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By Alfred James

John Stewart MacARthUr, born in 1856, was the son of Robert MacArthur of Glasgow, and came of Scots stock distinguished for character and religious conviction. His election as elder of the Free Kirk gave him greater pride than the receipt of the gold medal of the Institution of Mining and Metallurgy. The former honor was for character— it marked him as a son worthy to follow in his father's footsteps; the latter was awarded for his life work of eminent service to the gold industry. Cheery optimism, resolution, tenacity of purpose, and industry ever characterized his actions. Apprenticed to the Tharsis Sulphur & Copper Co., his work on the chemical staff brought him to the notice of the Cassel Gold Extracting CO.,. at that time struggling with an unworkable electrolytic process..He was engaged by that company, in 1886, as technical manager and before long brought out the perchloride process, which was speedily followed (in 1887) by the epoch-making cyanide process. This process revolutionized gold mining and directly led the way to the elevation of the mining engineer to the most broadly trained product of the engineering profession. A noteworthy feature of the cyanide process was its completeness when introduced. Over thirty years have elapsed and the use of the process has been worldwide, but no suggested improvement has stood the test of time. The extension of the process to the beneficiation of silver ores—containing far more metal per ton and thus requiring the employment of stronger solutions—has brought us the Merrill and Crowe improvements in precipitation and the Nipissing desulfurization process for certain silver-hearing minerals. Roasting apparatus, fine crushing, filtration, and settling equipment have all aided the extension of the process in and from its original field. As Hennen Jennings put it,, the cyanide process today is essentially that of 1890. This self-containedness of the cyanide process arose from no mere chance; it was directly due to MacArthur. It was he who personally investigated every known method of precipitation and then every form of zinc from sheet, punchings, filings, millings, rods and shaving down to fume; it was he who investigated the effect of protective alkalies, of so-called accelerators, and of the addition of lead salts; he was determined to leave nothing to chance.

Jan 1, 1921

By J. Laskowski

J. Laskowski (Associate Professor, Dept, of Mineral Processing and Coal Preparation, Silesian University of Technology, Gliwice, Poland) -Referring to the papers by J. A. L. Campbell and S. C. Sun, I must say that I am very pleased to see that type of work, because it is the only way to progress towards an understanding of flotation mechanisms. All those interested in the science of the surface chemistry of coals would find these papers a valuable contribution to the literature. In their extensive research, the authors attempt to synthesize their findings into a theory of coal flotation. To do this, the zeta potential of bituminous coals and their lithotypes, as well as that of an anthracite coal, was measured and H+ and OH- ions were found to be potential determining ions. The measured ZPC of bituminous coals was at a pH range from 3.5 to 4.6 and for the anthracites between 2.0 and 4.5. The authors have pointed out that since the hydrophobicity is pH-controlled, the flotation mechanism should also be. The Campbell and Sun papers confirm a good many of the conclusions on surface properties of coals reported in recent years. It is noteworthy to point out that the ZPC found in the paper on bituminous coals was approximately pH 4, similar to the ZPC for the anthracite coal. In fact, we have been investigating different coals from low to high ranks. Thus, the plot of the pH for ZPC against rank could be derived and this curve-an electrocapillary one-indicates a pH near which the hydrophobicity of the coal surface should be at maximum. This can be proved by so-called salt flotation, which, in a sense, can be treated as method of surface charge measurement. It is obvious that the salt flotation experiment is possible when the native hydrophobicity of the mineral surface is high, e.g., when the solid surface does not have an orienting influence on an adjacent water layer and the hydration layers are controlled by the electrical double-layer potential. The addition of electrolyte or a change of pH which decreases the thickness of the stabilizing double-layer "opens up" the hydrophobic surface micro-area mosaic. Thereby the surface becomes hydrophobic and particles become floatable. The orienting influence of surface on hydration layer increases even after very slight oxidation and flotation is affected by it. It seems that such an explanation agrees reasonably well with those of Campbell and Sun.

