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By J. J. Gilvarry

Recently, Gilvarry1,2 has given a rigorous derivation of the proper distribution function for fragment size in single fracture, based on a closely defined physical model and deduced strictly by the laws of probability. The physical point of departure is Griffith's theory of brittle strength, identifying sub-microscopic flaws as the cause of the low strength of a solid in comparison with values implied by cohesive energies. Gilvarry and Bergstrom,4-7 and Gilvarry8 have compared the predictions of the theory with experiment, and have found excellent agreement, in general. The purpose of this communication is to sketch the extension of the theory to the case of comminution, and to indicate the applications to some examples in nature. The present treatment represents an amplification of a brief discussion appearing elsewhere. 9 Although the basic ideas of the Griffith theory are perfectly general for rupture of brittle solids, it was originally formulated with very brittle materials such as glass in mind. Moreover, Griffith's original experimental work was carried out on glass specimens. Recently, however, the theory has been extended by race" to apply directly to rocks. This extension makes the theory immediately applicable to the materials generally of interest from the standpoint of comminution. GENERAL CASE To obtain the distribution function for fragment size in single fracture, three assumptions are made, that: 1) Fracture proceeds by activation of preex-istent Griffith flaws in the volume, faces, and edges of a fragment; 2) the distributions of flaws of these three types are independent of each other; and 3) activated flaws of a particular type are distributed at random, individually and collectively, in the sense of Fry.11 The last assumption implies that each distribution is separately of Poisson type.

Jan 1, 1964

By C. H. Mathewson, H. M. Day

The constitution of the system silver-mercury has attracted the attention of many investigators during the last two decades, but since their results are for the most part in poor agreement, there is little need for a review of their individual contributions. It remained for the very careful thermal and microscopic investigation of Murphy1 in 1931 to give the constitutional diagram in its present and unquestioned form, which is shown in Fig. 1. He devised methods for taking cooling curves on alloys under high pressures and for the microscopic observation of alloys which contained liquid mercury as a structural constituent at ordinary temperatures. The compositions of the intermediate phases were confirmed and supplemented through X-ray analyses by Preston2 and Stenbeck.3 According to Murphy, at 2760 C. silver is able to dissolve 44 to 45 weight per cent of mercury, which may increase at lower temperatures to about 50 per cent. Preston concluded that the saturation boundary occurred at 46 ± 2 per cent at 100° C. From the values reported in the literature, these are the only ones that may be accepted as lying even in the right region. Preparation of Alloys The silver used in the present investigation was supplied by the United States Metals Refining Co. through the courtesy of the Committee on Industrial Uses of Silver and, since a complete spectrographic and chemical analysis was furnished, no attempt was made to purify it or to further establish the impurities present. The analyses reported by the company are shown in Table 1. Milligan4 has found that the magnesium content is probably less than 0.0005 per cent.

Jan 1, 1938

By H. M. Day, C. H. Mathewson

The constitution of the system silver-mercury has attracted the attention of many investigators during the last two decades, but since their results are for the most part in poor agreement, there is little need for a review of their individual contributions. It remained for the very careful thermal and microscopic investigation of Murphy1 in 1931 to give the constitutional diagram in its present and unquestioned form, which is shown in Fig. 1. He devised methods for taking cooling curves on alloys under high pressures and for the microscopic observation of alloys which contained liquid mercury as a structural constituent at ordinary temperatures. The compositions of the intermediate phases were confirmed and supplemented through X-ray analyses by Preston2 and Stenbeck.3 According to Murphy, at 2760 C. silver is able to dissolve 44 to 45 weight per cent of mercury, which may increase at lower temperatures to about 50 per cent. Preston concluded that the saturation boundary occurred at 46 ± 2 per cent at 100° C. From the values reported in the literature, these are the only ones that may be accepted as lying even in the right region. Preparation of Alloys The silver used in the present investigation was supplied by the United States Metals Refining Co. through the courtesy of the Committee on Industrial Uses of Silver and, since a complete spectrographic and chemical analysis was furnished, no attempt was made to purify it or to further establish the impurities present. The analyses reported by the company are shown in Table 1. Milligan4 has found that the magnesium content is probably less than 0.0005 per cent.

