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Secretary's Note.—M. Beutter's introductory remarks, being simply a resume of Prof. Hone's paper, with a disclaimer of the intention to criticise it, have been omitted, and the remainder of this contribution lias been somewhat condensed, without omitting any essential statements. M. Beutter, St. Etienne, France* (communication to the Secretary†):—Professor Home observes in $ 47 of his paper that the fluid-compression of steel diminishes piping by forcing the liquid and viscous metal, while the pipe is forming, or after it has formed, into the space so produced, and proceeds to study the different systems of compression, alluding to the four principal ones: Whitworth, Illingmorth, Williams, and Harmet. Having now for many years had in use the last-named process, that of M. Henri Harmet, I shall attempt to explain the difference between it and the three other processes named. The Harmet process does not diminish or close the pipe after it has formed, but prevents it from forming; and I may add that it is the only one of the four which produces this result. It is true that the Whitworth process diminishes the interior hollow by localizing it around the central axis of the ingot, which is afterwards removed by trepanning the hollow forg-ings for which this process has been, I believe, always exclusively used. The Illingworth and Williams processes, which, in my opinion, are applicable only to small ingots, of necessity allow the pipe to form, or (to use the expression of Professor Howe) they allow the surface of the lake of liquid steel to sink into the interior of the ingot, since they involve waiting a certain time before compression, so that (in the case of the Williams process) the ingot-mold can be opened without danger, or (in the case of the Illingworth process) so as to avoid the risk that the steel may enter the grooves produced by the removal of the distance-bars. During the time required for

Jan 1, 1908

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

Bernard MacDonald, Guanajuato, Mexico (communication to the Secretary*):—Mr. Iceyes's paper is very interesting to me because of my personal experience with the development of the ore-deposits of Lake Valley.

Jan 1, 1909

Edward Halse, Puerto Berrio, Colombia, S. A. (communication to the Secretary): I have read with much pleasure the interesting and valuable paper by Mr. Kunz, and hope that the following brief notes, gathered a few years ago, while a resident in Mexico City, may help to elucidate the subjcct: Turquoise.—This was known to the Aztecs as Xihuitl. Santiago Ramirez states that they found it in the Cerro Xicohtzonc, close to Atzcapatzalco, a suburb of the City of Mexico (compare page 59). Opal.—This was known to the ancient Mexicans, for they named it mezcuitlatt (compare page 63). Jade.—Under this was iucluded a third mineral, prehnite, not mentioned by Mr. Kunz. According to James D. Dana, part of the "jade " of China is prehnite; and Humboldt informs us, in his work on New Spain, that the same species of jade is known in some parts of Mexico as mahagua (majagua ?). The same writer says, in his Views of the Cordilleras, that the Aztec name Tecpatl included flint, hornstone, and green jade; and finally, in his Travels in South America," he discusses the nature of the ancient amazon-stones, and declares them to have been made out of a jade resembling " compact feldspar," one of the constituents of the gabbro verde di Corsica. IIence those stones were probably composed of nephrite. According to Humboldt, the form given to them most frequently is that of the Babylomian cylinder, longitudinally perforated, and loaded with inscriptions and figures. They were also cut by the natives into very thin plates, perforated at the center, suspended by a thread, and worn as amulets. According to the historian Clavijero, the specific name given by the Aztecs to the nephritic stone (jadeite) was Quitzalitztli,

Jan 1, 1902

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

Prof. Henry M. Howe, New York, N. Y. (communication to the Secretary*):—The results presented in Mr. Mathewson's paper are of very great interest. Perhaps the most interesting is that shown in Table I. and Fig. 1, in which the arsenic decreases in 10 min. from 0.22 to 0.07 per cent. This is such a large decrease that it is to be hoped that Mr. Mathewson will verify it by repeating his tests with a matte of similar composition. This is particularly to be desired, because the simultaneous removal of sulphur appears to be very small. All three blows further agree in showing that the removal of arsenic is in the very early part of the blow. The fact that the removal of arsenic then ceases abruptly cannot be explained completely by the fact that the arsenic has fallen so low as by its lowness to resist further removal, because in the first blow the arsenic becomes stationary at 0.06 per cent., whereas in the third blow it does not become stationary until it has fallen to 0.034 per cent. The abrupt ending of the removal of arsenic is more likely to find its explanation in the composition of the slag, and it is to be hoped that Mr. Mathewson will supplement these extremely valuable data with others in which the composition of the slag at the same time shall be given. The sudden rise of arsenic toward the end of the third blow I suppose must be referred to an error in sampling or analysis.

