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[PRESIDENT AND DIRECTOR * R. R. McNAUGHTON, '63, Trail, B. C., Canada PAST-PRESIDENT AND DIRECTOR * JOSEPH L. GILLSON, '62, Wilmington, Delaware PRESIDENT-ELECT AND DIRECTOR * LLOYD E. ELKINS, '64, Tulsa, Oklahoma VICE-PRESIDENTS AND DIRECTORS * JOHN S. BELL, '62, Houston, Texas * A. B. CUMMINS, '62, Bound Brook, New Jersey * WAYNE E. GLENN, '62, Houston, Texas * C. C. LONG, '62, Monaca, Pennsylvania * J. S. SMART, JR., '63, New York, New York * J. W. WOOMER, '62, Pittsburgh, Pennsylvania]

Jan 1, 1961

[President and Director *JOSEPH L. GILLSON, '62 Wilmington, Del. Past President and Director *HOWARD C. PYLE, '61, Los Angeles, Calif. President-elect and Director *R. R. McNAUGHTON,'63, Trail, B.C., Canada Vice-Presidents and Directors *JOHN CHIPMAN,'62, Cambridge, Mass. *JOHN P. HAMMOND,'61, Tulsa, Oklahoma *WALTER R. HIBBARD, JR.,'61, Schenectady, N.Y. *BASIL P. KANTZER, '61, Los Angeles, Calif. *S. D. MICHAELSON,'61, Salt Lake City, Utah *J. W. WOOMER, '62, Pittsburgh, Pa.]

Jan 1, 1961

Institute of Metals Division SAM TOUR, Chairman J R FREEMAN, JR , Vice-chairman ZAY JEFFRIES, Past-chairman C H MATHEWSON, Vice-chairman WILLIAM M CORSE, Secretary-Treasurer 810 Eighteenth Street, N W Washington, D C Executive Committee Until February, 1031 Until February, 1932 Until February, 1933 T S FULLER J L CHRISTIE W M PEIRCE G E JOHNSON ARTHUR PHILLIPS A J PHILLIPS W A SCHEUCH H M WILLIAMS GUY C RIDDELL Research PAUL D MERICA, Chairman S SKOWRONSKI

Jan 1, 1923

By Donald P. Richards, John F. Abel

Geotechnical site investigation for new mine shafts can reduce the level of design uncertainty for shaft linings. The parameters which determine the lining strength required include rock strength and hydrologic properties, the in situ stress conditions, and the concrete strength. These parameters are applied to analytical methods of shaft lining design using the plastic and clastic assumptions of rock response to determine the required lining thickness to maintain the stability of the shaft excavation.

Jan 1, 1982

By John C. Shyne, Eric R. Morgan

BORON as a hardenability agent of commercial importance has been the subject of extensive study in recent years. It has been suggested in the past that boron increases hardenability by combining with nitrogen, thus rendering it innocuous.&apos; More recently it has been proposed that boron increases hardenability by reducing the free energy of sites of ferrite and pearlite nucleation.&apos; The segregation of boron to grain boundaries, the primary site of nucleation, would account for the large hardenability effect of minute additions of boron in steel. This grain boundary theory has found general acceptance while the concept of boron as a nitrogen scavenger has been disregarded. However, the interaction of boron and nitrogen in steel is considered to be important to hardenability because boron may be made ineffective by combination with nitrogen.". * The present work was undertaken to examine some of the effects of boron and nitrogen arid their interaction in steel. A base composition of moderate hardenability was chosen. This was a 0.35 pct C steel containing 2.50 pct Ni and 0.30 Mo. This composition was used because it contained no strong carbide, nitride, or Table I. Composition of Steels by Analysis, Wt Pct Steel C Ni Mo 0&apos; B N* Base 0.35 2.50 0.30 0.0012 nil <0.0001 Boron 0.35 2.50 0.32 0.0012 0.0022 <0.0001 Nitrogen 0.33 2.60 0.35 0.0015 nll 0.0052 Boron plus nitrogen 0.35 2.48 0.30 0.0006 0.0020 0.0040 * Obtained by vacuum fusion technique. boride-forming elements. The other alloys examined were modifications of the base composition and contained nitrogen, boron, or nitrogen plus boron. The compositions of the four alloys used are listed in Table I. The alloys were vacuum melted from electrolytic iron, electrolytic nickel, ferromolybdenum, and fer-roboron. When required, nitrogen was added by admitting a partial pressure of nitrogen over the melt after vacuum melting. The alloys were cast into 21h-in. diam ingots and hot rolled to %-in. sq bars. No ingot pattern was discernible on the polished and etched cross sections of the hot-rolled bars. The alloys were normalized at 1650°F, then machined into standard %-in. diam end-quench hardenability test bars. Four different austenitizing treatments were used: 60 rnin at 1550°F, 45 rnin at 1800°F, 30 rnin at 2000°F, and 20 rnin at 2000°F followed immediately by 30 rnin at 1550°F. The 1550" and 2000°F treatments were carried out in duplicate for each of the four steels. In order to prevent surface oxidation the bars were austenitized while buried under charcoal in an atmosphere of argon. After quenching the bars in a conventional end-quench fixture, the hardness surveys were made in the usual fashion on parallel flats ground along opposite sides of each bar. These were ground 0.050 in. deep rather than the conventional 0.015 in., to avoid decarburized or deboronized regions.5 The austenite grain sizes which resulted from each heat treatment were observed metallographically using Vilella&apos;s etch for martensite. The criterion used as a measure of hardenability was the distance from the quenched ends of the bars at which a hardness of RC 35 was observed. This hardness represented the inflection point on the hardness vs distance plot. Fig. 1 shows the hardenability of each steel after the several heat treatments. The duplicate tests demonstrated excellent reproducibility; the distance to Rc 35 was reproduced within 1/16 in. for duplicate test bars. All four alloys had the same grain-coarsening characteristics. Neither boron nor nitrogen had any observable effect on grain size. The grain sizes resulting from the various austenitizing treatments were ASTM 7 at 1550°F, ASTM 4 at 1800°F, and ASTM 2 at 2000°F. The small amount of boron in the boron steel greatly enhanced hardenability when the samples were austenitized at 1550°F. The low hardenability of the boron plus nitrogen steel showed that nitrogen eliminated the boron contribution to hardenability. Both steels containing nitrogen, with and without boron, exhibited lower hardenability than the base composition when quenched from 1550°F.

