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Last Updated on Tuesday, 16 June 2015 09:40

About Jiri | Bibliography 

Size of Things

Size and Amount of Multiple Things

Multiple Things 

Multiple things may be grains of sand but also stars of a globular cluster. 

Size is a geometric dimension expressed usually in linear units. It is the independent distribution variable, mostly indicated as X variable. 

Amount is a quantity defined by a number of items, by an area, volume or mass. It is the dependent distribution variable,  mostly indicated as Y variable. 

Distribution displays the dependent variable as a function of independent variable in order to quantify the size and amount of multiple things. . 

Distribution models are defined by special mathematical functions. The easiest description is their graphical appearance:

rectangular distribution, 
U-distribution, 
hyperbolic distribution; 

In the next text, I will focus onto the distribution around a central value, based on symmetric decrease to both sides. This distribution was defined by Carl Friedrich Gauss. 

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Last Updated on Tuesday, 31 March 2015 12:19

 Bibliography

1. Brezina, Jiri, 1956a, Report on geological mapping of the SE part of the south Moravian Lowland in the year 1955; petrographic evaluation of some Neogene sediments in the north and north-east part of the Inner-Alpine Vienna basin (typewritten manuscript in Czech); Geofond, Praha, 10 pages.
2. Brezina, Jiri, 1956b, Petrographic evaluation of some sediments of the Vah river valley Neogene (typewritten manuscript in Czech); Geofond, Praha, 10 pages.
3. Brezina, Jiri, 1956c, Inner-Alpine Miocene in south-east Moravia and western Slovakia; study in sedimentary petrography (typewritten manuscript in Czech); Master Thesis, Faculty of Natural Sciences, Charles' University, Praha; Geofond, Praha, 75 pages.
4. Brezina, Jiri, Tibor Buday & Ivan Cicha, 1956d, Report on geologic investigations in the South Moravian Lowland in the year 1955  (typewritten manuscript in Czech); Geofond, Praha,     pages.
5. Brezina, Jiri, 1957a, Report on sediment-petrographic investigations in the inner-Carpathian Miocene 1956, Turiec basin (typewritten manuscript in Czech); Geofond, Praha, 29 pages.
6. Brezina, Jiri, 1957b, Report on the petrography of Neogene sediments of the Turiec basin (in Czech); Reports on Geological Investigations in the year 1956, Central Geological Survey, Praha; p. 18 - 19.
7. Brezina, Jiri & Tibor Buday, 1957, Rhyolitic tuffites in the Upper Helvetian and Sarmatian of the Moravian Lowland (in Czech, German summary); Vestnik of the Central Geological Survey, Praha, vol. 32, No. 3/March, p. 178 - 182.
8. Brezina, Jiri, 1958a, Partial report on petrographic investigations in the year 1957; sedimentary-petrographic investigation of the Inner-Carpathian Miocene, South-Moravian Lowland (typewritten manuscript in Czech); Geofond, Praha, 21 pages.
9. Brezina, Jiri, 1958b, Partial report on petrographic investigations in the year 1957; planimetric estimations of microscopic objects (typewritten manuscript in Czech); Geofond, Praha, 15 pages.
10. Brezina, Jiri, 1959a, Preliminary report on new findings of pyroclastic materials in Miocene sediments in Moravia and western Slovakia (in Czech); Reports on Geological Investigations in the year 1957; Central Geological Survey, Praha, p. 14 - 15.
11. Brezina, Jiri, 1959b, Report on the petrography of Lower-Pannonian sediments of the Vah River valley - so called "Piestany beds" (in Czech); Reports on Geologic Investigations in the year 1957, Central Geological Survey, Praha, p. 15 - 16.
12. Brezina, Jiri, 1959c, A quick method of modal analysis (Czech, English summary); Vestnik of the Central Geological Survey, Praha, vol. 34, No. 3/March, p. 161 - 169.
13. Brezina, Jiri, 1959d, Report on the petrography of Neogene sediments from the boreholes of the Central Geological Survey in the Vah River valley in the year 1957 (typewritten manuscript in Czech); Geofond, Praha, 6 pages.
14. Brezina, Jiri, 1959e, Petrographic characteristics of the Lower Tortonian sediments of the Boskovice Graben (typewritten manuscript in Czech); Geofond, Praha, 9 pages.
