The general expression for the angular correlation between radiations produced in successive cascade transitions is derived by use of Racah algebra. The result is then specialized to the beta - gamma correlation and applied to two cases in which additional properties of the photon are specified, the circular polarization and the plane polarization. The prospect of testing time reversal and determining nuclear matrix element ratios by beta - gamma correlation measurements is explored using the nuclide Tm/sup 170/ as an example. The directional angular correlation between the 2.31-Mev beta and the subsequent 0.605-Mev gamma emitted in the decay of Sb/sup 124/ was measured as a function of the beta energy. The K-conversion coefficient of the 279-kev gamma following beta decay of Hg/sup 203/ was measured by comparing the x-ray and gamma intensities in a scintillation spectrometer. The measured valve of alpha /sub k/ = 0.195 plus or minus 0.014 indicates that the transition is M1 with E2 mixed to the extent of 63%. The angular correlation of the 107-1.24 Mev gamma cascade in Zn/sup 68/ following the decay of 68-min Ga/sup 68/ is shown. The Legendre polynomial expansion coefficients were deter-gular correlation in the decay of Sb/ sup 118/ was …