We report new high-resolution measurements of the heat capacity of liq
uid helium to within 2 nK from the lambda transition, performed with a
large sample in earth orbit. The optimum value for the critical expon
ent characterizing the divergence of the heat capacity below the trans
ition was found to be -0.01285, giving improved support for the renorm
alization-group theory of phase transitions. Some information on the t
emperature dependence of the thermal conductivity just above the trans
ition was also obtained.