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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 DANIELS, SAMUEL, LYON, A. J., and JOHNSON,. J. B.-Casting and Heat Treatment of Some Aluminum Copper-magnesium Alloys 1 ELLIS, O. W. and SCHEMNITZ, D. A.-Experiments on the Heat Treatment of Alpha-beta Brass : 4 ENOS, GEORGE M. and ANDERSON, ROBERT J.-Coatings. Formed on Corroded Metals and Alloys 5 COMSTOCK, GEORGE F.-Notes on the Hardness of Heat-treated Aluminum Bronze 6 Casting and Heat Treatment of Some Aluminum Copper-magnesium Alloys Discussion of the paper of SAMUEL DANIELS, A. J. LYON, and J. B. JOHNSON, presented at the Milwaukee Meeting, October, 1924, and issued, as Paper No. 1350-N, with MINING AND METALLURGY, July, 1924. D. HANSON and M. L. V. GAYLER, Teddington, England (written discussion).-At the National Physical Laboratory, the writers have made a number of researches on the relation between the constitution and mechanical properties of aluminum alloys of various types; the results obtained were in good general agreement with those of the authors. The writers, however, did not think that increasing the copper content of sand-cast low-copper duralumin to 4 per cent. necessarily caused a drop in the elongation to 1.5 per cent., as stated on page 9. In the case of sand-cast copper-aluminium alloys they had obtained much greater elongation, in some cases as great as 13 per cent. in heat-treated castings. For example, in a sand casting containing 3.5 per cent. of copper, a strength of 12 tons per square inch and an elongation of 13 per cent. were obtained; in a casting containing 4.5 per cent. copper, a tensile strength of 13 tons, and an elongation of 9 per cent. were obtained. These values were the maximum; the elongation varied considerably, being as low as 5 per cent. in some cases. In the writers' opinion, such variations are due more to unsoundness in the sand casting than to any other cause.

Jan 1, 1925

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

CONTENTS PAGE ANDERSON, ROBERT J., and ENOS, GEORGE M.-Corrosion of Brass as Affected by Grain Size. Discussed by Henry S. Rawdon, Robert J. Anderson, Francis B. Coyle, William B. Price, and W. R. Webster 1 RAWDON, HENRYS., and MUTCHLER, WILLARD H.-Effect of Severe Cold Working on Scratch and Brinell Hardness. Discussed by W. H. Bassett, John Livermore Christie, John R. Freeman, Jr., W. R. Webster, William B. Price, Norman B. Pilling, D. J. McAdam, Jr., F. G. Smith, Zay Jeffries, F. E. Carter 3 WILLIAMS, ROBERT S., and HOMERBERG, VICTOR 0.-Relation of Heat Treatment to the Microstructure of 60-40 Brass. Discussed by 0. W. Ellis 14 Corrosion of Brass as Affected by Grain Size Discussion of the paper of ROBERT J. ANDERSON and GEORGE M. ENOS, presented at the New York Meeting, February, 1924, and issued as Paper No. 1282, with MINING AND METALLURGY, December, 1923. HENRY S. RAWDON,* Washington, D. C. (written discussion).-So numerous and so varied are the factors that affect the corrosion of metals that particular care is necessary in corrosion tests to eliminate so far as possible all extraneous factors. It appears to the writer that the question may well be asked as to whether all the necessary precautions have been observed in this investigation. It may be that the points to be mentioned were considered by the authors and found to be insignificant; however, there is nothing in the report to show this.

Jan 5, 1924

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

CONTENTS PAGE GEISMER, H. S.-Coal Washing Practice in Alabama. Discussed by William Kelly, H. S. Geismer, H. D. Pallister, L. E. Bryant, Milton H. Fies, Elmer F. Harris, James A. Barr, George G. Crawford, E. C. Wright, George S. Rice, R. V. Norris 1 MILLER, F. W.-Byproduct Coking in Alabama. Discussed by Theodore Swann 4 FIES, MILTON H.-Alabama Coal Mining Practice. Discussed by Milton 11. Fies, R. V. Norris, R. D. Hall, L. E. Bryant, George S. Rice, H. S. Geismer 5 MUSSEY, H. E.-Blast-furnace Practice in Alabama. Discussed by C. A. Meissner, Franklin H. Crockard, H. E. Mussey, W. H. Oldham 14 Coal Washing Practice in Alabama Discussion of paper of H. S. GEISMER, presented at the Birmingham Meeting, October 1924, and issued, as Paper No. 1363-C, with MINING AND METALLURGY, September, 1924. WILLIAM KELLY, Iron Mountain, Mich.-Is the dry-cleaning method used? H. S. GEISMER.-Neither the dry-cleaning process nor the Chance sand-liquid method has been tested in Alabama; but all other methods used for cleaning bituminous coal have been largely brought to perfection in this state. H. D. PALLISTER, Tuscaloosa, Ala.-Have you the results from the recent work on the tables with reference to fine coal? H. S. GEISMER.-None of the iron-producing companies has adopted the tables, though three commercial operators have installed tables within the last six months. I tried to learn the results, but they were not willing to release the data just now. At the mines producing domestic coal, fines present a difficult problem; until within the past six months all the fine coal was wasted. The operators are trying to recover some of it on the table. L. E. BRYANT, Rockwood, Tenn.-Is there any connection between the sulfur content of the sludge and the effect of the sludge on vegetation?

