Molecular-beam deflection measurements of the static electric polarizability per atom, \ensuremath{\alpha}/N, are reported for sodium clusters up to N=40. The quantity \ensuremath{\alpha}/N decreases from the atomic polarizability to approximately 150% of the bulk value, at N=40. Potassium-cluster polarizabilities follow closely the same pattern up to N=20. There is some correlation between the polarizabilities and previously observed electronic shell structure.