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Air-sand Process of Cleaning Coal Discussion of paper by THOMAS FRASER and H. F. YANCEY, presented at the New York Meeting, 1926, and issued, as Pamphlet No. 1561-F, with MINING AND METALLURGY, February, 1926. T. DEVENNY, Edgarton, W. Va.-How near the size of the sand can the coal to be treated be brought? Do you use an 8-mesh coal on that cleaner? J. J. RUTLEDGE, Baltimore, Md.-From the little I have seen of the apparatus in operation, I should say 8-mesh. In my experience in metalmine concentration work, trying to separate different minerals on one jig, sometimes I have succeeded and sometimes not. This apparatus has appealed to me; something of this kind should be useful with the silicates and carbonates of zinc. I think this apparatus has possibilities in metal mining. Recently in our coal field a screen has been introduced for cleaning coal; it is giving excellent service. When I asked the inventor why he did not take it to the metal mines, he said there was a good and sufficient reason, in a patent way. There may be reasons why it would not be applicable for metal mining; but the simplicity of it appeals to me and I cannot see why it could not be so used. T. FRASER (written discussion).-We feel that 8-mesh would be about -the minimum size of coal practicable to treat by the air-sand process. This would depend partly upon the friability of the coal. The more nearly the lower size limits of the coal- approaches the size of the sand, the more .time will be required in screening the sand out of the cleaned coal, which would mean a little more chance of breakage. In regard to the treatment of ores; this would necessitate the use of some heavier mediums than ordinary silica sand, or some other means of making the separation at a higher specific gravity than is required for coal. We are now working on a method of obtaining this effect for the preparation of anthracite coal without resorting to the use of heavier and more expensive material than common sand.

Jan 1, 1927

By K. J. Ma, L. Ma, J. Stankus

The paper’s intent is to evaluate pumpable foamed cementitious mine seal material by determining the shear strength of a generic foamed cement in the laboratory. The tests were conducted on three scales: small-size specimens, consisting of cylinders 4 in. in diameter or 3-in. prisms; double shear medium- size specimens, measuring 13 in. by 10 in.; and large-size specimens, measuring 6 ft by 4 ft by 4 ft. The small-specimen shear tests resulted in average peak and residual shear strengths of 128 psi and 56 psi, respectively. These values are fairly consistent with published shear strengths of foamed cementitious material. However, the other two types of shear tests did not achieve the shear strength of a typical pumpable foamed cementitous mine seal material. Based on the test results, the paper concluded that the structural analysis of cement foam seals should be based on their residual shear strengths, approximately 20 psi, determined from small laboratory-scale tests of the cement foam/concrete or rock interface, and not be based on their peak strengths.

Jan 1, 2015

By D. C. Shelton, C. S. Ek

Corneille S. Ek (Assistant Professor in Ore Dressing, University of Liege, Liege, Belgium) — This is a very valuable paper, in that it shows how it is possible to take care of a multitude of laboratory routine tests, and derive from them successful modifications of flowsheets or of operating methods. The author and the Company appear to be test-minded and this is best seen through the case histories described. There are however some corrections to be made, and questions arise when one studies the paper. If all the equations are to be homogenous, one obviously has to write Eq. 4 On the other hand, it is difficult to accept the definition put on Eq. 7, for that equation, which represents the factor of transformation from tpd of solids to cu ft per min of pulp in Eq. 6, has nothing to do with conditioning. It is evidently assumed here that conditioning means, as Gaudin calls it,' modulation of collection. One would prefer, for Eq. 7, the appel-ation "pulp conversion factor". Eq. 8 and 9, giving the amount of reagent to be fed

Jan 1, 1965

By J. J. Scott, L. Adler3

L. Adler (Assoc. Professor, Department of Mining Engineering, Virginia Polytechnic Institute, Blacks-burg, Va.) - Dr. Scott is to be commended for undertaking the arduous and specialized task of applying three-dimensional photoelastic techniques to a mining problem. However, 1 feel his analysis suffers seriously from a lack of clarification on one important matter, among several others; and that the paper as a whole lacks balance and thus tends to confuse the reader. 1) The major technical criticism refers to the fact that nowhere are the boundary conditions for his mod-

