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By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

CHAIRMAN (J . E. JOHNSON, J R., New York, N. Y.).-It may be n matter of some interest that sodium cyanide is now being made commercially by melting together in an electric furnace calcium cyanide with a common salt, which produces calcium chloride and sodium cyanide. It seems to me entirely possible that you have here about the same results that would be obtained by melting calcium chloride and ordinary cyanide together, only you obtain it a good deal cheaper. There is no doubt about that reaction once it is being carried on on a large industrial scale for the manufacture of cyanide for other uses. I think probably the same, thing takes place here, with the possible exception of lowering the melting point due to the presence of the calcium chloride.

Jan 5, 1919

By J. Moore Samuel

THE prospective change in ore receipts at the Copper Queen reduction works necessitated a careful study of conditions to determine the most economical method of smelting. The first step, calculating the known, probable, and possible results, showed the economy of a unimetallurgical flow sheet f which the three pyrometallurgical stages would be roasting, reverberatory smelting, and converting. The past and future ore receipts (not including converter flux) are as follows: AVERAGE MONTHLY FUTURE MONTHLY RECEIPTS, 1918 RECEIPTS TONS PER PER CENT. OF TONS PER PER CENT. OF MONTH TOTAL RECEIPTS MONTH TOTAL RECEIPTS Ore 84,553 82.3 43,000 44.0 Gravity concentrates 16,375 15.9 25,500 26.0 Flotation concentrates 1,883 1.8 29,400 30.0 Total 102,811 100.0 97,900 100.0 Of the 102,811 tons per month received in 1918, only 28,945, or 28 per cent., was treated in the roasters and an average f 14.1 roasters out of 20 were in operation; the remaining ore was treated in the blast furnaces. The change to "all reverb." practice, therefore, called for considerable additional roaster capacity, which could be obtained either by building additional units, or by remodelling the present units so as to give increased unit capacity. In view of the progress in roasting practice since the construction of the Copper Queen roaster plant and the heavy investment in that roaster plant, the second plan seemed to be the more desirable. The Copper Queen roaster plant consisted of twenty six-hearth, McDougall roasters, 18 ft. in diameter, equipped with cast-iron arms that originally were water cooled but now are air cooled. They have no top dry hearth and the feed is discharged through the top arch, near its periphery, by plunger feeders from two bins at opposite sides of the roaster.

Jan 7, 1921

By James K. Richardson

FIRST indications that mineral industries expansion is beginning to show results are contained in the report by Defense Mobilizer Charles E. Wilson, The Battle for Production. The report, submitted to the President early this year, says that the United States has reached a $2 billion-per-month rate in military deliveries-three times that of 1950. Plant expansion in 1951 totalled $11.1 billion, the report states. Certificates of accelerated amortization have been approved to cover $11.4 billion in proposed plant construction. In reference to plant expansion significant to the mineral industry, the report states: •Steel industry goal is 120 million ingot tons by 1954, compared with present 108 -million ingot ton capacity. •Taconite beneficiation should result in 15 million tons by 1955. •An existing annual aluminum output rate of 860,000 tons. •An estimated 500,000 tons of sulphur by late 1953 •Manganese production up 50,000 tons as- the result of new projects in 1952. •Montana tungsten project coming into production in 1952. •Present zinc production expansion projects to add an estimated 150,000 tons to the 1951 production figure in 1953. Information gathered from official sources, other than Mr. Wilson&apos;s report, indicates an increase in the annual capacity of other segments of the industry by 1955, as shown in Table I. [ ]

Jan 1, 1952

By A. L. Blomfield

THE Golden Cycle Mining and Reduction Co. operates its custom mill at Colorado Springs on Cripple Creek ores exclusively. These ores are straight sulpho-tellurides, with practically no base metals such as Pb, Cu, Zn, As, or Sb. Upon entering the mill, the ore all passes through the sampler to storage bins, where beds of 5000 tons each are made to insure uniformity in roasting. CLASSIFICATION OF ORES For efficiency, it has been found advisable to separate the ores into two classes according to their line content. Other constituents have their effect, such as alumina and magnesia, but, speaking generally, these are roughly proportional to the line, which, as CaO, is used as the indicator. Class A contains not more than 2 per cent. CaO and comprises about 66 per cent. of the ore treated. Class B contains over 2 per cent. CaO, and comprises 34 per cent. of the ore treated. Typical analyses of both classes are as follows: Class A Class B Insol 56.70 75.90 Al203 2.30 3.40 Fe 3.26 3.48 CaO 1.57 5.12 S 1.79 1.80 Mg0 0.21 1.08 Ignition loss 3.20 6.50 99.03 97.28 The beds of each class of ore are made as large as possible with the available ore as it comes in, to avoid changing from one bed to the other any oftener than necessary. Each roaster will handle 50 percent. more of class A ore than of class B, with practically the same results. This necessitates changing the rate of feed for each new bed and tends toward a poor roast and loss of tonnage at each change.

