A transformation has been derived relating the number of spheres of a certain radiusRper unit volume (the “volume distribution of spheres”) to the number of circles smaller than a certain radiusrper unit area (the “area distribution of circles”) appearing on a plane cutting through the volume. The transformation was applied to several hypothetical grain‐size distributions for polycrystalline metals to find the resulting hypothetical area distribution of grain images on photomicrographs. Comparison of the hypothetical area distributions to experimentally found area distributions gave the following conditions that the true volume distribution of grains must meet: (1) It must be finite atR=0, and (2) it must have a nonzero decreasing tail for large values ofR. The common assumption of a single grain diameter is insufficient to explain the experimental area distribution of grain images. The functionsNV(R) = Rn exp(−kR)andNV(R) = exp[−(lnR/R0)2/2σV2]were judged plausible for the volume distribution function of grains, and a correction was computed for the attenuation formulas for Rayleigh scattering of ultrasonic waves in polycrystalline metals by taking averages ofR6andR3over these functions.