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By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986

By R. C. Kirkman

Your interesting and well-written paper brings up the issue of the purpose or use of a mineral property appraisal, specifically the value of these evaluations when the quality and quantity of the mineral resource to be exploited have not been thoroughly investigated. I am not a practicing professional in regards to valuation of limestone investment opportunities. I simply wish to make a few generic observations about the appraisal process in order to stimulate meaningful thinking by appraisal professionals whose reports may be reviewed by professional investors and "laypersons" alike. It is my contention that the analysis given in your paper is very thorough, considering the data that was made available to you. But I would not like to be the person responsible for investment decision making without having a feel for the risk involved. Therefore, the reviewer must classify this type of analysis as relatively "subjective" because they have not received an indication of the inherent risk involved in exploiting a mineral resource. This risk can best be quantified by using probabilistic methods in conjunction with the quality and quantity of the mineral to be produced. Most appraisals passively ignore this problem. Specifically, you have accurately identified the various costs and values entering the economic appraisal process. These can usually be quantified with a great deal more certainty than the capability of the resource to provide 25 years of quality material. Also, in Cases A (West Virginia)and B (Alabama), you are fortunate enough to have previous operations data. What if there had never been production from these properties? How does a potential mineral property investor evaluate the resource capability to meet various projected financial outcomes without spending a good deal of up-front capital to drill and delineate enough quality resources for a 20-plus year operation. These questions pose a substantial risk to any potential mineral investor. Only probabilistic methods should be used to quantify this type of problem, short of drilling and metallurgical testing. I might be considered a "layperson," not being familiar

Jan 1, 1991

By R. V. Colligan

[CONTENTS PACE Educating and Training Economic Geologists of the Future. By C. H. BEHRE, JR. (TP 2278, Min. Tech., Nov. 1948. Discussions by R. V. COLLIGAN and EVAN JUST) ....... I Mercury Industry in Italy. By EDWIN B. ECKEL. (TP 2292, Min. Tech., Jan. 1948. Discussion .............................. by C. N. SCHUETTE) 3 Chert in the Kingsport Formation at Mascot, Tennessee. By ARTHUR T. ALLEN. (TP 2299, ............... Min. Tech., Jan. 1948. Discussion by M. M. BUTLER) 5 Wall Rock Alteration at Butte, Montana. By RENO H. SALES and CHARLES MEYER. (TP 2400, Min. Tech., May 1948. Djscussions by C. D. HULIN, W. D. JOHNSTON, JR., and L. C. ................................... GRATON) 5] Educating and Training Economic Geologists of the Future R. V. COLLIGAN*-I can best illustrate my opinions by drafting another five year plan (Table 2). This plan is set up following the same stipulations outlined by Dr. Behre, namely: (I) the student is preparing himself for commercial work as a mining geologist; (2) he is attending an institution with a sufficiently broad curriculum (that is, engineering school and mining school as well as liberal arts college) to furnish the courses listed; and (3) he is not planning to continue his studies through to a doctor's degree before going into commercial work. A comparison of my study plan (Table 2) and that submitted by Dr. Behre (Table I) will at once point up the basic similarity, due to the obvious fact that there are so many essential courses which must be included in any outline of study. However, a more detailed analysis will show up certain differences, which, in fact, are only certain refinements on Dr. Behre's program. These I plan to discuss in order of their importance. The first and most important change is the addition of 12 hr of optional subjects, making a total of 24 hr of optional subjects as against a total of 12 hr under Dr. Behre's schedule. This of course entails the elimination of certain courses, which I shall discuss later. However, I wish to make it clear that I suggest eliminating these courses not because I feel that they are unnecessary, but rather because I feel the optional courses are more necessary to the complete education of the individual. I appreciate that Dr. Behre recognizes the importance of the cultural side of education, but I take issue with his thesis that the student will get it without credit and in his spare time. I do not think that the average college student, and certainly not the college freshman, is mature enough to know what he needs and where to get it in his spare time. I think it must be "spoon-fed"; he must be oriented through specific courses. University life (or should I say "college life") is too full of athletics, fraternity activities, dances, "bull sessions," and countless other enjoyable distractions, all of which contribute to the "full man." I fail to see how the average young American male can possibly sandwich in a necessary complement of "cultural activities" in his spare time. Since these latter activities do not fall within the pattern set by the "group," and show less promise of immediate return in enjoyment, or increased social status on the campus, they are bound to suffer in competition with the more popular, "group" activities. No doubt much of the criticism levelled against arts colleges, namely, that the cultural courses are useless, is well taken, for the culture

