Spectral data on extraterrestrial solar radiation, Rayleigh scattering, ozone absorption and absorption by the uniformly mixed gases are critically evaluated and used for computing the integral Rayleigh optical thickness of the clean and dry atmosphere for a given relative optical air mass or solar elevation angle. The results are compared to the corresponding values calculated with the help of the three parameterization formulae. Based on the comparison, the formula of Louche et al., slightly adjusted to the new values, may be recommended for general use. Equations are given for converting the earlier into the new values of the integral Rayleigh optical thickness and of the Linke turbidity factors based thereom. Both the earlier and the new algorithms yield identical values of the direct solar irradiance.