A technique is described in which the microstructure of cortical bone is analysed in terms of distributions of possible paths which ionizing particles take as they transverse the soft-tissue cavities and mineralized component. Measurements are restricted to transverse planes in the long bones, but a method is suggested for generating approximate omnidirectional path-length distributions from the measured transverse distributions. Results are presented for some long bones of a 50 year old man, a 9 year old boy and a young adult beagle, and these suggest that considerable structural differences occur between the two species. Values of some commonly quoted structural parameters are also given. For example, mean transverse cavity path lengths range between 67 and 99 micron in the long bones of the adult man compared with 29 micron in the beagle femur; the corresponding mean path lengths through the mineralized component are 830-1040 and 1500 micron. Finally, the total cavity plus periosteal surface for cortical bone in adult man is estimated to be about 6 m2.