15. Brezina, Jiri, 1959f, Petrographic evaluation of the borehole GB-2, Vcelna (south from Ceske Budejovice, South Bohemia), layer-groups from Zliv-Gmünd and from Mydlovary-Borovany (typewritten manuscript in Czech); Geofond, Praha, 5 pages.
16. Brezina, Jiri, 1960a, Methods of the determination of grain size distribution (typewritten manuscript in Czech);  Geofond, Praha,  3  pages.
17. Brezina, Jiri, 1960b, Principles of comminution (grinding) and calculation of characteristics of a granulometric composition; review (in Czech) of the Russian book by S. E: Andreev , V. V. Tovarov and V. A. Perov, Moscow (Metallurgizdat), 1959, 437 pages; Vestnik of the Central Geological Survey, Praha, vol. 35, No. 3/March, p. 179 - 180.
18. Brezina, Jiri, 1960c, Preliminary petrographic and geochemic investigation of the Neogene rocks from Eastern Slovakia (Explanations to the geological general map of Czechoslovakia, sheet Trebisov (typewritten manuscript in Czech); Geofond, Praha, 23 pages.
19. Brezina, Jiri, 1960d, Petrographic investigation of the Miocene sedimentary rocks of the Carpathian Fore deep (from the area of the geological general map of Czechoslovakia,  sheet Brno, M-XXIX, task XXX/16 (typewritten manuscript in Czech); Geofond, Praha, 9 pages.
20. Brezina, Jiri, 1960e, Petrographic investigation of the Lower Tortonian sedimentary rocks from the boreholes near Lobodice (for the underground gas reservoir); sheet M-33-95-D (typewritten manuscript in Czech);  Geofond, Praha, 3 pages.
21. Brezina, Jiri, 1960f, Petrographic investigation of the Neogene sediments of the Moravian Lowland (including the Hradiste graben) and from the Vah River valley (explanations to the geological general map of the CSR, sheet Gottwaldov) (typewritten manuscript in Czech); Geofond, Praha, 23 pages.
22. Brezina, Jiri, 1960g, Encyclopaedic Entries in Petrography of Sedimentary Rocks etc. (about 100 entries): Josef Svoboda et al., Naučný Geologický Slovník, díl 1 A-M (in Czech°; English: Encyclopaedic Geologic Lexicon, Part 1 A-M), ÚÚG+ČSAV, Praha, 704 pages.
23. Brezina, Jiri, 1961a, Overview of the current petrographic knowledge about the sedimentary rocks of the Miocene of the Moravian foredeep  (typewritten manuscript in Czech); Geofond, Praha, 32 pages.
24. Brezina, Jiri, Ivan Cicha + Frantisek Picha, 1961b, Lithologic description of the boreholes "AVB-VB" drilled in the year 1960 on the general map of CSR, sheets M-33-106-D (Slavkov near Vyskov) and M-33-118-B (Velke Bilovice)  (typewritten manuscript in Czech); Geofond, Praha, ... pages.
25. Brezina, Jiri, 1961c, Current knowledge about clay minerals of the Neogene of the Vienna basin in the area of CSSR  (typewritten manuscript in Czech); Geofond, Praha, 18 pages.
26. Brezina, Jiri + Bedrich Jellinek, 1961d, Report about the development state of an automatic apparatus for sedimentation analyses  (typewritten manuscript in Czech); Geofond, Praha, 11 pages.
27. Brezina, Jiri + Bedrich Jellinek, 1962a, Development of an automatic apparatus for grain size analyses (in Czech); Geol. pruzkum (SNTL Praha), vol. 4, No. 4/April, p. 121 - 122.
28. Brezina, Jiri, 1962b, Grain size composition of detritic sedimentary rocks (typewritten manuscript in Czech); a compilation work as a pre-requisite for the PhD Thesis; Faculty of Natural Sciences, Charles' University, Praha, 184 pages.
29. Brezina, Jiri, 1962c, Report about the sediment-petrographic investigations of the Miocene, map of CSSR in the scale 1:50,000, sheet M-33-106-B, Vyskov, in the year 1961  (typewritten manuscript in Czech); Geofond, Praha, p. 8 - 15.
30. Brezina, Jiri, 1962d, Contribution to the petrography and geochemistry of the Neogene pyroclastic rocks in the Eastern Slovakia (map of CSSR in the scale 1:200,000, sheet M-33-XXVII, Kosice, and sheet M-33-34-XXXIV, Trebisov) (in Czech); Reports about Geological Investigations in the year 1961, Central Geological Survey, Praha, p. 221 - 4.
31. Brezina, Jiri + Ivan Cicha, T. Czudek, J. Dvorak, F. Holanek, R. Rezac, and V. Spicka, 1962e, Explanations to the geological special map 1:50,000, sheet M-33-106-B, Vyskov (Task 5/2) (typewritten manuscript in Czech); Geofond, Praha, p. 19 - 28, and 58 - 87.
32. Brezina, Jiri, 1961f, Encyclopaedic Entries in Petrography of Sedimentary Rocks, Geochemistry etc. (about 100 entries): Josef Svoboda et al., Naučný Geologický Slovník, díl 2 N-Ž (in Czech°; English: Encyclopaedic Geologic Lexicon, Part 2 N-Ź), ÚÚG+ČSAV, Praha, 832 pages.
