A molecular beam apparatus has been built to make a precise test of T symmetry using nuclear spin resonance in the TlF molecule. Such tests are aimed at explaining why time reversal symmetry is violated in the neutral K system. It is proposed to improve the sensitivity of the apparatus more than an order of magnitude by means of a supersonic jet source. Additional measurements will be made on the Tl nucleus and new measurements on F. The technique will be extended to other systems. Preliminary runs will be made using CsF, a close analog of TlF. Techniques will be sought to deal with EuS and PbS, which present new experimental problems.