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By AIME AIME

THE 129th meeting of the American Institute of Mining and Metallurgical Engineers convened at New York City, in the Engineering Societies Building, Feb. 18-20, 1924. On February 21 an excursion was made to the Bethlehem Steel Co., at Bethlehem, where about 200 members and guests were splendidly entertained. An illustrated description of the Bethlehem Plant will be published next month. The meeting and excursion were largely attended; the registration at New York totalled 1276 versus 1201 in 1923. William Kelly, long identified with the iron-mining industry of the Lake Superior district, was elected President of the A. I. M. E. for the coming year, at ,the annual business meeting, Feb. 19, succeeding E. P. Mathewson. The following Directors were also elected (the date signifies year of termination of office; the final figure indicates the "District" the Director represents).

Jan 1, 1924

By Reynold Q. Shotts

Data are presented which show that fractions of varying densities from the same coals are oxidized at different rates by nitric acid. From oxidation data, the approximate quantity of "bright" and "dull" components may be calculated. Definite relationships between oxidation rate and rank are shown for density fractions from at least two bituminous coals.

Jan 8, 1950

By Albert Sauveur

(Winces-Barre Meeting, June, 1911.) THE instrument about to be described meets so perfectly the special needs of the metal microscopist that there seems to be little doubt but its merits must be readily appreciated by those who have had any experience in the microscopical examination of metals. The Microscope-Stand.-The microscope-stand proper, Fig. 1, consists of a microscope-tube, provided with both coarse and fine adjustments of the best construction, and with a draw-tube, rigidly mounted on a bar supported at both ends on substantial and firm cast-iron legs. The height between the table and the under side of the supporting bar is 5 in. and the distance between the supporting legs 12 inches. This arrangement' affords free space below the objective for the examination of large specimens of metals, such as full rail-sections, without detracting in the least from the value of the instrument when applied to the examination of the usual small specimen, as explained later. Many metal microscopists frequently have to examine bulky specimens, and this is altogether impossible with the ordinary microscopes as well as with the special metallurgical microscopes which have been designed and described from time to time. Recourse must be had to all sorts of makeshifts for the proper support of large specimens, or, more often, the microscopist gives up the attempt altogether, or else resigns himself to the cutting of the bulky samples into small pieces to -be laboriously polished and separately examined. It is believed that an instrument permitting the examination of large as well as of small specimens with equal ease and accu-

Dec 1, 1911

By William I. Rau

This presentation will examine the role commercial banks will be expected to assume in financing international minerals projects, including a discussion of various financing techniques such as project loans, production loans, and production payments. A discussion of the necessity for completion guarantees, finalized sales contracts, reserve evaluations, management contracts, and marketing undertakings in conjunction with financing availability are also included.

Jan 1, 1981

By Richard Rice

TURBO blowers for blast-furnace blowing have now been in use for some years, and a review of the experience gained and the present state of progress may be interesting. FIG. 1.-STEAM TURBINE DIRECT CONNECTED TO AIR COMPRESSOR. The first blast-furnace blowing engine of this type to be installed in America was built by the General Electric Co. and is installed at the oxford Furnace of the Empire Iron & Steel Co. This machine was put into operation March 8, 191.0. A duplicate unit is situated at the furnace of the Northern Iron Co. at Port Henry, N. Y., which unit was put into opera ion June 30, 1910 (Fig. 1).

Jan 5, 1914

By JOSEPH MACDONALD

STRIPPED of its romantic possibilities, mining is a commercial business, carried on for the profit there is in it, and the business of the manager, in its ultimate analysis, is to make the profit as large as possible. The general manager of a mining company should keep himself personally familiar with all the details of its operations. If be fails to do so, chaos results, labor becomes inefficient, costs go up, and profits go down. Nowhere is this emphasized more than in Mexico. If the mining operations are extensive and complex, involving, besides the work of mining the ore, its transportation and treatment by various milling operations, and the marketing of the products, the business, to be carried on properly, must be divided into a number of main departments, which are subdivided into minor departments. Each main department should be under the immediate charge of a superintendent, or a foreman, and each minor department under a shift-boss. Organized in this way, and with all the principal centers of activity connected by telephone, the manager can keep in touch at all times with the details of every branch of the business, and be in a position to perform effectively the full duty of manager. The ?total cost of mining operations may be broadly divided under the heads of Labor, Supplies, and Marketing. Of these, it will be found, on averaging a number of cases, that the cost of labor will be about two-thirds of the total cost. The importance, therefore, of an efficient labor-department will be apparent. This department must be sub-divided and organized differently, according to the peculiar conditions at each mine, and no one system, however well suited for one particu-

