Search Documents

By AIME AIME

GENERAL COMMITTEES. SAN FRANCISCO:-ExECUTIVE, Hon. William C. Ralston, Chairman; RECEPTION, Prow. Samuel B. Christy, Chairman; SESSIONS, Frederic W. Bradley, Chairman; PRESS, H. Foster Bain, Chairman; FINANCE, Mark L. Requa, Chairman; EXCURSIONS AND ENTERTAINMENTS, Edward H. Benjamin, Chairman. Assisted by Harry P. Stow, C. W.Merrill, F. W. Griffin, Gelasio Caetani, Albert Burch, Newton Cleaveland, Corey C. Brayton and R. E. Cranston. Los ANGELES :-EXECUTIVE, Theo. B. Comstock, Chairman; R. W. Hadden, Secretary; H. R. Simpson, Treasurer. Institute Headquarters at Hotel St. Francis. The first and opening session, held Tuesday afternoon, Oct. 10,. in the Reception-Hall of the St. Francis, was called to order by State Senator William C. Ralston, Chairman of the Executive Committee, who in a few well-chosen words welcomed the visiting members and guests of the Institute to San Francisco. He said it was twelve years since the last meeting on the Pacific Coast and that it was here that the greatest feats. of mining had been accomplished in the history of the country. He told of the work that had been done on the continent and of the new methods introduced by the mining engineers for the betterment of the nation. He then introduced Capt. Robert W. Hunt, twice past President of the Institute, and present Acting President for the San Francisco meeting and the subsequent visit to Japan, who responded cordially to Mr. Ralston's welcoming address. By unanimous vote, the Secretary was instructed to send a telegram to President Charles Kirchhoff expressing regret for his absence, and hoping for a rapid improvement in the health of his mother. The following papers were presented in brief oral abstract by the authors: . * Electrolytic Refining at the U. S. Mint, San Francisco, Cal., by Edward B. Durham, San Francisco, Cal. The Parral Tank System of Agitating Slime-Pulp, by Bernard MacDonald, Guanajuato, Mexico. * The Newport Iron-Mine, Ironwood, Mich., by B. W. Vallat, Ironwood, Mich. (illustrated by lantern-slides). * Distributed in pamphlet worm.

Nov 1, 1911

Thank you for your introduction and the opportunity to speak at such an important forum. I feel honoured to be the Tas McKee speaker for this yearÆs conference. I can honestly say that Tas McKee typified the spirit that has ensured the survival of the mining industry despite the modern-day challenges that we encounter. He was one of the most influential people in the New Zealand minerals industry. In 1938, with his father and brother, Tas established Lime & Marble Limited. Over its history, this company evolved from its original base of marble mining to diversify into gold mining and exploration for other industrial minerals, uranium, precious and base metals. He was truly a pioneer that persevered against the odds.   That leads me to the subject of my discussion today. I am going to delve into todayÆs challenges as they apply to gold companies. While we gold miners should be generating record returns, the gold industry shareholder return performance in this buoyant market has barely equalled that of the gold price. It is a dilemma but one that can be resolved with the right strategy.

Jan 1, 2006

By Robert E. Wallhagen

This report describes the results of a four year investigation into improved face ventilation systems for underground coal mines. The objective was to experimentally determine configurations for a diffuser fan system and a water spray (spray fan) system which will provide a maximum reduction in face methane concentrations without causing an increase in methane concentrations at the operator's position. The experimental evaluation was performed in full scale mock-up mine entries, simulating continuous mining operations in both a six foot and four foot coal seam complete with normal ventilation, water sprays, and methane emission. A limited study was also performed to assess the effect of scrubber discharge location on methane concentrations in the face area. The results indicated that diffuser fan and spray fan systems that were designed to augment the natural airflow pattern in the entry could provide a factor of 3 to 5 reduction in average methane concentration at the face, compared to a mining machine with just conventional water sprays. The properly designed diffuser and spray fan systems also significantly reduced the total methane present in the entry. A properly designed dust scrubber discharge can reduce face methane levels by a factor of two.