Jan 1, 1964

By C. C. Harris Discussion by B. K. Loveday

B. K. Loveday (National Institute for Metallurgy, Johannesburg, Republic of South Africa) - The paper and subsequent technical note' describing a method of determining the parameters of the three-parameter size-distribution equation developed in the paper were read with much interest. This equation was also used at National Institute for Metallurgy (NIM) to describe size distributions in grinding tests, because it was necessary to have a single equation to describe the size distribution at any time during a test. A graphical method also was used to determine the three parameters, and the use of this method as an alternative to Professor Harris's latest method is discussed here. The three-parameter model can be expressed as follows: Eq. 1 can be rearranged and transformed to Yield a linear reiationship between Y and X (transformed) log

Jan 1, 1970

By I. Hawke, K. Barron

I. Hawkes (Postgraduate School in Mining, University of Sheffield, Sheffield, England) — The photoelastic stressmeter is proving to be a very practical tool for 'in-situ' measurements in the fields of civil and mining engineering and Barron's article has therefore come at a very opportune time, supplementing as it does, the considerable amount of laboratory and field data which is being accumulated.1,2,3 There are however several points relating the application of Barron's conclusions to the practical use of the meter which require further elucidation. EASE OF READING If the photoelastic stressmeter is to have a wide application, the fringe orders must be easily measured. The system adopted by the writer and his colleagues at Sheffield for the uniaxial stress case is to read the fringe order at the 45 point, 0.20 in. from the center (11/4 in. diam meter). This procedure has been recommended because the fringes not at this point form a very distinct 'eye' which is obvious even to those who have had little experience with photoelastic fringe patterns. Barron points out that this point can also be used up to a stress ratio of 0.33 and in practice this is normally done. In biaxial fields above a ratio of 0.33 the 'eye' is no longer apparent and the fringe order must be ascertained at some other point. The writer and his colleagues experimented at various points and finally chose a point at a distance 0.175 in. (11/4 in. diam meter) on the minor stress axis and fixed this point on the meter by inserting a collar of this diameter. This procedure enables the 'eye' technique to be used for uniaxial stresses as the 'eye' falls outside the collar; any other technique for biaxial patterns would require lines to be engraved on the meter itself and reading difficulties would be experienced by all but the most highly trained. It is interesting to point out that in a great many field applications ranging from underground pillars to building foundation piles the stresses measured have been uniaxial. In such cases, reading the fringe order has been simple even for unskilled persons. SENSITIVITY The photoelastic stressmeter acts as an inclusion, and as such its theoretical behavior is as described by Barron's mathematical analysis. When considering its practical application, however, it must be remembered that rocks and concrete are not mathematically ideal substances. The theory relates the fringe order in the meter to the stresses and the E (Young's Modulus) and the µ (Poisson's Ratio) values of the surrounding material. There is of course no unique E or µ value for rocks or concrete. These values change both with stress level and time load application sometimes to the order of 300%. We at Sheffield have very accurately calibrated the photoelastic stressmeter in a wide range of materials and have also measured the average E values for these materials. The results prove that the meter sensitivity

Jan 1, 1965

By W. I. Duvall, D. E. Stephenson. Discussion by R. G. K. Morrison

R.G.K. Morrison (Chairman, Dept. of Mining Engineering and Applied Geophysics, McGill University, Montreal, Que. Canada) - The authors have introduced a subject, the intensive study of which has awaited scientific developments. These are now such as to justify a thorough review of our thinking on the causes and control of rockbursts. The formulae developed in the paper, the comparison between rockbursts and earthquakes in figure 1 and the energy data relating to explosives serve as an effective foundation. In the paper this writer is quoted as suggesting that energy of the order of 10 x 10 11 ft. lb. may have been released in some of the heaviest rockbursts in the Kolar Gold Field. He now hastens to add that such an estimate has no scientific validity. It arises only from a casual comparison of surface and underground effects of the medium heavy bursts, referred to in the paper and estimated by Jones at 3.0 x 1010 ft.lbs., with those of obviously greater magnitude. In any case, we have the estimate by Jones above, that by a team of seismologists 1 on the Witwatersrand of 10 x 1010 ft.lbs., that by Coates of 3.8 x 10" ft.lbs., also referred to in the paper, that by Blan-chard2 for the catastrophic rockburst at Springhill, N.S., of only 7.4 X 107 ft. lbs., and finally the range covered by Cook, referred to in the paper. It is probable also that data for the heavy rockburst at Merkers3 in the WERRA potash area of Germany are available as it was recorded on seismographs from Moscow to Spain. It is the writer's impression that some standardization is present in the estimates above for 10 x 10 10, 3.8 x 1010 and 7.4 x 107 ft.lbs., respectively. The latter, for Springhill, represents a relatively low order of magnitude. It is obvious that any energy estimate must be related to the local geometry of openings at the time of the event. It is also obvious that any explanation of the causes of rockburst must be capable of providing a wide range of energy. However, we must remember that the energy release is an effect indicating magnitude. The cause lies with the mechanism initiating the primary failure, generating the seismic activity, to which much of the damage is probably due.

