Abstract
SINCE both the harmonic mean particle size of a powder—number distribution—in terms of the equivalent diameter, di, 
or, in the notation for the expectation of a quantity, 
and its specific surface (surface area per gm.) for spherical particles 
where M is an average particle size, and ρ the density of the material, are functions of 1/di, it is sometimes assumed that the reciprocal of the harmonic mean 1/Mh, and the reciprocal 1/M in the formula for the specific surface, are more or less identical1.
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References
Dallavalle, J. M., “Micromeritics: the Technology of Fine Particles”, 35 (New York, 1943).
Mises, R. v., “Wahrscheinlichreitsrechung” (Leipzig and Vienna, 1931).
Herdan, G., Nature, 164, 502 (1949).
Kozeny, J., Sitz. Akad. Wiss. Wien, Mathnaturw. Kl., 136 (Abt. IIa), 271 (1927).
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HERDAN, G. Relation of the Harmonic Mean Particle Size to the Specific Surface of Participate Matter. Nature 165, 858–859 (1950). https://doi.org/10.1038/165858a0
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DOI: https://doi.org/10.1038/165858a0
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