Jan 1, 1938

By W. E. Bron, E. S. Machlin

GRAIN boundary migration in V-shaped thin specimens of high purity silver was studied. Each specimen contained two crystals having the relative orientation: (111)A/(111)B; (ll0)A/(101)B. The boundary between these two crystals varied between a continuous curved and an alternating two plane interface. The plane interfaces were oriented parallel to (101)A/(011B) and (121)A/(211)B. Traces of these planes are shown in Fig. 1. Evidently the two plane interface, although of higher area, comprises lower total interface energy than the average curved boundary it replaced. The plane boundaries were found to move at 650 °C to consume the broad segment of the V opposite to the direction of interface area and energy decrease. On investigation, using the thermal etching technique of Hendrickson and Machlin,1 it was found that the outer grain contained 8.3x108 more dislocations per cm" than the grain at the apex of the V. Consequently, the boundary moved to decrease the strain energy associated with the difference in dislocation density across the boundary. The rates of motion of specific {110} and {112} boundaries were measured during interrupted anneals at 650°C by referring the position of the boundaries to each other and a fiducial line on the specimen surface. The measured rates of motion are 0.075 and 0.025 mm per hr for the {110} and {112} boundaries, respectively. Plots of grain boundary motion vs time of annealing show straight lines with little deviation of data points from these lines.

Jan 1, 1957

By Max Hebgen

I. Natural Features of State Affecting Power Development .. 792 II. Early Developments. 1. Big Hole Plant................. 792 2. Canyon Feny Plant............... 793 3. Madison Plant No. 1............... 593 4. Black Eagle Plant................ 795 III. Later Developments. 1. Madison River System .............. 795 2. Missouri River System.............. 797 3. Great Falls System............... 797 4. Missoula River Development............ 797 5. Big Fork Development.............. 802 $ IV. Present Capacity of Power Developments....... 802 V. Transmission System...............: . 802 VI. Character of Load. 1. Lighting and Small Power Uses........... 804 2. Street Railways ................ 804 3. Mining................... 804 4. Railroads.................... 808 5. Irrigation................... 810 VII. Operation of System................. 812 VIII. Increase in Use of Power............... 811 IX. New Power Developments............... 814 X. Undeveloped Powers................. 815 It is estimated that the total stationary power now used in the United States. steam. water and gas. is probably over 30.000.000 h. p. The total developed water power is about 6.000.000 h. p. The water power in the United States now economically capable of development probably exceeds 25.000.000 h. p. The total developed and undeveloped power is

Jan 1, 1914

By Leon T. Eleiel

Ten years ago a broad knowledge of aerial mapping, coupled with a smattering of geology, qualified one to speak on the subject of the application of aerial mapping to geology. Today, with aerial maps a common tool in the hands of expert geologists on every continent throughout the world, it would be nothing short of presumptuous for the author of this paper, who is not a geologist, to give any geological statements on his own authority. Relatively, today we are only purveyors of general geological gossip, with a definite case here and there by way of illustration. But we can present a story of the really marvellous strides that have been made in the evolution of aerial mapping, built around a skeleton of geological tidbits, from which some useful conclusions may be drawn. The average geologist goes about reading his aerial maps much as one would approach the problem of deciphering a cryptogram. To begin with, typical key expressions appear in recurring sequences and under certain conditions. If once the meaning of these isolated bits of information can be ascertained, the message begins to take meaning. In a similar fashion, the geologist works out his key from aerial maps of territory with which he has some familiarity. He learns that a certain type of thin, white line may mean a vein of quartz. He sees that a certain change in the photographic tone of vegetation on the ground reflects two kinds of soils on opposite sides of a contact. He sees that a certain type of alignment of topographical features often means a fault. He learns that by the erosion pattern he can frequently distinguish soft formations from harder ones. And so, bit by bit, he ties together the information of the picture with his experience on the ground until he develops a reasonably creditable capacity of interpretation. Through the complete gamut of surface conditions, ranging all the way from flat, arid, exposed desert terrain to dense jungle, or rugged mountains, the evidence from which the geologist must make his interpretation varies with bewildering profusion. The quality of photographs which are obtainable may range from perfect pictures in the desert to almost useless smudges in the steaming jungles. One thing he has learned with certainty—the airplane carrying its mapping camera is a superb reconnaissance tool, only awaiting his ingenuity in correlating the pictures with the ground to simplify most exploratory problems.