Jan 1, 1908

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

William H. Blauvelt, Syracuse, N. Y.:—Is the coal itself from which the briquettes are made of good quality for steam-ing-purposes? Mr. Parker :—It is an anthracite coal mined near Bank-head arid used on the Canadian Pacific railroad. It contains about 83 of carbon, 8 of ash, and 8 per cent. of volatile material. With regard to briquetting of a mixture of fine coal and coke-dust, I understand that a plant has been installed near Detroit in which coke is mixed with anthracite; also the plant of the United Gas Improvement Co. near Philadelphia is briquetting a mixture of anthracite coal, the resultant briquettes being used in the gas-retorts. Mr. Blauvelt:—The purpose of the Detroit briquette-plant of the Solvay Process Co. has been partly to use up the coke-breeze from the by-product ovens and partly to utilize the pitch. There is no necessity for mixing anthracite with the coke-breeze, but the supply of breeze is limited, and anthracite

Jan 1, 1909

R. W. Raymond, New York, N. Y,:—Since the presentation of my note on this subject at the New York Meeting, Professor Louis has pointed out an error in my statement of his conception of " pitch "—namely, he understands the pitch, in the restricted sense which he proposes, to be the angle of inclination of the axis of an ore-body, measured on the vertical plane drawn through the body; whereas, I represented him as proposing to define " pitch " as the angle of inclination of an oblique body, measured on the plane of the dip, in the direction of the strike. The difference will appear upon consideration of the accompanying isometric projection, Fig. 1, in which ABCD represents the plane of the inclosing ore-deposit (vein or bed), and AC the axis of the oblique ore-shoot. ABE is the angle of the dip, as universally understood; and ACE

Jan 1, 1909

E. T. Dumble, Houston, Texas (communication to the Sec-retary?):—In addition to the list of publications mentioned by Mr. Schorr and those by Prof. Hofman, I call attention to the following references:— Sludi sulle Lignite, by Capacci. Turin (1890). (An excellent work.) Report of Brown Coal Industry in Germany. J. Cosmo New-berry. Department of Mines, Victoria (1892).

Jan 1, 1905

Olof Venstrom (communication to the Secretary*):—In order to do justice to a property, once the largest producer of copper in the world, which is now being reopened, with a fair promise of again becoming important, I beg to add a few words in connection with Mr. Souder's remarks on the El Cobre copper-mines. The El Cobre copper-mines were worked by the old English

Jan 1, 1905

A. Bement, Chicago,Ill. (communication to the Secretary*):— Formerly it was the general practice of engineers to designate coal that is free from moisture and ash as " combustible," notwithstandirig that it contains oxygen and nitrogen. The origin of this practice was more particularly due to the requirements in connection with boiler-testing, which demanded a consideration of that portion of the fuel which took part in the combuition-process because results based on a unit of either moist or dry coal were not comparable, since both moisture and ash were recognized as variable quantities. Thus, a pound of " combustible " became a standard of value, and was treated as a constant before employing measurements of heating-power and calculating therefrom the percentage of efficiency. The recognition of this term " combustible " was an advance to be credited to the engineer rather than to the chemist, because the latter, not having to do with the interpretation of analyses in practice outside the laboratory, usually saw no reason for reporting results in terms other than those of the moist-coal composition. Some years ago I needed a table of fuel-composition in terms of moist, dry, moisture-free and ash-free coal, and of the combustible components. This table required the use of the word combustible in its proper sense, for the purpose of designating carbon, hydrogen, and sulphur, instead of including these three elements with oxygen and nitrogen, to which aggregate the term combustible was formerly applied. To make such a tabulation involved either the use of the inconvenient and cumbersome term, "ash- and moisture-free coal," or of some other representative term, and for this purpose I adopted the expression pure coal, which is short, simple, convenient, and technically correct. It is also harmonious, because it agrees

