  Measurements are presented of the polarisation of W+W- boson pairs produced
in e+e- collisions, and of CP-violating WWZ and WWGamma trilinear gauge
couplings. The data were recorded by the OPAL experiment at LEP during 1998,
where a total integrated luminosity of 183 pb^-1 was obtained at a
centre-of-mass energy of 189 GeV. The measurements are performed through a spin
density matrix analysis of the W boson decay products. The fraction of W bosons
produced with longitudinal polarisation was found to be sigma_L/sigma_total =
(21.0 +- 3.3 +- 1.6)% where the first error is statistical and the second
systematic. The joint W boson pair production fractions were found to be
sigma_TT/sigma_total = (78.1 +- 9.0 +- 3.2) %, sigma_LL/sigma_total = (20.1 +-
7.2 +- 1.8) % and sigma_TL/sigma_total = (1.8 +- 14.7 +- 3.8) %. In the
CP-violating trilinear gauge coupling sector we find kappa_z = -0.20 +0.10
-0.07, g^z_4 = -0.02 +0.32 -0.33 and lambda_z = -0.18 +0.24 -0.16, where errors
include both statistical and systematic uncertainties. In each case the
coupling is determined with all other couplings set to their Standard Model
values except those related to the measured coupling via SU(2)_LxU(1)_Y
symmetry. These results are consistent with Standard Model expectations.