Jan 8, 1918

A mine in the mountains of southeastern British Columbia is fast earning a reputation as the safest metal mining operation of all time. Already officially proclaimed as the safest mine in Canada, the H.B. mine of The Consolidated Mining and Smelting Co. of Canada (Cominco) continues to advance its safety performance far in the lead of average accident frequencies in mines across the country. Official recognition came its way again this spring when the Cominco mine was awarded the John T. Ryan trophy for the fourth time in the last five years. This award is emblematic of top national safety performance of a metal mining operation. The H.B. mine is its only four-time winner. The Ryan award is based on a frequency of accidents involving lost time of more than six days. In each of the years that the H.B. has won the award-1958, 1959, 1961 and 1962-its frequency was zero, with no accidents involving a time loss of more. than six days

Jan 12, 1963

EUROPE continued to be unsettled, financially, commercially and socially. October opened with Germany in a state of turmoil following the Government&apos;s cessation of passive resistance to the French and Belgians. In many places there were riots with much bloodshed. In Bavaria a military dictator-ship was set up in order to keep peace. In the meanwhile France continued in an uncom-promising position.. Great Britain, having been diplo-matically discredited, disappeared from any prominence in the international picture. Under the constraint of circumstances the policy of deflation in Great. Britain was temporarily abandoned. Perhaps no other course was open, for with declining trade and heavily reduced revenue, and no chance for cutting expenses propor-tionately, a check to deflation comes of its own accord. The effects of this should become manifest in the course of a few months and should appear in the form of an improved margin between the prices for commodities and the wage costs in producing them. About Oct. 20 an effort was made to set up the Rheinland as a separate republic. On Oct. 26 were published communications from Lord Curzon to Secre-tary Hughes and the latter&apos;s reply. In these Lord Curzon drew attention to the gravity of the situation in Europe and expressed the hope that France might listen to renewed suggestions for a general inquiry. Secretary Hughes promised American cooperation, in this, with the reservation that the question of inter-national debts should not enter into the situation. In the latter part of October there were military mutinies and disorders in Greece, which resulted in the reestablishment of martial law by order of Col. Plas-tiras, who is virtually the dictator of Greece. The incipient revolt was promptly crushed.

Jan 10, 1923

By R. C. de Lange

An improved replica technique is developed for a nondestructive study of the nucleation and growth of fatigue cracks. Three different growth stages of a fatigue crack were observed. An initial stage of high growth rate is followed by a long period of very slow growth, until finally a third period of high growth rate leads to fracture. THE metal-fatigue process is of a very complex nature. The experimental approach towards fatigue is susceptible to many minor influences which, together with the unavoidable scatter in testing results, makes the interpretation a matter of extreme care. The generally accepted fact that, in a homogeneous material, the fatigue cracks start at a free surface indicates that surface studies may contri-but in an essential way to a better understanding of the fatigue mechanisms. Indeed metallographic observations of the fatigue phenomena have been very fruitful in the last decade. The study of extrusions, intrusions, and persistent slip bands has contributed much to the present knowledge of the early processes in fatigue.&apos; The drawback of the current metallographic techniques lies in the fact, however, that either observations of fatigue phenomena had to be made in a destructive way after an only partly executed test or a sequence of observations on the same test bar was only possible on notched specimens.2 4 In both cases an uncertainty exists as to the nucleation and growth of the fatigue crack in an unnotched test bar, where the crack can start at any place of a large area and develops in a test bar, which is macroscopically

Jan 1, 1964

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3&apos;) a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;&apos; hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.&apos; This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By T. A. Rickard

