An empirical equation, giving cumulative soil water infiltration as a power function of time, has come to be associated with A. N. Kostiakov. Reconsideration shows, however, that instead of the cumulative infiltration it was the hydraulic conductivity which he postulated to be a power function of time. Furthermore, within the setting he posed, there is no rational way of converting the hydraulic conductivity form to the cumulative infiltration form. It is therefore recommended that the cumulative infiltration form be attributed to M. R. Lewis, who made direct and unequivocal use of the cumulative form and appears to have been the first to do so. ¿ American Geophysical Union 1993