33. Brezina, Jiri + Ivan Cicha, 1963a, Stratigraphy and lithology of the Neogene; in: Ivan Cicha, Explanations to the geological special Map 1:50,000, sheet M-33-106-C, Zidlochovice (Task 5/2)  (typewritten manuscript in Czech); Geofond, Praha, p. 72 - 118.
34. Brezina, Jiri, 1963b, Expert evaluation of reserves of quartz-sand deposits (area of Znojmo, localities Dobsice and Havraniky) (typewritten manuscript in Czech); Geofond, Praha, 10 pages.
35. Brezina, Jiri, 1963c, Kapteyn's transformation of grain size distribution; Journal Sediment. Petrology, v. 33, No. 4/December, p. 931 - 7.
36. Brezina, Jiri, 1963d, Classification and measures of grain size distribution, a preliminary report (English, Czech summary); Vestnik of the Central Geological Survey, Prague, vol. 38, No. 6, p. 409 - 13.
37. Brezina, Jiri, 1964a, Report about the sediment-petrographic investigations of the Miocene, sheet Moravsky Krumlov, M-33-105-D, of the special map of CSSR 1:50,000  (typewritten manuscript in Czech); Geofond, Praha, 28 pages.
38. Brezina, Jiri, 1964b, An instrument for automatic grain size analysis of sands: an improvement suggestion No. ZN/64 (typewritten manuscript in Czech), Central Geological Survey, Praha, Archiv,    pages.
39. Brezina, Jiri + Ivan Cicha + Jano Dornic, 1966, Stratigraphy and lithology of the Neogene; in: Jano Dornic et al., Explanations to the geological special map of CSSR 1:50,000, sheet M-33-107-A, Ivanovice na Hane  (typewritten manuscript in Czech); Geofond, Praha, p. 44 - 91.
40. Brezina, Jiri, 1967a, Miocene sedimentary rocks of the Carpathian fore deep in Middle Moravia: Ph.D. thesis, Faculty of Natural Sciences, Charles' University, Praha, Czechoslovakia, typewritten 251 pages (particularly p. 5 - 8).
41. Brezina, Jiri, 1967b, Homogeneity of a statistical distribution, basic distribution types; examples from size distributions of sedimentary rocks (typewritten manuscript in Czech); Seminar on Application of Mathematical Methods and Modern Computing Technology in Geology; Czechoslovakian Scientific-Technical Society at Geologicky pruzkum, Central Geological Survey, Praha; 6 - 7 November 1967, pages II/1 - II/6.
42. Brezina, Jiri, 1969, Granulometer - a Woods Hole Rapid Sediment Analyzer directly writing grain size distribution curves: Jour. Sediment. Petrology, v. 39, No. 4/December, p. 1627-1631.
43. Brezina, Jiri, 1970, 
44. Brezina, Jiri, 1971a, Settling methods for size analysis of sands: Abstracts of the 8th International Sedimentological Congress of the International Association of Sedimentology, University of Heidelberg, West Germany, 30 Aug. - 4 Sept. 1971, p. 13.
45. Brezina, Jiri, 1971b, Investigations on an instrument for sedimentation analysis in the particle range above 60 µm: Report  about research studies of the author at the Institute for Mechanical Engineering, University of Karlsruhe (1968 - 1971); an unpublished typewritten report for the German Society for Scientific Research, DFG (in German), 48 pages.
46. Brezina, Jiri, 1972a, Stratified sedimentation above the Stokes' range and its use for particle size analysis: in M. J. Groves & J. L. Wyatt-Sargent (editors), 2nd Particle Size Analysis Conference, University of Bradford (England), September 1970, paper 22, The Society of Analytical Chemistry, London, p. 255 - 266
47. Brezina, Jiri, 1972b, Leaf-spring precision balance (in German); German Patent Office (Deutsches Patentamt), No. 2251838, registered October 1972, effective 1974;     4 columns and 1 drawing.
48. Brezina, Jiri, 1972c, Report about the thorium-protactinium method of dating marine sediments (development of chemical separation and chemical and physical quantitative determination of both elements) (in German); Laboratorium für Geochronologie, University of Heidelberg, March 1, 1971 - February 28, 1972;
49. Brezina, Jiri, 1973, Coastal Research, March, p. 2 - 6
50. Brezina, Jiri, 1978a, Computer-controlled grain size analysis of sand-sized materials, MacroGranometer (in German); Chemie-Technik (Heidelberg), February 1978, p. 1
51. Brezina, Jiri, 1978b, And another grain! Grain size analysis of sand sized solids (in German); Labo, September 1978, p. 922 + 924.
52. Brezina, Jiri, 1978c, MacroGranometer Standard 1978, Operation Program Manual: GranoMetry, D-6903 Neckargemünd-3, W. Germany, 3rd edition, 10 November 1978 (unpublished manual), 22 pages
