The ratio of the proton's elastic electromagnetic form factors, G{sub Ep}/G{sub Mp} was obtained by measuring P{sub t} and P{ell}, the transverse and the longitudinal recoil proton polarization, respectively. For elastic ep {yields} ep, G{sub Ep}/G{sub Mp} is proportional to P{sub t}/P{ell}. Simultaneous measurement of P{sub t} and P{ell} in a polarimeter provides good control of the systematic uncertainty. The results for the ratio G{sub Ep}/G{sub Mp} show a systematic decrease as Q{sup 2} increases from 0.5 to 3.5 GeV{sup 2}, indicating for the first time a definite difference in the spatial distribution of charge and magnetization currents in the proton.