Jan 1, 1972

By G. F. Raymond

Discussion by G.F. Raymond Knudsen's study presents two curious conclusions: • The kriging of blasthole assays can systematically overstate mill head grades by as much as 21% as a result of unbiased sample variance. • No estimation method is able to reduce this bias to a small margin. The study is based on a simulation using real data and what are presumed to be actual variogram parameters from a real deposit. Although I have no doubt that the first conclusion (21% overestimation) is correct for the author's simulation, I do not believe this represents a realistic mining situation. Over the past 15 years I have done extensive comparisons between exploration drill-hole assays, blasthole assays and mill head grades on seven major open-pit mines, including some very erratic gold deposits. Commonly, nugget effects on blasthole variograms were 10% - 20% higher than on exploration variograms. And in one extreme case, the difference was 50%. Even in the extreme case, ordinary kriging on blastholes agreed well with the mill head grade over the long term. In Knudsen's simulation, the blasthole nugget effect is assumed to be 200% higher than exploration data's. He supports this by variogram plots from each. My guess is that the apparent, large difference between these variograms results from a failure to account for the proportional effect (blasthole assays are likely from a higher-grade area). A simple check would be a comparison of the variance of exploration samples nearest blastholes. As for a nearly conditionally-unbiased estimator of a large random error, the arithmetic mean of all of the data certainly qualifies, provided there is an even data spacing. As a corollary, so does simple kriging, which would include, in this case, a large weighting to the arithmetic mean. Similarly, using a large number of samples with ordinary kriging or indicator kriging would significantly reduce the bias in the case of a large nugget effect for the variogram.[ ] Reply by H. Peter Knudsen Raymond questions two conclusions in the paper. First, he wonders whether a 21 % overestimation represents a realistic mining situation. I agree that 21 % is high, but overestimation in the range of 10% to 15% is certainly common in my experience. Furthermore, several years ago I consulted on a gold mine that was experiencing a 45% overestimation due, predominantly, to poor blasthole samples: In further questioning of the 21 % value, Raymond wonders whether the nugget effect of the blastholes is really so much larger than the nugget values of the exploration data. It is consistently larger throughout the deposit. In my experience with six Nevada gold mines, the high nugget value is not unusual. In fact, for some reason, nugget values for blasthole samples are typically about 0.0005 (opt squared). I am of the opinion that this high nugget effect observed at many gold mines is predominantly due to the inherent inadequacies of the blasthole sample and subsequent sample preparation. The second conclusion Raymond questions is the inability of the estimators tested to reduce the conditional bias. In fact, the conditional bias is extreme with the polygon estimator and greatly reduced by ordinary kriging. However, it was not eliminated. Raymond suggests using simple kriging, or perhaps a larger number of samples, to reduce the conditional bias. The technique of simple kriging may be less affected by the random errors in the data, but I did not test the technique. Using a larger amount of data presupposes that too few samples were used initially. In ordinary kriging and indicator kriging, the screen effect comes into play and ensures that samples beyond the second screen are given zero weight. Hence, increasing the sample size does not change the estimates nor the conditional bias. The main point of my paper is that the random unbiased errors (a fact of life in blasthole samples) cause a conditional bias in our estimates. The mechanics by which the conditional bias is introduced are nicely explained by Springett. My paper simply shows that the bias is also present when working with linear estimators, such as ordinary kriging, and even with nonlinear estimators, such as indicator kriging.[ ]

Jan 1, 1993

By A. J. Lynch, J. A. Holmes, F. C. Bond, D. W. Fuerstenau

This is an outstanding paper on comminution theory and represents a considerable advance in mathematical formulation. It clears the way for a discussion that should ultimately decide whether the work index should be considered as a parameter according to the Third Theory or as a constant. In the empirical differential equation dE = C dx/xn either C or n must be treated as a variable to satisfy known crushing and grinding conditions. The author has chosen the exponent n as the variable, with C as a constant.

