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The bulletin of mathematical biophysics

, Volume 15, Issue 3, pp 237–244 | Cite as

On the subnormal variance in the counts of randomly distributed particles: I. Approximate treatment of the three-dimensional case and discussion of experiments

  • Hissel de Vries
Article

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.

Keywords

Repulsive Force Small Standard Deviation Counting Chamber Convection Current Abnormal Sample 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. 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.Google Scholar
  2. Fisher, R. A. 1950.Contribution to Mathematical Statistics. New York: John Wiley and Sons.Google Scholar
  3. 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.MATHMathSciNetCrossRefGoogle Scholar
  4. Kreveld, A. van. 1938. “De microscopische bacterietelling in melk.”Genootschap t. bevordering v.d. melkkunde, 2–16.Google Scholar
  5. —. 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.Google Scholar
  6. —. 1946. “Repulsive Forces between Milk-fat Globules.”Ibid.,,65, 321–28.Google Scholar
  7. —. 1947. “Spatial Arrangement and Interactive Energies of Small Particles.”Physica,13, 265–78.CrossRefGoogle Scholar
  8. Levert, C. and W. L. Scheen. 1943. “Probability Fluctuations of Discharges in a Geiger-Müller Counter Produced by Cosmic Radiation.”Physica,10, 225–38.MATHMathSciNetCrossRefGoogle Scholar
  9. 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.MATHMathSciNetCrossRefGoogle Scholar
  10. Verwey, E. J. W. and J. Th. G. Overbeek. 1948.Theory of the Stability of Lyophobic Colloids. Amsterdam and New York: Elsevier.Google Scholar
  11. Zernike, F. and J. A. Prins. 1927. “Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung.”Zts. f. Physik,41, 184–94.CrossRefGoogle Scholar

Copyright information

© University of Chicago 1953

Authors and Affiliations

  • Hissel de Vries
    • 1
  1. 1.Rijks UniversityGroningenNetherlands

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