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By V. Miller

C. Hertzler The difference of means of milling characteristics by rock and ore type is tested in a statistical manner in the paper. The null hypothesis being tested is that the sample means of two different populations are equal. It is assumed that the null hypothesis is true when performing the test. Because of this, acceptance of this hypothesis leads to the conclusion that the sample means of the two different populations are equal (or there is no significant difference between the sample means), not that the samples come from the same population, as the author asserts. Rejection of the null hypothesis leads to the conclusion that the sample means of the two different populations are not equal. A P value for this test is reported in Table 2 and is incorrectly identified as the probability that the two samples came from different populations. Actually, what was recorded was 100(1 - p) where p is the usual p-value. The usual p-value measures, on a scale of zero to one, the extent to which the data agree with the null hypothesis. It is the probability of observing a value of the test statistic (Z score) that is at least as contradictory to the null hypothesis as the one computed from the sample data (McClave and Dietrich II, 1982). The author makes no mention of the fact that were these tests to be conducted together, the chances of determining that the null hypothesis is not true when it is really true are increased considerably (Snedecor and Cochran, 1980). This is a multiple comparisons problem and should be dealt with accordingly. The usual methods involve adjusting the level of the individual tests. Table 2 reports an incorrect 100(1 - p) value in the comparison of concentrate grades for other rock types with .30 to .69 % Cu vs other rock types with .70 + % Cu; 86 % should be 98.6 %. Although the article can be criticized for poor data presentation and discussion of that data, the point the author makes regarding the use of these statistics in the ore reserve estimation process is well taken. It does not appear that inaccuracies in the statistical interpretations have hindered that usefulness. References McClave, J.T., and Dietrich, II, F.H., 1982, "Statistics," Dellen Publishing Co., San Francisco and Santa Clara, CA, 766 p. Snedecor, G.W., and Cochran, W.G., 1980, "Statistical Methods," The Iowa State University Press, Ames, IA, 561 p. Reply by V. Miller After reading Ms. Hertzler's comments, it appears that the differences noted were basically semantics. If the paper is ever presented at a math symposium, some changes will be needed. When deciding the best way to present the data to mining engineers and geologists, I decided that presenting the probability that the two sample groupings came from different populations (reverse to the Null hypothesis) was easier and would require less verbage to explain. Hence, the 100(1 - p) difference which was noted. Ideally, I would have preferred to give the recovery and concentrate grades, then comment which ones had significant differences. Unfortunately, Kennecott Corp. did not grant permission to publish the ore body's actual recoveries and concentrate grades. The conclusion is that there was, as expected, a relationship between the ore's geologic properties and the metallurgical properties, and by determining this relationship, the overall mineral model was greatly improved.

Jan 8, 1984

By C. Hertzler

The difference of means of milling characteristics by rock and ore type is tested in a statistical manner in the paper. The null hypothesis being tested is that the sample means of two different populations are equal. It is assumed that the null hypothesis is true when performing the test. Because of this, acceptance of this hypothesis leads to the conclusion that the sample means of the two different populations are equal (or there is no significant difference between the sample means), not that the samples come from the same population, as the author asserts. Rejection of the null hypothesis leads to the conclusion that the sample means of the two different populations are not equal. A P value for this test is reported in Table 2 and is incorrectly identified as the probability that the two samples came from different populations. Actually, what was recorded was 100(1 - p) where p is the usual p-value. The usual p-value measures, on a scale of zero to one, the extent to which the data agree with the null hypothesis. It is the probability of observi" a value of the test statistic (Z score) that is at least as contradictory to the null hypothesis as the one computed from the sample data (McClave and Dietrich 11, 1982). The author makes no mention of the fact that were these tests to be conducted together, the chances of determining that the null hypothesis is not true when it is really true are increased considerably (Snedecor and Cochran, 1980). This is a multiple comparisons problem and should be dealt with accordingly. The usual methods involve adjusting the level of the individual tests. Table 2 reports an incorrect 100(1 - p) value in the comparison of concentrate grades for other rock types with .30 to .69% Cu vs other rock types with .70 + % Cu; 86% should be 98.6%. Although the article can be criticized for poor data presentation and discussion of that data, the point the author makes regarding the use of these statistics in the ore reserve estimation process is well taken. It does not appear that inaccuracies in the statistical interpretations have hindered that usefulness.

