  We find the exact solution for the stationary state measure of the partially
asymmetric exclusion process on a ring with multiple species of particles. The
solution is in the form of a matrix product representation where the matrices
for a system of N species are defined recursively in terms of the matrices for
a system of N-1 species. A complete proof is given, based on the quadratic
relations verified by these matrices. This matrix product construction is
interpreted in terms of the action of a transfer matrix.