Jan 1, 1909

Arthur Jarman, Sydney, New South Wales, Australia (communication to the Secretary*):—All designs for modern metallurgical and chemical laboratories should provide each student's desk with a hood or cupboard for the removal of fumes, but I doubt the advisability of placing air-baths and similar apparatus close to the hot plate. It seems to me that unless the draft be exceptionally strong the fumes from ordinary wet assay work will corrode the iron-work of the fittings, in which case the baths would have to be removed to a general desk in order to lighten the work of the laboratory attendant. Since the laboratory described by Mr. White has been in use for two years, I should like to ask if any inconvenience has resulted from this corrosion. If not, it is certainly an important improvement to have the air-baths and similar apparatus placed on the student's desk. The hoods described by Mr. White are supplied with a good draft by means of a fan, which gives them a great advantage

Jan 1, 1905

R. Culver, Colorado School of Mines I appreciated Professor Starfield's presentation, because his approach to blasting research reflects my feelings that a lot of practical work can be done toward making short-term advances that can be used by the blasting industry. We should not forget this in our attempt to obtain solutions to such idealized problems as a mathematical theory of cratering. The blasting industry would like very much to have the efficiency of the basic blasting processes improved from the range of 20 percent up into the range of 50 percent. And many of these problems should be approached and attacked in the laboratories. Blasting research at the Colorado School of Mines for the past two or three years has been aimed at improving the pre-splitting process, because we feel it will become increasingly important to the construction industry. We have attempted to develop a unified theory of how pre-splitting works; and the more we investigate, the more variables we find. We may never obtain an entirely satisfactory theory of pre-splitting, but we have developed a tentative explanation. One of our first conclusions was that we are making very poor use of the explosive in current pre-splitting practice. But to appreciate this we must first consider how pre-splitting works. A series of parallel boreholes are loaded with low density charges which are detonated simultaneously. (Delayed detonation has been tried, but most people agree that simultaneous detonation is best, and this is what we found.) Stress waves traveling out from each borehole interact with the stress waves from the two adjacent boreholes influencing the direction of the fractures that occur and propagate from each borehole. It has been suggested in private communication with Mr. Wilbur Duvall of the U. S. Bureau of Mines, that the fracture between the adjacent boreholes is a result of the net particle velocities above and below the pre-split plane which tend to set up a net tension along the pre-split plane. Regardless of what the exact mechanism is that causes the fracture to propagate from one borehole to the next, we know that it, in general, relies upon an interaction of the stress waves. However, if there is a large compressive stress normal to the pre-split place, it can practically eliminate any possibility of obtaining the desired pre-split by preventing the desired fractures from getting started. Aside from obtaining a fracture along the pre-split plane, the other major aim of pre-splitting is to minimize the fracturing that occurs around the borehole. We do this by drilling a large hole and putting a small charge in the middle of it. This results in a badly decoupled charge which is very inefficient; most of the energy is used in compressing the air in the borehole. Out of discussions about how pre-splitting works, we decided that perhaps there was some other explosive geometry which would make more efficient use of the explosive, and result in optimizing the pre-splitting process. Starting in the laboratory with small plexiglas blocks, we found that a fully-coupled explosive charge of 5 grains/in. of PETN gave random fractures extending about I in. from the borehole. A 1/4 in. plexiglas plug fit into a 1/4 in. hole in a similar block with the same fully coupled charge gave random fractures extending out only about 1/2 in. due to the energy absorbed in fracturing the plug. If the plug was split longitudinally but otherwise using the same geometry, it was possible to drive a fracture about 2 in. in either direction from the borehole, with an even smaller amount of fracturing around the borehole.