Jan 1, 1937

By A. M. Gaudin

THIS paper presents, with the help of colored photomicrographs, the new method of mineral identification termed "selective iridescent filming." This method pertains to the field of determinative mineralogy, which it provides with tools for: (1) phase identification, (2) solid solution analysis. The method should be particularly useful in the applied fields of: (1) paragenesis of ore deposits, (2) mineral dressing, (3) mineral synthesis and study of phase equilibria.

Jan 1, 1938

By J. R. Guard

Development of electrical power in coal mining has been an outstanding example of adaptability. It has accommodated itself to new inventions, changing mining methods, increasing demands, increasing safety requirements and many other new conditions. With the appearance of the continuous miner in the mining machinery picture, those engineers interested in the application of electricity to mining have been thinking about what new combination of electrical apparatus will best suit this newcomer. It is the purpose of this paper to discuss the relative costs of supplying d-c versus a-c power to mining equipment with particular reference to continuous miner setups. Assume that a-c power will be delivered to the mine at some high voltage suitable for transmission to the various substation locations. Typical voltage for this purpose is 4000 volts. The problem then is to change the power to some kind of power suitable for driving the motors of mining equipment. For safety and other reasons the voltage to be delivered to the motor terminals must be under 600 volts.

Jan 1, 1950

By Lester W. Strock

METALLURGISTS handling lead and zinc ores have long been familiar with the spectrograph as a routine analytical tool, as its earliest regular use by American industry was in controlling impurities of zinc metal and its alloys. This application has been extended to other metal industries on an extensive scale, accompanied by refinements of procedure to such an extent that a large part of some metals produced, especially magnesium, aluminum and steel, are checked only by spectrographic methods for conformity to specifications. The spectrographic analysis of ores and other poorly conducting powdered solids presents difficulties not encountered with metallic samples, which can be arced or sparked as self-electrodes or can be readily dissolved, so that their solutions can be analyzed, as in the American Society for Testing Materials standard methods for zinc and zinc-base alloys. Spectra of powdered solid samples can be prepared by using carbon electrodes provided with a crater of suitable size, into which the sample is packed. Ore samples and many other powdered solid materials usually analyzed in the chemical and metallurgical laboratory are more complex and varied in composition than samples of metals produced in large tonnages. More preliminary work therefore is usually necessary in devising a spectrographic method for analyzing a given type of powdered sample than for analyzing metal samples, in order to use that method with confidence. The knowledge that the standard samples and unknowns produce equivalent line intensities at equal concentration is the fundamental basis of any quantitative spectrographic method. On the other hand, powdered samples have an advantage over metals in that any desired number of chemical compounds can be mixed dry in any desired ratio to produce a synthetic standard. Experience has shown, however, that spectra of elements in finely divided compounds introduced into a standard in preparing a synthetic ore sample do not always behave in the electric arc in a manner that produces spectral line intensities similar to those observed at the same concentration in a natural mineral. In ore samples minor elements frequently are contained in the crystal lattice of larger particles of an abundant ore mineral. Their dissociation and volatilization from the sample into the arc then proceeds differently in the standard and sample, with resultant differences in intensity. During the past 10 years I have devised and applied several quantitative spectrographic methods for determining various elements in rocks and minerals in connection with studies on their geochemistry,1 but the incentive has gradually changed since the summer of 1940 to the specific practical problem of searching for domestic sources of rare and strategic metals. The

Jan 1, 1945

By Jim V. Rouse

In situ mining and dump leaching has been practiced for years. Recent environmental concern over conventional mining and milling techniques has rendered in situ mining more attractive. While there are many environmental advantages to in situ mining, there are disadvantages which, if ignored, can lead to environmental damages, followed by stringent control. The environmental advantages and disadvantages of the various types of in situ mining operations are discussed. Current legislation and regulations governing in situ mining are cited, together with a suggested program of environmental monitoring designed to protect the mining company as well as the environment. Suggestions are made for possible solution of existing pollution problems associated with previous mining activities by heap-leaching techniques. Present and indicated control of subsurface injection is traced, because of the many similarities in philosphy and monitoring requirements to in situ mining.