Jan 1, 1947

George A. Packard, Boston, Mass. (communication to the Secretary†):—The very interesting results obtained by Prof. Hofman and his assistants came to my attention when I had temporarily assumed charge of the metallurgical department of the Missouri School of Mines, and had found it, pending the completion of a new building, lacking a furnace in which to roast ore preparatory to the customary lead blast-furnace run. An attempt at lime-roasting had been already determined upon, but the use of a charge which would make a slag of definite composition was a new idea. The results following were obtained by Messrs. Aubrey Fellows, J. C. Long, E. R. Wash, and Dr. T. C. Tseung, under my supervision. It is regretted that the data are not more complete; but the work was done simply incidentally to securing the desired ore for the blast-

Jan 1, 1908

Edward A. UehlinG, New York City (communication to the Secretary*):—Mr. Baker's paper is one that brings up a subject of great importance, and if full statistics could be collectecl of the number of furnace-linings ruined by reason of bad distribution by skip-hoists, it would be found an astonishing array. Unfortunately a universal remedy has not yet been found. The fact that Mr. Baker has apparently succeeded in overcoming the trouble at Sydney, is no guarantee that the same remedy applied at another plant, where very different or even slightly different conditions prevail, mould cure the trouble. That it requires but a slight continuous difference of penetrability in the column of the descending stock of one section, over another, to produce channeling, is clearly demonstrated by Mr. Baker's experiments, by which he reversed the channeling from front to rear instead of remedying the trouble. Every change in the physical make-up of the charge necessarily requires a specific adjustment; even supposing this feasible, the regular working of the furnace is by no means assured, because with the high pressures now customary, the tendency of the ascending gases to plow their way through in a direct course, prevails, and having once opened up a passage, they will persist and cause trouble. Homogeneous filling-, hard driving and regularity of working are incompatible. The higher the furnace, the greater the

Jan 1, 1905

F. E. Bachman, Port Henry, N. T. (communication to the Secretary*):—In discussing Mr. o.o.Laudig's paper, the Action of Blast-Furnace Gases Upon Various Iron-Ores,' I took the ground that Mesabi-ore explosions were entirely mechanical; but more observation and later experience has caused me to

Jan 1, 1905

A discussion of the paper by Mr. Campbell, which was read by title at the Lake Superior meeting, but first presented at the New York meeting of the Iron and Steel Institute, October, 1904 (see p. 772). These papers are here published onder a mutual agreement between the Councils of the two Institutes, and will also be found in the Journal of the Iron and Steel Institute for the year 1901, vol. ii. Mr. William R. Webster, Philadelphia, Pa., said: We are under great obligation to Mr. Campbell for his exhaustive investigation, and the results he has put before us to-day. They are the most conlplete series of tests that have ever been made, where all the conditions of rolling, etc., were kept uniform. In discussing Mr. Campbell's first investigations, I claimed first, that the method of least squares, then used, would of necessity only gire the average value of any element, and that if the effect of any element was greater in the presence of high carbon than with low carbon this would not be shown by the method of least squares. Secondly, that the effect of manga nese should be considered on acid steel as well as on basic steel, instead of ignoring all the eff'ect of that element when it was below 0.60 per cent., as was then recommended by Mr. Campbell. I am pleased to note that the results of his present investigation confirm my views on these points. In presenting the results of his first investigation, Mr. Campbell referred to my investigation of 1893-94, and took exception to the value of phosphorus varying (depending on the amount of carbon present) from 800 to 1,500 lb. for each 0.01 per cent. He claimed that one might just as well consider the effect of phosphorus as being constant, and of carbon varying. I refer to this, as he now has introduced very similar conditions in his present tables, in that he gives variable values for manganese (depending on the amount of carbon present) for both acid and basic' steels. Can we now say, with more certainty than formerly, which element should be considered as haviup a constant effect ? There is one other point that I took up in my former discus-

Jan 1, 1905

Charles Catlett, Staunton, Va. (communication to the Secretary*):—Mr. Chance's suggestions that the brown hematite-ores of the Potsdam formation are due to the alteration in place of iron sulphide, and that their extension may reasonably he expected to contain valuable deposits of unaltered sulphide, are interesting; hut the facts marshaled by him are too limited

Jan 1, 1909

James GayleY, New Pork City (communication to the Secretary*) :—The main thing that is sought after in this matter is that all purcliases shall be made by analysis. This is done already in special lines, as in the manufacture of various grades of steel in which phosphorus, silicon and sulphur are specified within narrow limits, and I quite agree with Mr. Cook that specifications, which are over-rigid in unessential particulars, should be avoided, as they defeat their own purpose because unreasonable requirements permitting no variation are practically not fulfilled, and it is impossible to specify grade