Jan 4, 1958

The authors provide a discussion of the paper, ?Coal workers? pneumoconiosis prevalence disparity between australia and the united States,? a peer-reviewed paper that appeared in the technical papers section of the July 2012 issue of Mining Engineering magazine. The original authors, G.J. Joy (gjoy@cdc.gov), J.F. Colinet (jcolinet@cdc.gov) and D.D. Landen (dlanden@cdc.gov), respond.

Jan 1, 2013

Contribution by J.S. Kuijpers* Kirsten's paper discusses the potential for seismic activity on faults in relation to depth, span, stope support, and discontinuity strength, and puts forward some explicit conclusions. Quoting from the author, the main conclusions are as follows, together with my comments. Author's reply The author gratefully acknowledges the contribution to his paper. It provides further elucidation to the very complex problem of quantifying the effects of mining-induced seismicity. The mechanical behaviour of rock under seismic excitation has been sadly neglected over the past twenty years, during which attention was almost exclusively focused on the study of the spatial location of seismic events. It is to be lamented that, on the eve of South Africa's movement to significantly greater depths of mining, so little quantities information is known about the mechanical effects of seismicity. It is a challenge at this stage to make up for this lapse in knowledge in the shortest possible time.

Jan 1, 1994

By V. Rajaram

R.C. Rex, Jr. V. Rajaram's paper does not accurately reflect the status of Eastern oil shale development as it stands today. Today, there are numerous firms and research organizations pursuing development of the Eastern oil shale resource. Details of the current projects can be found in the symposium proceedings for the 1985 Eastern Oil Shale Symposium held in Lexington, KY, in November 1985. Additionally, the comparison of the Paraho and HYTORT processes is invalid because the HYTORT process design used it not an accurate representation of the HYTORT process. I will briefly address this point. It is disconcerting to see the author reference hydroretorting work conducted at the Institute of Gas Technology (IGT) (circa 1978) in the introduction, which indicates hydroretorting (the HYTORT process concept) yields of up to 250% of the Fischer Assay oil yield, and then turn around and base the remainder of the paper on the 1981 "Synthetic Fuels From Eastern Oil Shale Report," which depicts the HYTORT process as yielding only 115% of Fischer Assay. Indeed, work conducted at IGT to 1981 indicates commercial oil yields for the HYTORT process would be in the range of 200% to 210% of Fischer Assay. A more thorough literature search by the author would have yielded a 1981 publication by Schora et al., entitled "Update on the HYTORT Process" presented at the Symposium on Synthetic Fuels From Oil Shale in Nashville, TN, October 1981. This paper thoroughly discusses the shortcomings of the referenced study with respect to the HYTORT process. For the interested reader, I can also recommend a June 1984 report entitled "An Economic Comparison of Five Process Concepts for Using Eastern Oil Shale," published by Los Alomos National Laboratory (LA-10106-MS, Parkinson et al., NTIS No. DE84-015981). This study applies a realistic HYTORT design (circa 1982) and indicates that HYTORT is the most econom¬ical method of processing Eastern oil shales (about $20/bbl less than Paraho). Additionally, completion of the HYTORT feasibility study in June 1983 by Phillips Petroleum Co., Bechtel Group Inc., HYCRUDE Corp., and IGT has resulted in development of designs that will make the use of HYTORT on Eastern oil shales even more economic. HYCRUDE Corp., a second-tier subsidiary of IGT, is involved in commercialization and licensing of the HYTORT process and is active in efforts to develop the Eastern oil shale resource. As such, I am disappointed to see outdated material that has the potential for adversely affecting development of Eastern oil shale resources published in MINING ENGINEERING. I can only hope that this response will serve to mitigate any negative opinions that may have been formed. Today, activity in commercializing Eastern oil shales dominates the oil shale scene in the US and indicates a realization of the potential for these shales. Reply by V. Rajaram I appreciate the updates on the HYTORT process provided by R.C. Rex, Jr. I hope that Hycrude's work will lead to the funding of a pilot plant to demonstrate that yields of greater than 200% of Fischer Assay can be achieved in a commercial plant using eastern US oil shales.