Jan 1, 1967

By D. E. Stephenson. Discussion by R. G. K. Morrison, L. Obert

R. G. K. Morrison (Chairman, Dept. of Mining Engineering and Applied Geophysics, McGill University, Montreal, Que., Canada) - The discing of drill core has been a recognized pressure phenomenon for many years but only recently has an interest been taken in the mechanism involved. The work of Jaeger and Cook is referred to in the text. The authors have now advanced the study to establish, within certain loading limitations, a direct relationship between axial and radial stress at failure. This is an important contribution. In mines generally, where pressure conditions result in the spalling of openings, the faces of drifts and crosscuts, on scaling, usually show a concavity with respect to the opening very similar to the face of the drill hole after the separation of the stub. The same holds for shaft sinks. This suggests a similarity between the mechanism of the discing of core and that of the spalling of an opening, under pressure, to develop a more stable outline. The latter, commonly regarded as shear, is the most conspicuous type of failure observed in

Jan 1, 1967

By J. D. Miller Discussion by N. P. Finkelstein, M. C. Fuerstenau

The point designating 10 -4 nole/per liter sulfonate addition in Fig. 1 has been presented incorrectly. This figure, with the corrected scale, is shown at right. N. P. Finkelstein (National Institute for Metallurgy, Johannesburg, South Africa) - The qualitative conclusion the authors of this paper have reached in evaluating the influence of hydrocarbon chain length on collector effectiveness agrees with conclusions in several published reports. However, in two other

Jan 1, 1969

By W. H. Yarroll Discussion by W. A. Griffith

W. A. Griffith (Head, Research Department, Phelps Dodge Corp., Morenci, Ariz.) - It is gratifying to see the increasingly common use of classical statistical procedures by metallurgical researchers. Mr. Yarroll has given excellent illustrations of the utility of multiple correlation analysis of complex metallurgical data. Our experience in applying these procedures to historical plant operating data has differed, however, from that which he suggests. The uninitiated frequently assume that the volumi-

Jan 1, 1969

CONTENTS PAGE. WHITE, DAVID.-Environmental Conditions of Deposition of Coal. Discussed by E. C. Jeffrey, George H. Ashley, Reinhardt Thiessen, S. W. Parr, David B. Reger, Wilbur A. Nelson, James F. Kemp, E. S. Moore, Homer G. Turner, David White, A. C. Noé, W. A. I. M. van Waterschoot van der Gracht 2 THIESSEN, REINHARDT.-The Constitution of Coal. Discussed by Edward C. Jeffrey, Reinhardt Thiessen, Ralph H. Sweetser, David White 12 TURNER, HOMER G.-Microscopical Structure of Anthracite. Discussed by E. S. Moore, Edward C. Jeffrey, Reinhardt Thiessen, H. J. Rose, James F. Kemp, David White, Clarence A. Seyler, A. C. Noé 14 JEFFREY, EDWARD C.-Coal in Relation to Coke. Discussed by H. J. Rose, David White, E. S. Sinkinson, S. W. Parr, James F. Kemp, Edward C. Jeffrey, Reinhardt Thiessen, Chas. R. Fettke 17 FRANCIS, W., and WHEELER, R. V.-The Resolution of Coal by Oxidation. Discussed by Edward C. Jeffrey, S. W. Parr, E. S. Sinkinson, Reinhardt Thiessen, David White 23 TIDESWELL, F. V., and WHEELER, R. V.-The Constitution of Coal. Discussed by David White, A. C. Fieldner 24 JOLLY, J., and WHEELER, R. V.-Organic Sulfur Compounds in Coal. Discussed by S. W. Parr 25 SINNATT, F. S.-Selective Combustion in Coal. Discussed by J. D. Davis, A. C. Fieldner, Geo. S. Rice, W. M. Grant, H. J. Rose, S. W. Parr, David White 25 COBB, JOHN W.-Nitrogenous Constituents of Coal. Discussed by S. W. Parr, H. J. Rose, Reinhardt Thiessen 28 PARR, S. W., and HOBART, F. B.-Coal and Oxygen. Discussed by J. D. Davis, W. T. Thorm, Jr., S. W. Parr, H. J. Rose, A. C. Fieldner, F. F. Jorgensen, David White, W. M. Grant 30 FIELDNER, A. C., and DAVIS, J. D.-Modern Views of Chemistry of Coals of Different Ranks as Conglomerates. Discussed by S. W. Parr, David White, Reinhardt Thiessen, A. C. Fieldner, Clarence A. Seyler 32 EBY, J. BRIAN.-Contact Metamorphism of Some Colorado Coals. Discussed by Geo. C. McFarlane, W. T. Thom, Jr 35 WHITE, DAVID.-Progressive Regional Carbonization of Coals. Discussed by A. C. Fieldner, Homer G. Turner, W. A. J. M. van Waterschoot van der Gracht, A. C. Noé 37 THOM, W. T., JR.-Moisture as a Component of the Volatile Matter of Coal. Discussed by A. C. Fieldner, S. W. Parr, Clarence A. Seyler, W. T. Thom, Jr., R. D. Hall 39

