more than 4 per cent sulfur. A graphic method of estimating the calorific value of pure coal and determin-ing the relation of the coal ash to the mineral matter of coal, as proposed by Stansfield and Sutherland,2 was applied to a number of coals, and the results are given herein.

Jan 1, 1932

By William E. Ford, Edward Salisbury Dana

1. Normal Class (1) Galena Type 2. Pyritohedral Class (2) Pyrite Type 3. Tetrahedral Class (3) Tetrahedrite Type 4. Plagiohedral Class (4) Cuprite Type 5. Tetartohedral Class (5) Ullmannite Type Mathematical Relations of the Isometric System 50. THE ISOMETRIC SYSTEM embraces all the forms which are referred to three axes of equal lengths and at right angles to each other. Since these axes are mutually interchangeable it is customary to designate them all by the letter a. When properly orientated (i.e. placed in the commonly accepted position for study) one of these axes has a vertical position and of the two which lie in the horizontal plane, one is perpendicular and the other parallel to the observer. The order in which the axes are referred to in giving the relations of any face to them is indicated in Fig. 85 by lettering them a,, a2 and a3. The positive and negative ends of each axis are also shown.

Jan 1, 1922

By Alexander N. Mitinsky

UP to a certain limit, the increase of pressure on the diamond-drill increases the rate of progress in drilling. That limit is set by the resistance of the diamonds to compression; and beyond it, the destruction of the stones will involve an. economic loss, both in time and in money. It is, therefore, important to all diamond-drillers to know what is the resistance mentioned. In Europe, operators usually follow an empirical rule, which directs the maintenance of a pressure, on the area-of the bottom of the drilling-tool, of 12 kg. per sq. 4m. For the tools in ordinary use, this is equivalent to 1 kg. per sq. mm. of the diamonds set in the tool So far as I know, American drillers are using pressures as high as 50 to 60 kg. per sq. cm. of the total area of the drill, and the consumption of diamonds (on Denny&apos;s authority, 0.2 carats per meter bored) is greater in America than in Europe. But the reason for this difference may be the comparatively larger size of the diamonds commonly used by American drillers. With the assistance of my friend, the late S. Woisslaw, who was the pioneer of diamond-drilling in Russia, I selected from his stock a number of black diamonds, which I subjected in my laboratory to compression-tests. To prepare regular cubes for such tests, as is generally done with other stones, would have been not only costly, but, what is more important, practically useless. I therefore determined, in order to assimilate as nearly as possible the conditions of actual use, to place each sample between a hard plate (corresponding to the rock) and a softer plate (corresponding to the bottom of the tool), into which it would be pressed during the test.

Jan 1, 1906

By M. Stuart, R. F. Down

The Copper flotation concentrate produced at Gortdrum mines contains about 1% Hg. This article deals with the treatment used to produce a substantially mercury-free copper concentrate. Metallic mercury is a byproduct. Nearly all the mercury in the Gortdrum concentrate is present in the copper mineral tennantite-tetrahedrite. This mineral is variably distributed throughout the ore body so that by selective mining it was possible to produce salable concentrate relatively low in mercury while the treatment plant was being built. Roasting was the only feasible method found for removing the mercury from the concentrate, and it was decided that this should be done in an atmosphere with limited oxygen. A multiple hearth furnace is used. Mercury soot is condensed from the gas stream and treated to produce prime virgin mercury. Problems were experienced at first with materials handling, oxygen control, cooling of the calcined concentrate, treatment of the mercury soot, and in the metallurgical accounting. Precautions were necessary to avoid health problems. The plant is now operating reasonably well. The value of the mercury produced does not warrant the cost of the plant but without it, the copper concentrate could not be sold.

Jan 1, 1975

By R. W. Diamond

Three mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd.: (1) The Sullivan Concentrator, Chapman Camp, B. C. (near Kimberley, B. C.), (2) the St. Eugene Concentrator, Moyie, B. C., and (3) the Tadanac (Customs) Concentrator, Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Values in all ores treated are as minerals of some or all of the metals —lead, zinc, gold or silver. Occasional customs ores contain small amounts of copper. Sulfide iron content of ores treated varies from a low figure in some ores to 38 per cent. iron in Sullivan ore. Gangue minerals vary considerably. A few customs ores are somewhat oxidized and as a result present difficulties. Flotation equipment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sullivan Concentrator. In this paper I will not detail treatment nor equipment in any of our plants but will describe special features in, or in connection with, all of them. I will then deal with flotation reagents, describing our use of each of them, particularly where differing from general practice. I will conclude with comments on special subjects related to differential flotation.