Jan 1, 1985

By P. R. Sheorey

I read this interesting paper on pillar strength in some detail because this is also my area of interest. It has long been the desire of mining rock mechanicians to predict pillar strength from laboratory compression tests. Considerable literature is available on compression strength of rocks and coal but many of these experiments were conducted not for pillar design but for rock behavior. I have a few comments on the author's approach to pillar design, especially equation (33). Two important factors, which the author seems to have excluded, can be added to the right side of equation (2): time-dependence of strength and the influence of mine environment on strength (moisture and weathering.) The author has taken considerable pains to analyze a large amount of testing data in [Table 1], yielding the various exponents ci of equation (2) (or the subsequent equations derived from it.) He has, however, not shown by means of a worked out example how these values of [Table 1] could be applied to a practical pillar design situation. It would have been interesting to compare predicted pillar size using equation (33) with an actual case. Alternatively, equation (33) could have been used to explain the failure of a pillar, if such a case history were available. Consider we have a large number of case histories of stable and collapsed pillars in a seam and we conduct a large number of tests in a laboratory press. The exponents [ci] can then be determined for actual pillars as well as for test specimens. Thus, equation (2) will read [ ] Since laboratory testing conditions (e.g., between steel platens) are different from the conditions on pillars, the exponents [ci] in

Jan 1, 1983

By Donald P. Richards

The use of point load test data by the authors to estimate rock mass cohesion is a very ingenious approach. It must be emphasized that this estimate is indeed only an estimate since the point load strength index employed to predict the uniaxial compressive strength (and subsequently predict the cohesion) is likewise only an estimate.

Jan 1, 1980

By Roussey Roussev

The use of chemical additives on grinding is of significant importance considering the high energy consumption of grinding processes. My research indicates that the dispersant approach explains the effects, in this particular case of wet grinding. Further, the dispersant approach combined with torque measurements give the possibility of clarifying the mechanisms involved when using grinding aids. I find the conclusions derived from the data obtained to be correct and useful for grinding. In general, I agree with the explanations. However, I would like to discuss several additional points that I consider to be important, and in the same time to mention some of my own results from investigations similar to those presented in the study under discussion. The "bed volume concept" and the change of slurry viscosity explain adequately the data plotted on [fig. 3], in conjunction with [Figs. 1 and 2]. However, the significant increase of the average torque in the case of 83% solid with XFS-4272 introduces the necessity of establishing the optimum of percent solid when dispersant is used. For example, the optimum percent of solid for different materials varies. One of the reasons is the material's mass density. On the other hand, it is necessary to determine the concentration of the chemical used. Because of this, it would be interesting to know how the cited concentration was selected.

