New photometric diameters have been used to study transformation formulae to reduce all visual diameters to a common standard system (isophotal diameter at the limiting surface brightness of 25 B mag arcsec⁻²). A new interpretation of these transformations gives a good explanation of puzzling results found in earlier papers. The curvatures in a log-log plot are explained by the incompleteness of catalogues. Besides, the ESGC catalogue (Corwin and Skiff 1990) which covers the equatorial band, allows, for the first time, to test the North-South homogeneity of the reduction. The coefficients used in the reduction formulae have also been derived using empirical arguments. Both methods are in fair agreement. In addition, a correlation between the coefficients used for diameter and axis ratio also gives a confidence in the formulae. Finally, the standard error associated with each catalogue, has been found to depend upon the diameter, which seems more realistic than the previous approximation of a constant dispersion.