An experiment to measure parity non-conservation in the 6P1/2-7P1/2 transition in atomic thallium will be conducted and refined. The objective is to observe this effect with sufficient precision (~1% or better) to reveal the presence of a nuclear anapole moment in each naturally occurring thallium isotope: A=203 and A=205. Research will also be carried out on P and P,T odd effects in the rare earth dysprosium. In order to determine whether the proposed dysprosium experiments are practical, it is first necessary to measure electric polarizabilities and lifetimes of a pair of metastable levels of opposite nominal parity. This may lead to a major effort to search for the electric dipole moment of the electron in dysprosium.