53. Brezina, Jiri, 1979a, MacroGranometer 1979, parts; GranoMetry, D-6903 Neckargemünd-3, W. Germany (unpublished technical documentation), 18 pages.
54. Brezina, Jiri, 1979b, Particle size and settling rate distributions of sand-sized materials: 2nd European Symposium on Particle Characterisation (PARTEC), Nürnberg, West Germany, reprinted (+1 page of comments and corrections by the author on 26 May 2006); 44 pages.
55. Brezina, Jiri, 1980a, GranoMetry: for grain size analyses (in German), GIT Labortechnik (Darmstadt), February 1980, p. 86
56. Brezina, Jiri, 1980b, Sedimentological interpretation of errors in size analysis of sands; 1st European Meeting of the International Association of Sedimentologists, Ruhr University at Bochum, Federal Republic of Germany, March 1980, p. 9 - 11.
57. Brezina, Jiri, 1980c, Size distribution of sand - sedimentological interpretation; 26th International Geological Congress, Paris, July 1980, Abstracts, vol. 2, p. 442.
58. Brezina, Jiri, 1980d, Grain size analysis of sand-sized materials (in German); Labor-Praxis, Vogel-Verlag, D-8700 Würzburg 1, Federal Republic of Germany, vol. 3, p. 245 - 256.
59. Brezina, Jiri, 1981, Contribution to Sand Texture Sedimentology; Coastal Research (Florida State Univ., Tallahassee), vol. 5, No. 10, March, p. 5 - 9.
60. Brezina, Jiri, 1986, MacroGranometer, Operation Manual; unpublished manuscript issued by Granometry, Dr. J. Brezina, D-6903 Neckargemünd-3, West Germany, 16 December 1986, 34 pages.
61. Brezina, Jiri, 1989, Sand sedimentation analysis and separation - 25 years of research and development (in German); Deutsche Geologische Gesellschaft Nachrichten, vol. 41, No. 10/October, p. 149-153.
62. Brezina, Jiri, 1990, Grain size analyses of sand-sized solids upon contract (in German); Kontrolle (Stuttgart), No. 5/May 1990, p. 61.
63. Brezina, Jiri, 1992, Principles, Methods, and Application of Particle Size Analysis: review of the book by James P. Syvitski (Ed.); Basin Research, vol. 4/1992, No. 2/June, p. 165-167.
64. Brezina, Jiri, 1993, Geology in the Czech Republic; Geotimes, August 1993, p. 9 - 10.
65. Brezina, Jiri, 1996, SedVar™, version 6.2C, computer program for GRM data processing, enabling to convert PSI-laboratory distributions into those of any other sedimentational variable, such as PHI grain size specified by a grain shape, PSI-standard, PSI-local (to any physical terms, such as sea water salinity, temperature and local gravity acceleration), logarithmic Reynolds' number, logarithmic grain density, and logarithmic grain shape.
66. Brezina, Jiri, 2002: Grain Size and Grain Size Distribution (in German: Korngröße undKorngrößenverteilung), in: Wolfgang R. DACHROTH, 2002, Manual of Engineering Geology and Geotechnics (in German: Handbuch der Baugeologie und Geotechnik), chapter 1.7.1 (p. 86 - 103); Springer Verlag, Heidelberg, Germany, 3rd extended and overworked edition (681 pp.); http://www.springer.de/geosci/
67. BRUDOWSKY, John M., 2006: Mathematical Addendum to 'Particle Size and Settling Rate Distributions of Sand-Sized Particles' by Jiri Brezina (1979, PARTEC; see above), personal communication, 8 pages.
68. CHANDRASEKHAR, Subramanyan, 1961, Hydrodynamics and Hydromagnetic Stability: Claredon Press, Oxford University Press (reprinted by Dover Publications, Inc., 1981);
69. CLARK, Isobel, 1977, ROKE, a Computer Program for Non-Linear Least Squares Decomposition of Mixtures of Distributions; Computer & Geosciences (Pergamon Press), vol. 3, p. 245 - 256.
70. COLBY, B. C. and R. P. CHRISTENSEN, 1957, Some Fundamentals of Particle Size Analysis; St. Anthony Falls Hydraulic Laboratory, Minneapolis, Minnesota, USA, Report Nr. 12/Dec., 55 pages.
71. COREY, Arthur T., 1949, Influence of Shape on the Fall Velocity of Sand Grains; M. S. Thesis, Colorado Agricultural and Mechanical College, Fort Collins, Colorado, USA, December, 102 pages.
72. CURRAY, Joseph R., 1961, Tracing sediment masses by grain size modes; Proc. Internat. Association of Sedimentology, Report of the 21st Session Norden, Internat. Geol. Congress, p. 119 - 129.
73. DALY, Bart J., 1969, Numerical study of the effect of surface tension on surface instability; The Physics of Fluids (USA), vol. 12, No. 7/July, p. 1340 - 1354.
