Abstract
The question is raised concerning the possible causes of abnormally small standard deviations found in counting samples in which particles are distributed at random (e.g., blood cells, fat globules in milk, etc.). The effect of discarding abnormal samples is discounted inasmuch as small standard deviations occur even when all samples are counted. An approximation method is used to calculate the effect of finite particle size, of known repulsive forces between particles and of convection currents. This calculation shows that neither finite size nor the known repulsive forces are sufficient to account for the observed abnormality of standard deviation, but that convection currents can possibly account for it. The possible presence of long-range repulsive forces cannot, however, be excluded.
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Literature
Bergson, J., J. B. Magath, and M. Burn. 1940. “The Error of Estimate of the Blood Cell Count as Made with the Haemocytometer.”Amer. Jour. Physiol.,128, 309–23.
Fisher, R. A. 1950.Contribution to Mathematical Statistics. New York: John Wiley and Sons.
Kosten, L. 1943. “On the Frequency Distribution of the Number of Discharges Counted by a Geiger-Müller Counter in a Constant Interval.”Physica,10, 749–56.
Kreveld, A. van. 1938. “De microscopische bacterietelling in melk.”Genootschap t. bevordering v.d. melkkunde, 2–16.
—. 1942. “Regularity of the Arrangement of Fat Globules in Milk, and the Size Distribution of Fat Globules in Milk.”Rec. trav. chim. d. Pays Bas,61, 29–41, 41–53.
—. 1946. “Repulsive Forces between Milk-fat Globules.”Ibid.,,65, 321–28.
—. 1947. “Spatial Arrangement and Interactive Energies of Small Particles.”Physica,13, 265–78.
Levert, C. and W. L. Scheen. 1943. “Probability Fluctuations of Discharges in a Geiger-Müller Counter Produced by Cosmic Radiation.”Physica,10, 225–38.
Velden, H. A. V. d. and P. M. Endt. 1942. “On some Fluctuation Problems Connected with the Counting of Impulses Produced by a Geiger-Müller Counter or Ionization Chamber.”Physica,9, 641–57.
Verwey, E. J. W. and J. Th. G. Overbeek. 1948.Theory of the Stability of Lyophobic Colloids. Amsterdam and New York: Elsevier.
Zernike, F. and J. A. Prins. 1927. “Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung.”Zts. f. Physik,41, 184–94.
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The main part of this work was done in the Committee on Mathematical Biology at the University of Chicago and originated with a suggestion by Dr. A. Rapoport.
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de Vries, H. On the subnormal variance in the counts of randomly distributed particles: I. Approximate treatment of the three-dimensional case and discussion of experiments. Bulletin of Mathematical Biophysics 15, 237–244 (1953). https://doi.org/10.1007/BF02476399
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DOI: https://doi.org/10.1007/BF02476399