The τ polarisation has been studied with the \eett data collected by the DELPHI detector at LEP in 1993, 1994 and 1995 around the \Z resonance firstly through the exclusive decay channels \rm eννˉ, μννˉ, πν, ρν and \aoneν and secondly with an inclusive hadronic analysis which benefits from a higher efficiency and a better systematic precision. The results have been combined with those previously published on 1990 to 1992 DELPHI data, to produce results which reflect the full LEP-1 statistics. The fit of the τ polarisation dependence on the production angle yielded the polarisation parameters \atau=0.1359±0.0096 and \aele=0.1382±0.0116. From these results the ratio of the vector and axial-vector effective couplings \barvt/\barat=0.0683±0.0048 and \barve/\barae=0.0694±0.0058 have been derived, compatible with e−τ universality. With the assumption of lepton universality,the ratio of vector to axial-vector effective couplings for leptons \barvl/\baral=0.0687±0.0037 was obtained, implying a value of the effective weak mixing angle \s2thw=0.23282±0.00092.