Jan 7, 1925

By AIME AIME

THE Engineering Education Committee of the Institute convened at the Engineering Societies Building on Feb. 18, .1929, with. E. A. Holbrook, dean of the Schools of Mines and Engineering, University of Pittsburgh, in the chair. STATISTICAL' STUDY OF STUDENTS IN MINING The first paper, a statistical study of the students enrolled in courses leading to a mining degree in 40 institutions, was presented by H. D. Keiser,, assistant editor of the Engineering and Mining Journal; who gave a brief outline of an article he was about to publish in ?that journal?. The complete article appears in the issue for March 30; 1929: To avoid repetition the results are summarized as follows: A request was sent to 42 institutions which give courses in mining' for the number of students enrolled as freshmen; sophomores; juniors, seniors and special students in mining for the years 1925-26, 1926-27, 1927-28, 1928-29. Two of these colleges replied that there were no students in mining. Students' enrolled in courses in metallurgy, geology and engineering, other than mining, were excluded from the statistics:. The statistics received were arranged in, four groups, according to the completeness of the information. One complete group of 25 institutions 'shows as follows:

Jan 1, 1929

History of Production, of Salt Creek Oil Field, Wyoming Discussion of the paper of EDWARD L. ESTASROOK and CLARENCE M. RADER, presented at the Casper Meeting of the Petroleum Division and issued, as Paper No. 1503-G, with MINING AND METALLURGY, September, 1925. C. E. REISTLE, Laramie, Wyo.-The application of water analysis to petroleum engineering problems is successful in many cases, particularly if the water in the sands is of uniform chemical constituency and if each sand water varies definitely from the others in its chemical properties. At Salt Creek, the sand waters are not of uniform chemical character, and the waters in the various sands do not differ greatly; so a water from one sand might easily be classified as a water from some other sand. The water from the Shannon sand contains sulfates; this alone makes it possible to differentiate between the Shannon and the First and Second Wall Creek and Lakota sands. However, it is not so easy to differentiate between water of the First and Second Wall Creek sands. As a rule, the Second Wall Creek sand contains a higher concentration of mineral matter, but in Table 19, sample 2; of the First Wall Creek sand and sample 7 of the Second Wall Creek sand have approximately the same amount of total solids. As a rule, the chlorides are higher in the Second sand waters than in the First sand; but, the chlorides in sample 6 of the Second sand show practically the same amount as sample 3 of the First sand. The use of reaction properties does not. solve this trouble, as they generalize the conditions even more. For instance, the reaction properties of sample 3 of the First sand are almost identical with the reaction properties of sample 6, of the Second sand. The authors suggest that the chemical characteristics of the water in a sand are not uniform because of the concentration of the water by underground evaporation. In that case should not the ratio of the various chemical constituents remain the same? Gas does remove some mineral matter, as evidenced by deposits in the gas lines and packing in the absorbers of the natural gasoline plants, but why does the gas act selectively, removing one salt and not all of the salts in the ratio that they occur?