Jan 9, 1986

By V. Rajaram

R.K. Leininger, N.R. Hasenmueller, and D.D. Carr The content of the paper by V. Rajaram does not fulfill the expectations of the title. But Rajaram submitted the article in October 1983, and he could not have foreseen the numerous developments that would occur before his paper was published more than two years later. Nevertheless, Rajaram failed to mention the interest in oil shale development in southern Indiana beginning in late 1979 and continuing through the present as a result of special financial encouragement of three oil shale projects in May and August 1984 by the Indiana Energy Development Board and the Indiana Corp. for Science and Technology. A session at the 1985 Eastern Oil Shale Symposium in Lexington, KY, Nov. 18-20, 1985, gave the current status of oil shale developments in the eastern United States. Speakers at this session reported on the three Indiana projects. First, Gary D. Aho, Cliffs Engineering Inc., spoke on a feasibility study by Cliffs Engineering and Allis Chalmers for a site-specific pilot plant using the Allis Chalmers process. The plant site is in Clark County, IN, on property of the Midwest Energy Resources Co. The project is funded by $240,908 each from the Indiana Energy Development Board/Corp. for Science and Technology (EDB/CST) and the US Department of Energy (DOE) and $120,454 from the corporate sponsors (total $602,270). Completion is scheduled for mid-1986. Next, Edwin M. Piper, Stone and Webster Engineering Corp., discussed the American Syn-Crude/Indiana Oil Shale Project. This effort followed the completion of two smaller projects funded by the Indiana EDB/ CST: "Testing of Indiana Oil Shale in a Petrosix Pilot Plant" (total funding by EDB/CST at $50,000) and "Assessment of the Petrosix Process for an Indiana Shale Oil Plant" (total funding by EDB/CST at $100,000). The status at the time of the report at the Oil Shale Symposium was that a request for an extension of time for securing nonfederal support had been submitted to the US Synfuels Corp. The proposal included building an 11-m (36-ft) diam retort in southeastern Indiana to process the New Albany Shale and to produce 366 m3 (2300 bbl) of shale oil per day by the PETROSIX process. The Indiana EDB/CST had contracted with Stone and Webster at $401,100 from EDB/CST and $245,835 from Stone and Webster for activities to advance the project in the negotiations with Synfuels Corp. At the time of the report, this project was the only eastern oil shale proposal that was still on the agenda of the Synfuels Corp. As a result of Congressional action in late December 1985, federal support from the Synfuels Corp. is no longer possible. Finally, Victor H. Carr, Eastern Shale Research Corp., described his firm's project, which is jointly supported by DOE ($227,749) and the Indiana EDB/ CST ($73,850) and is entitled "Feasibility Study to Determine Suitability of an In-Situ Process to Recover Hydrocarbons from Eastern Shale." An area in Scott County, IN, had been chosen, but not a specific 9 x 15-m (30 x 50-ft) site. One burn of a small in situ retort is contemplated as part of the project. Besides these three projects, several reports on shale research were presented. Joseph Damukaitis, American Syn-Crude Corp., reported that a pilot plant using the hydrogenation-extraction (H-E) process (described at the 1984 Eastern Oil Shale Symposium) was 94% built and would go through shakedown with oil shale but would then shift mechanical devices to process coal mine waste. Current status of research on the HYTORT process was then presented by Raymond C. Rex, Jr. Oil shale beneficiation research at the University of Alabama/Minerals Research Institute was reported by R. Bruce Tippin. Scott D. Carter discussed continued research on fluidized-bed retort¬ing of shale at the Kentucky Center for Energy Research Laboratory. Carl E. Roosmagi of DOE, Morgantown, reported on the oil shale research at the Morgantown Energy Technology Center (METC) laboratory. Henry J. Gomberg, Ann Arbor Nuclear Inc., discussed "Radiation Combined with Donor Solvents for Extraction and Up-Grading of Kerogen." Aurora M. Rubel and coauthor Eileen Davis presented results of research at the Kentucky Center for Energy Research Laboratory under the title "The Effect of Shale Particle Size on the Products from the Bench Scale Fixed Bed Steam Pyrolysis of Kentucky Sunbury Shale." Lastly, Maria Rockwell, Technical University of Nova Scotia, presented "Processing and Up-Grading of Low Grade Nova Scotia Oil Shale for Potential Use." A review of shale oil prospects by Gerald Parkinson in Chemical Engineering for Feb. 3, 1986, covers both western and eastern projects and includes a report that the US DOE is funding a few relatively small projects; most of the fiscal 1986 budget of $12 million for shale oil is for fundamental research. Projects include a $3.2 million three-year contract with Hycrude Corp. (Chicago) for development of the HYTORT process and a $1.2 million three-year contract with the University of Alabama's Mineral Resources Institute on beneficiation of eastern oil shale by froth flotation. The report incorrectly states that current projects include a total investment of $466 million in a pair of 18-month technical and economic feasibility studies for proposed projects in southern Indiana. The correct figure is $468,657 [$240,908 for the Cliffs Engineering/