Jan 1, 1905

EdgaR S. Cook, Pottstown, Pa.:—Many friends and acquaintances seem to be under the impression that the Warwick Iron & Steel Co. received a' license from Mr. Gayley, free of cost, as an inducement to adopt the process. This impression is not correct, since the license was paid for, and I think it was the first payment that Mr. Gayley received for the use of his process. As president of the Warwick Iron & Steel Co., I am responsible for its earnings, and with only the experience at the Isabella furnaces as a guide, the directors of the company considered that there was a great risk in expending the large sum of money required for the plant. They, however, acted favorably upon my recommendation, and to this extent I am responsible for the installation at the Warwick furnaces. I made the best agreement possible with Mr. Gayley, and naturally our company received certain advantages. It will be contrary to all experience if subsequent plants do not show some improvements and economies in construction. It is to our indirect benefit that all subsequent licenses granted by Mr. Gayley should be charged at a much higher rate than we paid; and I trust that he will see to it that all such licenses granted, especially to companies making merchant iron, shall be at a maximum figure. The Warwick Iron & Steel Go. is not interested in any way in exploiting the merits of the Gayley dry-blast process; on the contrary, looking at the subject from a narrow and selfish standpoint, it is to the advantage of our company that no merchant blast-furnace competing with our iron-product should be equipped with a dry-blast plant. There is a clause in the contract with Mr. Gayley, whereby our company agrees to furnish him with all the data derived from the operation of the dry-blast plant, and that he or his

Jan 1, 1909

Edwin H. MessiteR, New Pork City (communication to the Secretary*):—Under the heading " Flues," Mr. Edwards refers to the Bee-hive construction, a cross-section of which is shown in Fig. 4 of his paper. A flue similar to this was designed by me about six years ago,' in which the walls though much thinner than those described by Mr. Edwards gave entire satisfaction. These walls, from 2.25 in. thick throughout in the smaller flues, to 3.25 in. in the larger, were built by plastering the cement mortar on expanded-metal lath without the use of any forms, or cribs, whatever, at a cost of labor generally less then $1 per sq. yd. of wall. Of course, where plasterers cannot be obtained on reasonable terms, the cement can be molded between wooden forms, though it is difficult to see how it can be done with an interior core only as stated by Mr. Edwards. In regard to the effect of sulphur dioxide and furnace-gases on the cement, I have found that, in certain cases, this is a matter which must be given very careful attention. Where there is sufficient heat to prevent the existence of condensed moisture inside of the flue, there is apparently no action whatever on the cement, but if the concrete is wet, it is rapidly affected by these gases. At points near the furnaces there is generally sufficient heat not only to prevent internal condensation of the aqueous vapor always present in the gases, but also to evaporate water from rain or snow falling on the outside of the flue. Further along, a point is reached where rain-water will percolate through minute cracks caused by expansion and contraction, and reach the interior, even though internal condensation does not occur there in dry weather. From this point to the end of the flue the roof must be coated on the outside with asphalt paint or other impervious material. In very long flues a point may be reached where moisture will condense on the inside of the malls in cold weather. From this point to

Jan 1, 1905

Discussions of the paper of Mr. Gayley read by title at the Lake Superior hieeting, but first presented at the New York meeting of the Iron and Steel Institute, October, 1904 (see p. 746). With the exception of Mr. Pourcel's discussion (p. 1038), these papers are here published under a mutual agreement between the Councils of the two Institutes, and will also be found, with others, in the Journal of the Iron and Steel In-slitute for the pear 1904, Mr. E. Windsor Richards, Past-President,' said that in 1799 Mr. Dawson, of Low Moor, read a paper before a scientific society in York pointing out the great diff'erence in the moisture of the air going into the blast-furnace in the hot months of the year and in the winter months. A cold blast-furnace was a very sensitive instrument, and showed this very clearly, for in June, July and August the furnace did not drive so well; it did not make the quality of iron and required more fuel; so that Mr. Gayley was on the right road to effect an enormous improvement in this direction. He considered that Mr. Gayley was on the way to great success, and hoped that the apparatus would not be a very expensive one. He supposed it mas too early for Mr. Gayley to let them know what the saviug was

Jan 1, 1905

Edward A. UehliNg, New York City (communication to the Secretary*):—In adding my mite to the discussion, I wish to touch on a few points which bear emphasizing and perhaps a little further elucidation. Mr. Grammer says that he "found the electric pig-breaker at Duquesne, if used in connection with the iron-chill, less expensive and more satisfactory " thau the casting-machine. The cost of handling the iron over the Duquesne casting-niachine is about double the average cost of the other Uehling machines at the several Carnegie plants. It is nearly as expensive to run as the Hey1 & Patterson machines, and while Mr. Grammer's statement is, no doubt, true, as applied to that particular machine and breaker, it should be borne in mind that the machine at Duquesne had embodied in it several new features, which were not improvements; also that it was taxed beyond its economic capacity. The machine at the Lucy furnaces under the management of Mr. Scott handled the output of the two furnaces, and saved