Jan 1, 1967

S. Tandanand, Twin Cities Mining Research Center, U. S. Bureau of Mines As an addition to the fine reviews on drilling presented in the foregoing papers, we feel it would be appropriate to mention briefly some work in this area by the U. S. Bureau of Mines. The Bureau has had under way for several years at its Twin Cities Mining Research Center studies directed toward a better understanding of basic drilling mechanisms. The work includes drillability investigations with diamond rotary, and with percussive drilling systems, as well as fundamental studies of rock behavior under drill bit types of loading. Results of our work to date have contributed the following to the state of the art. MECHANISM OF ROCK FAILURE-Rock fragmentation through use of mechanical energy systems, including drilling systems, consists of two major components-machine and rock. The two components are related to each other by their functional behavior and their resultant motion which the components mutually influence. Forces in the systems are transmitted directly to the bit which in turn induces stresses in the rock. When the induced stresses exceed the strength of the rock, the rock fails resulting in penetration. Rock strength is a function of the forces applied to the rock. Stresses under a drill bit, regardless of bit configurations, are essentially compressive, resulting in a condition where the rock has the highest resistance to failure. The ratio of principal stresses induced under drill bits is an indication of the mode of failure in the rocks. Initially, compressive stresses under the drill bit cause rock to undergo inelastic deformation. The impression observed at the first stage of crater formation under the drill bit shows that rock is no longer elastic. Associated subsurface failure at this stage precedes total rupture which subsequently appears at the rock surface. Thus, explanation of crater formation, by applying theory of elasticity alone, is likely to be over-simplified. ENERGY VERSUS VOLUME OF ROCK REMOVED-Experimental results show that energy per unit volume of rock removed is constant for a particular rock and bit type. Rock offers a definite resistance to penetration, depending on the method of the energy application; this may be defined as the drilling strength of a rock. Energy consumption in a drilling system may be divided into two components: 1) Energy required to move the machine parts; and 2) energy consumption in breaking rock. Component 1 is dependent on the type of the machine. Component 2 is dependent on the strength properties of rock and the efficiency of the bit in rock cutting. The sum of the energy required in both components determines the total energy required in breaking rock. Our work in this area has included consideration of both diamond and percussive drilling systems. PENETRATION RATE-For a drilling rate expression to be useful in predicting field performance, it should include the operating characteristics of the drilling machine. Eq. 37, for example, is simply a statement of the fact that the drilling rate is determined by the power output of the machine (2pNT) and the power requirements to break the rock in the hole (AER). In order to predict the performance of a particular drill and the effect, for example, of the rotary speed, on the drilling rate, R, Eq. 37 must be modified to include the

Jan 1, 1967

Several of the current concepts of brittle fracture involve consideration of, the existence of defects or flaws. Griffith 1 observed that the tensile strength of brittle materials was several orders of magnitude less than might be expected from the calculated strength of the molecular bonds. He was able to show that the stress concentration at the tip of an elliptical crack is sufficient to raise the local stress level many fold. He therefore proposed that real materials do contain such stress risers in the form of minute cracks and that this accounts for the rather large difference between theoretical and actual strengths of brittle materials. The degree of stress magnification depends to a great extent upon the orientation of the crack with respect to the general stress system, and to the general geometry of the crack. It is but a small step to extend the theory to include flaws and defects of other sorts which, though they may be less tractable mathematically than cracks, may still function as stress risers in a real sense in real materials. Brace 2 proposed that the application of the Griffith theory to rock material could be tested in two ways: "(a) by finding the orientation of cracks from which macroscopic fractures have developed and (b) comparing failure strengths from tests at different conditions of loading." In 1963 the author and coworkers at the Bureau of Mines, Twin Cities Mining Research Center, working on a problem involving relationships between strength, sonic velocity, and microstructure "eveloped an experimental technique to examine several somewhat similar questions; namely. does the frequency of occurrence of actual or potential stress risers dictate the relative strength of the material as proposed by Weibull;4 can actual flaws or defects in the rock structure be identified and related to strength and perhaps other properties in accordance with Griffith's theory; and is the anisotropic strength and elastic behavior of certain rocks related to the preferred orientation of these actual or potential stress risers? The experimental approach developed to answer these questions appears equally applicable to the testing of Griffith's theory as proposed by Brace. Basically the approach consists of a series of point-load tensile tests followed by petrofabric examination of thin sections prepared from the specimens in order to identify and apply a quantitative measure to microstructural defects which may have contributed to the failure process. In the point-load test, tensile stresses are induced by a compressive load applied to the center of a disc-shaped specimen by means of two opposing hemispherical indentors. Failure generally occurs as a single fracture parallel to the axis of loading and bisecting the disc. Because of the geometrical symmetrical the induced tensile stresses are symmetrical about the loading axis

