A method is given for the transformation of an arbitrary distribution of circles in the plane to the corresponding distribution of spheres in space when the circle distribution can be represented by a histogram in which the class intervals form a geometric progression. Such a progression is commonly employed in sieving.
Get full access to this article
View all access options for this article.
References
1.
S.D. Wicksell , "The Corpuscle Problem. A Mathematical Study of Biometric Problem,"Biometrika , Vol. 17 (1925), p. 84.
2.
S.D. Wicksell , "The Corpuscle Problem. Second Memoir. Case of Ellipsoidal Corpuscles,"Biometrika , Vol. 18 (1926), p. 151.
3.
S. Debbas and H. Rumpf, "On the Randomness of Beds Packed with Spheres or Irregular Shaped Particles,"Chem. Engr. Sci., Vol. 21 (1966), p. 583.
4.
P.L. Goldsmith , "The Calculation of True Particle Size Distributions from the Sizes Observed in a Thin Slice,"Brit. J. Appl. Phys., Vol. 18 ( 1967), p. 813.
5.
K. Mihira, T. Ohsawa, and A. Nakayama, "Geometry of Polymeric Foam or Cellular Structures (I),"Kolloid-Z. und Z. f. Polymere, Vol. 222 (1968), p. 135.
6.
G. Herdan, Small Particle Statistics, Butterworths , London (1960)
7.
H. Leeming and T.W. Gillis, "The Mechanics of Highly-Filled Propellants," Bulletin of the 4th Meeting, Interagency Chemical Rocket Propulsion Group, (1965 ), p. 1.
8.
E.D. Hyam and J. Nutting, "The Tempering of Plain Carbon Steels,"J. Iron and Steel Inst., Vol. 184 ( 1956), p. 148.
9.
D.E. James, "Particle Size Measurement of the Disperse Phase in Rubber Modified Polystyrene,"Polymer Eng. Sci., Vol. 8 (1968), p. 241.
10.
G. Bach, "Uber die Bestimmung von charakteristischen Grossen einer Kugelverteilung aus der unvollstandigen Verteilung der Schnittkreise,"Metrika, Vol. 9 (1965 ), p. 228.
11.
E.H. Blum, "Statistical Geometric Approach to the Random Packing of Spheres," Ph.D. Dissertation (1964Department of Chemical Engineering, Princeton University.