Jan 1, 1909

By C. A. Hartnagel

In 1939 the production of crude oil in New York totaled 5,105,000 bbl. This marks the third consecutive year production of crude oil has exceeded 5,000,000 bbl. and only once has this total been surpassed—in the year 1882, three years after the discovery of oil in Allegany County, when the annual production was more than 6,000,000 barrels. The most gratifying feature of the industry was the increased demand for lubricants, which resulted in advanced prices for crude. From a price at the beginning of the year of $1.68 per barrel, six advances totaling 82c brought the year's closing to $2.50 per barrel. A further increase in price on Jan. 1, 1940, to $2.75 per barrel places the local industry in a strong position for the year's operations. Most of the oil production of the state is now obtained by water-flooding, and the industry is practically stabilized. No new pools have been discovered in over 25 years, and border drilling indicates little prospect of extending the boundaries of the fields beyond their present limits. Deep drilling to the Oriskany sandstone in and close to the present oil fields hay failed to find oil in substantial amounts. Altogether, the oil pools of New York have produced during the 60 years that they have been exploited approximately 125,000,000 bbl. of oil. Following the flush production of 1882, the annual production gradually dccrcased and the year 1912 marked an all-time low of only 782,000 bbl. In 1919, as a result of flooding operations, a definite upward trend in oil production was recorded. During that year also the production of oil by water-flooding methods as approved by Legislative action. In the 21-yr. period beginning with 1919, oil production in the state ha.: totaled 60,338,000 bbl. Thus it will be seen that by the aid of flooding methods nearly as much oil has been produced in the last 21 yr. as in the preceding 40 yr., although the Iatter period included the flush production in 1882. As there is little hope of extending the area of the present producing oil fields of the state, producers and refiners are concerned regarding the future life of the fields. It is encouraging to observe that earlier esti- Published by permission of Director of New York State Museum, Albany, N. P. Summarized at meeting; manuscript received at the office of the Institute March 20. 1940.

Jan 1, 1940

By C. A. Hartnagel

In 1939 the production of crude oil in New York totaled 5,105,000 bbl. This marks the third consecutive year production of crude oil has exceeded 5,000,000 bbl. and only once has this total been surpassed—in the year 1882, three years after the discovery of oil in Allegany County, when the annual production was more than 6,000,000 barrels. The most gratifying feature of the industry was the increased demand for lubricants, which resulted in advanced prices for crude. From a price at the beginning of the year of $1.68 per barrel, six advances totaling 82c brought the year's closing to $2.50 per barrel. A further increase in price on Jan. 1, 1940, to $2.75 per barrel places the local industry in a strong position for the year's operations. Most of the oil production of the state is now obtained by water-flooding, and the industry is practically stabilized. No new pools have been discovered in over 25 years, and border drilling indicates little prospect of extending the boundaries of the fields beyond their present limits. Deep drilling to the Oriskany sandstone in and close to the present oil fields hay failed to find oil in substantial amounts. Altogether, the oil pools of New York have produced during the 60 years that they have been exploited approximately 125,000,000 bbl. of oil. Following the flush production of 1882, the annual production gradually dccrcased and the year 1912 marked an all-time low of only 782,000 bbl. In 1919, as a result of flooding operations, a definite upward trend in oil production was recorded. During that year also the production of oil by water-flooding methods as approved by Legislative action. In the 21-yr. period beginning with 1919, oil production in the state ha.: totaled 60,338,000 bbl. Thus it will be seen that by the aid of flooding methods nearly as much oil has been produced in the last 21 yr. as in the preceding 40 yr., although the Iatter period included the flush production in 1882. As there is little hope of extending the area of the present producing oil fields of the state, producers and refiners are concerned regarding the future life of the fields. It is encouraging to observe that earlier esti- Published by permission of Director of New York State Museum, Albany, N. P. Summarized at meeting; manuscript received at the office of the Institute March 20. 1940.

