### Abstract

Size distribution of rigidly embedded spheres in a groundmass is usually determined from measurements of the radii of the two-dimensional (2D) circular cross sections of the spheres in random flat planes of a sample, such as in thin sections or polished slabs. Several methods have been devised to find a simple factor to convert the mean of such 2D size distributions to the actual 3D mean size of the spheres without a consensus. We derive an entirely theoretical solution based on well-established probability laws and not constrained by limitations of absolute size, which indicates that the ratio of the means of measured 2D and estimated 3D grain size distribution should be r/4 (=.785). Actual 2D size distribution of the radii of submicron sized, pure Fe^{0} globules in lunar agglutinitic glass, determined from backscattered electron images, is tested to fit the gamma size distribution model better than the log-normal model. Numerical analysis of 2D size distributions of Fe^{0} globules in 9 lunar soils shows that the average mean of 2D/3D ratio is 0.84, which is very close to the theoretical value. These results converge with the ratio 0.8 that Hughes (1978) determined for millimeter-sized chondrules from empirical measurements. We recommend that a factor of 1.273 (reciprocal of 0.785) be used to convert the determined 2D mean size (radius or diameter) of a population of spheres to estimate their actual 3D size.

Original language | English (US) |
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Pages (from-to) | 244-249 |

Number of pages | 6 |

Journal | Bulletin of the Geological Society of America |

Volume | 117 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 2005 |

### Keywords

- Fe
- Grain size distribution
- Maximum likelihood
- Moment
- Probability
- Statistics

### ASJC Scopus subject areas

- Geology

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## Cite this

*Bulletin of the Geological Society of America*,

*117*(1-2), 244-249. https://doi.org/10.1130/B25000.1