Jan 1, 1967

E. P. Pfleider, University of Minnesota I would like to ask Bob Merrill whether he considers that horizontal concave curvature of a slope has any stabilizing effect, such as Jenike 1 suggested several years ago. R. H. Merrill, U. S. Bureau of Mines, Denver Federal Center The stabilizing effect is due to the restraint offered to radial movement by the curvature. We found in laboratory tests that if we constrained the rock with the same stresses as those measured in the pit then it would sustain a maximum stress about two or four times greater than when the same rock type was unconstrained. We are therefore definitely of the opinion that a constrained situation in a slope is favorable towards stability. G. A. Leonards, Purdue University I was interested in Mr. Lane's observations concerning the correspondence between rate of slide movement with rise of reservoir. Perhaps the most interesting feature is that the rate of movement at the time the rock slope failed was less than the rate at an earlier time when it did not fail. This is difficult to explain from current slope stability theory. K. S. Lane, U. S. Army Corps of Engineers I believe that reduced rate of movement is the result of the progressive type of failure, such as described by Patton and Deere. which occurs along the sliding surfaces. It is difficult to analytically define the progressive failure condition for inclusion in slope stability conditions, but its existence should be recognized in design. We should also realize that many apparently stable slopes undoubtedly contain overstressed regions. To design a slope with no overstressed region would be uneconomical and conservative. D. H. Deere I would pose the question-"What is the meaning of a factor of safety of one?" We were involved in the design of a large, irregularly shaped, underground cavity with an unsupported span of several hundreds of feet. Tests on rock specimens indicated a strength of 1300 lb per sq in. The RQD would have been between 90 to 100 percent indicating excellent structural continuity. In-situ stress determinations indicated an approximately hydrostatic state of stress at a level of 1400 lb per sq in. Calculation of stress concentrations at the walls indicated that the stresses there would be about 3000 to 4000 lb per sq in. Admittedly the rock is in a confined condition everywhere except at the very skin of the wall and the rock walls would thus on the average be somewhat stronger. Allowing for the effect of restraint the factor of safety was found to be less than 0.5 over a region several feet into the wall. Construction was started, using rockbolts only to support the walls. Failure around the immediate skin occurred after each

Jan 1, 1967

By C. Fairhurst, A. M. Starfield

As a practicing mining engineer, I face many rock mechanics' problems daily and would like to mention one or two examples to illustrate the current gap between laboratory investigations and actual field problems. I would like to endorse Dr. Obert's suggestion that more field measurements and observations should be undertaken. There is an ever-increasing body of data beginning with Hast's results in Sweden,l then measurements at Elliot Lake, Canada, and so on, including our own measurements at White Pine, which clearly indicate that the horizontal stresses underground are often at least as large as the vertical stresses. Visual obsenation of the deformation of roof and pillars (including failure due to horizontal compression) also demonstrates that the horizontal stresses are often most important. Yet almost every laboratory investigation begins with the assumption that the only stresses acting are vertical. Roof spans in layered formations. for example, are calculated on the assumption that the rock behaves as a gravity loaded beam. This is all too often unrealistic. Roof bolts are also often considered to be simply means of suspending the gravity loaded beams. As Dr. Reed has mentioned they are probably, in fact, acting to restrain a beam which is attempting to buckle due to lateral pressure. The fact that moisture can reduce the strengths of some rocks as much as 50 percent has been known for many years. In the mine me are almost always faced with wet rock, yet no one has investigated ways in which this wakening effect can be overcome. as, for example, by waterproofing the rock. C. Fairhurst, University of Minnesota I would like to mention that we have found,2 from stress-relief determinations, that appreciable (over 1000 lb per sq in.) horizontal pressures occur also at the surface in granites quarried in central Minnesota. Whilst I agree that more field measurements are desirable, it is important to point out that most university research is undertaken by graduate students who must attend classes daily. Their research is therefore restricted to the laboratory. A.M. Starfield, University of Minnesota No one denies the importance of obtaining: data from field measurements. It is equally important, however, that field measurements be guided by theory. Much time and money can be wasted by indiscriminate measurement. An example of the value of theory in interpreting measurements is given in Dr. Obert's comments on the time dependent strain observed in a salt mine. He anticipated that the stress at the wall of the opening would change with time because salt is viscoelastic rather than elastic. It can be shown from theory that if an excavation in a viscoelastic medium is unsupported, then the stress at the wall does

