Abstract
IN the automatic counting and sizing of a population of particles on a glass slide or a photograph1 errors arise when adjacent particles are closer than the limit of resolution of the counting apparatus or when they overlap along the scanning track: in both cases the two particles are counted as a single particle of larger size. If the centres of the particles are randomly distributed along the scanning track and the number counted is large, the probability that two successive centres will be less than a distance Z apart is 
where α is the mean number of particles per unit length of track. If the order in which particles are encountered along the scanning track is random with respect to size and their projections on the plane of the track are circular, the probability that the sum of the radii of two successive countable particles is between u and u + du is: 
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References
Walton, W. H., Nature, 169, 158 (1952).
Wicksell, S. D., Biometrika, 17, 87 (1925).
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HODKINSON, J. Coincidence and Overlap Errors in the Automatic Counting and Sizing of Particles. Nature 171, 351–352 (1953). https://doi.org/10.1038/171351a0
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DOI: https://doi.org/10.1038/171351a0
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