Jan 1, 1983

A. G. Cockbain—The paper by Burlingame, Bitsianes and Joseph is of great interest in extending the work done on high grade sinters, particularly that of Hessle, and the development and application to them of the technique of McBriar, Johnson, Andrews and Davies on ironstone sinters. In this laboratory the work of McBriar et al. has also been continued and extended to cover high grade sinters, and a sectioning technique similar to that used by McBriar et al. was attempted on sinter cakes made in the laboratory sinter unit, using magnetite concentrates (containing 64 pct Fe). In these experiments no attempt was made to flush out the products of combustion with nitrogen before cooling. It was considered that free air penetration would occur on only a limited scale with the size of sinter cake made (14 in. sq x 12 in. deep). Chemical analyses of the zones showed generally similar features of those described by Burlingame et al. and especially the FeO rich region at and just behind the flame front, i.e. zones of ignition and combustion. This seems to indicate that the nitrogen atmosphere does not materially affect the states of oxidation in the sinter cake or at least that special care is not required unless the sinter cake is small. Burlingame et al. consider that FeO present has some significant part to play in the mechanism of sintering. This view does not find favor with the author. The reduction of iron oxides in the presence of red hot coke is a well known phenomenon, whether conducted in an atmosphere of nitrogen or in a crucible in air, and in view of the presence of some carbon in the hot sinter, especially just at the ignition zone, cessation of the progress of the flame front will in no way affect the reduction of iron oxides near hot coke. Even in a nitrogen atmosphere some CO and CO, will be generated by reduction and by continual oxidation and reduction of CO as the transfer agent, the oxidation state of the iron oxides can be lowered quite rupidly so long as free carbon exists with enough heat. Knowing the composition of the gas at the flame front (obtainable by probes), it would be possible to calculate the static oxidation state of Fe2O3/Fe3O2 in equilibrium with it and hence obtain a check on the chemical analyses to see if in fact direct reduction of the Fe2O3/Fe2O1 to FeO has taken place. Have the authors attempted this? It appears to this writer that what is required is some means of reducing rapidly the heat content of the ignition zone and immediately behind, and at the same time insuring no oxidation by the air. In ironstone sinters the difficulty of oxidation state of the iron did not arise on account of the very large slag bulk. However, in high grade sinters knowledge of this, and also the mechanism whereby high oxidation states can be obtained in the final sinter, is of great interest. R. D. Burlingame (author's reply)—The question has been raised as to whether the high FeO content found in high-fuel sinters is due to actual reduction at the advancing flame front or due to unavoidable direct reduction during the quenching period. For such direct reduction to have taken place in the freshly-formed sinter, a considerable amount of solid carbon would have had to escape combustion and be available throughout the hot sinter zone during the quenching period. A simple stoichiometric calculation with the limited data available indicates that a zone of freshly-formed sinter over 2 in. wide must have averaged roughly 2 pct C to accomplish the amount of reduction found. Furthermore, the presence of this amount of carbon would indicate that the fuel in the charge had not burned over a narrow front but over a zone at least 2 in. thick. In contrast to such a condition, the data of the present investigation indicate that the combustion of fuel is confined mainly to a narrow front in which high temperatures and reducing conditions favor. the formation of excess ferrous iron.

Jan 1, 1959

H. H. Kellogg (Columbia University)—The accurate measurements of the equilibrium gas ratios for the reaction: Pb(1) + H2S = PbS(c) + H2 [I] reported in this paper are a distinct contribution to the literature, and the authors are to be congratulated. I wish to comment, however, on the correlation of the data which is presented. The authors show a straight line correlation of log H2S/H2 vs 1/T, Fig. 1, and are satisfied with this for calculation of ?Fo even when extrapolated to low temperature (427 °C). Heat capacity data for the constituents of this reaction are available (at least to 900°K), however, and ACP for reaction [I] is finite and positive in the temperature range studied. Simplification of the heat capacity equations yields: ?CP= 2.71 + 1.65 x 10-3T (298°-900°K) This positive value of ?CP should result in a small but noticeable curvature of a plot of log K vs 1/T. That the experimental data fail to show such a curvature may be traced to another oversimplification of the author's treatment of their data. They assume that the activity of liquid lead is unity for all temperatures, so that

Jan 1, 1961

Few people in the industry today are competent to comment on the O.G. system for vessel covers, but with papers as well prepared as Mr. Bradley's we will soon be well informed. I would like to direct these comments to Mr. Klaes of Ford Motor Company. Mr. Klaes' description of their steaming hood agrees with our experience at Weirton. We have been able to stay within design limits and, as a result, have had few problems with our auxiliary equipment. Our main problem, as with Ford, has been thinning of our vessel cover tubes. At Weirton, controlled circulation, high pressure boilers are in use as heat recovery units above the BOP vessels. The boilers are provided with "off cycle' oil firing equipment. A Venturi type wet gas scrubber follows the boiler to complete the vessel draft system.