Jan 1, 1974

THE Woman's Auxiliary now has its own publica-tion, a monthly news letter that is mailed direct to all its members. It is a lively and readable sheet. Any member of the Auxiliary failing to receive it should communicate with Mrs. J. E. Johnson, Jr., 49 Church Lane, Scarsdale, N. Y., and get on the mailing list. The detailed reports of the meetings will hereafter ap-pear in the News Letter rather than in MINING AND METALLURGY. The regular Board meeting held on March 3, with Mrs. Barron presiding, was well attended and the re-ports of the committees, and from local sections, showed a keen interest in the work. of the organization. Steps are being taken to endow a "Mary Young Westervelt Scholarship," libraries are being built up in mining towns, and interesting reunions .are being held by the members in the various local sections. The Auxiliary is filling an important place and doing it well. Women of the families of Institute members not already affili-ated with it would find it pleasant to get in touch.

Jan 4, 1927

By C. H. Wayman, D. W. Fuerstenau

THE gas phase is one of the indispensible ingredients in flotation operations. Flotation depends on the collision of an air bubble and a mineral particle in a pulp and their ability to remain in contact long enough for adherence to take place. Before it is possible to understand the mechanics of air bubble-mineral particle encounter, it is necessary to learn more about the nature of bubbles themselves before collision with a mineral particle has taken place. To date, little work has been done on air bubbles in flotation systems. In 1945 Fahrenwald1 presented a study of the role of frothers on air bubbles and on aeration in flotation, and recently Wark and Sutherland2 discussed the work of Rosenberg3 in relation to flotation. The research reported in this present article was undertaken to investigate systematically the effect of bubble size and the concentration of certain reagents on the terminal velocity, shape, path, and drag coefficient of single bubbles in distilled water. Most of the work is concerned with the effect of a-terpineol on bubble motion in water, but studies were made with potassium chloride, potassium hydroxide, potassium ethyl xanthate, and potassium amyl xanthate.

Jan 6, 1958

By R. G. Hall

An article on the subject of electrolytic zinc no longer needs to be preceded by an apology. The production of zinc by electrolysis is past the laboratory stage and has become an economic factor of considerable importance in the total production of zinc in the United States. The various methods of procedure to be followed fa the greatest economy of manufacture are fairly well known, consequently a detailed description of any method is no longer necessary or desirable. In this paper I shall endeavor to lay down some of the governing conditions in this industry, the relation of methods to ore deposits, freight rates, and sources of power supply. Power Points Assuming for a moment that, for the present at least, the electrolytic production of zinc will be confined to Those localities having developed water power, a glance at these powers so developed in the United States, with their relation to known zinc orebodies of economic size, will not be without interest. Northwest In the Northwest we have water powers, developed and undeveloped, . in Washington and Montana. These must, of course, bear a close relation to the rapidly growing zinc production of the Coeur d'Alenes and of the Butte districts. In general, the power of the territory in question is relatively low-priced, at least as compared with the cost of developing power from coal, and the near neighborhood of large bodies of more or less complex zinc ores makes these water powers of more than usual interest. The same remarks may be applied equally to the developed water powers of the Canadian side of the line in the Northwest, where we have again commercially available complex ore deposits such as are being exploited today at and near Trail. California One of the large complex ore deposits of the far West is to be found in Shasta County in the immediate neighborhood of the territory of the

Jan 1, 1918

By George S. Rice

A problem of possible subsidence of the surface from mining operations, which might have had disastrous results, arose in 1913 at the Brier Hill mine, of the Penn Iron Mining Co., near Norway, Mich., now managed by Pickands, Mather & Co. for the Bethlehem Steel Co. A double track and sidings of the Chicago & North Western Railroad passed over part of the mine, and if subsidence had reached the surface it might have affected the stability of the tracks. The chief purpose of this paper is to record the facts disclosed by investigations of underground movement from 1913 to 1919, when the tracks were moved, and subsequently at intervals, as engineering data of value from mining carried on below the tracks in the steeply pitching lenses. A secondary purpose of this paper is to describe a novel method for determining the rate of speed of upward breaking above the mine excavations. This method was found effective and might be used elsewhere under similar conditions. The mine workings under consideration were developed from the Brier Hill shaft, which was circular, concrete-lined, 14 ft. in diameter and about 900 ft. deep. They extended about 800 ft. westward from the shaft, and nearly parallel to a corresponding length of the railroad tracks. The highest part of these workings was at a depth of 400 ft. below the tracks (Figs. 1 to 12). The mining company had the right to remove the ore, the railroad assuming that the surface would be supported. Finally, without legal controversy, an amicable adjustment was reached as to what should be done to lessen or obviate the hazard of subsidence. Method oF Mining Before the problem became acute, the mining company, to decrease the possibility of subsidence, had been mining the part of the orebody that lay under the tracks by a room-and-pillar system, back-filling with