Jan 1, 1958

By F. F. Sharpless

ON Saturday evening, Sept. 9, a small party of Institute members, their wives and friends, left New York to attend the Fall Meeting of the Institute at San Francisco. In this party there were: President and Mrs. Arthur S. Dwight; Mr. and Mrs. George D. Barron; Mr. and Mrs. H. J. Stehli; N. S. Spencer and Miss Spencer; the Secretary and Mrs. F. F. Sharpless. They were joined at Chicago by E. F. Eurich, and by Mr. and Mrs. R. L. Baldwin and daughter. Our party was met at Chicago by Mr. and Mrs. L. V. Rice, Mr. and Mrs. A. D. Terrell and W. F. Boericke, who constituted themselves an impromptu entertainment committee and proceeded to carry out a delightful little program. We were taken to the Lake Shore drive, where a stiff wind off the lake refreshed us after a sultry day on the train, and on our return to the city saw Chicago illuminated with all its brilliance of electricity. We were entertained at dinner at the Drake Hotel. In spite of being two hours late getting into Omaha, we were right on the dot at Denver on Tuesday morn-ing. Horace F. Lunt came to the hotel soon after breakfast, and told us that a trip to the mountains had been planned. Having learned the number in the party, he began to gather up his automobiles for a 10 o&apos;clock start.

Jan 10, 1922

By P. Ramachandrarao, T. R. Anantharaman

CONSIDERABLE interest has lately been evinced as regards the nature of chill zones in solidified metals and alloys. Biloni and Chalmersl were the first to show through their study of segregation substructures in some nonferrous alloys that the formation of the dendritic region may be preceded by a diffusionless solidification process, viz., predendritic solidification. Subsequently Bower and Flemings2 tried a special solidification technique wherein the liquid was drawn into a narrow copper mold with polished surfaces and concluded that convection might trigger some multiplication mechanism leading to grain refinement. Using uncoated and partially coated surfaces for molds in the Bower-Flemings technique as well as in conventional molds, Biloni and Morando3 have very recently brought out the importance of the rate of heat extraction on the mechanism of solidification. We report here on the surface structures and substructures observed in a Sn-1 wt pct Pb alloy solidified at even higher cooling rates (riz., l05 to l07 ºc per sec) than those employed by earlier workers. The alloy was made by melting tin (99.99+ pct) and lead (99.9+ pct) in a silica tube under vacuum. Small quantities of the homogenized alloy (0.5 to 1.0 g) were then quenched (or splat-cooled) from the melt by the "gun technique" developed by Duwez et al.4 The thickness of the resultant foils varied from specimen to

Jan 1, 1970

By AIME AIME

THE following is the discussion of a paper, with the same title, by N. L. Alison, which appeared in our February issue: E. F. Tillson commented that while the fundamentals are well presented it would have been of interest to him to have had the author add some of his own experiences with fan installations. A. W. Hesse remarked concerning the use of the forward curved blade fan on the surface at a metal mine which has, ordinarily, but few airways, that the farther they are driven, the higher the resistance rises, and less air will be delivered, as the water gage will remain constant with a consequent loss in quantity. D. Harrington added that the metal mines do not or¬dinarily install fans until the mine is well developed, so changes are relatively slower after fan installation than at a coal mine.