Jan 1, 1977

The development and distribution of gold placers in Otago û Southland is related primarily to the evolution and architecture of three distinctly different drainage networks that developed during and since Gondwana breakup: +        Late-Gondwana û Pre-marine; +        Middle Tertiary Post-marine; and +        Modern. Late Gondwana û Pre-marine drainage was dominantly recti-linear and controlled by normal faults and sedimentary basins formed before or during Gondwana breakup. Placers formed dominantly in 2nd order transverse drainages with primary sources in their catchments. This drainage network was progressively destroyed by inundation and burial by marine strata during Late Cretaceous û Middle Tertiary marine transgression that ultimately covered most of New Zealand. Middle Tertiary Post-marine drainage evolved on and incised the newly emergent low-relief landscape during regional marine regression driven by development of the present plate boundary through South Island. Most of Central Otago was drained into Southland and to the southern coast via a large braided river system with an extensive network of tributaries in its Central Otago reach. East Otago was drained by several smaller systems. Placers formed dominantly in proximal and medial reaches of 1st and 2nd order drainages with primary or pre-existing placers in their catchments. This drainage network was destroyed by inundation and burial of the Central Otago reach of the major system by lacustrine strata following tectonic damning of its middle reach by range uplift and development of a lake complex that covered >5000km2 of Central Otago. The Modern drainage network evolved from the Middle Tertiary network through complex response, firstly to uplift of NW-trending and NE-trending ranges throughout the region since the Late Miocene, and secondly to the effects of major Pleistocene glacial advances in West Otago. Placers formed in alluvial fans at range margins, proximal and medial pre-glacial fluvial systems and glacial outwash sequences. Evolution of each of these drainage networks has been accompanied by widespread sedimentary recycling of alluvial gold from older to younger placers, augmented locally by input of first-cycle gold derived from erosion of primary sources in the repeatedly exhumed basement rocks.