74. DALY, Bart J., & Williams E. PRACHT, 1968, Numerical study of density-current surges; The Physics of Fluids (USA), vol. 11, No. 1/January, p. 15 - 30.
75. DUFF, R. E., Francis H. HARLOW, & C. W. HIRT, 1962, Effects of diffusion on interface instability between gases; The Physics of Fluids (USA), vol. 5, No. 4/April, p. 417 - 425.
76. EHRLICH, Robert, 1983, Size analysis wears no clothes, or have moments come and gone? (Editorial); Jour. Sediment. Petrol., vol. 53, No. 1/March, p. 1.
77. EMERY, Kenneth Ornis, 1938, Rapid method of mechanical analysis of sands: Jour. Sediment. Petrol., vol. 8, No. 3/Sept., p. 105 - 111.
78. FLEMMING, Burghard Walter & Alexander BARTHOLOMÄ, 1991, Response of the Wadden Sea to a rising sea level: a predictive empirical model; Deutsche Hydrogr. Ztschrft. (German Journal of Hydrography), vol. 49, No. 2/3, p. 343 - 353.
79. FLEMMING, Burghard Walter & Karen ZIEGLER, 1995, High-resolution grain size distribution patterns and textural trends in the back-barrier environment of Spiekeroog Island (Southern North Sea); Senckenbergiana Maritima, vol. 26, No. 1+2, p. 1 - 24.
80. FOLK, Robert Louis, 1962, Of skewnesses and sands; Jour. Sediment. Petrol., vol. 8, No. 3/Sept., p. 105 - 111
81. FOLK, Robert Louis, 1966: A review of grain-size parameters; Sedimentology, vol. 6, p. 73 - 93
82. FOLK, Robert Louis & William C. WARD, 1957: Brazos River bar: a study in the significance of grain size parameters; Jour. Sediment. Petrol., vol. 27, No. 1/March, p. 3 - 26
83. GIBBS, Ronald J., Martin D. MATTHEWS, & David A. LINK (1971): The relationship between sphere size and settling velocity; Jour. Sed. Petrology, v. 41, No. 1/March, p. 7 - 18.
84. HERDAN, George, M. L. SMITH & W. H. HARDWICK (1960): Small Particle Statistics. 2nd revised edition, Butterworths (London, Toronto, etc.), 418 pp.
85. INMAN, Douglas Lamar, 1952: Measures for describing the size distribution of sediments. Jour. Sediment. Petrology, vol. 22, No. 3/Sept., p. 125 - 145
86. JONASZ, Miroslaw, 1991: Size, shape, composition, and structure of microparticles from light scattering; in SYVITSKI, James P. M., 1991, Principles, Methods, and Application of Particle Size Analysis; Cambridge Univ. Press, Cambridge, 368 pp., p. 147.
87. KRUMBEIN, William Christian & Francis J. PETTIJOHN, 1938: Manual of Sedimentary Petrography; Appleton-Century-Crofts, Inc., New York; 549 pp.
88. McNOWN, John S. & Pin-Nam LIN, 1952, Sediment concentration and fall velocity; Proc. of the 2nd Midwestern Conf. on Fluid Mechanics, The Ohio State University, Columbus; State Univ. of Iowa Reprints in Engineering, Reprint No. 109/1952, p. 401 - 411.
89. McNOWN, John S. & J. MALAIKA, 1950, Effects of Particle Shape of Settling Velocity at Low Reynolds' Numbers; American Geophysical Union Transactions, vol. 31, No. 1/February, p. 74 - 82.
90. REYNOLDS, Osborne,1883: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. Roy. Soc., 174, Papers, vol. 2, p. 935 - 982
91. ROSIN, P. & E. RAMMLER, 1934: Die Kornzusammensetzung des Mahlgutes im Lichte der Wahrscheinlichkeitslehre. Kolloid. Ztschr. 67, Heft 1/April, p. 16 - 26
92. SARKISIAN, A. A., 1958: Settling of loads in turbulent flow (in Russian); Collected Papers "Open Channel Processes"; USSR Academy of sciences, Moscow, p. 338 - 351.
93. SCHMETZER, Karl & Jiri BREZINA, 1975, Emeralds from Ghana (a short note in German); Zeitschrift der Deutschen Gemmologischen Gesellschaft (Idar Oberstein, Germany), vol. 24, No. 2/June, p. 94
94. SCHULZ, E. F., R. H. WILDE & M. L. ALBERTSON, 1954, Influence of Shape on the Fall Velocity of Sedimentary Particles; Colorado Agricultural & Mechanical College, Fort Collins, Colorado, MRD Sediment Series, No. 5/July (CER 54EFS6), 161 pages.
95. SKIDMORE, H. J., 1948, Development of a stratified-suspension technique for size-frequency analysis; Thesis, Department of Mechanics and Hydraulics, State Univ. of Iowa, p. 2 (? pages).
96. SYVITSKI, James P. M., 1991, Principles, Methods, and Application of Particle Size Analysis; Cambridge Univ. Press, Cambridge, 368 pp.
97. van ANDEL, Tjeerd "Jerry" H., 1973, Texture and Dispersal of Sediments in the Panama Basin; Jour. Geology, vol. 81/1973, No. 4/July, p. 434 - 457.
98. WENTWORTH, Chester K. , 1922, A scale of grade and class terms for clastic sediments; Jour. Geology, vol. 30, No. 5/July - August), p. 377 - 392