Jan 10, 1986

By Y. C. Kim

M.S. Azun The article unfortunately has some serious flaws negating the usefulness of the paper. The authors claim that kriging (linear kriging) is superior to other methods such as polygon. This is not the case. The deterministic methods (referring to polygon, ID, IDS, etc.) should not be compared with the statistical methods (linear kriging, disjunctive kriging, etc.) because they differ not only in their assumptions, but also their tools used in estimation. Thus, they give different results. By comparing the results of deterministic methods and linear kriging, the authors conclude that polygon, IDS, and linear kriging give an average thickness close to the value obtained from realizations. Besides, they argue that linear kriging gives less variance than the others (Fig. 2). The first conclusion is expected, due to the well-known central limit theorem. The second is the result of the statistical properties of different estimators. Thus, the comparison presented in the paper is rather meaningless because the authors have failed to follow basic statistical procedures. The numerical results of different approaches to an estimation problem cannot be generalized. In conclusion, the paper is not a meaningful contribution, and sadly, quite erroneous. Reply by E.Y. Baafi and Y.C. Kim The two key contentions made by M.S. Azun regarding the paper are: deterministic methods should not be compared with statistical methods and, hence, the results are erroneous; and the paper does not make a meaningful contribution. The first contention is an academic one. Most practitioners in ore reserve estimation could care less whether the tool they are using falls under a deterministic or a probabilistic method, so long as it gives the desired answers. It is probably for this reason that, whenever any new tool such as linear kriging is introduced to practioners in the mining industry, they would like to see a comparison test performed between the existing and the more familiar tools with a new and "strange" tool. Only when a new tool passes such a test, the generally conservative mining community would begin to utilize the new tool to its advantage. The second contention, is a subjective one. The final judgment should be left up to the readers within the mining community. If kriging is accepted more among practitioners, partly due to the paper, then the paper makes a practical contribution to the state-of-the art in ore reserve estimation. Finally, M.S. Azun entirely missed two main points in the paper. The first is that any comparative study of kriging vs. Polygonal or IDS should be performed for local estimation and not for global estimation. In the past, kriging was frequently compared with other existing tools in its performance on global estimation. Such results were nearly identical due to the central limit theorem effect, which further prevented the acceptance of kriging by practitioners. The second point is that a single case study using an existing property, as it was frequently performed in the past, is not sufficient because results depend not only on the tool itself, but also on the nature of the mineralization.