Jan 1, 1940

By W. J. Sharwood

Cupellation is well known to be one of the most effective methods of separating silver and gold from base metals and other impurities, as well as one of the most accurate means for their estimation. In the latter application it consists in absorbing in some porous medium the fused lead oxide formed by the oxidation of the lead "bath," which carries with it the oxides of other base metals present. It has long been recognized that small amounts of both silver and gold were removed and absorbed together with the base metals, as well as being to some slight extent volatilized, and in work of the highest accuracy a correction is made for the "cupellation loss." Thus in the assay of bullion this is done by means of "proofs" of like composition, which are manipulated throughout in precisely the same manner as the assay pieces, and are assumed to lose or gain like amounts. In the case of certain very rich ores and commercial products the loss is adjusted by assaying the cupel itself and recovering the precious metal absorbed, but this doubles the labor and does not remedy the loss by volatilization. Arbitrary tables have been drawn up by various authorities with the object of enabling a correction to be applied without the use of a check. These have been of very limited practical use owing to the fact that a number of factors affect the losses sustained. For a fixed amount of precious metal the loss varies with the amount of lead used, with the nature and amount of the impurities, with the porosity of the cupel, with the air supply, and above all with the temperature at which cupellation is carried on. Pure silver loses relatively much more than gold, but the loss in either is diminished by an addition of the other metal. The concentration of precious metal in the litharge increases as the concentration in the lead increases, but little work has been published connccting the two. If all other conditions remain the same the actual total loss increases, but the percentage loss diminishes, with an increase in the weight of precious metal treated. The results of an immense number of experiments have been published at various times- during the past hundred years giving the actual or the percentage losses suffered under various conditions of cupellation, but the data are widely scattered and few attempts have been made to correlate them, so that no definite law has heretofore been shown to exist

Jan 1, 1916

By Walter H. Bucher

THIS symposium is designed to lay the basis for a general discussion of the place of geophysics in the training of geologists. As there is danger that in the ensuing debate individual interests may be given emphasis out of proportion to their place, we shall do well to view the whole field of geological inquiry in order to see the problem in true perspective. THE NATURE OF GEOLOGICAL INQUIRY "Basic" and "Complex" Sciences It is convenient to divide all science into two major divisions, the basic and the complex sciences. The basic sciences separate out from reality such entities as "substances" and "movements," describe their behavior in terms of arbitrary units of measurement and derive from them by progressive abstractions concepts and patterns of behavior that exist between them, so-called general "laws" and "properties" of nature. The complex sciences, on the other hand, deal, with little or no abstraction, with those objects of reality that are accessible to man in the atmosphere, the hydrosphere, the lithosphere and the biosphere.† Their work comprises two types of inquiry. One is concerned with abstractions to the extent of dealing with types rather than individuals-that is, with such things as plants, animals, protoplasm; clouds, streams, glaciers; volcanoes and mountain ranges. It comprises the search for general properties and patterns of behavior or "laws" that characterize the objects and their reactions to each other. These properties and laws apply always, everywhere. They are independent of the stream of time. We may call the results of this sort of inquiry timeless knowledge. The other type of inquiry is concerned with the objects themselves-that is, with this animal and that plant; this river system and that mountain chain; this glacier and that valley. Like all concrete objects in nature, they are subject to change with the passage of time, especially when it is measured in years, centuries, eons. The characteristics by which we recognize them -indeed, their very existence are dependent on their position at this point in the stream of time. This we may call time-bound knowledge. The so-called descriptive sciences are all bound to the past of which the objects of their study are the product and through which alone their present properties can be understood. They are historical sciences. This obvious fact is easily overlooked, which leads to serious misunderstanding, as we shall see later. Dynamic Geology With this broad picture in mind, let us now examine the nature of geological inquiry, defining, for the purposes of this discussion, geology as the science of rocks. Air is not a rock; water is. Meteorology and climatology are, correspondingly, gen-

Jan 1, 1941

By W. E. D. Jr. Stokes

THE application of aviation to mining and petroleum operations, on the basis of economy and attainment, has become a demonstrated fact. According to Dominion Government records, 30 Canadian companies engaged in air transportation with northland mining camps, carried 13,000 tons of freight in 1935, and in 1936 carried 16,000 tons. In addition, many mining companies used planes to transport prospectors with canoes, outboard motors, gasoline drums and supplies to remote locations, and one company maintained a plane to take radium-bearing ore from its mine on Great Bear Lake nearly 1000 miles south to the rail-way at Waterways, Alberta. Heavy pieces of mining machinery weighing 2 tons are being carried by Ford trimotor planes over the Andes, at an altitude of not less than 15,000 feet. At Bulolo, New Guinea, 17,500 tons of disassembled gold-dredging equipment has been flown over inaccessible terrain, while supplies and building materials for a community of 1000 whites have been transported by airplane. A 31 z-ton shaft was carried on one notable trip, while at another time an automobile, 2 tons of rice and a large safe went over the mountains in one plane. Fig. 1 shows an electric generator that was carried by plane to Bulolo. Many large American oil companies operated fleets of planes during 1936, ranging from fast, luxurious air liners for executives to elaborate geological prospecting units, ambulance planes, freight carriers and pipe-line repair crews.