Jan 1, 1934

By C. G. Dunn

Identification of the kinds of orientation relationships that may exist among crystals is an important problem in the metallurgical field. As an aid to its solution standard orientations of several orders of twins would be very useful for rapid analyses to discover high-order as well as low-order twin relationships. Although data have been published that give orientations for three generations of twins, these data are not readily useful in the form presented; i.e., in a stereo-graphic projection with one pole per orientation.' However, accurate data based on calculations of the positions of all {1001 planes for such groups would be very useful when presented in tabular form. Therefore, calculations have been made for a group of four orders of twins and the data are listed in Table 3. Illustrative applications are considered briefly, with the idea of pointing out what may be done with large groups of orientations. Method of Computing Orientation OF a Twin It is common practice to describe the orientation of a crystal in terms of the positions on a stereographic net of the poles of certain planes of the crystal. A single position on a net may be given in terms of two angle variables, two sets of which appear in the following equations: Polar Net Wulff Net x = , sin ?p cos Fbp x = r COS ?w y = r sin ?p sin Fp y = r sin ?w cos Fw % = r cos ?p z = r sin ?w, sin +, The three numbers z, y and z determine a length r as well as a direction (0, 4) in an X, Y, Z coordinate system. In the present case, r will be set equal to (h2 + k2 + L2)1/2, where h, k and I are the usual Miller indices for a crystallographic plane, a restriction that facilitates determination of the positions of poles of new planes from those of old or known ones,2 as will become evident later. Furthermore, since twinned lattices have certain planes in common, it is an easy matter to determine the orientation of a twin of a crystal if the orientation of the crystal itself is known. We start therefore with a crystal of known orientation (positions of three {Ioo} poles given) and determine where the cube poles occur in first, second, third and fourth-order twins. Methods for identifying twinned lattices and for making the calculations to find the orientation of a twin have been published.3,4' Reference 4 will be illustrated in the calculation of the orientation of a twin, even though this method differs from the one used by the writer in obtaining the following data on four orders of twins. Consider a crystal S and its twin A1, A' being one of the four {112} or {III} type* first-order twills of S. The orientation of S—i.e., the positions of poles of (I00)

Jan 1, 1945

By Norman Carmichael, John Kiddie

The problem of transportation in the Clifton-Morenci district of Arizona has been one of peculiar difficulty and consequently has been an important factor in the cost of mining and treating the ores produced. From the crude beginning made over 50 years ago, many changes have been necessary to keep pace with the increased output of copper. A heavy-duty haulage system has developed on the original 20-in. track gage to meet the existent metal-mine conditions. Topography The transportation difficulties of this district may be readily appreciated from the relief map shown in Fig. 1. The northern half of the district is high mountainous country and there is a general but irregular drop toward the southern part, where the country, although still rugged, is in reality a great sloping plain. This is cut by numerous ravines from which the waters, in the rainy season, discharge into the channel of the San Francisco River. A chasm, 1000 ft. deep, has been eroded through the center of the district by Chase Creek, which is flanked by high irregular mountain masses, notably Copper Mountain, American Mountain, Coronado Mountain, and Markeen Mountain. The latter rises 2300 ft. above the bed of the creek, The San Francisco River has also cut a deep channel, though it is somewhat broader than Chase Creek. Eagle Creek traverses the extreme southwest portion of the area, where it has carved picturesquely through vast volcanic flows. Faulting has left its mark upon the topography of the district by adding to the irregularities caused by erosion. Strong faults occur at the Coro-