Flaubert, as we know, laid stress on the selection of the right word, le mot juste, the precise epithet, the word that belongs to the thing. A sentence, or even a paragraph, may be spoiled by the use of a word that is not proper, that does not fit or is foreign to the meaning intended. An Australian mining expert is reported to have said: You have a property of considerable value, and what I saw warrants a good development of very rich cubicular galena, with gossan intermixed. &apos;Cubicular&apos; means `belonging to a small bedroom&apos;, a `cubicle&apos; being a sleeping compartment. He meant `cubic&apos;, of course. This is a malapropism, and reminds me of the lady from Chicago that, on her return from Europe, said how much she had enjoyed the rural parts of France, because, among other things, it was "so delightful to hear the French pheasants singing the mayonnaise to the tune of the Los Angelus". It is impossible to amalgamate coal-tar thoroughly with the pulp in the agitating-tank. In metallurgy, `amalgamate&apos; refers to the combination of mercury with one or both of the precious metals, forming an amalgam, which is an alloy of mercury with another metal. It differs from other alloys, such as brass or bronze, in being made without the aid of heat, inasmuch as mercury is molten at the ordinary temperature. The word comes to us from the Greek. through Old French and means `something soft&apos;. It is a mistake to use technical terms, having a specific meaning, for purposes that are foreign to that meaning. The writer of the quotation is not discussing any combination of metals; he is dealing with the physical process of mixing and is using &apos;amal-

Jan 1, 1931

ALABAMA Anniston.-Bretz, J A Carnngton, F G Gerber, A B Ashland -Barton J Sturdevant, J C Bessemer -Abbott, C E Ball, T L Ferguson, V Salmon, H S Schaber, C F Thompson, N E Whatley, W J Birmingham.-Adams, J H -Aldrich, T H Aldrich, T H , Jr ALASKA Anchorage -Dyer, B W. Parker, H C Smith, S S Chichagof.-Baumann, H N , Jr Copper River.-Douglass, W C Cordova.-Hazelet, G C Fairbanks -Davis, J A Hyder -Pitt, D L Juneau -Jackson, G. T Murphy, R E R..11 ti At i

Jan 1, 1923

By J. D. Vincent, Paul A. Weyler

Climax Molybdenum&apos;s plan for the Henderson 30,000 tpd molybdenite plant didn&apos;t just happen. It slowly evolved over a period of 3% years. Many plants cannot afford similar delays, but the Henderson project will take about 10 years to complete from the time the orebody was first discovered until production begins. Pilot plant testing results with both the single stage and two-stage semi-autogenous grinding circuits were highly favorable in terms of operating costs reduction-so much so, that the Amax subsidiary made the decision to go with semi-autogenous grinding for the Henderson mill.

Jan 5, 1972

By A. Gittens

In two recent papers stevens13,14 has compared the methods used by various investigators to calculate the contribution of grain boundary sliding to the total creep strain. In previous work Gittins15 has shown that the strain due to grain boundary sliding Egb may be estimated from the lateral, d, and vertical, v, displacements of a longitudinal marker line as it crosses a grain boundary. He obtained the formula, where nL is the number of grains per unit length measured on the specimens before creep, and \p and ?2 are, respectively, the angle between the grain boundary and the stress axis in the plane of the surface and normal to the surface (see Ref. 13, Fig. 1). The subscript L indicates that observations are made in a longitudinal direction parallel to the stress axis. It was generally found more convenient to measure the grain size of a specimen before creep; this was necessary to characterize the specimen. Stevens13,14 however prefers to define Egb in terms of NL, the number of grains per unit length after creep. Since nL - NL(l + €1) where cr is the total strain, Eq. 1 11 becomes The quantities d and ?, can be determined directly from the marker lines, while v and ?2 are found by sectioning normal to the surface. In the interior when symmetry considerations suggest that v = d and ?1 - ?2 the strain due to grain boundary sliding may be estimated from a suitable internal longitudinal marker line by the equation To determine cgb at the surface using either Eqs. |1| or [2] requires a large number of observations, particularly if many estimates of cgb are required, and also it is impossible to determine the variation of cgh with creep strain on the same specimen because the specimen must be sectioned to determine ?2. Gittins15 found that for a number of materials the sliding vectors d and v were related to each other so that provided one was measured the other could be estimated. Also during creep, grain boundaries tend to migrate to meet the surface at angles close to 90 deg,16 so that the term nL(v/tan?2)L was comparatively small when 4,- 90 deg. By determining the frequency distributions of ?2 on control specimens this term can be estimated without sectioning the creep specimen. In this way an empirical equation based on Eqs. |1| and |2| enables cgb to be determined with reasonable accuracy with fewer observations of the angles and sliding components. For B brass, the relationship between the sliding vectors indicated that ceb = 0.85nLVL . In Table I of Stevens paper this equation is stated to be incorrectly derived. However it should be pointed out that this is an empirical equation derived from Eq. |1|, based on a knowledge of the relationship between d and v and on the frequency distributions of ?1 and ?2 for a particular material under given experimental conditions. It was used only when these relationships were known, to reduce the number of observations required to estimate cb. Therefore the comment "derivation incorrect does not apply. Gittins did in fact make use of Eqs. |1| and 131. Author&apos;s Reply I must apologize to Dr. Gittins for the inadvertent misrepresentation of his work. Other slight errors in Table I have been pointed out to me. Langdon (No. 12 Table I), Gifkins (No. 7, Table I), and possibly other workers did not measure the number of boundaries per unit length after creep (A&apos;) but the corresponding quantity bejove creep (n). As Dr. Gittins points out, a completely analogous set of equations to those given in the paper can be derived by the same method: using the number of boundaries per unit length before instead of after creep. The basic equations corresponding to Eqs. [2] and 171 of the paper, from which all the others can be derived, are

