Proton-proton correlations were observed for the two-proton decays of the ground states of $^{19}$Mg and $^{16}$Ne. The trajectories of the respective decay products, $^{17}$Ne+p+p and $^{14}$O+p+p, were measured by using a tracking technique with mi
crostrip detectors. These data were used to reconstruct the angular correlations of fragments projected on planes transverse to the precursor momenta. The measured three-particle correlations reflect a genuine three-body decay mechanism and allowed us to obtain spectroscopic information on the precursors with valence protons in the $sd$ shell.