Jan 1, 1972

By Ossi E. Palasvirta

The authors are to be congratulated for their interesting article, which thoroughly illustrates the variables inherent in filtration of taconite concentrate. The work and the conclusions based thereon largely parallel the test work done by the writer at the Pilotac plant* and the experience gained with a commercial size agitating disk filter in the same plant. At Pilotac, however, a thorough study was also made of the effect of depolarizing (demagnetizing) the filter feed, and it is the purpose of this discussion to comment on the merits of depolarization of the magnetite concentrate prior to filtering. The work at Pilotac was done in three phases: 1) preliminary laboratory testing with a circular filter leaf of 0.047 sq ft, followed by 2) plant testing using a 4-ft diam, single-disk agitating filter that was purchased on the basis of the pilot tests on the 4-ft model. In the laboratory tests depolarization was achieved by slowly withdrawin4 batches of thickened concentrate from a coil producing an alternating field of about 300 oersteds. In plant tests the standard Pilotac procedure1 was employed, wherein the pulp falls freely through the depolarizing coil.

Jan 5, 1958

Prior to any detailed discussion, I'd like to say that Dr. Aplan has made direct hits on two important considerations: 1) The most demanding need in Fine Coal research is to develop improved methods of sulfur reduction. 2) The areas of particle (impurity) liberation and froth flotation hold real near-term promise as techniques for improved sulfur removal. Digressing for a moment, I thin kwe can all remember the time when the biggest problem facing coal research was simply defined - "No money!" In the mid 70's we suddenly found ourselves dealing with a product worth five to seven times the value it carried in the mid60's. All of a sudden, we're talking about a high-profile, high- value commodity. The coal industry still hasn't made the complete psychological adjustment - especially in the operating areas (prep plants included). We have a valuable material at hand which is, in' many cases still being processed as though it were a two or three dollar per ton item. Simply put, I think that while the industry has made some major strides during this transition, a stronger commitment of attitude (and finances) needs to be made toward deeper definition of beneficiation work. Back to specifics - Dr. Aplan has really highlighted three areas where strong research efforts are needed. 1) Liberation processes - not limited to mechanical comminution - must be more fully studied.The industry certainly needs a better handle on value returned (improved ability to beneficiate) for dollars spent on improved liberation. 2) Flotation processes probably hold the most promise for near- term improvement in fine coal beneficiation technology. Dr. Aplan’s.

Jan 1, 1979

By John F. Myers

Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity.

Jan 8, 1958

I have attended these meetings, every year, since 1926 and have served on both the Pittsburgh and the National Executive Committees, so that I am fully aware - of the ruling of this organization regarding, "No Papers by Vendors". Since I am now classified as a VENDOR, I wish to express my sincere appreciation for the invitation to formally discuss these very interesting papers --all of which herald the coming of an entirely new era in the manufacture of quality steels. I also appreciate the references by Mr. Mosser and Dr. Swinkels to my first paper on the oxygen probe which was presented at the meeting of this group, here in Chicago, in 1966 and was subsequently published in the NOH Proceedings of that year. (1)

Jan 1, 1972

Doctor David Yang has presented an important new flotation development in the area of fine particle flotation technology; at the same time Dr. Yang presents an explanation for the effectiveness of this improved new fine flotation system in terms of an optimum dispersion state. The same statement is made for the case of carrier flotation (ultraflotation), in the removal of anatase from kaolinite by addition of calcite (selective flocculation of the anatase - calcite system and dispersion of kaolinite). Dr. Yang's data and statements raise some important questions, and I will adress myself to the more fundamental aspects of this new flotation system. The addition of sodium silicate, well known as a good depressant-dispersant agent for siliceous gangue minerals, is proved to be greatly enhanced by the incorporation of polyvalent metal salts into sodium silicate prior to flotation, producing in this manner a condition, as described by Dr. Yang, of optimum dispersion, which in the case of fine-grained oxidized taconite can be described as selective flocculation (coagulation) of hematite and almost complete dispersion of siliceous gangue components. Dr. Yang recognizes that the main mechanism, while not completely understood at this time, seems to operate by modifying the surface characteristics of the gangue slime particles so as to prevent collector from bonding there to, and making the particles strongly hydrophilic so they will become fully dispersed and consequently will not float during froth flotation. At the same time it appears that the conditioning reagent also modified the surface characteristics of the floated minerals (hematite and spodumene in this case) so that they will aggregate and tend to more readily adsorb the collector, resulting in an improved flotation kinetics and selectivity.