Jan 1, 1930

Members whose deaths were reported from Apr 7, 1923, to Apr 5, 1924 Elected Died 1918 ADKINSON, HENRY M 1923 1900 AGNEW, WILLIAM C 1923 1894 ASHLEY, H H 1923 1897 AUSTIN, KENNETH 1924 1903 AYERS, EMMA L C 1923 1913 BAECHTOLD, CHARLES A 1924 1900 BAIN, HUGH A 1924 1919 BASHORE, E GORGAS 1923 1920 BATTELLE, GORDON 1923 1923 BAYLES, GERARD L 1924 1881 BROCK, CHARLES 1923 1903 BROOKE, HENRY 1923 1876 BROWN, HARVEY H 1923 1904 BROWN, THOMAS E 1923 1919 BUCK, DANIEL M 1924 1906 CHALMERS, THOMAS S 1924 1881 CLEMES, JOHN H 1923 1896 COLLINS, HENRY F 1924 1871 COURTIS, WILLIAM M 1923 1915 CRESSON, B F, JR 1923 1921 CROWE, WALDO P 1923 1920 DARNELL, J ORA 1923 1911 DAVIS, HENRY G 1924 1918 DAVIS, ROBERT S 1923 1916 DEANE, WILLARD A 1924 1901 DEMPSTER, WILLIAM 1924 1911 DEVEREUX, W B, JR 1923 1895 DICKENSON, F M 1924 1904 DRUM, FRANK G 1924 1875 DUDLEY, P H 1924 1916 EATON, ARTHUR 1923 1919 EATON,SHERMAN 1924 1911 GRIFFITH, WILLIAM 1924 1919 HILSDALE, PAUL 1923 1922 HODGES, I F 1923 1916 HOFIUS, MAX, T 1924 1914 HUGHES, HOWARD R 1924 1919 HUMMEL, CARL B 1923 1874 HUNT, ROBERT W 1923 1921 JONES, ERNEST EVANS 1923 1917 JOSLIN, CHARLES T 1923 1918 KASJENS, JACOB G 1923 1899 KIRKEGAARD, PETER 1924 1920 KLAUS, HARRY C 1923 1892 KNOERTZER, HENRI1924

Jan 1, 1923

By N. A. D. Parlee, I. D. Shah

THIS communication reports the results of some work done on the effect of gold, palladium, and platinum on the liquid-gas-solid equilibrium in the Ag-O system,1,2 see Fig. 1. Recently several investigators3, 4, 5 have reported the effects of gold, palladium, platinum, and copper on the solubility of oxygen in liquid silver. This communication represents only a portion of the work done here on the solubility of oxygen in liquid silver and liquid Ag-Au, Ag-Pd, and Ag-Pt alloyss—the greater part having already been reprted. The apparatus, materials, and procedures used were similar to those of earlier work.&apos; l The main precautions observed in obtaining these freezing points at constant temperature and PO2 = 1 atm were as follows: 1) The points were approached very slowly from higher temperatures. 2) In the very near vicinity of the L-G-S equilibrium point precautions were taken to see that the melt was in equilibrium with oxygen at one atm. Equilibrium was considered to have been attained when no more absorption of oxygen was observed in the last 15 min at a fixed temperature. 3) In the case of these alloys, the freezing point of the melt at 1 atm of oxygen and the equilibrium amount of oxygen absorbed by the liquid "infinitesimally" above this point were determined by lowering the temperature in very, very small steps, equilibrating at

Jan 1, 1969

By John R. M. Hill, Gerald Zink, Fun-Den Wang

The work described in this paper is sponsored by the Bureau of Mines for the purpose of accelerating the drilling of roof bolt holes and reducing the quantity of materials needed to fill each hole. A high-speed, small-hole drill has been fabricated and tested in the laboratory. High Priority has been given to safety, reliability, and compatibility with underground coal mining practice. The combination of drag bits and erosion jets is designed for high penetration rate, long wear life, and uniform hole size in a variety of sedimentary strata. A reliable high-pressure, high-speed swivel feeds water to the bit at about 4 L/min (1 gpm). The duplex hydraulic intensifier which drives the jets has a 40-kW (30-hp) capacity. Results of recent full-scale laboratory testing (Now. 1977) are presented.

