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We apply the new distance measuring technique of Hendry, O'Dell and Collier-Cameron, 1993, to the Pleiades and $\alpha$ Persei clusters. The method relieson knowledge of the periods, rotation velocities and angular diameters of asample of late-type stars within each cluster. The angular diameters were foundby recalibrating the Barnes-Evans surface brightness relation. Applying our newdistance method we derive a Pleiades distance in very good agreement withprevious ZAMS fitting determinations, whereas our $\alpha$ Persei distanceappears substantially greater. In response to this greater distance, we apply arecent semi-empirical main-seqeunce fitting technique to $\alpha$ Persei andconfirm the findings of our new distance indicator. (Figures / preprintavailable on request)Comment: Plain Latex version 3.1, 15 pages, Sussex-AST-93/9-3. Submitted to  MNRA

New distance measurements to the Pleiades and Formula Persei clusters