Jan 1, 1979

By M. R. Yalamanchili, J. D. Miller

Discussion by M.R. Yalamanchili and J.D. Miller The authors, M. S. Celik et al., should be recognized for their efforts to describe the flotation behavior of boron minerals. In the case of borax and other soluble salt minerals, analysis of the flotation chemistry has been difficult because of the high ionic strengths associated with these soluble salt systems. However, considerable progress has been made in this area, and recently a surface charge/collector colloid adsorption model was proposed by Miller and his coworkers to explain the collector adsorption phenomena observed in soluble salt flotation systems (Milleret al, 1992; Yalamanchili et al., 1993; Miller and Yalamanchili, 1994; Yalamanchili and Miller, 1994a: Yalamanchili and Miller, 1994b). In this work, the sign of the surface charge of alkali halides in their saturated brines was established on the basis of nonequilibrium electrophoretic mobility measurements by laser-Doppler electrophoresis (Miller et al., 1992). Generally, these results are what would be expected from the simplified lattice-ionhydration theory. This electrokinetic information coupled with the stability and prevalence of collector colloids in such soluble salt flotation systems indicates that the selective flotation of alkali halides is due to the adsorption of oppositely charged collector colloids by heterocoagulation. Experimental flotation/bubble attachment results for 21 different alkali halides (Yalamanchili et al., 1993; Yalamanchili and Miller, I994b) confirmed that the flotation response of soluble salt minerals with weak electrolyte collectors can best be explained by the adsorption of oppositely charged collector colloids rather than by the adsorption collector ions and/or neutral molecular dipoles as originally suggested by many researchers (Fuerstenau and Fuerstenau, 1957; Schubert, 1967; Roman et al., 1968). In addition, the flotation of certain alkali oxyanions (Pizarro et al., 1993) and double salts such as schoenite and kainite can be explained by the same collector colloid adsorption mechanism (Miller and Yalamanchili, 1994). The borax flotation results reported by Celik et al. need to be examined in terms of the above mentioned surface charge/ collector colloid adsorption model. Unfortunately, the authors seem to be unaware of this recent work that nicely describes soluble salt flotation with weak electrolyte type collectors such as amines and carboxylates. In view of our past work, the flotation characteristics of borax were of particular interest, and, in this regard, the results of dodecyl amine flotation of borax reported by Celik et al. have been examined in further detail in the light of experimental results from our laboratory. In our research, a vacuum flotation technique was used to study the flotation response of borax (Na2B407.10H20), which has a solubility of 39 g/L at 25 °C) with dodecyl amine hydrochloride as collector. These chemicals were purchased from Eastman Kodak and used as received. Saturated solutions of borax at desired pH values were prepared by continuously stirring the salt solutions over a period of about 10 hrs. It should be mentioned that the conditioning time to achieve equilibrium is an important variable and can significantly change the flotation response of some soluble salts (Yalamanchili et al., 1993). Collector was added to the saturated borax solutions containing about one gram of 100x 150 mesh borax particles, and conditioning was done for about 20 minutes prior to flotation. The borax flotation recoveries from saturated brine are presented in Fig. 1 as a function of collector addition at the natural pH of 9.3, as reported both by Celik et al. and as measured in our laboratory. In addition, the region of precipitation for the dodecyl amine hydroborate is included in Fig. 1. It can be seen in Fig. 1 that the flotation response curves are separated by about one order of magnitude in R12NH3CI collector addition. The flotation results of Celik et al. show that the maximum borax recoveries can be obtained below the solubility limit of the dodecyl amine hydroborate collector. However, in our experiments borax flotation seems to occur only after the precipitation of the dodecyl amine hydroborate collector as might be expected from the collector colloid adsorption model (Yalamanchili et al., 1993) if borax were negatively charged. Further analysis by nonequilibrium and equilibrium electrophoretic mobility measurements for borax indicates that borax is negatively charged at the natural pH of 9.3, as discussed below. The reliability of the nonequilibrium electrophoretic measurements has been demonstrated previously for alkali halides and alkali oxyanions (Miller et al., 1992; Miller and Yalamanchili, 1994). The equilibrium and nonequlibrium electrophoretic measurements for borax were found to be consistent and are presented in Table 1. These results provide clear evidence that borax carries a negative surface charge in its saturated brine (pH 9.3), and the sign of the surface charge of borax reverses and becomes positive if the pH is reduced to 8.6. The equilibrium between borax and its saturated brine can be described by the following reaction: [2Na2B407.1OH2O-4Na++B407=+HB4O7 +OH+19H20] It appears that the oxyanions of the borax lattice provide

