Using lattice quantum chromodynamics on a 16(3) x 24 lattice at beta=6.0, we examine the elastic limit of charge overlap functions in the quenched approximation for the pion and rho mesons; results are compared to previous direct current insertion calculations. A good signal is seen for the pion, but the electric and magnetic rho meson results are considerably noisier. we find that the pion and rho results are characterized by a monopole mass to rho mass ratio of 0.97(8) and 0.73(10), respectively. Assuming that the functional farms of the electric and magnetic form factors are the same, we also find ti rho meson g-fractor of g=2.25(34), consistent with the nonrelativistic quark model. (C) 1997 Academic Press.