Distributions of discontinuity spacings along finite length scanlines are derived on the basis of negative exponential and log-normal probability density functions. The error percentages are presented for mean discontinuity spacings estimated from short scanlines. Procedures are presented allowing unbiased mean discontinuity spacing values to be obtained for negative exponential as well as log-normal distributions of spacings between discontinuities. Analytical expressions for the expectation and variance of the Rock Quality Designation (RQD) have been derived for short scanlines, which are assumed to be samples of spacings from negative exponential or log-normal probability density functions. The validity of modelling discontinuity spacings with log-normal distributions has been demonstrated using field measurements obtained in Saudi Arabia. © 1984.