Jan 3, 1984

By M. S. Azun

The article unfortunately has some serious flaws negating the usefulness of the paper. The authors claim that kriging (linear kriging) is superior to other methods such as polygon. This is not the case. The deterministic methods (referring to polygon, ID, IDS, etc.) should not be compared with the statistical methods (linear kriging, disjunctive kriging, etc.) because they differ not only in their assumptions, but also their tools used in estimation. Thus, they give different results. By comparing the results of deterministic methods and linear kriging, the authors conclude that polygon, IDS, and linear kriging give an average thickness close to the value obtained from realizations. Besides, they argue that linear kriging gives less variance than the others [(fig. 2)]. The first conclusion is expected, due to the well-known central limit theorem. The second is the result of the statistical properties of different estimators. Thus, the comparison presented in the paper is rather meaningless because the authors have failed to follow basic statistical procedures. The numerical results of different approaches to an estimation problem cannot be generalized. In conclusion, the paper is not a meaningful contribution, and sadly, quite erroneous.

Jan 1, 1985

By R. H. . T. Garnett

Contributed remarks on paper published in the Transactions, Mining industry section, vol. 100, September- December 1991, A121--45

Jan 12, 1992

By L. O. Howard

R. HATCH, Garfield, Utah.-The object of the meeting, I believe, is to determine the proper chemical composition to insure long wear of a ball in a mill, This might also apply to rods. I feel that there is only one way of determining accurately the wearing qualities of balls in mills, and that is by actually wearing out 400 or 500 tons of different kinds of balls. Two things add to the wearing qualities of a ball: (1) the tenacity, with which the particular particles of iron or steel are cemented together; (2) the individual hardness of each particle. My experience is that a ball that has a Brinell of 550 to 650 will give comparatively long life. There is considerable difference of opinion as to the best steel and iron alloys necessary to produce a satisfactory grinding ball. Some favor chrome, some manganese and some nickel. Personally, I believe cast iron alloyed with chrome makes the best ball for small sizes; for large sizes (3 1/2 in. and up) steel alloyed with manganese is best. L. 0. HOWARD, Pullman, Wash.-How would this method apply to lining? A. KissocK, New York, N. Y.-I do not subscribe to that exactly. As I am connected with the Climax Molybdenum Co. you would hardly expect me to. We have been much interested in trying to work out this grinding-ball problem and have spent a great deal of thought and effort on it. As we are associated with the American Metal Co. and have a number of properties of our own, we are in position to try our ideas on ourselves first. We have tried different compositions, but have not done anything very remarkable with them yet, except that we have been able to say that the combination of chrome and molybdenum has given the best wearing ball. Mr. Hatch feels that iron is the best medium for grinding, but since toughness as well as hardness is a factor in wearability we feel that a well made steel is better for this purpose. Another difficulty with cast, or chilled, iron is lack of uniformity from day to day or from heat to heat and the impossibility of producing balls free from blow or shrinkage holes which materially affect their life. If cast iron is made hard it becomes brittle and lacks stretch or toughness. This prevents its use in the larger sizes, as breakage is a serious handicap to efficiency. We have tried hard and brittle balls and softer but very tough balls and have proved that maximum hardness, with sufficient toughness to prevent breakage, is the most important factor in resistance of a steel to abrasion. It is well known that chromium is one of the best hardening agencies for either iron or steel, and molybdenum is recognized as an element capable of introducing toughness. In other words, the proper combination of chromium and molybdenum permits unusual hardness with still sufficient toughness to stand up under severest impact. It is yet too early to give any actual mill results of this new combination and though we are proving our ideas at our own properties we have to depend on others to help us make the data more general and more worth while and would like to get some tests