Jan 1, 1928

By J. W. Rutter, K. T. Aust

Observations are presented of the formation of annealing twins during the growth of a recrystallized grain into a striated, melt-grown crystal of high-purity lead. The formation of an annealing twin resulted in replacement of the original migrating boundary by a large-angle grain boundary of the caincidence-site type or by a near-twin boundary. The results support the Fullman-Fisher theory of annealing twins and demonstrate the usefulness of the coincidence-site model. FULLMAN and Fisher1 have advanced the following theory to account for the formation of annealing twins during grain growth. Whenever a grain A grows into a matrix of grains S1 and S2, a twin A&apos; of grain A may form, as shown in Fig. 1, if the following energetic condition is satisfied: where "E" and "a" refer to the specific interfacial free energy and the area, respectively, of the boundaries indicated by the subscripts. In effect, the twinned grain will persist when the energy of the boundary between the twin(A&apos;) and the matrix grain (S, or S,) is less than that of the boundary between the original growing grain (A) and the matrix grain by an amount which exceeds the energy of the coherent twin boundary between A and A&apos;. Experimental observations on the changes in grain boundary free energy accompanying the formation of twins1 are in agreement with the theory outlined in Eq.[l]. Direct observations of the formation of annealing twins at moving grain corners1"3 and the depend-

Jan 1, 1961

Chairman, MRS. JESSE SCOBEY The Foreign War Relief Committee closed its dispensary fund during the past month with a contribution to the American Fund for French Wounded of $1720.51, balance on hand, principal and interest, as a gift from the New York Section of the Woman&apos;s Auxiliary for pressing emergency dispensary work in France. The American Fund for French Wounded was authorized to cable this sun at once, in consideration of the fact that their existing dispensaries, including the one established by the New York Section at Briey, were in excellent condition, while their mobile dispensary fund was confronted by the most urgent need for work among the refugees now returning in pitiable condition and in great numbers to certain distressing centers. The committee sewing at Fund headquarters every week has had seven working days, with an enrollment of twenty: The average attendance was ten; largest attendance for any one day, thirteen; smallest attendance, eight. Interest in this activity is growing steadily and it is the intention of the committee to push the work vigorously for the next few weeks.

Jan 3, 1919

By R. H. Sweetser

The Committee on Evaluation of Coal for Blast-furnace Coke reports progress in the working out of the problem of evaluation. There has been no full meeting of the Committee but there have been several conferences with two or more of the members present, and the different members have expressed themselves freely on the five points that have been under consideration since the meeting of the Committee in New York on Feb. 16, 1932. The need of a method of coal evaluation, not only of coking coals but all other kinds, is obvious. Under NRA it becomes imperative that coals of the same size from the same seam be priced according to their variations in quality, especially in reference to cleanliness in respect to freedom from extraneous ash-forming materials. In looking over the correspondence that has passed between members of our Committee, it is evident that much of the confusion and misunderstanding would disappear if we could realize that practically all of the variations in value of coal from the same seam of coal are due to variations in the amounts of extraneous materials that are contained in the coal as it passes over the scales for shipment. It is not now a question with our committee as to the differentials in value, or in prices, between different kinds of coking coals or between noncoking and coking coals; our present problem is to arrive at the method for determining the scale of values of the coal from a certain coal seam according to the increase or decrease of extraneous ash and moisture from a predetermined base line adopted for that particular coal. The five points mentioned above are the same as discussed at the meeting in February, 1932, except that the temperature for determining the moisture content has been changed from 212" F. to 221" F., at the suggestion of Dr. A. C. Fieldner. The points are: 1. It is proposed that the coal industry adopt as a base line for evaluating all coals the analysis of the coal as it passes over the neighing device that determines the tonnage of coal bought and sold. 2. It is proposed that the Committee on Evaluation of Coal for Blast-furnace Coke approve the adoption of the base line for Pittsburgh seam coal presented by F. A. Jordan at the annual meeting of A.I.M.E.