Jan 1, 1937

By Junnosuke Yamamoto

Substituting sodium hydroxide for sodium carbonate as a binder in a glass batch yields harder pellets with a lower melting point. This paper explores the degree of NaOH substitution that is feasible, and compares pellet hardness, and amount of dusting with the degree of NaOH substitution. The effects of the the amount of soluble silicate in the pellet and residual hydroxide concentration in the pellet on pellet hardness are also studied.

Jan 1, 1977

By Robert L. Gower, John H. Cash

Interconnections for integrated circuits operating at rnicrowaue frequencies rzust be formed as microwave transmission lines. This paper describes the fabrication of one type of microwave transmission line known as microstrip, which can be fabricated on momlithic integvated circuits by deposition of 0.1- to 2.0-mil-thick metal and dielectric films. A microstrip line consists of a narrow conducting strip separated from a gvound plane by a dielectric material. Thick films of good conducting materials are required for low loss at high frequencies. Vacuum-evaporation methods for depositing aluminum and silver films are described. The narrow conducting strip forming the top conductor is defined by photoresist-etching techniques after the thick rnetal film is deposited. Gold plating with a photoresist-masking technique is also used to forrrz thick metal conductors. The microstrip dielectric layer is formed by deposition of suitable dielectric films 0.1 to 2.0 mils thick. Several deposition techniques were investigated. Electron-beam evaporation of quartz is described. Electrical characteristics of deposited microstrip lines at microwave frequencies are included and the microwave power attenuation as a function of conductor and dielectric thickness is given. It is concluded that the deposition of microstrip transmission lines is a practical way to achieve low-loss interconnections in monolithic integrated circuits. CONNECTIONS between devices in low-frequency and digital circuits are usually made by connecting the devices with a length of conductor such as a metal lead oi- a wire. If this method were applied to microwave integrated circuits, the reactance of the connection due to the series inductance and parasitic capacitance would be very high, in fact too high to permit successful circuit operation. In addition, resonance and antenna effects would occur at high frequencies, especially when the connections approach the wavelength.' Connections which are sections of transmis- sion line will overcome these difficulties. The electromagnetic field is confined to the volume of the transmission line, parasitic effects are not present, and circuit design utilizes familiar transmission-line techniques. TRANSMISSION LINES One type of transmission line geometrically adaptable to integrated circuits is known as micrstri. A microstrip line can be generated from a coaxial line as shown in Fig. l(a). The outer conductor of the coaxial line is distorted into an ellipse (b) and finally separated at the extremities of the ellipse to form the strip transmission line shown in (c). One of the ground planes is then removed, leaving a conducting ground plane and a narrow conducting strip separated by a dielectric. Two configurations of the microstrip line were considered in this investigation, Fig. 2. Type (a) is fabricated from a semiconductor slice with the ground plane and top conductor deposited on each side of the slice. The semiconductor slice serves as the die lec-

Jan 1, 1967

By P. BOURY

THIS account of a contrivance which has been found serviceable in practice may be of interest to engineers, and' especially to those engaged in hydraulic mining. In that process, one feature which seems at first sight to possess little significance, is highly important in its effects, namely, the regular supply of water to the " giants." The chief condition of this regularity is an even flow in the pipe-line from the penstock to the nozzle. This, of course, requires that the penstock be kept full. Any considerable surplus of water, overflowing at the penstock, is a simple waste, unless it be otherwise utilized in the sluices. At all events, it does not affect the delivery of the nozzles. But a deficiency at the penstock may admit air into the pipe; and this may produce hydraulic recoil, injuring the line by incessant vibrations, giving rise to leaks, and even to blow-outs, and (when a partial vacuum exists at the time of the fracture the collapse of the pipe. An accident of this sort in our main pipe-line, occasioned partly by a settling of the ground and partly by the presence of air in the pipe, led to the employment of the device here described. The line referred to is made of 30-in. pipe, successively reduced to 18 and 15 in. in diameter, for the supply of two giants. By reason of the causes above mentioned, the 30-in. pipe burst more than 1,400 ft. from the penstock, and, despite the air-valve, the 30-in. pipe was collapsed to such a degree that one length of it, next to the penstock, was squeezed together and positively swallowed by the main pipe, through which it traveled for 750 ft., piercing through a short elbow on the way. This remarkable result was undoubtedly the effect of the vacuum suddenly produced when the pipe burst.

