The asymmetry of the positron distribution in
polarised muon decay provides confirmation that
the weak interaction maximally violates parity.
Since 1957 the quantity P_mu*xi has been
measured with increasing precision, where P_mu
is the polarisation of the muon, and xi is a
parameter describing the asymmetry. Thus far the
results have been consistent with the standard
model using a (V-A) interaction.

A new measurement of P_mu*xi using the TRIUMF Weak
Interaction Symmetry Test (TWIST) spectrometer is
presented in this thesis. The result is a factor
of 3.2 more precise than a previous TWIST direct
measurement, and a factor of 7.1 more precise than
the pre-TWIST value of P_mu*xi. New limits are set
on physics beyond the standard model, including
the weak decay of right-handed muons, and left-right
symmetric models where a (V+A) current is
introduced to conserve parity at higher energies.