Jan 12, 1925

P. H. ARGALL, Magdalena, N. Mex. (written discussion *).-The Chilean mill has generally been considered a fine-crushing machine and as such has had many advocates; it has also. had quite a number of denouncers; hence, the action of the Portland engineers in using the Chilean mill for the preparatory work usually accomplished in, rolls or rock breakers and adding a ball mill to do the fine grinding is novel, though of doubtful utility in the long run, even though a fair efficiency is obtained for the combination machines, as measured by Chilean mill practice. In order to follow the development of Chilean mill practice on Cripple Creek ores, I might say that two 6-ft., Chilean mills were placed in operation in Stratton's Independence mill in April, 1908, treating ore crushed by rolls to pass Y4 in. screen aperture. Screening was, however, found to be an unnecessary refinement, as was also the use of plows in the mills; both screening and plowing were abandoned before the Portland engineers finished the experiments in stamp milling upon which they were then engaged. Two additional 6-ft. Chilean mills were added in the spring of 1911, three of them giving the required 10,000 tons per month capacity, one being always in reserve. The Portland company began using Chilean mills in June, 1910, at its Victor mill, and the same company purchased the Stratton's Independence mill in June, 1915, and remodeled it; it is now known as the Independence mill. A description of Stratton's Independence milling practice, is given in the November, 191.1, issue of Mining Majazine (London). These Chilean mills were used as fine grinders and that they accomplished their purpose is shown by the screen analyses, in which 62 per cent. of the pulp passed 150-mesh screens. To make coarse crushers of these Chilean mills, the Portland engineers have increased the speed, substituted steel in various parts for cast iron, provided new and enlarged thrust bearings to take care of the centrifugal force incident to higher speed, and have, thereby, greatly increased the cost of the machines. They have also reduced the width of the tires and dies from 8 in., as used in the original mill, to 7 in., a reduction of 12 ½ per cent. in the crushing surfaces, to say nothing of the loss of abrasion or attrition incident to the larger surface. At the same time, they have apparently increased the weight of the rollers by using tires 5 7/8 in. thick as against tires varying between 3 and 4 in. on the original mills, thereby increasing

Jan 4, 1920

CONTENTS PAGE Simons, Theodore.-Basic Principles of Gravity Concentration-A Mathematical Study : :.. 1 Taggart, Arthur F. and Gaudin, A. M.-Surface Tension and Adsorption Phenomena in Flotation 11 Hersam, Ernest A.-Factors Controlling the Capacity of Rock Crushers 12 Shaw, S. F.-The Ore Deposits of Sierra Mojada, Coahuila, Mexico 12 Wilson, Philip D.-The British Columbia Batholith and Related Ore Deposits 26 Greensfelder, N. S.-Shot-firing by Electricity 27 Mitke, Chas. A.-Metal Mine Ventilation in the Southwest 28 Foley, F. B. and Howell, S. P.-Neumann Bands as Evidence of Action of Explosives upon Metals 30 Schwartz, H. A., Payne, H. R., Gorton, A. F., and Austin, M. M.-Conditions of Stable Equilibrium in Iron-carbon Alloys 30

Jan 12, 1922

Sykes, W. P.-Effect of Temperature, Deformation, Grain Size, and Rate of Loading on Mechanical Properties of Metals. Discussed by Zay Jeffries, W. H. Bassett, F. E. Carter 3 Evans, Geo. Watkin.-Alaskan Coal Fields. Discussed by P. N. Moore, H. H. Stoek, G. S. Rice, H. Emerson 4 Eavenson, Howard N.-Run-off and Mine Drainage. Discussed by J. R. Campbell, Andrew B. Crichton, J. B. Warriner, R. V. Norris, H. G. Moulton, H. B. Wright 7 Andrews, Allen, and Garcia, John A.-Skip Hoisting for Coal Mines. Discussed by R. V. Norris, Geo. S. Rice, H. N. Eavenson, E. A. Holbrook, Robert Obert, Andrews Allen, T. M. Chance 12 Rice, Geo. S.-Coal-pillar Drawing Methods in Europe. Discussed by Carl Scholz, D. Harrington; H. 1. Smith 16 Knapp, Arthur.-Modified Oil .well Depletion Curves. Discussed by Roswell H. Johnson 21 Alvey, Glenn H., and Alden W. Foster.-Barrel-day Values. Discussed by Roswell H. Johnson 22 Matteson, W. G.-Secondary Intrusive Origin of Gulf Coastal Plain Salt Domes. Discussed by Eugene Coste, E. W. Shaw, Joseph E. Pogue, F. G. Clapp, E. DeGoIyer, W. G. Matteson, H. W. Hixon, R. Van A. Mills 23 Reger, David B,-Carbon Ratio of Coals in West Virginia Oil Fields. Discussed by J. T. Singewald, Jr 33