Jan 1, 1905

Jan 1, 1908

JAmes E. Howard, Watertown, Mass.:—In connection with this paper, it is the desire of the Watertown laboratory to receive suggestions as to the lines of work and the particular direction along which the examination of the ingot-metal should proceed, and any suggestions so offered will be noted with care, and the tests conducted so as to embrace such features as it is thought desirable to have investigated. To me the question of structural continuity seems of para-

Jan 1, 1909

P. H. Dudley, Yew York, N. Y. (communication to the Secretary*) :—The characteristics of Professor Home's metallurgical papers are, that he is able, from the mass of confusing evidence on the subject, to make an analysis and present hypothetical and essential principles in concrete form for consideration and discussion. I can appreciate, from the practical side of the subject, the labor of collecting and investigating the data which was essential to prepare the paper. Much of it necessarily came from material of preceding years of manufacture in which time was allowed for chemical reactions of the re-carburizer, and for the elimination of the oxidation-products before teeming the ingots. This practice gave a favorable time-element to free the metal from slag and other impurities— a requisite condition for the production of sound steel in the ingots. But, in allowing them to become cold before they were charged into the furnace, a subsequent time-element entered as a detrimental factor in the development of the pipe or shrinkage-cavities, which gave an ingot-structure deficient in soundness, at least in the upper portion. (The term slag is used in a general rather than in a strictly technical sense.) Traces of manganese sulphide are often associated with manganese silicates in the same thread or seam, and at other places they are separate and distinct. Interpretations from material thus manufactured must be made with due allowances for the methods of fabrication and the requirements of service. The only way we now have to estimate what the degree of soundness of the ingot-structure was, in the early foreign and American manufacture of steel rails, is by examination of the worn and failed material after years of service. We must remember also that the poorest material was long since consigned to the scrap-heap without any full record of its history. The rails from a given ingot cannot now be identified ; and in many

Jan 1, 1909

C. D. Demond, Anaconda, Mont. (communication to the Secretary*) :—In order to throw some light on this interesting subject, a series of experiments were made with strips of mild steel, containing about 0.14 per cent. of C and 0.22 per cent. of Ma. These strips were thoroughly cleaned and brightened before use, salts were added to distilled water until it corresponded as nearly as possible to the analysis given by Mr. Lee, and in this water at different temperatures were placed four strips of steel; while four other strips, at corresponding temperatures, were placed in the water used at the Washoe Reduction Works. The latter plant has had no trouble from corrosion of furnace-jackets, pipe-lines or boilers. The analysis of the water used at the Washoe works is: Grains er U. S. Gallon. CaCO3........... 2.92 CaSO3........... 0.76 MgCI3........... 0.64 MgCO3........... 0.58 A1203........... 0.12 Fe2O3........... 0.12 SiO2........... 0.58 NaCl........... 0.35 Organic matter, etc.,........ 1.16 7.23 This water is neutral to litmus; while the artificial Copper Queen water was very slightly alkaline, which Mr. Lee informs us is also true of the water at Douglas. Both waters mere well aerated by pouring from beaker to beaker, and by blowing in air from the experimenter's lungs. The results of these tests, given in Table I., show that there is no significant difference between the effects of the two waters.

Jan 1, 1909

AlFred JamEs," London, Eug.:—I thank you, gentlemen, for Sour kind invitation to address you. It is a very great pleasure for me to be here at your annual meeting, and, although I have been a member since 1894, this is the first opportunity I have

Jan 1, 1909

J. E. Johnson, Jr., Glen Wilton, Va. (communication to the Secretary*):—Mr. Meissner announces early in his paper that one of its purposes is the discussion of my paper entitled, Notes on the Physical Action of the Blast-Furnace,' with which he disagrees in part; and as the second stage of the discussion of this important subject has centered around his paper, some reply by me may not be amiss. Unfortunately, Mr. Meissner has not indicated a single statement or conclusion in my paper that he wishes to controvert; but as there is evidently a difference of opinion between us I will disregard this fact, and will discuss those conclusions of his that seem to me not to be justified by the facts of general practice, or even by the data which he produces to support them. Let me say, however, that I am a believer in the dry-air

Jan 1, 1908

Richard Moldenke, New Pork, N. P. (communication to the Secretary*):—Iu following the discussion of the specifications for cast-iron and finished castings, I mas strongly impressed with two points which might be ventilated to advantage more fully from the view of the practical foundry-man. First, the reasons why only silicon and sulphur were specified and not phosphorus, manganese and carbon; and second, why but little was said concerning the presence of iron oxide in the material.

Jan 1, 1905