  The prospects of measuring triple gauge couplings in W pair production at
future linear colliders with transverse beam polarisation are studied. We
consider CP conserving and CP violating couplings with both real and imaginary
parts. The maximum achievable sensitivity in a simultaneous measurement of all
couplings is determined using optimal observables, extending an earlier
analysis for longitudinal beam polarisation. We find good sensitivity to the
coupling Im(g^R_1 + kappa_R), which is not measurable with longitudinal
polarisation. In contrast, for the real parts (including the CP violating
couplings) the sensitivity is better if both beams are longitudinally
polarised. We conclude that a comprehensive measurement of all triple gauge
couplings requires both transverse and longitudinal beam polarisation.