Jan 12, 1979

SAMUEL L. HOYT,* Minneapolis, Minn. -I was privileged to see the apparatus used by Mr. Scott, which is quite unique. It is, as the author says, a modification of the apparatus designed by Dr. Rosenhain, but it is evidently quite an; improvement. The author is to be congratulated on the fact that lie has given us, with his apparatus, a quantitative thermal analysis of these critical points. I notice the author refers to Ac3, Ac2, and Ac1. His designation of the Ac2 point is all right, but naturally in a steel with as much carbon as this, which would mean a hypereutectic steel, the other point might better be considered as an Ac, point with possibly another point above the Ac, point. Another important point brought out is the fact that, in Fig. 3, the lines representing the Ar1, transformation and the Ac,1_3 transformation do not intersect at the zero rate curve,

Jan 5, 1919

By J. E. McConnell

No. 1 Electric Furnace and Billet Casting Shop, located in Plant No. 4 adjacent to our new 12 inch merchant bar mill, represents Inland Steel Company&apos;s first venture into both electric furnace steelmaking and continuous casting. Construction of the shop began in September, 1968 with excavation and foundation work, followed by awarding of general construction and major equipment contracts from December, 1968 to April, 1969. The first heat was tapped from No. 90 furnace on December 18, 1970, and the first cast attempted on December 29, 1970. The rated shop capacity is 500,000 tons per year of semi-finished billets and blooms, and was justified on the basis of approximately 85 percent of the product mix falling into the special bar quality category of steel grades. Auxiliary equipment has been designed into the shop to pursue free machining steels, including leaded and tellurized grades. The start-up and operation of the shop for the first year was essentially based on a two-part philosophy: 1. Initially operate with the "open stream" casting technique to accomplish machine shakedown and operator familiarization and training. 2. Operate with special bar quality, or "submerged casting", practices, make necessary refinements and gain customer acceptance

Jan 1, 1972

By AIME AIME

BY COMBINING the sessions on reduction and refining of copper, lead and zinc it was possible to devote an entire day to nonferrous metallurgy. Four interesting papers were presented at the morning session and four more in the afternoon. In the discussion of papers on copper, F. R. Pyne acted as chairman, with H. M. Shepard as vice-chairman, whereas for those on lead and zinc, F. F. Colcord acted as chairman, with C. R. Hayward as vice-chairman. The paper by P. D. I. Honeyman on the smelting of raw concentrates in the reverberatory furnace was presented by Mr. Pyne and discussed by Messrs. Mazany and Hayward. The interesting paper by E. S. Bardwell, com- paring the use of various fuels in copper-refining furnaces at Great Fails, Mont., was presented by Mr. Shepard and discussed by Messrs. Boggs, Gronningsater and Hayward. That by R. G. Knickerhocker, describing the stationary basic copper converter at Messina, Transvaal, was presented by Mr. Pyne, together with a written discussion by c. R. Kuzell, of the United Verde Copper co. It was an interesting illustration of how well-known processes may sometimes be modified to fit into unusual conditions.

Jan 1, 1932

By F. Keller

ALUMINUM alloys containing magnesium and silicon are susceptible to strengthening and hardening by suitable heat-treatments, and they constitute a class of alloys of considerable commercial importance. Generally, they contain these two elements in the proportions required for the formation of the intermetallic compound Mg2Si, or an excess of silicon; no commercial wrought alloys are made with an appreciable excess of magnesium. The reason for not having excess magnesium is obvious from the results given in this paper, since it is shown that excess magnesium results in a proportional decrease in the solubility of Mg2Si. This is the eighteenth1 of a series of papers from the Aluminum Research Laboratories dealing with the equilibrium relations in aluminum-alloy systems; most of the previous publications concerned binary aluminum-alloy systems; this is the fourth of a group pertaining to ternary aluminum-alloy systems. The work on this system was com-pleted in 1930, but the results were not published because of the pressure of other work. Hanson and Gaylor2, in 1921, presented the results of an extensive investigation of the aluminum-magnesium-silicon system. Their results indicated that an excess of magnesium over the amount required to form the compound Mg2Si caused a noticeable decrease in the solid solubility of Mg2Si in aluminum. A more recent investigation3 in these laboratories showed that the solid solubility of Mg2Si in aluminum was 1.85 per cent at 595° C. and decreased to 0.30 per cent at 300° C. The results of the latter investigation were used as the basis for the present work.