Jan 1, 1995

In his paper, Sastry proposes the use of flotation methods other than the "conventional flotation!' process as possible economical methods of removing mineral fines, The practice of Liquid/Solid separation employing microbubbles to assist or induce the flotation of suspended solids is common to both municipal and industrial waste- water treatment; and is also used as a separation step in some processing industries. The pretreatment (if any) of the stream prior to flotation, the source of the microbubbles, and the design of the separation vessel depend on the application. For example: a metal finishing plant would use an elaborate chemical conditioning scheme to precipitate metal hydroxides for removal by a dissolved air flotation unit operating in the effluent recycle mode, while some oily waste can be separated using a dispersed air flotation cell with no chemical conditioning. At the present time, the "conventional flotation" process employed by the mineral processing industry makes use of mechanical agitation and aeration to generate certain sizes and quantities of bubbles and to mix these bubbles with the pulp. Specific types of chemical conditioning are used to obtain the desired results. For the separation of mineral fines, the type of chemical conditioning, bubble generation and separation device needed to obtain optimum results will have to be determined through research. The point to be made is that while the principles of flotation separation can be applied to a wide variety of applications, the specifics of the flotation process may vary with each application. Sastry's paper has dealt with the many areas of research required to fully understand and utilize the flotation process for the beneficiation of mineral fines.

Jan 1, 1979

By J. J. Predali, J. M. Cases

J. J. Predali and J. M. Cases (Attachè de Recherche and Charge de Recherche, respectively, Centre de Recherches sur la Valorisation des Minerais, Institut Polytechnique de Nancy, Nancy, France)-The role of CO, in carbonate flotation is one of the parameters of a complex phenomenon: the adsorption of salts of fatty acids onto minerals. The authors therefore must be congratulated for their work. Their experimental results suggest some questions: 1) Recovery with C02, benzoic acid, or HCl, look very similar [(Fig. 1)] to that with the use of air; however, the recovery decreases very slightly (<10%). But in these two kinds of experiments, two parameters are different: the pH which is near 5.8 (with C02) becomes 9.1(without C02) and the concentration of Ca* I x 10-3 mole per 1 (without C02) becomes 1.9 X 10&apos; mole per 1 (without COO. 2) Adsorption experiments (Fig. 2) permit computing the surface coverage 9 which is 7.4% (without C02) and 8% (without CO_.) for an initial concentration of 12 X 10-6 mole per 1 in sodium oleate. It seems doubtful to us that this small variation can produce large increases of the recovery in flotation. 3) It is difficult to correlate adsoption and flotation experiments because they do not seem to have been done with the same size of particles. The concentration needed to obtain 95% recovery (Fig. 1) is about 3.0 X 10_" mole per l, that is, 1.13 X 10-6 mole for about

Jan 1, 1973

By Andre Hubaux

In the writer&apos;s opinion, more stress should be put on field and microscope observations, as J. L. Gillson does. His discovery of relics of big labradorite feldspars from the Marcy anorthosite in all the other rocks is proof enough that previous field observations have been inadequate. The writer&apos;s field experience with anorthositic massifs is limited to the Egersund-Sogndal district in southern Norway; however, this is a very large and well exposed area. It seems to have so many points in common with the Adirondack region that a detailed comparison should be beneficial. This comparison was not possible 20 years ago, owing to the scarcity of geological data, at least for Norway. Both regions are now far better known-the Norway district because of the work of Professors Bugge and Barth33-35 and especially because of the extensive field and microscopic research of P. Michot,36-46 who introduced me in the field to the problems of that region.