Jan 1, 1928

By G. Johnston, P. K. Chatterjee, S. Holguin

M. Gershon The article is an excellent one, providing a basis for the conduct of the major tasks in underground mine planning and scheduling. I object to only one word. Since that word is featured in the title, it is a strong objection. The word used erroneously is optimization. There is no optimization performed in the article. By definition, an optimization is an approach that yields the best of all possible solutions. We can limit this definition to its narrowest sense, the optimization techniques of operations research such as linear programming, or broaden it to include less sophisticated search procedures that find the best mine plan or schedule. No such claim is made in the article. No optimization of any kind is performed. The major tool used is a simulation, which, in truth, is probably more appropriate for this problem than any optimization. But simulation does not optimize. It only allows for quick evaluation of many options, leading to the selection of the best plan "of those tried," not "of all possible plans." This article, of course, is not the first mining paper to make this error. It seems that the word optimization is used more to impress people than to refer to any act of optimizing. It is used in a way that implies "try to optimize"or "come close to optimize," but not to really do it. It is usually appropriate to quietly ignore this error. But when Dr. Chatterjee, who has done so much good work in true optimization projects and whose work I have come to admire, makes such an error, it is time to publicly dispute it. Having discussed this very point with him in the past, I am sure that he will agree. If he can support this position in his response, perhaps people will start to listen and we can reduce the number of false claims of optimization. This should be easy for him in this case since the approach he used, simulation, is the more appropriate one anyway.

Jan 8, 1988

By M. Gershon

The article is an excellent one, providing a basis for the conduct of the major tasks in underground mine planning and scheduling. I object to only one word. Since that word is featured in the title, it is a strong objection. The word used erroneously is optimization. There is no optimization performed in the article. By definition, an optimization is an approach that yields the best of all possible solutions. We can limit this definition to its narrowest sense, the optimization techniques of operations research such as linear programming, or broaden it to include less sophisticated search procedures that find the best mine plan or schedule. No such claim is made in the article. No optimization of any kind is performed. The major tool used is a simulation, which, in truth, is probably more appropriate for this problem than any optimization. But simulation does not optimize. It only allows for quick evaluation of many options, leading to the selection of the best plan "of those tried," not "of all possible plans." This article, of course, is not the first mining paper to make this error. It seems that the word optimization is used more to impress people than to refer to any act of optimizing. It is used in a way that implies "try to optimize" or "come close to optimize," but not to really do it. It is usually appropriate to quietly ignore this error. But when Dr. Chatterjee, who has done so much good work in true optimization projects and whose work I have come to admire, makes such an error, it is time to publicly dispute it. Having discussed this very point with him in the past, I am sure that he will agree. If he can support this position in his response, perhaps people will start to listen and we can reduce the number of false claims of optimization. This should be easy for him in this case since the approach he used, simulation, is the more appropriate one anyway.

Jan 1, 1987

By M. J. McPherson, R. Venkataramani

R. Venkataramani (Assistant Professor of Mining Engineering, Dept. of Mining, The Pennsylvania State University, University Park, Pa.)-Y. J. Wang and L. W. Saperstein are to be congratulated for their paper on the computer solution of ventilation problems. The limitations on the problem size to be solved by the program (Appendix II) has been outlined in the paper. I would like to add the following additional limitations of this computer program: The dimensions of the variable J1and J2 should be changed to J, (550) and J2 (550) to handle problems containing more than 400 branches, and up to 550 branches. If there are a large number of branches common to the various meshes, another limitation on the problem size will be the dimension of the variable NA. While a higher-order polynomial fitting for the fan characteristic data points is more rigorous, a quadratic relation, if linear interpolation between the points is inadequate, will result in saving computing time without much loss of accuracy. Of course, this can be handled by minor modifications to the existing polynomial fitting routine in the program. M. J. McPherson (Dept. of Mining Engineering, University of Nottingham, Nottingham, England)-The