Jan 1, 2006

The September General Meeting of the Institute was held in Kelvin House, Johannesburg, on 16th September, 1970, at 3.00 p.m. Mr V. C. Robinson (President) was in the Chair. There were also present one hundred and eighteen Fellows, including Dr J. M. Bereza, H. P. Carlisle, R. J. C. Goode, Dr J. P. Hugo, P. Lambooy, Prof R. P. Plewman, W. W. Malan, Dr J. T. McIntyre, Dr M. D. G. Salamon, L. W. P. Van den Bosch, P. A. von Wielligh (Council Members), A. Bain, G. P. Bennet, D. L. Carson, G. L. H. Diering, M. E. E. Douglas, F. A. B. Fouche, R. Fourie, A. R. C. Fowler, E. B. Gordon, J. S. Hay, G. H. Henderson, S. D. Hill, A. C. Hofmeyr, J. M. Jacobs, A. F. Lee, D. G. Malan, L. J. Prince, W. G. Pyne-Mercier, A. H. Mokken, Dr W. S. Rapson, R. R. Richardson, H. V. Solomon, C. G. Sowry, G. G. Stanley, G. R. Still, D. L. Starkey, D. L. Taylor, E. W. Thiel, I. E. Van Aswegan, M. van Ryneve1d Steyn, N. B. Vinson, H. Wheeler, Dr A. Whillier, R. A .Wilson, C. F. Ziervogel. Forty-two Members including R. C. Bertram, F. Collier, G. C. Currie, O. Davel, J. M. Gosnell, A. Hazell, Dr N. C. Joughin, F. Kleinschmidt, D. Love, R. B. Macgillivray, D. Mather, R. D. R. Munro, R. S. Pearson, J. J. Peisl, T. J. Pole, A. J. Rossouw, R. G. B. Skirving, G. S. Schwartz, K. Stee1e, H. A. G. Slater, A. Taylor, B. A. Thomas, P. L. Vaughan, D. T. Watt, W. Wilson. Nineteen Associates including R. K. Briggs, S. I. Du Preez, P. G. Gaylard, P. H. Hartslief, W. M. Mackay, A. D. Ross. Three Students: V. S. Care, R. J. Drummond, P. J. Pretorius. Thirty-one Visitors including C. P. S. Barnard, D. W. Bosch, M. Bain G. L. Brown, G. D. Behrens, C. Coetzer, D. M. Gilbart-Smith, R. L. Man, Dr G. J. Stander, M. W. L. Steinobel, R. H. E. Thorpe, T. D. van Wyk, P. H. van Zyl, E. Vereecken, J. J. H. Viljoen. Secretary, D. C. Visser. Total present: 215. OBITUARIES The President: "It is my sad duty to announce the death of the following: Bruce Donaldson Crawford, Fellow, who joined the Institute in 1951 and passed away on 29th April, 1970. Donald Joseph Powrie, Life Fellow, who joined the Institute in 1935 and passed away on 22nd July, 1970. As a mark of respect to the memory of the deceased and in sympathy with the bereaved I would ask you all to rise and observe a few moments' silence." MEMBERSHIP The President: "I have much pleasure in announcing that the names of the under-mentioned candidates, having been published in accordance with By-Law 5.2.2, Council has elected them to membership of the Institute in the following grades: Associate: WiIliam Norman Carter. Students: Roman Michael Dabrowski, Sean George Dean Eaton, Alan Philip Stonham Howard, Anton du Preez Roos, Richard Harold Tourle. MEMBERS TRANSFERRED TO A HIGHER GRADE From Graduate to Member: Terrance Alexander Ward. From Associate to Member: Bernard Andre Thomas. "I welcome the newly elected members to the Institute and congratulate the members who had been transferred to a higher grade." CO-OPTION The President: "I wish to advise members that, in terms of clause 3.9 of the Constitution, Mc. H. P. Carlisle had been co-opted to serve on Council." PAPERS FOR PRESENTATION The President: "We have two papers today, and I am first going to call on Dr Stander the Head of the Water Division of the C.S.I.R., who IS well known to many of you for his work and talks on pollution, who has had more than a little to do with this industry, and who has been I would say, of the greatest possible assistance to the mining industry in overcoming the problems of pollution which are so prevalent in industry of this nature. He, Mr Henzen and Mr Funke have written this paper, 'The disposal of polluted effluents from mining, metallurgical and metal-finishing industries, their effects on receiving water and remedial measures.' This is the Water Year, as you know, and it is most appropriate that we should have such an authority to talk to us on this very important topic. I now have much pleasure in asking Dr Stander to introduce his paper." After the presentation of the paper the President said, "Gentlemen, I am sure that you would like me on your behalf, to thank Dr Stander very sincerely for a paper which I think has enabled us to get a completely new slant on the Water Year. There are many people who have put their finger on this campaign and said, it is all a gimmick. There are others-I suppose notably some of the bridge clubs which operate on week-day afternoons in Parkview-who seem to think that this is a quick way of getting early rain. Of course, it is not. This is a most important paper which we have had given to us this afternoon. You probably found it here when you arrived and have not read it-I was very lucky to be able to read it last night, and there is an awful lot of meat in it. For as long as I have been associated with mining in any way, there has been a problem of polluted effluent-of effluents carrying a mineral load from mining, and I think Dr Stander is absolutely right-and, of course, the Commission is right when they say that this is not merely the problem of mine management or mine owners-this is a problem which affects every single human being in this country.

By Ruth F. Brinkley

This report is the 16th of a series of reports originally issued annually and more recently biennially to acquaint the reader with the work of the Explosives and Physical Sciences Division, Region VIII.3/ In the majority of instances the results of the investigations are made available to the public through Government publications and journal articles. In certain instances (specifically as regards security-classified research, investigations of a confidential nature, and short-range programs of very limited scope) results are reported only to those immediately concerned.