Jan 1, 1934

By Olin G. Bell

At the beginning of the year 1935 the older fields in Southwest Texas, and particularly those discovered during 1934, had been practically delimited and only normal development continued. As a result, operations in this area were somewhat slowed down. Shortly after the first of the year, however, activity in the area was greatly accelerated, due largely to the fact that the Loma Novio field, discovered during the last few days of 1934, indicated the presence of a new productive trend east of and parallel to the Government Wells field and also indicated the presence of a new productive horizon, the Loma Novio sand, approximately 100 ft. lower than the Government Wells sand zone. Other discoveries during the year greatly augmented the activity in the district. During the year there were 651 oil wells, 53 gas wells and 275 dry holes drilled in this area during the year. Most of the operations were in the Government Wells, Cole, Loma Novio, Seven Sisters and Lopez fields. New Fields Four new fields were discovered during 1935 as follows: Seven Sisters and Piedra de Lumbre in Duval County; Loma Alto in McMullen County; and Lopez in Webb County. Seven Sisters Field.—The Seven Sisters field, opened in May, was the direct result of a systematic search for new productive areas northeast of the Loma Novio field. The first producer, Harvey & Henderson NO. 1 Chernosky, survey 226, was completed in the Labbe (Chernosky) sand at 2220 ft. However, the second producer, Santa Clara Oil Co. No. 1 Welder in survey 385, drilled about one mile south of the discovery well, failed to find production in the Labbé sand and was carried on down and completed in the Government Wells sand at 2473 ft. with an initial production of 20 bbl. of oil per hour. These two discoveries, in the Labbé and Government Wells sand, started an active leasing and drilling campaign in this part of Duval County and drilling operations continued especially active throughout the remainder of the year.

Jan 1, 1936

By Olin G. Bell

At the beginning of the year 1935 the older fields in Southwest Texas, and particularly those discovered during 1934, had been practically delimited and only normal development continued. As a result, operations in this area were somewhat slowed down. Shortly after the first of the year, however, activity in the area was greatly accelerated, due largely to the fact that the Loma Novio field, discovered during the last few days of 1934, indicated the presence of a new productive trend east of and parallel to the Government Wells field and also indicated the presence of a new productive horizon, the Loma Novio sand, approximately 100 ft. lower than the Government Wells sand zone. Other discoveries during the year greatly augmented the activity in the district. During the year there were 651 oil wells, 53 gas wells and 275 dry holes drilled in this area during the year. Most of the operations were in the Government Wells, Cole, Loma Novio, Seven Sisters and Lopez fields. New Fields Four new fields were discovered during 1935 as follows: Seven Sisters and Piedra de Lumbre in Duval County; Loma Alto in McMullen County; and Lopez in Webb County. Seven Sisters Field.—The Seven Sisters field, opened in May, was the direct result of a systematic search for new productive areas northeast of the Loma Novio field. The first producer, Harvey & Henderson NO. 1 Chernosky, survey 226, was completed in the Labbe (Chernosky) sand at 2220 ft. However, the second producer, Santa Clara Oil Co. No. 1 Welder in survey 385, drilled about one mile south of the discovery well, failed to find production in the Labbé sand and was carried on down and completed in the Government Wells sand at 2473 ft. with an initial production of 20 bbl. of oil per hour. These two discoveries, in the Labbé and Government Wells sand, started an active leasing and drilling campaign in this part of Duval County and drilling operations continued especially active throughout the remainder of the year.

Jan 1, 1936

By L. Adler

Analysis of a mine roof can be based on fixed-end beam behavior. The author here analyzes the effects of zero restraint at deflecting beam supports. Formulae are given for determining permissible support deflections. Analysis of a mine roof in a bedded deposit usually follows the assumption that the behavior of the roof is analogous to a beam with both ends fixed. Yet it is recognized that the end restraint itself varies with the thickness of cover, so that at shallow depth the restraint is minimum, and at great depth, maximum.&apos; Consequently, an analysis on the basis of fixed ends or full restraint represents only one extreme in the possible range of conditions. Since the actual amount of restraint is difficult to ascertain, a more rational approach is to consider the two extreme cases of end restraint. Such situations regarding uncertainty of the restraining effects of supports are not uncommon in structural analysis, and are handled in a like manner.&apos; Since previous studies9)4 have dealt with full restraint, this paper will analyze the effects of zero restraint at deflecting beam supports. In such a case a mine roof with several intermediate supports becomes analogous to a uniformly loaded continuous beam on simple supports, as shown in Fig. 1A. Such a structure is statically indeterminate to a degree equal to the number of intermediate supports, n. Therefore, with the three equilibrium equations, n additional equations are needed. A number of methods exist to analyze this problem, but The Theorem of Three Moments is Simplest. The continuous beam is divided at each support into a sequence of simply supported single span beams, with the unknown end moments, as appears in Fig. 1B. Continuity requires that the common ends of adjacent beams have the same slope (Fig. 1C). eiB= B(i+l)~= ei(i+l)and MiB= Mti+I)A= Mi(i+i). [1I A Glossary of all terms is given in Table I. Furthermore, if we first consider that the supports do not deflect, the slope at a support is the sum of the slopes due to each of the individual loads shown in Fig. 2, yielding:

Jan 1, 1961