Jan 5, 1921

DAVID WHITE,* Washington, D. C.-This paper is very timely since the Philippine Islands are presumably open to the enterprise of the American driller, whereas much of the territory in that part of the world is closed to us. The United States has ambitious plans for the operation of a great merchant marine, which is to be oil burning in the main, and it takes but a glance at the world map to see the strategic advantage of oil supplies in the Philippines for such marine operations. It is a little difficult to understand why more attention has not been given to the Philippines, in spite of the difficulties attending development in these islands. A number of American oil companies are, I believe, at the present moment taking an interest in the possibilities of the Philippines. Important factors in the formulation of opinion regarding the importance of the oil deposits of the Philippines, as brought out by Mr. Pratt,1 are the point of view and the breadth of experience of the examining geologist. The average oil geologist, whose experience has been mainly in the Appalachian region, the Mid-continent, or Louisiana, or possibly even in California, on seeing the narrowness of the basins, the closeness of the folding, and the presence of igneous rocks here and there, would be likely to draw unfavorable conclusions as to the possibilities of the Philippine Islands. Geologists visiting that region should be familiar with the geological conditions of oil occurrence in Japan, Formosa, the East Indies, or in the Baku district, and their conclusions should be formulated with the knowledge and understanding of the occurrence of oil in those regions rather than in the United States.

Jan 8, 1920

Jan 1, 1951

Jan 1, 1951

By F. C. Bond, J. T. Wang

H. J. Kamack (E. I. du Pont de Nemours & Co., Inc., Wilmington, Del.)—Rittinger's law usually is stated to the following effect: "The work (or energy) consumed in particle size reduction is proportional to the new surface area produced." The law has been stated substantially in this way by Taggart20 Berry21 Dalla Valle22 Coghill and DeVaney,23 Richards and Locke," Gross,25 and many others, and, according to Gaudin,26 was originally expressed by Rittinger in the same form. Consequently there can be little doubt that this is the understanding of the law among most workers in the field of particle size reduction. Bond and Wang, however, express the law in the form "the useful work accomplished . . . ." (italics theirs). The distinction is critical, for in the form used by Bond and Wang the law becomes, as they themselves remark "merely a more or less arbitrary definition of useful work," while in its usual sense the law expresses a physical hypothesis which has been verified experimentally within certain limitations. Considering the way the law has been used, it might be stated more explicitly as follows: "In a given machine operating under a given set of constant operating conditions, the work consumed in the particle size reduction of a given material is proportional to the new surface area produced." Or, as Coghill and deVaney have said,27 "the (Rittinger) law holds only when the tests being compared are made under analogous conditions." There are occasions when the law transcends these limitations; for example, the surface area produced per unit energy consumption for a given material in a ball mill does not vary much over a fairly wide range of operating conditions. But by and large, the surface area production per unit energy consumption will vary with the operating conditions, the type of machine, and the material. The essence of Rittinger's law is that the surface area production per unit energy consumption is independent of the particle size, and this has been verified experimentally by numerous workers for numerous materials, within certain limits. An important limitation is that when one grinds to very small particle sizes, agglomerative forces may tend to interfere with size reduction so that the surface area increases less rapidly than Rittinger's law would predict. Within such limitations, Rittinger's law can be regarded as empirically established. The law has, however, certain theoretical implications, and it seems to be chiefly against these that Bond and Wang direct their criticism. Solids are believed to possess surface energy which is proportional to surface area. Thus, Rittinger's law implies a proportionality between surface energy produced and mechanical energy expended (for a particular material in a particular machine). It does not imply that all or most of the mechanical energy is transformed into surface energy; in fact it is known that most of the mechanical energy is transformed into heat. Bond and Wang assert that most of this heat arises from the damping of elastic vibrations of stressed particles. This may possibly be true for crushing (with which they are chiefly concerned), although in grinding it is probable that much of the heat arises from friction between particles. However, the fact that the surface energy is small compared to the heat energy does not invalidate Rittinger's law, which implies merely that they are proportional. The authors also criticize Rittinger's law on the grounds that "this theory cannot be justified mathematically, since work is the product of force times distance, and the distance factor is ignored," and "energy input must be the product of force times distance, and the Rittinger theory completely ignores large variations in the distance (strain dimension or deformation) throughout which a force must act to produce breakage of different materials." However, the quantities force and distance as such are irrelevant to Rittinger's law, which considers energy input as an integral quantity. The fact that different materials require different forces and strains (hence, different amounts of energy) to break them is incontrovertible but again is irrelevant to Rittinger's law, which, as mentioned before, applies -only to a single material. Even in theory, it would not be expected that the surface area produced per unit energy consumption would be the same for different materials, because the surface energy per unit area is presumably specific to each material. Bond and Wang advance another argument of a

Jan 1, 1952