Jan 1, 1968

By W. M. Corse

AS THE outstanding contribution of the Committee on Correlation of Research of the Institute of Metals Division for 1932, may be mentioned the publication of Bureau of Mines Information Circular 6637, entitled "Research Activities in the Mineral Industries of the United States." This circular was compiled by A. C. Fieldner and Alden H. Emery, members of the Committee, in cooperation with the Bureau, and comprises a285-page list of research problems reported to the Bureau as engaging the attention of the various mineral industries. To obtain this information questionnaires were sent to 106 governmental agencies, 338 trade and professional associations, 524 colleges and universities, 9 endowed research institutions, and 1847 private companies and consulting laboratories. In order that the returns should be as complete as possible, the original mailing list included names from which it was not expected much pertinent information would be obtained. However, the procedure was justified as significant returns were obtained from many of these.

Jan 1, 1933

ARIZONA Established July 10, 1915 ROBERT W. THOMAS. Chairman ROBERT W. HUGHES, Vice-Chairman HUBERT O. WOODS. Secretary-Treasurer American Smelting & Refining CO., Hayden, Ariz. FRANK A. WARDLAW, JR., National Director THEODORE BROOKS I H. C. HENBIE THOMAS C. CHAPMAN P. D. I. HONEYMAN CARL H. COLE JOHN E. LANNING JOHN H. DAVIS ALBERT MENDELSOHN EDWARD G. DENTZER BRENT N. RICKARD MORRIS G. FOWLER F. A. WARDLAW, JR.

Jan 1, 1942

By F. D. Waltman

Under the hot, baking sun, engineers at the AEC&apos;s Nevada Test Site have been busy for several years in the sinking of 48-in. diam shafts to depths varying anywhere from 1800 to 4800 ft below the surface. In so doing these men have evolved several new techniques which should be of interest to the mining industry. Surface Facilities Designed For Speed: "Expediency plus efficiency" is a key phrase at the Site. Because of the relatively short duration of actual mining operations, all equipment has been packaged to decrease time and cost of "set up" and "take down". The headframe, designed specifically for use over 48-in. cased shafts, can be erected or dismantled within 48 hours. The back legs are pinned and hinged to the front legs for ease of installation and, when dismantled, for movement to another site with a minimum of delay.

Jan 6, 1966

By Paul M. Tyler

DOES mining pay? Inasmuch as the whining of minerals from Nature is one of the world&apos;s principal sources of new wealth, this question is of general economic interest but it is obviously of even more vital concern to investors and those engaged in mining. In a previous article on "Wage Costs in the Mineral Industries,&apos; published in the November issue, I attempted to show that wages paid workers on the job accounted for, roughly, 50 per cent of the mine dollar. Salaries normally range over 5 per cent - lower for large metal mines but higher in stone quarries and minor nonmetallic min. in, industries. Purchases of supplies, materials. fuel, and power generally aggregate within the range of 15 to 25 per cent of total receipts, with the average well under 20 per cent. The total of all such specified expenditures which may he loosely described as