Jan 3, 1958

By E. J. Garrison

Discussion by E.J. Garrison A.C. Noble presents a clear and concise summary of the factors pertinent to a competent reserve evaluation of a mineral occurrence. However, I believe that he confuses the difference between a resource and a reserve. By definition, a reserve estimate includes all known economic, legal, mining, metallurgical and environmental factors impacting the recovery of the product(s) found in the deposit. A resource estimate, however, is an estimate of what is there - what is available for exploitation and should not include economic and other considerations. Only after defining the resource, its extent, location, physical and chemical properties, can an intelligent selection process begin of the extraction and processing technologies most appropriate to the circumstances encountered. The early and almost certainly inappropriate application of these often cookbook choices has probably lead many companies to walk away from good properties. (How many mines have been found in others rejects?) An example of the process is the early selection of metallurgical samples, after encouraging values are found in a few holes or surface samples, in an attempt to determine the economics of the prospect. Unfortunately, the sampler does not know how representative of the occurrence the sample is because he does not know what the deposit looks like. As a consequence, the property becomes saddled with a bad metallurgical sample that is often inappropriately used in evaluating the deposit which it does not represent. Reply by A.C. Noble E.J. Garrison asserts that I confuse the difference between a resource and an ore reserve. In fact, this paper was motivated by the observation that resources and reserves are almost universally confused throughout the industry. While Garrison is concerned that too-early consideration of engineering, metallurgical and economic factors will result in dropping properties too soon, some issues that must be considered include: •The purpose of exploration is to discover ore reserves, not to discover resources. •Ore reserves are always smaller than resources. • Decisions on exploration expenditures must be made based on the expectation of the quantity of ore reserves that will ultimately be defined. Noble&apos;s Fig. 2 can be used to give guidance as to when it is appropriate to begin reserve calculations. When exploration enters the "flat" portion of the curve, representative samples can be selected for metallurgical studies and appropriate mining methods chosen. It is at this stage that we know enough about the deposit to make intelligent choices of representative samples and recognize constraints on mining caused by the deposits shape, environment and physical properties. Once the appropriate technologies have been chosen, then their cost can be estimated with reasonable accuracy. Early entry of economic and process factors gives the false appearance of reserve status to the resource estimation. It would be more informative and less subject to abuse and misunderstanding if resource calculations were made at a number of cutoff grades. The cutoff grades should be chosen to cover the range of grades found in practice in existing operations of similar type. This would emphasize the open nature of resource estimates and encourage creative evaluation of mining and process technologies. It does not preclude the use of economic, environmental and recovery technology factors in deciding the advisability of continuing exploration expenditures, but would highlight their speculative nature. It is thus hoped that decisions on the future of the deposit would not be made on the presumed suitability of a given technology but on the actually known reality. I agree that resource estimates should be reported as a range of cutoff grades. Since reporting at a cutoff implies application of underlying economics (even by analogy to similar properties), however, it should be clearly stated that resources do not consider economic, mining or cost factors, and that ore reserves will be substantially less. The dilemma of the explorationist is that until the continuity and limits of ore-grade mineralization have been established, it is difficult to make quantitative estimates of either resources or ore reserves. Further industry discussion is needed regarding standards for disclosing early exploration information in such a way as to fairly represent the potential of an exploration property.

Jan 1, 1995

By L. H. Hart

Because of a widely recognized association between breccia pipes of one form or another and many important copper deposits, conditions under which breccia pipes develop have been of great scientific interest for many years. Since these phenomena first attracted attention, many theories have been advanced to explain their origin. This is not unexpected, since it is likely that they have been formed by and under a wide range of conditions. Moreover, the entire subject is confused by the fact that the term breccia pipe is applied to a wide variety of occurrences. To discuss any part of the subject intelligently, therefore, it is necessary to start with definitions of the terms used. In their discussion of the Toquepala deposit, Richard and Courtright have carefully defined the terms they have used in their presentation of a very logical geo- logical history of Toquepala breccias. This is a real contribution, as there is no reference in the literature known to the writer where the history of a series of breccia pipe epochs, confined essentially within one channelway, may be read with the degree of certainty that appears to be possible at Toquepala.

Jan 6, 1958

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The authors claim that their proposed jack-knife method, which is a rekriging of each block by eliminating, in turn, one sample from m the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" .of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors&apos; selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn&apos;t the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner&apos;s toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper con¬sist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data value-based measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text.

Jan 1, 1997