Jan 1, 1972

Jan 1, 1953

Jan 1, 1953

By M. Lonoff

G. Campbell The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff's theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which Reply by M. Lonoff Campbell's comments give me an opportunity to clarify a few points in "Copper and Its Byproducts." That paper examined the affect of byproducts on the copper market and considered the relative riskiness of multi-metal deposits from an investment standpoint. That brief note made no attempt to be exhaustive. Nevertheless, Campbell's comments miss the point of the paper and necessitate a response. My "theoretical model" was static and I freely conceded after introducing the assumption of identical deposits that "none of the assumptions hold." These simplifying assumptions allowed me to bound the possible effects of higher byproduct prices on the copper price by assuming identical deposits and computing average price effects. I took great pains to subsequently explain that since deposits are not identical the identity of the marginal deposit might change due to byproduct price changes. In this case, average price affects will overstate the affect of byproducts on copper prices. According to Campbell, I dismiss as speculation any "real world behavior that does not always follow this pattern" (of metals prices moving in opposite directions). In the byproducts paper I noted that gold, copper, and silver price movements often parallel each other on an intra-day or day-to-day basis. Such movements are largely due to market anticipation of or reaction to changes in interest rates that affect carrying costs of metals stocks. Other movements may be due to anticipated changes in available supply or physical requirements. I loosely grouped these effects as speculative. To distinguish this statement from the main thrust of the paper, I contined "In the long run if gold and silver prices remain high the equilibrium copper price will be lower." The paper set out long run equilibrium conditions rather than attempting to explain price movements on a daily basis or on a year-to-year basis.

Jan 11, 1983

By G. Campbell

The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff’s theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which

Jan 1, 1984

By Shiou-Chuan Sun

SHIOU-CHUAN SUN (author's reply).-Thanks are extended to Professor Hassialis for his recognition of the usefulness of a new tool, the cataphoretic cell, as an adjunct to the bubble machine and the abstraction test. His questions concerning adsorption, dielectric constant, floatability, activation, and depression are interesting and worthy of discussion. I According to Mueller,28 it is questionable that any of the present formulas gives absolute values of zeta potentials which are completely accurate. The problem is further complicated by the question" of whether the "dielectric constant" has any meaning at all for such a microscopically thin layer. With these in mind, the results in this paper should be considered in the relative sense as a first approximation and not as absolute quantities. Adsorption Referring to item a of Fig. 8, the dielectric constant and the viscosity of the xanthate solutions are the same for galena, sphalerite and quartz. If dielectric constant and viscosity (but not the adsorption) were the first-order variable of the cataphoretic system, as claimed by Professor Hassialis, then the magnitudes of zeta coefficient of galena, spha)erite and quartz would have been similar to each other. These are not. The big difference of zeta coefficient of these three minerals in the same xanthate solutions is not altogether unjustified to be attributed to their difference in adsorption of xanthate ions. This is supported by the results of chemical abstraction tests reported by Ince.14 Again, the big difference of zeta coefficient between wollastonite, calcite, and fluorite in the same laurylamine hydrochloride solutions (p. 118, Figs. 58, 59, and 60 of ref. r5) also indicates that the cataphoretic system is not governed chiefly by the dielectric constant. Beside the data shown in Fig. 8, other experimental evidences15 which support the idea of correlation between adsorption and zeta coefficient are: (I) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of various concentrations of sodium cyanide, (2) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of constant concentration of copper sulphate at different pH values, and (3) there is a qualitative parallelism between zeta coefficient curve and chemical abstraction curve of quartz in solutions with constant concentration of barium chloride at different pH values. The above mentioned experimental results are generally in agreement with Gouy's double layer theory,1-5 and support this idea that the concentration and the kind of ions adsorbed at the mineral surface and in the adjacent surrounding liquid chiefly govern the electrokinetic phenomena. Dielectric constant and viscosity of the liquid medium may be of somewhat lesser importance. It follows that the correlation between the coefficient and adsorption as claimed in this paper is justified. Dielectric Constant The term "dielectric constant " was first introduced into the electrokinetic equations by Perrin.30 In a footnote of his publication he states that Holmheltz has forgotten to include the dielectric constant. The conversion of the moment29 to the zeta potential involves an additional difficulty and confusion not involved for the moment, namely, assigning a value to the dielectric coefficient. This is conventionally assumed to be constant and equal to the dielectric constant of the bulk liquid. 21 The published literature 10, 12 indicates that the values of dielectric constant for dilute chemical solutions have been assumed as those of pure water.

Jan 1, 1947