Using anthracene scintillation counters in coincidence, the angular correlation between annihilation quanta produced by the decay of positrons in the following materials has been measured: the pure elements Mg, S, Cu, Sn, Pt, and Hg, and the chemical compounds LiCl, KCl, CsCl, KF, and KI.Calculations were performed to determine the effect of the geometry on the shape of the angular correlation curves, and the effects of scattering were investigated.The curves for copper, platinum, and possibly mercury could be approximated to by the expression[Formula: see text], where C(θ) is the coincidence counting rate as a function of θ, the angular departure of the two quanta from collinearity, and K and θ0 are constants. The curves for the other materials are more complicated and suggest that there is a relation between the shape of the curves and the outer electronic structure of the atoms with which the positrons annihilate. In alkali halides the positrons appear to annihilate only against the outer electrons of the negatively charged halogen ions.