The fluctuations of the local order parameter above a nematic to smectic A phase transition give rise to singularities in the elastic constants, and in the viscosities of the nematic. We have used the dynamics of a Fredericks transition to measure the temperature dependence of the twist viscosity γ1 above a weakly first order nematic to smectic A phase transition. γ1 diverges as the transition temperature is reached, but too weakly to allow the determination of a critical exponent. We also observe a large pretransitional increase of the splay elastic constant K1