Jan 1, 1934

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

W. H. Blauvelt, New York, N. Y.—One thought lias been running through my mind during the wholc of this meeting and that is that the scientific and the practical men must recognize very clearly their interdependence. The value of scientific classification of coal is going to be of the very greatest importance to the users, the practical men. Is not the scientific investigation and the great amount of work that is being done in a measure at least lost to the world? Therefore the scientific investigations and the practical needs of the users should bo brought as close together, and the work should be done as closely together, as possible; that is, the scientific man should know what the practical man needs, and the practical man should not feel that the scientific man is merely a theorist. Scientific investigation is going to have a great effeet and be of great valuc to the practical man who is trying to solve his problems. In the subject which I discussed&apos; for instance, we must look to the scientific man to tell us why coal cokes in one way and not In another and why certain coals will do certain things and others, which appear on the surfacc to be generally similar, do not act in the same way. Need or Physical Data on Coal H. J. Rose, Pittsburgh, Pa.—There is a subject which is a sort of hobby of mine; that is, the need for what might be called critical tables of constants for coal. The chemist has big volumes giving constants, such as the density, solubility, specific heat, thermal conductivity and all other physical and chemical data that have been determined for chemical compounds. Data arc also available on many common materials, for example, the density, hardness, modulus of rupture or maximum crushing strength of swamp white oak as compared with some other wood. In fact, physical data for practically cvery hype of wood commercially produced in the world can he found. In the same way the metallurgical man has handbooks giving the properties of alloys, etc., but we havc very little tabulated information about coal. Our principal reference works are the volumes published by the U. S. Bureau of Mines on the proximatc and ultimate analysis and calorific values of coals of the United States. That is 3 pioncer work of enormous value, but we have reached the point where we need more diversified information. Mr. Fulweiler raised the question of the relative strength of the different coals and cokes. Dr. Campbell and Dr. Ashley wanted to have some information on the resistance of coal to air slacking. It was brought out in the discussion that we want to know something about the coking properties of coal. There are any number of physical tests that we need, such as the thermal conductivity of certain coals, the coefficient of expansion, or the coefficient of friction; or other constants. A smattering of such information is scattered through the literature; for instance, a research worker in Wales will report a coefficient of expansion on Wclsh coals and one in South Africa will report something else for one or two kinds of African coals, hut it is difficult to find the information that is needed on our own coals. Would it not be worth while to consider collecting reliable critical

Jan 1, 1930

By W. Rogers Wade, Alfred Wandtke

The Pilares mine of the Moctezuma Copper Co. is situated at Los Pilares de Nacozari, Sonora, Mexico, about 75 mi. (120.7 km.) south of the international boundary and about 7 mi. (11.26 km.) east of the town of Nacozari de Garcia. It is situated at an elevation of 5000 ft. (1524 m.) in one of the northward trending ridges that form part of the mountain mass that culminates in the Sierra Madre de Mexico. To the east, south, and west, the topography is rugged and diversified; to the north less diversity exists, ranges of mountains rise sharply out of almost level ground and give the basin range structure characteristic of the Southwest. The climate is dry, the average rainfall of 15 in. (38 cm.) being confined almost entirely to the months of June, July, and August. The winter consists of a few days of disagreeable weather when a little snow may fall; the remainder of the year is thoroughly delightful. Vegetation is typical of a semi-arid region. In the canons near the mine, where water flows intermittently, willows thrive; on the northern slopes of some of the mountains and in some of the broader canons pines may even become abundant. The dominant rocks are flows and pyroclastics which are cut by dykes, stocks, and batholiths. The mountain just west of Nacozari is, in part, composed of limestone of an unknown age which occurs as a syncline and is undoubtedly a part of a prevolcanic land surface. Overlying the limestone and faulted against it, are the volcanics; cutting the limestone is a coarse biotite granite. Whether the granite is older or younger than the volcanics has not been definitely established. No attempt has been made to differentiate the rock types of the volcanic~, of which there are exposed 3000 ft. (914 m.) in thickness of basic and acid flows (andesites, latites, and rhyolites) and andesite and latite tuffs and breccias. The latite breccias, the youngest of these volcanic~, cover the highest mountains in the immediate vicinity. The

Jan 1, 1920