Jan 1, 1957

By Eric R. Jette, Earl S. Greiner

Although the mechanical and chemical characteristics of certain iron-nickel-silicon alloys have been investigated,1 the available literature shows no results of a systematic investigation of the constitution of this system. 'This paper describes the results of an X-ray investigation of the constitution of the iron-rich iron-nickel-silicon alloys at 600°C. Data 011 the constitution of the included binary systems obtained in other investigations have been correlated with the structure of the ternary alloys. Jette and Foote2 have presented a tentative constitutional diagram of the iron-nickel system. following X-ray studies on quenched specimens. This diagram shows that the alloys at 600°C. containing from zero to approximately 4 atomic per cent nickel consist of a body-centered cubic (alpha) phase, the alloys containing 4 to 24 atomic per cent nickel consist of body-centered cubic (alpha) and face-centered cubic (gamma) phases, and the alloys containing from 24 to Ioo atomic per cent nickel consist of a face-centered cubic (gamma) phase. These investigators recognized that it was not possible to retain the gamma phase in equilibrium by quenching alloys containing less than approximately 25 atomic per cent nickel and that high-temperature X-ray methods were desirable to determine the gamma-phase solubility limit. In a later investigation of the iron-nickel alloys, Owen and Sulley3 determined the alpha-phase solid solubility limit to be 3.5 atomic per cent nickel at 600°C. High-temperature X-ray methods showed the solid solubility limit of the gamma phase to be 14 atomic per cent nickel at 600°C. Since the high-temperature X-ray method should reveal equilibrium conditions in these alloys better than the quench method of other investigators, the results of Owen and Sulley pertaining to the gamma-phase boundary are to be preferred. As the result of an X-ray investigation of quenched iron-silicon alloys, Greiner and Jette4 have shown these materials to consist of a body-centered cubic (alpha) phase containing from o to 26.4 atomic per cent silicon at 600°C. The alloys containing from 26.4 to approximately 50 atomic per cent silicon consist of two phases at 600°C.; namely, alpha and eta. The eta phase corresponds to the stoichiometrical formula FeSi (33.4 wt per cent Si)." The literature pertaining to the constitution of the nickel-silicon alloys has been reviewed by Ackerman,' who found disagreements in the results of various investigators on several parts of the system. Subsequent data on the constitution of the nickel-silicon alloys were reported by oSawa and okamoto.6

Jan 1, 1943

By Earl S. Greiner, Eric R. Jette

Although the mechanical and chemical characteristics of certain iron-nickel-silicon alloys have been investigated,1 the available literature shows no results of a systematic investigation of the constitution of this system. 'This paper describes the results of an X-ray investigation of the constitution of the iron-rich iron-nickel-silicon alloys at 600°C. Data 011 the constitution of the included binary systems obtained in other investigations have been correlated with the structure of the ternary alloys. Jette and Foote2 have presented a tentative constitutional diagram of the iron-nickel system. following X-ray studies on quenched specimens. This diagram shows that the alloys at 600°C. containing from zero to approximately 4 atomic per cent nickel consist of a body-centered cubic (alpha) phase, the alloys containing 4 to 24 atomic per cent nickel consist of body-centered cubic (alpha) and face-centered cubic (gamma) phases, and the alloys containing from 24 to Ioo atomic per cent nickel consist of a face-centered cubic (gamma) phase. These investigators recognized that it was not possible to retain the gamma phase in equilibrium by quenching alloys containing less than approximately 25 atomic per cent nickel and that high-temperature X-ray methods were desirable to determine the gamma-phase solubility limit. In a later investigation of the iron-nickel alloys, Owen and Sulley3 determined the alpha-phase solid solubility limit to be 3.5 atomic per cent nickel at 600°C. High-temperature X-ray methods showed the solid solubility limit of the gamma phase to be 14 atomic per cent nickel at 600°C. Since the high-temperature X-ray method should reveal equilibrium conditions in these alloys better than the quench method of other investigators, the results of Owen and Sulley pertaining to the gamma-phase boundary are to be preferred. As the result of an X-ray investigation of quenched iron-silicon alloys, Greiner and Jette4 have shown these materials to consist of a body-centered cubic (alpha) phase containing from o to 26.4 atomic per cent silicon at 600°C. The alloys containing from 26.4 to approximately 50 atomic per cent silicon consist of two phases at 600°C.; namely, alpha and eta. The eta phase corresponds to the stoichiometrical formula FeSi (33.4 wt per cent Si)." The literature pertaining to the constitution of the nickel-silicon alloys has been reviewed by Ackerman,' who found disagreements in the results of various investigators on several parts of the system. Subsequent data on the constitution of the nickel-silicon alloys were reported by oSawa and okamoto.6

Jan 1, 1943

By J. Ivon Graham, T. D. Jones

This paper presents methods in use in British coal-mines for the suppression of dust. While the effect of present-day treatment will not be apparent for several years, in pits in South Wales, concentrations as high as 50 gm./1,000 cu. ft. were some years ago fairly common in various operations at or near the coal-face, with an average concentration of 20 gm./1,000 cu. ft. Now the average concentration in what were previously dusty pits is probably not greater than 3 gm./1,000 cu. ft.Nevertheless, every effort must be made to improve conditions still further. In South Wales it is claimed that 99% of the coal-faces requiring treatment have been dealt with either by wet cutting, infusion, or hand-spraying. The extent of the treatment by these methods can be gauged by the fact that the total length of coal-faces now being treated by water infusion in Cardiff and Swansea areas is about 33,000 yds., by wet cutting 25,000 yds., and by hand-spraying nearly 14,000 yds. The influence of methods of mining upon dust production is only mentioned very briefly in this review, and there is no doubt that much more is to be learned concerning this aspect. It can be stated, however, that good mining practice is essential to prevent unnecessary dust production, and the problem of dust in mines will be solved only by the closest co-operation between mine managers, workmen, and scientists.