Jan 1, 1967

By Y. C. Kim, F. Szidarovszky

G.M. Philip and D.F. Watson The article cited above reflects the difficulty that is often encountered in interpreting different aspects of kriging. Baafi et al. write : "Due to negative kriging weights, negative block grades may be obtained in some extreme situations, which makes no practical sense." Their solution to this particular problem is to constrain the kriged estimates to data values that have positive weights, i.e., reduce the subset size contributing to the estimation. As Journel (1986, p. 133) has already observed, "Negative weights are no evil." Indeed, they are an ineluctable result of the Lagrangian multipliers in the system of simultaneous equations. The fact that data distant from the estimation point may be given negative weights simply means that the influence of such distant values must be negated because their influence is contradictory to closer values (as illustrated by Baafi et al. in their Figs. 3 and 4). Of course negative kriging weights applied to distant grade values will not in themselves induce negative grade at some central interpolation point. Negative grade values, rather, seem to be a particular artifact of automatic methods of estimation involving accu¬mulations (Philip and Watson, 1985a, 1985b, 1987b). The elimination of negative weights, suggested by Baafi et al., is likely to exacerbate a quite different problem of kriging and piecewise spline interpolation discussed elsewhere (Philip and Watson, 1987a). In interpolating large data sets of scattered observations, changing local subsets or neighborhoods must be selected automatically. Because of the mathematical formulation of kriging and spline interpolation, discontinuities then occur between closely-spaced estimation points as the subset used in the estimation changes. If this subset is reduced in number and size, the discontinuities will be amplified and more common. ? References Journel, A.G., 1986, "Geostatistics: models and tools for Earth Sciences," Journal of Mathematical Geology, Vol. 18, No. 1, pp. 119-139. Philip, G.M., and Watson, D.F., 1985a, "Theoretical aspects of grade-tonnage calculations," International Journal of Mining and Geological Engineering, Vol. 3, pp. 149-154. Philip, G.M., and Watson, D.F., 1985b, "A deterministic approach to computing ore reserves. I, Grade Estimation," Earth Resources Foundation, Occas. Paper 2, The University of Sydney, 24 pp. Philip, G.M., and Watson, D.F., 1987a, "Neighborhood discontinuities in bivariate interpolation of scattered observations," Mathematical Geology, Vol. 18, No. 1, pp. 69-74. Philip, G.M., and Watson, D.F., 1987b, "Estimating interactions of topological functions," Mathematical Geology, Vol. 18, (at press). Reply by Y. C. Kim Before replying to the comments by Philip and Watson, it is desirable to establish the original perspective of our paper, which was intended primarily for the practitioners of mining who possess a working knowledge of ordinary kriging. The paper tried to convey the following practical points: (1) there are circumstances in which one observes negative weights, (2) illustration of circumstances under which one can expect negative weights, (3) should one obtain a negative estimated grade, one can resort to elimination of negative weights using the technique outlined in the paper, and (4) one could normally select only the first layer of surrounding assays to estimate the block grade. Under such a perspective, most of the comments by Philip and Watson are irrelevant and misdirected. For example, the practitioners do not find it difficult to "interpret" the results of ordinary kriging, as evidenced by the fact that they have been using the results for nearly a decade. Nor are the practitioners concerned with discontinuities in estimated block grades due to changing neighborhood of assays during kriging. What matters to the practitioners is the fact that kriging does provide the best estimate among all the estimation tools available to them as of today. ?

Jan 2, 1987