Jan 7, 1925

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

Page McGREGOR, A. G.-Features of the New Copper Smelting Plants in Arizona. Discussed by L. D. Ricketts, E. P. Mathewson 2145 HOWARD, L. O.-The Basic-Lined Converter in the Southwest. Discussed by Walter Douglas, E. P. Mathewson, Kuno Doerr 2145 SAMUEL, J. MOORE-Determination of Dust Losses at the Copper Queen Reduction Works. Discussed by Walter Douglas, E. P. Mathewson, S. J. Jennings, C. E. Arnold, A. G. McGregor, L. D. Ricketts 2148 MORSE, H. W., AND TOBELMANN, H. A.-Leaching Tests at New Cornelia. Discussed by H. W. Morse, Lawrence Addicks, G. D. Van Arsdale, S. J. Jennings, F. S. Schimerka, C. G. Grabill, F. N. Flynn, Stuart Croasdale 2151 LAIST, FREDERICK, AND ALDRICH, HAROLD W.-The 2,000-Ton Leaching Plant at Anaconda. Discussed by F. N. Flynn, E. P. Mathewson 2159 ADDICKS, LAWRENCE-Possibilities in the Wet. Treatment of Copper Concentrates. Discussed by F. N. Flynn 2160

Jan 12, 1916

Callow, John M. Notes on Flotation. Discussed by R. H. Richards, Joseph W. Richards, Leonard Waldo, George Van Arsdale. 881 Horwood, E. J. Broken Hill Underground Mining Methods. Discussed by Albert R. Ledoux, W. L. Saunders 885 Lindgren, Waldemar, and Ross, Clyde P. The Iron Deposits of Daiquiri, Cuba. Discussed by Waldemar Lindgren, Max Roesler, Benjamin B. Lawrence, Louis C. Graton, Harrison Souder, Charles P. Berkey, Alfred C. Lane, John D. Irving. 886 Powers, Sidney and Lane, Alfred C. Magmatic Differentiation in Effusive Rocks. Discussed by N. L. Bowen, Alfred C. Lane, Sidney Powers 893 Tolman, C. F. Observations on Certain Types of Chalcocite and Their Characteristic Etch Patterns. Discussed by Louis C. Graton, Alfred C. Lane, Joseph T. Singewald, Jr., Charles P. Berkey, E. Posnjak, E. T. Allen, H. F. Merwin, C. F. Tolman, Jr. 895 Warren, H. M., Biesecker, A. S., and Powell, E. J. Tests on Various Motor-Driven Equipment Used in the Preparation of Anthracite Coal. Discussed by R. V. Morris, William Kent. H. M. Warren. K. A. Pauly 901

Jan 5, 1916

Tooele Flue-type Cottrell Treater Discussion of the-paper of A. B. YOUNG, to be presented at the New York meeting, February, 1921, and printed to accompany MINING AND METALLURGY No. 162, June, 1920. HARRY V. WELCH,* Los Angeles, Calif. (written discussion).-The basic requirement in the electrostatic process of electrical precipitation is that gases containing solid particles in suspension are forced to pass through an electrical field consisting of an insulated high-potential wire, or other type of discharge member, and a grounded plate, or other, type .of collecting member. Commercial. operation and efficiency of precipitation are secured by electrical and structural arrangements to provide the maximum value of the variable factors modifying the degree of precipitation. That is to say: 1. A unidirectional flow, of high-potential current is vastly more effective in precipitation than a high potential alternating-current flow.

Jan 2, 1921

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

ROESLER MAX-Geology of the Iron-Ore Deposits of the Firmeza District, Oriente Province, Cuba. Discussed by William Kelly, J. T. Singewald, Jr., B. L. Miller, J. D. Irving, L. C. Graton, C. P. Berkey 439 SINGEWALD, J. T., JR., AND MILLER, B. L.-The Manganese Ores of the Lafayette District, Minas Geraes, Brazil. Discussed by L. C. Graton, J. T. Singewald, Jr., F. Lynwood Garrison HARDER, E. C.-Manganese Ores of Russia, India, Brazil, and Chile. Discussed by J. T. Singewald, Jr., E. C. Harder 454 SCHRADER, FRANK C.-Geology and Ore Deposits of Mohave County, Arizona. Discussed by J. C. Anderson McDOWELL, J. SPOTTS-A Study of the Silica Refractories. Discussed by J. W. Richards, H. D. Hibbard, W. F. Rochow, J. B. Umpleby-: 460 PHALEN, W. C.-The Conservation of Phosphate Rock in the United States. Discussed by E. G. Spilsbury 462 NORTON, S., AND LEFEVRE, S.-The Magnetic Concentration of Low-Grade Iron Ores. Discussed by G. C. Foote, J. L. W. Birkinbine, F. L. Nason 462

Jan 4, 1917

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

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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