Jan 1, 1924

By AIME AIME

THE second blast furnace of the Azov steel mill was blown in on Feb. 17, says the Economic Review of the Soviet Union. This furnace, the 111th in the U. S. S. R., has a volume of 930 cubic meters, and a daily output of 775 tons of pig iron. The 1934 program at the Azov plant includes three 250-ton-open-hearth furnaces, two coke-oven batteries, a repair shop, mine and agglomeration plant at Gamysh-Burum, and two ports, one at the latter town and one at Mariupol. On Feb. 21 the sixth open-hearth furnace of the Stalinsk (Kuznetsk) mill started operations; on Feb. 12 the fourth open-hearth furnace at the Liebknecht mill at Dniepropetrovsk, produced its, first steel, 47 tons of high-grade boring steel. The fourth open-hearth furnace

Jan 1, 1934

By Jack A. Simon, M. E. Hopkins

GENERAL GEOLOGY Coal is defined as a combustible rock that had its origin in the accumulation and physical and chemical alteration of vegetation. Coal can be ignited and burned like the wood that was man's earliest fuel, but coal gives more heat than the same amount of wood and has many industrial uses. Unlike wood, coal is not generally found on the surface of the ground but is mined from the solid rock of the earth. Before taking up the occurrence, formation, and the somewhat unique character of coal in the rock sequence, let us briefly consider the general character of all rocks in the crust of the earth. Relatively little is known about the very earliest history of the earth, although a number of logical theories have been developed. Manned exploration of the moon and the rocks being returned to earth will, we hope, provide some answers to questions concerning the earth's origin and history. The period of earth history with which we concern ourselves here begins after great areas of water had evolved on earth and substantial land areas of once molten (igneous) rock existed. Weathering and other processes that attacked the surface of the rocks reduced them to small particles. Water provided by rainfall transported this material, ultimately, to large bodies of water where it was deposited. Thus was initiated the geologic sequence of sedimentary rocks that lie above the once molten igneous rocks. The crust of the earth is not completely stable, and throughout the geologic past portions of the crust have moved laterally and vertically. Even today, many coastal areas are slowly rising or sinking. More sudden earth movements are recognized by the earthquakes they cause. Throughout geologic history, rises in sea level or the sinking of the land areas have many times permitted the oceans to cover much of what are now the areas of the continents. Only relatively small parts of the present continents appear to have been above sea level throughout geologic time. Great

Jan 1, 1973

By William H. Shockley

[SECRETARY'S ]NOTE.-The following notes, arranged and edited in this office, but not yet revised by the author, were placed at my disposal with much modest hesitation (due to their incomplete and fragmentary character), upon my earnest request, and my argument that such recent and trustworthy data concerning a new and important mining industry ought not to be withheld from our Transactions, simply because they are not sufficient to constitute a, complete academic treatise on the subject. This argument is recommended to the attention of many other members, who are waiting for the opportunity to contribute something "monumental" to our Transactions. In a number of instances, death has nulli¬fied this ambition, and the intended "monumental" contribution has turned out to be an obituary notice by the Secretary, instead of a valuable record of the professional experience thus hopelessly lost to the world.-R. W. R.] The official publications of the the Russian Government give fairly complete statistics of the dredges operated in the Empire; and in a recent English bluebook, Mr. Cook's report on Siberian Trade presents a brief account of dredging in Siberia. The data in Table I. (not given by Mr. Cook) have been taken from the Gold Mining Messenger (Russian) for July, 1905. These interesting statistics, though incomplete, show that the Yenisei dredges are working on poor ground and yield small returns. According to report, but few yield a profit exceeding 10 per cent. per annum on the capital invested. In the summers of 1904 and 1905, I traveled in the Urals as far north as lat. 61° N., long. 61° E., on the the Lozva river, a part of the vast system of the 01) river. This clear-water stream starts from the summits of the Urals at an altitude of 4,000 ft., and flows through a flat country, densely wooded with larch, spruce, pine, fir, birch and poplar. The river is full of fish, and is navigable for good-sized steamers as far as Ivdell. Winter lasts from early November to late April, the temperature rang¬ing from -60° F. to a summer maximum of 90° F. The rain¬fall is 20 in.. The climate is healthy, although mosquitoes,

Jul 1, 1906

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937