Jan 1, 1936

By Owen S. Roberts

During the design phases of a conveyor system, the question arises regarding the type of drive required for each application. The paper shows that the correct drive for any particular application is the one that satisfies the criteria established for that application in the most economical manner consistent with such considerations as site location, availability of spare parts, area environmental conditions, power supplies available, etc. Following discussions of various mechanical arrangements for the drives, motor types and their characteristics are considered along with the control means of modifying these characteristics to satisfy individual requirements. These characteristics are all illustrated graphically. After selecting the motor and its starter, control accessories and interlocking arrangements as applied to material handling systems are discussed.

Jan 1, 1973

By Thomas Read

IN speaking of immaterial problems of industry I am using the word immaterial in its original sense, not consisting of matter; not in its derived sense, unimportant. There is nothing of a paradox in saying that immaterial problems are the most important in human life, for His a matter of everyday observation that much of the news in the daily papers, and most of the world&apos;s best literature and drama, deal with human conduct that has for its motive forces that are but little concerned with material things. The engineer&apos;s preoccupation with physical forces, in extending his control over them, has not blinded him to the impor-tance of forces that, for want of a better word, I call immaterial; but he has considered that dealing with the one is his job and the other is not. All the evidence of the past decade indicates that the latter are so in-extricably interwoven with the former in modern in-dustrial life that the engineer will have to concern himself with them whether he wants to or not. Some of the most important of the problems arising from the action of these forces relate to the mental hygiene of the workers in industry. Mental hygiene in industry was concisely defined, in terms of the best present knowledge, by Dr. C. Macfie Campbell, speaking last April before the executive com-mittee of the Associated Industries of Massachusetts, and as his statement can scarcely be bettered, I quote it below: "The term mental hygiene is apt to appear vague. The actual stuff with which mental hygiene deals may be briefly reviewed.

Jan 9, 1927

By Lawrence W. Teufel

An anelastic strain recovery technique is presented as a method of determining the directions and ratio of the maximum and minimum horizontal in-situ stresses from oriented cores from deep wells. Predictions of hydraulic fracture azimuth inferred from principal stress directions determined from both elastic and time-dependent (anelastic) strain relaxation measurements of volcanic tuff are consistent with the observed orientations of hydraulic fractures produced in simulation and mineback experiments, underground at the Nevada Test Site. In addition, anelastic strain recovery measurements on oriented cores of shale and sandstone from well depths of about 1680 meters show consistent relaxation directions of the principal horizontal strains and have enabled a prediction of the principal horizontal stress directions and hydraulic fracture azimuth.

Jan 1, 1982

By C. W. Lawr

The ores mined by the Santa Gertrudis Co. at Pachuca, Mexico, arc mainly silver-bearing; they also yield some gold and carry a little copper. Strong cyanide solutions are used to dissolve the silver and gold, and the mechanical loss of cyanide at the tailings filter has been considerable. Prior to the year 1923, the pulp, after agitation, was given a 35 to 37-min. wash with barren solution in a Butters-type leaf filter; the discharged slime cake was repulped and pumped into eight Merrill self-sluicing slime presses in which the slime was given a further wash with barren solution for 25 to 35 min., followed by a 10-min. water wash. At that time the barren solution titrated around 0.350 per cent. free KCN and 0.500 per cent. total KCN. (Aero brand cyanide is used.) It can readily be seen that a 10-min. water wash would leave considerable cyanide in the filter cake, which of course was a total loss. This averaged 0.522 kg. (1.15 Ib.) KCN per ton of solution. As the daily discharge to the dam was 1600 tons&apos; of slime of a 2:1 ratio of liquid to solid, the value of this mechanical loss of cyanide was an important item and it&apos;s recovery held alluring possibilities. Principle of Cyanide-recovery Process As it had acquired the patent rights to theLayng (H. R.) and Halvor-sen (A. L.) processes, also those of Mills (L. D.) and Crowe (T. B.) after considerable experimental work in its own laboratory and at Tonopah, Nev., The Merrill Company of San Francisco early in 1923 notified the Mexican Corporation and compania de Santa Gertrudis of its process for the recovery of cyanide from weak wash solutions, or for the transference of cyanide from a foul mill solution to a clean alkaline solution. This method is known as the Mills-Crowe process, the principle of which is as follows: The solution from which the cyanidc is to be removed is made acid by bringing it into contact with sulfur dioxide (SO2). The acidified solution is the; transferred to a closed tank in which air and solution are brought into intimate contact. The air leaving the tank charged with HCN is then passed to another tank in which it is mixed with an alkaline solution,

Jan 1, 1930

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-&apos; the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:&apos; and, if some simplifying assumptions about particle shape are allowed, the total number of particles.&apos;2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.&apos; Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968