[en] Induced-fission track densities have been compared on mica external track detectors (2π geometry) and internal mineral surfaces (4π geometry) for the minerals apatite, zircon and sphene. The track-density ratios indicate that the geometry factor relating these two track-registration geometries is indistinguishable from the ideal value of 0.5 (i.e. 2π/4π) for these minerals. External track detectors are not geometrically equivalent to external etching surfaces of a uranium-bearing material. Values significantly higher than 0.5 are caused by a low etching efficiency on the internal mineral surface. The etching efficiency varies with crystallographic orientation in zircon, and may be lowered after thermal annealing in sphene. Etching a mineral surface for spontaneous tracks has no observable effect on the uranium concentration of that surface. These observations have important implications for the use of the external-detector method in fission-track dating. (author)