Jan 1, 1947

By L. M. Litz

In reply to Mr. DeVries comments on my paper, I would like to say that it is true, as pointed out by Mr. DeVries, that under some special conditions, the use of high concentrations of hydrogen peroxide might provide higher short term in-situ …

Jan 1, 1982

By D. P. Bishop, G. J. Kipouros, R. L. Hexemer Jr., I. W. Donaldson, W. F. Caley

Aluminum powder metallurgy (APM) is an advanced metal forming technology frequently employed to fabricate complex structural components in a near-net-shape fashion. Exhibiting nearly 100% material utilization, APM continues to rise in popularity. Recent research initiatives in this field have emphasized the development and processing of advanced 2xxx and 7xxx series alloys. In particular, APM equivalents to wrought 7075 and 2024 have been sought. An overview of work completed in this area is presented. Included are data on the various production stages (powder compaction, sintering, forging, and heat treatment) as well as the microstructure and mechanical properties of the finished products.

Jan 1, 2010

By David R. Ziegler

The concept and facts concerning "threshold blast damage" are not considered "general knowledge". Perhaps because of a lack of knowledge, understanding, and experience of blasting effects, property owners and lay-persons may attribute a wide range of common cosmetic conditions to "blasting damage".

Jan 1, 1997

By M. Mathiba

High CO2 fluxes associated with reclaimed coal mine spoils pose an environmental hazard where such sites are used for building. CO2 concentrations in excess of 25% have been reported in homes constructed on or down gradient of such spoils. The objective of this study was to investigate the effect of a mitigation trench used at one mine site on CO2 fluxes across the trench using chamber?based trace gas measurement. LI8100 automated CO2 flux system was used to measure CO2 fluxes from 32 sample points located across a deep mitigation trench on June 8 and 9. The maximum recorded fluxes were 7.29 and 8.18 µmol/m2/s, with averages of 4.15 and 5.50 µmol/m2/s, up and down-dip respectively. These preliminary results show CO2 flux is higher up-hill than down-hill at 95% significant level. This work shows that flux measurement can be used to investigate CO2 migration on reclaimed mine land. Further work is necessary to allow geostatistical modeling of the spatial variability of CO2 fluxes over reclaimed coal mine spoils. Knowledge gained would assist mining practitioners and regulators in reclamation planning for envisaged post-mining land uses.

Jan 1, 2010

By J. Bruce Clemmer

[Gypsum is one of the mo .. t iJf.l)ortant nonmp.tal1.ic T!1inerals, as is indicat-? ed by the fact that tlle Uni ted states cO!1sUl:Ied p, roximn..tely 3,500,000 tons of natura.l and calcinecl e::,j;-psum in 1937. The b\.'.ilr:.in.; traces \"fe.ro the largest users and required 2,520,000 tons of calcine for the r-roductiop. of plaster,]

Jan 1, 1941

By Vicente Palacios

Southern Perú es el productor de cobre más grande del país y una de las 10 principales empresas cupríferas del mundo que mantiene un complejo minero-metalúrgico en el sur del país (Tacna y Moquegua). Sus principales instalaciones son las minas de cobre con sus respectivas concentradoras en Toquepala y Cuajone, las instalaciones de lixiviación, extracción por solvente y electrodeposición en Toquepala, fundición y una refinería en Ilo. En ese sentido, el presente texto señala el análisis del cobre a través del método secuencial como una herramienta que define el modelo minero y mejora los parámetros de extracción de cobre lixiviable de acuerdo con la clase mineral. Asimismo, mejora del diseño mineralógico y geológico, sobre la base de lo cual se planea desarrollar pruebas de lixiviación de acuerdo con las características del mineral y su relación con el IS, como herramienta para estimar las recuperaciones a escala industrial.