Sep 1, 1906

By Frank Julian

The determination of manganese by precipitation with potassium chlorate from a solution in concentrated nitric acid, filtration through asbestos, and solution in a reducing agent whose excess is estimated, is open to the objections that the filtration and subsequent solution of the binoxide are apt to be very slow, and that the asbestos may (according to Troilius), unless perfectly purified, affect the titration. In the following modification, filtration is avoided. I give the method as I use it for Bessemer steel. In an 8-ounce Griffen beaker dissolve 1 gramme drillings in 15 c.c. nitric acid (1.2 sp. gr.). Evaporate to 5 c.c.; add 20 c.c. concentrated nitric acid and precipitate with chlorate as usual, avoiding a large excess; then add about 60 c.c. warm water, and 10 c.c. of the oxalic solution; stir until of a clear light yellow color, and titrate with permanganate while the solution is at about 80' C. The binoxide should dissolve immediately when the oxalate isadded. The titration is rapid, and the end-reaction, though transient, easily caught after a little practice. The standard solutions used are: 15 grammes crystallized ammonium oxalate to a liter, and 1.6 grarnmes potassium permanganate to a liter. For standardizing the permanganate, to 10 c.c. of the oxalic solution is added 50 c.c. of hot water, and a solution of 1 gratnme of steel in concentrated nitric acid, from which the manganese has been removed by potassium chlorate and filtration through asbestos. I have made a large number of determinations in steel, pig-iron,

Jan 1, 1888

By Mark D. Zoback, Bezalel C. Haimson

INTRODUCTION A Workshop on Hydraulic Fracturing Stress Measurements was convened by the authors in December 1981 in Monterey, California under the auspices of the U.S. Geological Survey and the U.S. National Committee on Rock Mechanics. There are now over a dozen groups of investigators around the world who are actively using the hydraulic fracturing method for making in-situ stress measurements. Because of the extensive recent experience of these different groups, the Workshop enabled forty investigators from eight countries to comprehensively assess the status of the method. Based on the presentations and discussions at the Workshop, in this paper we briefly discuss the current status of the hydraulic fracturing stress measurement method concentrating on problem areas where further research needs to be done. A complete account of the presentations at the Workshop will be available through the Proceedings of the Workshop which will be published by the U.S. National Committee on Rock Mechanics in early 1983. The most exciting aspect of the Workshop was the discovery by the various groups of investigators that others were having very similar experiences with the method. The consensus among the different groups of investigators at the Workshop was that they were recording very similar pressure-time data in the field, they were able to interpret them in similar ways, and they were achieving results that were quite encouraging because of several factors. First, the results at various locales were found to be internally quite consistent. This was reported by investigators from Germany (Rummel, Baumgartner, and Alheid, 1982), Japan (Tsukahara, 1982), Australia (Enever, 1982), and the U.S. (see, for example, Haimson, 1978, 1982a; Zoback