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Last Updated on Wednesday, 21 September 2016 02:56

"The Method of Brezina" — A Quick Method of Modal (Mineral Percent) Analysis 

Brezina, Jiri, 1959c: A quick method of modal analysis (Czech, English summary); Vestnik of the Central Geological Survey, Praha, vol. 34, No. 3/March, p. 161 - 169.

The article is based on a simple fact, that the microscope eyepiece view with a 100 portions scale has an area of 100 by 100 portions = 10,000 square portions. It is true for the same shape of the eyepiece view as the shape of the portions: both may be squares, circles etc.. Therefore, a component-percent in the circle eyepiece view, such as a mineral-percent, equals 

I recommend to average both values per each eyepiece-view in order to increase the representativity and accuracy of this simple method. 

In the time when I wrote the article (1958), there were no calculators and smart-phones. This is why I constructed a simple nomograph of the above formula, in which the co-ordinates cross-section gives the component (mineral) percent (diagonal scale).

You are welcome to print out my nomograph either in format A4 here (or in format Letter here) — enjoy it.

This common-sense method has three advantages: 

1. It is very fast and economic; 
2. One does not need to determine all components up to 100 percent; 
3. It is accurate, and for accessoric components most accurate.

In these days, it may be easy to design a simple smart-phone application or an Excel table for the above formula. 

However, I believe that even when using the most sophisticated image analysis programs, you may enjoy this rapid, economic and common-sense method, for example — to check the results of your object recognition routine.

The Spreadsheet Excel Table can be used according to the following example showing calculation of ten eyepiece views. Here is an active Excel Table example: you may fill in the columns "size" and "number" with your data and the Table will display immediately the results - the calculated percentages in the column "%" . 

Good luck!  

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Last Updated on Wednesday, 09 August 2017 04:42

Bibliography 

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1. Publications by Jiri
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