Sep 13, 2001

By A Brodbeck, AT Spathis

Australian regulatory control of ground vibration and airblast arising from mining, quarrying and civil construction operations is spread across a number of federal, state and local authorities and across a number of departments with various jurisdictions. The Australian Standard AS 2187.2 contains an informative appendix on damage-related criteria and it is the primary reference for the regulators. The complete standard and the informative appendix is currently undergoing major revision with a focus for the latter on implementing frequency-dependent criteria for ground vibration. Certain directions for change have been raised for consideration by the standing committee, ranging from fundamental issues of measurement and interpretation and others that overlap human comfort criteria. It is anticipated that some of the suggestions will eventually make their way into future standards after an adequate period of consultation and consideration by both the Australian public and others involved in the associated industries.

Jan 1, 2005

By M. Z. Emad, N. Abbas, Y. Majeed

Room-and-pillar mining is commonly employed for the extraction of rock salt in undergroundmines. Pillar stress is a major concern in these mines as it is directly related to stability and mineralrecovery. In this study a flat jack method was used to measure pillar stresses in three undergroundrock salt mines in Pakistan. The field work included determination of in-situ stress, in-situ elastic modulus, recording of field variables (pillar length and width, height and width of opening, opening width to height ratio, extraction ratio, and overburden height) and collection of salt block samples. The geomechanical properties of rock salt (uniaxial compressive strength, Young’s modulus, Brazilian tensile strength, and density) were also determined to estimate overburden stress, pillar strength, and factor of safety (both estimated and actual). It was found that the measured pillar stresses are proportional to the overburden stress values, with their magnitude ranging from 6.05 MPa to 11.97 Mpa, and the pillars were found to be stable. Regression analysis was performed to develop statistical models for in-situ stress and in-situ elastic modulus. Finally a quick guideline chart was developed to determine the suitable length of pillar for a given span and required level of safety.

Jun 5, 2023

By C. Golumbic

Most early research on solvent extraction of coal has been concerned with the molecular structure of coal. Although rush work is continuing, practical aspects of the subject also are being emphasized. For example, development of the Pott-Broche extraction process resulted from the discovery of very efficient solvents for the pressure-extraction of coal. Recently, Orchin and Storch reported the use of even more efficient solvents under similar conditions. In addition to the discovery of more effective solvents, the possibility of efficient extraction at atmospheric pressure is obviously of practical interest. H. J. Rose observed that phenanthrene at its atmospheric boiling point readily dispersed 80 percent or more of Pittsburgh-bed bituminous coal. This fact served as the starting point of the present investigation, ill which determination of the chemical specificity of this solvent and the chemical nature of the resulting extracts was undertaken. This paper represents a progress report of the results obtained to date.

Jan 1, 1950

By C. H. Bucknam

Classical acid-base accounting using modified Sobek titration methods has resulted in interpretation of results for materials with neutralization potential (NP) less than 20 tons of CaCO3/1000 tons of material (2% CaCO3) as "uncertain" due to lack of sensitivity within that content range. Standardization of a "fizzless" acid neutralization potential (ANP) method was undertaken in the American Society for Testing and Materials (ASTM) International using two ranges of sulfuric acid additions based on reaction pH and carbonate carbon estimates rather than subjective fizz testing as well as hydrogen peroxide additions to correct for mineral acidity. The method is identified as the acid neutralization potential acidity (ANPA) titration method. During interlaboratory testing a positive bias was discovered within the "uncertain" range which was further investigated and resolved by increasing the test sample weight from one to five grams for samples needing improved accuracy in materials with ANP <2% CaCO3. Test results from the interlaboratory testing of the low range method is presented and compared with the results from the original ANPA method in the paper.

Feb 27, 2013

By J. Weng

The equations of heat conduction are numerically solved for two kinds of artificial freezing- mechanical freezing and liquid nitrogen freezing. A two dimensional finite difference model simulating the freezing field is developed. The procedure introduces a way to simulate the effect of latent heat released when water transforms from liquid to solid. The procedure also produces a way to calculate the harmonic mean of heat conductivity used when dealing with heterogeneous material. The theoretically derived temperature distributions in frozen soil are given and compared with measured data. An analysis is made on the thermal design in shaft freezing. The average temperature of frozen soil is calculated by using numerical integration. The regularity of development of frozen soil radius is revealed and given in an appropriate mathematical model.

Jan 2, 1984