Jan 1, 1982

By H. E. Swanson

A description of the field apparatus has been published by D. G. Brubaker. Data from laboratory model studies of the in-line and broadside methods of operation are detailed. The conductor models include a single sheet conductor at several strike and dip angles and a schistose-type conductor. In addition, data on the effects of the strike length and of the depth of the conductor are presented for the broadside method of operation. All of the data show that the inclintion reverses direction over the top edge of dipping single sheet conductors. Differences between anomalies over conductors dipping between 90" and 30" are subtle,but flat-lying sheets can be readily distinguished from steeply dipping sheets. Schistose conductors are easily distinguished from single sheet conductors, and a procedure is given for determing the direction of schistosity. The depth of penetration under ideal conditions is 0.7 of the coil separation. In 1950, The New Jersey Zinc Co. (of Pa.) developed a lightweight apparatus for electromagnetic prospecting. A description of this apparatus has been published by D. G. Brubaker.1 It consists of a small, battery-powered vertical source coil and a direction-finding receiving coil. Source and receiver are kept a fixed distance apart and move as a unit along the survey lines. At each receiver station the inclination of the magnetic field created by the source is measured. Two methods of operation are used, in each of which measurements are taken with a constant source-to-receiver distance and with the plane of the source oriented to pass through the receiver station. In one procedure, called the in-line method, source and receiver travel in tandem along the same line. In the other procedure, called the broadside method, source and receiver move along adjacent lines, with the source-to-receiver direction oriented parallel to the assumed strike direction. The data recorded in either case are the inclinations, measured in degrees from the horizontal, of the magnetic field created by the source. These data are plotted at the receiver stations on a map. Scale-model studies of both methods of operation have been conducted in the laboratory and are reported in this paper. APPARATUS Small source and receiving coils wound with many turns of fine copper wire were used to produce and measure an alternating magnetic field in the same manner as the field apparatus. The model source coil was mounted in a vertical position and oriented so that the receiving coil was in the plane of the source. The receiving coil was mounted in a frame so it could be rotated to obtain the inclination measurements. The source coil was excited by a 100-kc signal generator. A tuned amplifier and a voltmeter were used to detect the null position of the receiving coil. The coils used in the field apparatus are usually spaced about 400 ft. The coils used in the model work were spaced from 4 in. to 4 ft apart. Thus the scale of the model work ranges between 1/1200 to 1/100 natural size. The model conductors were aluminum-coated building paper supported on wooden frames. The conductivity-thickness product was measured using a four-electrode system and was found to be about 300 ohms-'. CONDUCTIVITY CONSIDERATIONS The electromagnetic response from a thin sheet conductor is a function of the product of the conductivity of the sheet times the thickness of the sheet times the frequency of the alternating electromagnetic field times some linear dimension of the system such as the coil separation which indicates scale. The secondary electromagnetic field produced by the conductor increases in amplitude from zero at zero conductivity to a maximum value for infinite conductivity, while the phase of the secondary field with respect to the primary field shifts from 90" at zero conductivity to 0" at infinite conductivity. Several authors2-' have shown that most of both the increase in amplitude and the change in phase of the secondary field takes place over a three-decade range of the conductivity-thickness-frequency product. Only small changes in the amplitude and

Jan 1, 1961

By George W. Becker, Blair R. Benner, Ronald J. Roman

A computer model for the leaching of oxide copper heaps is developed and verified in laboratory tests. The model can be used to scale-up laboratory test data and to simulate the results of various operating philosophies on heap leaching. The model is applicable to leaching processes where the rate of leaching is controlled by a deficiency of reactant or diffusion of a reactant through the leached rock. Several examples are presented showing the sensitivity of the recovery vs. time curve to the variables in leaching.

Jan 1, 1975

By David H. Carlson, John H. Johnson

The paper presents background information, a description of mine characteristics that affect air monitoring techniques, and a review of Portable measurement techniques and instruments for gas and particulate matter sampling. A general review of the laboratory and field research being conducted at Michigan Technological University in the area of diesel emissions is presented. The facilities involved with this research are also described. These are the experimental mine, the diesel dilution tunnel test cell, the mine air monitoring lab (MAML), portable instruments, and the production mines used.

Jan 1, 1982

By M. Gangal, B. Paul

It may be seen from Maurer's survey (Maurer,l 1966) that most of the common methods used in rock drilling today depend upon mechanical loading of the rock. In order to predict the behavior of rock under an imposed system of stresses, it is necessary to have a valid criterion which delineates those combinations of stress which cause macroscopic rock failure from those which do not. Admittedly, the conditions under which brittle materials fracture depend very much upon statistically variable local effects such as inclusions, grain boundaries, minute imperfections, etc. However, it is extremely desirable to be able to predict fracture under complex states of stress by means of a stress-criterion of failure, where, for a given material, the effects of the other variables mentioned are incorporated into a small number of experimentally observable parameters. One of the most successful of these "macroscopic stress criteria" has been the Coulomb-Mohr theory 2,3 (also see Jaeger 4 and Terzaghi 5), modified by the addition of tension cutoffs (Paul 6). At first thought it might seem rather odd that a macroscopic theory is capable of predicting fractures which originate at highly localized random imperfections at an atomic level (or more likely at the level of individual mineral grains in rocks). However, Griffith7 showed that fractures originating near the tips of randomly oriented elliptical cracks lead to the macroscopic stress criterion of failure indicated in Fig. 1 (a). Fig. I (a) is to be interpreted in the following way: P and Q represent the maxi mum and minimum principal stresses (compression is considered positive) in a macroscopically isotropic body; fracture will not occur for any combination of principal stresses lying within the 'fracture curve' shown, but

Jan 1, 1967